106 M. Girard on Navigable Canals. 
tal section of the lock, and whose height is represented by 
the lift of the lock. 
Furthermore when the boat passes from the lock into the 
basin, its place in the lock is necessarily supplied by a 
quantity of water = St,,equal to the volume of water which 
it displaces, and which flows from the basin into the lock. 
Thus the quantity of water expended to bring things to 
their present state, may be expressed by Sx+St,. 
Let us suppose that, the communication remaining open 
between the upper basin and the lock, another boat is ready 
to descend, the manceuvre is reduced to 
Ist, Introducing the boat into the lock, and shutting the 
upper gate ; 
2d, Emptying the lock until its surface is on a level with 
that of the lower basin; and 
3dly, Opening the lower gate and passing the boat inte 
the lower basin. 
The introduction of the boat from the upper basin into 
the lock has caused a reflux from the lock into that basin, of 
a volume of water = S¢,,, equal to that displaced by the 
boat. 
In letting off the water from the lock to lower its surface 
to a level with that of the lower basin, things are replaced 
in the same state as they were before the ascent of the first 
boat. 
This operation, which we shall denominate a double pas- 
sage, has caused an expenditure of water, represented by 
Sz—S (t,—t) = Sy’, 
since the quantity of water expended may always be repre- 
sented by a prism whose base is equal to the horizontal sec- 
tion of the lock, and whose height is represented by an in- 
determinate line y’. 
Dividing this equation by the factor S, common to all its 
terms, it becomes 
y!' =r— (t,—t,), 
which belongs toa right line of simple construction. It ex- 
presses moreover, between the lift of the lock, the draught 
of water of the boat, and the quantity of water expended, 
relations which, notwithstanding their extreme simplicity, 
have not hitherto been remarked, 
