88 Mr. C. Ohree on Rotating Elastic 



Table III. also accompanies an increase in rj. In particular, 

 it may be pointed out that in the limiting case b/a = Q — 

 which means practically a body resembling an elongated thin 

 parallelepiped rounded at the ends — the reductions per unit 

 of length are the same in the dimensions 2b and 21 for all 

 values of rj. 



If we denote the numbers assigned in Table IV. for the 

 values of (Ea/a)+ {co^pa 2 /^) by / 4 (n, b/a), the increase in the 

 major axis answering to the limiting speeds on the stress- 

 difference and greatest-strain theories may be found from the 

 formulae — 



(^ l /a) = (8/H)x{A(v,m\^A(v,bIa), . . . (48) 



(&b) r I x{Mv,b/a)}*xMr„b/a), . . . (49) 



where f ti f 2 have their previous significations. 



For instance, in a circular disk of material rj = '25, 



(Scti/a) -i- (S/E) = -4615 approximately, 



(Sa 2 /a)-7- s = *615 „ 



§22. Sufficient data have already been given to enable the 

 reader to deduce numerical results for any special case. The 

 following table is, however, added on account of the special 

 importance of the case it represents. The velocity eoa is 

 taken as 1000 feet per second, and the material is one for 

 which 



,=•25, 



E = 20x 10 8 grammes weight per square centim., 



p = 7'5 times the density of water. 



Table V. 



b/a. 



Maximum stress- 

 difference in tons 

 per square inch. 



Greateststrain 

 XlO 3 . 



\(-8l/l)xW. 



(£a/«)xl0 3 . 



W)xl0 3 . 







15-03 



1-184 



•296 



•789 



-•296 



•2 



15-37 



1-199 



•315 



•795 



-•264 



•4 



16-27 



1-230 



•372 



•807 



-•159 



•6 



17*34 



1-242 



•464 



•804 



+•032 



•8 



18-09 



1-197 



•584 



•760 



+ •312 



1-0 



1832 



1-082 



•721 



•666 



+ •666 



The material to which the table refers has properties fairly 

 representative of steel, though the density is a trifle low for 



