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



the fall of the lock which terminates that level, as between 

 the co-ordinates of the ri^ht line. 



This hypothesis of an equal rise on all the levels of a 

 canal, besides the advantage it offers of replacing the wa- 

 ter lost by absorption in homogeneous ground, possesses also 

 that of maintaining the falls at their primitive height, so 

 that the succeeding double passages, whatever interval of 

 time elapses between them, will uniformly produce an ele- 

 vation of water, and this independently of the greater or 

 less degree of activity in the navigation. 



We have said that the volume of water which served t© 

 augment all the levels of a canal, wc'^ always taken from 

 its lower level, or reservoir ; we may now suppose that this 

 volume passes wholly into the highest reservoir, or summit 

 level, which will necessarily be the case if each of the lev- 

 els comprised between the two extremes are neither raised 

 nor depressed, that is, if they gain by the double passage 

 through their lower lock, what they lose by the double pas- 

 sage through their upper lock : we may satisfy this condi- 

 tion in supposing the rise null in all the intermediate locks ; 

 in this case also, the equation which expresses the relation 

 between the superficies of these levels and the fall of their 

 lower locks, is that of a right line. 



It may be advantageous to adopt this principle whenev- 

 er the levels contiguous to the culminating point, are those 

 which are exposed to the greatest losses, as is generally the 

 case. The water raised to the summit level may then be 

 applied to repair those losses, without descending to the 

 lower levels which suffer less. 



Retaining the same hypothesis of an equal rise on all 

 the levels of a canal, I examine the case, where several 

 consecutive levels are each equal in extent to the basin of 

 a lock. And I find, by the comparison of the falls of the 

 successive locks, in a series of adjoining locks, that they 

 diminish in an arithmetical ratio from the highest down- 

 wards : disposing them according to this law, and keeping 

 the connected locks filled with water to the same depth as 

 in the canal, which is always easily effected when the falls 

 of the locks are small, the passage of the boats through such 

 a series of locks, will occasion no loss of water, as is the 

 case when the falls of the locks are greater. It may even 

 be asserted that the loss of water at the locks is less than 



