R. I^". GwVTUi'.R, specification of t lie elements of str 



ess. 



which appear in the theory of elastic strains, from which 

 it follows that, if 



the expressions given for P, O, R 

 identically. 



I however omitted to notice the great simplification 

 which this latter fact allows us to make in the form of the 

 solution of the equations. 



For it appears that, whatever forms the functions 



Oi, O.,, 0,, may have, we may equate them to 



du dv , dw 



, — , and — 



dx dy dz 



respectively, and then find some allied functions ^ \,^'2,^\, 



such that 



- , dw dv 

 2^' = + — ) etc, 



dy dz 



and therefore such that 



0=^^_2^>' + ^^,etc. 



dy' dydz dz" 



On subtracting these six equations from the corres- 

 ponding expressions for P,Q,R, etc., we shall eliminate the 

 functions 9,, O., O3, and alter the values of the corres- 

 ponding functions ^j, ^., , ^,. 



But as all the functions are arbitrary functions, this 

 amounts to the statement that if we equate each of the 

 functions 8,, O.,, G.,, in the values of P,Q,R, to zero, the 

 remaining terms in M',, ^o and ^., alone still constitute 

 a general solution. 



By similar reasoning, we may omit the terms in '^j, 

 •^,, and ^5, and the remaining terms in 0,, 0„ and 9„ 

 alone will constitute the general solution. 



