224 ON FARADAY'S LINKS OF FORCE. 



XI. Spherical electro-magnetic Coil-Machine. 



We have now obtained the electro-tonic function which defines the action 

 of the one coil on the other. The action of each coil on itself is found by 

 putting n 1 or n* for nn'. Let the first coil be connected with an apparatus 

 producing a variable electro-motive force F. Let us find the effects on both 

 wires, supposing their total resistances to be R and R, and the quantity of 

 the currents / and /'. 



. < _ , 



Let N etand for j^r r> then the electro-motive force of the first 



3 



wire on the second is 



-Nnn'^. 

 at 



That of the second on itself is 



The equation of the current in the second wire is therefore 



-Nnn'~-Nn^=Rr ......................... (1). 



at at 



The equation of the current in the first wire is 



(2). 



Eliminating the differential coefficients, we get 



R j R r _F 



J. ~ /" -i ^~ 



n n n 



,, n" dl F ,, n* dF 



and 



from which to find I and F. For this purpose we require to know the value 

 of F in terms of t. 



Let us first take the case in which F is constant and / and f initially = 0. 

 This is the case of an electro-magnetic coil-machine at the moment when the 

 connexion is made with the galvanic trough. 



