344 Mr. G. G. Stokes on the Comtitution of 



has not been made manifest in such fluids by any phaenomenon 

 hitherto observed? I have already attempted to offer. an ex- 

 planation on the latter supposition (Phil. Mag., volxxix. p. 6). 

 Professor Challis, in his last communication, has considered 

 the aether as an ordinary fluid. 



In my paper last referred to, I have expressed my belief 

 that the motion for which ndx + &.c. is an exact differential, 

 which would take place if the aether were like an ordinary 

 fluid, would be Unstable; I now propose to prove the same 

 mathematically, though by an indirect method. 



Even if we supposed light to arise from vibrations of the 

 aether accompanied by condensations and rarefactions, analo- 

 gous to the vibrations of the air in the case of sound, since such 

 vibrations would be propagated with about 10,000 times the 

 velocity of the earth, we might without sensible error neglect 

 the condensation of the asther in the motion which we are 

 considering. As far as the case in hand is concerned, Pro- 

 fessor Challis might have regarded p as constant, and treated 

 J) as he has treated s. Suppose, then, a sphere to be moving 

 uniformly in a homogeneous incompressible fluid, the motion 

 being such that the square of the velocity may be neglected. 

 There are many obvious phaenomena which clearly point out 

 the existence of a tangential force in fluids in motion, analo- 

 gous in many respects to friction in the case of solids. When 

 this force is taken into account, the equations of motion be- 

 come (Cambridge Philosophical Transactions, vol. viii. p. 297) 



dp (In (dhi (Pu (t^u\ . , 



with similar equations for ?/ and r. In these equations the 

 square of the velocity is omitted, according to the supposition 

 made above, p is considered constant, and the fluid is supposed 

 not to be acted on by external forces. We have also the 

 equation of continuity 



du dv dtso ,^ , 



^-^^+5r=^' ('•) 



and the conditions, (1) that the fluid at the surface of the sphere 

 shall be nt rest relatively to the surface, (2) that the velocity 

 shall vanish at an infinite distance. 



For my present purpose it is not requisite that the equa- 

 tions such as (1.) should be known to be true experimentally ; 

 if they we.e even known to be false they would be sufficient, 

 for tliey may be conceived to be true without mathematical 

 absurdity. My argument is (his. If the motion for which 

 udx+,., is an exact differential, which would be obtained 



