REPORT FOR 1897-PART II. APPEND1X NO. 10.

645

where HH and H'H' = picture traces, 8 and 8' = horizontal projections of tlie caméra stations, P and P' = traces of the principal lines//and//', and h = selected positions for the first scale.

To flnd the corresponding position of the second scale, draw a line M'parallel to 881 through h,

s'il : s'Ji = S\i : sji'

whence S\h' = distance of the second scale from the “kernelpoint” Si in the second picture plane.

The conditions and relations just described, and first discussed by Prof. G. Hauck, may often serve with advantage in iconometric platting (in the following we will refer to them again).

For example: If we consider the case of a straight line P, fig. 18, shown on MN as l, of which, however, only the short piece V is pictured on M'N', and it is desired to locate a point x, identified on l in MN, but falling on the prolongation of V outside of the picture limit of M'N', we may proceed as follows :

The pictured point a? on Z in MN is connected with the “kernelpoint” (s') and this line (sf ) x is prolonged to intersect Ii in (x). After transferring this point (x) to the line i I of the second

Fig. 18

picture plane MJ N' to ((x)), the latter point is connected with the “kernelpoint” (s), and the intersection of ((x)) (s) and line V will be the point sought, x', of the prolonged line l'.

VIII. TO PLAT A FIGURE, SITUATED IN A HORIZONTAL PLANE, ON THE GROUND PLAN RY , MEANS OF ITS PERSPECTIVE.

In topographie surveys, figures in level planes are not frequently dealt with, except when locating the outlines of lakes and marshes, including coast lines, and the simplest way to plat these would be to expose photographie plates (held in a horizontal position) from a balloon at points of known positions and at identical or known élévations.

The platting of such figures, when photographed on vertically exposed (also inclined) plates from stations higher than the figure’s plane, will also be an easy matter. It may even be accomplished if but one view of such figure had been obtained from only one station (of a known position), provided the différence in élévation between the caméra station and the figure’s (horizontal) plane, the principal point, and the focal length of the view are known.

With reference to fig. 19: H H = Horizon plane of the caméra station 8, M N = Picture plane (vertical), GG — Ground plane or horizontal plane coinciding with the surface of the lake A B G H, 8 80 = h = différence in élévation between the caméra station 8 and the surface of the water in the lake A B G H.

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