302 M. P. 8. Girard on Navigable Canals. 
* We shall have the particular case of a number of contigu- 
ous locks (sas accolés) in making B=S; in which ease the 
general expression of the fall x(n) becomes 
x(ny=D —a(n+1); ‘ se 
by means of which we may determine the height of the . 
fall of any one of a series of contiguous locks, in order that 
the level of water may be raised in each of them, by the 
descent of a boat, by a constant quantity =a. 
It is the usual practice to give to each basin of a series of 
locks, precisely the dimensions necessary to contain a sin- 
gle boat. This is also what we have hitherto supposed ; 
but if, instead of representing the draft of water of a de- . 
scending boat, the quantit D represents the difference of 
draft between the poe and the ascending boats, it 
will then be necessary that two boats going in opposite ; i- 
rections. can meet in each of the basins, and as it will al- 
so be necessary that they should pass each other in the ba- 
_ sins in which they meet, it will be proper to augment the 
dimensions of the basins sufficiently to facilitate their ope 
rations, which may be done by giving to the basin the ca 
pacity of three boats; we shall then have B=38S, and the 
equation : 
x(n) =D —a(3n+1) 
will express the fall of any one of the sluices in a series of 
contiguous locks, according to the numerical ran! it occu- 
pies in that series. : 
We shall extend no farther the application of our, formule 
to particular cases, but shall content ourselves with remark- 
ing that the same equations by which we express the rise 
of water in the levels of a canal, give also the fall or lower- 
ing of the same levels when the* quantity D-—z is negative, 
that is to say, when the fall of the lock is greater than the 
difference of draft of water between the boats which a5 
and those which descend through those locks. 
In this case we find 
, B 7 E 
u = rer ngs e . 
BS" (B.+S) 
, 
Bu +Bu 
) poe 3 ( ia AR Site Whe 
(x a“ - B,+5 Fr. 
