2 R. F. GWYTHER, Specification of tJic chifients of stress. 



Cartcsiati Coordinates. 



The equations of stress, with the usual notation, are 



dP dU dT ^ 

 dx dy dz 



dx dy dz 



dx dy dz 



where X, V, Z are to inchide ' inertia terms ' as well as 

 forces. 



I shall assume that we may write 



^_d<\, dN _dM 

 dx dy dz 



V= ^^' 4- '^^ - '^^^ 



dy dz dx 



^ dd) dM dL , V 



Z=-l + - — (2). 



dz dx dy ^ ' 



The equations (i) can, of course, only have solutions 

 which are to some extent indefinite, but the fonn of the 

 solutions may be quite definite, and it is proposed to 

 find these formal solutions or specifications of stress. 



We shall, in the first place, find particular integrals^ 

 and then the complementary finctionSy to use the termin- 

 ology of ordinary differential equations. 



When the values of X, Y and Z are given in any 

 special case, the particular integrals will probably be 

 readily found. But for the purpose of what follows later, 

 it will be well to give a general method of procedure, 

 although that method need not be followed in each special 

 case. 



