DE. OLIVER LODGE ON ABERRATION PROBLEMS. 
779 
More detailed Discussion of Allied Problems. 
Effect of a different Entire Medium upon Aherration. 
48. If, instead of air or vacuum, the whole medium contemplated in fig. 4 is 
changed, the velocity of light is reduced from V to V/p,; wherefore the aberration 
will change too, unless the telescopic velocity be suitably reduced, or unless the 
medium is constrained to move in some compensatory manner. If the new medium is 
just as stationary as the old, and only the receiving telescope, or line of vision, moves, 
then the aberration angle will become jx times as great as before. 
Minuie Influence of Motion of Entire Medium on Aherration. 
49. But if the medium, in.stead of being stationary, is drifting in some direction 6, 
with velocity v, then, perhaps, its motion may have some effect on the aberration. 
For, though a drifting medium cannot by itself cause aberration, yet it may modify it 
when otherwise produced. And this we shall find true in the second order of 
minutiae. For, in the drifting medium, the rays differ from the wave-normals by the 
angle e, such that 
V 
sin £ = Y sin d = a sin 9, 
and the velocity of light is 
Vj = V cos e + r cos $ = Y (cos e -{- a cos 0). 
Hence an aberration caused by motion of telescope at speed u and angle which 
would naturally be 
sin ^ ^ sin f = /3 sin cf) 
becomes 
. u. . /CO.S e — « cos d\ 
sm gj = — sin (p = sin e ---^- 
\ I \ 1 — or j 
— /3 sin (f) — oi/3 sin f cos 0 + higher powers. 
The conditions most favourable for observing the second term are when the tele¬ 
scope moves across, and the ether moves along, the ray. 
Unless the ethereal velocity near the earth were very great, much greater than the 
earth’s orbital velocity, it would be hopeless to look for this term, as it would require 
the fixing of a star’s position to the five-hundredth of a second, which must be con¬ 
sidered quite impossible. The effect is connected with the slight alteration of focal 
length of the telescope (the difference between sin e and tan e), and may be regarded 
as a secondary sort of Doppler effect (§ 20). 
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