46 Mr. C. Chree. Isotropic Elastic Solid Ellipsoids wider 



From this we see that the " extension per unit of length "* is 

 greatest in the longer of the two principal diameters perpendicular to 

 the axis of rotation. 



Very Flat Ellipsoid. 



6. Supposing 2 c the short axis, we find, neglecting higher 

 powers of c/a and b/a, 



xx = /j Pa 2 ( i , irl+B/c 2 7 \ ( ! ir~ 3 ~ 



\ a 2 6 2 / 2(1 f/)\ a 2 6 2 c' 



4a 4 + 36t'V-i-46 4 + J ;a^ a "^ a 8 fe 2 )J 



.... (29), 



a 3 /i2 >2 



U C/ 



__g 



c 2 ' 



{Pa 2 076-a 

 - 



1 17 a 2 

 Pa 2 (^ 2 -a 2 ) + Q^(v ? a 2 -& 2 ) + R C ^ (a 2 +& 2 ) 1 



( 

 J ---- k 



?/2/ is got from xx, and 2/2 from z* by interchanging P with Q and 

 a with fe. 



The forces P, Q, B may occur independently, so the most important 

 term in the coefficient of each has been retained. 



When P and Q alone exist, or the forces are perpendicular to the 



small dimension, zx and yz bear to xx, yy, and xy ratios of the order 

 c : a, while zz bears a ratio of the order c 2 : a 2 . Thus for a first 

 approximation the three stresses HKK, yy, and xy alone need be 



retained. To a first approximation xx, yy, and xy are constant 

 along any line parallel to the small dimension. These conclusions 



* Used here and subsequently in sense of total change in length of axis divided 

 by original length, whether strain be uniform or not along the axis. 



