Prof. Challis on the Dispersion of Light. 463 



satisfy the condition of making a- vanish for large values of r. 

 This equation gives, by putting r — b, the pressure at any point 

 of the sphere, from which the acceleration of the sphere by the 

 total pressure might be calculated. It is not necessary, for the 

 present purpose, to perform this calculation. 



According to the above solution the absolute velocity of each 

 fluid particle in contact with the sphere is directed from or towards 

 the centre of the sphere, and is equal to T cos 6, Hence at 



points for which = — the velocity is zero. This result stands 



in direct contradiction to the corresponding one of the former 

 solution, according to which the velocity for the same value of 

 is at the surface of the sphere half that of the sphere itself and 

 in the contrary direction. Also since at any point for which 



IT 



0= 9 the velocity is transverse to the same plane, and varies 



inversely as the cube of the distance from the centre of the 

 sphere, it follows that at each instant just as much fluid is flow- 

 ing backwards as in the direction of the sphere's motion, and 

 that there is absolutely no transfer of the fluid by the impulse 

 of the sphere. Certainly the condition of constancy of mass is 

 satisfied by this result, the general equation expressing that con- 

 dition having, in fact, formed an essential part of the basis of the 

 reasoning. But when it is considered that the fluid is unlimited 

 in extent, and that the impulse is propagated indefinitely into 

 space, the result clearly involves an incompatibility which indi- 

 cates that the premises of the reasoning are either false or insuf- 

 ficient. According to the views I am maintaining, they are in- 

 sufficient. 



A fixed point on the straight line in which the centre of the 

 sphere moves being the origin of the rectangular coordinates 

 x, y, z, and the axis of x coinciding with this line, let the plane 

 containing that axis and any point xyz make an angles with the 

 plane cf xy. We shall then have, at any time t, 



x=\Tdt + rcosd, y=rsm0GO$7], z=r sin 0sin?7, 



Tb 2 Tb 2 . Tb 2 



u=— j- cos 2 6, v = — £- cos sin cos% w — —^ cos sin sin 77, 



and consequently 



Tb 2 

 udx -f vdy -f- wdz = — cos dr. 



It thus appears that for this motion udx + vdy + wdz is not an 

 exact differential, and that it may be made such by the factor 



25. It has already been argued generally that that differential 



