M. Girard on Navigable Canals. 119 
sjantly, whatever be the degree of activity of navigation, 
the lift of each lock must be proportioned to the sum of the 
volumes of water furnished by the summit level and by all 
the collateral féeders above the lock in question, after de- 
ducting therefrom the sum of the losses by evaporation and 
filtration throughout the same extent; now as the quanti- 
ties of water acquired and lost in a given jength of canal, 
are exceedingly variable according to the localities (and the 
seasons ?) it follows that the equality of lift recommended to 
be established in all the locks of a canal, is reduced toa 
simple rule of practice that is not justified by any theory, 
and which can find no reasonable application except under 
a concurrence of circumstances rarely to be met with. 
We have just seen according to what laws the lifts of the 
locks of a navigable canal should be made to vary in a given 
case, abstracting, as we have done, the consideration of a 
difference in the draft of water of the boats. It would be 
easy, taking that difference into account, to deduce from 
our formule the law of variability of those lifts in similar 
circumstances. The simplicity of these calculations ren- 
ders their application here unnecessary. 
The quantity of dynamical action, or active force expend- 
ed in mancevreing the locks, has not yet fixed the attention 
of any engineer. I shall now proceed to demonstrate in 
what manner the consideration of this expense may lead to 
the improvement of navigable canals. 
. I shall begin by recalling this incontestable principle: that 
active forces and dynamical actions, from whatever source 
derived, and in whatever manner they are disposed of, can 
always represent the useful effect of some machine. The 
economy of these forces, by the adoption of appropriate 
means, will therefore leave a greater portion of them free to 
be disposed of; for example, if we regulate in a proper 
manner the rise and fall of the locks of a navigable canal, 
the quantity of active force economised may be applied to 
the use of mills on the banks of the canal, or to any other 
useful purpose. 
In the second place, I shall recal this mrineiplie, tnat the 
expense of active force, indispensably incurred at the pas- 
sage of a lock, in raising one boat and lowering anotiier, is 
always proportionate to the square of the lift ef such lock, 
