Theory of the Contact of Elastic Bodies. 



323 



and the pressure perpendicular to this plane (" hoop-pres- 

 sure ") is p 3 . 



Along the normal (fig. 1) the transverse pressure begins 

 with five-sixths of the magnitude o£ the normal pressure ; it 

 decreases rapidly and changes to a tension at distance 1*67 X a. 

 The tension beyond this distance is too small to be shown on 

 the diagram. 



Fiir. 1. 



It is easy to deduce these results from the general theory. 

 It can be shown that, on the axis of z, we have 



r 02 oz 



(The same expression represents the (zz) pressure at any 

 point ; it is independent of the elastic constants of the body.) 

 When there is symmetry round the axis 



4tt/?s 



,p-d +2 .) 



3* 



Be 



It follows that, for z = 0, ihllh = 0" + i • 



Y2 



