342 Prof. Maxwell on the Theory of Molecular Vortices 
Equating the two values of 6a and dividing by d¢, and remem- 
bering that in the motion of an incompressible medium 
ddxe daddy. dd 
da dt Gy dk de Be =); e e ° e e e (71) 
and that in the absence of free magnetism 
de dB. dy 
a dy een eT ne ae 
we find 
1/dQ dR d dx d dz YY d dx 
a a, ee re ee + B— 
b\ds dy dz dt dz dt “dy dt dy dt 
dydx dadz dady dBdx da 
Putting 
an (SF di (74) 
and 
de). Mf erG = la ee 
ha ro et . 
where F', G, and H are the values of theelectrotonic components 
for a fixed point of space, our equation becomes 
dx dz dG d dy ao) = 
(Oto G — 1a EG) ~ lB eg HOG ay. 
The expressions for the variations of @ and y give us two other 
equations which may be written down from symmetry. The 
complete solution of i three equations is 
dz = dv | 
P=pyt He, they rs 
Qk : dx ‘ ay 
sal iid: eid oe oe3 dt dy? f 
da Fiat di dV 
Mott ge Oe dsct ager anit 
The first and second terms of each equation indicate the effect 
of the motion of any body in the magnetic field, the third term 
refers to changes in the electrotonic state produced by alterations 
of position or intensity of magnets or currents in the field, and 
Y is a function of 2, y, z, and ¢, which is indeterminate as far 
as regards the solution of the original equations, but which may 
always be determined in any given case from the circumstances 
of the problem. The physical interpretation of V is, that it is 
the electric tension at each point of space. 
