/ 
5 
which brings the galvanometer to zero is proportional to the length of the arc h 
traversed by the telescope L' from the position of parallelism to L. 
Now the angular traverse of the telescope is equal to the parallax; on the 
other hand, the smallness of this angle permits of its being represented by its 
sine, as will be done frequently in the following pages ; and it Avill be admitted 
that the distance moved by the slide on the bars is proportional to the sine of 
the parallax. Let us express that thus : 
n 
n— K sin. y, whence sin. y —— 
K 
In the case of a line of sight normal to the base we have 
b b 
d= - = K— 
sin. y n 
The distance is therefore inversely proportional to the length n, and can be 
directly read on a graduation traced on the bars. But in the case of an ordinary 
line of sight which is oblique to the base we have seen that 
d=b cosec. y cos. a 
b 
whence d— K —cos. a 
n 
A graduation of the bars will therefore only give the distance within the approx¬ 
imation cos. a. 
The necessary correction is made as follows by the instrument itself (Fig. 5). 
The bars of resistance mn, mV, are placed upon the same plateau as one of the 
Fig. 6. 
b 
telescopes, one on each side of the pivot, and normally to the base; the gradu¬ 
ation in successive values of b cosec. y is traced, not on the bars, but on the 
telescope needle. The needle is then moved by the telescope till it is in the same 
vertical plane as the optic axis, making with the bars of resistance an angle 
equal to a, the azimuthal angle of the object. The guide-line of the slide, the 
