2a REPORT—1885. 
etc., and lead to terms in the volume integral 
d?(u —U) d?(u — U) d?(u —U) 
a (let us suppose) . (55) _ 
Then /’ is a function of — yw, etc., and four possible forms are found 
for A,, etc., viz. putting yx, etc., for the differential coefficients 
a(t U) etc. 
dx 
(5) f’s,a homogeneous function of x; . . . xq 
(oh fie 
— (A,); =, ete. 
( x) 5 dx ? ete 
Thus — A, = Din,; x, etc., 
with ,,=7,;. 
dx; 
(6) ore A, a =p jj a etc., 
with the conditions p,;;= 0, 
Pi = —Piis 
giving f’, = constant. 
— xy. Px: 
(7) — Aa = Bry 
with r= 1;;, 
and — 2f/, = 23r, dx: ax; 
; Y “dt dt 
3 
(8) — A= Bid Xx 
dt’ 
with qi = 0, Vi = — Via 
d?y; dx; dx, d 
df, = ae Xs), 
ee: 16\ Ge at ae df 
We have thus eight possible forms of values for A, etc., all or any of 
which may occur in the equations. In the equations for the ether, 
U, V, W, being very small compared with w, v, w, are omitted. 
An isotropic body is one in which no one direction differs in its 
properties from any other. For such a body it is supposed that the forces 
defined by 2, 4, 6, and 8 above do not exist, and a, a’ being the 
coefficients in —2/’; and — 2’, respectively, it is shown that the equation 
for plane waves travelling parallel to z is— 
du du d4 
3 pede. 4 au ! Bos Be 
(m +r) aie (e+ a) 78 +a agit nu. (56) 
