18.91.] Mr Chree, On thin rotating isotropic disks. 211 



On the maximum stress-difference theory 



1 — rj a' 



>>'= 2 ( 1+ ^) <42) - 



On the greatest strain theory 



»>„-2- (1 _ v)(s + v) (43). 



When (a' /a) 2 is negligible, or there is only a very small axial hole, 

 these give respectively 



&)j/&) 2 = a/2 for all values of in, 



a>Jta z = J2/(1 — rf), or nearly 1*633 for 77 = -25. 



The former result was given by Professor Ewing in Nature, and 

 he also directed attention to the great diminution it represents 

 in the strength of a disk due to the removal of a small axial 

 core. The effect is even more striking on the greatest strain 

 theory for ordinary values of rj. 



Since the striking character of this result may arouse doubts 

 in some minds as to the validity of any investigation which leads 

 to it, I would point out that it is not an isolated fact. The 

 removal of a central spherical core of any radius however small 

 from a sphere rotating about a diameter has, as I have shown 

 in a previous paper 1 , a precisely similar effect, increasing very 

 largely the greatest values both of the stress-difference and great- 

 est strain. The same result also follows the removal of a thin 

 axial core from a rotating right circular cylinder whose length 

 is constrained to remain constant 2 . 



In discussing the nature of the strains and stresses we may 

 for most purposes leave out of account in the first place terms of 

 order I 2 or V, regarding them in the light of small corrections to 

 the principal terms. 



According to the Maxwell solution, every originally plane 

 section parallel to the faces of a complete or annular disk ap- 

 proaches at every point the central section, z = 0, and assumes 

 the form of a paraboloid of revolution about the axis of rotation. 

 In this respect the phenomena are precisely similar to those 

 presented by a flat oblate spheroid rotating about its axis of 

 symmetry 3 . 



The latus rectum of the paraboloid into which is transformed 



1 Transaction*, Vol. xiv. pp. 467—83. See Tables IV. and VIII. and their 

 discussion. 



2 Transactions, Vol. xiv. p. 339. 



3 Transactions, Vol. xv. pp. 10 — 13. 



VOL. VII. PT. IV. 17 



