M. Girard on Navigable Canals. 105 
the Canal of Languedoc, attributes these formule to Mr. 
Clauzade, one of the engineers of that canal; they were 
generalized by Mr. de Prony, in a report made to the Gen- 
eral Assembly of civil engineers, on Mr. Ducros’ memoir, 
in such a manner as to give an easy method of calculating, 
in all cases, the quantity of water expended by the passage 
of one boat or more through a system of locks, the falls of 
which are severally known. 
But does there not exist a necessary relation between 
this fall, the quantity of water expended for the passage of 
boats, and the draft of water of the boats which ascend or 
descend through the locks ? 
This is a question which, notwithstanding its importance, 
has never yet been treated, and which I propose to resolve. 
To reduce the question to its most simple expression, we 
shall suppose ; Ist, that the boat is to pass from one level 
to another by a single lock. 
Qdly, That the boats are of a prismatic form, and that 
their dimensions are such that the interval which separates 
their sides from the sides of the lock, when compared with 
the space occupied by the boat, may be neglected without 
sensible error. 
Let § represent the horizontal section of the lock and the 
boat ; 
x, the lift of the lock, that is, the difference of level be- 
tween the two basins which it unites : 
t, the draft of water of a boat which ascends the lock. 
t,, the draft of water of a boat which descends. 
The manceuvre of passing a boat from a lower to a higher 
level consists in a é 
Ist, Drawing the boat into the lock through the lower 
gate, which is closed when the boat is in. 
2d, Introducing, by no matter what means, from the 
higher basin into the lock a quantity of water sufficient to 
bring the two surfaces to the same level ; 
3dly, Opening the upper gate of the lock, and passing the 
boat through into the upper basin. 
Hence we see that, to effect this passage, and in order to 
raise the surface of the water in the lock to a level with that 
in the upper basin, it is necessary to draw from that basin 
a prism of water = Sz, whose base is equal to the horizon- 
Mov lV.....Noot: 14 
