m 
THE ROBERTS' RANGE-FINDER. 
Theory of the Instrument. 
For simplicity, we assume that the prisms coincide with indices. 
01 (Fig. TV.) is the range we require. We have seen that OTF 
(Fig. IV,) and OIT must always be right angles wben the readings are 
being taken. 
Let IF be the distance at the first reading measured on the rod, 
from the rod-index 7 to the point F, Thus from Euclid— 
01 x77=(77) 2 .(i) 
We will now consider the second reading :— 
As the permanent angle subtended by the wires is always |q, it is 
evident that when the right-hand wire is on 7, the left-hand wire will 
be at P, if— 
i.e., if(7y)3=1600 (Plf . (ii) 
and PI determines the second reading. 
Substitute in (i) the value of (IT) 2 
we get 
07 = 
1600 (Plf 
IF 
(iii) 
Suppose the base 77=40, then from (ii) 
77=1 .\ 07 = 
1600 Xl 2 
IF 
(iv) 
and with this constant base let any first reading (f) represent the 
range expressed in yards ; that is let/= 01 
/ = 
1600X 1 2 
IF 
W 
or 
77= 
1600xl 2 
/ 
(vi) 
In (vi) give,/ any value we please (say from 800 yds. up to 4000 yds.), 
and the scale is graduated by measuring the various values of IF thus 
obtained, from the point 7. 
Thus if /=1600:77=1, 
so measure 1 yd. from 7, mark the rod, and number the mark 16 
(hundreds understood). 
N.B.—I his scale may be made from a table of cotangents. Its index point is 
cot 0° X 40. If the rod is 2 yds. long it would read down to cot 2° 51' x 40. 
Now suppose the base to vary, and any second reading, obtained at 
