674

UNITED STATES COAST AND GEODETIC SURVEY.

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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