M. Ps S. Girardon Newigable Cuhalei OR 
so that, naming generally X, X,, X,, Xiv, &c. the falls of 
the locks E, E,, E,,, Ej, &c. and V, V, V,,, Vir &e. the dife 
ference of Jevel produced by any number of double passa- 
ges in the levels B, B,, B,, B;, &c. whose transverse sec- 
tion is supposed rectangular, the general formula, 
S pre 
Vfi= et a. ae ui 
ppg tD+%u) 
S 1” B,V 
V=———A+D X,)-—— 4 
a oe eae ES 
S oe ‘ 
=> eS acini: ‘4 fy é 
Me abbot os has 
will express either the rise or fall of the levels accordingly 
as the quantities D and X shall be affected wit t 
ot the lower signs ; and we may therefore, in either case 
deduce analagous consequences from them. 
Let us nevertheless repeat what we have already stated 
at the commencement of this Memoir: that in projecting 
navigable canals, we shall much more frequently find it ne- 
céssary to raise water from the lower levels, which never 
dry, into the upper levels which are sometimes subject to 
that inconveniency, than to take from the latter, the water 
required to render the others navigable ; it will therefore 
be proper, whenever circumstances will permit, to con- 
fine ourselves to the case where the difference D—- 
itive quantity. ; Sg e 
- ° ranean a few words what we have said hitherto : 
of draft of water in the ascending and the descending boats. 
We have found that, the number of double passages in- 
el, and the number of assages to which these elevations 
are due, may be graphically represented by the co-ordi- 
