4 R. F. GwvTHKK, Specijicatioii of the clciitcuts of stress. 



A justification ma)* be founded on the formal solution 

 of the moie general statical equations 



dp^ dp, dp,, _Q 

 dx dy dz 



with two similar equations. 



J'Vom these we obtain in the most general case 



_ di\)^ _ d(\>^ 



^'- dx "^ dz 



d<p, dd^ . 

 dx dy 



with two other sets of three equations each. 



Now making /,„=/>,,^= 6^, etc., we obtain the equa- 

 tions of which the general solution is sought. 



Accordingly^ we get 



dx dy dz 

 dx dy dz 



dx dy ' dz 



Without going through the steps to obtain the conse- 

 quent values of/, , S, T, and U, it is clear that the 



values will depend on the second differential coefficients 

 of some arbitrary/ functions, and, if this is the case, the 

 values must be tho.se which have already been found, and 

 accordingly the result must be general. 



The fact that by the equality of /^, and /^,„ etc., the 

 number of arbitrary functions in the solution of the equa- 

 tions can be reduced to t/i?-ee is, 1 think, established, but 

 on the physical interpretation of the reduction I have not 

 formed a definite opinion. 



