56 Mr. C. Cliree. Isotropic Elastic Solid Ellipsoids under 



Elongated Ellipsoid Rotating about a Short Axis 2a. 

 12. We have to substitute in equations (46) to (49) 



P = 0, Q = R = w 2 . 

 Putting for shortness 



4 (l-Y) (3a 4 + 2a 2 & 2 + 3b 4 ) = n" ............ (63), 



we get 



2 7 2 r~ 



= ^- {5a 4 



,7 = '!^ I" _ { 3 a 4 + 2 a 2 6 2 + 3 6* + /; (5a + 9 a s 6 3 + 6 F) - V 2 (s a 1 - a 2 6 3 - 6 Z> 4 ) 



l" + terms of order a 2 /c 2 and 6 2 /c 2 } ( i_ . jl ____ (66), 



V c "/J 



7/2 = \w~pyz .......................................... (67), 



zx = ^o> 2 oza; .......................................... (68), 



6 2 } ................ (69). 



First approximations to the values of the stresses, strains, displace- 

 ments, and increments of the semi-axes may be obtained by writing 

 w- for R in (51). 



To this degree of approximation it makes no difference which of 

 the two short axes is that about which rotation takes place. The two 

 short axes shorten to the same extent per unit of length, while the 

 long axis lengthens. 



By writing w 2 for Q and R in (54), we get a very close approxima- 

 tion to the strain s z parallel to the long axis. 



