528 PROFESSOR KELLAND ON THE THEORY OF WAVES. 



Let K represent the area of the section of the fluid at the point x, z/, z. 

 Then K„=(K.i^a,)(„4;5.), 



= K-- + a- 



dt dt 



News K is a function of the height s ; therefore, s is a function of K. 



Let 5=/K 



ds _ ^ dYi 



Tt ~-' ' Tt 



a dt 



NoAv the moving force, on the mass of which the thickness is a 



ds 



where 0^=^ is the equation to the generating curve of the boundary of the 

 section. 



And P=9g (s-y)--gu% 



dp _ ds du 



dx dx ^ dx 



moving force A , C'^'^ i / 1 oX 



dt 



^j 



7^s , f ds du 1 , 



/ds . 1 . 



'^Tx'' dy[gs-y--^u'^\(py. 



Let f(pydy = Fy 



fy^ydy =fy 



moving force _ _ / o?5 _ du \ tji / a 

 p V^ ^dx)"' ^^ 



(1 ,\ c?« _,, ds ., 



^'-2n''d^-^'-"'d^'^' 



