290 =Prof. Maxwell on the Theory of Molecular Vortices 
dQ dR_ da 
Eee | 
Similarly, 
sales dR dP_ 4B sit» ene 
dz dz" dé? 
and 
From these equations we may determine the relation between 
the alterations of motion = &c. and the forces exerted on the 
layers of particles between 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 Philosophical 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 mag- 
netism. 
Let us then find three quantities F, G, H from the equations 
dG dil | ‘) 
de dy rare | 
dH: dF 
pe das iz 55 
dx dz HB; ie 
dF dG | 
dy nant ar = MY; J 
with the conditions 
i a d 
and 
dF dG dH 
dx dy + —_ “dz =0, e e *-e@ e e e (57) 
Differentiating (55) with respect to ¢, and comparing with (54), 
we find 
dF dG dH 
P= ae? Q= — Wi? R= Fon e . © (58) 
* Cambridge Philosophical Transactions, yol. x. part 1. art. 3, “On 
Faraday’s Lines of Force.” 
