T 
M. P.S. Girard on Navigable Canals. 299 
DS, must be equal to each other; making this common 
quantity =a, we shall have , 
a=Byg (D—2') Si 
~ Ra ig 
a=B +s (P-*)—(B +8) 
. _ 5, BeBe, 
a= Rpg (P—*,.)— (BS) 
5 _ ._ (B,,+B,+B ja 
=B,48 20> %)- B48 
| And generally : 
5 F B+B,4+B_+6,.+. . -+Bini, 
‘B.S ( m+) 
Now the position of the level Bg.), in relation to the 
summit level of the canal, or, which amounts to the same 
thing, the sum of all the levels B+B,4+B,,+....Bu-, 
which precede it, being given and represented by (B), we 
have : . 
s Bi enqrg WAR) 
ue oO tS 
(n 
or, to abridge, by making 
is Ba) +S=y; D-2@)=% 
n) 
- we have 
whi ' tes it, in order that tl ' ‘ 
bine eT ba it, shall acquire an uniform rise of 
level at each passage of a boat, whatever may be the num- 
For chet ¥ passage of the first boat, the falls of the 
sluices on the whole length of the canal have become: 
vj+a —a=s', : 
- gah 
3 . igs I ‘n the extent of the 
Since nothing is changed, either in sap cgpeltie: 
levels, or in the primitive fall of its sluices, it 1 i 
d boat will cause the same rise @, 
d so on indefinitely. 
