306 M. P: 8. Girard on Navigable Canals. 
the. fall of the lock which terminates that level, as between 
the co-ordinates of the right line. ; 
is 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 te 
augment all the levels of a canal, was always taken from 
its lower level, or reservoir ; we may now suppose chat 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. _ Gi ¥ 
_ 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 
alock, 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. dow®- 
wards: disposing them according to this law, and keep!?8 
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 seriesiof locks, will occasion no loss of water, as is thé 
case when the falls of the locks are greater. It may A 
be asserted that the Joss of water at the locks is less | 
