108 M. Girard on Navigable Canals. 
der to determine the lift proper to be given to the locks te 
fulfil one of these three conditions, it is necessary to know, 
not only the number of boats which will navigate a canal, 
but the nature and quantity of importations and exportations, 
which will take place on that canal; thus the improvement 
of this species of navigation requires the iiminisdiats appli- 
cation of certain statistical knowledge, which, at first view, 
appears to have but a very remote connection with the art 
of projecting navigable canals. 
This succession of boats which meet at each lock, and 
which arealternately raised and lowered, by taking advantage 
of the state in which the lock is left by the ascension or 
the descent immediately preceding, is evidently the best fit- 
ted for economizing in the expenditure of water; but 
the movement of boats on a canal may take place in a dif- 
ferent order ; it may sometimes happen that, for certain 
reasons, it becomes necessary to pass the boats in files, or 
convoys, in such manner that all the ascending boats shall 
follow each other immediately, and all the descending boats 
shall also follow each other at a different hour of the day. 
The ascension of the first boat will require the introduc- 
tion of a quantity of water = Sz, into the lock, to raise it to 
a level with the upper basin. 
The boat im leaving the lock is replaced by a volume of 
water = St’. 
Thus the passage of the first boat of the ascending con- 
voy, from the lower to the upper level of the lock, has oc 
casioned the expence of a volume of water = S (x+t',.) 
The second boat finds the lock filled, and the first opera- 
tion consists therefore in letting off the water which it con- 
tains, until its surface comes on a level with the lower basin, 
when the lower lock-gate is opened and the boat introduced 
into the lock, and, to raise it to the upper level a volume of 
water = $ (w+?) must be drawn from thence. The as- 
cension n of the third boat will occasion an expense of water 
= $ (v+',). Therefore, the number of boats in the as- 
cending convoy being represented by n’, there will have 
been drawn from the upper level a volume of water repre- 
sented by 
S (n’ ett +t, +ty+, &c.) 
Let us now exariine the operation of the ascending con- 
voy. 
