Mb maxwell, ON FARADAY'S LINES OF FORCE. 79 



along the whole length of the wire. The equation of the wire is 



\ = -^ 

 where w is a large number ; and therefore 



cos 9 = -7— , 

 n IT 



ds = a sin 6d(p, 

 = - an'irsm^OdO, 

 „, 47r „ , Stt ,, 1 • 



^ S 3 3k + k 



E may be called the electro-tonic coefficient for the particular wire. 



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? or n'' for nri. 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 T. 



Let N stand for -— — -7- , then the electro-motive force of the first wire on the second is 

 3 {3k+k) 



That of the second on itself is 



AT '^^ 



- Nnn -— . 

 dt 



dt 



The equation of the current in the second wire is therefore 



-Nnn'~-Nn"% = R'r (l) 



dt dt ^ ' 



The equation of the current in the first wire is 



-Nn'>--Nnn'~ + F = RI. (2) 



dt dt ' 



Eliminating the differential coeflicients, we get 



nnn 



, ,, /to' n"\ dl ^ F n'^ dF , . 



from which to find / and T . 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 T initially = 0. This is the 

 case of an electro-magnetic coil-machine at the moment when the connexion is made with the 

 galvanic trough. 



