M. Girard on Navigable Canals. iii 
when the number of boats ascending, is equal to the num- 
ber of boats which descend ; this supposition being more 
simple than any other, it is that to which we shall confine 
ourselves. 
Now it is evident that if any number n of boats pass the 
lock one by one, ascending and descending alternately, the 
condition of no expense of water ot be expressed by 
: eb 
If, on the contrary, the same cighiahae of boats go in two 
convoys, the same condition will be phigh by 
fa a 
oe 
Which neue that the it of ‘ths lock will seligges s0 
much nearer a a 
oa * 
as the number n of boats become greater; whence it follows 
that the two quantities 
T’— 
T’-T 
an 5} 
are the two ini between which the lift of the locks of a 
canal should be confined, i in order that the expenditure of 
water from bon upper level should be null, in whatever num- 
ber of convoys the given number of boats: igs as- 
cend and descend. 
If therefore, we give to the locks a lift which is an. ati 
metical mean proportional between the heights which ren- 
r the me null in the two extreme cases we enste 
: eee 9 make pe s(t"—T) 
ha — 6 set 9 iin Wiis 3 
this hate ae be’ most Hel to full the aie which 
we have proposed, of rendering the expense of er null, or 
nearly so, on the passage of any Sect of toes distri- 
buted in ‘convoys as chance may 
This lift is, as we see, 2 of that which ae be proper if 
the boats alternated one by one at the passage of each lock : 
this last order of passing is the one general y adopted, as far 
as practicable, in navigable canals, and the preceding analy- 
