DR. OLIVER LODGE OX ABERRATION PROBLEMS. 
781 
Now, 
CB sill (% — t) , . . V-. 
“ =-:—= tan ^ cos r — sin r = , 
AC cos % Vlfi 
where v-^ is the necessary velocity of drift; so 
V . ./cos?’ 1'’ 
t'l = — sin i 
cos ^ flj 
The bending will be usual or unusual according as is less or greater than this. 
Ordinarily, of course it is far less. 
51. But now suppose the obliquity i has been caused by the aberration necessary to 
bring a ray to a telescope (moving with velocity u) which except for motion would be 
looking straight at source ; for instance, the telescope whose position was OqEq when 
the light started from S and has moved to AM when light has reached A; in other 
words, let i be an aberration angle ; then 
]\IB u . . 
AB “ V ~ 
But, when a dense medium is inserted in the telescope, or say between the two 
planes, the time recj[uired for the shorter light journey, AC, is longer, and the 
telescope may get carried as far as OE, where 
_ u 
XG 
To bring the ray to the eye-piece at the right moment, C must drift to E, and the 
Hiiyghenian centre A to A'\ in the same time. So if Vq is the ethereal velocity able to 
undo the effect of the dense medium, and to leave the aberration what it was, 
Hence 
Therefore 
or 
A(J YI ix ' 
MC u — ?•„ . siai V 
AC ~ ~ fxY' 
P' 
/ 1 \ 
If this condition is satisfied, the observed aberration caused by any motion of a 
