Solid Cylinders of Elliptic Section. 87 



than 0, when b/a is sufficiently reduced the minor axis abso- 

 lutely shortens. Since ha/ a and 8b jb are linear in rj, it would 

 suffice to give their values for the limiting values and *5 

 of 77, but owing to its special importance the case t; = *25 is 

 also treated in the following table. 



Table IV. 

 Values of (8S/a)-+-(»V*/ B ) arld Wt^/E). 



b/a= 



0. 



•2. 



•4. 



•6. 



•8. 



10. 





(V=0 



•2 



•2251 



•2327 



•2417 



•2480 



•25 



(Sa/a)- 



-(w 2 p«' 2 /E)= ■! jj="25 



•2 ! 



•2239 



•2272 



•2263 



•2141 



•1875 





U=-5 



•2 



•2228 



•2217 



•2109 



•1801 



•125 





f?7=0 







+ •0090 



+ •0372 



+•0870 



+ •1587 



+•25 



(8b/b)- 



(w 2 pa 2 /E)= | /; = -25 



-•083, 



-•0742 



-•0448 



+•0089 



+ •0878 



+•1875 





U=-5 



-•16 1 



-1575 



-•1269 



-0691 



+•0169 



+ •125 



The results for b/a = l and for any case in which less than 4 

 figures are given are exact. 



Comparing Tables III. and IV. we see that ( — 81/1) and 

 8a/a are in general quantities of the same order of magnitude. 

 The former, though usually the smaller quantity, is decidedly 

 the larger of the two in disks of small eccentricity of material 

 for which rj is large. Since l/a is small, the increase in the 

 major axis would in general be much more easily detected 

 than the reduction in thickness. _ 



§21. For 7] = the value of (8a/a)-i-((o 2 pa 2 /E) continually 

 increases with b/a, but for other values of rj the lengthening 

 of the major axis attains a maximum — the corresponding value 

 of b/a being less the larger n is — and then diminishes as b/a 

 is further increased. 



The alteration per unit length of the minor axis algebraic- 

 ally considered always increases with b/a ; but for values of rj 

 other than this axis shortens when b/a is less than a certain 

 critical value bi/a, shown in Table VI. for a series of materials. 

 The value of b x /a increases with rj. 



If we were to regard Gt) 2 pa 2 /E as constant, w r e should con- 

 clude from Table IV. that answering to an increased n there 

 is a smaller lengthening of the major axis and a smaller 

 lengthening — or greater shortening — of the minor axis. The 

 greater shortening of the minor axis seems analogous to the 

 greater reduction in axial thickness, which according to 



