210 
RANGE-FINDERS. 
The application of this principle is evident from Fig. 1, in which AC 
represents the auxiliary base, 0 the object, AB the main base, and 
AO or BO the range. The angles OAB, OB A, BCA, and BAC are all 
equal, therefore the triangles OAB and BCA are similar. Hence the 
proportion 
OA : AB :: AB : AC. 
Therefore 
. 
.(1) 
But 
AB — AC x 18*973666. 
.(2) 
Substituting in 
(1) the value of AB in (2), we obtain 
nA AC* x (18-973666) 2 
°A - , c 
OA = S60AC. 
In other words, each inch in the auxiliary base AC is equivalent to 
360 ins. or 10 yds. in the range OA. For the accurate measurement 
of AC a short tape is provided, 50 ft. long, or 600 ins., which represents 
a range of 6000 yds.; and each inch graduation of the tape is figured 
according to its corresponding range, which dispenses with all cal¬ 
culation. In a high wind a piece of inextensible fishing-line is used to 
measure AC\ and the range is ascertained by winding up lengthways 
on a stick 25 ins. long, graduated in inches in opposite directions on 
each side. Thus each complete turn is 500 yds. range, a half-turn 
250 yds., and the odd tens are read from the side scales. 
Instruments such as Major Richardson describes, though extremely 
simple, do not measure angles with sufficient accuracy for an artillery 
range-finder. Telescopic power is almost indispensable, for more 
reasons than 'one. In the first place, the object is frequently ill- 
defined ; secondly, it is necessary to guide the eye in the true direction 
through the duplex mirrors : otherwise there is a considerable variation 
in the angle reflected, according to the way the instrument is held. 
With a telescope, however, the eye can only look through the optical 
axis of the telescope, and if the mirrors are fixed in the proper position 
with regard to this axis, only one angle can be seen between objects 
by reflection, and that the true one. 
In the system under consideration the constant angle is 88 ° 29 ' 23 * 657 // , 
or, roughly, 884 °. The natural secant of this angle is 37 * 947332 , which, 
divided by 2 , gives 18 * 973666 , the constant proportion above mentioned. 
The instrument for reflecting this angle is made in two forms. Either 
a small square metal box, open in front and on one side, containing a 
prism fixed in a frame and screwed to the bottom of the box, with a 
telescope to screw into a circular hole in rear; or a pair of mirrors 
similar to those of a sextant may take the place of the prism. The 
telescope is of the Galilean construction, of considerable field and 
light, but low magnifying power. A complete set of three such 
instruments will fit into a binocular case, and weighs about 2J lbs., 
