ON OPTICAL THEORIES. 185 
off with the velocity of light, which is about 10,000 times as great as 
that of the earth, so that at the end of the second interval the ether near 
the sphere is at rest again and the same effect is repeated. It seems, 
therefore, probable that there will be a tendency to set up a motion in 
the ether not having a velocity potential, but that the beginnings of such 
motion will be propagated away into space at a very great rate, and that 
the actual motion will satisfy the condition that wde+vdy+wdz is an 
exact differential. 
In a subsequent paper Professor Stokes gives the solution of the - 
equations of motion of a sphere moving in a viscous fluid, and then 
proves that when the fluid becomes perfect the motion becomes unstable, 
so that udx+vdy+wdz is not a complete differential ; but if the tangential 
force depends, not on the relative velocities, but on the relative displace- 
ments of the molecules—that is, if for the beginnings of the variation from 
irrotational motion we must consider the rigidity of the ether (i.e, in 
our mathematics use the equations of an elastic solid)—then, as shown 
already, this nascent variation from irrotational motion will be propagated 
away by transverse vibrations, which, however, do not produce optical 
effects, either because they are too feeble or because they are discon- 
tinuous, or, if continuous, because their period falls outside that of the 
visible spectrum. , 
Or, to put it slightly differently, if the fluid has any very slight 
rigidity, a given arrangement of its parts is not necessarily one of equi- 
librium. Suppose, then, the fluid displaced from rest by the sudden 
motion of the solid, and that after a short interval the solid is stopped, 
the velocity of the fluid will be reduced everywhere to zero, but the 
resulting configuration will not necessarily be one of equilibrium, and the 
motion arising from this slight strain will be set up. 
Thus, without making Fresnel’s somewhat violent assumptions as 
to the relation between the ether within and without a transparent body, 
a perfectly reasonable and consistent account can be given of aberration 
depending only on the irrotational character of the motion induced by the 
moving body in the surrounding fluid. Unfortunately, as Professor Stokes 
points out, we have as yet no experiments competent to decide between 
the two, and he does not see how such experiments could be devised. 
§ 5. Ketteler is the author of a long series of papers connected with 
the subject of aberration, which have appeared in Poggendorff’s ‘ Annalen.’ 
The last of these! contains a summary of the results of the whole. 
The problem of reflexion and refraction at a moving surface is con- 
sidered, and it is shown that the intensities of the reflected and refracted 
rays will not be modified by the motion if the vibrations be at right 
angles to the plane of polarisation, as Fresnel supposed. 
§ 6. The papers also deal with the problem of the emission of light 
from a moving source, and the principle first enunciated by Doppler,? in 
consequence of which it follows that if the source and receptacle approach 
each other in time ¢ by a space equal to n times the wave length in the 
medium between the two, then the receptacle receives in that time n 
more vibrations than it would if the two were relatively at rest ; and if 
this nomber be N, the apparent frequency is increased in the ratio N+” 
1 Ketteler,‘ Ueber den Einfluss der astronomischen Bewegungen auf die optisch n 
Erscheinungen,’ Pt. VI., Pogg. Ann. t. cxlvii. 
? Doppler, Das farbige Licht der Doppel-Sterne. 1842. 
