122 Lord Rayleigh and Dr. A. Schuster. [May 5, 



and, if a denote the section of the wire, and S(=wo-), the aggregate 

 section of the coil — 



-o na n^a 

 B,oc_oc -; 



a fe 



so that if S be given/tan is independent both of the number of terms 

 n and of the mean radins a. If be given, the correction for self- 

 induction depends upon L/GK, while both L and GrK vary approxi- 

 mately as n 2 a. So far, therefore, there is nothing to help ns in deter- 

 mining n and a. The following considerations, however, tell in favour 

 of a rather large radius : — 



(1.) Easier measurement of coil. 



(2.) Smaller correction for moment of suspended magnet. 

 (3.) Smaller errors from maladjustment to centre, and from size of 

 magnet. 



The question of insulation is important. During the rotations the 

 electromotive force acts independently in every turn, and there is no 

 strain upon the insulation ; but in taking the resistance, when a battery 

 is employed, the circumstances are materially different. Any leakage 

 from one turn to another would, therefore, be a direct source of error. 

 It is proposed to use triply covered wire. 



In order to obtain room for the tube encasing the fibre, it is neces- 

 sary to use a double coil. In the new apparatus there will be oppor- 

 tunity for a much larger diameter, by which it is hoped to obtain an 

 advantage in respect of stiffness ; but the further question presents 

 itself, whether the interval between the coils should be increased so as 

 to obtain a very uniform field, as in Helmholtz's arrangement of 

 galvanometer. The advantages of this plan would be considerable in 

 several respects, but on the whole I decided against it mainly on the 

 ground that it would magnify the errors due to imperfect measurement. 

 If we call the effect (so far as it depends upon the quantities now 

 under consideration) u, we have, in previous notation, 



u=a sin 3 «=a 4 (a 2 -f & ,2 )"t, 



du 4tda ^ada-^V dV 



u a + 



lf&'=0, du = da^ 



u a 



but if, as in Helmholtz' arrangement, b f =^a, 



du 8 da 6 dV 



u ha ha 



The increase of V from to \a not only introduces a new source of 



