476 ON PHYSICAL LINES OF FORCE. 



the vortices, or, in the language of our hypothesis, the relation between changes 

 in the state of the magnetic field and the electromotive forces thereby brought 

 into play. 



In a memoir "On the Dynamical Theory of Diffraction" (Cambridge Philo- 

 sophical Transactions, Vol. IX. Part 1, section 6), Professor Stokes has given a 

 method by which we may solve equations (54), and find P, Q, and R in terms 

 of the quantities on the right hand of those equations. I have pointed out* 

 the application of this method to questions in electricity and magnetism. 



Let us then find three quantities F, G, H from the equations 



dG_dH 

 dz dy 



dH 



(fj5\ 



rfo : ~ dz ~^ t I 00 /' 



dF__dG 

 dy dx 



lid . d d 



with the conditions l-j- pa + -r-pB + , p.-y}=m = Q ................ (56), 



dF dG dH 

 and + + - 



Differentiating (55) with respect to t, and comparing with (54), we find 



- - 



dt ' - dt' ' dt 



We have thus determined three quantities, F, G, H, from which we can 

 find P, Q, and R by considering these latter quantities as the rates at which 

 the former ones vary. In the paper already referred to, I have given reasons 

 for considering the quantities F, G, H as the resolved parts of that which 

 Faraday has conjectured to exist, and has called the electrotonic state. In that 

 paper I have stated the mathematical relations between this electrotonic state 

 and the lines of magnetic force as expressed in equations (55), and also between 

 the electrotonic state and electromotive force as expressed in equations (58). We 

 must now endeavour to interpret them from a mechanical point of view in 

 connexion with our hypothesis. 



* Cambndge Philosojrfiical Transactions, Vol. X. Part I. Art. 3. "On Faraday's Lines of Force," 

 pp. 205209 of thia vol. 



