120 M. Girard on Navigable Canais. 
whatever be the expense of water, and the draft of the as- 
cending and the descending boats. 
But we have already concluded from the equation which 
expresses the relation between these quantities, that if the 
lift of the lock be made equal to the difference in the 
drafts of water of the two boats, the expense of water from 
the upper level is null. 
In this particular case, the expense of active force neces- 
sary for the passage of the two boats is therefore as it were 
repaid by the descending boat, in the same manner as if 
this boat, in descending on an inclined plane, drew the oth- 
er boat up along the plane, at the same time, by means of 
a chain passing over a pulley. In the same manner, when 
the lift of the lock is less than the difference of draft of wa- 
ter of the two boats, we have seen that a certain volume of 
water was raised from the lower to the upper lavel ; in this 
case the active force of the descending boat is not only em- 
ployed in raising the other boat but in raising at the same 
time a certain quantity of water, precisely as if the two 
boats were still connected by the chain and moved on an in- 
clined plane, and a certain volume of water was added to 
the weight of the lightest boat. 
We must also observe that the quantity of active force 
expended by the descending boat to raise a mass of water 
into the higher level, is not deducted from the useful effect 
of the lock considered as an ordinary machine ; for the de- 
scent of the boat, by means of the lock is itself a part of the 
effect which we expect from it. Hydraulic locks then, 
classed among machines proper for the transmission of 
movement, offer this singular advantage, to the exclusion 
of all other machines, that the expenditure of active force 
necessary to the production of movement is in itself a por- 
tion of the useful effect which the machine is intended to 
produce. 
To obtain this advantage, it is true, the following condi- 
tions are necessary ; 1st. That the draft of water of the boats 
which descend should be greater than that of the boats which 
ascend; 2ndly, That the rise and fall of the locks should 
in no case exceed that difference of draft of water. 
It is evident that the last condition can always be fulfilled 
whenever the first shall exist : and, although in determin- 
ing the quantity of water necessary to supply a canal, it has 
