ON SOME NEW TELEMETERS, OR RANGE-FINDERS. 505 
prism, and after the two observers have taken up their correct positions 
and the requisite coincidences have been effected, 
: b 
Hence the equation Baa a Tein B 
poses of graduation when the values of the constants a, B, 6, and b have 
been determined. 
This question may, however, be looked at from a different standpoint. 
For constant-base range-finders the scale of ranges is naturally a scale of 
reciprocals, as is represented for another of our instruments in fig, 14, 
This scale of reciprocals is shown marked in fig. 8 on a horizontal line, 
and it is drawn by taking points marked 6, 7, 8, 9, &c., at distances from 
the mark co proportional to +, 4, 4,4, &c. The sum of the angles set 
out by the two reflecting prisms (viz. A+B) determines with a particular 
b 
(et NE 
yards in drawing fig. 8. The point corresponding to 920 yards is to be 
taken as the ceutre of the circle of graduations. The radius of this circle 
wili be dependent solely on 6, the angle of deviation of the refracting 
prism, and the particular base selected for observation. The distance, in 
7—A—B—O sin 0. 
could be utilised for pur- 
base b a range = This range we have supposed to be 920 
fact, on the scale from co to the point corresponding to : will give the 
radius required. In fig. 8 this distance is that between the points co and 
15. With centre 920 and radius equal to this distance a circle has been 
described, and the points on the graduated circle have been so selected 
that their projections fall on the corresponding points on tke horizontal 
reciprocal scale. By producing these lines downwards to meet the lower 
semicircle, and doubling the numbers to be read at each, a scale is obtained 
for a base of length 2b. 
The complete instruments are shown in figs. 9,10, 11l,and12. Fig.9 
is a plan of the two instruments connected together by the cord, A being 
Fié. 9. 
geen 25 Or 50 YAROS ————————— 
A 8B 
the assistant observer’s instrument, and B the chief observer’s instra- 
ment. The cord is attached to each instrument by two chains, whose 
lengths are adjusted once for all, so that when the instruments are pulled 
apart the chains direct them into such a position that the mark upon 
_ each instrument is brought into the reflected field of view of the other 
instrument. M M are the marks (white upon a black ground) which are 
seen in the plan on account of being placed sloping, as shown in fig. 11. 
