Note sur l'application de la photographie aux mesures micrométriques des étoiles

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  - TREASURY DEPARTMENT
  - U. S. COAST AND GEODETIC SURYEY
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  - W. W. DTTFFIELÜ
  - SUPEBINTENDENT
  - TOPOGRAPHY
  - PHOTO-TOPOGRAPHIC METHODS AND INSTRUMENTS
  - By J. A.. ITLiElVIER, Assistant
  - APPENDiX No. 10—REPORT FOR 1897
  - WASHINGTON
  - GOVERNMENT PRINTING OFFICE
  - 1898
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- - TREASURY DEPARTMENT
  - U. S. COAST AND GEODETIC SURYEY
  - W. W. ÜTJFFIELT)
  - SUPERINTENDENT
  - TOPOGRAPHY
  - PHOTO -TOPOORAPHIC METHODS AND INSTRUMENTS
  - lîy J-. Tr'T-jTClYITniî, -Assistant
  - APPENDIX No. 10—REPORT FOR 1897
  - WASHINGTON
  - GrOYEENMENT PEINTING OFFICE 1898
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- - APPENDIX NO. 10—1897.
  - PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.
  - By J. A. FEEMER, Assistant.
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- - [PHOTOTOPOGRAPHIC METHODS AND INSTRUMENTS.]
  - CONTENTS.
  - Page.
  - PREFACE......................................................................... ........... 625
  - Introduction................................................................................ 627
  - Chapter I.
  - FONDAMENTAL PRINCIPLES OF ICONOMETRY.
  - I. Orienting the picture traces on the working sheet..................................... 631
  - 1. Using a surveying caméra....................................................................... 631
  - 2. Using a caméra or phototheodolite.............................................................. 632
  - II. Arithmetical détermination of the principal and horizon lines.................................... 633
  - 1. Détermination of the principal point and of the distance line of the perspective.............. 633
  - 2. Détermination of the position of the horizon line on the perspective........................... 634
  - III. Graphie method for determining the positions of the principal and horizon lines on the perspective.... 635
  - IV. The five-point problem (by Prof. F. Steiner). Locating the position of the caméra station by means of
  - the perspective when five triangulation points are pictured on one photograph.......... 636
  - 1. Détermination of the principal point and of the distance line................................ 637
  - 2. Simplified construction for locating the caméra station by means of the five-point problem... 637
  - 3. Application of the five-point problem for the spécial case when the five points are ranged into a
  - triangle............................................................................... 638
  - 4. To find the élévation of a caméra station that had been located by means of the five-point problem. 638
  - Y. The three-point problem.............................................................................. 639
  - 1. Using the three-arm protractor ; mechanical solution of the three-point problem.............. 640
  - 2. Graphie solution of the three-point problem.................................................. 640
  - () Using the so-called two-circle method................................................... 640
  - () Using the method of Bohnenberger and Bessel............................................. 640
  - VI. Orientation of the picture traces, based upon instrumental measurements made in the field......... 641
  - VII. Relations between two perspectives of the same object viewed from different stations ; Prof. G. Hauck’s
  - method............................................................................... 641
  - 1. “Kernelpoints” and “kernelplanes”.............................................................. 641
  - 2. Use of the line of intersection of two picture planes showing identical objects viewed from two
  - different stations....................................................................... 643
  - VIII. To plat a figure, situated in a horizontal plane, on the ground plan by means of its perspective.... 645
  - IX. To draw a plane figure on the ground plan by means of the “ method of squares” if its perspective and
  - the éléments of the vertical picture plane are given................................... 649
  - X. The use of the “vanishing scale”.................................................................... 651
  - Chapter II.
  - PHOTOGRAPHS ON INCLINED PLANES.
  - I. To plat the picture trace of an inclined plate............................................. 654
  - II. To plat the lines of direction to points pictured on an inclined photographie plate....... 656
  - III. Détermination of the altitudes of points pictured on inclined photographie plates.......... 656
  - IV. Application of Professor Hauck’s method.............................. ................... 657
  - Chapter III.
  - PHOTOTOPOGRAPHIC METHODS.
  - I. Analytical or arithmetical iconometric methods............................................... 659
  - 1. Method of Prof. W. Jordan.............................................................. 659
  - ‘ 2. Method of Dr. G. Le Bon.................................................................. 660
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  - CONTENTS.
  - Chapter III—Continued.
  - PHOTOTOPOGRAHIC METHODS—COütinued.
  - I. Analytical or aritlimetical iconometric metkods—Continued. • Page.
  - 3. Method of L. P. Paganini (Italian method)................................................ 661
  - General détermination of the éléments of thé Italian photographie perspectives............ 662
  - (a) Orientation of the picture trace................................................. 662
  - (b) Platting of the lines of direction to pictured points of the terrene............. 662
  - (c) Détermination of the élévations of pictured points............................... 663
  - (d) Checking the position of the horizon line on a photograph........................ 664
  - (e) Détermination of the focal length................................................ 665
  - (/) Détermination of the principal point of the perspective......................-.... 665
  - (g) Application of Franz HafferFs method for finding the focal length of a photographie perspective from the abscissæ of two pictured known points.............................. 668
  - 4. General arithmetical method for finding the platted positions of points pictured on vertieally
  - exposed photographie plates (négatives)............................................... 668
  - 5. General arithmetical method for finding the platted positions of points pictured on inclined photo-
  - graphie plates........................................................................ 671
  - 6. General arithmetical détermination of the éléments of photographie perspectives............ 672
  - II. Graphical iconometric methods................................................................... 674
  - 1. Method of Col. A. Laussedat.............................................................. 674
  - (a) Locating points, identified on several photographs, on the platting sheet........... 676
  - (b) Détermination of the élévations of pictured points.................................. 676
  - (c) Drawing the plan, including horizontal contours..................................... 677
  - 2. Method of Dr. A. Meydenbaur................................................................ 677
  - (a) Détermination of the focal length for the panorama views............................ 678
  - (b) General method of iconometric platting............................................... 678
  - (c) Détermination of the élévations of pictured points of the terrene................... 681
  - 3. Method of Capt. E. Deville (Canadian method)............................................. 681
  - (a) General remarks on the field work................................................... 681
  - (b) General remarks on the iconometric platting of the survey........................... 683
  - (c) Platting the picture traces......................................................... 684
  - (d) The identification of points, pictured on several photographs, representing the same points of
  - the terrene........................................................................... 685
  - (e) Application of Professor Hauck’s method for the identification of points on two photographs. 685
  - (/) Platting the intersections of horizontal directions to pictured points.............. 686
  - (g) Platting pictured points iconometrically by “vertical intersections”................ 687
  - {h) Iconometric détermination of élévations............................................... 689
  - (i) Iconometric détermination of élévations by means of the “scale of heights”..........: 690
  - (j) The use of the so-called “photograph board”........................................... 691
  - (fc) Constructing the traces of a figure’s plane......................................... 692
  - (l) Contouring............................................................................ 694
  - (m) The photograph protractor............................................................ 696
  - 4. Method of Y. Legros for determining the position of the horizon line....................... 697
  - 5. Method of Prof. S. Finsterwalder for the iconometric location of horizontal contours....... 697
  - Chapter IV.
  - * PHOTOGRAMMETERS.
  - I. Eequirements to be fulfilled by a topographie surveying caméra................................. 699
  - II. Ordinary caméras (with bellows) made adapted for surveying..................................... 699
  - III. Spécial surveying caméras with constant focal lengths........................................... 701
  - 1. Dr. A. Meydenbaur’s surveying caméra..................................................... 701
  - 2. E. Deville’s new surveying caméra........................................................ 701
  - 3. Use of the instruments comprised in the Canadian phototopographic outfit................... 705
  - 4. United States Coast and Geodetic Survey caméra............................................. 706
  - IV. Surveying caméras combined with geodetic instruments (phototheodolites, photographie plane tables, etc. ). 706
  - 1. The new Italian phototheodolite, devised hy L. P. Paganini............................... 708
  - 2. The photogramme trie théodolite of Prof. S. Finsterwalder................................ 711
  - 3. Phototheodolite for précisé work, by O. Ney.............................................. 712
  - 4. The phototheodolite of Dr. C. Koppe...................................................... 715
  - 5. Phototheodolite devised hy V. Pollack.................................................... 716
  - 6. Col. A. Laussedat’s new phototheodolite.................................................. 717
  - 7. The phototheodolite of Starke and K ammerer.............................................. 717
  - 8. Captain Hübl’s plane table photogrammeter................................................ 721
  - V. Panoramic caméras.............................................................................. 722
  - The topographie cylindrograph of E. Moessard................................................. 722
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- - CONTENTS.
  - 623
  - Ch APTE R y.
  - ICOXOMETERS AND PERSPECTOGRAPHS.
  - Page.
  - I. The graphie protractor.......................................................................... 725
  - II. The graphie sector (“settore grafico”)...............................................T........... 725
  - III. The graphie hypsometer........................................................................... 725
  - IV. The centrolinead.................................................................................. 725
  - 1. To set the arms of the centrolinead, if the direction to the vanishing point is given, hy a line in the
  - ground plan.......................................................................... 727
  - 2. To set the arms of the centrolinead if the given line belongs to the perspective.......... 727
  - Y. The perspectometer................................................................................. 728 *
  - The use of the perspectometer................................................................. 728
  - VI. The perspectograph (H. Kitter’s instrument)....................................................... 729
  - The use of the perspectograph.................................................................„ 731
  - VII. Professor Hauck’s trikolograph................................................................... 732
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- - PREFACE.
  - In the annual report of the Superintendent of the United States Ooast and Geodetic Survey for 1893, Appendix Ho. 3, a description is given of phototopography as practiced in Italy and in the Dominion of Canada.
  - The Canadian surveying caméra and the Italian phototheodolite, which hâve been described in said appendix (Ho. 3,1893), bave both been replaced by improved and more effective instruments, which will be described in the paper herewith presented, together with other photographie surveying instruments that may be regarded as typical représentations of the different forms now in use.
  - Hotwithstanding the rapid rise in the popularity of photographie surveying in general, we still meet with many who express doubt as to the practical value and accuracy of photographie surveying methods, either from ignorance of those methods, from defective results obtained from the application of photography to the survey of areas not adapted for a phototopographic development, or, more frequently, from that extreme conservatism which meets ail innovations with more or less doubt and distrust. Others, again, may hâve failed to take kindly to photographie surveying, supposing a thorough familiarity with the théories and laws of optics, descriptive geometry, perspective drawing, and general cartography to be essentials, without which no practical knowledge and understanding of photogrammetry may be obtained.
  - Although it should be admitted that such knowledge will enable the student to master photo-topography in a rapid and easy manner, giving him a great advantage in and an enlarged field for the practical application of the same, or in teaching its methods to others, yet the fundamental principles underlying this art are so simple that it is believed any topographer or land surveyor, with the knowledge that he should posseSs as such, can readily acquire enough of the theoretical fondamental principles to become fully able to apply photography successfully to practical survey s.
  - Although it will not fall within the scope of this paper to enter into the study of either optics, descriptive geometry, perspective, photo-chemical analysis, or cartography, it will show in a general manner how photography has been applied to topographie surveys by describing the simple processes and methods that will suffice to direct beginners in their practical applications, leaving it to expérience and subséquent spécial study to détermine the measure of success, the more so as several excellent works and text-books on photographie surveying hâve recently been published in the English, French, Italian, and German languages.
  - The compiler of this paper having consulted ail available publications describing phototopographic methods, both foreign and domestic, gladly expresses his indebtedness for information on this subject to Capt. E. Deville, surveyor-general of Dominion lands; to Mr. W. F. King, Alaskan boundary commissioner to Her Majesty, Ottawa, Canada; to Col. A. Laussedat, director of the Conservatoire des Arts et Métiers, Paris; and particularly to the following publications:
  - La Fototopografia in Italia, Eivista Marittima, L. P. Paganini, 1889, Fasc. YI and YII.
  - Huovi Appunti di Fototopografia, Eivista Marittima, L. P. Paganini, 1894, E. C. Forzani.
  - Zeitschrift fur Yermessungswesen.
  - Die photographische Messkunst, Prof. Franz Schiffner, Halle a. S., Wilhelm Knapp, 1892.
  - Photographie Surveying, E. Deville, Ottawa, 1895.
  - Zeitschrift fur Instrumentenkunde.
  - Comptes Eendus de l’Académie des Sciences, Paris, Eevue Scientifique, Ho. 26, I; Ho. 3, II; 1894.
  - Die photographische Messkunst, Franz Schiffner, Halle a. S., 1892.
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- - A.PPENDIX NO. 10—1897.
  - PHOTOTOPOGfBAPHIC MBTHODS AND INSTEUMENTS.
  - By J. A. Flemer.
  - INTRODUCTION.
  - Topography is that brandi of surveying which pictnres the shape of the outer visible surface of the earth, in reduced scale, as a horizontal projection, yet showing the relative positions of points of the terrene also in the vertical sense. It is, therefore, supplementary to geodesy in representing areas of the earth’s surface, inclnding ail the necessary details and changes in the terrene, by means of instrumental measurements made in the field.
  - The work of filling in the details—topographie surveying in the doser sense—may be accomplished by various methods, differing in the matter of costs, time, and attainable accuracy; one may be advantageously employed for one class of work, while another may be préférable for another class or locality, under different conditions, and the method best adapted for any partic-ular région should be employed to obtain the best resnlts. Minute and detailed methods, with ensuing accurate results, should be applied to cities and ail closely settled régions, to the Coastal belts, larger river valleys and lakes, particularly when navigable, and this work should be platted on a large scale.
  - Arid, barren, and mountainous régions, as well as prairies and swamp lands, when sparsely settled, should be more generalized in their cartographie représentation and platted on a small scale.
  - Topographie surveys may be accomplished in various ways, of which the following are the methods and instrumental outfits more frequently in use :
  - I. The direct platting to scale in the field of ail features to be represented on the finished chart:
  - (a) With a plane-table and steel tape measure.
  - (b) With a plane-table and telemeter or stadia rods,
  - (c) With a tachygraphometer and telemeter or stadia rods.
  - (d) With either outfit mentioned under a and 6, but with a leveling instrument in addition for a more précisé location of the horizontal contours.
  - (e) Using a barometer instead of a level for less accurate work.
  - II. The compilation of ail available data—cadastral surveys, public land and county surveys, raiïroad and canal surveys—giving principaliy the horizontal distances and rnaking a supplementary survey to supply the missing data, which in this case are principally élévations that may be supplied by leveling profiles, by trigonométrie leveling, by interpolation and sketching.
  - III. The records of the survey are in the shape of field notes and sketches (tachymetry), the map being produced by platting the recorded data in the office:
  - (a) With a surveyor7s compass and steel tape, locating the relative positions of characteristic points in the horizontal sense, while their relative élévations are ascertained by means of a level and minor details are sketched.
  - (b) By means of a transit and steel tape points are determined both geographically and hypsometrically (using vertical angles), and minor details by sketching.
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  - UNITED STATES COAST AND GEODETIC SURVEY.
  - (c) By means of a transit and telemeter or stadia rods.
  - (d) By means of a tachymeter and stadia rods (élévations being obtained mechanically with tbe instrument).
  - (e) By means of a transit with steel tape or telemeters, combined with a leveling instrument (fer locating horizontal contours).
  - (/) By using a specially constructed aneroid barometer (Goldschmidt’s) in place of the level for locating and tracing the horizontal contours in the fleld.
  - IV. The fleld records for developing the terrene are represented by photographie négatives, taken under spécial conditions (for phototopographic purposes) from known stations :
  - (a) With a caméra or phototheodolite, telemeters, or other distance measures (and often a barometer for obtaining élévations).
  - (b) With a surveying caméra, a separate théodolite, telemeters and aneroid barometer.
  - (c) With a photographie plane table, a distance measure, and aneroid barometer.
  - (d) With a surveying caméra, a separate plane table, and distance measure, frequently using an aneroid barometer for caméra stations occupied without the plane table.
  - Y. The topographie survey may be accomplished by means of a specially constructed surveying caméra attached to a free or captive balloon.
  - After the area which is to be surveyed has been covered with a net of triangles and polygons it will hâve been provided with a framework of lines of known lengths and direction (triangulation), forming a skeleton survey of the coüntry, and after the natural and artificial features hâve been filled in by one of the numerous topographie methods (just mentioned) with more or less detail and aceuracy we will hâve a topographie survey of the area of more or less précision.
  - A good example of chaugii g the method with the locality may be cited in the new survey of Italy, where Paganini’s results fully proved the efficiency of phototopography for alpine work (platted on a scale of 1:25000 and 1:50000) and led to the adoption of the phototheodolite as an auxiliary instrument to the plane table, the latter being used for mapping the areas below 2,000 meters, while the phototheodolite was exclusively used for the délinéation of the terrene situated above that altitude.
  - Photogrammetry proper (or metrophotography) should be applied to the art of taking perspective views of buildings with a photographie caméra for the purpose of constructing therefrom their élévations and ground plans, and it is used principally for architectural, archæological, and engineering purposes.
  - The term phototopography (or topophotography) should be generally adopted for ail topographie surveys based on perspective views of the terrene obtained by means of the caméra.
  - Under photographie survey we could then class ail surveys based on photographie data which do not include the orographie délinéation of the terrene.
  - Iconometry means the measuring of dimensions of objects from their perspectives (“Bildmess-kunst”), and this term could well be applied to those graphie constructions which serve to convert perspectives into horizontal projections ; iconometry is the reverse of perspective drawing.
  - Photography has been very successfully employed for topographie surveys in Italy, Austria, and Canada, and for the production of the extensive topographie reconnaissance maps of south-eastern Alaska.
  - Although this method, invented and elaborated by Colonel Laussedat, found its flrst application in France, still, both in France and in Grermany, it was originally preempted by the mili-tary authorities, under whose auspices it was developed and chiefly used for so called sécret or military surveys ; lately, however, photography has found a wider and more general application to surveying in those two countries, and we find this method now in use also in Greece, Spain, Portugal, Norway, Belgium, Mexico, Chile, Peru, Tonquin, Brazil, Argentine Republic, Switzer-land, and England.
  - Although Lieut. Henry A. Reed has, for several years past, taught phototopography, theoret-ically and practically, at the United States Military Academy at West Poipt, there seems to be no record of any further work of this kind undertaken by otbers in the United States.
  - In the following paper we will treat principally of those photogrammetric methods which are
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- - REPORT FOR 1897--PART II. APPENDIX NO. 10.
  - 629
  - applicable to topographie surveys, although the same principles underlie also the methods in nse when applying photography to—
  - Geological surveys.—For the study of changes in glaciers (glacial motion or variation) based upon the comparison of glacier maps, obtained at stated time intervals from identical and known caméra stations; for volcanic éruptions and their elfects; for the study of periodical changes in sand dunes due to récurrent winds blowing from one direction at regular intervals, etc.
  - Météorologie observations.—For the study of the higher aerial currents and cloud altitudes, based upon iconometric cloud charts, obtained by simultaneous photographie records on plates exposed at different stations at stated time intervals; for the study of the paths of lightning, their lengths, etc.
  - Hydrographie surveys.—For the location of rocks, buoys, etc. ; for the study of fluvial currents, riparian changes due to corrosion, érosion, etc. ; for obtaining coast views from points marked on the sailing charts to facilitate the locating of the position of vessels when approaching land, etc.
  - Engineering.—To estimate the amount of work done at any date by means of photographie surveys that show the status of the work (excavations, fills, structural buildings, etc.) at stated time intervals, etc.
  - Architectural purposes.—For constructing the ground plans and élévations of old buildings from their perspective views (photographs),for purposes of remodeling, renovation, or préservation.
  - Military and secret surveys, and so on.
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- - CHAPTER I.
  - FUNDAMENTAL PRINCIPLES OF ICONOMETRY.
  - If only one perspective of an object, including its distance line, the principal point, and the horizon line is given—in other words, if the point of view and the central projection upon a vertical plane of an object are given—the object itself can not yet be determined regarding its position and dimensions. In the same way the géographie position of a point can not be located
  - Fto.l
  - by means of the plane table from a known station, nnless direct measurements to ascertain the distance of such point from the station are resorted to.
  - If, however, two different perspectives (including their éléments) of the same object, obtained from two different known stations, are given, the dimensions and the position of the object with reference to the two stations may be determined iconometrieally in à manner analogous to that in
  - Fig. Z
  - which a point is located (by intersection) on the plane-table sheet by being observed upon from two différent plane-table stations. *
  - Referring to fig. 1, the positions of the caméra stations A and A', also the distance A Amay be given, and two photographs containing the image t of an object T, including the image a1 of the other caméra station, may hâve been obtained from the two stations.
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- - REPORT FOR 1897-PART II. APPENDIX NO. 10.
  - 631
  - If the base line A Afig. 2, be laid down on paper, in reduced scale, and if the pictures MW and M1 W, fig. 3, be brougkt into the same relative positions with reference to the platted line vvhich they had at the time of their exposnre in the field, the position T of the pictured point (with reference to the platted points A and A') may be located by drawing the rays A t and'A' t'to their intersection. To locate the platted position of T the horizontal projections of the rays A t and A' t' are brought to their intersection on the platting sheet, fig. 4, which may be done by ascertaining
  - M
  - 1 1 i A X r ,p à
  - t a*
  - N
  - F. g. 3
  - the proper positions of the lines of intersection of the picture planes with the horizontal platting plane with reference to A and A' (by “orienting” the picture traces).
  - The map being the orthogonal projection of the terrene in horizontal plan, the horizontal projections of the perspectives (or picture planes exposed in the vertical plane) will appear as straight lines, termed u picture traces,” fig. 4.
  - The correct orientation of the picture traces forms the most important part of iconometric
  - , ' T ''
  - platting, the subséquent location of picture points being accomplished by bringing the horizontal projections of the Visual rays—lines of direction—drawn to identical points to their corresponding intersections.
  - I. ORIENTING THE PICTURE TRACES ON THE WORKING SHEET.
  - (1) A base line AA', measured in the field, has been platted to scale, fig. 2, and two pictures, MW and M'W, fig. 3, had been obtained from the caméra stations A and A1 respectively by means of a surveying caméra. The focal lengths of the pictures (=/ and f respectively), the positions of the principal points (P and P1), and the horizon lines may also be given.
  - It is desired to locate T with reference to AA' upon the working sheet.
  - The distances: ÀP=f; A'P' =f (fig. 4); /P, t'P1, Pa‘ and P'a (to be measured on the pictures MW and M'W' respectively) and the line AA' are given.
  - The distances Aa' and A'a may be found graphically (by constructing the right-angle triangles APa' and A'P'a), or they may be computed from the équations:
  - Aa' = V (AP)2 + (Pa')2
  - A'a= V(A'P')2 + (P'af
  - These distances are now laid ofl* upon AA' from A and A' respectively, semicircles are described over Aa' and A'ay and two circles are drawn about A and A' with/and f respectively, as radii.
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  - UNITED STATES COAST AND GEODETIC SURYEY
  - The intersections P and P' of these two pairs of circles locate the horizontal projections of the principal points on the two picture-traces, the latter being represented by the tangents Pci' and P'a. The distances x (= Pt) and x' { = P't') are now measured on the pictnres and laid off on the tangents as indicated in flg. 2, when the intersection of the lines drawn from A and A' through the points (just found) t and t' will locate the horizontal projection of T with reference to A and A'.
  - (2) The instrument used was a caméra or phototheodolite :
  - In this case the angles a and a' (fig. 2) may be measured directly in the field.
  - We now plat the angles a and a' upon the base line AA' and make AP = /and A'P' =f.
  - The perpendiculars to AP and A'P' in P and P', respeetively, will represent the picture-traces (ta' and t'a) in correct orientation.
  - (3) When several pictured points (triangulation points) and the base line are given on the working sheet, the orientation of the picture-traces upon the map-projection may be accomplished as follows (fig. 5):
  - ' "s
  - / N
  - "s
  - / X
  - Fi G 5
  - The rays AB, AC, AD, and A'B, A'C, A'D are drawn upon the iconometric platting sheet, the points B, C, and I> being already platted on the same.
  - Fig 6
  - The points b, c, P, d, and a are transferred from the horizon line 00' of the négative MN (fig. 6) upon the perfectly straight edge of a strip of paper, which is placed upon the radiais drawn from A (as center) to the points B, C, D. The strip is now moved about until
  - b falls upon the ray AB c falls upon the ray A G d falls upon the ray AD a' falls upon the line AA'
  - I
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  - The line AP should now be perpendicular to the straight edge of the paper strip, and the line bcda' drawn upon the workiug sheet (along the straight edge of the paper strip) will represent the oriented pieture-trace of MJV—
  - AP will be the distance line, and
  - P will be the horizontal projection of the principal point.
  - The same having been doue regarding the point A‘ and its picture M'JSf', both picture-traces will be oriented and the positions of any additional points, that may be identified on both pictures, may be located by platting their abscissæ (measured on the horizon lines of the pictures, regarding P as the origin of the coordinates) upon the picture-traces on the proper sides of the principal points. Lines drawn from the station points, A and A’, through such corresponding points on the picture-traces will locate the relative positions of such points on the platting sheet by their points of intersection.
  - II. ARITHMETICAL DETERMINATION OF THE PRINCIPAL AND HORIZON LINES ON THE PICTURES.
  - In the preceding it had been assumed that each perspective was provided with the principal and horizon lines, which would be the case when an adjusted surveying caméra or phototheodolite
  - had been used for obtaining the pictures. When an ordinary caméra (with provisions to maintain the picture plane in a vertical position) or an unadjusted surveying caméra is used, the correct position of the principal and horizon lines as well as the length of the distance line (focal length) *must be ascertained, which may be accomplished in various ways:
  - (I) Détermination of the principal point and distance line of the perspective.—A plumb-bob, suspended in such a way that the plumbline will be photographed upon the négative, may serve to establish the direction of the principal line VV (fig. 7) upon the trial plate.
  - The négative may also contain the images a, b, e, . . . . of three or more points A, B, G,
  - . . . . of known positions. A line hh is drawn upon the négative perpendicular to VV, and the straight edge of a paper strip is placed upon this line. The pictured points a, b, c, . . . .
  - are now projected upon the straight edge of the paper by drawing parallels to VV through the points a, b, c, . . . . (fig. 7).
  - After having drawn radiais from the platted station 8 to the points A', B', G',..........
  - the paper strip is adjusted over the former in such a way that the image projections a', b1, c' will fall upon their corresponding radiais, when the position (as indicated by the line hh) of the paper strip’s edge will be the oriented picture trace. If we now draw a line .(/SP) from the platted station S perpendicular to hh, the point P' will be the horizontal projection of the principal point P, and SP' will bethe distance line (=/) for the picture MN.
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  - Whenever the positions of thé points A, B, C, . . . . with reference to tke station S are not known, it will become necessary to observe the horizontal angles A SB, BSG, CSB, .... instrumentai^ from the station S, and plat the same upon a sheet of paper in order to adjust the paper strip upon the radiais, in the manner just described, to find the principal point and distance line (focal length).
  - (2) Détermination of the position of the horizon line on the perspective.—When the élévations AA',BB',CC', .... of the points A, B, C, .... above the horizon of the station ($) are known, the position of the horizon line (oo') (fig. 8) may be found by constructing or by computing the lengths of the ordinates aa', W, ce', .... from the relations:
  - aa1 : AA' = Sa' : SA'
  - W : BB' = Sb' : SB' ceCC' = Se': SC'
  - whence
  - aa' = W =
  - Sa'. A A' SA'
  - Sb'.BB' ~ SB'
  - = y>
  - =y', etc.
  - A
  - — -i-----------f —
  - The distances Sa', Sh', Se', . . . are taken from the platting sheet (fig. 8) and the distances
  - SA', SB', SC',............as well as the différences in élévation AA', BB', CC',..............'
  - are known (if the points A, B, C, . . . had been located in the horizontal and vertical sense with reference to the station S).
  - For example :
  - Différence in élévation between A and A' = 100m.
  - Distance of A' from the station S = 1000™.
  - Distance Sa', measured on the platting sheet, = 0*5m.
  - The ordinate aa' = 9 ^ qqq ^ =
  - The horizon line {oo') on the négative will be 50 mm. vertically below (parallel with VY) the pictured point a. ,
  - The direction of FF (the principal line) being parallel to the pictured plumb line, this distance aa' is laid off in the same direction below a, and a line oo', drawn at right angles to FF through a', will locate the horizon line. The ordinates W, ce', . ... oî the other pictured points may
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  - well serve to eheck this position of oo'. The horizon line will be the tangent to the arcs described with aa', bb', cc', . . . . about a, b, c, . . . . respectively, as centers.
  - The principal point P, may now be transferred to the négative by using the paper strip, and the line drawn through P perpendicular to oo' will be the principal line for the picture MN.
  - III. GRAPHIC METHOD FOR DETERMINENTGr THE POSITIONS OF THE PRINCIPAL AND HORIZON
  - LINES ON THE PERSPECTIVES.
  - The following graphie method for orienting the picture trace and locating the principal and the horizon lines was published by Prof. F. Schiffner in 1887 ; it is also mentioned by Prof. F. Steiner.
  - Three points, A, B, and G (iig. 9), may be given with reference to the station S npon the platting sheet.
  - B
  - Fig.9
  - From 8 radiais are drawn through A, B, and (7. Through a point a on the ray 8A a parallel to SC is drawn, and the distance a'b' (taken from the négative MN) is laid off from a (= ab\) upon this parallel, while the distance b'c' is laid off upon the same line from b\ (= b'ic'i). Parallels to the radial SA are now drawn through the points and c\ and prolonged to intersect the radiais SB and S O. The line {h'W) connecting these two points of intersection will be parallel with the direction of the picture trace.
  - The same distances a'b' and b'c' (tajien from the négative) are laid off upon this line h'W from a2(— a2b2) and from b2 (=b2c2). The lines drawn through these points b2 and Cj, and parallel with the radial SA, are brought to intersections with the radiais SB and SG, when the line (hh) passing through these intersections will represent the picture trace correctly placed (oriented) with reference to S, A, B, and C.
  - The distance SP of 8 from hh represents the distance line (focal length) of the picture MN, while the point P‘ will be the horizontal projection of the principal point P.
  - After having transferred P' (with reference to a', b', and &), by means of a paper strip, to the négative MN, a parallel to VV, drawn through the transferred point P, will locate the principal line upon the négative.
  - The horizon line may now be located in the same manner as shown under II, 2, adopting the graphie solution.
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  - IV. THE FIVE-POINT PROBLEM (BY PROFESSOR STEINER).
  - In the methods just described it had been assumed that tbe position of the caméra station was known with reference to the surrounding points A, B, G. . . . .
  - In case the panorama pictures were taken from a caméra station of nnknown position and a sériés of known points are pictured upon the panorama views, the position of the caméra station may be found (with reference to the surrounding points of known positions), and the orientation of the picture trace may be accomplished by means of Prof. F. Steiuer’s so-called u five-point problein” (flg. 10), if one of the views contains the pictures of five or more points of known positions.
  - The panorama view MN may contain the images a, b, c, d, and e of the points A, B, G, D, and E (already plotted upon the working sheet), and also the picture of a suspended plumb line or other vertical (or horizontal) line.
  - The points a, b, c, d, and e of the négative are again projected upon the straight edge of a paper strip = a1, b1, c', dand e'.
  - Radiais are now drawn from one {A) of the five plotted points, as a center, to the other four, R, G, -D, and E. The marked paper strip is then placed over the radiais in such a way that
  - b' falls upon AB, d'falls upon AD, e' falls upon AE,
  - when the strip will hâve the position ax, bx, cx, dx, ex. The line drawn through A and ax (the latter transferred by means of the strip) will be the tangent in A to the ellipse Ex (passing through A, B, D, E and through the station point S).
  - The paper strip is now placed over the radiais AB, AG, and AD, so that
  - b1 falls upon AB, c1 falls upon A G, d'falls upon Alf,
  - when the strip will hâve the position a2 b2 c2 d2 e2, and the line Aa2 will be the tangent in A to the ellipse E2 (passing through the points A, B, G, D and the station point S).
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  - The position of the station point S on the working sheet (with reference to the five points A, B, 0’, D, and JE) will be identical with the point of intersection of the two ellipses Ex and JE2.
  - (1) Détermination of the principal point and distance line in the perspective.—The distance line and the principal point are now found by drawing the radiais SA, SB, SC, SD, and SJE, and placing the paper strip over these in such a way that
  - a' falls upon b' falls upon SB, cl falls npon SC, d'falls upon SD, e‘ falls upon SB,
  - which position is indicated by the line HH. The perpendicular upon HH passing through S (= SP) is the distance line and P is the principal point projected into horizontal plan, which
  - /
  - P
  - /
  - /
  - may now be transferred to the picture by meaus of the paper strip in order to locate the principal line in a similar manner to that mentioned in the preceding pages.
  - (2) Simplified construction for locating the caméra station by means ofthe five-point problem.—The preceding method is rather complicated, but Professor Schiffner devised the following construction (fig. 11), in which the drawing of the ellipses B\ and B2is avoided:
  - The same five points, A, B, G, D, and E, with their images a, b, c, d, and e, on one plate MN, may be given.
  - The two lines, b3 B and &4 B, tangent in B to the two ellipses Ex and E2, respectively, are located precisely in the same manner as the two tangents ax A and a2 A were found for the point A.
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  - The intersections Rx and B2 of the tangent pairs ax A, b3 B and a2 A, ô4 B (belonging to the ellipses Ex and E%, respectively) are situated upon a line Qx, forming one side of the polar triangle QxT, common to hoth ellipses. This line Qx intersects the diagonal AD in x and the quadrilatéral side BD in Q, and the lines drawn through Q from A and through x from B will intersect each other in the fourth point of intersection (S) of the two ellipses.
  - The quadrilatéral ABDS, obtained by connecting the four points of intersection of the two ellipses, has the point x as the intersection of its diagonals. By prolonging the sides BD and to their point of intersection Q and the sides AB and 8D to their point of intersection T, the three diagonal points QxT will form the polar triangle common to the two ellipses.
  - Also this method remains complicated and requires many lines to be drawn before the picture trace and the caméra station ( 8) may be plotted.
  - (3) Spécial application of the fixe-point problem for the case when the five points range themselves into a triangle.—The application of the “five-point problem” becomes very much simplified, how-ever, for the spécial case when the five points range themselves into a triangle, of which two sides (AG and CE) contain three points each (fig. 12).
  - c
  - Fie. Il
  - If we now place the strip of paper upon the radiais drawn from A, so that
  - e' falls upon AE, d1 falls upon AD, & falls upon A C,
  - it will hâve the position a2 b2 c2 d2 62, and the first ellipse (Ex) will résolve itself into the lines CE and Aa2.
  - If we now place the paper strip a! b' c' d'e' upon the radiais drawn from E to A, B and C, so that a' falls upon EA, b1 upon EB, and c' upon EC, it will assume the position ax bx cx dx ex, and the second ellipse (E2) will hâve resolved itself into the lines AC and Eex.
  - The intersection 8 of the two lines Aa2 and Eex will locate the station point with reference to the five given points, and by placing the paper strip upon the radiais SA, SB, SC, SD, and SE in such a way that a' falls upon SA, b’ upon SB, etc., its edge will locate the pfcture trace.
  - (4) To find the élévation (x) of a caméra station (S) that has been located by means of the “ five• point problemP—In order to ascertain the élévation of the unknown station S, platted after one of the preceding methods, it will become necessary to know the élévations of at least two of the five points.
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  - Let the élévation of the station 8 flg. 8 be designated by x.
  - The élévation of A = R and of B = Ri. The ordinates aa' = y and W = ylt From the relation 8*ai' : 8'Ai' = aa' : AA' ; or
  - 8a' : SA1 = y : (R — x)
  - we ünd *
  - Sa1 jj-
  - y=si7 (H~ and
  - Sb1 .
  - Vi — (-“î æ)‘
  - The différence between y and y\ may be measnred on the négative, hence
  - y _ î/i = m
  - is known, and the value for x may be found from the équation
  - y — yl = (H—x)
  - Sa' SA'
  - (-HÎ — SD)
  - 8b'
  - SB' ~ m'
  - The values for Sa1, SA', 8b', and SB' may be taken directly from the platting sheet, while those for H and Ri are found in the triangulation records.
  - If we write the above équation in the general form—
  - H — x Ri — x
  - = m>
  - the élévation x of the caméra station S may be computed from—
  - mno — Ro + R\n
  - The numerical values for the ordinates y and yi (locating *the position of the horizon line on the perspective) may now be computed from the équations—
  - R — x _ y = —-— and 9 n
  - II x
  - V. THE THREE-POINT PROBLEM.
  - If the triangulation points are not sufficiently close together that five or more points may be pictured on one perspective, and if stations are occupied with the caméra that are not connected with the trigonométrie survey, it will become necessary to employ other means to détermine the position of the caméra station with reference to the surrounding triangulation points.
  - In order to connect the caméra station with the triangulation System by direct measurements and observations, made at the caméra station, it will be requisite that at least three triangulation points be visible from such station, unless the location of the caméra station is to be made by observations made from other stations. In the latter case the occupation of two (better three) triangulation points, if favorably located, would suffice to establish the (u concluded”) position of the caméra station.
  - The détermination of the position of an occupied point by observing upon three fixed and known points is generally known as the uthree-point problem,” “station platting,’7 “station pointing,” or “ Pothenofs method,” although Snellius had used the same method in his trigonométrie work in the Netherlands in the second decade of the seventeenth century. Let A, B, and G, fig. 13, be the three points, the positions of which are known. A fourth undetermined point 8
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  - may hâve been occupied from which the horizontal angles A S B — M and B S G — N may hâve been observed instrumentally. The position of S with reference to A, B, and G may then be ascer-tained in various ways.
  - (1) TIsing the three-arm protractor (mechanical application of the threepoint problem).—The simplest (and crudest) method is purely mechanical in its application. The two horizontal angles M and JVare laid off upon a three-arm protractor (“station pointer”), or upon a piece of tracing paper, moving the three radiais SA, SB, and SG over the three fixed and platted points A, B, and G nntil the three radiais 8A, SB, and SG bisect their corresponding points A, B, and G. Holding the two angles M and Af unchanged in this position, the point S is transferred to the working sheet.
  - (2) Graphie solution ofthe three-point problem—
  - (a) TIsing the so-called “ two-eircle problem.”—Theoretically the best graphie method is that which locates the position of the fonrth point 8, fig. 13, as the intersection of two circles, one passing through A and B and having ail angles of circumference = A SB = M over AB that may be drawn over the line AB as chord, the other circle passing through B and G and having over B G as chord ail angles of circumference equal to B SG — TT.
  - B
  - From the platted triangle side AB we lay off at A and B the angles BAG, and ABCi each equal to :
  - 180-2J^B)=9#0
  - ASB = 90° — M
  - and about the point ch thus obtained, a circle ABS is described with the radius = exA = cxB. The observed angle ASB = M will then be an angle of circumference over AB, and the point S will be located somewhere on the arc over the chord AB.
  - By means of the angle B SG = N a second circle BGS is described over the triangle side B G, m a similar manner, about c2 as center with the radius e^B = cfO. The observed second angle BSG = N will be an angle of circumference over the chord BG, hence the f)oint S will be situated also upon the arc over the chord BG and the true position of S is at the point of intersection S of the two circles.
  - (b) TIsing the method of Bohnenberger and Bessel.—The foliowing constructive method (devised
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  - by Bohnenberger and Bessel) is readily applied and of a ver y simple character, fig. 14. If we deseribe a circle througb two of the tbree given points A and B and the station 8 as tlie third point the angles
  - A8B = ACB = M and
  - B SG = BAC = N (being angles of circumferenee npon the
  - same arcs AB and BG respectively).
  - Hence, if we lay off the observed horizontal angle M on the base line AC at G and the other horizontal angle N on A G at A, the point of intersection B of their convergent sides CB and AB will be on the line connecting the third point B and the platte'd station 8. After having thus found the direction of the line BB the position of 8 on the line BB may be found as fol" lows :
  - At any point x of the line BB the ob. served angles M and A are laid off to either side of BB, in the sense in which they were observed. Lines A8 and C8 drawn through A and C parallel to xy and xz, respectively, will locate the position of the station 8 (upon B B) with reference to the three points A, B, and C.
  - This construction is only recommended when BB is sufficiently long (in fig. 14 it is evidently too short) to admit of a correct prolongation of its direction toward 8.
  - The picture trace containing the horizontal projections of the pictured points a, b, and c may now be oriented in the known 8A, 8B, and 8C.
  - B
  - __i___
  - manner by adjusting the paper strip over the radiais
  - YI. ORIENTATION OF THE PICTURE TRACES, BASED UPON INSTRUMENTAL MEASUREMENTS
  - MADE IN THE FIELD.
  - When no points are known of the area to be mapped phototopographically the éléments of the perspective (horizon line, principal point, and distance line) can no longer be ascertained from the photograph alone, but instrumental observations will hâve to be resorted to. This method, having been adopted by Capt. E. Deville, will be described in Chapter III, II, 3, in connection with the Oanadian method.
  - VII. RELATIONS BETWEEN TWO PERSPECTIVES OF THE SAME OBJECT VIEWED FROM BIFFERENT STATIONS (“KERNELPOINTS” AND “KERNELPLANES”).
  - A more generalized application of photogrammetric methods has been inaugurated since Prof. G. Hauck published his investigations and results regarding the relationship existing between Systems of three lines, each of the latter being in a different plane. (“Théorie der tri-linearen Verwandtschaft ebener Système,” Journal für reine und angewandte Mathematik, herausgegeben von L. Kronecker und A. Weierstrass, 1883, Bd. 95.)
  - The practical value of Professor Hauck’s déductions had been tested by the students attend-ing his lectures in 1882 during the exercises which are connected with the course in descriptive geometry at the Technical High School in Berlin (Charlottenburg).
  - (1) Kernelpoints and kernelplanes.—In his discussion of the relationship existing between two perspectives of the same object taken from different stations, Professor Hauck has evolved some G584--------------41
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  - properties which may be very useful* and of value in iconometrie platting. The principal law involved in the application of photogrammetry may be stated as follows :
  - If two projections (perspectives or pliotographs) of the same object are projected by perspective rays emanat-ing from the “ kernelpoints” (“kernpuukte ”) as centers the line of intersection of the two planes of projection (picture planes) will be their perspective axis.
  - With the aid of this law the projection on a third plane of an object may be deduced from the given projections on two planes of the same object. Or, for our case :
  - If two photographs, MN and M'N', taken from two stations S and S1 (and representing the same object), are given, the orthogonal horizontal projection [gronnd plan) of the same object may be constructed therefrom.
  - Professor Hauck’s methods are also applicable to photographs obtained when the plate was exposed in an inclined position. In order to illustrate the connection existing between two different perspectives of the same object, we will refer to fig. 15, representing the simple case
  - where the two perspective planes (MN and M'N') are vertical.
  - Let 8 and 8' represent the two caméra stations (centers of projection or points of view for the vertical picture planes MN and M'N'), s' the picture of 8' in MN, s the picture of 8 in il/7 N, Ifl the line of intersection of the two picture planes MN and M1 N', a image of the point A in MN, a' image of the point A in JP N'.
  - The two pictured points s and s'are the so-called “kernelpoints” (kernpunkte), and any plane (“ kernelplane”) passing through the line (base line) 881 will contain the “kernelpoints” s and s'.
  - The position of the “kernelpoints” may be found graphically by passing a plane (“kernelplane”) through the
  - two stations and a third point A (pictured in both planes MN and JP N'), which will intersect the first picture plane MN in the line as' and the picture plane M' N1 in sa'. Then the following conditions will prevail :
  - 1. The lines of intersection as' and a' s will intersect the line Ifl in one point (fl).
  - 2. The pictures a and a' of the point A will be on the lines as' and a' s.
  - 3. The lines as' and a' s will pass through the pictures (s' and s) of the two caméra stations (S1 and S).
  - The lines 8' A, SA, 88', as', and a' s being situated in the “ kernelplane” Jf2 N2, ail lines as' (for ail points of the object pictured in MN) will pass through the picture s1 (“kernelpoints”) of the second caméra station 8', and ail lines a' s (for ail points of the object pictured in M' N') will pass through the picture s of the first caméra station 8. Furthermore, ail lines (as' and a' s) joining the two perspectives (pictures) of identical points (A) with the tcorresponding “kernelpoints” (s' and s) will intersect the line of intersection (Ifl) of the two picture planes (MN and JP N') in the same point (.Q).
  - Therefore, if two photographs (MN and M' N') of the same object (A) contain the pictures (s' and s) of their reciprocal stations (S1 and 8), conditions peculiarly adapted for the facilitation
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  - of the iconometric constructions will arise, inasmuch as such pictured stations (s and s1) will be “kernelpoints.”
  - The line of intersection (JO) of the two pictnre planes (MN and M' N‘) may also play an important part in the iconometric platting, not only for pictures exposed in vertical planes, but even more so when they are exposed in inclined planes.
  - . If two pictures MN and M' N' are given (in fig. 16 their traces are represented as HH and H' H', respectively) representing the same object (viewed from two stations S and S'), then the pictures s and s' (“ kernelpoints”) of the reciprocal caméra stations may be located upon the picture planes by construction (if they are not shown in the field of the pictures), as shown in
  - fig. 16.
  - The horizontal projections (s, and si) of the “ kernelpoints” (s and s') are identical with the points of intersection of the base line (SS') and the pictures traces (HHand H1 H1). The horizontal projections of the line of intersection (JO, fig. 15) of the two picture planes (MN and M1 N') will be represented by the point of intersection (i) of the two picture traces (HH and H' H').
  - Hence, if we revolve the picture planes about their ground lines until they fall within the horizontal plane of the ground plan, the line JO, fig. 15 (common to both picture planes), will be represented by the lines
  - i(J), fig. 16, and the “kernel- h h'
  - points” s and s' of the re-volved planes will fall upon the lines Si(s) and s'i(s'), respectively. (These lines are perpendiculars upon the picture traces (IIH and H'H’) in the horizontal projections of the “kernelpoints”.)
  - To find the lengths Si(s) and s\(s') (ordinates of the “kernelpoints” in the picture planes), perpendiculars are erected in S and 8f, fig.
  - 16, and their lengths are made equal to the élévations of the respective caméra horizons above the ground plane = $($) and S1 (S'), respectively. The line (8)(8f), connecting the caméra stations 8 and (in fig. 16 the vertical plane passing through
  - the caméra stations 8 and 8' h as been revolved about the horizontal projection of the base line SS' until it coïncides with the horizontal ground plane) will intersect the lines s fs) and s'^s') (which are perpendicular to the horizontal projection of the base line in the “ kernelpoints” sx and s'i), and the lengths sx(s) and s'i(s') will equal the ordinates of the kernelpoints. In this manner the “kernelpoints” may be located in the picture plane of any photograph.
  - (2) Use ofihe Une of intersection ( JO) oftwo picture planes (MN and M'N‘) which show identical ohjects viewed from two different stations (s and sr).—If a sériés of characteristie points of the terrene, pictured in a vertical picture plane MN, fig. 17, are connected with the “kernelpoint” s by straiglit lines, these will (when prolonged) intersect the line JO, and if the pictures of the identical points in the vertical picture plane M'N' are joined with the “kernelpoint” s', and if these lines are likewise prolonged to intersect the line (JO), forming the intersection of the two picture planes (MH and M'N1), the sériés of intersections of JO with the first group, belonging to MN, will be identical with the intersections of JO with the second group of lines, belonging to M'N'.
  - If we now imagine the line JO provided with a scale of equal parts, with zéro in the ground plane 6r6r, fig. 17, lines drawn through the “kernelpoints” and identical points of objects pictured
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  - in both picture planes (MN and M'N') will intersect identical points of the scale. The space (00') intercepted on the scale by the horizon lines of the two picture planes will represent the différence in élévation between the two caméra stations (8 and 8'). This scale may be drawn to show on both lines Ifl of the pictures when separated.
  - The picture (photograph) itself frequently may not be sufficiently extended to contain the line Ifl, in which case the scale may still be utilized by laying it ofif on a line xx" on picture MN and on a line zz" on picture M'N', where xx" and zz" are parallel with the line of intersection (ID.) of the two picture planes MN and M'N' and as long as the following relation remains fulfilled:
  - s fl : sx' = s'fl : s'z'
  - For a second point B pictured as b and b' on the two picture planes MN and M'N', respectively, the following proportions must stand :
  - s fi : sxo = s'p : s'z{)
  - From the similarity of the triangles sxftx', s fi fl, s'z0z', and s'fi fl, we find:
  - x(}x' = z0z'
  - (fifl being common to both triangles s/J fl and s'fi fl), which means the spaces on the scales xx" and
  - Fig. 17
  - zz" are the saine in numerical value. The two scales (or one of them) may also be placed beyond s and s'—for example, at tt"—in which case :
  - s fi : st0 = s fi : sx0 = s'fi : s'z0
  - when the scale tt" should be read in the directions from V toward t0. It may generally be stated that the scales should be placed parallel to Ifl and at distances from the “ kernelpoints” in proportion to the distances from the latter to the line of intersection of the picture planes, their correct positions being best found graphically from the horizontal projection or from the ground plan. To avoid the obscuring of details on the photographs it is recommended to draw these scales outside of the picture proper.
  - To find the best position of the second scale on the second picture, graphically, after the position for the first scale on the first picture has been decided upon, we will again refer to flg. 16,
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  - where HH and H'H' = picture traces, 8 and 8' = horizontal projections of tlie caméra stations, P and P' = traces of the principal lines//and//', and h = selected positions for the first scale.
  - To flnd the corresponding position of the second scale, draw a line M'parallel to 881 through h,
  - s'il : s'Ji = S\i : sji'
  - whence S\h' = distance of the second scale from the “kernelpoint” Si in the second picture plane.
  - The conditions and relations just described, and first discussed by Prof. G. Hauck, may often serve with advantage in iconometric platting (in the following we will refer to them again).
  - For example: If we consider the case of a straight line P, fig. 18, shown on MN as l, of which, however, only the short piece V is pictured on M'N', and it is desired to locate a point x, identified on l in MN, but falling on the prolongation of V outside of the picture limit of M'N', we may proceed as follows :
  - The pictured point a? on Z in MN is connected with the “kernelpoint” (s') and this line (sf ) x is prolonged to intersect Ii in (x). After transferring this point (x) to the line i I of the second
  - Fig. 18
  - picture plane MJ N' to ((x)), the latter point is connected with the “kernelpoint” (s), and the intersection of ((x)) (s) and line V will be the point sought, x', of the prolonged line l'.
  - VIII. TO PLAT A FIGURE, SITUATED IN A HORIZONTAL PLANE, ON THE GROUND PLAN RY , MEANS OF ITS PERSPECTIVE.
  - In topographie surveys, figures in level planes are not frequently dealt with, except when locating the outlines of lakes and marshes, including coast lines, and the simplest way to plat these would be to expose photographie plates (held in a horizontal position) from a balloon at points of known positions and at identical or known élévations.
  - The platting of such figures, when photographed on vertically exposed (also inclined) plates from stations higher than the figure’s plane, will also be an easy matter. It may even be accomplished if but one view of such figure had been obtained from only one station (of a known position), provided the différence in élévation between the caméra station and the figure’s (horizontal) plane, the principal point, and the focal length of the view are known.
  - With reference to fig. 19: H H = Horizon plane of the caméra station 8, M N = Picture plane (vertical), GG — Ground plane or horizontal plane coinciding with the surface of the lake A B G H, 8 80 = h = différence in élévation between the caméra station 8 and the surface of the water in the lake A B G H.
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  - 646 UNITED STATES COAST AND GEODETIC SURVEY.
  - From the picture a b g cl (of tlie lake A B C B) with focal length = SP and known différence in élévation = h the horizontal projection of the lake A B G D is to be plotted.
  - The ground line 0o 0o' (intersection of g round plane 6e G and picture plane M N) is drawn through P0 parallel to the horizon line 0 0' (P P0 = h, measured in the platting scale). If we now Project the pictured points a, b, c, and d upon 0o 00' = b0, c(„ and d0, and draw radiais from the
  - platted station SQ through the points a0, b0, c0, and d0, they will pass through the points A, B, C, and B (which are to be platted), and the latter could be located if their distances from S0 were known. *
  - We now regard the vertical plane, passing through the caméra station S and pictured point a, which intersects the gronnd plane in the line S0 a0 or in S0 A. From the similar triangles S SQ A
  - Fig.19
  - and a a0 A we can find the distance S0 A (the horizontal distance from the caméra station to the point sought, A) either graphically or arithmetically.
  - When the vertical plane SS0A is revolved about S0A until it coincides with the ground plane GG, the points S and a will assume the positions (S) and (a) respectively, in the ground.plane, and the line connecting (S) and (a) will pass through the point A of the lake. Hence, A may be located in the ground plan as the intersection of (#)(«) with S0aQ.
  - The same may be done for the points B, G, and B by revolving the vertical planes S80B, SS0C, and SS0B about S0b0, S0c0, and S0do, respectively, into the ground plane to locate the positions of B, C, and B.
  - »
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  - To avoid a multiplieity of lines on the working or platfcing sheet, tliese constructions are preferably made on a separate sheet of paper, and the following construction ma y be adopted :
  - The vertical planes 80a0, 80b0, 80e0, and 80do may be revolved about 880 as axis until they ail coincide with the principal plane S80 PP0 (ûg. 20), where the paper surface may represent the principal plane.
  - HH = trace of the horizon plane in the principal plane.
  - MN = trace of the picture plane in the principal plane.
  - GG = trace of the ground plane in the principal plane.
  - S80 = différence in élévation between the station 8 and the ground plane (surface plane of the lake ABG1)), measured in the platting scale.
  - SP — 80P0 = true length of the focal distance for the photograph MN. ,
  - The radiais S0aa, 80ba, S0co, and 8ad0 are laid off upon the line GG from 80. The verticals (aQ)(a), (b0)(b), (e0)(c), and (d0)(d) are made equal to the ordinates aa0, bb0, cc0, and dd0 (measured on the picture). Radiais drawn from S through (a), (b), (c), and (d) will eut off on the line GG the horizontal distances 80(A), 80(B), 80{G), and 80(J)), equal to the horizontal distances 80A, S0B,
  - 80G, and 80D, measured in the platting scale. If these distances are laid off upon the radiais
  - S0a0, S0b0, Soc0, and S0do the positions of the characteristic points A, B, O, and D of the lake will be platted in the scale of the map with reference to the ground line 0o0'0 (which on the platting sheet is identical with the picture trace) and the platted station 80.
  - The same resuit may be arrived at by utilizing the orthogonal projection of the points a, b, c, and d and A, B, G, and D in the principal plane, instead of revolving the vertical planes into the principal plane.
  - With reference to fig. 21: PP = Principal plane, MN = Picture plane, HH = Horizon plane (containing caméra station 8), GG = Ground plane or surface plane of the lake.
  - If we draw the radiais 80a01 80bo, S0cOJ and 80do from S0 (orthogonal projection of 8 in GG) through the orthogonal projections a0, b0J c0, and d0 of the pictured points a, b, c, and d on the ground line 0oOo', the points sought will be situated upon those radiais.
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  - If we now project the points a, 6, c, and d (in the picture plane) upon the principal line = a, />’, y, and â, the radiais Sa, S/3, S y, and Sâ, drawn in the principal plane PP, will locate the
  - Fig.2
  - points a0, [3o, y0, â0 npon the line S0P0 (in the ground plane), they are the orthogonal projections of the points A, B, C, and P in GG npon S0P0. The points A, B, O, and JD in the ground plane
  - may therefore be found by erecting perpendiculars upon S0P0 in a0, /30, y0, and <30. The intersec-
  - Fig.22
  - tions of these with the radiais S0a,0, S0bQ, S0c0, and S0do will locate the positions of the points A, B, G, and JD on the platting sheet.
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  - This construction is also preferably made on a separate sheet of paper. The radiais 80a0, 80b0, S0c0, and S0d0, fi g. 22, are drawn through their corresponding points on the platted picture trace (or ground line) 0o0o', and the rest^of the construction (fig. 23) is made by regarding the paper surface as the principal plane. The désignations are the same as in fig. 20. The points d, j3, a,
  - H —9*r
  - Fig. Z 3
  - and y, fig. 23, on the line PP0 (principal line) represent the projections of the pictured points a, b, c, and d in the principal plane; hence, their positions are found by transferring the ordinates of the pictured points to PP0 from P0 :
  - P0 ô = dd0 ; PG = bb0 ; P0 a — aa0, and P() y = cc0
  - The radiais from 8 through d, /?, a, and y locate the points d0, /?0, a0, and y0 on the line GG (or S0P0), fig. 23.
  - By transferring the distances $0d0, S0/G>, S0a0, and S0y0, fig. 23, to the line 80P0 from S0, fig. 22, and drawing lines through d0, yd0, a0, and y0 parallel with 0000', their intersections with the corresponding radiais S0d0, 80b0, 80a0, 80c0 will locate the platted positions of the points P, B, A, and C of the lake.
  - IX. TO DRAW A PLANE FIGURE ON THE GROUND PLAN, BY MEANS OF THE SO-CALLED “METHOD OF SQUARES,” IF ITS PERSPECTIVE AND THE ELEMENTS (POINT OF VIEW AND DISTANCE LINE) OF THE VERTICAL PICTURE PLANE ARE GIVEN.
  - If we imagine the figure covered with a net of squares, one set of its sides being parallel with
  - Fig. 24-
  - and the other set being perpendicular to the ground line, such net may be utilized to draw the outline of the figure upon the ground plan, it being only necessary to cover the pictured figure
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  - UNITED STATES COAST AND GEODETIC SURVEY.
  - a b g d with the perspective of the selected net in the ground plane, i. e., thé lines forming tlie squares of the perspective must hâve the proper relation to the principal ray and horizon line.
  - The simplest disposition of the lines (forming the auxiliary network) for locating the figure is the one mentioned above (parallel with and perpendicular to 0o0o'), but an y other sélection may be made. The squares may be of equal size or not, and the directions of the lines composing the network may be given any direction. «
  - In fig. 24, in illustration of this method, the lines in the perspective which correspond to the
  - H -"—'©r*
  - Fig.25
  - sides of the rectangles that are perpendicular to the ground line 0o0o' will vanish in the principal point P, and those parallel with the ground line 0o0o' will be parallel with the horizon line 00'. Selecting the lines of this network so that two lines of each System will pass through one of the
  - Fig.26
  - characteristic points of the figure abcd, the perspective of this net will appear as shown in fig. 24, where 0o0J represents the ground line of the picture plane MN. »
  - If we now plat the principal plane SS0P0P, fig. 25, retaining the same désignations as for fig. 20, the points ô0, fi0, a0, and y0 will represent (in the ground plane) the intersections, with the horizontal projection of the principal ray SP ( = S0P0), of those net lines that had been drawn through P, P, A, and G parallel with the ground line.
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  - After platting the pieture trace 000o' (of the perspective MW, fig. 24) in the ground plane by
  - means of the radiais 80a0, 80b0..........., the distances 80ôc, 80tf0............(fig. 25) laid
  - off npon S0P0, fig. 26, will locate those net lines (parallel with O000') in the ground plane which correspond to the lines dô, bfi . . . . shown in the perspective MW, fig. 24.
  - If we now transfer the points aQ', PQ, b0', d0', and cQ' from fig. 24 to a strip of paper, and place this upon the pieture trace 00(V, fig. 26, that the points P0 will coincide, the lines a0'A, bJB, . . . drawn parallel with 8QP0 will represent the net lines which are perpendicular to the ground line 0o0'o.
  - Thus the platted positions of the points A, B, C, and B are located on the ground plane by the intersections of the corresponding net lines of both Systems, as shown in fig. 26.
  - The points A, B, C, and B will, of course, also be bisected by the radiais 80a0, 80b0 . ,
  - which fact may make it more advantageous to select some other disposition of the net lines for a figure of a different shape.
  - When the figure has a sinuous perimeter the squares of the network should be selected of a size sufficiently small to enable the draughtsman to draw the perimeter sections falling within the squares sufficiently accurate to obtain a correct représentation of the general outline.
  - X. THE VANISHING- SCALE.
  - We had seen, fig. 26, that the radiais drawn from the so-called u foot of the station” (80) represent the directions to the points A, B, C . . . . in the ground plane, and if we eould détermine the distances 8aA, 80B .... (from the foot of the station 80 to the points to be
  - platted A, B,.............) from the perspective in some manner the location of the platted
  - positions in the ground plane would become an easy matter.
  - The distances 80A, 80B . ...... fig. 26, may be determined from the perspective by
  - means of the so-called vanishing scale, which may be constructed as follows, fig. 27 :
  - Fig.27
  - MW = trace of pieture plane in the principal plane, ER = trace of horizon plane in the principal plane, GG — trace of ground plane in the principal plane, 880 = élévation of the station 8 above the ground plane GG, or above the foot of the station 80.
  - A scale of equal parts is laid off upon GG, to either side of P0, and radiais are drawn from 8 through the graduation points of the scale ; their intersections with MW form the vanishing scale, which may serve to locate distances from the foot of the station to points to be platted in the ground plane.
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  - The picture trace 0o0o', fig. 28, may hâve been platted and the radiais SQa0, &>0b0, .... may hâve been drawn on the working sheet.
  - It is desired to locate the position of a point, A, in the ground plane by means of the vanishing scale and the pictnre a, fig. 29, of the point A.
  - Take the ordinate aa0 from the perspective MX, fig. 29 (vertical distance of a above the ground line 0o0o'), and lay it oif upon the vauishing scale (fig. 27), PP0 from PQ = P0x.
  - Fig. 28
  - Fi g.29
  - The line ax, fig. 29, parallel with the horizon line 00' and passing through a in the perspective, corresponds with the line AX, fig. 28, parallel with the ground line and passing through A in the ground plane.
  - Hence, if we lay off S0X, fig. 27, upon 80P0 from $0, fig. 28, the point A (in the ground plane) will be situated upon the line XA, fig. 28, drawn through X and parallel with the ground line 000o'. The intersection of the*radial S0ao with this line XA, fig. 28, will be the point A.
  - I
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- - CHAPTER II.
  - PHOTOGRAPHS ON INCLINED PLATES.
  - In the preceding we hâve regarded photographie plates (perspectives) only that had been exposed in a vertical plane, and although the use of inclined plates for phototopographic purposes is not to be generally reeommended (on acconnt of the complications that will arise in the ordinarily simple constructions in iconometric platting from vertically exposed plates, and because the relations which exist between the éléments of the perspective and the orthogonal projection in horizontal plan of the pictured objects will not be so readily recognized), still, occasions may arise wbere the sélection of the available or accessible stations will be so circumscribed that the exposure of inclined plates will become necessary in order to control the inaccessible terrene (above or below the caméra station).
  - Photographs may also hâve been obtained with an ordinary caméra, without any device for adjusting the plate in vertical plane, or the use for iconometric platting of the photographs (perhaps taken only for illustrative purposes) may hâve been an afterthought.
  - With reference to fig. 30 we hâve :
  - PP = principal plane.
  - PH = horizontal plane passing through the second nodal point of the caméra lens (at the station S).
  - GG = ground plane.
  - MN = picture plane.
  - O'P = trace of picture plane MN, in the horizon plane HH.
  - 0'oPo = ground line of picture plane MN.
  - S0 = foot of the station S.
  - P'P0 = principal line of the picture plane.
  - P' = principal point of the perspective MN.
  - SS0 = vertical of the station; it will penetrate the picture plane MN above (or below) the horizon line at s. The trace s of this vertical s80 in the picture plane is the vanishing point for the perspectives of ail vertical lines that may be pictured on MN. •
  - P'SP = PsS = a = angle of inclination of the plate MN.
  - SP = (horizontal) line from S perpendicular to horizon line O'P.
  - SA = line of direction from S to a point A, pictured in MN as a.
  - If we revolve SP, in the vertical plane PP, about P until SP falls within the picture plane, then the point S will fall into (S) and the line Sa will fall into (S)a.
  - The vertical plane containing the line SA and passing through SS0 will intersect the ground plane in Soa0. If we now revolve the line SoP0, in the vertical plane PP, about P0 until S0P0 falls within the picture plane MN, then the point S0 will fall into (S0) and the trace S0aQ will hâve assumed the position (S0)a0, and the intersection A of the trace S0a0 with the line of direction Sa will locate the platted position of the pictured point a in the ground plane GG.
  - The line sa intersects the ground line in a0, and S0a0 will be the radial in the ground plane to the platted position of A and passing through the foot S0 of the station S.
  - To find A on S0a0 we first locate in the picture plane the intersection (A) of the revolved lines / (S)a and (S0)a0. This point (A) revolved in the vertical plane a0S0S about a0 will locate A upon$0a0.
  - To locate the position of A in GG, in the manner just shown, we should know the position of the line O'P, as well as the points S and P. These are known or may readily be found if the position of the principal point P1, the length of the distance line SP', and the value of the angle of inclination (a) for the plate are known.
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  - When a photographie plate in a surveying caméra is intentionally exposed in an inclined position, it will generally be exposed in such a way that the principal line ff still coïncides with the intersection of the picture plane MN and the principal plane PP, flg. 30.
  - When the angle of inclination a is an angle of élévation (dépréssion) the horizon line (intersection of horizon plane and inclined picture plane) will fall below (above) the line representing the horizon line on the plate when exposed vertically. In order to use the inclined plate for
  - Fig. 30
  - iconometric purposes the angle of inclination should be observed directly in the field, and, if the constant focal length of the caméra ( = /) is known, the line SP, fig. 30, may be found as the hypothenuse of the right-angle triangle with angle = a and adjoining side = /.
  - I. TO PLAT THE PICTURE TRACE OF AN INCLINED PLATE.
  - »
  - In order to plat the picture trace the horizontal angle, included between the optical axis of the inclined caméra and the horizontal direction to some known point, should be measured. Should the length SS' (élévation of station S above the foot of the station, flg. 32), the position of
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  - the line connecting two caméra stations, and also the position of a ttiird point A (visible from botli stations) be known, no horizontal angle a needs to be measured instrumentai^, provided the plates containing the picture a of the third point A are oriented in such a way that the picture a be bisected by the vertical thread or principal line ff of the perspective.
  - With reference to fig. 31 we hâve
  - Fig. 3
  - 8' = platted position of the station 8 S'SS = platted length and direction of the base line.
  - The horizontal angle a (at 8') inclnded between this line of direction S1 SS and the principal plane (or horizontal projection of optical axis S'P0) may hâve been observed in the field. The line S'Sm fig. 32 represents the élévation of the station 8 (laid off in theplatting scale). If we revolve this line 8'S about S'P0 into the platting plane it will assume the position shown as S'(S) in fig. 31. After erecting at (S) a line (8)(P) perpendicular to 8'(8) the angle of inclination y of the plate MW is laid off upon (8)(P) from (8).
  - (S)(P') is made equal to the constant focal length (=/) of the caméra, and the line drawn perpendicular to (S) (P') through (P') will represent the principal line (/)(/') of the perspective MW, revolved about S'P0 into the platting plane. The point of intersection (s) of (8)8' with (/)(/') represents the vanishing point for ail vertical lines shown on the picture.
  - The point of intersection P0 of the line (/)(/') and the horizontal projection of the optical axis S'P0 will be the trace in the ground plane of the inclined principal line ff.
  - The line P0g, perpendicular to S'P0 in P0, is the ground line or the trace of the inclined picture plane MW in the platting plane GG.
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  - II. PLATTING THE LINES OP DIRECTION TO POINTS PICTURED ON AN INCLINED PHOTOGRAPHIC
  - PLATE.
  - The inclined picture plane MN, fig. 32, is revolved about P»g into the drawingor ground plane, when the picture will appear as (üf)(W), the principal point P falling upon 8'P0 = (/)(/7) in (P) and (P)P0 = PPG.
  - To plat the direction to a point A from we first locate the orthogonal projection a0 (in the ground plane) of the pictured point a, fig. 31.
  - The image point a, fig. 32, projected upon ff or upon PP0= oc and a circle described about
  - P0 with P0 (a) will locate the position (a) of the projected point on the principal line (/)(/'), revolved into the platting or ground plane.
  - The perpendicular to S'P0 in a0 and the vertical to the ground plane 0 G from a, fig. 32 intersect each other in a0, and S'aOJ fig. 31, is the horizontal projection (in the ground or platting plane) of the line of direction or radial from 8' to the point A.
  - III. DETERMINATION OF THE ALTITUDES OF POINTS PICTURED ON INCLINED PLATES
  - We refer again to fig. 32. It is desiréd to find the élévation H of tbre point A (pictured in a) above the ground plane G G.
  - Projecting a upon the principal plane PP we find a on ff) the vertical through a intersects the horizontal projection of the principal ray S'P0 in a0, fig. 32; hence, aa0 represents the élévation of the point A above GG, measured in the platting scale.
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  - With reference to fig. 31, this élévation aa0 (fig. 32) of a above the ground plane is found by projecting a upon P'P0 ( = a in fig. 32) ; tbe corresponding point on the principal line revolved about P0 into the platting plane is (a) and its orthogonal projection upon the principal plane, the latter revolved into the platting plane about S'P0, fig. 31, is (a) ; hence, the élévation of A above the ground plane is = (or) a0 — h, to be measured in the platting scale.
  - If P = distance of the platted point from 8', taken from the platting sheet, H == élévation of
  - A
  - ..-o
  - 1
  - 1
  - 1
  - 1H I
  - —ô
  - Fig. 33.
  - the point A above the ground plane GG, h = (a) a0 — aa0, fig. 32, = («) a0, fig. 31, = aa0, fig. 33 S'a0 = d (fig. 31), taken from the platting sheet, the élévation H of the point A may be found either graphically from a diagram, fig. 33, or it may be computed from the relation :
  - IV. APPLICATION OP PROFESSOR HAUCK’S METHOD.
  - The constructions just described for locating the horizontal directions to points photographed on inclined plates may be greatly simplified by applying Professor Hauck’s method, by utilizing the properties of the “kernel points” of two photographs obtained from different stations but comprising the same ground.
  - With reference to fig. 34: 8 and 8' = the two caméra stations.
  - 80 and 80! = the foot points of 8 and 8' respectively.
  - MN and M'N' = inclined picture planes 5 both contain the image a and a' of a point A and the pictures s' and « ( “kernel points”) of the stations 8' and 8. a0 and aQ' = orthogonal projections (in the ground plane GG) of a and a' respectively.
  - A0 = orthogonal projection of A in the ground plane.
  - 2, s' and tc — kernel points for picture plane MN. s and n' = kernel points for picture plane M'N'.
  - These “kernel points” are of importance, inasmuch as—
  - The horizontal direction 80A0 (or 80'A0) intersects the ground line gg' of MN (or M'N') in a0 (or a'o). The line connecting a and s' (“kernel point”) in MN and the connection of a1 and s in M'N1 intersect each other in the same point il of the line of intersection of the two picture planes, and also intersect the ground lines gg' of the picture planes in the “kernel points” n and n', respectively. Ail lines in MN, connecting s' with pictured points, and those in M'N', connecting s with the pictures in M'N' of the same points, intersect each other in points £1 of the line of intersection of the two inclined picture planes. The kernel points 2 and 2' are the intersections of the verticals passing through the caméra stations (S and S'), with the inclined picture planes. They are the “ vanishing points” for the pictures of ail vertical lines shown on the négatives, and when-ever the pictures contain images of vertical lines the intersections of these would locate 2 and 6584---------------42
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  - 2' on MN and M’N', respectively. Still, wlien the picture plane is inclined in such a way that the principal line of the same would coincide with that of the vertically exposed plate (when the former were revolved about a line as axis passing through the second nodal point and parallel
  - with the horizon line 00' or HH1, fig. 34) the kernel point N may more readily be locatèd upon ff, as previously shown for s in fig. 32.
  - In order to locate the position of A0, fig. 34, with reference to a on MN and a' on M'N' we connect a and 2 and also a1 with N', which lines locate a0 and a0‘ upon the ground lines of the picture planes MN and M'N'. The intersection of the lines 80a0 and So'Uo' will give the position of A0 in the ground plane GG.
  - i
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- - CHAPTEE III.
  - PHOTOTOPOGRAPHIC METHODS.
  - I. ANALYTICAL OR ARITHMETICAL METHODS.
  - (1) Method of Prof. W. Jordan.—In 1874 Professor Jordan made a raap of tlie oasis “Dachel,7 including the village “ Gassr-Dachel,” based on photographs taken witli an ordinary caméra by Eeinelé, obtained on Gerhard Bohlf’s African expédition during the winter of 1873-74. Care was exercised to expose tlie plates in vertical plane, and horizontal directions to at least three points for each photograph were instrumentally measured to obtain the data needed for the proper orientation of the pictures. Vertical angles to at least two such points (for every pieture) were also observed to give the means for locating the horizon lines of the pictures and thus enabling the draftsman to dednce the élévations of other points pictured on the photographs.
  - With reference to flg. 35 we hâve: OO1 — horizon line, ff' = principal line, P = principal point, SP = focal length =/, variable for different pictures.
  - The ordinates au7, bb', and ce' = yx, 3/2, and y3, respectively.
  - The abscissæ of the three points a, 6, and c be xx, x2, and x3 respectively. ,
  - The horizontal angles included between the principal ray and the horizontal directions Sa', SI/, and SP = aly a2, and a3 respectively.
  - The azimuthal angles (between the meridian SN and the horizontal directions Sa', Sbf, and SP) = cp\, cp2, and <p3
  - Then a2 — «1 = cp2 — <p\= £1 and a3 — a2 = cp3 — cp2 — e2 The élévations of the points A, B, and G above the plane of
  - FiG. 35
  - reference or above the ground plane = Hi, H2, and R3
  - As the photographie plate MN had been exposed in vertical plane, it will be évident that for the three points a, b, and c pictured on the perspective MN, fig. 35—
  - X\ —f tan a x2 =/tan a2 x3 = f tan a3
  - or,
  - sin (a2 — Æi) cos ai cos a2
  - x2 — Xi=f (tan a% — tan ax) = /
  - and
  - sin (a3 — <^2) cos a3 cos a2
  - x3 — x2 = f (tan a3 — tan a2) = f
  - The values x2 — x\ and x3 — x2 may be scaled off directly on the photograph, and the values for a2 — ai and a3 — a2 may be taken from the field records of the observed angles.
  - Hence cos 012 may be computed from the équation cos ai
  - Xi — Xi _ cos sin (a2 — <*x)
  - x3 — x2 cos «1 sin (a3 — a2)
  - If we substitute tan y for — s <a'3
  - cos ai
  - and as
  - 659
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  - we may now write
  - ^ cos «3
  - tan (46» + y) =_______008 a> = 008 + 008
  - 1 — C0S a3 C0S al ~ C0S a3 COS (Xi
  - cos^ + ^cos"1--^
  - 2 2i
  - sin sin ^ ~ g°
  - cot
  - “> + cot "> - “>
  - 2
  - and tan *** a'3 = cot (45° + y) cot 013
  - 2i 2
  - From this équation we compute ai + a3, and after subtracting
  - from
  - a3 — a2 = cp3 — q)2 — e2
  - we find
  - — ai = qh — cp\ — £1
  - <*1 — = <£>1 — <^3
  - knowing «i -f «3 and <*1 — we can readily find ai and a3, also,
  - a2 = a-! + fi or
  - We had found:
  - = a3 — f2
  - _Ta _ Tl -/ sin (”* - "0 -/ sin gl . bence l#2 - ^1) cos cos n2 J cos ax cos a2 J cos ai cos a2 J sin fi
  - 7 sin • «»:, — a,) =f_sinjj_ whence/ = (*3 - «0 cos cos or,
  - cos a2 cos a2 cos a3 cos a2 sin e2
  - Tbus the abscissæ xu x2, and x3, (tbe principal line//7) and tbe focal length/may be found.
  - Witb the aid of the observed vertical angles fi the horizon line 00' may be located on the photograph. For example, if the vertical angle fi3 = c S c‘ had been observed to the point O, we find :
  - y3 = S& tan fi3
  - = 55iVan#>
  - f
  - The horizon line 00' will fall below the pictured point c by the vertical distance cQg — tan /?3, and for the point a the vertical distance to the horizon line would be
  - V i=
  - /
  - cos a i
  - tan fii
  - At least two vertical angles having been observed for each plate, the horizon line 00' may thus be located and marked upon the négative, when the principal point P may also be marked on 00' by means of the abscissæ Xi, x2, and x3 = a'P, b'P, and Pc', respectively.
  - (3) Method of Dr. O. Le Bon.—Dr. Le Bon, who used his instrument chiefly for the draughting of ancient buildings and monuments in India, provided the ground-glass plate of his caméra with a net of squares, each square having sides 1 centimeter long, the latter béing drawn parallel with the horizon—and principal lines, which latter two were subdivided into millimeters.
  - This arrangement enabled the operator to obtain the measurements of objects directly by inspection of the image on the (graduated) ground-glass plate. To détermine the dimensions of
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  - the front of a building, a certain distance is measured directly upon the same and a picture is then taken by exposing a photographie plate in vertical plane and parallel to the base of the front of the building.
  - For example :
  - (a) To find the distance _D of an object of unknown height H.
  - Two stations, S and 8', are occupied on a base line (which is measured directly in the field) laid off in a direction at right angles to the base of the object, fig. 36.
  - If the height of the image, measured on the graduated ground glass, at the first station S is h and the focal length for both exposures be the same = /, then
  - and for the second station 8'
  - D : H =f: h
  - B + B : ü =f : h'
  - By dividing the second équation by the first, we find :
  - whence :
  - B + B _h B _h t h-W D ~y ’ b~w~y- y
  - B
  - B.y -h-y
  - B is given and h and h' are measured directly on the ground glass.
  - (b) It is desired to find the height H of an object of which the fractional length H' had been measured directly, fig. 37.
  - FlG.37
  - ï
  - On the image of the object on the graduated ground-glass plate the heights h and h' may be read off directly, and II' being known we find H from the équation
  - Il = IB
  - h
  - y
  - (3) Method of L. P. Paganini (Italian method).—This method was developed for the topographie survey of Italy, made under the auspices of the Boyal Italian Military Geographical Institute, and a detailed description of the same, with numerical examples, has been pub’lished in Appendix
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  - ï7o. 3, Report for 1893 of the Superintendent of the United States Coast and Geodetic Survey. Also, Dr. C. Koppe and Prof. P. Steiner give preference to the arithmetieal method for photo-grammetric surveys in general.
  - GENERAL ARITHMETIC DETERMINATION OE THE ELEMENTS OF THE ITALIAN PHOTOGRAPHIC PERSPECTIVES.
  - The panoramic views which subserved the map making were obtained by ten successive exposures. After each exposure the caméra was moved in azimuth by a horizontal angie of 36°,
  - and as each plate subtends a horizontal angle of 42°, the two ends of adjoining plates hâve a common mar-gin of a width of 3° in arc, corresponding to a width of 15 millimétrés. These common margins of two adjoining plates serve principally to ascertain whether the adjustments of the phototheodolite hâve g been changed during the occupancy of a station.
  - ——(«) Orientation of the picture trace.—The horizontal projection of one complété panorama com-posed of ten plates will be a regular decagon, fig. 38, with a radius of the inscribed circle equal to the principal focal length (constant) of the caméra.
  - P', P2, .... P10--(horizontal) picture traces,
  - V = panorama station,
  - DP'=UP2 = . . . . DP10 =/ = principal focal
  - length of caméra.
  - After the position of one panoramic view has been platted on the map, its picture trace will be oriented, and with it the remaining nine views of the panorama.
  - After the horizontal angle go, fig. 39, included between the principal ray VP' of view P' and the horizontal direction to the triangulation point S, fig. 39, bas been platted
  - the orientation of each succeeding view P2, P3............P10 is accom-
  - plished by adding successively 36°, 72°, 108°.............(36°—go°) to
  - the angle go.
  - (b) Platting the Unes of direction topieturedpoints of the terrene.—The orientation of the panorama hav-ing been made, the lines of direction to points pho-tographed on the panorama plates may readily be platted.
  - The plate ilOT, fig. 39, may represent a vertical photographie plate oriented with refer -ence to the known point 8, pietured on MN as s.
  - s
  - O O1 = horizon line, O— —
  - V = point of view of the perspective v MN,
  - œ = angle of orientation for this plate with reference to 8,
  - VP=f= (principal) focal length, ss1, perpendicular to 00' =y = ordinate of the image s,
  - sxperpendicular to ff =x= abscissa of the point s.
  - • S
  - ,û
  - -&
  - Fig.39
  - From the rectangular triangle VP1 s', fig. 39, we find :
  - x = f tan go.
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  - If thé caméra station F and the known point A hâve been platted and the picture trace OO', fig. 40, bas been oriented, tlie horizontal projection of the ray from F to 8 may be found as foliows:
  - s
  - V o*
  - \
  - Fig.4-0
  - x
  - -<>p
  - S
  - The abscissa P's' = x, fig. 39, is laid off on OO', fig. 40, from P' in the sense of the direction to 8 (whether 8 is to the right or to the left of the principal line ff, fig. 39) with reference to the principal point P1, locating s' (the orthogonal projection of the pictured point in the gronnd plane) and a line drawn from F through s' = TV, which will be the ray VS, fig. 39, projected in the platting plane.
  - The position of 8 on the platting sheet is obtained by finding the point of intersection of two or more lines of direction, obtained in a similar manner, from other pictures containing images of 8 and taken from different stations, as ail rays to the same object, seen from different stations, rnust intersect each other in the same point on the platting sheet.
  - The élévations of pictured terrene points are readily determined after the selected points (identified on several pictures) hâve been determined and platted in horizontal plane, in the manner just described.
  - If the élévation of the station V is known, the élévation of the line of horizon OO' on the plate, fig. 39, may easily be obtained by adding the height of instrument to the élévation of V.
  - (c) Détermination of the élévations of pictured points.—Disregarding the effects of curvature and refraction, the élévations of ail the points on the plate which are bisected by the horizon line OO' hâve the same élévation as the optical axis of the instrument at V.
  - The élévations of pictured points, above or below the horizon line, are obtained by determining their élévation above or their dépréssions below the line O O1.
  - If D — horizontal distance from station F to a point S, fig. 39,
  - = VS', fig. 39, to be measured in the platting scale.
  - L = différence in élévation between point 8 and station F.
  - = 88' (8' being the orthogonal projection of 8 upon the platting plan). d = horizontal distance of the picture s of S from F.
  - We find from the similar triangles Vs's and V88':
  - L : D =y : d
  - 1
  - L
  - i>y
  - d *
  - 2
  - From the rectangular triangle VP's' follows :
  - d = f
  - COS GO
  - =f sec go,
  - 2 a
  - whence
  - Dy
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  - Should the point S be bisected by tbe vertical tbread (principal plane) then
  - go = O and sec oo = 3, or,
  - L = By. 3 a
  - f
  - This formula would answer for ail points of the perspective if the image plate were a cylin-drical surface of radius =/ (instead of being a tangential plane to such cylinder), if the decagon were a circle (as it is the case for the sensitive film of the panoramic caméras, and Colonel Moessard’s cylindrograph, which will be described later).
  - Différences of élévation, taken from the perspectives, are positive or négative according to the relative positions of the pictured points with reference to the horizon line 00', fig. 39, whether above 00' or below the same, and the apparent élévations of such points (above mean sea level) are obtained by adding their ordinates {L, fig. 39) to or subtracting them from the élévation of the caméra station ( F, fig. 39).
  - By comparing the élévations thus obtained for identical points from photographs exposed from different stations the hypsometric déterminations of secondary points of the terrene may be checked.
  - (d) ChecJcing the position of the horizon line of a photograph.—To check the position of the horizon line OO', fig. 39, photographs are selected which show the images of two or more triangulation points, the élévations of the latter, determined from the photographs, are compared with those given in the triangulation records and discrepancies are adjusted by shifting the line 00'. Should the élévations of the triangulation points be unknown, or should the pictures from any station not contain the pictures of such points, this check may still be made by measuring the vertical angles («, fig. 39, with the vertical circle of the phototheodolite from such caméra station) to a sériés of prominent points (8, fig. 39) and comparing their computed ordinates (L, fig. 39) with those obtained from the pictures.
  - We find from the similar triangles VS S' and FsF, fig. 39:
  - tan 8VS' = tan a = B = M-D d
  - and we had according to formula 2a :
  - d = f
  - cos 00
  - hence
  - 4
  - 5
  - where oo is the horizontal angle included between the vertical plane ( V8S') passing through the caméra station F and the point 8, fig. 39, and the principal plane (17ff). This angle oo should be measured (with the horizontal circle of the phototheodolite) for several points 8 at every station, whence a limited or insufficient number of triangulation points may be seen.
  - If the computed values for y, formula 5, are not in accord with those obtained by direct measurement on the photograph, the horizon line 00', fig. 39, must be adjusted until the values for the ordinates measured on the picture are the same as those computed by aid of formula 5.
  - The necessity of the précisé détermination of the value / (focal len^th) is évident from the preceding, and if the panorama pictures contain a sufificient number of well-defined pictures of surrounding triangulation points, the détermination of / may readily be made by means of the adjusted horizon line 00', fig. 39.
  - tan a
  - = 1 f
  - cos oo. or
  - y =
  - f. tan a
  - co s oo
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  - (e) Détermination of the focal length f.—The phototheodolite is set up over a well-determined point and adjusted. A plate is exposed in vertical plane in such a way that the vertical thread ff bisects a known geodetic point S, fig. 41, which can readily be identified upon the ground-glass plate of the caméra. (It is also désirable that the ordinate y, fig. 41, be sufficiently long to assure a correct measurement of its length to be made on the picture.) There will be given, fig. 41 :
  - S
  - L = différence of élévation of bisected point 8 and panorama station F, D = horizontal distance between 8 and F, y = ordinate of pictured point s.
  - From équation 3a we find
  - f-1*'!*
  - J ~ L
  - which will be a fairly accurate value if the horizontal position of the caméra was assured and if the ordinate y was correctly measured on the négative.
  - Another value for f may be found from équation 5 :
  - if the picture contained triangulation points enough to adjust the horizon line by computing their ordinates :
  - L.â
  - By using the mean of these déterminations for / the computations (based upon the new values for x and y) may be repeated until perfect agreement is reached.
  - (f) Détermination of the principal point of the perspective.—The great number of triangulation points established in Italy, with spécial reference to the phototopographic survey, facilitâtes the application of the photogrammetric method and assures the accurate détermination of the perspective éléments. Although the Italian pictures command a horizontal angle of but 42°, the greater number of them contain the pictures of several triangulation points, and it can be ascertained simultaneously with the détermination of the value of f whether the picture P, of the
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  - intersection of the cross wires (00' and //') coincides with thé principal point of view, P, upon the perspective, fig. 42.
  - s and s' = pictures of two triangulation points 8 and 8' on the photograph MW, V = station point or point of view; ss and s's' = y and y' respectively = verticals upon the horizon line 00' through the picture points s and s', — ordinates of the triangulation points; 88{ and S'Si = L and L' respectively, = différences in élévation between the triangulation points and caméra station; D and D‘ = horizontal distances from V to 8 and S1 respectively ; x and x' = abscissæ of pictured
  - S
  - - *_ __
  - D----
  - points s and s'; d and d' = horizontal distances of the pictured triangulation points from the point of view F.
  - It is desired to find VP and the position of P with reference to s and s', or the abscissæ x and x1.
  - L, L1, P, D1, y, and y' are known, or they may be found by direct measurements on the chart projection and upon the photograph. Hence:
  - vi.y
  - L
  - The horizontal angle s Fs' ( = œ + œ') being observed in the field the other two angles, y and ô, of the horizontal triangle s Fs', may be computed as follows:
  - - ô d1
  - tan2V=<j+<î'
  - d . s Fs' cot -
  - By substituting H for vre will find
  - y — â
  - and M for
  - Y + â — 2
  - 90°
  - s Fs'
  - y = M 4- N ô = M-W
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  - 667
  - From thé two triangles s VP and P TV (both are reetangular at P) we find
  - f=d. sin y — d'sin ô x = f. cot y x' = /. cot d
  - also, as a check, tlie angles of orientation :
  - go = 90° — y go' = 90° — ô
  - To check the abscissæ the length ss’ is carefnlly measnred upon the négative, which length should equal the computed value of
  - x + x/ and also =
  - (d + d') sin iZ®_
  - cos
  - ô — y
  - Should the horizontal angle s TV not hâve been measured in the field for some reason, then the angles y and â may be found by computation, after carefully measuring ss' on the négative and using the formulas
  - where :
  - tan(P-™') 2 V p (p — d)
  - tan Y - ](P »«')
  - 2 V p {p - d')
  - m d + d' + ss' p = T T—
  - and
  - the angles of élévation a and a1, which are obtained either by direct measurement in the field or computed from the formulas
  - tan a = ~
  - tan a'
  - D1
  - serve to obtain checks on the values, measured on the négatives, for y and y1 by using the formulas
  - f tan a and
  - y =
  - COS GO
  - yt _ ----f
  - cos go'
  - tan a'
  - the value for/ in above formulas being the same as found from the équation
  - f — d. sin y = d1. sin ô
  - By repeating the computation with these Values for y and y' (if any discrepancy is noted between these new and the former values for y and y') the true value for f may be obtained very closely.
  - For ail practical purposes, however, it suffices to take several pictures with a constant focal length, and to take the mean value of the different f determined from those pictures.
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  - (g) Franz HafferVs methodfor finding the focal length of a photograph from theabscissœ oftwo pictured triangulation points.—When the horizontal distances D and I)' are great, compared with
  - the différences in élévation (L and L') between the points in question (8 and 8') and the caméra station V, fig. 42, the ordinates y and y' will be short, their lengths will be difficult to be measured, and it may be better in that case to détermine the value for / by means of the abscissæ of the pictured points, fig- 43.
  - 00' — platted (and oriented) picture trace, Fs and Vs' = platted horizontal directions from the caméra station F to the triangulation points 8 and 8' (pictured as s and s'), VP = perpendicular to the picture trace through F.
  - It is desired to find/.
  - Describe a circle through the three points F, s and s', the center of which may be at G.
  - The angle sCs' = 2 (s Fs'). The perpendicular through G to ss' (= GM) will bisect this line and the center angle sGs1 into two equal parts; hence, s GM and s' GM each = s Fs', and if the radius of the circle passing through s, s' and V = B we will hâve the following relation (from the triangle sMG) :
  - sM x + x’ 1 x + x‘
  - st -B- sin sCM- 2 sin s CM’ sM = —2~~
  - Having drawn the diameter mn parallel with 00', we will hâve
  - / = VP=VA + AP
  - VA being vertical to mn it will be the middle proportional to mA and An:
  - mA : AV = AV : An or mA • An = A F2
  - /K
  - ' * \r ' \
  - P M
  - -o—o-
  - /
  - /
  - I
  - ’m
  - \
  - \
  - \
  - \
  - \
  - \
  - /! N
  - // X
  - ! /
  - ! / /
  - J/ / \
  - /
  - /
  - /
  - /
  - /
  - Fie. 4-3
  - We can now replace mA by (mG — AG) = B — —^— and as
  - /W _ /V#
  - An = nC + AG = B + —g—
  - we find :
  - AF=7(«_^l£)(iî + ^£f)
  - and finally:
  - AP = CM = 8M cot MCs
  - x' + x ,
  - = —2— c°l’ sGM
  - (4) General arithmetical method for finding the platted positions of points pictured on photographie perspectives (exposed in vertical plane).—If we refer the pictured points to the principal point P by
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  - 669
  - means of the rectangular System of coordinates formed by tbe principal line ff and the horizon line 00' we will hâve with reference to fi g. 44:
  - 8 and 8' = two caméra stations; MW and M'Wl = two picture planes exposed in vertical plane, one from station 8, the other from station 8'-, aa' (= y) and a' P (= x) = coordinates of pictured point a on MW) a' a\ (= y') and a\ P' ( = x') = coordinates of a' pictured on M' W) f = focal length (the same for both pictures MW and M' W)) B = 80A0 = horizontal distance of A from station 8) I)' — 8'0A0 = horizontal distance of A from station 8' ; d = 8a' = 80a0 — horizontal distance of pictured point a from point of view 8$ d' = S'cW = 80'a0' — horizontal distance of pictured point a' from point of view 8' ; R = élévation of A above horizon plane of station 8. H1 = élévation of A above horizon plane of station S') B = 8080' — horizontal distance between the stations 8 and 8' ; a and a' = horizontal angles included between B and the principal planes passing through 8 and S', respectively.
  - If the caméra (théodolite) was in perfect adjustment, if the base line B is known, and if the
  - A Fjg.W •
  - angles a and a' had been observed, we will know the values of B, a, a1, f, and the coordinates x, y, xand y', the latter being obtained by direct measurement on the négatives.
  - We can now compute—
  - (1) The horizontal angle y, included between the principal plane and any horizontal direction, 8afig. 44, from the équation :
  - cc * cc^
  - tan y =j or tan y' = y
  - (2) The angle of élévation fi of the line of direction 8a to any point, A, pictured as a on the photograph MW, from the équation :
  - tan /? = ^ or tan As
  - d = Vf2 + x2 or d' = y/f2 + (x')2
  - y
  - we may also Write :
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  - UNITED STATES COAST AND GEODETIC SURVEY.
  - We know the length 808o' (= B) of the triangle 80A080and the angles y, a, y' and a' also being given, we hâve
  - J) : B = sin (y' + a') : sin [180° — (y + a. + y'A «0]
  - _ sin (y' + a') sin (y + a + y' + a')
  - Fis. 4-5
  - whence
  - or
  - 80A0 =D =
  - B sin (y* -f «0 sin {y A A y' A a')
  - 80'A0 = JD'
  - B sin {y + a) sin [y + a + y' A oc')
  - The différence in élévation, B, between the point A and caméra station 8 may be found from
  - jy — tan
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  - 671
  - whence ,
  - H = D tan fi or
  - 11' = D'tan fi.
  - (Ç) General arithmetieal method for finding the platted positions of points piotured on photographie perspectives for inclined picture planes.—For inclined picture planes we will hâve to take into considération the angle of inclination of the plate—the angle which is included between the optieal axis of the inclined caméra and the horizon plane of the caméra station.
  - We hâve, with reference to flgs. 45 and 46:
  - a = horizontal angle between the principal plane of station 8 and the vertical plane passing throngh station 8 and the point A, pictured as a on inclined picture MW; fi = angle of élévation of the point A observed from S; y = angle of inclination of the photographie plate MW; â = 180° — y; 00' — horizon line on MN when vertical, permanently marked on the caméra; P — principal point for the vertical plate, also permanently marked as the intersection of the principal
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  - and horizon lines when the plate is vertical; Pn = y = ordinate of a on MN (fig. 46); an = x = abscissa of a on MN, very nearly = a1 P1 ; 2 = vanishing point (“kernel point”) for ail vertical lines pictured on MN.
  - From inspection of fig. 46 it will folio w directly :
  - and
  - tan fi =
  - aa' nn' STI
  - Sfi1 Sa' Jfoÿ
  - Pp — PII _ y cos y —/ sin y Vx* + (Sn'f ~ s/+ (Sn + nn J y cos y —/sin y JW+ {Sn+ pn)2
  - y cos y —f sin y Vx2 + (/cos y + y sin y)1
  - tan a =
  - a'n' 'Sn7
  - x
  - Sn+ pn
  - x
  - f cos y + y sin y
  - (We had found for the vertically exposed plate
  - tan fi —
  - tan a = -
  - and
  - The preceding formulas for tan a and tan fi will assume the form of the latter if the angle of inclination y is reduced to zéro, as sin y = sin 0 = 0 and cos y = cos 0 = 1.)
  - After having thus found a and fi (also a' and fi1) we can now compute the value for D = S0Ao and for II = AA1
  - With reference to fig. 45 we hâve
  - hence
  - and from
  - we find
  - P _ sin (e/ — a')
  - B ~~ sin [180°—(a + € + a'— a')]
  - jy_ B sin (a' — a')
  - ~~ sin (a + e + a1 — a1)
  - tan fi = ^
  - H = B tan fi
  - _ B {y cos y — f sin y)
  - V x2 + (f cos y + y sin y f
  - If an ordinary surveying caméra, with a constant focal length, is used, and when it should become désirable to expose a photographie plate in an inclined plane, the complément d of the angle of inclination of the optical axis (= y) may be determined more readily (but only approximately) than the latter by carefully measuring the distances AB, fig. 47 (in the direction of the line of a suspended plumb bob), and BB, supposing AB to be parallel with the photographie plate.
  - (6) General analytical détermination of the éléments of a photographie perspective.—If, in addition to the photographs, data obtained by instrumental observations are given for a ^raphical détermination of the focal lengths of the pictures, their horizon lines and principal points, then these éléments may also be determined by computation.
  - A picture, MN, may contain the images a, b, and e of three known points, A, B, and G, the
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  - 673
  - position of tlie caméra station (whence this picture was obtained) being likewise known with reference to the tbree platted points AB', and C7, fig. 48.
  - To orient tbe pictnre trace (or ground line) gg' with reference to the platted station 8', and the platted points A', Band G', the latter are preferably referred to a System of coordinates having the platted station 8' as origin.
  - In fig. 48, for example, a rectangular System of coordinates, 8'Y and S'X, has been adopted, with the origin in 8', and axis of abscissa passing through one of the three triangulation points.
  - The coordinates of the three triangulation points A7, B1, and C', platted on the chart projection, are found by measurement = Xi Yx, X% and X3, respectively.
  - The coordinates of the orthogonal projections (on the picture trace gg') of the corresponding points, pictured on the photograph MX, may be designated by &'nyn, and xm, respectively.
  - The horizontal distances between a and b, b and c, a and c (which are the same as those between a' and b', b' and c7, a' and c' on the picture trace) may be m1, m11, and m111, respectively. We will find directly, from an inspection of .fig. 48:
  - (1) yl:xI=Yl: Xx
  - (2) y a : ®\i — Y% : X2
  - (3) yv : yn = m111 : m11
  - (4) (xm — : {xn — x^ = mln : m1
  - (5) (xm — xi)2 + yi = (m111)2
  - From these five équations the five unknown quantities x„ yx, xn, yw and xm—the coordinates of the points a7, b7, and c', which are to be located—may be computed.
  - From the area of the triangle S'a'c'
  - we find the focal leugth
  - y_i • _f.mm
  - ~2 ~ " 2
  - ___y i • ^iii
  - J w111
  - 6584----43
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  - The horizontal angle of orientation y—included between the principal ray 8'P' and the horizontal direction to G (= 8'G')—may be found from the équation:
  - cos y = or = Jp
  - xm
  - The principal point P1 may now'be located upon gg1 from & by matin g
  - P’& = xm sin y.
  - The différences in élévation between the caméra station 8 and thethree triangulation points ri., Bj and G hein g known, it will tiow be an easy matter to draw the horizon line npon the photograph and mark the position of the principal point P on the same
  - II. GRAPHICAL ICONOMETRIC METHODS.
  - (1) Method of Gol. A. Laussedat.—Colonel Laussedat’s methods of constructing topographie maps from perspective views of tlie terrene, having been widely publisied, form the groundwork for ail subséquent work in this direction ; they are chiefly of a graphieal character and they are in harmony with the laws of perspective.
  - Laussedat considers two cases in reconnaissance surveys for géographie expéditions to which photo-topographie methods may be applied with advantage:
  - (1) The explorer may remain sufficiently long in one locality to make a survey on a large scale, say 1:20 000, and even larger for spécial purposes.
  - (2) The explorer moves rapidly from place to place, gathering only the most necessary data on his itinerary to enable him to plat the topography of the traversed country as a “running survey” on a small scale—say 1:50 000 and even smaller—preserving and representing only the principal topographie f'eatures met with on the track survey.
  - In the first-mentioned case the explorer will measure one or more base Unes, with as great an accuracy as the means at hand and the time at his disposai will admit,. He will then cover the area to be mapped with a System of triangles, connected with (or founded upon) the base line, and, inasmuch as the triangulation stations will be occupied with tle surveying caméra, the seheine should be laid out with due reference to the subséquent iconometric platting of the topographie features.
  - When applying the ordinary surveying methods the triangulation scheme would probably be laid out with a view toward covering as large a territory as possible, occupying the least number of intervisible points. With the use of photography, however, the conditions are changed; every topographie feature that is to be platted iconometrically should be seen from two or more caméra stations. The latter are to be triangulation stations, or they will hâve to be tied on to the general scheme by spécial supplementary instrumental observations. Still it isnot always essential that the highest peaks, which may be included in the trigonométrie survey (asconcluded points), should also be occupied with the caméra, as frequently other caméra stations will answer the requirements just as well.
  - Regard in g the second case, where the explorer follows a certain route, making only the most necessary (and at best but short) side excursions, the photo-topographie method is even of greater value than in the first case, particularly when traversin g open and broken country. For this kind of reeonnoissanee it may be well claimed that the photographie method surpasses ail other surveying methods regarding the amount of data which may be collected in a limited time period.
  - Ail topographie operations and instruments serve to measure vertical and horizontal angles, and a photographie perspective (of which the focal length and the positions of the horizon line and principal point are known) will give ail the data needed to détermine the vertical and horizontal angles of lines of direction drawn from the point of view to ail points pictured on the photograph. »
  - The points ri and R, pictured on the vertical plate ÜOT, fig. 49, mav represent the images of two distant mountain peaks; a and b will be their orthogonal projectbns upon the horizon line HH' (picture trace in horizontal plane HH).
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  - a S b = a = horizontal angle between Unes of direction from the station to tbe two peaks, A and B. SP (perpendicular to HW) — distance line or focal lengtb of tbe picture MN.
  - Tbe vertical angles fi and y may be sbown, in horizontal plan, by revolving tbe vertical
  - Fi G. 4-9
  - planes passing through SA and SB about tbe lines Sa and Sb, respectively, until they coincide with tbe horizon plane 1111. This bas been done in fig. 49 for the vertical plane S a A:
  - a A = a (A) and (A) a S = A a S= 90°
  - A Sa = [A] S a =fi.
  - The vertical angles fi and y may norbe measured in horizontal plan as (fi) and (y).
  - To indicate tbe general metbod of iconometric platting, and to show bow tbe platted features of tbe terrene may be obtained from the pbotograpbs, we will refer to figs. 50 and 51.
  - Fl G. 50
  - A, B, and G- are three caméra stations, platted in horizontal plan, whence three perspectives, I, II, and III, fig. 51, of tbe saine knoll D were obtained. The traces of these three pictures on the platting sheet, fig. 50, may be HA Aa, HB1 Hc Hc. Ail three pbotograpbs may bave been obtained witb tbe same caméra of constant focal lengtb—tbe distance lines PA A, PB B, and Pc G are of equal lengtb.
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  - (a) Locating points identifed on several photographs on the platting sheet.—The three stations A, B, and G are platted, either as parts of the triangulation System, or by measuring the base line AB on the'ground and measuring the* horizontal angles CAB, CB A, and A CB, after which the sides AC and BC may be found graphically (or by computation) and the triangle ABC may now be
  - T I IC
  - Fi 6.51
  - platted upon the working plan. Horizontal angles or directions to JD having also been observed from A, B, and C, its position with reference to those three points may also be platted. To plat the three picture traces HH we must know the horizontal angles P Ad ( = a), which are observed in the fleld for each picture by means of the horizontal circle attached to the phototheodolite.
  - The angles a are platted as aA, aB, and ac, fig. 50, and the constant focal length (=/) of the three négatives 1,4
  - Fl 6.52
  - O-—
  - \
  - 1
  - (A)
  - /
  - \
  - /
  - I
  - II, and III, fig. 51, is laid off on the radiais APa, PPB, and CPc. Perpendiculars erected to these lines in PA, PB, and Pc, respectively, will represent the oriented picture traces HAHA, HPHr, and HCHc, when the abscissæ PAdA, PBdB, and Pcdc, measured on the négatives I, II, and III, should equal the lengths PAdA, PBdB, and Pcdc on the picture traces.
  - The point D is termed a “reference point.” Every picture that is to be used in iconometric platting should contain the image of at least one such reference point of known position in both the horizontal and vertical sense.
  - After the picture traces HH hâve once been platted, any other point, T, of the terrene, shown on two or more photographs, may readily be platted from the photographs without requiring instrumental measurements in the field.
  - To locate the platted position of the point P, shown on two pictures, I and III, as t, the abscissæ, PAtA and Pctc? are laid off on the picture traces HAHA and HCHC, respectively, from PA and Pc and on the proper si de of P to correspond with the position of the image t with reference to the principal point, P, of the perspectives. Lines drawn from A and C through tA and tc, fig. 50, represent the lines of horizontal directions to P, and their point of intersection locates the position of P on the plat with reference to A, B, and C.
  - (b) Détermination of the élévations of pictured points.— The horizon line HH' of a perspective, fig. 49, being the intersection of the vertical picture plane MN with the horizon plane (passing through the optical axis of the caméra), will intersect points in the picture which in nature hâve the same élévation as the optical axis of the caméra or as the point of view S.
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  - The distances Sa and SA, fig. 52, are measured on the platting sheet and the ordinate aA, fig. 49, of the pictured point a, on the négative. Perpendiculars are then erected to SA in A and a and the latter is made ec^ual to the ordinate of a taken from the picture — Aa = a (a), fig. 52. If we now draw the line S (a) (to its intersection with the perpendicular in A), then the triangles Sa (a) and SA (A) will be similar and the angle AS (A) will represent the vertical angle (of élévation) of the visual ray from S to A revolved about SA into the plane of the horizon or into the platting plan. From the similar triangles Sa (a) and SA (A) we dérivé the proportional équation:
  - whence
  - A (A) : SA = a (a) : Sa
  - A(A) =
  - a (a). SA sa
  - The value found for A (A) measured on the platting scale will give the différence in élévation between caméra station horizon and the point A.
  - In practical work the élévations of the caméra stations are known, and by adding the heiglit of the instrument including the value A {A) to the élévation of S, fig. 49, the absolute height of A will be found, which, however, is still to be corrected for curvature and refraction.
  - A second value for the élévation of A may be found in the same manner for another négative •containing the image a (taken from another station), and the mean of several such déterminations is adopted for the final value for the height of A.
  - (c) Drawing the plan, including horizontal contours.—After some little practice points, pictured on different négatives but representing identical points in nature, will readily be identified by the observer and he will soon be able to pick out the characteristic points to reproduce the water courses, watersheds, roads, canals, etc., on the platting sheet. After these principal guide lines hâve been well located on the chart, buildings, outlines of woods, marshes, etc., are platted, including everything that is to be shown on the finished map.
  - Enough points should be platted iconometrically to give a good control for a correct délinéation of the relief. When the number of points determined on the plan is sufficient, or if they are favorably located to give an adéquate control only for the délinéation in the horizontal sense, additional points should be platted in order to obtain an equally good control of the terrene in the vertical sense.
  - The planimetric work completed, élévations of as many of the platted points as seem neces-sary (or additional ones) are determined and inscribed on the chart. Horizontal and équidistant contours may now be drawn, by interpolation, to harmonize with the élévations suffixed on the chart to the points of control, conforming their courses (between the located points) to the configuration of the terrene, as it is shown on the photographs.
  - It can not be denied that a certain amount of study and practical application are required to enable the draftsman to correctly interpret forms of the terrene, shown in perspective. Yet, it should also be admitted that such translation or conversion of the relief of the terrene into the horizontal map projections may be far more accurately accomplished (at one’s leisure) by means of geometrically correct perspectives, than could be accomplished by sketching in the field. When topographie features are sketched, as seen from one direction, they will frequently be found to hâve been misconceived when they are seen again from another (not anticipated) point of view. Of course, the platted forms may then be corrected in a measure, at least, still, many details are sketched which will not be seen again from other stations, and, even those that are seen again under other conditions may not be modified to conform to their true shapes, unless the original station, whence they were first seen and sketched, could be reoccupied to verify the suggested changes and corrections. Generally speaking, topographers regard a second occupation of a station with little favor, it being considered too great a waste of time, retarding progress, and considerably increasing the cost of the work.
  - In iconometric platting, however, it is always an easy matter to refer back again to panoramic views obtained from some other station, and the platting of topographie details should not be attempted without having first made a careful study of and a close comparison between the various pictures representing the same features but seen from different points of view.
  - (2) Method of Dr. A. Meydenbaur.—The pantoscopic lens (made by E. Bush, Rathenow,
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  - UNITED STATES COAST AND GEODETIC SURYEY.
  - Prussia) of Dr. Meydenbanr?s surveying caméra commands an angle of about 100°. By exclnding an extern al ring of the effective disk of tbese lenses by means of a diaphragm, pictures are obtained subtending an angle of but 66°, requiring six plates for a complété panorama.
  - This caméra bas neither telescope nor vertical circle but it is provided with a horizontal circle, thus enabling the operator to control the révolutions of the caméra in azimutb.
  - After this caméra bas been set up and adjusted over a station the panorama is pbotograpbed by exposing six plates in succession, eacb successive turn in azimutb of the caméra covering an angle of 60°, flg. 53, and two adjoining plates lapping over eacb other by 3° in arc. Tbese com-
  - mon margins (like Paganinfs plates) contain identical sections of the panorama view. Tbey may serve to find the value for the focal lengtb of the pictures, and tbey control the permanency of the camera’s adjustmentsdur-ing one complété révolution in azimutb.
  - (a) Détermination of the focal length for the panorama views.—From the six plates, covering the entire horizon from one station, objècts may be selected on the center lines of the common margins of adjoining plates which sbould be équidistant from the principal lines of the two plates.
  - After having selected a sériés of sucb reciprocal points (using a magnifying glass if necessary) on ail six plates, we will bave obtained twelve déterminations, represented by the lengtb l, for the position of the principal line. The greatest discrepancy between any two values should not exceed 0’2 mm, if the instrument was well adjusted. The sum =21 of two sucb distances (between two of the corrected principal lines) will rep-resent the effective lengtbs of one picture, or the lengtb of one side of a regular hexagon, witb an inscribed circle of the radius equal to the constant focal lengtbs (=/) of the négatives.
  - This length =/may be found grapbically or it may be computed from the formula:
  - J tan 30° •
  - When positive prints are to be used in the iconometric map construction it will become necessary to correct this focal lengtb / to correspond with any changes tbat may bave taken place in the dimensions of the prints when compared witb their négatives. By comparing the distances between the “ teetb ” (marking the principal and horizon lines) on the négative witb those included between their contact prints on the positive the total linear changes of the print in the directions of the principal and horizon lines are readily found.
  - We bave witb reference to flg. 54 : ab — original lengtb included between the teetb marking the horizon line on the négative, a'b' = lengtb of horizon line (included between the pictured teetb) on the positive print. co = f = constant focal lengtb of caméra or négative.
  - If we draw the triangle abO, place the line a'b'
  - (measured on the print) parallel witb ab and move the same (maintaining its direction parallel witb ab) toward (or.from) O until a' falls upon ao and b' upon bo, then c'O will be the focal lengtb of the photograpb (“contracted,” in our case). This détermination of /sbould be made for every print that is to be used in the iconometric map construction.
  - The topographie map is grapbically constructed from the négatives and prints in a manner very similar to tbat described for Colonel Laussedat’s metbod.
  - (6) General method of iconometric platting.—Witb reference to fig. 55 we bave:
  - I and II = two négatives of plates exposed from caméra stations I and II, respectively.
  - III = baseline, measured in the field.
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  - The élévations of caméra stations I and II may be known and négative I may contain the image of station II, négative II that of station I. After the baseline I II has been platted in reduced scale (in the scale of the proposed map), circles are described about I and II as centers
  - with radii = cO =/ = constant focal lengtli of the négatives. Then make
  - I Il0 = OII0 (PL I) and III0 — OI0 (PI. II).
  - Describe ares frorn II0 with II0e = xln (plate I) and from I0 with l0c = xl\ (PI. II) as radii, transpose ct0 = x\ (PI. I) on the tangent II0c and ct0 = æx\ (PI. II) on the tangent J0e.
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  - The prolongations of t0I and t'0I will be tangential directions to the sides of tbe tower T (pictured on Pis. I and II) front caméra station I, and t0II and will be tbe tangential directions to tbe sides of the same tower T from station II. Tbese four tangents intersect each otber at T in a quadrangle, the inscribed circle of whicb will represent tbe position of tbe tower (in horizontal plan) witb reference to the baseline III.
  - Any otber points, common to botb Pis. I and II, may be located in horizontal plan in pre-
  - 1
  - FiG.56
  - cisely the saine manner. The method just described is general in character, but when tbe caméra is provided witb a horizontal circle, enabling tbe observer to cover the horizon witb six plates by revolving the caméra exactly 60° in azimuth after each exposure, the following method is generally applied :
  - The constant focal length=/of the négatives is laid off on the principal line below the principal point = c'0 for négative I and = c"0 for négative II. The images of tbe stations are projected upon the horizon lines, 8n upon HlHl (Plate I) and SL upon HnHn (PI. II) when
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  - FlCr 57
  - \
  - c'OSll = a' represents the horizontal angle inclucled between the principal plane and base line
  - I II, and c" O Si = a" represents the corresponding horizontal angle for station II. These angles a' and a" are transferred from the négatives I and II to the corresponding ends of the base line III, as indicated in fig. 56.
  - After laying ofï the focal length/from the base stations I and II npon the sides of the angles a‘ and a" ( = le' and Ile" respectively) and erecting perpendieulars {If'H1 and H"H") in c1 and c" to le’ and Ile" respectively, they will represent the oriented picture traces of négatives I and II.
  - The remaining two sets, of five plates each, of the panorama view s at the stations I and II, are easily oriented and platted, the next plate in order at station I, for instance, will hâve the I y.
  - optical axis" in the direction a' + 60°, the third : a' + 120°, etc.
  - After ail the horizontal projections of the ver-tical plates (picture traces) -Si-Hi, ....
  - HeHc, fig. 57, hâve been platted at both stations I and II, the horizontal projections of ail points that may be identified on two plates are marked and platted by locating the intersections of the lines of direction drawn througk the projections on the picture traces of the pictured points in the same manner as shown in fig. 56 for the tower T. Every platted caméra station will be surrounded by a regular hexagon formed by the picture traces of the six plates comprising the panorama set.
  - (c) Détermination of the élévations of pictured pomts of the terrene.—The projection in horizontal plan of an object having been platted, the élévation I(Si) of that object S, above (or the dépréssion of it below) the horizon, HH, of the caméra station
  - II may be found as follows :
  - The lengths IItfx(= 0$ on PI. II) and III, fig.
  - 56, may be measured on the platting sheet, and the ordinate ya may be taken from the négative II.
  - We erect perpendieulars to III in St = ys = St (SL) and in I, then draw the line II(Si) to its intersection (Si) witli the perpendicular to I II in I, when the length 1(8;), measured in the platting scale, will represent the différence in élévation between the points I and II.
  - By computation we would find from : '
  - I(Si) :ya = III: StII
  - m)
  - Vu
  - III
  - 8,11
  - If
  - the scale of the map is
  - _1
  - M’
  - we will hâve :
  - I(Si) = M.ys
  - III * Si II
  - The values of ya, III, and Sill are found by direct measurements with a small ivory scale divided into 0*5 mm., of which 0*1 mm. may be estimated after a little practice.
  - (3) Method of Capt. D. Deville (Ganadian method).—This*so-called Canadian metliod has been in use under the auspices of the department of the interior of the Dominion of Canada since 1888. Deville has given a full account of these methods in Photographie Surveying, published at the government printing bureau, at Ottawa, in 1895, and the following paragraphs hâve been largely taken from Deville’s book :
  - (a) General remaries on fiéld worlc.—The area to be surveyed is covered with a triangulation net, preferably before the phototopographic survey is commenced, and a secondary triangulation is
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  - carried along with the phototopographic work to locate the caméra stations in botli the horizontal and vertical sense, with reference to the primary triangulation stations already established.
  - The surveyor makes a rough plat of the entire triangulation (in the field), on which he locates ail the stations occupied to enable him to recognize the weak points of his work and to plan Ms operations with a thorough understanding and good assurance of success. The instrumental work in the field is done me,rely to locate the caméra stations and certain reference points (if the triangulation points are not sufficiently close together), ail topographie features being deduced from the pictures.
  - The caméra stations are located either by angles taken from the station to surrounding triangulation points, by resecting, or by angles observed from the latter to the signal left over the caméra station, by intersecting, or by both methods combined.
  - The final value of the work dépends in a great measure upon a judicious sélection of the caméra stations in order to bring the relief of the entire terrene under proper control and to be enabled to plot ail points needed for a full development of the terrene by the method of intersections of horizontal lines of direction.
  - Other methods for platting the topographie features and details are employed only when the method of intersections fails on account of the caméra stations not being well situated, or on account of an insufficiency of data to give the requisite number of horizontal lines of direction for a good location of points by “intersecting.”
  - Each caméra station should be marked by a signal of some kind before leaving it, not to be shown on the pictures, but to be observed upon with the transit or altazimuth from other stations in order to locate the correct position of the caméra station on the platting or working plan.
  - Frequently it will be of advantage to set the caméra up excentrically over a triangulation station in order to include certain additional parts of the landscape in the views. The position of the excentric caméra station, with reference to the triangulation point, can readily be ascer-tained, and should always be carefully recorded.
  - Complété panorama sets are not taken at every caméra station, it being preferred, rather, to increase the number of stations, often occupying a station to obtain a single view only, if by doing so better intersections for the iconometric location on the platting sheet of some spécial feature are obtained. Multiplicity of stations demands but a small increase in labor, either in the field, in the extra observations of directions to reference points for their location, or in the iconometric platting in the office, and enough stations should always be occupied to give a full control of the relief of the area to be surveyed.
  - A certain section of the terrene may bë so located that it will be a difficult matter to select more than one station whence it may be seen. In such a case the method of “ vertical intersections” may often become useful: Two or more views of such area are taken from stations at different élévations, the greater the différence in altitude between such stations the longer will the base line be, and the better are the intersections which locate the features in question, if the latter are not too far away.
  - * As enough plates should be exposed to cover the ground completely, the caméra stations will hâve to be distributed in such a way that ail valleys, sinks, and dépréssions, that may be represented in the scale of the map, are well controlled (i. e., seen from different caméra stations). It is évident, therefore, that the number of stations to be occupied for the phototopographic development of a certain area will dépend in a great measure upon the character of the terrene and upon the scale of the chart.
  - Two or three well-defined points (so-called reference points) in each panorama view (covered by one plate) are observed with the transit or altazimuth noting and recording the vertical and horizontal angles upon the outline sketch made f>r every plate exposed. Such sketches serve to identify points with far more certai'nty than a inere désignation or description of the points observed upon. The general triaugulation notes are kept in the usual manner.
  - Vertical angles are observed to check the position of the horizon linefon every photograph and to correct errors due to small changes in the level adjustments of the caméra that may arise during the transportation of tbe instrument over a rough trail. The horizontal angles are needed for the location of the caméra stations and for the orientation of the pictures (picture traces) on the ïfiattmg sheet for the subséquent map construction.
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  - (b) General remaries on the iconometric platting of the survey.—The field notes of the phototopo-graphic survey s made in the Northwest Territory of the Dominion of Canada by the topographical surveys branch of the department of the interior (under Capt. E. Deville, surveyor of Dominion lands), are platted on a scale of 1:20000, but the maps are published on a scale of 1:40000, with (équidistant) contours of 100 feet vertical intervals.
  - The phototopographic reconnaissance in southeastern Alaska, executed by Dominion land surveyors under Dr. W. F. King, Alaskan boundary commissioner to Her Majesty, was platted on a scale of 1:80000 and published on a scale of 1:160000, with horizontal contours of 250 feet vertical intervals.
  - It is assumed that the triangulation computations hâve been made and that the triangulation points hâve” ail been platted, and that their élévations above the adopted reference plane hâve been affixed to the marked points on the platting sheet.
  - The triangle sides of th,e secondary triangulation scheme (executed during the phototopographic survey) are now computed (the corrections to the horizontal angles, indicated by the closing errors, haying been applied), the latitudes and departures (from every secondary point to the nearest primary station) are computed, and the secondary stations are then platted by their latitudes and departures (unless the primary triangulation sides are too long).
  - The caméra stations (not included in the secondary triangulation scheme) are now platted with reference to the triangulation points, using a table of chords or a station pointer (three-arm vernier protractor). If many points had been observed upon from the caméra station, the horizontal angles are preferably laid oft* on a piece of tracing paper, and this improvised multi-arm protractor is used like a station pointer to locate the station.
  - The surveyor should endeavor to obtain at least one direction from a triangulation station to every caméra station; the (iconometric) platting will then be less troublesome and more accurate.
  - Photographs should not be used for platting the positions of caméra stations, as this would not locate them with sufficient précision, and enough angles should always be observed in the field to locate every occupied station in the manner just mentioned.
  - From the original négatives copies are made, enlarged to 9£ by 13 inches on heavy bromide paper, more recently, however, a spécial brand of bromide paper, known as “platino-bromide,” has been used by Captain Deville. The enlargement adopted in Canada for these bromide prints is about 2.1 times larger than the négatives, which ratio was selected to utilize the full width of the paper found in market.
  - These bromide enlargements are used extensively in the map construction, and they should be made with great care to reduce distortion to a minimum. Before using the prints for the map construction any distortion due to the enlarging process should be ascertained, which is done in the foliowing manner :
  - Fs g. 58
  - Join the middle notches H and H', indicating the position of the horizon line, and P and P7 represeuting the position of the principal line, fig. 58, and with a set square test these two lines for perpendicularity. Take with a pair of dividers the distance between the two notches A and B (which on the négative is equal to one-half of the constant focal length) and see whether it is/
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  - equal to the distance of the eorresponding two notches G and D. IsTow apply one of the points of the dividers in P; the other should corne in E and F. Transfer the point to P' and check the length P'G and P'J in the same way. If the print satisfies ail these t< sts, it may be used for the iconometric platting; if it does nof, it is returned to the photographer with a request for a better one.
  - (c) Platting the picture traces.—Every photograph contains at least one, generally several, of the triangulation points platted on the working sheet, and the traces of both the picture plane and principal plane are found and platted on the plan as follows :
  - The distance, or principal line PS, fig. 59, is made equal to the focal length of the picture, and the image point a of the point A is projected upon the principal line (= a) and upon the horizon line ( = «'). If Si represents the platted position of the caméra station S on the plan, and if &A1 represents the horizontal direction on the plan from S to A, we make Siüi — Sa' (taken from the photograph) and from au as center, with a a (= Pa') as radius, describe a circle to which Sip is drawn tangent, theu Sip = trace of principal plane and the perpendicular to Sip through a, = pai = trace of picture plane.
  - Instead of making this construction on the “photograph board,” which will be described further on, it can be made on the plan itself, as follows :
  - On take S\B, fig. 60, equal to the focal length of the print; erect BG perpendicular to /Si^! in B and equal to a a, fig. 59. Join SXG and take S{p equal to the focal length; at^9 erect a perpendicular to SiG and it will represent the trace of the picture plane, while S{G is the trace of the principal plane.
  - »
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  - Another simple method, avoiding the drawing of constructive lines on the plan, is as follows:
  - Take a triangle of liard rubber or wood and mark off along one side the focal distance SP, fig. 50, of the print, = ab, fig. 61, and carefully notch the triangle side at b so that the center of a fine needle, marking the platted station point, will just fit into the notch. Front the print, fig. 50, take the abscissa of the pictured point a = aa = Pa' between the points of a pair of dividers, move the triangle, fig. 61, about the needle (which marks the platted station) with the left hand until ac, fig. 61, is equal to the distance aa held between the points of the dividers. The triangle is held securely in tliis position and lines are drawn along the triangle sides ab and ac. Prolong ac beyond a and check the distance ac again to be = aa. The line bc represents the horizontal direction from the platted station b to the platted reference point c (on the négative, fig. 50, the picture of the corresponding reference point is a). We will now hâve: ba = trace of the principal plane, ac = trace of the picture plane, a = projection of the principal point on the platting sheet.
  - The trace of the principal plane (= ab) is preferably marked on the platting sheet by a short line only, bearing an arrow pointing toward the platted station (b) whence the picture was taken, and the principal point a is marked to correspond with the désignation of the print. It may be remarked here that as few lines as possible are drawn on the platting sheet to avoid confusion and mistakes. (See photograph board.)
  - (d) The identification of pictured points on several photographs repre-senting identical points of the terrene.—The topographie survey being platted mainly by the intersections of horizontal directions, points eon-trolling the relief of the same area must be identified on sets of pietures taken from different stations. When selecting such points on a photograph preference should be given to those which best define the surface relief or terrene, like characteristic points of ridges, peaks, saddles, changes of slope, changes in the river courses, etc., each point being marked by a dot in red ink on the photograph and having a number or Symbol afîixed to it. It will now be necessary to identify as many of these points as possible on other photographs, covering the same area, and these are similarly marked by red dots, and identical points are given the same désignation by number or Symbol in red ink.
  - The identification itself of points on several pietures offers no serious difficulties, and, with some practice, as many points as may be needed for a full development of the terrene, even under different illumination of the pictured areas, may be picked out with rapidity and certainty.
  - (e) Application of Prof essor HaucPs method for the identification of pictured points.—In cases of doubt, when attempting to identify the same point on two different photographs, beginners may take advantage of Professor Hauck’s method, which lias been described in Chapter I, Paragraph VII.
  - The two photographs are pinned side by side on a drawing board. The images of the caméra stations whence the pietures were obtained are “ kernelpoints,” and if they fall outside of the picture limits they are determined from the ground plan and platted on the drawing board. The parallels to the principal lines of the photographs on which the scales are to be laid off are drawn in the mariner explained in Ghapter I and the scales are fixed in position. A fine needle is now inserted into each of the “ kernelpoints” and the loop at one end of a fine silk tliread is dropped over each needle, the other end of the thread being secured by a slender rubber band to a small paper weight (fig. 62).
  - A well defined point is now identified on both photographs, sufficiently far from the “kernel points,” and one thread is moved by taking the paper weight up and passing its thread, under gentle tension of the rubber band, tlirough the point just identified on the photograph, when the weight is deposited upon the drawing board, holding the thread in the given position. The same operation is repeated with the other silk thread and the other photograph, when the two threads should intersect the scales at identical division marks. If they do not, one of the scales is to be moved until both threads bisect the same division marks of the scales.
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  - Now the identification of the doubtful points may be proceeded with. Having seleeted a point on one of tfie photographs, tfie corresponding silk thread is moved to bisect that point, noting the position of the thread with reference to the scale in this position. The other thread is moved to bisect the corresponding graduation mark on the second scale, when this thread will also bisect the corresponding point on the second photograpli.
  - (/) Platting the intersections of horizontal directions to pictured points.—After enongh pictnres hâve been seleeted to control the cartographie development of a certain area and the identification and marking of corresponding points hâve been completed, projections of ail these points on the horizon lines of the pictures are marked (their abscissæ are measured) and transferred to the straight edge of a strip of paper, including the marking on the paper strip of the principal point of every photograph. Each paper strip bears the same désignation (in red ink) as the picture to
  - which it belongs.
  - These strips are now placed up-on the platting sheet on the picture traces to which they belong in such a manner that the principal points of paper strips and picture traces coin eide, and in this position they are securely held to the working sheet by means of small thumb tacks or paper weights.
  - To plat the horizontal projections of a point, shown and marked on two prints, two fine needles are inserted into the jilatted station points I and II, fig. 62 (of the two prints) and a fine silk thread at-tached to a small paper weight w (by fine rubber band b) is secured to each needle by a loop.
  - The thread attached to station needle I is now moved over the weighted paper strip (indicating the picture trace on the plan) until it bisects the horizontal projection a' of the picture point a. The weight is now placed upon the working plan, holding this thread (under slight tension) in this position. The second thread, attached to the needle in station II, is placed over the projection a" of the image of the point A, also under tension of the rubber band. The point of intersection of the two threads will be the position on the plan of the point to be platted (= A). After this position of A upon the plan lias been checked, in the same manner, by means of another photograph (thread and paper strip) taken from a third station, III, and containing the image a"f of the point A, its platted position is marked by a dot in red ink and its désignation corresponding with that given on the prints is also affixed.
  - After a suflicient number of points hâve been platted in this manner by intersections, and after they hâve ail been supplied with the letters or nuinerals given them on the prints, their élévations are determined and also added in red ink. Frequently the désignation of the points by letters or symbols are only added in pencil on the working sheet, to be erased after the élévations of the points hâve been affixed to them in red ink. f
  - When the strips of paper should overlap each other, as shown in fig. 63, the part CD of the picture trace PQ is marked off on the strip MM lying under PQ, the paper strip PQ is placed in proper position, and the marks on its edge are transferred to the line GP. The strip PQ is now placed uuder MM, the marks on the latter along GP serving the same purpose as those of PQ.
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  - Fig. 63
  - When a station, A, fig. 64, falls so close to tlie edge of tlie working board that the trace QB (of the picture plane) falls outside of the limits of the plan, then the trace AG of the principal plane is prodnced to jB, making AB = AC = focal length of the pictnre, and MN is drawn perpendicular to B G or parallel to QB. The line MN will, with reference to QB, occupy the same position as the focal plane of the caméra does to the picture plane of the perspective. The direction of a point of the photograph projected in Q on the picture trace is fouud by joining N'A and producing to the opposite side of A.
  - As mentioned before, the intersection of the first two lines of direction should be checked either by a third line or other-wise before the position on the plan of a pictured point should be accepted as correct. Such intersections may, for instance, be checked by determining the height of the point from both photo-graphs. Unless correctly platted and correctly identified, the two values for its height will not agréé. This check, however, does not guard against slight errors in platting. A check may also be obtained by drawing a line, on which the point is situated, with the perspectograph or perspectometer, but the best check will al-ways be a third intersecting line of direction from a third station.
  - (g) Platting pictured points iconometrically by vertical intersections.—We had seen how the base line between two stations is projected into horizontal plan for the method of horizontal intersections hitherto considered, but when two caméra stations are occupied at different élévations (and close together horizontally) to locate features of the terrene by intersections, the so-called “method of vertical intersections” is employed. With this method the base line (its horizontal projection being either too short or more frequently falling into the direction in which the points to be located iconometrically are situated) is projected upon a vertical plane. The greater the différence in élévation between the two stations, the greater the length of this base-line projection in vertical plane, and also the better the location of the points by vertical
  - intersections will be.
  - We will hâve with reference to fig. 65:
  - A and B=positions of the two caméra stations, platted upon the working sheet. (A is more elevated than B). aB = horizontal projection of the base line AB. AN and Bn = two négatives (showing the images dA and dB of the same point D) exposed at the stations A and B respectively. HABHAB' and HBHB' = picture traces of the two négatives on the ground plane or working sheet. aPA' = BPQ = focal length of the négatives AN and _BN.
  - We will assume that the horizontal plane passing through the lower station (B) is the ground or platting plane, and the principal plane of the négative A may be taken as the vertical plane of projection. PL^H^ will then be the trace of the picture plane AN on the ground plane.
  - Furthermore, the principal plane, of which aPA' is the trace in the ground plane, is supposed to be revolved about aPA' into the ground or platting plane in order to simplify the construction.
  - To plat the position in the ground plane of a point JD, pictured on AN and BN as dA and dB respectively, the rays AdA and BdB are projected upon the vertical plane (revolved about aPA‘ into the ground plane) when (dQ, in fig. 65, will represent their point of intersection d, projected into the vertical plane = dh and revolved about aPA' into the platting plane = (dx).
  - The ray AdA = AD intersects or pénétrâtes the picture plane AN at a distance = dAdAB vertically above dA', on its picture trace HABHAB' (ground line of picture AN). This ordinate is laid ofif upon PAHAB = PA (dA), when (dA) will be the projection on the vertical plane of the pictured point dA.
  - The vertical through a projected upon the vertical plane is represented as a (A), and if we make a {A) — PAPAB (of picture AN) = différence in élévation between the two stations A and B,
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  - then (A) will be the upper caméra station A projected into the vertical plane, and the line connecting A with the point (dA), just found, will be tbe projection into vertical plane of the ray AdA or AD (revolved about a,PA' with the vertical plane into the platting plane).
  - The ray BdB = BD intersects the second picture plane BN in dB. If we draw through dB' (projection of dB in gronnd line RBHB') a perpendicular to aPA' = dB'diBi then dlB will be the projection into the vertical plane of the horizontal projection in the picture trace of the pictnre
  - —Ç~£L._.
  - — O—
  - Fig.65
  - point dB. Producing dB'dlB and making dlB (dB) = dBdB' (measured on the négative BN) will locate at (dB) the projection of the pictured point dB upon the vertical plane.
  - The perpendicular to aPA' through B will locate the projection into the vertical plane =bx of the platted station P, hence the line connecting bx with (dB) will be the projection into the vertical plane of the ray BdB = BD.
  - The intersection (dx) of bx (dB) with (A) (dA) locates the projection into vertical plane of the point sought, d, and the horizontal projection of this point d (the platted position of the original point, D) will be on the line (dx) d/ (which is the vertical througfi d, or in our case the perpendicular to aPA from (d,)), andeither horizontal directions adA' or BdB, produced to intersect this perpendicular (dx) dx will locate the horizontal projection d'of the point d, representing the position on the platting sheet of the point D with reference to the platted stations a and B. (The
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  - location of d' as the intersection of the horizontal directions adA ' and BdB' would not be very accurate for our case, and far less so for pietured points on the other side of the principal point PB', where the angles of intersection of the horizontal directions would be even smaller than at d'.)
  - The point d/ being the projection into the vertical plane of the point d' ( = horizontal projection into the ground plane of the point d) the lengtn (dx) d/, measured on the platting scale, will represent the élévation of the point D above station B.
  - (h) Iconometric détermination of élévations.—Grenerally speaking, one perspective will not suffice to détermine the height of a point, although there are exceptions, like the points on the horizon line, which hâve the same élévation as the caméra station.
  - With reference to fig. 66 we hâve: dx = horizontal projection of the point P. . Bdx = horizontal distance between platted station B and platted position d of point D (measured in platting scale on working sheet). BdXB = horizontal distance between station B and projection of pietured point dB in ground line HB ÏÏB', measured on platting sheet. diB (dB) = h = ordinate of pietured point dB above ground line (revolved with vertical plane about J5diB into platting plane), measured
  - on picture. dx (d) — H = height of point d above the ground plane (revolved into the ground plane with the vertical plane about Bdx). Measured on the platting scale, it will give the height of D above the caméra horizon (ground plane = horizon plane).
  - The height H is a fourth proportional to the three known lengths Bdx, BdUi, and dlB (dB).
  - After projecting the platted point d and the pietured point dB into the principal plane, and after revolving the latter about the principal line BP into the platting, or ground plane, we will hâve:
  - P (d^) = h = height of pietured point dB above the platting plane. (d'B) = pietured point dB, projected into the principal plane and revolved with the latter about the principal line into the platting plane, (d') dx = vertical height of the point d, projected into the vertical plane and revolved with the latter, about the principal line, into the platting pr horizon plane; hence (d') dx — H = élévation of d above the horizon plane.
  - This height = H being the fourth proportional to the three known lengths :
  - BP —f= focal length of the print. P (dB) = ordmate of pietured point dB, measured on 6584----------44
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  - photograph, and Bdi' = f + JW; where: Pdx' = vertical distance between the platted point dx and tlie picture trace HRHf, to be measured on the platting sheet, its value ( =E) may be found mechanically with aid of an ordinary sector, fig. 67, as follows :
  - Take with a pair of dividers the (ordinate) distance froin the pictured point dB to the horizon line (on the photograph), place one point of the dividers on the division G of the sector, fig. 67,
  - Fig.68
  - where OC = focal length of the photograph, and open the arms of the sector until the second point of the dividers coincides with the corresponding division I) of the other arm of the sector (OE being equal to OC = focal length), now add the length dx'P, fig. 66 (horizontal distance of the platted point dx to the picture trace EBEB projected into vertical plane), to the focal length =/ = OG, fig. 67, by placing one point of the dividers in G, when the other point may coincide with the division A of the scale O G. Hold the sector nnchanged, turn the dividers about the point A, and bring the second point to the graduation mark B of scale OE, B corresponding to A, or O B = OA ; when AB will represent the height H of the point d above the horizon plane of the station P, to be measured on the platting scale.
  - (i) Iconometric détermination of élévations by means of the so-called, u scale of heightsP—Another method consists in making use of the “scale of heights,” fig. 68. Make SP=f = focal length of the perspective, erect PA perpendicular to SP in P, and divide both fines into equal parts. Draw radiais from S through the points of division on PA, and through those of SP draw parallels to PA. Now, with a pair of dividers take from the photograph the distance from the pictured point to the horizon fine (the ordinate of the pictured point eorre-B sponding to P{d'h) = h, in fig. 66) and transfer it to PA from P = Pfx. The position of \x may be found to correspond to the line Sjx, passing through the point 9 of the graduation on PA.
  - With a pair of dividers take now (from the platting sheet) the. vertical distance from the horizontal projection of the point to the picture trace (= ôdx in fig. 66) and transfer it to the right or left of P according as the point of the plan falls beyond the picture trace or between the platted station and the picture trace. In fig. 68 it is shown as falling between the station and the picture trace into m. The line mB, drawn parallel with PA, is intersected by the radial S/.i (corresponding to scale division mark 9) in M. The distance mM, measured on the platting scale, will be the height of the point above (or below) the station. ’
  - A scale, fig. 69, is conveniently pinned somewhere, perpendicularly to a fine AB, the division G of the scale, corresponding to AB, being the height of the caméra station. One point of a pair of dividers with which the length AB was taken off the “ sector,” or with which the length mM
  - Fie. 69
  - e c
  - —M
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  - was taken off the “scale of heights,” is set in <7, flg. 69, and the division mark D of the scale, coinciding with the other point of the dividers, will indicate the height of the point above the plane of reference or datum plane.
  - This height is entered in pencil on the plan, inclosed in a small circle, to distinguish it from the number of the station. It is checked by means of a second photograph, and when the discrepancy between the two values for the élévation of the point is within the permissible limits of error, their mean value is entered in red ink on the plan and ail pencil figures are erased.
  - Any marked différence in the value for the height of a point obtained from two photographs would indicate either that the two points selected on the photographs do not represent the same point of the terrene, or that an error in platting or in finding the height had been made. A third intersecting line from a third station wonld dispose of the first two alternatives, and a new measurement of the height will show whether an error had been made, or whether the discrepancy is due to unavoidable errors.
  - (j) The use of the so-called uphotograph board.”—The various constructions described in the preceding pages, if made directly on the platting sheet and on the photographs, would produce confusion in the iconometric platting, owing to the intricacy of the lines, and would obscure many details in the pictures. Captain Deville, therefore, has h ad a spécial drawing board prepared on which as many of the construction lines are drawn, once for ail, as would hâve to be repeated for the different prints of uni-form size and which had been obtained with the same caméra.
  - This so-called “photograph board” is an ordinary drawing board, covered with tough drawing paper, the surface of which is to represent alterna-tively either the picture plane or the principal plane (both revolved into the horizon plane). It is used in conjunc-tion with the photographs or négatives.
  - Two lines, DD' and SS', fig.
  - 70, are drawn at right angles to each other. They represent the horizon and principal lines, while PD = PD1 = PS' =/= focal length, so that D, D', S, and S1 are the left, right, lower, and upper distance points, respectively.
  - The photograph is placed in the center of the board, the principal line coinciding with SS/ and the horizon line with DD1, in which position ( TYZO) it is secured to the board by means of small thumb tacks or pins. The four scales, forming the sides of the square OTYZ, serve, among other purposes, to locate lines parallel either with SS' or DD1 (without actually drawing the parallels) on the photograph, the latter falling within the limits of the square OTYZ. At a suitable distance from the distance point D' a perpendicular QR is drawn, on which are marked by means of a table of tangents the angles formed with DQ by lines drawn from D. This scale may be used for measuriug the altitudes or azimuthal angles of points of the photograph, as will be explained in a separate paragraph later.
  - From S as a center with SP =/ = focal length an arc of a circle PL is described and divided into equal parts. Through these points of division, and between PL and PD', lines are drawn converging to S. Parallels MN to the principal line are also drawn, as shown in fig. 70. Ail these lines are used in connection with the scale of degrees and minutes QR.
  - FiG.70
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  - The studs of the u centre lineads ” (to be mentioned later) are fixed in A, B, <7, and E, the lines AB and GE joining their centers, and those required for adjusting the centro lineads are drawn on the photograph board to be used as will be explained in a later paragraph. The square EGKH is constructed on the four distance points $, S', D', and I).
  - (Te) Construction of the traces of a figuras plane.—If one wislies to use a perspective instrument for converting a figure—situated in an inelined plane of which the perspective (photograph) is given—into the projection of the figure, into horizontal plan, it will be necessary to locate the traces of the figure’s plane on the principal and picture planes.
  - ô—-
  - —o-
  - We may distinguish between two cases that frequently arise in practical work.
  - (1) The inelined plane, containing the figure, may be given by the liqe of greatest slope, or,
  - (2) The inelined plane may be given by three or more points.
  - First case: The inelined plane containing the figure is given by its line of greatest slope; this may be an inelined road, the drainage line of a straight valley, the trend of a torrent, the surface of a live glacier, etc.
  - This line of greatest slope may be represeuted on the plan by a line ab, fig. 71, the altitude of a being known.
  - After the photograph has been pinned to the photograph board, the ground line XY is drawn, taking the horizontal plane through a as the ground plane. ’
  - On the platting board aO is drawn through a perpendicular to the horizontal projection ab of the line of greatest slope, and it is produced to its intersections A s and O with the principal line Sipx and with the picture trace XxYx.
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  - On the pliotograph pL1 is made equal to pib ; at E a perpendicular to XY is erected and produced to the intersection fi with the pictured line of greatest slope.
  - If we uow make pN (on the photograph) = piO (of the plan) and join N fi on the picture, the line N fi will represent the trace of the required plane (the figure’s plane) on the picture plane.
  - If pQ (on the photograph) is made equal to pJj (of the plan) and Q joined with M, MQ will represent the trace of the required plane in the principal plane, revolved about SS' (on the photograph board) into the picture plane, the station S falling in D.
  - Producing MQ to E, DE will represent the vertical distance of the station S above the plane EM fi.
  - Second case: The inclined plane containing the figure is given by three points.
  - Take for ground plane the horizontal plane containing one of the points a, fig. 72, and draw the ground line XY on the photograph. On the platting sheet join a to the two remaining points, b and e, and produce these lines ab and ac to the intersections E and F with the picture trace.
  - On the photograph make piK equal to pE and draw KL perpendicular to XY. Join the perspectives a and fi of the points shown in a and b on the plan and produce to the intersection with KL. Make piT equal to pF, draw TX perpendicular to XY, and produce to the intersection N with the line joining the perspectives a and y (of a and c). Join X and L, when XL will represent the trace of the required plane on the picture plane.
  - Produce LXto O and make^?Cr =piO; join a and O and make piQ =pE. The line MQ will represent the trace of the required plane on the principal plane, revolved about SS1 into the pictwre plane, the station S being now in D. Here again DE is the vertical distance of station S above the plane containing the three given points a, b, and c.
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  - (?) Contouring.—After the heights of a sufficient number of points bave been determined to give a good development of tbe terrene tbat is to be mapped, tbe contour lines are drawn in by interpolation between the points of which the élévations had been established.
  - In a moderately rolling country a limited number of points of known élévations will suffice to draw the contour lines with précision ; but in a rocky région, where abrupt changes and irregular forms predominate, it is almost impossible to plat enough control points to enable the iconometric draftsman to render a faithful représentation of the relief of the broken terrene, and it is here that a close study of the photographs will give the greatest assistance in modifying the courses of the contours to represent the characteristic features of the terrene.
  - The value of photographie views for a correct or naturalistic délinéation of the topography of a given area is generally acknowledged by experienced topographers, even when using
  - instrumental methods alone for the control work, as a minute study of the pictured terrene (the photographs) will always aid the draftsman (when inking the topographie sheet) to draw the contours (of which the main deflections had been located instrumentally) with a more natural and artistic reproduction of nature’s forms than could be attained by mechanically inking the penciled lines as obtained solely by instrumental measurements.
  - Instead of drawing the contour lines at once on the plan, the draftsman may begin by sketching them on the photographs, foliowing the same rules for thefr location as if he were drawing them on the plan, for the image of every platted point is already marked on the photo-graph and its élévation may be taken from the working plan. By following this course he wfll be enabled to follow the inequalities of the surface very closely. Those perspectives of the contours
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  - 695
  - on the pictnres will greatly facilitate their horizontal projections to be drawn upon the plan. They may also be transferred to the plan by means of the perspectograph or perspectometer if accuracy is to give place to rapidity.
  - A sufficient number of tertiary points having been platted by intersections, there will be no difficulty in drawing the contour lines (by interpolation) between snch points. It may happen, however, that the number of the control points is too small and that the latter are too far apart to give a good définition of the terrene (as in a topographie reconnaissance), and then it will become necessary to resort to other (frequently less accurate) methods for locating the contours on the plan.
  - For example, the ridge a b c d of a mountain range appearing as a fi y â on a photograph, fig. 73, may be divided by the contour planes by assuming it to be contained in a vertical plane.
  - Fig.74
  - On the plan, fig. 73, we produce the projection ad of the ridge to the intersection F with the picture trace X\Y\ and draw through the projection Si of the station SiG parallel to ad.
  - The photograph having been pinned to the photograph board, take from the principal point P on the horizon line PF = piC and PG =pxF. At G place the scale of équidistances perpendic-ular to the horizon line, the division at G corresponding to the height of the station, and join the marks of the scale to the vanishing point F.
  - Having now the successive points of intersection of the ridge by the successive contour planes, their distances from the principal line SS'—their abscissæ—are marked upon the edge of a strip of paper in the usual manner. The intersection of the radiais from Si through the points marked on the paper strip with the projection a . . d of the ridge a . . y will give the intersections
  - of the contour lines.
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  - Should the mountain bave rounded forms and no well-defined ridge, the visible outline on tbe photograph may be assumed to be contained in a vertical plane perpendicular to the line of direction drawn to the middle of the ridge outline.
  - The construction, fig. 74, is made by drawing the line of direction SM to the middle of the ridge outline and S V perpendicular to SM. On the plan px Jfi is made = PM, and from the projection a of the summit a of the mountain a perpendicular ac to Sx Mx is drawn, which will represent the horizontal projection (ac) of the pictured outline (ay) ; it is produced to the intersection X with the picture trace Xx Yx. PQ is taken (on the photograph) equal topiX (on the plan), and the scale of équidistances is placed at Q perpendicular to the horizon line PD'. The division mark at Q corresponds with the élévation of the station S, and the points of division corresponding with the contours are joined to V and produced to their intersections with the outline a . . y. The platting is done as in the preceding case, or the lines of direction drawn to the points of intersection of the outline ay by the contour planes may simply be platted and the contour lines on the plan may be drawn tangent to these lines of direction.
  - The horizon line, containing the perspectives of ail points having the same élévation as the
  - station, represents the perspec-Fig. 75 tive of a contour line when
  - the caméra horizon is identical with a contour plane. The iconometric draftsman should pay particular attention to géologie forms and to the origin of topographie features, as with-out such applied knowledge a correct interprétation of such forms and their cartographie représentation would require the cartographie location of a vast number of control points to obtain a faithful représentation of the terrene forms. Although the latter may often resuit from the successive or combined actions of manyagen-cies, they will yet hâve similar récurrent characteristic shapes when produced by the same causes, and the contours, being the means for delineating the cartographie représentation of the terrene shaped by identical agencies, should also show a corresponding characteristic similarity.
  - (m) The photograph protractor.—The angle included between the line of direction (to a point of a photograph) and the horizon, or the principal plane—the vertical or altitude and the horizontal or azimuth angle—is sometimes wanted.
  - The horizontal angle may be obtained directly on the photograph board by joining the station S, fig. 75, and the projection a (on the horizon line) of the pictured point a. If required in arc measure, the distance Pa may be transferred to the principal line SS' from P = PG; D is joined to G and produced to the scale of degrees and minutes BG, where the graduation mark Je indi-cates the value of the horizontal angle in arc measure.
  - Whenmany such angles are tobemeasured, thehorizontal scales TY and OZ, fig. 75, may be divided into degrees and minutes by means of a table of tangents, using as radius the focal lengtli SP.
  - The altitude is the vertical angle at S of the right-angle triangle, having for sides Sa and aa. To construct it, take DF = Sa, draw FF parallel witli and equal to aa, join’D and F, and produce DF to the scale B G of degrees and minutes.
  - This construction wrill be facilitated by the lines already drawn on the photograph board, fig. 70. With a pair of dividers take the distance (abscissa) from the pictured point a to the
  - oc
  - El
  - r-O-
  - a. p
  - S‘
  - D'
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  - principal line 88', fig. 75, and carry it from P, fig. 70, in the direction PP', and from the point so obtained take the distance to the arc ML, fig. 70, measuring in the direction of the radiais marked on the board, which will represent the distance PP, fig. 75. Then, with the dividers, carry aa to PP, fig. 75, which is that one of the parallel lines MN~ of fig. 70 that corresponds to the point P. The construction may now be completed in the manner already explained.
  - A protractor may be constructed to measure these angles directly by drawing lines on a transparent plate parallel with the principal line—they çontain points having identical azimuths— and curves containing points of identical altitudes.
  - The azimuthal lines may be found by platting the horizontal angles in 8, fig. 70, and drawing lines parallel to the principal line 88' through the points of intersection of the radiais with the horizon line PP'.
  - If we regard the horizon and principal lines as axes of coordinates and dénoté the altitude aa of a point a pictured as a, fig. 75, by h, the équation of the curve of altitude h may be written—
  - y2 = (æ2 + f2) tan2 h.
  - H
  - O- —
  - < P tC
  - -O
  - dl
  - •et
  - o-
  - H
  - Fig.76
  - This also is the équation of an hyperbola of which the principal and horizon lines are the transverse and conjugate axes, and of which the principal point is the center.
  - One of the hyperbola’s branches represents the points above thé horizon, and the other branch the points of equal altitude below the horizon. The asymptotes are lines intersecting each other at the principal point, and including angles with the horizon line equal to h. This hyperbola represents the trace on the picture plane of the cône of visual ray s which include the angle h with the horizon plane.
  - These hyperbolic curves of equal altitude may be obtained by computation, using the preceding formula and substituting different values for h, or they may be obtained graphically by platting a sériés of points for each curve by reversing the construction given above for finding the altitude of the pictured point a, fig. 75. The angular distance between the lines representing points of equal azimuths (or those of equal altitudes) will dépend upon the degree of précision required.
  - The complété protractor is shown in fig. 76. It may be made in the same manner as mentioned for the perspectometer by drawing it on paper on a large scale, reducing it by photography, and making a transparency by bleaching in bichloride of mercury.
  - (4) Method of V. Legros for determining the position of the horizon line.—Commandant V. Legros recommends the use of these hyperbolas for locating the horizon line of a vertically exposed photographie plate :
  - When a caméra with the photographie plate adjusted in vertical plane is rotated horizontally in azimuth, the plate remaining vertical, any point a, fig. 76, will describe a hyperbola aa' on the ground glass plate. The nearer the observed point a approaches the horizon lme the smaller the curvature of its hyperbolic trace on the ground glass will become, and a point a0 which traverses the ground glass plate in a straight line HH' will hâve the same élévation as the second nodal point of the caméra lens. Its angle of élévation will be ± 0 or HH' will be the horizon line of the plate. To locate the horizon line experimentally in this way the ground glass plate is best provided with a sériés of équidistant horizontal and vertical lines, after the manner of Dr. Le Bon’s ground glass plates.
  - (5) Method of Prof. 8. Fimterwaider for locating contours on the plan.—Prof. S. Finsterwalder’s method for the iconometric location of horizontal contours is based upon the following considération :
  - The pictured outline of a terrene form is regarded as the trace of the terrene surface in a plane vertical to the platting or ground plane and containing the pictured outline. This method is well adapted for the development of the terrene forms of a modérately rolling country.
  - The caméra stations are speeially seiected with reference to the use of this method, with a
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  - view toward obtaining pictures with a sufficient number of such outlines of tbe terrene forms to enable tbe iconometric draftsman to give a good définition of the relief of tbe région to be platted.
  - Tbe pictured outlines of terrene forms may be regarded as falling within vertical planes, and tbe rays from tbe point of view—second nodal point of caméra lens—to tbe pictured points of such outline will form a cône witb apex in tbe point of view, its base being formed by tbe pictured outline.
  - Any horizontal plane containing a contour A will intersect such a cône of rays in a curve B, the latter toucbing A in one point. This curve B may be platted on tbe working slieet by laying otf, upon a few rays from tbe platted station to points of the pictured outline, the distance :
  - h cot fi
  - and tbe points tbus located on tbe radiais from tbe station point, if connected by a continuons line, will represent tbe curve B platted in horizontal plan.
  - h=différence in élévation between tbe station (wbence the picture was taken) and tbe horizontal contour A.
  - fi=vertical angle to eacb point of the outline bisected by tbe vertical plane passing tbrough its radial or visu al ray.
  - The direction of tbe pictured outline is now platted on tbe plan, and wbere it bisects the curve B will be a point of tbe contour A. As we naturally would draw not only one curve B, but ratber a sériés of them eorresponding to several horizontal planes, passing througb a sériés of contours A of various elevatious, the construction may be simplified, inasmucb as the curves B—being lines of intersection of tbe same cône of rays with a sériés of parallel (horizontal contour planes) planes— will ail be similar in sbape, tbeir eorresponding points (points on tbe same radiais) having the same relative positions witb reference to tbe platted station, the value li cot fi need only be determined for one point of tbe otber curves B if one curve B bad been drawn, tbe otbers being parallel witb tbe first.
  - I
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- - CHAPTER IY.
  - PHOTOGRAMMETERS.
  - The praetical value of a photogrammeter (photographie surveying instrument) dépends greatly upon the quality and general uniformity of its lens or lenses, upon the rigidity of the eomponent parts of the apparatus, its easy transportability, and on the rapidity with which it may be put into adjustment.
  - A good phototopographic lens should be free from spherical aberration (or diffusion of the light rays) ; it should possess no chromatic aberration, nor should the image show distortion of any kind, and the field of view (the range of lens) should be large, rapidity of the lens being désirable, but less important than the other requirements just mentioned.
  - The principal lenses in use for phototopographic purposes are : Dallmeyer’s rapid rectilinear, SteinheiVs aplanat, Bush1 s pantoscopic, Gorz’s double anastigmat, and, more reeently, Zeissh anas-tigmat lens.
  - The nodal points, the focal length, arc of visibility, and the arc which is perfectly free from distortion of every kind should be known for every lens used for phototopographic purposes, and the manufacturers of ail good lenses are best fltted to détermine those values with great précision for every lens.
  - I. REQUIREMENTS TO BE FULFILLED BY A TOPOGRAPHIC SURVEYING CAMERA.
  - A good surveying caméra or photogrammeter for topographie work should produce négatives which are geometrically true perspectives the éléments of which should be known, and the follow-ing desiderata should be fulfilled :
  - First. The plates to be exposed should be adjustable into vertical plane.
  - Second. The distance between image point and sensitive plate should be maintained unchanged for ail plates.
  - Third. This distance—the constant focal length—should be known or will hâve to be determined for every instrument.
  - Fourth. Means should be provided to trace or locate the horizon line upon every négative or print.
  - Fifth. Means should be provided for locating the principal point upon every négative.
  - Sixth. A ready orientation of the photographs (the picture traces) for iconometric platting should be provided for; and we may add as
  - Seventh. Enough characteristic stations (besides the triangulation points needed for the instrumental control) are to be occupied with the surveying caméra to give a full development of the terrene, which is to be mapped.
  - Until reeently photographie surveying instruments were not procurable in open market. Nearly every observer who made praetical application of the photographie methods for topographie surveys had an apparatus constructed for his particular need and according to his individual îdeas.
  - In the following we will describe such photogrammeters as may be regarded as spécial types, constructed to fulfill different requirements.
  - II. ORD1NARY CAMERAS ADAPTED FOR SURVEYING PURPOSES.
  - These caméras are generally supported by three leveling screws, and they are provided with a cireular level, or with two cross levels, for adjusting the sensitive plate into vertical plane. The distance between lens and sensitive plate (focal distance) may be made invariable by means of
  - 699
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  - two rods Sp, fig. 77 ( WernerJs apparatus, made by E. Lechner, of Vienna, in Austria), or by means of two arms H and clamp screw M, after tbe bellows bad been extended by aid of the pinion K and rack movement to that point indicated by the vernier n, fi g. 78, as the proper focal length for
  - R.LECHNER
  - infinité distance. The arrangement shown in fig. 78, represents the apparatus of Dr. Vogel and Professor Doergens, made by Stegemann, of Berlin, in Prussia.
  - Dr. G. Le Bon also used a similarly modified caméra for his archæological researches in India (undertaken under the auspices of the French ministry of culture).
  - Short brass points M, fig. 79, serve to locate the horizon and principal lines on the négatives by
  - protecting the sensitive plates against the action of those light rays which they intercept. In some instances those points M may be brought into direct contact with the sensitive film surface of the plate by turning a button,
  - F.g. 79
  - Fig. 80
  - Fig.81
  - thus produeing a sharp, well-defined image of the outlines of the teeth on the négative.
  - The use of such modified caméras should not be extended beyond preliminary work; for extensive use tbe results will not be sufficiently uniform and accurate.
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- - U. S. Coast and Geodetic Survey Report for 1897. Appendix No. 10.
  - No. 82.
  - CAN ADI AN (E. DEVILLE’S) SURVEYING CAMERA.
  - ?
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  - CAN ADI AN (E. DEVILLE’S) SURVEYING CAMERA—VERTICAL POSITION.
  - f
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  - III. SPECIAL SURVEYING CAMERAS WITH CONSTANT FOCAL LENGTHS.
  - (.1) Dr. A. MeydenbauPs surveying caméra.—Among the numerous patterns of this class of instruments Dr. Meydenbaur’s is probably the earliest form. Fig. 80 shows Meydenbaur’s new, small-sized magazine caméra. The plates are successively pressed against a métal frame secured at a constant distance from the lens. After an exposure the plate is dropped into a leather sack b, fig. 81, attaehed to the caméra. The dimensions of the caméra box are 9 by 12 centimètres, it weighs 750 grammes, and it is mounted on a rod which is joined at its lower end to three short legs in sueh a way that the four pièces may be folded together to form a stout cane 0*85 métré long. The lower ends of the three legs of this tripod, and the upper end of the supporting rod are con-neeted by twisted violin strings to which tension may be given by turning the ratchet wheels indicated in fig. 81\ The leather pouch, together with twelve plates, weigh about 500 grammes.
  - The sensitive plate may be adjusted into vertical plane by meansof a bail and socket connec-
  - Fig.85
  - tion between the caméra and upper end of the tripod rod, together with the circular level F, shown on the upper face of the caméra box in fig. 81.
  - (2) F. Deville1 s new surveying caméra.—The following description of the new Canadian surveying caméra is taken from Deville1 s Photographie Surveying, Ottawa, 1895. This caméra is shown in figs. 82 and 83. Figs. 84 and 85 represent sections of the instrument.
  - The caméra proper is a rectangular métal box AB (figs. 84 and 85) open at one end. It carries the lens L and two sets of cross-levels (7(7, which may be observed through openings in the outer mahogany box. The métal box is supported by wooden blocks and a frame FF, held in position by two bolts DD.
  - The plate holder is made for single plates; it is inserted into the carrier FF, which may be moved forward and backward by turning the screw G.
  - A folding sliade HH, hooked to the front of the caméra, and diaphragms KK, inside of the métal box, intercept ail light that does not contribute to the formation of the image on the photo graphie plate.
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  - The caméra rests on a métal triangular base, fi g. 86, with three-foot screws, exactly like the base of the transit which is nsed in conjunction with Deville’s caméra, so that either caméra or transit may be placed on the same tripod at any time. The caméra may be set np with the longer side either horizontal or vertical, figs. 82 and 83. Both transit and tripod are carried by the surveyor, while one caméra with one dozen plates (in the single plate holders), without a tripod, are taken by one of .the men who always accompany the surveyor. The assistant surveyor has a second caméra, with 12 plates and a separate tripod.
  - The legs of these tripods, when folded together, are 20 inches long and are placed nnder
  - the box of the transit, in a separate sole-leather case, to be carried on the back of the surveyor. The tripod of the assistant surveyor’s caméra is similarly attached to the sole-leather case of his caméra.
  - The lens of this caméra is a Zeiss anastigmat, No. 3 of sériés Y, focal length = 141 millimétrés with a deep-orange color screen in front.
  - Having set the caméra up on the tripod, the plate-holder carrier E is moved back as far as it will go by turning the screw G. the plate holder is inserted throngh the opening ME, the slide is with-drawn, and the carrier is moved forward by revolving the screw G, nntil the plate is in contact with the back of the métal box AB. In order to secure a perfect contact, the carrier has a certain amonnt of free motion. The caméra shonld now be turned in the proper direction ; the field embraced by the plate is indicated by lines drawn on the outside of the mahogany box. The caméra is now carefully leveled, the exposure made, and the plate holder withdrawn (after the slide had been inserted) by repeating the same operations, however, in the inverse order.
  - The levels CC are rigidly attached to the métal caméra box without any means of adjustment. They are, however, very nearly adjnsted by the maker. For this purpose he takes the métal box out of the mahogany casing and places it on a piece of plate glass which had been leveled like an artificial horizon. By filing dowu one end or the other of the level’s outer case he brings each bubble very nearly into the middle of its tube. These tubes hâve continuons numbers on the graduation marks, as illustrated in fig. 87.
  - Accompanying each caméra is a piece of plate glass, ^ inch thick and 11 inches long, which can be inserted into the carrier in place of the plate holder. That end of the plate glass which projects outside of the caméra when it is thus inserted is coated on the back with a varnish of gum guaia*
  - cum (dissolved in alcohol) to which some lampblack has been added. This coating has very nearly the same re-fraetive index as glass, preeluding ail reflections from the back of the plate glass.
  - When the caméra is received from the maker tlie exact readings of the levels, GG, when the back of the métal box (against which the photographie plate is pressed) is vertical, should be aseertained. To do this the bolts P, fig. 85, next to the opening M, are unscrewed and removed. Q may The piece of coated plate glass is now inserted into the carrier E, figs. 84 and 85, and pressed into contact with the métal box by revolving the screw G. The caméra is placed on its tripod and leveled. Immediately in front and at the same height as the caméra a transit (or a leveling instrument) P,-fig. 88, is set up, and, after carefully adjusting it, a distant but well-defined point P is selected on the same level with the transit and caméra. The intersection of the threads of the telescope is brought to coincide with P, and the telescope is clamped in this position to the vertical circle. Turning it in azimuth the image of P, reflected by the plate glass, should appear at the intersection of the telescope’s threads. If it does, the face of the plate glass is vertical and the position of the bubble in the tube of the level, directed
  - then slide backwards and be taken out.
  - FiG. 86
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  - 703
  - at right angles to the plate glass, is the correct one for adjusting the instrument in the future. If it does not, the caméra must be tilted forward or backward by means of the foot screws until coincidence is established. The bubble of the level may or may not now be iu the middle of the tube, but its position, whatever it is, will be the correct one for the future when adjusting the caméra at any station. This level reading should therefore be recorded, and whenever the caméra is to be leveled in its subséquent use it must be remembered that the bubble is to be given the same position.
  - This level reading détermination is to be made for the two positions of the caméra in which it is used, figs. 82 and 83, horizontal and vertical.
  - The next step is to locate the position of the principal point on the vertical photographie plate, and to détermine the length ofthe distance line or the constant focal length.
  - Select a station so that a number of distant and well-defined points may be found on the horizon line, as laid down by the maker of the caméra. The view selected may be the distant shore of a lake, a large building, or a row of buildings. Set up the tripod and adjust the transit. Find two points JE and F, fig. 89, on the horizon line ( with a zénith distance of 90°) that both corne within the field of the caméra, when set horizontal, both points being near the edges of the plate. Measure the angle go between them.
  - Find two other points G and H, also on the horizon line, and such a distance apart that they both corne within the field of the caméra when the same is vertical, fig. 83. Now replace the
  - transit by the caméra in the horizontal position, fig. 82, turn it in azimuth to take in F and F, level carefully and exposé a plate.
  - Set the caméra in the vertical position, fig. 83, turn it so that it takes in the observed points
  - Fig.Ô9
  - G and H, level carefully and expose another plate. The first plate, after development, will show the two points F and f’ona line very nearly parallel to the edges AB and CD, fig. 89, of the métal box. The principal point, of course, will be on this line. Out this line into the film with a fine needle point and straightedge.
  - The second plate, exposed in the vertical position, after development gives another horizon line GH, fig. 89, which may be transferred to the first plate by means of the distances AK, and CL to the corners of the métal box. This (principal) line is likewise eut through the film with a fine needle point and straightedge, the principal point P is at the intersection of both fines EF and GH.
  - The length of the distance line, SP = f, fig. 90, may be computed from the observed horizontal angle go, included between SE and SF, and from the distances EP = a and PF = b, measured on the négative.
  - Let S, fig. 90, be the second nodal point of the caméra lens, a and (J the angles ESP and PSF.
  - (X —(- /J = GO.
  - The lengths of a and b are known and if we designate the focal length SP by /, we will hâve :
  - tan a = tan f3 = tan a X tau jd =
  - a
  - f
  - b
  - f
  - a.b P
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  - Henee :
  - a b
  - tan {a + /S) = tan g? = ^ f
  - tan g?
  - aV
  - P
  - ab = O
  - or:
  - after resol ving this quadratic équation we find :
  - y" ____ Cl -j— b
  - 2 tan go
  - 4- I (a + A)2 , + \ 4 tan2 g? +
  - Having found thé focal length and the principal point, reference marks are to be made on the edges of the métal box to indicate the horizon line, the principal line, and the focal length on the négatives, or on the enlargements made from the latter.
  - Measure the distance m, fig. 89, from P to AC. From the corresponding corners A and G, fig. 91, of the métal box, lay off m on AB and CT. With a very fine and sharp file held in the direction of the lens,cut into the edge of the métal a clean and sharp notch at P and another at B.
  - Repeat the same operation at the corners A and P, fig. 91, with the distance n from P to AB, fig. 89.
  - The lines OQ and BT will be the horizon and principal lines of the négatives when the caméra is leveled to bring the bubble into its proper position, as has been mentioned in the foregoing.
  - From P and T, fig. 91, lay olf the distances Br, Br', Tt, Tt‘ = / = one-half of the constant
  - 2i
  - focal length.
  - From O and Q measure Oo, Oo1, Qq, Qq' = = one-fourth of the focal length, and at each one
  - of these points make a notch with the file held in the direction of the lens.
  - Every photograph will now show twelve triangular projections into the dark border of the
  - —o—.
  - - -------
  - _ -o- '
  - Fi G'. 91
  - B
  - Q
  - D
  - photograph. Four of these projections serve to fix the horizon and principal lines; the remaining eight give the focal length value.
  - It now remains necessary to find the correct readings of the transverse levels (those placed parallel with the sensitive plate), when the horizon and principal lines pass exactly through their notches of the métal box.
  - Again set up the caméra facing the same distant view as before, but in adjusting it bring the bubble of the transverse level near one end of the tube, note the level reading and expose a plate. After development it will give an horizon line BF, fig. 92, cutting the border of the négative in A and B at some distance from the pictured notches O and Q. îsTow change* the adjustment of the caméra by bringing the bubble of the transverse level to the other end of the tube, note the level reading and expose another plate. This will give another horizon line F' Fcutting the border of the négative in G and B.
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  - Great care should be exercised in both cases to maintain the other level (tbe one at right angles to the sensitive plate) at its proper reading in order to expose both plates in vertical plan.
  - After measuring CO and OA or BQ and QD, a simple proportion will give the proper reading of the transverse level, which will bring the horizon line of the vertically exposed plate throngh the two notches O and Q of the métal box.
  - The correct reading of the other transverse level is found by the same method, with the caméra in the vertical position, fig. 83.
  - Ail these operations must be executed with great care and précision, and with the help of a microscope of moderate power, as the subséquent iconometric platting of pictured points is based upon the détermination of the ordiuates and abscissæ of sueh points on the photographs, with reference to the principal and horizon lines, as a System of rectangular coordinates.
  - It had been assumed that the levels were placed very nearly in correct adjustment by the maker, as previously mentioned. If found too much out, they should of course be first approxi-mately adjusted by setting the métal box on a leveled plate. For this purpose the plate glass sent out with every instrument is set on the caméra base and leveled like an artificial horizon.
  - (3) Use of the instruments eomprised in the Canadian p ho to top ograp hic outfit. —The instruments and tripod being made as light as possible, steadiness is secured by a net suspended between the tripod legs in which a heavy stone is placed. With this device better photographs and more précisé observations are obtained, and there is no risk of the instruments (resting upon the tripod) being blown over during one of the sudden and strong gusts of wind so fr'equently encountered on elevated peaks in the mountains.
  - After having arrived at a triangulation station, the surveyor adjusts the transit and observes the azimuth and zénith distances of ail signais marking the triangulation and caméra stations that may be visible from his position. If accompanied by his assistant, each reads one vernier and both enter the readings in record books. After completion of the observations they compare notes. Any discrepancy that may be discovered in the recorded data is corrected on the spot.
  - The caméra is carried in a sole-leatker case containing also twelve fllled plate holders. When more plates are needed they (with the necessary holders) must be carried in a separate réceptacle. Taking the caméra out of the case, the leveling base, lig. 86, is screwed to it, and the caméra is then placed upon the tripod, from which the transit had been removed, without disturbing the position of the tripod 5 the shade or hood is now unfolded and attached to the hooks at the front of the caméra, fig. 82. A plate holder is inserted into the carrier, and its number is recorded upon a rough outline sketch of the view commanded by the field of the caméra image, entering also such notes as may be of value for the development of the plate and for the iconometric platting of the topography recorded upon it (by the action of the light). Having made sure that the cap is on the lens, the slide is withdrawn from the plate holder and the plate is brought into contact with the frame of the métal box by turning the screw G, figs. 84 and 85, devised for this purpose. The surveyor now turns the caméra in azimuth until the lines on the upper face of the wooden casing show that it is properly directed or oriented to include the panorama section to be photographed between the lines, the field of view coinciding with the outline sketch bearing the number of the plate holder in the caméra. Sighting along the converging lines, shown on the side face of the wooden caméra casing, he can assure himself whether the view on the image plate reaches high or low enough. If it does not, he will put the longer dimension of the caméra upright, unless the caméra was already in that position. He levels carefully, in the manner previously described, and exposes the plate. Whenever the sun shines inside of the front hood it should be shaded off during the exposure of the plate by holding something above the hood. Under no circumstances should the snn be permitted to shine upon the lens.
  - Every evening, after returning to the survey camp, the surveyor replaces the exposed plates in his dark tent by new ones, using a ruby-colored light. He also marks the exposed plates in one corner, before removal from the holder, with his initiais, the number of the dozen and of the plate (the same number as given to the corresponding outline sketch), using a soft lead pencil for this purpose; e. g., IV, 5, means plate No. 5 of the fourth dozen, or the forty-first plate. The exposed plates are now placed into a double tin box, fig. 93, which can be closed hermetically, and which will float when filled with two dozen plates, should the same be accidentally thrown into 6584---------------45
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  - water. These boxes are shipped to the head office in Ottawa, wliere tbe plates are developed by a specialist.
  - The data obtained with the aid of the transit for triangulation purposes are recorded in the field book in the usual manner, as customary for such work.
  - The horizontal angles observed with the transit (or altazimuth instrument) to the points of the terrene marked on the outline sketch which accompanies each négative, serve not only for the orientation of the horizontal projection of the plate on the plan (the so-called “picture trace”), but they also serve to counteract in a measure and to ascertain the distortion of the paper prints (or photographie enlargeinents). The vertical angles, together with the platted distances, are used to check and verify the position of the horizon line on the different photographs.
  - The most important caméra stations are occupied by the surveyor ; the secondary stations by
  - the assistant surveyor, with his own caméra. ISTo trigonométrie observations are made by the assistant while occupy-ing the secondary stations.
  - Ail views are taken with the same stop : //36.
  - (4) The United States Goast and Geodetie Survey caméra.— The original type of the Coast and Geodetie Survey caméra, used in connection with the Alaskan boundary survey, was similar in form to Deville’s original caméra, except that it had a spécial tripod with bail and socket adjustment and that the teeth which serve to mark the principal and horizon lines on the négative could be turned by revolving one button to be pressed into contact with the photographie plate.
  - This caméra was also provided with a ground glass, enabling the surveyor to inspect the entire field controlled by each plate before exposure, and giving ready means for test-iug the positions of the teeth which mark the horizon line.
  - The caméra itself was a plain rectangular box made of well-seasoned mahogany 6f by 5| by 9^ inches in size, and it was used always in the same position, with the short faces vertical. The bamboo tripod legs were composed of three pièces, each 16 inches long, and screwed together at the joints. When dismembered the tripod was carried in a sole-leather packing case together with the caméra, twelve plates (in six double plate holders), notebook, barometer, ther-mometer, yellow color screen, etc.
  - The new phototopographic caméra of the Ooast and Geodetie Survey is a phototheodolite, resembling Colonel Laussedat’s latest pattern which will be described in the following pages.
  - IV. SURVEYING CAMERAS COMBINED WITH GEODETIC INSTRUMENTS.
  - (Phototheodolites, photographie plane tables, etc.)
  - The data acquired in the field with photogrammeters of the class just described had to be supplemented with observations made in the field with some geodetie instrument (transit, plane table, etc.) in order to obtain complété topographie survey s of the régions traversed by the phototopographic surveying party.
  - The idea of combining surveying instruments with a photographie caméra into single compact and serviceable instruments originated very early with phototopographic workers, and refined phototheodolites and photographie plane tables are to this day the favorite phototopographic instruments in Europe, whence they are also exported to other countries.
  - These more or less complicated instruments bave been devised to secure great précision in the work undertaken with them, and refined methods are employed for the field observations, for the culling of data from the photographie perspectives, and for the computations made in the office to increase the general précision of data derived from the operations executed in the field.
  - Generally speaking, the best results for topographie purposes are obtained by means of photography, if we bear in mind that phototopography essentially and primarily is a constructive and graphie art, based upon graphie or pictoiial records (which are nothing more t-han central
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  - projections in vertical plan of objects and their dimensions, that are to be transposed graphically into orthogonal projections into horizontal plan). Instrumental observations being required only to furnish such éléments as may be needed to make the graphie transpositions (iconometric platting in a reduced scale) of the lines of directions and distances, and also to obtain checks or a proper control for the work in its entirety.
  - Photographie surveys hâve been conducted principally in régions where otber surveying
  - g. 9 4-
  - methods are either preclùded or where their application would entail great cost and consume too much time, and such régions are characterized chiefly by a rugged and broken topography.
  - The necessity, therefore, lies close at hand to devise instruments that will not readily get out of adjustment or drop to pièces when transported over rugged mountain traits, and the more simplified their structural composition the more available will they become for the production of rapid and accurate work.
  - It is at once évident that the combination of a caméra and a surveying instrument into a well-united, well-balanced, easily manipulated, and essentially light and withal rigid instrument is not easily accomplished. It is not surprising therefore, when searching the published descriptions of
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  - photo théodolites and other photogrammeters, to corne upon a great number of types in which the many difficultés hâve been overcome, more or less successfully, by various devices.
  - We may flnd: A large-sized théodolite with a small caméra, placed centrally between the Y supports, after removal of the telescope from the latter, both being interchangeable;
  - A large caméra mounted upon the horizontal circle with a telescope and vertical circle attached eccentrically (at either side of the caméra);
  - A large centrically located caméra, the lens of which serves at the same time as objective of
  - the telescope, the correspond-ing eyepiece being at the een-ter of the frame that ordinarily supports the ground glass plate (in this form the caméra itself is the telescope) ;
  - Instruments where the board of the plane table has been replaced by a surveying caméra, the upper face of which receives and supports the plane-table sheet and plane-table alidade; also various other combinations (some with compass attachments).
  - This class of instruments has been in use for large scale surveys and where the instrumental outfit could readily be brought very near the stations to be occupied by convenient means of transportation, the instruments rarely being sub-jected to such primitive and rough methods of transportation over long distantes, as it generally has been the case on our continent when surveying caméras hâve been used.
  - (1) The new Italian photo-theodolite, devised by L. P. Paganini. — Paganini’s model of 1884 has been described in Appendix No. 3, United States Ooast and Geodetic Siîrvey Report for 1893.
  - The following description of Paganini’s new phofcotheod-olite, model of 1890, has been extracted from L. P. Paganini’s “Nuovi appunti di fototopograûa,” Roma, 1894:
  - The general form and the dimensions of the caméra box of Paganini’s new phototheodolite remâin about the same as with the older model, the principal change resting in the omission of the eccentric telescope which has been replaced by the centrally mounted caméra, which may, at will of the observer, be converted into a telescope. ,
  - The télescopes which we generally flnd attached to surveying instruments consist of a tube, slightly conical in shape, having a positive lens or a System of convergent lenses at one end (the “objective”) which produce within the telescope a real and inverted image—the same as the caméra lens—of any object toward which the lens may be directed. The other, smaller end of
  - s \ y
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  - the telescope tube, has a still smaller tube inserted into it whicb may be jnoved in tbe direction of tbe axis of tbe tube. Tbis second tube also contains a System of convergent lenses—so-called “ocular lens” or “eyepiece” of tbe telescope—whicb serve to project an enlargement of tbe image in tbe telescope upon tbe retina of tbe observeras eye. In tbe image plane of the objective (witbin tbe telescope), is tbe so-called diaphragm—a ring-shaped métal disk—to one side of which a pair of cross bairs—spider webs, cocoon tbreads, or lines eut into a tbin piece of plate glass—is attached in sucb a way tbat tbe bairs fall witbin tbe image plane. One bair is vertical and tbe other horizontal, tbeir point of intersection coineid-ing witb tbe optical axis of tbe telescope.
  - The oldcaméra was provided witb tbe objective, and a corresponding eyepiece bad only to be added to convert tbe caméra into a surveying telescope.
  - In the instrument under considération tbe eyepiece consists of a positive lens set, known in optics as “ Ramsden’s ocular lens.” Tbe inner wall surfaces of the caméra box sbould be well blackened to avoid any side reflection and a conséquent dimness in tbe appearance of tbe cross wires.
  - Tbe caméra proper consists of two parts, a trun-cated x>yramid A, figs. 94 to 98, and a cylindripal attachaient JB, into wbicb tbe tube t is inserted.
  - A second tube witbin tbe cylinder t may be moved in the direction of the optical axis by means of a screw, tbe threads of wbicb bave a rise of one millimétré. By revolving tbe inner tube tbe lens is brought nearer to or farther from tbe image plane, tbe lens remaining parallel witb tbe image plane at any position that may tbus be given to the lens.
  - A scale a, ligs. 94 and 98, graduated to millimétrés, is permanently attached to tbe tube t and itlies very close to the ring n, tbe circumference of wbich is divided into ten equal parts. (Tbis graduated ring n is soldered upon tbe cylinder u containingtbe caméra lens.) This scale a (extending in a direction parallel to the optical axis of the lens) bas a mark, coinciding witb tbe index rim of tbe ring n, tbus indicating tbe focal length of tbe caméra lens wlien focused upon objects at infinité distance. The millimétré graduation of the scale a, extending from tbe zéro mark in tbe direction toward tbe ground glass serves to ascertain tbe focal lengtbs for objects nearer tbe caméra station. Tbe circumferential graduation on the ring n serves to read one-tenth of one révolution of the tube u, whicb is equal to an axial motion of tbe lens of 0*1 millimétré, bence the focal length for any object focused upon may be read to single millimétrés on the scale a and to tentbs of a millimétré on tbe graduated ring n.
  - The construction of this phototheodolite is sucb that the optical axis of the caméra lens is always at rigbt angles to the picture plane—the ground-glass surface or the sensitive film of tbe photographie plate. The intersection of the optical axis and the picture plane, the principal point, is marked by the intersection P, fig. 97, of the two very fine platinum wires O O' and ff, one horizontal and the other vertical when tbe instrument is in adjustment. These wires are stretebed across the back of tbe caméra box as close as possible to tbe picture plane. The buttons b, figs. 94 and 95, serve to give tension to the wires. The wire O O' corresponds to tbe horizon line and the vertical wire ff corresponds to tbe principal line of tbe perspective repre-sented by the image on the ground-glass plate.
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  - Fig. 96 shows the»rear view of this instrument, the ground glass having been replaced by an opaque plate, strengthened by a métal frame and ribs, winch supports the Eamsden eyepiece in the center, its optical axis coinciding with that of the caméra lens. The cross wires O O', //', at the rear of the caméra, serve also for the astronomical telescope into which the caméra may be converted by attaching the opaque plate with central eyepiece as shown in fig. 96. 'The fitting of this eyepiece allows for axial motion to adjust its position to avoid parallax.
  - The rear opaque plate and the other sides of the caméra box
  - Fig.97
  - to hold the horizontal axis of rotation of the caméra in a flxed position, avoiding accidentai changes during the execution of a set of panorama pictures.
  - After unscrewing the nuts d', fig. 98, the tripod legs may be removed. They serve as “alpenstocks” when the instrument is being transported from station to station. The camera-telescope is lifted outof the wyes and packed in a separate case ; the lower part of the instrument is packed in another case, and the plate holders and plates are transported in a third case.
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  - (2) Photogrammetric théodolite of Prof. 8. Finsterwaider.—This phototheodolite (manufac-tured by Max Ott (A. Ott), of Kempten, in Bavaria) was devised by Dr. Finsterwalder after many years of practical work and expérience incidental to his Alpine surveys and studies of glacial motion. Tbis expérience taught bim tbe desirability of producing a caméra compactly built, ngidly constrncted in ail îts parts, and yet baving a minimum of weight. To avoid tbe extra weigbt wben transporting a separate théodolite (witb tbe surveying caméra) for tbe trigonométrie location of tbe stations occupied witb the caméra, be provided tbe surveying caméra with tbe means for observing horizontal and vertical angles.
  - Professor Finsterwalder’s phototheodolite is illustrated in fig. 99. The entire outfit weighs 10 kilogrammes, wbicb weigbt is distributed as follows:
  - Kilogrammes.
  - The instrument per se.................. 2-7
  - Carrying case for same................ 2-4
  - The tripod ............................ 1*7
  - One dozen leather plate holders, including
  - the twelve plates.................... 2’5
  - Packing case for the latter............ 0-7
  - Professor Finsterwalder has used a double ana-stigmat of Gorz and later an anastigmat of Zeiss, witb a constant focal lengtb of 150 millimétrés. Witb this fôcus tbe lens will photograpb perspectively correct a plate of 160 by 200 millimétrés. Tbe plates hâve a size of 120 by 160 millimétrés and tbey command an effective horizontal fleld of 53°, enabling the observer to cover tbe complété panorama witb seven plates.
  - For tbe central or normal position of the objective the caméra commands an effective vertical fleld of ± 20°.
  - This range would often be insufficient, particularly wben photographia g mountainous terrene of an alpine cbaracter, therefore it was deemed advisable to mount tbe objective on a slide, wbicb will permit a considérable change in the vertical sense. Owing to this de-vice, objects subtending an angle of dépréssion of 35°, togetber witb otbers subtending an angle of élévation of 5°, may still be photograpbed on tbe same plate, giving a vertical control of 40° in ail.
  - In extreme cases, wben it sbould become désirable to pbotograpb objects subtending angles of + 35° and of —35°, or 70° in ail, Professor Finsterwalder recom-mends tbe exposure of two plates in succession, com-manding the same (identical) horizontal angle, exposing one witb the maximum élévation of tbe objective slide and tbe other witb tbe maximum dépréssion of tbe lens.
  - Tbus, inclined pictures are not only avoided, but tbe effective surface of tbe plate is utilized to the best advantage, and tbe weigbt of glass to be carried is reduced to tbe minimum.
  - In order to obtain uniformly accurate results witb tbe relatively short focal lengtb (maintaining a constant distance between tbe lens and tbe sensitive surface of
  - tbe plates), the plates are not inserted into plate holders (where tbe variable tbickness of tbe glass would affect tbe so-called “constant focal lengtb”), but tbey are pressed directly against a métal frame, wbicb forms tbe back of tbe caméra box, very similar to tbe arrangement described for Cap-tain Deville’s (Canadian) caméra. To do this, use bas been made of Dr. bTeuhauss’s leather plate holders, formed like a sack B, fig. 99. Tbe inner edges of the métal frame are graduated in order to locate the principal and horizon lines upon tbe négatives.
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  - These leather sacks hâve métal slat arrangements, and the transfer of the plate from the sack to the caméra is made by hooking the sack with its mouth to the upper edge of the rear caméra side. While holding the bag in a vertical position the slats are opened and the plate is allowed to slide from the sack mto the carrier to be exposed.
  - Springs are provided at the back of the caméra box to check against a sudden dropping of the plate into the métal carrier, to avoid a breaking or cracking of the plate by striking the closed lower métal slide of the plate carrier too hard. These springs also serve to press the plate, when in position for exposure in the carrier, into perfect contact with the graduated métal frame at the back of the caméra box.
  - By withdrawing the upper curved handle, flg. 99, at the back of the caméra, the tension of the springs may be reduced and the plate glides into position to be exposed. After exposure the lower slide is withdrawn and the plate will slip into the empty sack B, which had been hooked to the lower edge of the caméra back for this purpose, as illustrated in fig. 99.
  - The eccentricity of the center of gravity, by applying the weight of the sack and plate to one side of the caméra, does not affect the adjustments of the instrument sufficiently to throw the photographie plate out of the vertical plane in which the exposure should be made. This caméra théodolite is accurately balanced when no sack is attached, in which form it is used to measure the angles that may be needed to locate the caméra station (geographically, and also in the vertical sense) with reference to surrounding trigonométrie signais.
  - In order to convert this caméra into a théodolite (with centrally located telescope), the back of the caméra is provided with a telescopic eyepiece JE7, of a magnifying power of from 7 to 8. This eyepiece is adjusted to form a surveying telescope with the caméra lens O as objective. It is provided with cross wires or webs, and a shutter affords the means to shut out the light when the instrument is used for photographing.
  - The caméra lens (objective of “caméra telescope”) being movable in the vertical sense within a range of 100 millimétrés, ail objects falling within a range of ± 17° may be bisected with this telescope. The définition of points to be bisected, when above or below the caméra horizon, would be very poor if the eyepiece E were rigidly fixed in the horizontal position, but by means of the métal arms NN the eyepiece may be revolved about a horizontal axis in such a way that it will always be directed to the center of the caméra lens.
  - With the double anastigmat of Gorz, which produces a perfectly fiat picture (with neither spherical, chromatic, nor astigmatic aberration or distortion), a change in the focus of the eyepiece will rarely be required.
  - Horizontal angles may be observed directly by means of a horizontal circle of 120 millimétrés diameter, which is provided with two verniers reading to single minutes. A sériés of experimental tests has proven that horizontal angles observed between points of considérable différence in altitude may be obtained within a limit of error of 0*4'. This instrument, therefore, gives results sufficiently accurate to locate the caméra station trigonometrically with reference to surrounding fixed points of «known positions, if they are not too far distant to be defined with this low-power telescope.
  - Yertical angles, however, can not be obtained directly. Still, by means of a scale and vernier attached to the camera-lens slide (or front board) the change of the caméra lens from its central or normal position (that is, a value directly proportional to the tangent of the vertical angle) may be read to 0*05 millimétré. The slide motion of the front board is accomplished with a rack and pinion, and expérience has proven that the observations may be obtained within a limit of error (converted into arc measure) of 1 minute.
  - The three rods, designated by h in fig. 99, are each 100 millimétrés long. They serve to elevate the instrument support and the three leveling screws 8 sufficiently high above the tripod to allow full play for the leather plate holders B, when they are placed in position to reeeive the exposed plate. The tripod legs may be folded together to one-half their length.
  - No ground-glass plate being provided, a spécial finder has been devised correctly showing the field controlled by the plate for any position of the caméra lens. (See Zeitschrift fur’Instru-mentenkunde, October, 1895.)
  - (3) Photo-theodoUte for précisé worlc, by O. Ney.—This instrument has been patented in the
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  - German Empire, and the following description has been taken from Zeitschrift fiir Instrumenten-kunde, page 55, 1895 :
  - In the construction of this instrument, figs. 100 and 101, it has been sought to satisfy the following requirements:
  - First. The caméra should be sufficiently large to produce clear and well-defined perspectives.
  - Second. The general disposition of weight and mass should be symmetrical (the caméra and the telescope of the théodolite were to be mounted centrally).
  - Third. The weight of the instrument should be reduced to the minimum consistent with rigidity and sufficient strength to assure a free and easy manipulation, as well as durability or permanency of its adjustments when used in tlie field.
  - This instrument is composed of two distinct parts, the caméra proper (with horizontal circle)
  - and a complété transit. They may be used sepa-rately and independently, but always upon the same support and with the same tripod. The interchange
  - between caméra and transit is readily accomplished (both being centered over the same instrument support) with accuracy and expediency.
  - The principal advantages attached to this disposition of the component parts of the photo-theodolite may be cited as foliows :
  - First. The symmetrical and central mounting of the caméra and transit telescope insures accuracy in the results.
  - Second. The weight of each separate instrument—caméra and transit—has been reduced to a minimum.
  - Third. A disturbance of the adjustments of the instrument support (including tripod) may be completely avoided by having the plate inserted and the slide withdrawn before placing the caméra box into position upon the upper alidade limb.
  - The carrying into effect of the ideas just mentioned has been greatly aided by supplying ail
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  - leveling and clamp screws with spherical ends resting upon plates in sueli a manner that a free play of motion will take place. These spherical terminations of the screws were originally devised by Beichel.
  - The two forms in which this instrument may be used are shown in figs. 100 and 101. The former shows the photo-topographie caméra (similar to Professor Finsterwalder’s instrument), and the latter shows the transit with compass B.
  - I) is the very rigid, yet essentially light, instrument support, the three arms being cast into one piece with the bearing for the conical pivot attached to the horizontal limb T.
  - T is the lower graduated limb and A is the upper limb of the alidade bearing the verniers.
  - A large circular level is attached to the center of the upper limb of the alidade. The latter has three hardened plates inserted into its upper surface (at S, figs. 100 and 101), one with a plane surface, the second with a conical cavity, and the third with a v-shaped groove or slot. They form the supports for the spherical terminations of the three screws K, fig. 100, attached to either the transit or the surveying caméra. These screws are received between the flanges C that form a part of the base ring supporting either the caméra or the telescope wyes H, fig. 101.
  - The two sets of three screws K (one for caméra and one set for the transit) serve to adjust the horizon lines of both instruments and to bring them into the same horizontal plane.
  - The transit telescope is arranged for stadia reading (after Porro’s method), with 100 as the constant factor. The telescope level reads to 20", and the final adjustment of the transit is accomplished by means of this level. The striding compass B, fig. 101, is graduated to read to 30', whereas the horizontal circle reads either to 10" or 20", according to the size of the instrument.
  - In order to secure the transit and the caméra to the horizontal circle (which both hâve in common) three horseshoe-shaped clasps (shown near G, figs. 100 and 101) are hinged to the upper limb A of the alidade in such a way that they straddle either set of the three screws K of the projecting flanges C (when they are turned up as shown in the figs. 100 and 101).
  - Each of these clasps has a clamp screw with lever handle B, fig. 101, and by tightening these three clamp screws they are brought to bear upon the hardened heads of the screws K, making a firm connection between the upper limb of the alidade and the superimposed transit or caméra. This connection is easily made, and it does not disturb the adjustments of the instrument.
  - This instrument is made in two sizes; one has plates 13 by 18 centimètres, and the other 18 by 24 centimètres. To avoid changes in the dimensions of the caméra box, due to hygroscopic influences of the atmosphère, the box is'constructed entirely of aluminium. The plate holders and the movable plate carrier, however, are made of mahogany, impregnated with Chemicals to make the wood impervious against moisture.
  - To avoid any possible change in the constant focal length, due to an uneven thickness of photographie plates or of the plate holders, the movable carrier may be moved toward the caméra lens by means of the levers L, fig. 100, until the sensitive surface of the photographie plate is brought into contact with a métal fraine, securely fastened to the sides of the caméra box, and which has a centimètre graduation filed into its inner edges. The distance of the rear surface of the graduated frame from the second nodal point of the caméra lens constitutes the constant focal length of the caméra.
  - The centimètre graduation on the inner edges of the métal frame, reproduced on the margin of the négatives, serves to ascertain whether the sensitive films (or the contact prints) hâve under-gone any change during the processof development and also to ascertain the amount of correction to be applied to the perspective, if found to be distorted, before using it for the iconometric platting.
  - The caméra is provided with a pair of cross levels to enable the observer to detect any change in its adjustments prior to exposing a plate. These levels are graduated to read to 20" of arc. When the instrument is in perfect adjustment, thé picture plane will be in a vertical plane and the principal ray will be in the same horizontal plane as the optical axis of the telescope (when level), if the caméra were replaced by the transit without disturbing the*tripod’s position.
  - When this caméra théodolite is adjusted, the vernier M, fig. 100, will read zéro for the normal position of the lens. Still, the objective may be elevated or depressed by 35 millimétrés, which change from the normal or central position of the lens may be read correctly within 0.1 millimétré
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  - on the scale and vernier M, fig. 100. The pneumatic caméra shutter is arranged both for time and for instantaneous exposures, a spécial device guarding against the possibility of exposing a plate before it is brought into perfect contact with the graduated métal frame, previoasly mentioned.
  - The plate holder can not be withdrawn from the caméra before the slide h as been replaced, nor as long as the plate is in contact with the graduated frame.
  - (4) The phototheodolite of Dr. G. Koppe.—Dr. O.
  - Koppe, professor at the Technical High School in Braunschweig, Germany, is an ardent advocate of pho-togrammetry and he has done much toward populariz-ing photographie surveying in Germany. His work on photogrammetry, published in 1889, is an excellent mannal both in respect to theory and practice. In 1896 he published a treatise on photogrammetry applied to cloud photography for meteorological research.
  - This phototheodolite, fig. 102, has a centrally mounted caméra with the telescope on one side and the vertical circle on the other. The horizontal axis between the two wyes has been widened into a conical ring R, into which the caméra G may be inserted. Four stout springs f press the caméra G tightly against the ring surface forming the base of the conical ring R.
  - After insertion into the ring, the caméra G is revolved witliin the former until the end of the screw 6 abuts against the stop d, when the horizon line of the perspective (négative) should be horizontal.
  - The caméra axis is parallel with the optical axis of the telescope T, both axes being in the same horizontal plane when the vernier of the vertical circle reads zéro. When elevating or depressing the telescope T the caméra axis will follow the
  - same motion, both remaining parallel. The instrument will be in equilibrium with the caméra de- or attached. The horizontal axis of this instrument may be adjusted by means of the striding level A, which, when necessary, may be replaced by a striding compass in a manner similar to that illustrated in fig. 101.
  - Since the telescope may be reversed in the wyes, an error of collimation and any index error of the vertical circle may be found or eliminated.
  - There are neither slides nor plate holders provided with this instrument, the plates being inserted directly into the caméra. This may be done in the field by aid of the packing case specially constructed to serve as a dark chamber, fig. 103.
  - This case is made of wood with double doors, each door having a circular hole A, which is filled in with a flexible, light-tight, and dark-colored material, forming sleeves in such a way that the hands of the operator may be thrust through an elastic opening in the center (of the
  - 1_______________________
  - Fig. I 03
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  - circular openings). The fabric will close tightly around tlie wrists—when the interior of the case will be perfectly dark—and the sleeves A will permit free play to the hands for manipulating the caméra and plates within the space L of the case.
  - This case is inclosed with a tight-fitting sole-leather covering, having two flaps S to protect the openings A against the admission of dnst when the packing case is transported on the baek of the instrument bearer.
  - The entire instrument, except the tripod, may be packed into this case for transportation. It also contains two boxes, Ki and the former receives the exposed plates (négatives) while the lutter contains the supply of unexposed plates.
  - When a plate is to be exchanged the caméra G is placed into the packing case and both doors as well as theleather main flap or cover are securely closed ; both hands are now inserted through A, and after the sleeves are tightly closed about the wrists the caméra is opened, the exposed plate removed and placed into the box Kx (as shown at P, fig. 103). The door T is closed and a new plate, taken from the box K2, is placed into the caméra (as shown by g, fig. 103) and the caméra back is closed, when the caméra will be ready for another exposure.
  - The constant focal length of this caméra is represented by the distance between the second nodal point of the lens and the rear surface of a métal frame (similar to that of Ney’s photo-theodolite) permanently attached to the rear of the caméra box.
  - The inner edges of this métal diaphragm or frame are graduated into centimètres; the middle
  - graduation marks of the horizontal sides of the frame locate the principal line, while the middle graduation marks of the vertical sides represent the termini of the horizontal line on the perspectives. The focal length, once determined, will remain unchanged for a 11 plates.
  - This instrument has been manufactured for Professor Koppe by F. Randhagen, in Hanover, Grermany.
  - The “Topographie Bureau” of the Swiss Republic has used a phototheodolite constructed after the model of Dr. Koppe’s instrument. The expérience in Switzerland, however, seems to hâve decided the topographie bureau not to replace the plane table by the phototheodolite for general topographie surveys executed by that bureau.
  - (5) Phototheodolite devised by V. PollacJc, manufactured by B. Lechner in Vienna, Austria.—With this instrument (fig. 104) the caméra O is centrally located, and it rests ux>on a horizontal circle. The telescope F and the vertical circle are mounted at one side of the caméra, a weight G counterbalancing both on the other side of the caméra.
  - Aluminum has been used very freely in the construction of this phototheodolite in order to reduce the weight as low as possible. This instrument has been manufactured in two sizes; the horizontal circle of the small sized one is graduated to 30', the verniers reading F, while the larger one has a circle graduated to 20', and its verniers read 20//. The telescope F is mounted similarly to that of the so-called Danish plane table alidade.
  - The adjustment of the horizontal axis of révolution of the telescope F is accomplished by means of a spécial level. Clamps and slow motion screws are provided for both the horizontal and vertical circles. The telescope has a focal length of 27 centimètres and an opening of 31 millimétrés, with a magnifying power of 9 to 18 diameters. The telescope is arranged for stadia reading, and it has 100 as the constant multiplier. The telescope level L is graduated to 10" or 20". The vertical circle is graduated to 20' and its two verniers read to 20".
  - The caméra box is made of aluminum and it is provided with a Zeiss anastigmat. By means of the rack and pinion z the lens may be elevated or depressed by either 30 or 50 millimétrés, according to the size of the instrument. The scale t, with vernicr serves to measure the vertical déviation of the lens from its normal position. Also this caméra is provided with a graduated métal frame, the inner edges of which hâve either a centimètre or five-millimétré graduation, winch is reproduced upon the margins of the négatives. They serve not only to locate the horizon
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  - and the principal lines upon the perspectives, but they also give the means to discover any distor-tion that may arise in the pictures due to the wet process of development.
  - This métal graduated frame is brought into contact with the sensitive surface of the film by a simple mechanical contrivance in such a way that the focal leugth for ail négatives is constant, even if the plate holders or glass plates should not be equally thick.
  - (6) Col. A. Laussedafs latest phototheodolite.—This instrument (figs. 105 and 106) has been manufactured by E. Ducretet and L. Lejeune, in Paris, France.
  - Both transit telescope L and caméra G are centrally mounted, the latter above the former. The caméra may also be used alone, independently of the transit, and it may then be mounted upon the tripod (fig. 106) by means of a spécial pivot or spindle 8'. The transit may likewise be used alone, without the caméra, for trigonométrie observations.
  - 8 = leveling screws. cx == central clamp screw. G = caméra, and B = magazine for fifteen plates. O = objective of the caméra; it is a rectilinear wide-angle lens of 75 millimétrés focal length. R = sliding front plate of caméra, provided with pinion and rack movement, P, to elevate or depress the lens. V = finder to show the extent of the field covered by the photographie plate, although a focusing glass, G, fig. 106, is also provided. L = transit telescope provided with stadia wires. Ce = vertical circle, graduated to 30'. M = Wye supports of the telescope axis of révolution, their prolongation forming the caméra support. A = horizontal circle graduated to 30' ; its clamp and slow-motion screw are indicated at P'. N = adjustable level.
  - D = déclination or box compass.
  - Several loaded magazines, each containing 15 plates, may be carried with this instrument and the plates may be exchanged in full daylight without having to remove the caméra. The photographie plates are 6^ by 9 centimètres, but enlarged prints are
  - used for the iconometric platting.
  - Six plates cover the entire horizon and will form a complété panorama.
  - The lens is provided with an iris shutter. It may be focused for
  - short distances or infinity by turning a lever over a scale showing the distances in métrés attached to the front board, R, of the caméra.
  - In fig. 106 the caméra is represented with the magazine, B, removed and replaced by the ground glass plate, G.
  - The entire outfit, excepting the tripod, may be transported in one carrying case (with shoulder or pack straps) of 39 by 28 by 17 centimètres size and 8 kilogrammes weight if but one magazine filled with 15 plates is included.
  - (7) The phototheodolite of Starlce and Kammerer.—This instrument, fig. 107, is somewhat similar in construction to Professor Finsterwal-der’s phototheodolite; both hâve neither telescope nor vertical circle, being provided with caméra télescopes instead.
  - An ordinary skeleton tripod supports the three leveling screws, 8, and a central clamp screw with spiral spring, P, securely connects the tripod head with the instrument proper. R represents the horizontal circle, graduated to 20', but by means of two verniers and microscopes, L, horizontal angles may be read to 1'.
  - The vertical axis of révolution, ending in three horizontal afms, B2, P3, may be adjusted with the aid of the leveling screws S and the cross levels lu l2. The plate P, forming the support of the cross levels, is firrnly united with the arm B2.
  - F«g. t OS
  - Fig. I 06
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  - E = upper clamp screw. M = upper tangent screw for slow motion. Fh F2, F3 = three level-ing screws supporting the caméra telescope ; they rest in grooves on the arms Bx, B2, B3. l3j lA = cross levels, attached to the caméra telescope, figs. 107 and 108; they serve to adjust the photographie plate into vertical plane, using the three leveling screws Fx, F2, F3 for this purpose. 8 — movable front board or lens slide, figs. 107 and 108. Q = handle to facilitate the mounting of the caméra,
  - STAFIKE. 3c • n
  - KAMMERER
  - C, upon the three arms BL, B2l B3. Kx = pinion for elevating or depressing the front board 8, which has a corresponding rack, as illustrated in fig. 107. K2 = differential pinion for slow motion of the front board. H = clamp screw for fixing the lens in any position above or below its central or normal position, m = millimétré scale for measuring any vertical change of the lens from its normal position, the vernier n permitting such change to be read to 0’05 millimétré.
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  - The caméra may be securely united with the vertical axis of the horizontal circle by a clamp screw manipulated from within the caméra box.
  - When the zéro mark of the vernier n coincides with the 70 mark of the scale m, the lens should be in its central or normal position. The slide 8 may be moved 70 millimétrés up or down; from 70 to 140 it falls above the normal position.
  - The lens is a Zeiss anastigmat, f/l8j with a focal length of about 212 millimétrés.
  - When the caméra lens is suitable for photo-topographie purposes, the horizontal change in the distance between its second nodal point and the image plane should only be:
  - 0*09 0*11 0*15 0‘22 0*45 millimétré for :
  - distances of 500 400 300 200 100 métrés.
  - Hence focusing may be dispensed with for general photo-topographie purposes; still, in order that this instrument—for spécial purposes—may also produce sharp and well-defined pictures of objects close to the caméra, the lens mount is such to allow a motion in the direction of the optical
  - h,
  - Fig. 108
  - axis within a range of 2 millimétrés, whereby objects but 23 métrés away from the caméra may still be brought into focus.
  - The external tube of the lens mount has a helical groove or slot, fig. 108, in which a small métal block t, provided with an index mark, may glide freely. This block is attached to the inner tube of the lens mount, and a screw r at one end of the slot serves to clamp the two tubes together, when the focal length will be maintained constant for any length of time. When the screw r is loosened and the outer tube revolved from left to right, the focal length will be shortened. When the block t has passed from one end of the slot to the other, the focal length will hâve sulfered a change of 2 millimétrés. The two positions of the index mark on the block t, for these extreme limits, are marked on the edge of the slot on the outer tube, 0 and 2, fig. 108; the interval being divided into twenty equal parts, one part will correspond with an axial motion of the caméra lens of 0*1 millimétré.
  - A métal frame is attached to the back of the caméra box, its rear surface coinciding with the picture plane. The inner edges of this frame are provided with a centimètre graduation; the middle marks (triangular file cuts) of the vertical sides of this frame designate the termini of the horizon line on the négative, while the middle notches of the two horizontal sides indicate the position of the principal line. When the instrument is in adjustment, the principal line will bè
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  - vertical, the horizon line will be horizontal, and. their point of intersection will be the principal point of the photographie perspective. The opening of this métal frame is 17*8 by 22-8 centimètres, which is also the effective size of the pictures.
  - The two frames J and II in figs. 109 and 110 give the means at hand to make a light-tight connection between the single plate holders (or gronnd-glass plate) and the caméra telescope. The short bellows w, connecting frame I with JJ, will admit the frame II to be moved a little while J remains fixed to the caméra box. Each of these two frames is provided with two hooks, frame J having one upper hook hx, figs. 1Q7 and 108, and a similar hook near the lower corner diagonally opposite h\. The hook h2, fig. 108, is attached to the npper corner (opposite hook hx) of frame JJ, which also has a similar lower hook diagonally opposite h2 and directly under hx.
  - Fig. 110 represents a partial section of the rear end of the caméra, showing the gronnd-glass attachment V. Frame JJ is fastened to frame J by means of the upper left hook h2 and the lower right hook.
  - . The ground-glass frame V is supported by the screws zx and z2, figs. 110 and 111, the points of which rest upon the métal plates 7r, figs. 108 and 110, attached to the permanently fixed frame J. The face of the ground glass G, fig. 110, is brought into contact with the rear surface of the graduated métal frame B, fig. 110, by means of the upper right and lower left hooks.
  - The ground-glass attachment V also has the eyepiece, which forms a telescope with
  - Fi G- 109
  - FiG.no
  - the caméra lens, converting the caméra into a caméra telescope. The position of the optical axis of the eyepiece may be adjusted vertically by turning the screws zx and z2 until the line of collimation of eyepiece and caméra lens fall together into the plane of the caméra horizon (the caméra lens being in its normal position, or the zéro mark of the vernier n coinciding with the 70 mark of the scale m, fig. 107).
  - In this position points on the horizon may be sighted through the eyepiece of the ground-glass attachment; but when the caméra lens had been moved up or down some distance away from its normal position the eyepiece can no longer be used with its optical axis horizontal, and the stops pi and p2, fig. 111, are now unfas-tened and the eyepiece is tilted up or down (rotating it about the horizontal axis xx x2, fig. 111) until its optical axis is directed to the center of the object glass, when the image of the point to be bisected will appear well defined.
  - Fi G. III
  - The circular openings p, shown in the ground-glass attachment, fig. 111, serve to examine the middle notches of the inner edges of the sides of the graduated métal frame B, which define the horizon, and the principal lines of the perspective, thus giving the means to test the positions of those lines and to adjust the same, if necessary.
  - The outer wooden frame V, fig. 110, of the ground-glass attachment is strengthened with two métal diagonal ribs Dl7 fig. 111, which are joined at their intersection by a ring r, the latter form-ing the support for the eyepiece, which may be revolved about the horizontal axis xx x2, as has been already mentioned. ,
  - Each holder contains a single plate, and fig. 109 illustrâtes a section through the upper rear part of the caméra box with a plate holder K in position :
  - P = dry plate; it rests at its four corners upon the springs /' JS = hard rubber slide, which
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  - is completely withdrawn when mailing an exposure of the plate. B — graduated métal frame permanently flxed to the rear end of the caméra box G.
  - We will now describe how the plate holder is attached to the caméra for exposing a plate:
  - Frame II is set free from frame I, and K is hung to the frame II by means of the bent plate l, fig. 109, when the beveled projecting edge of K closes into the rebate of frame J/, producing a light-tight connection. K is now secured to frame 11 by the upper left and lower right hooks (Avhicli is the position shown in fig. 109). The hard-rubber slide S is now withdrawn, and the pair of hooks— upper right and lower left—are tightened to draw the holder K forward until the sensitive film surface is brought into contact with the graduated métal frame B at the back of the caméra C, the springs /taking up any lost motion and insuring a perfect contact.
  - The lens is now uncapped, the exposure made, and the plate holder is withdrawn by repeating the same operations in the inverse order: unfastening the pair of hooks—upper right and lower left— inserting the slide S, and drawing back the last two hooks—lower right and upper left.
  - (8) Captain HübVsplane-tablephotogrammeter.—This instrument is made by E. Lechner in Yienna, Austria, and it has been described in “ Lechner’s Mittheilungen aus dem Giebiete der Photographie und Kartographie,” Yerlag von E. Lechner (Wilhelm Millier) Graben 31, Wien.
  - The resuit aimed at in topography generally being the graphie représentation of the terrene, Captain Hübl replaced the théodolite of the ordinary photogrammeter by a plane table with alidade, thus being enabled to plat the directions required for the orientation of the picture traces, as well as those needed for the location of the caméra stations, directly in the field upon the plane table.
  - For this purpose the top M, fig. 112, of the caméra G, (21 by 21 centimètres) is disposed for use as a plane table. It receives the paper sheet, which is held in position by four métal corner clamps n.
  - Fig. 113 shows the plane table (or upper surface of the caméra) a b ed, which has two pivots, z and z1, about which the ruler LL of the alidade K may be revolved in azimuth. If zf, fig. 113, represents the constant focal length, eg will be the horizontal projection of the picture trace. By
  - placing the ruler LL of the alidade upon the pivot z the horizontal projections of horizontal directions emanating from z (representing the platted station point) as a center to those points of the perspective which serve to orient the picture may be drawn upon the paper between the sector e z g.
  - The central pivot fig. 113, serves as the vertical axis of rotation for the alidade ruler LL when drawing the horizontal directions to known points (signais over trigonométrie stations, visible from the caméra station) to locate the position of the station The line zf or z'f represents the horizontal projection of the principal ray (or of the optical axis of the caméra). It is the trace of the principal plane upon the horizontal-projection plane.
  - With reference to fig. 112:
  - c = caméra box made of aluminum, with constant focal length. It = plane-table alidade, arranged for stadia reading, with vertical circle. « = pivot over second nodal point of the caméra lens. z1 = pivot vertically above center of instrument (in prolongation of the vertical axis of rotation for the caméra or plane-table).
  - 6581----40
  - Fig. 113
  - with' reference to surrounding triangulation points.
  - J*
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  - At e and g, fig. 113, are two stops representing the ends of the photographie field ezg, which is identieal with the horizontal angle commanded bv each plate. 1
  - The lever h, fig. 112, serves to locate the principal point /, fig. 113 ; when the edge of the ruler LL abuts against the upturned lever h, and the principal ray zf (bisecting the angle ezg) inay be drawn npon the plane-table sheet.
  - With reference to fig. 112 : b = rubber bnlb for operating the pneumatic shutter of the caméra. t = head of pinion which serves to elevate or depress the caméra lens, the change from the normal position of the lens being read on a scale with vernier. n — spirit level, two being provided (at right angles) for adjusting the instrument. R = movable plate carrier. LL = lever for moving the plate carrier R forward (toward the lens) until the sensitive surface of the plate is brought into contact with the graduated métal frame vv.
  - The horizon and the principal line may be located upon the perspectives by means of the centimètre graduations on the inner edges of the métal frame vv, or two fine wires may be attached to the corresponding points of the graduation.
  - The caméra is supported by the three leading screws s, their upper ends resting in three slots of the lower face of the caméra box. The latter is firmly united with the tripod head by means of a central clamp screw with spiral spring. T=graduated horizontal circle with clamp screw. It serves to enable the observer to turn the caméra by an equal amount in azimuth after each expos-ure. xx^=-correction screws to adjust the graduated métal frame vv to bring the principal point into the optical axis of the caméra lens.
  - The plane-table M, with alidade K, serves to locate the caméra station in both the vertical and horizontal sense. If the caméra stations are not very close together, the plane-table may also serve for the location of tertiary points and for the sketching of details.
  - This photographie plane-table is well suited for topographie reconnaissance surveys. The results obtained by means of the same may not be as précisé as those obtained with the more complieated and refined phototheodolites, but it is more easily transported, is very simple in manipulation, and the adjustments are not liable to be easily disturbed. The instrument is compact, well conceived, and excellently executed.
  - The size of the photographie plate is 12 by 16 centimètres, giving an effective picture within the graduated margin of 10 by 14 centimètres.
  - The cube shaped caméra has sides of 21 centimètres length, and weighs 3*5 kilograms. The packing case, including the entire outfit and stout tripod (three folding legs), weighs only 11*5 kilograms. The cost in Yienna of the complété instrument is 400 florins.
  - V. PANORAMIC CAMERAS.
  - The lenses of the older surveying caméras gave correct perspectives only for small angles, rarely exceeding 30°, and Martens, in Paris, was probably the first to devise a so-called panoramic caméra to photograph larger sections of the horizon on one plate, even with lenses that ordinarily would cover but a small angular field.
  - If the objects to be photographed are far enough distant to permit the use of a constant focal length of lens for the picture, and if the lens may berotated about a vertical axis passing through the second nodal point of the lens System, such panoramic views may be obtained upon a sensitized surface bent into a half cylinder whose radius equals the constant focal length of the lens and whose axis coincides with the vertical axis of rotation of the caméra lens.
  - The topographie cylindrograph of R. Moessard.—The foliowing-described apparatus has been devised by It. Moessard (commandant du Génie, attaché au service géographique de l’armée), of St. Cyr, France.
  - The hemicylindrical caméra box, fig. 114, rests upon a tripod, with three leveling screws to adjust the verticality of the axis of révolution aa of the caméra lens O, which axis coincides with that of the half cylinder formed by the sensitized surface of the film. The latter may be replaced by a half-cylindrical ground-glass plate.
  - The caméra lens O may be rotated by hand about aa, using the sight ruler 8 as lever. By viewing the landscape through the sights PP' of the lever 8, the proper timing for the exposure
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  - of the ‘different panorama sections may be estimated. The space between the lens O and the frame RR is fflled in with a light-tight fabric, allowing full play for the rotating objective O.
  - The upper surface of the topographie cylindrograph is provided with an azimuth compass G and a pair of cross levels A and B. The bent frame forming the guide for the sensitive film has graduations on the inner edges, which form the margins of each pano-ramic view.
  - The divisions of the upper and lower (horizontal) scales correspond to degrees in arc, while the divisions of the vertical sides are graduated to read
  - where f= constant focal length of
  - the lens O = radius of the cylindrical sensitive surface of the film.
  - Four movable indices are provided, two, H and H', fi g. 115, serve to mark the horizon line of the half panorama, and the other two, H and JS, indicate the magnetic north-and-south line and the magnetic east-and-west line for each half panorama, the compass C, with the sight ruler 8. giving the means for prop-erly setting the index marks N and JS for each view. Thus the magnetic azi-muths of horizontal directions may be taken directly from the pietures.
  - The vertical angles are readily
  - H ï— N a’ fe. ? E H1
  - L
  - LA
  - found by means of the ordi-nates of pictured point» (above or below the horizon line HH1) measured in one-hundredths of the focal length /, using the photo-graphed scales on the vertical margins of the pietures for this purpose.
  - For example: The angle of dépréssion of the ray Oa (to the base of the pictured tree a), fig. 115, may be found from
  - tan JJ —
  - aa'
  - T
  - Fig.I 15
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  - or when aameasured on the side scale, is found to be equal to 25 divisional parts :
  - aa'
  - tan fi
  - 100
  - = 0.25
  - \
  - I
  - To détermine whether tbe levels A and B, fig. 114, read zéro when tbe cylindrieal film is vertical, and also to ascertain whether the index marks R and R1, fig. 115, representing the horizon line, are correctly placed, we may proceed as foliows :
  - A théodolite, fig. 116, is set up about 10 or 15 métrés behind the cylindrograph (after the back of the caméra had been removed to bring the index marks H and R' into view), and both instruments are leveled. After bisecting the upper edge of the cylindrograph the telescope of the théodolite is moved in azimuth, when the bisection should continue. The same should be the case lor the lower surface edge of the cylindrograph after depressing the telescope of the théodolite to
  - bisect that edge. Does this not take place, the cylindrograph will hâve to be adjusted by means of the leveling screws until the bisection takes place, when the level A is to be changed to read zéro for this position of the cylindrograph.
  - The théodolite is now set up in the direction of the level A, at one side of the cylindrograph, and the level B is adjusted in the same manner as just indicated for A.
  - To adjust the indices H and R1 into the horizontal plane (con-taining the optical axis of the adjusted cylindrograph) a comparison may be made on a cylindrograph picture, showing several points of known élévations, the élévation of the cylindrograph being also known, or the théodolite may be set up with the horizontal telescope at the same élévation with the optical axis of the adjusted cylindrograph. The horizontal telescope of the théodolite is now moved in azimuth until a well-defined point is bisected, which point may be identified on the ground glass of the cylindrograph. The image of this point on the ground glass is marked and the cylindrograph is moved in azimuth, marking the image on the ground glass in two more places. A (horizontal) line passing through these marked points should pass through R and R'.
  - The objective O is attaehed to a funnel-shaped box within the caméra, permitting the simultaneous exposure of a vertical strip of film having a width of but 62 millimétrés. Points of the film that would be pictured outside of this strip can not be acted upon by the light unless the objective is revolved about the axis aa.
  - After the time needed for the correct exposure of this strip (of 62 millimétrés width) has been ascertained, the correct exposure may be given the entire semicylinder by moving the sight ruler 8 with a quick and uniform motion about aa from one extreme end of the film to the other.
  - The semieylindrical film being 860 millimétrés long, each strip of the film would then hâve been exposed the sixty-two eight hundred and sixtieth part of the time required to make one full révolution of the objective. If one complété révolution required ten seconds, and if the correct exposure for the strip was found to be five seconds, each strip would hâve received an exposure of 10 x 62
  - \
  - /
  - /
  - I Fi G. ' 16 /
  - /
  - \
  - \ l ' ^THEODOLITE
  - 860
  - seconds = 0.72 second. To give each strip the required exposure of five seconds the entire
  - 5
  - révolution of the lens should be repeated times in succession, or about seven times, each com-
  - U* / A
  - plete révolution taking ten seconds.
  - As yet these instruments are not made sufiiciently précisé to be recommended for phototopo-graphic surveys. The conception of this instrument, however, is ingenious, and where the question of transportation need not be considered the topographie cylindrograph in a more perfected form may give good results for surveying purposes.
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- - OHAPTER Y.
  - ICONOMETERS AND PERSPECTOGRAPHS.
  - We understand under iconometers a sériés of instruments that hâve been devised to simplify the constructions of phototopographie platting (iconometry).
  - After two drawing boards bave been covered with paper (gumrned down on tbe edges) both sheets are provided with a chart projection upon which ail trigonométrie (triangulation) points are platted and their élévations inscribed.
  - The constructions incidental to the iconometric platting of the phototopographic survey may be divided into three classes:
  - First. The platting of ail horizontal directions, that had been observed instrumentally, for the
  - location of the caméra stations and for the orientation of the panorama views.
  - Second. The détermination of the horizontal projection of points pictured on three or more photographs taken from different stations.
  - Third. The détermination of the élévations of the various caméra stations and tertiary points (that are located iconometrically) to facilitate the platting of the horizontal contours of the terrene.
  - The principal instruments used for the iconometric
  - platting of the phototopographic survey in Italy hâve been described in Appendix No. 3 of the United States Ooast and.
  - Geodetic Survey Report for 1893. They are :
  - I. The graphie pro-tractor. — It is used for platting horizontal directions observed instrumen
  - II. The graphie sector
  - L
  - Fig.117
  - nini, serves to plat hori without first drawing the
  - III. The graphie hyp Paganini. It serves to as well as points platted the intersections of lines
  - tally in the field on the platting sheet in the office, (“settore grafico”).—This instrument, devised by Paga-zontal directions to points pictured on the photographs picture traces on the working sheet. sortieter. — This instrument «has also been invented by détermine the élévations of ail points (caméra stations, from the photographs) platted on the working sheet by of direction.
  - IV. The eentrolinead.—Reference has been made to this instrument under the description of the Canadian photograph board. Captain Deville uses this instrument for drawing lines to a vanishing point falling outside of the limits of the platting sheet.
  - The distance between the principal point and the vanishing points of lines increases the nearer parallel to the picture plane such lines are. Lines parallel with the picture plane hâve their vanishing point at infinité distance from the principal point; practically they hâve no vanishing point. Their perspectives are parallel with the original lines.
  - It often occurs in iconometric platting that the vanishing points of some lines fall outside of the limits of the drawing board, and, in order to draw a line which, if produced, would pass through the distant vanishing point, spécial constructions would hâve to be made to locate the direction of such a line.
  - This instrument, fig. 117, is used instead of making such auxiliary constructions on the photograph board. It is composed of a wooden straightedge, L, and two wooden movable arms,
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  - I and l', whicli may be given any inclination against tbe straigbtedge L. The clamp screws, r and r', serve to fix the arms l and V permanently in any position.
  - The photograpk board, fig. 70, is provided with four, points, A, B, G, and B, indieating the centers of the studs against which the arms l and V play or rest when the centrolinead is used on the photograph board. The distance between the stnds may vary, but each two forming a pair are generally placed from 6 to 8 inches apart, and, the arms of the centrolinead being held in contact with the studs, the various directions of the ruler L will intersect each other in one common point.
  - With reference to fig. 118 we hâve:
  - A and B = one pair of studs permanently fixed upon the photograph board. OA and OB = movable arms of the centrolinead, now clamped in the position given them in the figure. O G = ruler of the centrolinead ( = P in fig. 117).
  - If we describe a circle through the three points A, O, and B—the angle AOB remaining constant—the angle AOB will be an angle of the periphery AB for any position given the ruler OG (= L, fig. 117) as long as OA and OB (l and V, fig. 117) remain in contact with the studs A and B. When OG is changed to assume the position O'G' the intersection, F, of the two lines OG and O'G' will alsd be on the periphery of the circle because the angle AOV (AO' F) remains the same and must subtend the same arc A F as long as the studs A and B remain unchanged.
  - Heu ce, for the assumed position of the studs the directions of ail lines drawn along the fiducial edge of the ruler OG (giving O ail positions on the arc AOB) will pass through the point F—they will vanish at F.
  - In the iconometric work of the Canadian surveys the centrolinead is used only for drawing the perspectives of horizontal lines, their vanish-ing points being on the horizon line. The studs A and B are placed on the photograph board on a line AB, per-pendicular to the horizon line and at equal distances from the latter. The horizon line RH' {DD' in fig. 70) becomes a diameter of the circle AOBV, and VA = VB. If the movable arms of the centrolinead include the same angles with the direction of the fiducial edge of the straightedge, the line OG, bisecting the angle AOB, must pass through Fmidway between A and B.
  - The distance of the vanishing point, F, from the principal point, P, may be varied at pleasure by changing the inclination of the arms, l and V, against the direction of the fiducial edge of the ruler L. When the direction of the arms l and V falls together and is perpendicular to L, the vanishing point will fall at infinité distance from the principal point P and the lines drawn along the fiducial edge of the straightedge L will become parallel with the horizon line HR'.
  - The distance of the vanishing point F from P may also be varied by changing the distance between the studs A and B or G and E, fig 70—increasing this distance will enlargè the circle AOB F and Fmoves farther olf from P, reducing that distance will decrease the diameter of the circle AOBV and F will approach the principal point P. The practice in Canada, however, is to retain the position of the studs unchanged on the photograph board and to change the inclination of the arms l and V of the centrolinead instead.
  - If we gradually close the arms l and V, V will approach the line AB and when the angle J. OP becomes equal to 90° the arc AOB will hâve become a sejnicircle, andfthe intersection of AB with RR' will be the center of the circle AOBV, the distance of both O and F from’A P will be equal AB
  - to continuing to close the arms l and V, V will approach doser to AB without ever reaching it.
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  - (1) To set the arms (l and V) of the centrolinead if the direction to the vanishing point ( F) is given by a line in the ground plan.
  - With reference to fig. 119 we hâve :
  - P = principal point on the photograph board. A and B = positions of the studs. Sv = given direction of the line on the ground plan, when V will be the vanishing point for that line.
  - We revolve the picture plane about the horizon line, as axis, into the horizontal platting plane when the station may fall in S, fig. 119, SP being then the distance line or focal length projected into horizontal plan. Should the point V fall upon the drawing board we could describe a circle through AB and Y and place the fiducial edge of the centrolinead’s straight-edge upon DP (upon the horizon line) with the axis of rotation O of the arms l and V in D upon the cir- H cle, then bring the arms Z and V into contact with the studs A and B and clamp them in this position. Still, in this case there would be no use for the centrolinead, the point Y being accessible.
  - To set the arms for
  - an inaccessible point Y we again refer to fig. 119. Join the points Y and B, the angle YDB—the inclination of the lower arm l' against the ruler L—is equal to VBA, both angles subtending equal arcs of the same circle. Draw the lines CS and BS. At any point c on CS draw cM and cv par-allel to AB and DP and join b and v. By reason of similarity of triangles, vb must be parallel to VB and the angle
  - vbc = VBC = BDY.
  - Hence, the arms of the centrolinead may be set in the case under considération by placing the ruler L on Mb, the axis of rotation, O, coinciding with b, and adjusting the lower arm V of the centrolinead to coincide with bv. The other arm l, having the same inclination against the ruler L as the arm V, may be set by placing the ruler L upon the horizon line DP and moving it along this
  - line until the lower adjusted arm V cornes into contact with the stud B, then moving the other arm l about O until it cornes into contact with the stud A and clamping it also.
  - The lines BS, CS, Mc, and cv are drawn once for ail upon the photograph board, fig. 70. The only line to be drawn for setting the arms of the centrolinead is Sv, which is the direction of the given line on the ground plan. The line bv need not be drawn, the points b and v being located by drawing cv parallel with the horizon line and cM or cb parallel with the distance line SP.
  - {2) To set the arms ofthe centrolinead, if the given line YE belongs to the perspective:
  - Take any point F, fig. 120, on the horizon line, join F with E and F with B, then draw cM parallel to AB. Through e draw ev parallel to EY and join vb. Owing to the similarity of triangles vb will be parallel with VB and the angle vbc = YBA, which is the inclination of the arm against the ruler L of the centrolinead.
  - FB and cM are permanently drawn on the photograph board, but FE and ve will bave to be drawn for every given line. In this case two lines will hâve to be drawn instead of one, as in the preceding case.
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  - Centrolineads are usually sold in pairs 5 one serves to work on the left side of the principal point and the other on the right side.
  - V. The perspectometer (as used by Capt. E. Deville).—The perspectometer is used to dispense with the construction of the squares on the perspective when applyiug the “method of squares” (Ohapter I, Paragraph IX) to draw a figure in the ground plan by means of its perspective.
  - On a thin, transparent film (glass, xylonite, isinglass, horn, etc.,) two parallel lines AB and DD', fig. 121, are drawn intersecting the common perpendicular pP. Make DP=PD' =pA=pB= distance line (focal length) and froinp lay off on AB (to both sides oip) equal distances:
  - pm = mn = no...................=pm'—m'n'—n'o/=....................
  - Join these points of division to P and draw lines through the corresponding intersections of the
  - radiais froin P with the perpendiculars AD and BD1, rr1, tt'...............which lines will
  - be parallel with AB and DD'.
  - The use of the perspectometer. —The perspectometer is placed upon a perspective with P on the principal point and DD' coinciding with the horizon line. The ground line of the perspective may fall in XI, fig. 121, it will be divided into equal parts by the radiais froin P, and the trape-
  - zoids of the perspectometer represent the perspectives of the squares in the ground plane having the equal parts on XY as sides.
  - By placing the perspectometer on the perspective in the manner indicated above the squares covering the perspective of the figure that is to be platted iconometrically on the ground plan are at once apparent, and only those re-quired for the drawing of the figure in question are drawn on the ground plan.
  - The sides of the squares to be drawn on the ground plan (their side lengths are equal to the divisions on the ground line between the radiais drawn from P) are laid off from the trace of the principal plane on the ground line, and the position of the front line nearest the picture trace (or ground line) is laid off on the ground plan either by estimation or construction. The estimation of the position of this line (corresponding to tt') on the ground plan is made by noting the fraction of a square’s side which represents the distance (between tt' and XY, fig. 121) from the ground line on the perspective.
  - The same perspectometer serves only for perspectives which hâve the same distance line (like photographs of distant objects taken with the same lens), different distance lines requiring different perspectometers.
  - The width^ P should be equal to the height of the horizon line above the foot of the picture; the radiais from P need not extend beyoüd the width of the picture, the distance points D and D1 having been taken as the limit of the perspectometer in the figure (121) merely to show more fully the principles involved in its construction.
  - The length of a single division on the line AB should be selected with reference to the resulting equal division lengthsof the lowest ground line usedfor the pictures, as the dimensions of thedivision lengths on the latter give the measure for the sides of the squares to be drawn on the ground plan.
  - These division lengths 011 the ground line should be in harmony with the scale of the plan and with the degree of accuracy that may be required for the délinéation of the topographie features. The smaller the size of the squares is selected on the ground plan the more accurately the transfer of the figure from its perspective to the ground plan may be made, the same principles being involved in this method of iconometric platting as in the well-known method of reducing drawings by means of two sets of (hair) squares, the ratio of their sides corresponding to the scale of the required réduction.
  - d p D
  - Fig.IZI
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  - •Captain Deville recommends the perspectometer to be made by first drawing it on paper in a fairly large scale, and tben inaking a négative of it, reduced i>hotographically to tbe desired size of tbe finished perspectometer. A positive copy may now be made on a transparency plate, whicb, if bleacbed in a solution of bickloride of mercury, will show white lines on clear glass. For the sake of better préservation such perspectometer, when completely dry and hard, should be var-nished.
  - When using the perspectometer for transferring figures from their perspectives to the ground plan, when such figures are situated in planes perpendicular to the picture plane but inclined against the horizon plane, the center of the perspectometer is placed upon the principal point P of the picture plane, the same as before, but the perspectometer is now revolved about P until the parallel lines of the same are parallel with the trace of the inclined (figure’s) plane on the picture plane. In this case the trapezoids of the perspectometer represent the perspective of a net of squares situated in the inclined plane, the squares of which are now to be projected into the ground plane.
  - This net of squares in the inclined plane, when projected into the ground plane, will be com-posed of rectangular figures of equal size, their long sides being in a direction at right angles to the picture trace (or ground line) and of a length equal to that which is intercepted between two adjoining radiais of the perspectometer on the trace of the inclined plane (on the picture plane), while the short sides of those rectangles (forming the projection in the ground plan of the squares in the inclined figure’s plane) will be equal to the lengths obtained on the ground line by project-ing the points of intersection of the radiais of the perspectometer with the inclined plane’s trace on the picture plane upon the ground line of the picture plane.
  - The construction of the rectangular net on the ground plan may now be made in an analogous manner to that mentioned for the squares, and the drawing in of the figure on the ground plan with reference to its position within the trapezoids of the perspectometer is accomplished in the usual manner.
  - Should the figures be situated in planes that are inclined to both the picture and the ground planes, then the figure is first projected upon a plane perpendicular to the picture plane, and having the same trace in the latter as the inclined plane.
  - VI. The perspeetograph.—Numerous instruments hâve been devised for drawing perspectives from plans or from nature, mechanically, or by means of optical devices, some of which may inversely become of use for transcribing perspectives of figures into orthogonal projections.
  - The perspectograpk, invented by H. Eitter, serves to construct the orthogonal projection of a plane figure from its perspective, or to draw the perspective from the plans of the object without referring to the object itself.
  - Bitter’s instrument, manufactured by O. Schrœder & Co., in Frankfort-on-the-Main, bas been patented in Germany, October 13, 1883, under No. 29002. It was devised primarily for architectural purposes.
  - This instrument in its présent form, composed largely of wood, is not well suited for surveying purposes, as it contains too many sources of error due to lost motion in its bearings, still, its theory being sound, there is no reason to question its ultimate value, even for précisé work, if it were carefully made by an expert mechanician (excluding the use of wood and using métal throughout), being guided in its construction by the demands of the greatest précision attainable. As a carefully constructed instrument based on the présent pattern may become useful in platting the data of a topographie reconnaissance where, in the nature of the work, rapidity in making the results practically available is of greater importance than a high degree of accuracy, the following description of this instrument may not be out of place here. For its methods of use in photo-topographie surveying we respectfully refer to Capt. E. Deville’s work on u Photographie Surveying” already mentioned.
  - Wehave seen (Chapter I) that the platted position of a point in the ground plan may be found from its perspective (in vertical plane) by locating the point of intersection of the horizontal projection of the ray: ustation—pictured point” with the line of direction itself. (The latter with its vertical plane is revolved about the trace of the vertical plane in the ground plane (as axis of rotation) into the ground plane in which plane the point of intersection is located.)
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  - With reference to fig. 122 we hâve:
  - 8 = caméra station or point of view. /j = perspective (image) of a point M, to be platted in the ground plan, s = foot of the station 8. XY = ground line of the picture plane (vertical) MX. M = platted position of the point M in the ground plane GG.
  - If we draw through the foot of the station s a line parallel to the ground line XY, and make its length s (8), equal to s8, join (8) and the platted point M, then it will follow from the similarity of the triangles 0/jM and s8M that:
  - s8 : O/j =Ms : MO
  - From the similar triangles s(8)M and 0(/j)M we find
  - s(8) : 0(/j) = Ms : MO hence
  - s(8) : 0(/j) = sS : O/j,
  - Having made s S = s(8), the last équation can only prevail if O/j — 0(/j).
  - To find, therefore, the perspective /j of a point M, given on the ground plan, we first draw.a line s (8) through the platted station in the ground plane parallel with the ground line XY, mak-ing s(S) = height of the station 8 above the ground plane. Draw the lines sM and (8)M, which will intersect the ground line XY, in O and (jj), fig. 123. On the ground line X'Y', drawn in another place of the working sheet, we assume a point O', representing O of the ground plan, and erect o/j perpendicular to X' Y' in O'
  - and make O'/j = 0(m), when /j will be the perspective of M in the reverse position of the perspective. The perspective of any other point, H, given on the ground plan may be found in the same way, making O'Q' = OQ and Q'v = Q(v).
  - Eitter devised the perspectograph to perforai this construction, illustrated in fig. 123, meehanically.
  - Fig. 124 illustrâtes the general arrangement of Ritter’s perspectograph. sM and (8)M = two slotted wooden arm s carrying the tracer, M, at their point of intersection.
  - The connections at s, O, (8), and (/j) are such that the rulers sM and (8)M may slide through these points. The slide connections, s and (8), may also be moved along the groove or slot df the wooden ruler HT. The sliding piece O is secured to a rod which in turn may slide in the groove of the wooden ruler XY, being connected at its other end H with a systein of arms or levers joined together after the manner of a pantograph. The distance OD is maintained unchanged while the instrument is in use.
  - (Si
  - & \fo) Y
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  - The eenter of s is placed directly upon the point that marks the platted caméra station on the ground plan. The ruler BT is placed parallel to the ground line of the picture plane, and s and BT are now secured in this position on the ground plan.
  - When the arm sM is moved, s being held in a fixed position (to coincide with the platted station point), the point O will follow the motions of the arm sM, also applying its motion directly to the arm OD (which slides in the groove of XY) and indirectly to the arms of the pantograph System.
  - The fourth sliding piece {/Y), being connected with the joint A of the pantograph System by means of a separate piece, insures a permanently fixed distance between (yu) and A while the instrument is in use.
  - The pantograph System is composed of six pièces: Four straight arms, AB, AG, F/j, and F/Y and two double arms or levers, GDF and BD G, which are bent at right angles at their points of junction D. The sides of the two parallelograms ABGD and DGFE are ail of equal lengths, and the six arms are joined in A, B, G, D, F, F, and G. The arms F/j. and F/j' are twice as long as the length of the side of the parallelograms.
  - The pencil which describes the perspective may be attached to the free end of either arm F/j or F/j‘ .
  - The angles GDB and FDG being each equal to 90°, the sum of the two other angles GDB
  - and GDF must be equal to 180°, and as the sum of two adjacent angles in a parallelogram is equal to 180°, it follows that
  - GDB + GDF = GDB + DGA or:
  - GDF = DGA
  - This shows that the two parallelograms FGDF and GDB A must be equiangular, and as their sides are equal in length, the parallelograms themselves must be equal, and the diagonals FD and GE of the one are equal to B G and AD of the other, respectively.
  - The two long arms F/j' and F/j being of equal lengths, /j/Y will be parallel to GF, both will be perpendicular to the direction of XY, and /j/j' will pass through D. We hâve, therefore, D/Y = D/j = GF = DA.
  - Use of the perspectograph.—The sliding piece s is secured to the working board, over the platted position of the caméra station on the ground plan, still permitting a gliding movement of the arm sM in the direction sM (fig. 124). The eenter line of BT is brought into a position parallel to the platted ground line, and its position is also secured to the board. The sliding piece (S), ünally, is moved from s (in the groove of BT) until s (S) is equal to the élévation of the station S above the ground plane, also securing (S) in this position, when it will still permit a gliding movement of the arm (8) M in the direction of (S) M. The eenter line of the wooden ruler XY is placed upon the ground line (picture trace) on the ground plan.
  - The manipulation of the instrument and its general working will now readily be understood.
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  - For instance, when the tracer M is moved in a direction parallel to BT or to XY, tlie arm sM will move the slide OD in the same direction. The distance O (pi) remaining unclianged—as long as s (8) undergoes no change—(/a) A will also remain of a constant length. Hence, AD and also GI1, as well as D/a, undergo no changes, and the pencil in ja or in /a' will trace a line parallel to XY, representing the perspective of a line of the ground plan (the one traced by M) parallel to the
  - picture plane.
  - When M is moved in the direction of sM, away from XY, the positions of O and D remain the same, but O/a will be lengthened, (/a) moves to the right, or away from 0, carrying the point A with it (A (/a) being a constant length) and increasing the length of the diagonal DA in proportion to the increase of the length of 0 (pi). DA being eqnal to GEJ = Dpi (Dpi1), the latter will also be lengthened, and /a will be moved down, or away from XY, by the same amount as (ja) is moved to the right. The relation between the construction made in fig. 123 and the mechanical platting by means of the perspecto-grapb will now be évident.
  - VII. Prof essor HaucWs trikolograph.—This instrument has been described by Dr. G. Hauck in a memorial commemorating the opening of the new building of the Boyal Teehnical High School at Charlot-tenburg, near Berlin, hTovember 2, 1884. It serves to reconstruct an object from two perspectives of the same that had been obtained from two different points of view.
  - The principles which underlie the construction of this instrument hold equally good for the construction of an instrument to be used for the mechanical platting of the ground plan of any object represented on two photographs obtained from different stations.
  - In 1887, Prof. F. Schiffner already suggested the changes to be made to Dr. Hauck’s instrument, in order to render it available as an instrument of précision for the use of the phototopographer ; still it seems that mechanical diffi-culties in its manufacture are yet to j[a.)
  - be overcome, as the writer has not met with any record of such a per-fected instrument havingbeen either in use or even been constructed.
  - In Chapter I it had been shown that a point, A, photographed from two stations S and Sx, may be platted in horizontal plan, if the two picture traces, gg and gxgx, and the two caméra stations, S and Sx, are given on the horizontal plan, fig. 125.
  - The two picture planes may be revolved about their ground lines, gg and gxgx, into the ground or platting plane, when (a) and (af) will be the two images of the point, A, revolved into the ground plane. If we draw lines through (a) and (ax) perpendicular to the corre-sjmnding ground lines gg and gxgx, then a' and a/ will be the (horizontal) projections of the picture points, a and ax, into the platting plane, and the intersection, A', of the radiais Sa' and Sxax' will locate the positions on the platting sheet of the point A, pictured on the two plates as a and aH respectively.
  - This graphie détermination of the platted position A' of the point A may be accomplished mechanically by placing slotted rulers with their center lines upon gg and gxgx, fig. 126, and indicating the directions of the perpendiculars, dropped from the pictiired points (revolved into the horizontal plan) upon the ground lines, by two arms (a) be and a'b of a pantograph combination, where
  - (a)b = bc — a'b
  - or '
  - (ax)bx — bxCi = a'ifti.
  - Fig. 126
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  - The points (a)a' and c will always be situated on the periphery of a semicircle described about b as the center, and, as the points c and a' are permanently held on the line gg, the angle (a) a'c (angle of the periphery subtending the semicircle) will be equal to 90° for ail inclinations that may be given (a)c against gg. The directions of the radiais Sa' are laid down mechanically by means of two slotted rulers Sa' and Sxa'x, held in position by the studs in S and a' (and Si and a'x, respectively), both rulers being revolvable about the fixed points S and S.
  - This instrument, of which the characteristic features are illustrated in fig. 126, performs the constructions mechanically that were made graphically or geometrically in fig. 125.
  - The slotted rulers gg and gxgx are secnred to the platting board (their center lines on the picture traces) by means of thumb tacks T. The pantograph arms (a) c — {ax)cx — and a'b — (a\) bx — are connected with these rulers by means of sliding joints c (and cx) and a' (and a'x), while the studs which mark the stations S and Sx end in cylindrical projections that fit into the slots of the rulers Sa' and Sxa'i, the latter fitting also over similar cylindrical attachments to a' and a'x, in such a way that the rulers Sa' and Sia\ may freely glide over the points S and a' (or Sx and a'x) and at the same time may revolve about the fixed points S and Sx, respectively.
  - The points (a) and (ax) are provided with tracers, and a pencil slide is attached to the intersection of the rulers Sa' and Sxa'x (in A') in such a way that the pencil point may freely slide either way in the grooves of Sa' and Sxa'x.
  - A comparison between the figures Nos. 126 and 127 will plainly show that A' will always represent the platted position of the point A, derived from its two images a and (ax) (revolved into horizontal plan). Still, it may not always be possible to identify both images of the same point on the two pictures, and, in order to apply Professor Hauck’s method to identify the second image (on the second photograph) by means of the so-ealled “kernelpoints,” the instrument shown in fig. 126 should be modified in such a way that the point of the second tracer may always be upon the image (on the second picture) which corresponds to the point designated by the first tracer on the first picture (revolved into the ground plane).
  - We had seen (Chapter I) that the line connecting the image of any point A on the first picture with the image of the second caméra station (with the kernelpoint (sx), fig. 127)—and the line — connecting the image of the same point A on the second picture with the image of the first caméra station (with the kernelpoint (s), fig. 127)—will bisect the same point g of the line of intersection of the two picture planes.
  - The picture planes being vertical, this line of intersection will be represented by the vertical line through the point £2 of the ground plane (through the point of intersection of the two picture traces or ground lines gg and gxgx). The picture planes having been revolved about their ground lines as axes into the horizontal plane, this line of intersection, g£2, also revolved into the ground plane (once about gg and once about gxgx) will appear twice in the platting plane, once as £î(g), perpendicular to gg in £2, and again as £2{gx), perpendicular to gxgx in £2.
  - As the points (g) and (gx) represent the same point g revolved into the horizontal plane, once about gg and again about gxgx as axes, the lengths (g)£2 and {gx)£2 must be equal.
  - In order, therefore, that this instrument, fig. 126, may work in harmony with the principles that underlie Professor Hauck’s method, it will hâve to be modified to fulfill the following conditions :
  - A line drawn through the kernelpoint «i, fig. 127, and any point pictured on the first photograph and a line drawn through the kernelpoint s and the image of the same point on the second photograph are to intersect the line of intersection of both picture planes in the same point g, or the two lines revolved (with the picture planes) into the horizontal plane must bisect the revolved lines (g) £2 and (gx)£2 (of the line of intersection of the picture planes) in points (g) and (gx), both to be équidistant from £2.
  - The complété instrument, in a general way, is represented in fig. 127. The two slotted rulers gg and gxgx of fig. 126 hâve been supplied with additional arms £2{g) and £2{gx), each arm includ-ing an angle of 90° with its ruler. These rectangular elbow pièces are secured to the platting board by four thumb tacks T after the rulers g £2 and gx£2 had been placed with their center lines upon the picture traces gg and gxgx, respectively, in such a way «that the intersections of the center lines of the elbow rulers (at the rectangular elbow ends of the rulers) coin eide with the intersection £2 of the ground lines or picture traces gg and gxgx.
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- - 734 UNITED STATES COAST AND GEODETIC SURVEY.
  - The pantograph arms, representing the ground lines of the pictures, are attached to the rulers the same as shown in fig. 126. Studs are inserted into the kernelpoints (sx) and (s), and the arms {1(0) and {l(0i) support a ruler (^(oï), which may glide freely over these arms of the elbow pièces. To eut off equal leugths by this ruler (o')(o'i) on the elbow arms 11(0) and £l(0i), the angle d(0)e is adjustable, and it should be regulated for each set of two picture traces to make :
  - (0)£l = (0x)a
  - When (0)d is moved along the slot of (o')Xl the slide point (o"i) will move along (&i){i, £1(0) always being equal to fl (01).
  - The screw d serves to clamp the angle d(0)e for any opening corresponding to the angle
  - /
  - k
  - g£lgi included between the picture traces. Slotted rulers are now placed over the studs that mark the kernelpoints (s‘i) and (s), their slots also receiving the cylindrical prolongations of the tracers (a) and (ax) and those of the slide points (0) and (o'i), respectively. To complété the instrument, two slotted rulers BS and B1S1 are finaily placed over the studs S and St (marking the platted positions of the two stations) and over the sliding joints a' and a' (which are the same as those in fig. 126). At their point of intersection A' the sliding pencil point is inserted (into the slots of these two rulers), which finally complétés this instrument as illpstrated in fig. 127.
  - If we now move the tracer (a) on the first photograph, the pantograph arms (a) c and ba1 will change the position of the ruler SB (into the direction of the radial from S, to the horizontal projection, on the picture trace, of the pictured point designated by the tracer point (a) on the first photograph), and the ruler (a) (Si) is moved, locating the point (0).
- p.734 - vue 124/126
- - REPORT FOR 1897-PART II. APPENDIX NO. 10.
  - 735
  - This change in the position of (g) produces a corresponding change in the sliding point (<?i), which in turn changes the position of the tracer (a{), causing the pantograph arins (cti) Ci and bxa\ to move, and a change in the position of will cause the radial ruler RiSi to assume a new position also. The intersection of ES with the new position of RiSi will locate the platted position in horizontal plan of the point under the tracer (a) on the first photograph, without having actually identified the corresponding image of the (same) point under the tracer (ai) on the second picture.
  - If a line on either photograph is followed out by one of the tracers (a) or (ai), the pencil point A' will draw the horizontal projection of the line given in perspective (the second tracer being observed ehiefly as a check or to aid the general working of the instrument by a gentle tappiiig when the movements of the various parts of the instrument are retarded by too much friction or lost motion).
  - Until now no perfect perspectograph has been constructed, and, no matter how accurately such instruments, like the one just described, may be made by the mechanician, there will always remain some unavoidable imperfections in the material or in the workmanship of the instrument that will produce more or less error in the results.
  - For accurate and précisé work, therefore, the iconometric platting should be accomplished with the aid of graphie or geometrical constructions for ail the control work of the survey, using perspective instruments only for filling in such details which, in an instrumental survey of a similar character, would be sketched in by the topographer.
- p.735 - vue 125/126
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- p.736 - vue 126/126