M. P. S Girard on Navigable Canals. 298 
Whence we see, further,that the passage of a boat will 
always produce a real elevation of water in the lock, whence 
it descends, unless the number of boats already gone through = 
is ae and in this case the number of terms 
La hae) 2 eee : os 
(srs) +(aes) +(pps) + eee) tee 
B+S 
B + 
aS a Agee) a 
Therefore 
Ss B+S 
whe! pu! ul +. u(.-)=Bpg(D—2) =D —Z5 
as we have already found. 
The fall of the jock then becomes 2-+D—2=D. Con- 
sequently, the descent of an infinite number of boats 
through the lock which terminates the level B, would ren- 
- der the fall of that lock, equal to the common dral re) 
ter of the boats which pass through it; but it is evident that 
the fall can never attain that limit since the number of 
boats can never become infinite. . 
Substituting ¢,, ~t, for D in the general expressien 
n_t 
“=BreD—2)(Brs) 
of the rise on the level of B by the passage of the nth boat, 
it becoines . i 2 
Ss oe 
An) = prs ts -1)—=)(Bz8) 3 
and all that we have hitherto said of a simple succession of 
descending boats, will apply to the double passage. or to 
the case of boats passing alternately up and down the locks. 
If all the boats are equally charged. or in other words, if 
t,=t, the proce Se becomes 45 
Ss rie 
x 
ee —pzsl B43) : i Age 
which is always negative, and indicates that the height of the 
upper level diminishes instead of increasing. ox 
After a certain number of double passages, the gta 
height of the water in the level A will evidently, in this by- 
pothesis, be represented by 5 B 
id B . eee ose eee 
h—Ba5( 1+3 78+ BTS)? B+S)°* 
