300 M. P. 8. Girard on Navigable Canals. 
Deain)) ge +Bit-- . &e.) 
Bois peo) Ss Bi) +8) 
whence we immediately conclude that the length of the 
level Bin being given, the fall of the sluice x(n) should be 
so much the smaller as the rise of water A, destined to re- 
place the loss attributed to this level, hecqmmes more con- 
siderable. 
stream. The quantity A changes its sign in this hypothesis 
and the equation 
== (D cee Q) ___(B.+B,+B,,+ ) 
(n) +5 (ny +S 
shews that the fall x(n) of the sluice, which terminates the 
level, may be so much the greater as the volume of water 
brought back to the propositions laid down in our first me- 
moir, : 
If, in the general equation, 
ae D—x,))- (Bu +B,u,4+B,w,,.. be) 
MO a ee a i ae 
Bo)+S (Bin) +8) 
we suppose the rise of water in all the levels, except the 
summit level u', to be null, the equation will then become 
uv * 5 
0 
Ss + 
Ps Zn) ~_ 
