78 



Mr. C. Chree on Rotating Elastic 



§ 8. By reference to (23), (24), and (20) it will be seen 

 that in a disk of given material * and eccentricity S and s both 

 vary as (<oa) 2 . Thus coa is a more convenient quantity to 

 tabulate than on. Also as a basis for the comparison of 

 limiting speeds in disks of different eccentricities, it is con- 

 venient to suppose that the major axis has in all the same 

 length 2a. In a given material E, rj and p are constants, and 

 so are the greatest values permissible theoretically in S and s. 

 Materials may, however, have the same value for rj and yet 

 differ widely in their other properties, and this should be 

 borne in mind in applying the following results. 



Table I. is based oii (23) and Table II. on (24). For the 

 purpose of distinguishing between the two theories of 

 "rupture," the angular velocity is termed a> l in Table I., and 

 G> 2 in Table II. If we ascribe to S and s in the tables the 

 limiting values permissible to the stress-difference and greatest 

 strain in the material under consideration, then the values 

 we deduce for o) y and co 2 are the limiting speeds according to 

 the respective theories. If, on the other hand, we ascribe to 

 o>! and g> 2 a given value, we deduce the corresponding maxi- 

 mum stress-difference and greatest strain occurring in the 

 disk. 



Table I. 



Value of (o^a -=r yS/p. 



b/a. 



rj = 0. 



•2. 



•25. 



•3. 



•5. 







1-732 



1-732 



1-732 



1-732 



1-732 



•2 



1-721 



1-714 



1-713 



1-711 



1-705 



•4 



1-693 



1-670 



1-665 



1-659 



1-638 



•6 



1-661 



1-622 



1613 



1-604 



1-569 



•8 



1-639 



1-591 



1-579 



1-568 



1-525 



1-0 



1-633 



1-581 



1-569 



1-557 



1-512 



* For convenience this is here employed to signify absolute identity 

 in physical properties. Materials nominally the same, e. g. steels of dif- 

 ferent brands, or even the same brand under varied treatment, may 

 differ in the values of E and p, and in the values permissible to S or s. 



