Dil. OLIVER LODGE ON ABERRATION PROBLEMS. 
795 
slightly tilted, to a divergent beam as if slightly curved. But either eftect, as observ¬ 
able in the result, is almost hopelessly small. 
(9) Similar statements are true for refraction. 
65. In considering a plane mirror in a drifting medium it is very tempting to image 
the direction of drift of successive wave centres (hg. 4); in which case everything will 
be symmetrical, and the law of reflexion will be obeyed altogether, by both waves and 
rays, in the simplest possible manner. But a little thought shows that this is 
illegitimate, for it would make the reflected waves assisted in their progress by the 
reflected drift just as much as the incident waves are assisted ; whereas they are really 
travelling in the teeth of the wind, their progress being impeded and their wave-length 
shortened just as much as the incident waves are helped and lengthened (or of course 
vice versd). Plainly the drift is not reflected, but must be supposed to act on the 
waves emitted by the image exactly as it acts on the waves emitted by the source. 
Another tempting thing to do is to start a system of waves from source and its 
ordinary image simultaneously, both subject to precisely the same drift velocity, one 
being the incident, the other the reflected system. But applying this, and taking a 
pair of waves intersecting at any one point of the mirror, it will be found they have 
not travelled the same distance to get there, nor have they taken the same time, and 
the drift of their centres has been different. Moreover, they do not intersect at a 
second point of the same wave, and, in fact, the system behind the mirror is not in 
any sense the image of the front set. 
The really essential thing is that the phase of the reflected wave shall be identical 
with that of its incident exciter at the point of contact with the mirror, and accord¬ 
ingly that the time of virtual journey from any point to be considered as an image is 
to be equal to the time of journey from the corresponding point of the source. 
Nothing less direct or more geometrical than this seems satisfactory, so it had better 
be applied in its usual Huyghenian baldness. At the same time a little caution is 
necessary in using Huyghens’ construction in a moving medium, for the centre of the 
elementary waves does not remain at tire point of incidence, but drifts away, as in 
fig. 4, and the construction has to remember this, or it will go wrong. 
Laws of Ref exion and Refraction in a Drifting Medium. 
66, Since the direction of drift need not be in the plane of incidence, it will be con¬ 
venient to resolve it into two components, respectively in and perpendicular to that 
plane, and consider them separately. 
Component of Drift Perpendicular to Plane of Incidence. 
The perpendicular component is very easily disposed of, as was shown by Sir 
George Stokes.* For looking down the normal to the mirror we shall see the 
* ‘ Math, and Rhys. Papers,’ vol. 1, p. 144. 
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