Pa 
r. 
288 M. P. S. Girard on Navigable 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. 
I] preserve for the same nrg the denominations 
which I adopted in my first mem 
Thus, considering only two ae Oe levels of the same 
canal, I make the ag of the lock which oe 
them, - 
The horizontal iinction’ of the —_ ond of the boats 
which navigate the can al, - = 
The draft of water of the setanding boats ts, ~ aay 
The draft of water of the descending boats, - =, 
And the expenditure of water from the upper level, 
occasioned by the passage of two boats in succession, =Sy. 
The relation existing between og quantities is, as we 
have seen, expressed by the equatio 
=r —(t,,— re 
which belongs to a right line, easy to co 
We have already remarked that in ait "artificial canals, 
three causes, essentially different from each other, coneur 
to —— an expenditure of the water necessary to its 
on Evaporation; filtration, and the passage of the locks. 
The first cause is entirely out of our srstarae = is more 
or less active according to climates and se: 
The second, purely accidental, Sipaada 0 on n localities, and 
may, with a or less efforts; be more and more attenv- 
ated by art 
The third and last belongs entirely to er it is of this 
that we have undertaken the examinati 
general equation, 
=r —(t,—t,) | 
supposes that two wie de one descending and the other as 
cending, traverse, one after the other, the lock at which 
they meet : now, if we admit that the difference #,,—!, 
positive, we may substitute for it the draft of water 'D of a. 
single boat which agg descend, and then the above equ 
tion would beco 
y=or—D. 
It would onthe contrary, become 
¥ y=r+D ; 
in the supposition that ¢,,—t were negative, in which cas¢ 
