ON OPTICAL THEORIES. 183 
normal to the wave, and from the extremity of this line a second of length 
v/p? in the direction of motion of the ether; the ray is the line joining 
the first. point to the extremity of this second line. The velocity of the 
ether is resolved into its components perpendicular and parallel to the 
reflecting surface, and the effect of each component is considered ; it 
is shown that rays are reflected and refracted according to the ordinary 
law of sines. 
§ 3. But in a paper six months previously Professor Stokes! had 
considered the problem in a much more general manner. He supposes 
that the earth and planets carry with them a portion of the ether sur- 
rounding them, so that close to their surfaces the ether is relatively at 
rest, while the velocity alters as we recede from the surfaces until, at no 
great distance, it is at rest in space. 
The direction in which a body is seen is normal to the waves which 
have reached the observer from the body, and the change in this apparent 
direction which arises from the motion of the ether is investigated. 
The axis of z is taken in the direction of the normal to the undisturbed 
wave, and a, 3, y are the angles which the normal to the actual wave 
makes with the axes ; u, v, w are the velocities of the ether at a point 
2, y, zat time t; V the velocity of light. The equation to the wave is 
z=C+Vi+, 
¢ being a small function of w, y and t. 
Then, by considering the displacement of the extremity of an element 
Vét, drawn normal to the wave, it is shown that at time ¢+ d¢ the equa- 
tion is j 
2=C+Vi+04+(w4+V) di, 
and hence we see that 
Ob wshiss 
dt 
From this we find— 
T 1 (dw T 1fdw 
=_ ok aes a Bs | (ase 
2 = wae" seal 2 mi vlan? 
If now 
dw __ du dw _ dv 
de dz dy dz 
so that udw + vdy + wdz is a complete differential, then 
_ Ug— Uy a) = ig, — Vv) 
er ee 3, — By == 
and these equations, it is easily seen, imply the known law of aberration. 
In an additional note it is shown that if a,, 3, be the inclinations of 
a ray at any time to the axes, then 
= ds. di. dt 
“1 =\ dz da NS 
lv dw 
dG, = ( aw way 
: da dy ) 
' Stokes, ‘On the Aberration of Light,’ Phil. Mag. vol. xxvii. p. 9 (July, 1845): 
Mathematical Papers, vol. i. p. 134. g p. 9 (July, ); 
