M. Girard on Navigable Canals. 107 
It follows from this equation that the expense of water, 
y, will be positive, null or negative, according as we have 
Thus it appears that the expense of water from any lev- 
el may not only be diminished at pleasure, but that it may 
‘be rendered null, and that a certain quantity of water may 
even be raised from a lower to an upper contiguous basin. 
If two other boats successively pass the same lock, and if 
their respective drafts of water be represented as follows, Sg 
for the ascending boat, and ¢,, for the descending one, the 
expense of water occasioned ‘by this double passage will be 
reprepenses es 
y’: = (tiy — t,,) 
In the same. MS ag ke ag MDT aR 
third double passage 
= @7—(h; — 
The total expense of the upper level of a lock, for any 
number n of double alternate passages will therefore be 
ye ye + &e. =nx—((t, + tiy-+-s-tan) — (+t, 
, +t,+.. stent) ) 
designating by odd numbers ste inte of water of the as- 
cending boats, and by even numbers those of the boats 
which descend. Therefore, a make the sum of the 
drafts of water of the first =T, the sum of those of the lat- 
ter =T”, andthe total expense of water yty jedan 
we shall bien 
Y=nzr —(T’—T). 
i aeecace of waters for any number of double passa- 
ges through the same lock, will therefore be aa toes null or 
negative, eer as we ea 
re. 
Aud 64 the dna at wuardd ie emieibhagh tepresent 
their weight and that of their cargoes, it follows that, in or- 
