REPORT FOR 1897-PART IL APPENDIX NO. 10.

697

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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