M. Girard on Navigable Canals. 109 
The first boat finds the lock filled, and on entering it, for- 
ces back into the upper basin a volume of water equal to 
that which it ee The first expense is therefore neg- 
ative, and = 
The water ‘boing let off from the lock the boat is taken in- 
to the lower 
The seewuit’ oe finds the surface of the water in the lock 
on a level with that of the lower basin. Water must there- 
fore be let in from above to raise its surface to a level with 
the upper basin, this requires a volume of water = Sz, 
which, after the introduction of the second boat is reduced 
to 
5 (¢— 
The expense of water for ie third beat is 
And the expense for the Sia ‘convoy, if we denote by 
m' the number of boats of which it is composed will be ex- 
pressed by 
8(2 (m'—1)—t',, —ty—t'y,—Ke. be 
The expense of water for a second convoy composed of a 
number m” of ures boats will be 
+t, +t") +t’ +, &e.) 
That of a sein descending wiikey composed of m” 
host. will be ; 
a ea (m"—1)—1, Se Be, a 
"Sty pig mg &e. e'pe’ $24, &ec.= 
Sas nett +t,,+t.+, &e 
eee a oe hth &e. 
+S pte iste ie 
+5 fe (m 1) t,—big=fg—y OY 
+S (x (m”—1)—t”, —tg—t i —, Be.) 
+S (x (m" Dat te E -, &c.) 
