560 
Proceedings of the Royal Society 
If we take both the front and rear coils this must be doubled, 
thus — 
F, = 2m[(u, - wg] 
Q • r 1 1 ~\ 
— oin\ cos“^ — QOS — , ■■ 
L \/(c? + a^){c\ + 52) x/(c| + a2)(c| + 52 ) J 
= 8m(<^i - <^ 2 ) say. 
Whena= 10 ; 6- 2 ; = 2 ; ^ 3 = 10 , 
<^i - <^2 = 35°56' or 0.627 radians. 
Thus Fc = 8 zV« X 0. 627 = 5.02m . 
Hence 
F„ 0.000042m 
~ F^~ 5.02m 
= 0.0000084 radians 
= 1".7. 
In practice there should be no difficulty in keeping Sa and Sc 
within J mm., in which case the error will be limited to one quarter 
of the above. 
The paper has been kindly revised by Professor J. A. Ewing, for 
whose instructions my obligations are manifold. 
[Note added August 1884. — In a letter of dated April 27, Mr 
Tanakadat^ describes how, by the use of spider-thread instead of 
silk-fibre for the suspension of the magnetometer mirror and magnet, 
he has succeeded in reducing the error due to initial torsion to an 
altogether insignificant amount. He also suggests a method of 
optically magnifying the displacement of the mirror by hanging it 
in a chamber containing a liquid with a high index of refraction /a. 
The front of the chamber is of glass, and the mirror hangs parallel 
to it. If if/ be the angle of incidence, on the outside of the face of 
the chamber, of the entering ray, then for any small angular dis- 
placement of the mirror the reflected ray, on leaving the chamber, 
will be turned through an angle which is 2 - 1 ) sec^if/ -h 1 times 
the angle turned through by the mirror. The reflected image will 
of course form a spectrum, but this is of no consequence when, as 
here, the method of observation is a md method. — J. A. E.]. 
