730

UNITED STATES COAST AND GEODETIC SUR VE Y.

With reference to fig. 122 we hâve:

8 = caméra station or point of view. /j = perspective (image) of a point M, to be platted in the ground plan, s = foot of the station 8. XY = ground line of the picture plane (vertical) MX. M = platted position of the point M in the ground plane GG.

If we draw through the foot of the station s a line parallel to the ground line XY, and make its length s (8), equal to s8, join (8) and the platted point M, then it will follow from the similarity of the triangles 0/jM and s8M that:

s8 : O/j =Ms : MO

From the similar triangles s(8)M and 0(/j)M we find

s(8) : 0(/j) = Ms : MO hence

s(8) : 0(/j) = sS : O/j,

Having made s S = s(8), the last équation can only prevail if O/j — 0(/j).

To find, therefore, the perspective /j of a point M, given on the ground plan, we first draw.a line s (8) through the platted station in the ground plane parallel with the ground line XY, mak-ing s(S) = height of the station 8 above the ground plane. Draw the lines sM and (8)M, which will intersect the ground line XY, in O and (jj), fig. 123. On the ground line X'Y', drawn in another place of the working sheet, we assume a point O', representing O of the ground plan, and erect o/j perpendicular to X' Y' in O'

and make O'/j = 0(m), when /j will be the perspective of M in the reverse position of the perspective. The perspective of any other point, H, given on the ground plan may be found in the same way, making O'Q' = OQ and Q'v = Q(v).

Eitter devised the perspectograph to perforai this construction, illustrated in fig. 123, meehanically.

Fig. 124 illustrâtes the general arrangement of Ritter’s perspectograph. sM and (8)M = two slotted wooden arm s carrying the tracer, M, at their point of intersection.

The connections at s, O, (8), and (/j) are such that the rulers sM and (8)M may slide through these points. The slide connections, s and (8), may also be moved along the groove or slot df the wooden ruler HT. The sliding piece O is secured to a rod which in turn may slide in the groove of the wooden ruler XY, being connected at its other end H with a systein of arms or levers joined together after the manner of a pantograph. The distance OD is maintained unchanged while the instrument is in use.

(Si

& \fo) Y

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