324 Prof. W. B. Morton ajtd Mr. L. J. Close on Hertz s 



At a great distance from the origin, <j> approaches the 

 value P/s, and the limiting forms for the pressures become 



27T^i = 3<2'- 2 , 



47r/? 2 =-(l-2o>- 2 , 



so —p 2 /pi approaches ^(1 — 2<r). 



Figs. 2 and 3 show that as the normal is "departed from 

 the hoop-pressure p z becomes the greater of the two sub- 

 ordinate stresses. Along the line = 30° both these stresses 



Fig- 2. 



change to small tensions, p 2 at r = l'56 x a, p 3 at r = l'95 x a. 

 Along = 60° the hoop-stress remains a pressure at all 

 distances ; the other changes to tension at r = l'35 x a. 



The directions of the principal axes of stress and strain 

 are shown by the curve for the angle between p x and the 

 normal. It will be seen that, as the distance from the 

 contact increases, the direction of the chief principal stress 

 approaches that of the radius vector from the origin, but 

 does not tend to coincide with it. The broken lines at the 



