68 Prof. Challis's second Reply to Mr. Airy. 



velocity is directed to or from the centre of the sphere. But 

 as the velocity is not the same in all directions from the centre, 

 the motion of a given particle is not rectilinear, but is con- 

 tinually directed to or from the varying positions of the centre. 

 When the motion is wholly in radii from a centre, it is as ne- 

 cessarily different in different directions from a moving centre, 

 as it is necessarily the same in different directions from a 

 ■fixed centre. 



Although I agree with Mr. Airy that mixed considerations 

 should be avoided in questions of this nature, I cannot forbear 

 entering upon one which appears to furnish a test for deciding 

 between Poisson's results and mine. From what has just 

 been said, it follows that the velocity of a fluid particle at the 

 surface of the sphere relative to the surface = velocity of the 

 sphere x sin 0. Consequently if we impress on the sphere 

 and the fluid the sphere's velocity in the opposite direction, 

 the sphere will be reduced to rest, the fluid will impinge upon 

 it, and the actual velocity of a fluid particle along the surface 

 of the sphere will be, the velocity of the fluid x sin 6. This 

 result, which we can hardly conceive to be in error when the 

 motion is slow, is at variance with Poisson's conclusions. 



I have now, I think, sufficiently shown that the results I 

 long since obtained respecting the resistance of the air to an 

 oscillating sphere are legitimately derived from a general 

 hydro-dynamical principle. The accordance of these results 

 with experiment is not of itself a proof of the truth of the 

 principle, and I do not therefore see that any advantage can 

 be gained by further consideration of this particular problem. 

 At the same time that I say this, to avoid fruitlessly prolong- 

 ing the present discussion, I willingly express the satisfaction 

 it has given me, that the Astronomer Royal, in the midst of his 

 many and arduous engagements, should have thought this 

 subject worthy of so much attention ; and though I do not 

 see reason for changing my first views, I acknowledge that 

 they have become clearer on several points by the remarks 

 which this discussion has elicited. 



I am, Gentlemen, yours, &c. 



Cambridge Observatory, June 19, 1841. J. ChalLIS. 



