108 M. Girard on Navigable Canats. 
der to determine the lift proper to be given to the locks to 
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 immediate appli- 
cation of certain statistical knowledge, which, at first view, . 
appears to have but a very remote connection with the art 
of pr aed navigable canals. 
“his succession of boats which meet at each lock, and 
which are alternately 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 th: ang a the ascending boats shall 
follow z oaeh other im ately, and all the seeing boats 
hour of the da 
follow ea “ge 9 ate different 
The ascension of the first boat will require the deaeciliie- 
tion of a quantity of water = Sz, into the lock, to raise it to 
a level with the upper basin 
The boat in leaving oe. 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 San) 
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 = $(x-+?f’, ) must be drawn from thence. The as- 
cension of the third boat will occasion an expense of water 
= S(a-+t,). Therefore, the number of boats in the as- 
ee convoy being represented by n’, there will have 
n drawn from the upper kava: a volume of water sil 
sente d by 
ee. S(n' r+t +t, Agek, &e.) 
“Lets : nowy examine the operation of the 2 ascending con- 
