86 Mr. C. Chree on Rotating Elastic, 



For instance in a circular disk, of material for which ^ = *25, 

 ( - Bk/l) -r- (S/E) = '500 approximately, 

 (_S? 2 /Z)-*- s ='6 

 Thus answering to a greatest strain s = *001, we should have 

 (-SZ/Z)=-0006. 



Since the disk's thickness must he small compared to its 

 radius, it is clear that in general a direct measurement of its 

 reduction in thickness would not he easy. 



For disks in which e A is negligible we easily deduce from 



(42) 



(-o7/Z)=o>>M3 + 7?)/(4E), .... (45) 



or the reduction is the same as in a circular disk of the same 

 thickness and area of section, rotating with the same angular 

 velocity. 



§ 20. Referring to (14) and (15), we see that the alterations 

 produced by rotation in the semi-axes of an elliptic section 

 vary with its distance from the central plane. The mean 

 values ha and 8b of these alterations taken between ±1 are, 

 however, the same as the alterations supplied by the first 

 approximation. Employing e as before for the disk's eccen- 

 tricity, we easily find 



U 6)V 2 (l-^?)ri , 6 s M-£ 2 + 77(32-35* 2 + 12*V 



L + m-vHS^Se^ + Se') J' • * [ } 



8b 

 b 



fi>y> a (l-q) f t e*\e* + v (l-e*)-\32-29e* + 9e*)\ -} u J 

 4E L 3(l-77)(8-8^ 2 + 3^) J' l ] 



Both 8a/a and 8b/b are obviously linear in rj. For actual 

 numerical calculation formulae in which b/a appears are more 

 convenient, but the above show most clearly the effect of a 

 departure from the circular form. 



The major axis is always lengthened by rotation, and the 

 lengthening is greater than in the diameter of a circular disk 

 of radius a possessed of the same angular velocity, unless 



Since the right-hand side of this inequality only equals I 

 when e=l, and continually diminishes with e, the exception 

 to the general rule is perhaps hardly of practical interest. 

 The alteration in the minor axis is always algebraically less 

 than in the diameter of a circular disk of radius b rotating with 

 the same angular velocity. Further, for all values of rj other 



