M. P. S. Girard on Navigable Canals. 297 
which, at the commencement, were Blog ati) 2 yy {Mace 
will have become 2”, 2”, 2",,, x"i,, &c., and by nchatites 
ting these quantities in lieu of the original falls, we may, 
in the same manner, determine the angmentations, uu, 
ul", Ui, occasioned on the levels as as : 
passage of a second boat, we shall therefore have — ae 
(D—=z")) 
; B ul 
BSO z a) ee (B, +5) 
Fas -#")- Sa 
vs Bias 
Wn 
u , pope 
v= 5, = - B,,+S : 
, ” (B, ul" 7B, * +B,,u",,,) 
Tne eee ix) - (By +5) 
gee Ca which will give the snemce eee: < sete 
w";,, Sc. in. functions of the quantities S, BB B,, Bi , 
&c, and in functions of the primitive falls 2’, 2 de Ss 2 iy 
&e, of the locks E, E, E,,, Ej, &c., in paying Sy al is 
the new falls of, these locks 
=v, +u,,— wiv &e- 
The levels B “ B,,, — ‘&e. pie be respectively raised 
by the quantities 
when Ubu, oe Maen tu" iv, &e. 
After the . passage of the second rl the all of locks 
EE i. &c. will become x”, x”, 2", 
a the same manner may be determined the nations Hy 
m at", wy &. of water by the passage of a third boa 
a the hei hts assigned in functions of the primitive eae 
tities S, B, ie i Bj,, Sc. 2’, we Bn, Sih. in consider 
ing that we have 
=2) 4 tu.-—u —u', 2 
=a +e. Sa Ogee we 
a0! yea ‘ate i) aye iv aM oe 
' 
m 
8 
—u 
(nt 
sai og all sass falls of the bike A te hin 
to the last, we h ci 
ol i aly bales fe.-pa! ‘ ., 
el bu! a’, e’ mits &e.-+2 oe W ntt) —* (nt1) 
Vor. VII._—No. 2 
co (n) 
