Coefficients of Mutual Induction of Eccentric Coils. 44& 



The positive molecules so formed are able to dissociate 

 the gas. When this occurs the complex H 3 is formed.. 

 H 3 cannot be regarded as a stable gas, since it is not present 

 when there is no dissociation of the hydrogen molecules. 



Ryerson Physical Laboratory, 

 University of Chicago, 



January 22, 1916. 



LIII. On the Coefficients of Mutual Induction of Eccentric- 

 Coils. By S. Butterworth, M.Sc, Lecturer in Physics r 

 School of Teclinology, Manchester*. 



1. TN certain types of variable inductances f one coil 



JL moves so that its plane remains parallel to, and at 

 a constant distance from, the plane of a fixed coil. By this 

 means the mutual induction between the two coils may be- 

 made to range from a considerable value to zero and then 

 to change sign during a comparatively small motion of the 

 coil. This use of eccentric coils lends a certain interest to* 

 the problem of determining the mutual induction between 

 two non-coaxial circular filaments. 



2. The principle to be made use of is to treat the mutual 

 induction between the two circles as a potential function of 

 the position of the centre of the moving circle. The proof 

 of this is as follows : — 



Replace the moving circle by its equivalent magnetic 

 shell and consider the variation in potential energy of this- 

 shell as it moves in the magnetic field due to the current 

 in the fixed circle. It is clear that the variation in potential 

 energy of the individual particles of the shell follows the 

 law of potential, so that, since for motions of translation the 

 displacement of every particle is the same, the potential 

 energy of the whole shell also varies in accordance with 

 the law of potential. Identifying the potential energy of 

 the shell with the mutual induction between the two circles,, 

 the proposition is proved. 



For parallel circles the mutual induction (regarded as- 

 a potential function) has a symmetrical distribution about 

 the axis of the fixed circle, so that if the mutual induction is- 

 known in the coaxial position the mutual induction in any 

 other position can be derived by the usual methods for 

 determining potential. 



* Communicated by the Author. 



t Campbell, Phil. Mag. xv. p. 155 (1908). 



