[ SCO ] 



LVI. On the Vibrations of an Elastic Fluid. By the Rev. J. 

 Challis, M.A., F.R.S., F.R.A.S., Plumian Professor of 

 Astronomy and Experimental Philosophy in the University of 

 Cambridge* . 



IN accordance with the intention expressed at the close of 

 my communication to the Philosophical Magazine for 

 August last, I proceed to draw some inferences from the equa- 

 tions (B.) and (C). But, first, it will be proper to point out 

 two inaccuracies contained in that communication. The third 



bH 

 term of equation (C.) in p. 100 should be ~ instead of b^f; 



and in the same page, in the series for the form of p, the 

 quantities in brackets should bez — a't + c v z — a't -{-c^z — a't + c 3 , 

 &c, c v c 2 , c 3 , &c. being certain constants. No inferences are 

 in the least degree affected by these alterations. 



Let us now, for the purpose of testing equation (C), suppose 

 thatyis a function of x^+y*. By this supposition the equa- 

 tion becomes, on putting r 2 for a: 2 -f y% 



U ~ W \ a 2 rfr 2 ) r dr + a 2 * 



showing that the supposition is allowable. In any case of 

 vibrations not very large, the second term in the brackets is 

 too small to have anv appreciable effect. Omitting this term, 



and putting 4e for —$ the integral of the resulting equation in 



a series is 



f=l-er*+ r^-pr^+fcc. 



I have already stated (Phil. Mag. for April, p. 281) that 



df 

 according to this result /and 4- cannot vanish together, 

 o J dr ° 



Hence, since the velocity of the vibrating particle in any di- 



rection perpendicular to the axis of * is <p.-y-, and parallel to 

 7_ dr 



the axis of z, f. -—, it follows that the fluid cannot be con- 

 '"' dz 



stanlly quiescent at a certain distance from that axis. This 

 conclusion is inconsistent with the non-divergence of the vibra- 

 tions, and would be enough to condemn the whole of the pre- 

 vious investigation, if the reasoning by which it was arrived at 

 be good. 



It is now proper for me to state the grounds on which that 

 conclusion is to be rejected. I have maintained, and still 

 * Communicated by the Author. 



