M. P.S. Girard on Navigable Canals, 307 
elsewhere on the canal, since these parts are generally con- 
structed with greater care and solidity, and no filtration is 
to be apprehended through the ground where they are situ- 
ated si 
ea. . 
It is nevertheless proper to observe that, to affect the 
double passages of a multiplicate lock, as it is done in a 
simple lock, each basin of that lock must be of sufficient 
capacity to contain two boats ; this condition may gener- 
ally be fulfilled by giving to the basins the breadth of the 
other parts of the canal. Thus, exercising double func- 
tions, the basins of a multiplicate lock considered as basins 
should have only the length of a boat, whereas, considered 
as levels, they should preserve the same breadth as the oth- 
er parts of the canal, of which they form a part. 
The formule to which we have arrived, contain, proper- 
ly speaking, the whole theory of canals of artificial naviga- 
ion, and we may comprehend in asingle formula the two ca- 
ses of the rise and the depression of the levels, by affecting by 
the double sign + the difference of the draft of water between 
the ascending and the descending boats, and the variable 
falls of the locks. From this formula we arrive immedi- 
ately at the following conclusion, which besides is self evi- 
dent : that when the water is accumulating on the higher 
levels, the quantity of water contained on those levels may 
be augmented in proportion as the navigation becomes 
more active : whilst on the contrary, when the levels are 
depressing, that quantity of water necessarily diminishes to 
acertain point, beyord which the navigation of the canal 
comes impracticable. This conclusion reduced to this 
summary expression, shows all the advantages that may be 
derived from the application in practice, of the theoretical 
Principles, which form the object of this memoir. 
have been enabled to develope them with sufficient 
clearness, we are indebted for it to the application we have 
matle of Mathematical analysis to a question which had 
hitherto appeared not be out of its reach; and in this we 
believe we have rendered a real service to the cause of 
science ; for so perfect an instrument as analysis should al- 
ways be employed when it is question of improving any 
“Useful invention; and, in our days no invention is better 
Wiculated than navigable canals, te ameliorate the condi- 
