If the two sectors are coupled up as shown, with a battery, h, and a
galvanometer, by the wires, a b and c d, then since the arm, e, on being
aligned on the object takes the position c1 while d remains at zero, the
Wheatstone bridge formed by these segments and their connections will be
out of balance, and a current will flow through the galvanometer, which
may be so graduated as to give the range by direct reading, since the
current through it will increase with the angle A T B.
Fig. 281. RANGE FINDER.
In general, however, the angle A B T will not be a right angle, but some
other angle. In this case AT = AB / sin(A T B) * sin( A B T), and hence
it will only be necessary to multiply the range reading on the
galvanometer by the sine of the angle A B T, which can be read directly
by the observer at B. This multiplication is not difficult, but by
suitably arranging his electrical appliances Lieutenant Fiske has
succeeded in getting rid of it, so that the reading of the galvanometer
always gives the range by direct reading, no matter what the angle at B
may be. To explain this, consider the two telescopes shown in the cut in
the positions C and D; the whole current then has a certain resistance.