REPORT FOR 1897--PART II. APPENDIX NO. 10.

641

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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