794 
DR. OLIVER LODOE ON ABERRATION PROBLEMS. 
and although the theory has been to a certain extent, and with fairly high accuracy, 
verified, yet it can hardly be yet said to have a secure rational basis. 
In a drifting medium we must draw a clear distinction between w'aves and rays; 
the laws obeyed by one need not be obeyed by the other, for they are inclined to each 
other, and may become differently inclined after reflexion or refraction. 
Now it is pretty plain that if motion is to have any effect upon these aherration 
angles, the rays must be differently inclined to the direction of drift; and on the other 
hand, if motion is to affect the reflexion of waves, that it must act during the period 
of contact of a wave with the reflecting surface ; so that if a wave comes down plumb 
it will rebound as it comes, because its time of contact is then infinitesimal and no 
finite motion could cause any disturbance. But even in this case of normal incidence 
the law of reflexion need not be obeyed for rays, for they are not normal to the 
waves, and will be differently inclined to the direction of drift, unless indeed the 
latter be either normal or tangential. 
64. The following are statements which I will afterwards justify :— 
(1) The planes of incidence and reflexion are always the same. 
(2) The angles of incidence and reflexion, as measured between rays and normal to 
surface, in general differ. 
(3) If the mirror is stationary and medium moving, they differ by a quantity 
depending principally on the square of aberration magnitude, t.e., by one part in a 
hundred million, and a stationary telescope Avould be able to observe the effect, if it 
were delicate enough. 
(4) If the medium is stationary and mirror moving, the angles differ by a quantity 
depending principally on the first power of aberration magnitude, he., by one part in 
ten thousand, but a telescope moving with the mirror will not be able to observe this 
large effect ; for the apparent (or commonplace) aberration caused by the motion of the 
receiver will obliterate the odd powers and leave only the even powers of the aberration, 
so that the observed effect should be the same as in case 3. 
(5) As regards the angles which the reflected and incident waves make with the 
surface, ie., as to the obedience to the law of reflexion shown by ivaves instead of by 
mys, in case 3 the angles differ by an amount depending on the first order of 
aberration, but in case 4 they only differ by rhe square of this quantity. 
(6) At grazing incidence the ordinary laws are accurately obeyed by the rays as 
observed, and at normal incidence the error is a maximum. 
(7) The ordinary laws are obeyed whenever the dii’ection of motion is tangential or 
normal to the mirror. 
(8) In geneial the shape of the incident waves is not precisely preserved after 
reflexion, so that, when spherical waves impinge on a mirror in a moving medium, 
the reflected waves from a plane mirror diverge from a sort of caustic instead of from 
a point, and the position of the image varies (but almost infinitesimally) with the 
position of the observer. In other words, such a mirror acts to a parallel beam as if 
