M. P. 8S. Girard on Navigable Canals. © 298 
wy pu tu’, +i, +, &e ; 
wut, ul! + +, &e.; 
Wy; U oe +ul",, +u,,+, Xe ; 
indicates the total rise of each of the levels B, B,, B,,, B;,, 
&c. after any number n of successive passages. ‘ 
Let us follow and examine the effect of a boat going 
from the summit level B, through all the levels B, B,, &c. 
of the canal. 
We have just found that the boat DS. in passing through 
the lock E,, whose fallis «',, has produced in the first lev- 
el B, , a rise 
Ss U 
“=p 75(D-« ). 
But the volume of water to produce this rise has been 
borrowed from the second level B,,; the height of water in 
the latter is consequently diminished by a quantity 
4 u, 
———— 
? : 
whence we see that the primitive fall x’, of the second lock 
e B,, . . 
making this fall =z, ; and representing by v’, the rise pro- 
decal’ the level B,, by the descent of the boat DS in the 
evel B.,. ; igs 2 
We shall find, in applying the same reasoning as indeter- 
mining the rise in the first level B: 
Ss 
“= 5 19 (D—-2.)- 
But it is evident that the final rise of water u’ of the level 
1» above its primitive state, is equal to what is gained by 
the passage of the boat into the second lock E,, minus the 
quantity it lost by the passing 0 the same boat into the first 
E, ; that is to say, we have 
4 et 
w=0,—z > - 
or by substituting for v’,, and 2 their value 
a 
4 s 4 ge a 
RQ =p pg(D—-« a we B,+5 
