Solid Cylinders of Elliptic Section. 159 



Table XIII. — Value of G^a-f- n/^ . 



n> 



b/a= 



0. 



•2. 



•4. 



•6. 



•8. 



10. 









1-732 



1-721 



1-693 



1-661 



1-639 



1-633 



•25 





1-732 



1-745 



1737 



1-706 



1-703 



1-732 



•5 





1-732 



1-724 



1-734 



1-784 



1-848 



2-0 



Table XIV. — Value of co 2 a+- sfETs/p . 







b/a= 0. 



•2. 



•4. 



•6. 



•8. 



10. 



1-732 



1-721 



1-693 



1-661 



1-639 



1-633 



•25 



1-746 



1-734 



1-710 



1-704 



1-745 



1-852 



•5 



1-789 



1-775 



1-762 



1-822 



2-066 



2-828 



The last result in Table XI II. is exact, the rest are approximate. 

 When 7} — the results are the same on the two theories, and 

 apply, as already stated, to cylinders of all lengths. For large 

 values of rj the greatest-strain theory would allow a con- 

 siderably more rapid rotation than the other theory for all 

 values of b/a. But for values of rj such as *25 the difference 

 between the two theories is remarkably small. For a given 

 value of rj, other than 0, the limiting speed has on both 

 theories at least one minimum as b/a increases from to 1 ; 

 but for ordinary values of ?; the limiting speed depends 

 wonderfully little on the value of b/a. 



§ 39. We shall next consider the principal displacements 

 in the cylinder. The longitudinal displacement vanishes 

 when rj = 0, and for any other value of rj the cylinder 

 shortens under rotation. Each cross section remains plane, 

 which is perhaps the most striking difference between the 

 phenomena and those in thin disks. The reduction in length 

 per unit length ( — 81/1) varies directly as 77, so it will suffice 

 to give its value when 97 = *25. 



Table XV.— Value of (-8Z/Q, V = -25. 



b/a= 



0. 



•2. 



•4. 



•6. 



•8. 



1-0. 



(-M/l) + (u 2 payE) = 



•0625 



•065 



•0725 



•085 



•1025 



•125 



