304 | M. P.S. Girard on Navigable Canals. 
nates of certain points of the negative branch of a logarith- 
mic curve. ae 
From the nature of this law it follows that, continuing to 
draft between the ascending and the descending boats. If 
that limit could ever be attained, the relative height of the 
two levels would change no more, and an indefinite num- 
ber of boats might pass through the lock in both direcaons 
alternately, without producing either a loss or gain of wa- 
ter fo either level. 
This leads us to remark that, in all cases where we caf 
raise a portion of water froma lower to a higher ‘level, it 
is proper to profit of this faculty as far as we can dispose 
of it to advantage—for we raise so much the less as there 
through a single lock, because those consequences are s!0” 
fall of the lock which terminates it, but also on the 
tent of all the levels, and the fall of all the locks situate 
above the one in question. 
In general, the rise of water in any given level, the 
length of that level, and the fall of the lock which term! 
hates it, may be considered as the three co-ordinates of ® 
curved surface, so that from the equation of that surface: 
the value of one of these three variable quantities May 
‘mmediately determined, when the other two quantitie 
are known. 
