760 Rotation of Elastic Bodies. 



This is when ^ is infinite, but a itself is not necessarily 

 throughout. M 



For all known material bodies, although E/p is large, 

 E/M = pc 2 is very small. Hence no experiments on the 

 rotation of bodies could decide between Newtonian and 

 Relative mechanics. 



Two interesting special cases can be worked out by 

 methods practically the same as in Newtonian mechanics 

 (cf. Love, 'Elasticity' (2nd ed.), p. 144). 



Case 1. — Long cylinder, assuming a uniform longitudinal 

 extension e so that a) = ez. 



When r = a the relative radial extension - is given by 



r M(l-<r) I! 

 L E 2j 



u_M rM(l-o-) 

 a ~ 4c 2 



co 2 a 2 Mo- 



e — 



2c 2 E 

 For a " semirigid " body 



e = 0, - = 



u oy*a 



a <5c 



Case 2. — Thin disk, with the same assumptions as in 

 Love's ' Elasticity.'' 

 When r—a, z = 0, 



u_co 2 a 2 r~K(l— a) 1 Mo-(l + o-) 2l 2 



2P 11 



a ~ U 2 L JG 2 ' E 3a 2 a a 2 J ' 



When r = 0, z=l, 



1 ~~~ So 2 l(\ + pXZ\ + 2fi) * V "" J* 

 For a " semirigid " body 



_ AV l\ 



u 



a 



iv co 2 a 2 _ 



6(7. 



I 8c 2 



According to some an electron is supposed to possess no 

 non-electromagnetic mass. In this case M would be infini- 

 tesimal and the electron would appear, at first sight, to be 

 " semirigid w rather than absolutely " rigid." Such an 



