410 Mr. G. Chiystal on Bl- and Unilateral 



Considering now what happens during a complete oscilla- 

 tion, let P be the uniform force whose action during that time 

 is equivalent to the action of the varying force due to induced 

 magnetism, then 



p l ^V f g 2 shl 20^dt-¥ 2 .- .sin2(«9-a)l . 



i 



The middle term disappears because I idt = 0. Hence, if I 2 

 " Jo 



denote \ i 2 dt -. — , i. e. the mean square of the induced cur- 

 rents, then P=A / l 2 sm20-B / sin2(0-a), . . (1) 

 where 



1 + 2™' 1 + 2™' 



Adding now the couple due to the permanent moment of the 

 needle, we get for the whole force tending to decrease 6, 



mFsm(0-a)-A / I 2 sm20 + B / sm2(0-cL). . . (2) 



In all the experiments of verification to be afterwards de- 

 scribed (and in all the experiments discussed in this paper) 

 the permanent field on the galvanometer was very much weak- 

 ened by properly adjusting permanent magnets. Under these 

 circumstances B / is very small compared with niF and A'l 2 . 

 It is easy to verify this by comparing the observed values of 

 the times of oscillation of the needle when the currents are going 

 and when they are not, with the values calculated by means of 

 (2). The verification, however, is suppressed, as it is long 

 and uninteresting. 



The expression for the couple therefore becomes 



7nFsin((9-a)-A / I 2 sin2(9, .... (3) 



the same as that obtained above by looser reasoning. It ap- 

 pears, then, in the first place, that if we make a series of 

 observations of unilateral deflection, and if a define the posi- 

 tion of the needle for no current, and 6 the position when the 

 currents are going, then, other things being equal, 



sin(0-a) A'l 2 , n 



. a/x / = — ^r = const = C say. 



sin 20 m¥ J 



To verify this law I used the following arrangement : — The 

 galvanometer (designed by Professor Maxwell and originally 

 made by Warden, Clark, and Muirhead, but rewound by myself 

 last summer) has two coils wound in channels |- inch broad, 

 1-Jg inch deep, and 4 inches in external diameter. The number 



