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.

653

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