M. P. S. Girard on Navigable Canals. 309 
Now a body which floats in a fluid, represents in weight 
a volume of the fluid precisely equal to that which is dis- 
placed by the floating body. 
When, therefore, a loaded boat descends from a higher 
to a lower level, it is capable of producing by its weight 
the same effect as could be produced by the descent of the 
volume of water of which it occupies the place. 
In the same manner, a boat which is raised from the low- 
er to the higher level of a lock, is equivalent to a certain 
volume of water which should be raised to the same height ; 
and as the basin-lock is such in its nature that the loss of 
active force, indispensable to elevate one boat and to low: 
er another through the lock, is always proportional to the 
square of the height, it is easy to conceive that accordin 
to the relation which shall be established between the lift 
of a lock, and the draft of water of the boats which ascend 
and descend through it, the expense of water from the up- 
per level may be rendered positive, null or negative: now 
in the latter case, which we have specially examined, it 
will happen, by the sole effect of the operation of this ap- 
ratus, that a certain volume of water will pass from the 
wer to the upper level: this ascension of water, as we 
see, is the’ immediate and necessary consequence of the 
fundamental principles of Dynamics; it is moreover evi- 
ent that this elevation of water can only take place, inas- 
much as the draft of the descending boats is greater than 
that of the ascending boats added to the lift of the lock. 
; first memoir, | noted some considerations on the 
nature of the transportations to which artificial navigation 
's usually applied, and proved that in general, the weight 
of articles which descend from the plains and the mountains 
‘nto the valleys is much greater than that of the articles 
Which ascend from the vallies to the mountains. This 
Scation opens a wide field for the application of our 
theory. . 
It may not be amiss to cite a few examples taken on © 
known localities. 
The Foundery of Creuzot and the coal mines which are 
there Wrought, are situated at 10 Kilometres (about 6} 
miles) from the centre canal, (Canal du Centre,) by which 
the productions of these establishments descend, to the 
“aone on the one hand, and to the Loire on the other ; but 
they must be transported by land to the creek of Torcy, 
