8 
PROFESSOE A. E. H. LOVE ON THE INTEGRATION OF THE 
Equations of Propagation of Electric Waves. 
9. The equations of propagation of electric waves in free aether are 
^|(X,Y.Z) = curl(a,/3,y) 1, 
,3 ;■. w, 
- ^ I <“•! 
where (X, Y, Z) denotes the electric force, measured electrostatically, (a, /3, y) the 
magnetic force, in electromagnetic measure, and c the velocity of propagation of 
electrical effects. I propose to adopt, as a means of formal simplification, and without 
attaching to it any definite physical meaning, the view"^ that («, y) may be regarded 
as a “ generalised velocity,” and to introduce the corresponding “ generalised 
displacement” (w, v, iv), so that 
0 
ct 
(u, V, iv) = (a, 13, y) 
(5). 
I also introduce the vector (f g, h) by the equation 
(/ ^7, /') = curl {u, V, w) .(6), 
so that {f g, h) is twice the “ rotation ” corresponding to the displacement (ii, v, w). 
The first of equations (4) becomes 
(X, Y. Z) = C (/; ffj,) .(-), 
and, according to tlie view above inferred to, this equation may be regarded as 
expressing a purely kinematical relation, while the second of e<piations (4) gives the 
equations of motion of tlie mther. They are 
with the circuital relation 
G' 
^ {u, V, w) = C'Vfn, V, w) 
dll do dir 
a -f- — 0 
d.r djj dz 
( 8 ), 
(9). 
Furtlier, it is convenient to derive {u, v, w) from a Y^ector potential (F, G, H) by 
tlie equation 
(u, V, iv) == curl (F, G, H).(10), 
* J. Larmor, ‘Phil. Trans.,’ A, vol. 185, Part II (1894). 
