228 
MR. J. LARMOR OX A DYNAMICAL THEORY OF 
obtained on the supposition that the structure of the matter is not affected by its 
motion. The conductors on which these charges are situated will, however, if the 
results of the more fundamental analysis of §16 are admitted, change their actual 
forms to a slight extent depending on (u/c)^ when they are put in motion, and this 
change will react so that the distribution of charges and displacements will be the 
simjDle one there given.] 
16. The circumstances of propagation of radiation in a material medium moving 
with uniform velocity v parallel to the axis of a: will form another example. We may 
here (§13) employ the circuital relations, of types 
where 
d/ 
u = -- 
(It 
+ 
Sf' 
dt ’ 
dy 
K - 1 
AttC'- 
d^ 
dz' 
8ci 
Jt 
dR 
dy 
dQ 
dz 
1 
(P, Q, 11), if, cj, h) = ^ (P, Q + VC, P - vh) 
There readily results, on eliminating the electric force (P, Q, P), 
477 (w, V, lu) = curl (a, y), {a, h, c) — lirC' curl {u, v, w), 
where 
= d^Jdd + (K - 1) {djdt + vd;dxf ■ 
^\dlich agrees with the equation obtained in Part I. §124 and Part II. §13, leading to 
Fresnel’s law of alteration of the velocity of propagation. 
Now let us consider the free aether for which K and /x, are unity, containing a 
definite system of electrons which are grouped into the molecules of a material body 
moving across the aether with uniform velocity v parallel to the axis of x; and let us 
remove the restriction to steadiness of § 15. We refer the equations of free aether, 
in which these electrons are situated, to axes moving with the body : the alteration 
thus produced in the fundamental aethereal equations 
iTTdjdt . (/, g, h) = curl {a, h, c), — djdt . (a, h, c) = 477C' curl (/, g, h) 
is change of d/dt into djdt — v d/dx, leading to the forms 
iTrdjdt. {f g, h) = curl («', h', c), — djdt . {a, h, c) = 47rc~ curl (/', g\ h'), 
where 
{a, V, c) = (n, h + 47ru/q c — ^Trvg), (/', g', li), = {f, g — v c/IttC^, h + v h/lirC-) ; 
from which eliminating the unaccented letters, neglecting and writing as before e 
for (1 — we derive the system 
