Solid Cylinders of Elliptic Section. 91 



the curve of no radial strain, and the two curves have common 

 tangents at the double point. The inclination 6 of one of 

 these tangents to the major axis decreases from 90° as b/a is 

 reduced from b 2 /a. Its values for a series of values ry and la 

 are shown in the following table : — 



Table VII.— Value of O . 



b/a. 



n = 0. 



•2. 



•25. 



■3. 



•5. 







90° 



65° 54' 



63° 26' 



61° 17' 



54° 44' 



•2 



__ 



68° 7' 



65° 16' 



62° 51' 



55° 35' 



•4 



— 



78° 31' 



72° 59' 



69° r 



58° 42' 



•5 



— 







90° 



76° 55' 



61° 52' 



•6 



— 















67° 33' 



•7 



— 















83° 26' 



The blanks signify that for the corresponding values of tj and 

 b/a the curves do not pass through the centre of the disk. 



The curve of no radial displacement lies between the 

 tangents at the centre when that is a double point on the 

 curve. Within the disk, however, it departs but little from 

 these tangents, so that the portion of the disk wherein the 

 distance of elements from the axis of rotation is reduced is 

 never, comparatively speaking, very large. The interval 

 between by/a and b 2 ja is narrow, and these values alter some- 

 what rapidly with r). Thus experimental observation of these 

 values, if possible, might prove a delicate method of deter- 

 mining Poisson's ratio. 



§ 2b. The variations in the nature of the curve of no 

 radial strain are most conveniently traced by supposing b/a to 

 increase from 0. Figures 1, 2, 3, and 4 show the several 

 types of the curve for the value '25 of rj. The same types 

 occur with other finite values of rj, the only difference being in 

 the critical values of b/a. The curve is of course symmetrical 

 about both axes of the ellipse, so w T e need consider its form 

 only in one quadrant. In each figure OA, OB are the semi- 

 axes of the elliptic quadrant whose perimeter is the thick 

 curve. The thin curve is that of no radial strain ; any part 

 of it lying outside the ellipse is without physical import. 



When b/a is small the curve cats the major axis very near 

 its extremity, and between it and the rim lies a very thin 

 area wherein the radial strain is a compression. This area, 

 though very thin, has a finite thickness, unless ?7 = 0, for 



