50 Mr. C. Chree. Isotropic Elastic Solid Ellipsoids under 



bears to that in the thin disc, of the same material and axes, a ratio 

 which is the square root of the reciprocal of (41). 



If the limiting angular velocities be ta for the ellipsoid, ia' for the 

 disc, then the approximate values of lajca' when rj = '25, are as 

 follows : 



/a= 

 lw' =- 1-155 



0-2 

 1-158 



Table II. 

 0-4 , 0-6 

 1-167 1-177 



0-8 

 1-184 



1-0 

 1-186 



In the case of the thin disc many very simple results were found 

 for the radial strains ; these apply without modificatiou to the strain 

 s r in the flat ellipsoid. 



Flat Ellipsoid rotating about one of its longer axes 2a. 



9. Putting P = o, Q = R = a; 2 , 

 and employing n' as in (39), we find 



yy = 





y Z = 



As bja passes through the critical value ^/rj, the stresses xx, zx, 

 and xy vanish and change sign ; and at the critical value, to a first 

 approximation, the only stress is 



x*la z -y z ltf) ...... ........ (43) 



The stretches answering to (42) are 



