1890.] vibrations of a revolving cylinder or bell. Ill 



is due to Lord Rayleigh's conditions of inextensibility not being 

 strictly fulfilled in the neighbourhood of the free edge. 



The results of this paper may therefore be of interest in con- 

 nection with the recent controversy on this subject by showing 

 how far Lord Rayleigh's theory of thin shells is capable of practical 

 application. We see that, if his conditions of inextensibility hold 

 good, the number of beats per revolution depends only on the 

 shape of the surface and on the law of distribution of density, and 

 is in no way dependent on the elasticity of the substance. It is 

 therefore readily calculable for a given thin bell. Moreover, the 

 number of beats per revolution when the bell is rotated uniformly, 

 can easily be counted. If there should be any discrepancy between 

 the observed and calculated results which is otherwise unaccounted 

 for, this will give us a probable indication to what extent the 

 deformation differs from one of pure bending in the bell which is 

 the subject of our experiments. 



(2) On Liquid Jets (continued). By H. J. Sharpe, M.A., 



St John's College. 



1. In Vol. VII. Pt. I. I gave an approximate solution of a case 

 of liquid flowing from a vessel and becoming a jet, the ultimate 

 breadth of the jet being half the diameter of the vessel. I now 

 propose to give in detail another case which may perhaps have 

 more interest, since in the following the diameter of the orifice 

 may be as small as we please compared with the diameter of the 

 vessel. In the former solution some ambiguity was attached to 

 the position of the orifice. In the present solution there is none. 

 Some further observations will be made after the solution has 

 been obtained. 



2. We take a case where the outer stream-line (fig. 1) 

 AFGBHG cuts the axis of y in a point B such that OB = Ox' the 

 semi-breadth of the jet at infinity. 



Let y}r be the stream function on the left of Oy. 

 Let OE = 7r, OB = Ccc = ir/p, where p is supposed to be a large 

 integer. 



On the left of Oy, let 



— -— = - u = a x e x cos y + a 3 e 3r cos Sy + a 5 e 5x cos hy \ 



+ Xc n ^ nx cos pny + A 

 a 3 e 3x sin Sy + a, 

 + Xc n e pnx sin pny 



— -^- = v = a^ sin y + a 3 € 3x sin Sy + a 5 e 5x sin 5y 



(IX 



10—2 



