M. P. S. Girdrd on Jstavigable Canals, 289 



D would express the draft of water of a single ascending 

 boat ; thus we have 



for the general expression of the expenditure of water from 

 an upper level of a lock, when a boat whose draft of wa^ 

 ter is expressed by D passes that lock in ascending or in 

 descending. 



It is often difficult and expensive to accumulate on the 

 summit level of a canal, a volume ofwater sufficient to sup- 

 ply the deficiency occasioned by evaporation, filtration and 

 the passage of the locks ; whilst its lower level, almost al- 

 ways confounded with a river, naturally contains a greater 

 or less quantity of superabundant water. The essential ob- 

 ject of the theory should therefore be to seek the means, if 

 not of raising from the lower to the summit level, a quantity 

 ofwater sufficient for the purposes of navigation, at ie;ist 

 enough to supply the losses occasioned by evaporation and 

 filtration throughout the whole length of the canal. We 

 repeat that the only circumstances which can render the 

 elevation of water practicable are those, where the weight 

 of the productions which descend is greater than the weight 

 of the articles which ascend the locks; we have therefore 

 only to treat the case comprised in the equation 

 y=x~D. 

 Now as we are always at liberty to reduce the lift x suf- 

 ficiently to make it less than the draft of the descending 

 boats, it follows that we may always render the expendi- 

 ture y negative, or, in other words, raise a certain quan- 

 tity ofwater from the lower to the upper level of the lock* 



In this hypothesis, the volume of water, gained to the up- 

 per level, will evidently be S (D—x.) and if we designate 

 by B the superficies of this level, it is also evident that the 

 primitive height of water contained in the upper level will 

 be augmented by the quantity 



S(D-x) 

 B 

 So long as the surface B of the upper level is very large 

 when compared to the superficies S of the basin of the lock, 

 or which is the same thing, to the horizontal section of the 

 boats, this augmentation of the height of water on the sum- 

 mit level will be insensible, so that if a second boat should 

 follow the first in its descent through the lock, it would find 

 the water at the same height as the first. It would there- 

 VoL. VII.— No. 2. 37 



