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

639

Let the élévation of the station 8 flg. 8 be designated by x.

The élévation of A = R and of B = Ri. The ordinates aa' = y and W = ylt From the relation 8*ai' : 8'Ai' = aa' : AA' ; or

8a' : SA1 = y : (R — x)

we ünd *

Sa1 jj-

y=si7 (H~ and

Sb1 .

Vi — (-“î æ)‘

The différence between y and y\ may be measnred on the négative, hence

y _ î/i = m

is known, and the value for x may be found from the équation

y — yl = (H—x)

Sa' SA'

(-HÎ — SD)

8b'

SB' ~ m'

The values for Sa1, SA', 8b', and SB' may be taken directly from the platting sheet, while those for H and Ri are found in the triangulation records.

If we write the above équation in the general form—

H — x Ri — x

= m>

the élévation x of the caméra station S may be computed from—

mno — Ro + R\n

The numerical values for the ordinates y and yi (locating *the position of the horizon line on the perspective) may now be computed from the équations—

R — x _ y = —-— and 9 n

II x

V. THE THREE-POINT PROBLEM.

If the triangulation points are not sufficiently close together that five or more points may be pictured on one perspective, and if stations are occupied with the caméra that are not connected with the trigonométrie survey, it will become necessary to employ other means to détermine the position of the caméra station with reference to the surrounding triangulation points.

In order to connect the caméra station with the triangulation System by direct measurements and observations, made at the caméra station, it will be requisite that at least three triangulation points be visible from such station, unless the location of the caméra station is to be made by observations made from other stations. In the latter case the occupation of two (better three) triangulation points, if favorably located, would suffice to establish the (u concluded”) position of the caméra station.

The détermination of the position of an occupied point by observing upon three fixed and known points is generally known as the uthree-point problem,” “station platting,’7 “station pointing,” or “ Pothenofs method,” although Snellius had used the same method in his trigonométrie work in the Netherlands in the second decade of the seventeenth century. Let A, B, and G, fig. 13, be the three points, the positions of which are known. A fourth undetermined point 8

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