6 
line rr', horizontal and parallel to the base, intercepts the graduation at a distance 
n 
n' from the origin, equal to-. Substituting this value in the foregoing- 
cos. a 
equation for distance we have 
b b 
d= K-cos. a =K— 
n r cos. a n’ 
We see thus that if the movement of the slide is made dependent, not on the bars 
of resistance, but on the needle which is inclined to them at the angle u, that 
movement is always inversely proportional to the distance. In other words a 
graduation, in functions of b cosec. y, traced upon the needle, will give the dis¬ 
tance for every line of sight. 
The practical working of the instrument is as follows : two observers, having- 
agreed on a signal, point both the telescopes at the object; a third one moves the 
slide till he brings the needle of the galvanometer to zero, and then reads off the 
distance at the point where the guide-line of the slide crosses the graduation of 
the telescope needle. 
The Automatic Range-Finder. 
In this improved telemeter Captain Fiske has succeeded in obviating all 
manipulation, and the range is read on the face of the galvanometer. In the case 
where the line of sight is normal to the base we have already seen that the dis¬ 
tance is inversely proportional to the parallax (or more strictly speaking* its sine), 
and consequently also to the displacement of the galvanometer needle. 
Where the line of sight is oblique to the base we have also seen that the range 
varies for the same parallax as the cosine of the azimuthal angle. If then the 
deviation of the galvanometer were constant for the same parallax, whatever the 
direction of the line of sight, the graduation on its face would only be correct for 
the normal case. But it is not so. In such cases the intensity of the current 
which passes through the galvanometer increases with the azimuthal angle of the 
object. (A calculation of the resistances of the four parts of the Wheatstone’s 
Bridge, set forth in “ La Lumiere Electrique,” tome XXXIX., p. 155, demon¬ 
strates the above fact.) With the increased current comes an increased deviation 
of the galvanometer, i.e., a diminution of the range read upon that instrument. 
It will be remembered that the reading zero corresponds to the parallelism of the 
telescopes, i.e., to an infinite range. In other words, the increase of current 
which results from the increase of the azimuthal angle, tends of itself to compen¬ 
sate the error due to the obliquity of the line of sight. If the intensity of the 
current which passes through the Bridge were exactly in inverse proportion to the 
cosine of the azimuthal angle, that compensation would be constant, and the 
graduation of the galvanometer for range would be exact in all cases. In point 
of fact a calculation of the intensity of the current in the transverse wire of the 
Bridge gives the three following results :— 
1°—The intensity of the current cannot be made rigorously proportional to 
the inverse of the cosine, or secant, of the azimuthal angle. 
2°—The resistances can be regulated for a particular azimuthal angle, what- • 
ever the range. That being so, the graduation of distances on the 
galvanometer which accords with normal lines of sight, accords also 
with the lines of sight in the direction a, and if this angle a be suitably 
chosen the errors due to the graduation for intermediary lines may be 
disregarded. 
