Theory of the Contact of Elastic Bodies. 325 



right of the figures show the limiting directions of pi, 

 making an angle with the normal of 28° 21' instead of 30°, 

 56° 3' instead of 60°. 



K«. 3. 



0=60 



>0 



.50° 



40° 

 .30* 

 20° 



a 



10 



Fig. 4 shows the state of affairs on the boundary (supposed 

 to have only small curvature). Inside the area of contact 

 the three principal pressures are of comparable magnitudes. 

 Outside this area the normal pressure of course vanishes, 

 while the tension across the radius is equal in magnitude to 

 the pressure across it. This is on account of the vanishing 

 of the dilatation and the reduction of the strain and stress to 

 pure shears. On the general theory the expression for the 

 dilatation is 



~dcj> 



2tt(A. + ^). 



which obviously vanishes on the plane of the supposed 



attracting distribution. 



