DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
791 
Case when the Mirror Moves too. 
60. It is observed that in this investigation the mirror has been supposed stationary 
witli respect to the medium, it is therefore possible, if the mirror is moving at the 
same rate as the source, e.g., if they were both fixed and the medium streaming 
past both, that the circumstances may be a little different; because since the whole of 
the wave-front does not strike quite simultaneously, there may be time for some effect 
to occur during its period of contact, short though of course it is. Not even for normal 
incidence is the time of impact of a finite portion of a wave infinitesimal; for even 
when the source is infinitely distant (or ivhen a collimating lens is used) it has to be 
remembered that the waves are not normal to the rays in a moving medium, and that, 
accordingly, when the incidence of the ray is normal and the medium movement not 
normal, the wave is inclined to the surface, a minute, but possibly important, angle. 
But in Michelson’s arrangement the ray is not exactly normal on the tangentially 
moving mirror, but is inclined so that the mirror is precisely parallel to the wave- 
front ; and so the time of contact is nothing on either mirror. 
The statement of theory, therefore, proceeds as follows, without apparent error. 
Let S be and remain the position of the source, and let a mirror MN (fig. 15) be 
arranged normal to SM, so as to send a ray back upon itself, when everything is 
stationary, in time 2T. 
It is required to find if any tilt must be given to the mirror to send the ray back 
upon itself when the medium is moving, and whether a different time wdll be taken 
in the journey. 
While light travels from S to M the wave-front’s centre has drifted to Sj, and, 
accordingly, it strikes the mirror obliquely and is reflected as if coming from ; 
hence it would travel towards but for the drift. The drift will carry it precisely 
back to S if SSg = vTg, T.j being the time of the return journey ; just as SSj = vTj, 
when Tj is the time of the outward journey. 
Hence, no tilt whatever is required by the mirror, but it reflects the light back 
upon itself just as when the medium was stationary, and the distance really travelled 
is exactly the same as it was, viz., 2r. The velocity of the light is, liowever, different 
on the out and in journeys, for 
Vj = V cos € — V cos 9, 
Vg = V cos e V cos 9, 
so 
rp , rr ■ 7 ’ 2T cos e \/ (1 — sin- 6) 
as before (§ 59). 
61. In the actual experiment, as performed for instance by Michelson, it is natural 
to use a collimator and plane waves, and since his null result is very surprising and 
remarkable, it may be as well to examine whether the introduction of the lens pro- 
