288 M. P. S. Girard on Mivigable Canals. 



adoption. This is an additional reason for us to lose no 

 time in developing the principles more minutely, and 

 pointing out some new applications of it. 



1 preserve for the same quantities, the denominations 

 which I adopted in mj first memoir. 



Thus, considering only two contiguous levels of the same 

 canal, I make the lift of the lock which separates 

 them, . - . - _ =x 



The horizontal section of the lock and of the boats 

 which navigate the canal, - - . =S 



The draft of water of the ascenoing boats, - =t, 



The draft of water of the descending boats, - =t„ 



And the expenditure of water from the upper level, 

 occasioned by the passage of two boats in succession, ==%. 



The relation existing between these quantities is, as- we 

 have seen, expressed by the equation : 



y=:x-{t„-t), 



which belongs to a right line, easy to construct. 



We have already remarked that in all artificial canals^ 

 three causes, essentially different from each other, concur 

 to occasion an expenditure of the water necessary to its 

 existence : 



Evaporation, filtration, and the passage of the locks. 



The first cause is entirely out of our reach, and is more 

 or less active according to climates and seasons. 



The second, purely accidental, depends on localities, and 

 may, with greater or less efTorts, be more and more attenu- 

 ated by art. 



The third and lasi belongs entirely to theory: it is of this 

 that we have undertaken the examination. 



The general equation, 



y=x-{t,-t) 

 supposes that two boats, one descending and the other as- 

 cending, traverse, one after the other, the lock at which 

 thev meet : now. if we admit that the difference t,, — t^ be 

 positive, we may substitute for it the draft of water D of a 

 single boat which should descend, and then the above equa- 

 tion would become 



y = x—Y). 



It would on the contrary, become 

 y=x-\-Y) 

 in the supposition \haXt„ — t were negative, in which case 



