32 Canon Moseley on the steady Flow of a Liquid, 



The whole work of the resistance of this filament is represented 

 therefore by 



( -7- J and \-f) being the partial differential coefficients of v with 



respect to x and y ; or, passing to the limit, the work of the re- 

 sistance of this filament is represented by 



Therefore the aggregate work U4 of the resistances of all the fila- 

 ments is represented by 



If h represent the actual head of liquid in the reservoir, then, 

 supposing the channel to be horizontal, 



\]=^wh\\vdx dy. 



The effect of the resistance whose work is Ug, however, is prac- 

 tically to diminish the head of liquid h. 



Let - represent, as before, this diminished head; then, if we 

 7 



substitute - for h in the above equation, we may neglect Ug in 



the preceding equation. If moreover we suppose the liquid 

 after leaving the reservoir to descend through an inclined chan- 

 nel whose length is I, we must substitute 



( - +Zsinz I for - : 

 Vi / y 



.-. U = w( — |-/smMJ \vdwdy, 

 Ui= half the vis viva of the discharge per unit of time 



Hence, neglecting Ug, we have by equation (2), 

 w(- H-/sinzlj \vdxdy=^ \ \i^dx dy + V^ 



