147 
u 0n the Galvanometer,” by William Jack, M.A., Pro- 
fessor of Natural Philosophy at Owens College. 
A current of intensity i passes through a circular wire 
(radius r) fixed in a vertical plane passing through the 
magnetic meridian. A needle of length l (between the 
poles) is suspended in the usual way, on a fine point, situated 
on the axis of the plane of the coil, at a distance e from its 
centre, and can rotate round the point in a horizontal plane. 
Let E represent the earth's magnetic intensity, a the angle 
of deviation of the needle, and p— Je* + r 2 , the distance of 
the needle point from the circumference of the coil. Then 
^ 2 7 rt> 2 / 1 JW — r 2 )(\ — 5 sin 2 a) 451* /Q 4 1022 
E tan a = 3 |l-3^ ^ / + __(8e 4 -12e 2 ,- + r‘) 
(1 — 14sin 2 a + 21 sin 4 a) 
(Wiedemann, Galvanismus, vol 2, p. 165.) 
Accordingly, 
i = tana|^ { 1— 3 ^W— ^)(1— 5sm 2 a) _ i 2e y + r*) 
2tt r 2 4jo 4 64p 8 v ; 
/i i a ‘ i oi • 4 a - 1 + P 3 E fi ./(4e 2 — r 2 )(l—5sin 2 a) 
(1 — 14 sura + 2 1 sin 4 a) | = tana r 2 -j 1 + 3 - a. L 
4.574 
- ^-r-g (8e 4 — 12eV + r 4 )( 1 — 14sin 2 a + 21 sin 4 a) 
04rp 
+ -||^g(16e 4 — 8 e 2 r 2 + r 4 )(l — 10sin 2 a + 25sin 4 a) j- 
+ higher powers iii — j which may be disregarded when £ is 
small compared with p. 
As a first approximation, therefore, we have 
• p 3 E , 
& = £ — 5 - tan a, 
which shows that to this approximation the intensity varies 
as the tangent of deflection. 
The first term to be applied in correction is 
tan a|^(4e 2 — r 2 )(l — 5sin 2 a) (A) 
