236 Mr. R. F. Gwyther on the Equations for 



stressed body not only natural forces, but also reactions 

 against acceleration in case the body is in motion. Whatever 

 the forces may be, it will always be possible to express their 



components as p-^— , p-^-- , and p s - respectively. 



Cartesian Coordinate System. 



We shall have, firstly, the Mechanical Stress Equations^ 

 namely, 



BU BQ BS BV 2 .. 

 B^ + 3y + 37 + ' , B7 =0 ' 



BT BS BR , BV 3 



The six conditional Stress Equations, obtained by the 

 method I have indicated, are * : — 



V'P+ ^ m+n) V 2 (P + Q + R) 

 n(6m— n) 



n(5m — n) ' 



-£-.(£*S)™*»>+*3£-* 



or 



n{6m — n) 



and 



V2T +^slk (P+Q+B)+ ''BlBl (Vl+V3) = ' 

 V 2 U+^-^ ..(P + q + r) +/9 3!_(v 1 + v,) = 0.( 7 ) 



* Manchester Memoirs, " Specification of Stress/' Part iv. (continued)* 

 vol. lx. no. 14 (1916). 



