Oscillations of a Rotating Ellipsoidal Shell containing Fluid. 

 i 



Hale (G. E.) On some attempts to Photograph the Solar Corona 

 without an Eclipse. 8vo. [Chicago} [1894]. [With an 

 Excerpt.] The Author. 



May bridge (Eadweard) Descriptive Zoopraxography, or the Science 

 of Animal Locomotion. 8vo. Chicago 1893. The Author. 



Spencer (J. W.) " Reconstruction of the Antillean Continent. 8vo. 

 Rochester, U.S.A. 1895. The Author. 



Van Erden (F. W.) Flora Batava. Aflev. 307, 308. 4to. Leiden 

 [1894]. The Netherlands Government. 



Whitehead (John) North Derbyshire Mosses. 8vo. Oldham 1894. 



The Author. 



February 7, 1895. 



Sir JOHN EVANS, K.O.B., D.C.L., LL.D., Vice -President and 

 Treasurer, in the Chair. 



A List of the Presents received was laid on the table, and thanks 

 ordered for them. 



The following Papers were read : 



I. " The Oscillations of a Rotating Ellipsoidal Shell con- 

 taining Fluid." By S. S. HOUGH. Communicated by Sir 

 R. IS. BALL, F.R.S. Received January 18, 1895. 



(Abstract.) 



The paper contains an application of the analysis used by M, 

 Poincare, in his memoir " Sur 1'equilibre d'une masse fluide animee 

 d'u-n mouvement de rotation,"* to the determination of the free 

 oscillations of a system consisting of a fluid mass contained within a 

 rigid ellipsoidal envelope, rotating about one of its principal axes. 

 It is found that, when such a system is oscillating in one of its 

 fundamental modes, the disturbances of the fluid are all expressible 

 by means of Lame functions, the functions involved being all of the 

 same order ; and a method of obtaining the frequencies of these 

 oscillations, similar to that used by M. Poincare for a fluid ellipsoid 

 with a free surface, is given. 



The oscillations, however, which involve Lame functions of the 

 second order, demand exceptional treatment in consequence of the 

 fact that these alone imply any disturbance of the containing shell. 

 Poincare's analysis, with slight modifications to adapt it to the 



* ' Acta Matliernatica/ vol. 7. 

 VOL. LVII. Z 



