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

663

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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