218 REPORT-——1885. 
disturbed and execute small harmonic vibrations; but the matter par- 
ticles themselves will not generally coincide with their positions of 
instantaneous rest, and so we have to consider their vibrations about these- 
positions. The equilibrium position of the matter at any instant is made 
to depend on the configuration of the ether at that instant, and may 
clearly be expressed, under the given circumstances, as a simple har-. 
monic function of the time, so that if £,,,¢, be the equilibrium co- 
ordinates at time ¢ of a given matter particle of mass m’, we may put 
Bp iad te oh ent Nl ae 
The amplitude a, will be very small. 
The force acting on the particle m’ is then considered on the assump- 
tion that the action between two particles of ether and matter respectively 
depends solely on the distance, and may be expressed by mm/f(v), and it 
is shown that, supposing that (7) is a continuous function of the co-ordi- 
nates,' the force per unit mass tending to draw m’ to its instantaneous. 
position of equilibrium is 
. ae 
RS (Ef) eee 
0 
where ¢ is a quantity depending on f and the configuration of the medium, 
which may be a function of the direction. Thus, for an isotropic medium 
we have as the equation of motion of the matter particles— 
i 
oy DAT 
a & 18 — dg sin — (t+a)}, 
which leads, of course, to the integral 
pape ay sin ™(t+a)+dsin-"+ A) . . (13) 
rf 
i eee 
except when r=6, when 
é=—7 
“ag cos 2T(rta) + bsin“(t+8) - . (4) 
ra) 
The question as to the legitimacy of the assumption involved in the 
equation 
% oe TT 
E) = ay sin —(t+a) 
is then discussed, and it is finally shown that it is correct. 
Again, it follows with great probability, from the experiments of 
Fizeau and Foucault ? on interference with long difference of path, that in 
aray of light the amplitude of vibration resolved in a given direction is not 
constant. We have, therefore, to treat a) as varying—slowly, it is true, 
compared with the rapidity of the vibrations—but still, it is probable, 
passing through many series of changes in one second. 
This leads to the result that 6, the amplitude of the natural vibrations 
1 See Stokes, Brit. Assoc. Report, 1862, p. 261. 
2 Ann. de Chim. s. ili. t. xxvi. p. 138. 
