RECIPROCAL FIGURES, FRAMES, 



Then the equations of equilibrium of an element of the body are, by 697 

 of that work, 



dP dU . dT 



dx dy dz 



JJl + dS + dR 

 dx dy dz 



.(1). 



If 



we assume three functions A, B, C, such that 

 <I i/<l:' dzdx' 



d*JB TT _ d*C 

 </:'/./ ' dxdy 



v <IV dV dV 



and put A = 5^ = dy~> Z= ~dz' J 



then a sufficiently general solution of the equations of equilibrium is gi 

 putting 



(2), 



given by 



p=^ 



dz* + dy* 



XA_ 

 dz* 



.(3). 



dy* dx* 



I am not aware of any method of finding other relations between the com- 

 ponents of stress without making further assumptions. The most natural assump- 

 tion to make is that the stress arises from elasticity in the body. I shall 

 confine myself to the case of an isotropic body, such that it can be deprived 

 of all stress and strain by a removal of the applied forces. In this case, if 

 y are the components of displacement, and n the coefficient of rigidity, 



a, 



the equations of tangential elasticity are, by equation (6), 670 and 694 of 

 Thomson and Tait, 



(I 



c//8 dy I 1 



j H -- j O ~~ 



dz dy n n 



1 d*A 



-- i - }~ 



n dydz 



.(4). 



