M. P. S. Girard on Navigable Canals. S0j5 



Whatever may be the rise of water in each of the consec- 

 utive levels of a. navigable canal, it is evident that the whole 

 body of water which constitutes this augmentation, and is 

 spread throughout the extent of them all, is taken from the 

 lower level, or rather, from the river in which the canal ter- 

 minates. 



If, by the effect of a first double passage through all the 

 locks of a canal, the surfaces of its different levels become 

 elevated, the primitive falls of its locks will be altered, 

 and we must calculate, assuming the falls as thus modified, 

 what will be the effect of a second double passage ; and so 

 of a third, a fourth &;c. whence we see that after a certain 

 number of passages of boats the rise of water on any given 

 level will depend not only on the rise of water on all the 

 levels above the one under consideration ; but also on the 

 number of double passages which shall already have taken 

 place. So that the expression of the rise on any given 

 level, becomes so much the more complicated as that level 

 is farther removed from the reservoir of the summit level, 

 and as the number of boats which have already passed be- 

 comes more considerable. 



But all this supposes that the levels thus raised, preserve 

 all the water they receive, while in reality that which is 

 Raised is only destined to replace , in whole or in part, that 

 portion which is lost by absorption or evaporation ; and as 

 the amount of these losses varies according to the nature 

 of the ground where the canal is made, and according to 

 the extent of its levels, it follows that the rise of water on 

 each level should be made to vary to suit the permeability 

 of the ground, or such other considerations as experience 

 may prove to be necessary. 



Now Ihe most simple, as well as the most natural suppo- 

 sition that can be made, is that of homogeneity in the na- 

 ture of the ground throughout the whole length of the ca- 

 nal, in which case the chances of loss would be equal in ev- 

 ery part ; and it is evident that, in this case, it would be ne- 

 cessary that each double passage should raise the 

 water in each level equally, or, which comes to the same 

 thing, that the water raised from the lower level should be 

 divided among the higher levels in proportion to their re- 

 spective lengths. 



Our formulae, applied to this particular case, shew that 

 the same relation exists between the length of a level and 



Vol. VII.— No. 2. 39 



