184 REPORT— 1885. 
So that, if wdz + vdy+wdz be a complete differential, da; and dj, both 
vanish, and the path of the ray is a straight line. 
Thus, if the motion of the ether produced by the passage of the trans- 
parent medium through it have a velocity potential, all the phenomena 
of aberration will be such as are actually observed. The important ques- 
tion as to whether such a motion is probable in the ether is discussed in 
another paper.! 
§ 4, Professor Stokes’s views on the constitution of the ether are given 
in his well-known paper on fluid friction.?, He distinguishes there between 
the properties of rigidity and plasticity, pointing out that an elastic solid 
may under different external conditions become a viscous fluid, while 
the gradation between viscous and perfect fluids is quite regular. There 
seems, then, a probability that the property of rigidity will run to some 
extent through the whole series, becoming, in the case of fluids, masked 
by some other more important property. The mobility of a fluid is the 
limiting case of great plasticity ; but even a perfect fluid may admit of 
a finite, though extremely small, amount of constraint of the nature of 
shearing stress before being relieved from its state of strain by its mole- 
cules assuming new positions of equilibrium. A consideration of the 
length of a wave in light motion—abonut ‘00003 inches—renders it pro- 
bable that ‘ the relative displacement of the ether particles may be so small 
as not to reach, or even come near, the greatest relative displacement 
which could exist without the molecules of the medium assuming new 
positions of equilibrium.’ 
These same views also tend to confirm the belief that for fluids, and 
among them the ether, the ratio of A to B (the elastic constants of the 
medium in Green’s notation) will be extremely great. 
We are led, then, to conclude that, in considering the motion set up 
in the ether by a moving body such as the earth, we may treat the 
ether as an incompressible fluid, while, on the other hand, when 
dealing with the extremely small disturbance produced by the passage of 
a light-wave the rigidity of the ether may come into consideration, and 
the equations required will be those of an elastic solid. In the first case 
any tangential forces which may arise, if the fluidity be not perfect, will 
depend on the relative velocities of the parts of the fluid; in the second 
case such tangential forces will depend on the relative displacements of 
those parts. In the paper in the ‘ Philosophical Magazine’ for 1846 
Professor Stokes shows that it is probable that a velocity potential will 
exist unless the action of the air on the ether be such as to prevent it, 
and, further, that it is improbable that the air will so act. 
For suppose a sphere started from rest in such a medinm, and then 
after a short interval stopped for a time, then started, and so on. 
The initial motion will have a velocity potential, and if the fluid 
were perfect this would continue, so that reducing the sphere to rest 
would stop the motion everywhere. But the motion with the velocity 
potential is shown to be unstable, and hence there is left in the neigh- 
bourhood of the sphere a small outstanding disturbance. This is carried 
1 Stokes, ‘On the Constitution of the Luminiferous Ether viewed with reference 
to the Phenomenon of the Aberration of Light,’ Phil. Mag. vol. xxix. p. 6; Math. and 
Phys. Papers, i. p. 153. 
2 Stokes, ‘On the Theories of the Internal Friction of Fluids in Motion, and the 
Equilibrium and Motion of Elastic Solids,’ Zrans. Camb. Phil. Soe. vol. viii. p. 287; 
Math. and Phys. Papers, i. p. 75. 
