of Mixed Solutions. 281 



where a is a quantity containing some linear relation of the form 



(Pn- 

 a^h ,- -*, j9 ^ 2. We may at once remark that if the value for 



8 (Aa?) is put into (14) and we go to the limit A^ = 0, we find that 

 the term depending on S (A^) disappears. 



From equation (11) we get 



Po being the pressure at the bounding surface is not altered by 

 the variation. Putting these expressions into (14a) and using 

 (14c) and (15) 



where etc. is of the form a^Ax'i + a^Aw'^^^ + ... q^ 2. 

 From equation (5) 



\dxJo \dx/o \dxjQ o\dx/o 



Putting the expressions for Sooo and S ("j-") ^^^^ i^^)' ^^^ 

 using (146) the equilibrium conditions take the form 



or letting Ax converge towards zero 



We drop the index (0), and remember that all values refer to 

 the same point 



8p =iMs8n„ 







These values put into (17) give 



^ ^ s=o\ ' dx i=Q dus dx) 



19—2 



