302 M. P. S. Girard on Jnavigahlt Canals. 



We shall have the particular case of a number of contigu- 

 ous locks (sas accoies) in making B=S ; in which case the 

 general expression of the fall x(n) becomes 



a;(n) = D-a(n+l); 

 by means of which we may determine the height of the 

 fall of any one of a series of contiguous locks, m 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- 

 scendina; boat, the quantity D represents the difference of 

 draft between the descending and the ascending boats, it 

 will then be necessary that two boats going in opposite di- 

 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 

 dimen-ioos 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=3S, and the 

 equation 



will express the fall of any one of the sluices in a series of 

 coHti^'-uous locks, according to the numerical rank it occu- 

 pies in that series. 



We shall extend no farther the application of our/ormw/c^ 

 to particular cases, but shall content ourselves with remark- 

 ine that the same equations by which we express the rise 

 of water in the levels of a canal, give also the fall or lower- 

 in°- of th& same levels when the quantity B -x 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 ascend 

 and those which descend through those locks. 



In this case we find 



«' = _— (x'-D) 



B7+S^ " (B.„+S) 



