50 



Ar*. 7. — K. Terazawa : 



for ré a. lu the annexed diagram the approximate course of tlie 

 vertical displacement is shown in proper scale. 



§37. By a similar process the distribution of stress can l>e 

 found. Here we shall calculate the stress at the boundary. It 

 ma}^ be shown that 



/ 



"^ sin ka — ka cos ka 



.2^2 



k'a 



J^[kr)dk = 





(lOGj 



and, therefore, as tlie expressions for the stress-components at the 

 surface we liave 





H/x 



27r.7 + /^) r^ 

 27r(/ + //) ■ r 



(107) 



(.a)o = 0, (H-)(i = 

 for r ^ a, and 



2 

 3// 



)(108) 



27r«- 



1-4^* 



a' 



{^r\ = 0, 



for r £ a. 



The result of this example may be looked upon as a special 

 case of what has been discussed by H. Hertz in his papers'^ 

 concerning the contact of two elastic bodies. He assumed the area 

 on which pressure acts to be an ellipse instead of a circle. If we 

 put b = a in his results, we get exactly the same formulae for the 

 pressure and for the vertical displacement. And therefore this 



1) Oesammelte Werke, I, p. 154 — and p. 175. 



