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 floaling body. 



When, therefore, a loaded boat descends from a higher 

 to a lower levej, 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 according 

 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- 

 paratus, that a certain volume of water will pass from the 

 lower to the upper level : this ascension of water, as we 

 see, is the immediate and necessary cont^equence of the 

 fundamental principles of Dynamics; it is moreover evi- 

 dent 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. 



In my first memoir, I noted some considerations on the 

 nature of the transportations to which artificial navigation 

 is usually applied, and proved that in general, the weight 

 of articles which descend from the plains and the mountains 

 into the valleys is much greater than that of the articles 

 which ascend from the vallies to the mountains. This 

 consideration opens a wide field for the application of our 

 theory. 



It may not be amiss <o 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 &\ 

 miles) from the centre canal, (Canal du Centre,) by which 

 the productions of these establishments descend, to the 

 Saone on the one hand, and to the Loire on the other ; but 

 they must be transported by land t© the creek of Torcy. 



