214 



Mr Ghree, On thin rotating isotropic disks. [May 4, 



we see that the radial strain is a compression at both edges for 

 all ratios of a' : a, and for all possible values of 77 except 0. For 

 77 = 0, 



/(r) = ^(r 2 -a> 2 -r 2 ) (51), 



and so the radial strain is for all ratios of a : a an extension 

 everywhere except at the edges, where it vanishes. 



For all other values of 77 there are always portions of the 

 disk immediately adjacent to the edges wherein the radial strain 

 is a compression, and it is easily proved that the radial strain is 

 everywhere a compression when 



a' /a > 7(1-^(3 + 77) -=- {3^ (1 + 77) + V477 (2 + 77)} . . .(52). 



An idea of the nature of the radial strain under various conditions 

 for the value *25 of 77 may be derived from the following table : 



Table I. 



du 



Sign of -=- , and loci where it vanishes for 77 = '25. 



From the Maxwell solution in (32) and (37) it is obvious that the 

 radial stress is a traction for all possible values of 77 at all points 

 not on the edge or edges of the disk. 



The terms in rl 2 and rz* in (31)— (33) and (36)— (38) show 

 that the complete solution gives algebraically greater values for 

 the radial and transverse displacements, strains and stresses at 

 all axial distances in the central plane than the Maxwell solution. 

 It will be noticed, however, that the mean of each of these 



