528 PROFESSOR KELLAND ON THE THEORY OF WAVES. 



Let K represent the ai'ea of the section of the fluid at the point x, z/, z. 

 Then K«=(E + i^a;)(a + ^5.), 



dt dt 



Now, ]\ is a function of the height s ; therefore, s is a function of K. 

 Let « =/K 



ds ., „ rfK 



Tt =^^-1T 



a dt 



Now the moving force, on the mass of which the thickness is « 



where </>y=« is the equation to the generating curve of the boundary of the 

 section. 



And P=9Q{?-y)—^9^-', 



dp ds du 



-i- = a P — - — p u . 



dx dx * dx 



moving force A , C'^^ j I 1 A 



ds 



7^s < ds d II ) , 



Let /<py dy = ^y 



fy<py(iy=fy 



moving force ^ _ ( g JL - u^-^\ a¥ (s) 

 g y dz dx) ^^ 



(\ .\ ds Tu ds ,, 



I 



