M. P. S. Girard on Kavigahle 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. 



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 formulae to which we have arrived, contain, proper- 

 ly speaking, the whole theory of canals of artificial naviga- 

 tion, and we may comprehend in a single formula the two ca- 

 sesofthe rise and the depression of the levels, by affecting by 

 the double sign -f 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 

 a certain point, beyond which the navigation of the canal 

 becomes 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. 



If we have been enabled to develope them with sufficient 

 clearness, we are indebted for it to the application we have 

 made of Mathematical analysis to a question which had 

 hitherto appeared not be out of its reach ; and in this we 

 feelieve 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 

 calculated than navigable canals, t® ameliorate the cou4i- 



