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



The principal axes all shorten in any material which is not very 

 nearly incompressible. 



For absolutely incompressible material, 



8a 4 TrwrtV 2a 2 fc 2 c 2 







57 E 



thus a principal axis shortens or lengthens according as the square 

 on it is greater or less than the arithmetic mean of the squares on 

 the principal axes. In a spheroid b a, we find. from. (21), 



a j Sc 4 7r,M/3 2 (a 2 c 2 ) 5 S fO9\ 



~~a ~*~c ~~ 57 ~ E ~ 6 E " 



\vher3 S is given by (17). 



Taking the numerical value (18) for fc>, and for E the high value 

 20 x 10 8 grammes weight per square centimetre, we should get from 

 (22) for a spheroid the shape and size of the earth, a shortening of 

 some 5 miles in equatorial diameters and a lengthening of some 10 

 miles in the polar diameter relative to what these lengths would have 

 been in the absence of gravitation. 



Rotating nearly Spherical Ellipsoid. 



5. Suppose next that the nearly spherical ellipsoid rotates with 

 uniform angular velocity w about 2 a. The values of xx, yy, xy, and 

 yz are as follows : 



a 2 -6 2 



-|r J2 (7 + 5^(3-6^-5^)-^ 



_ , 



--2 (7 + 5J/) (3-6^-5^) _T_ (9 

 c 



