298 M. P. S. (jrirard on Navigable Canals. 



And, since the last level B^ of the canal, is the river 



in which it ternninates, and which may be considered as an 

 inde.'jnite reservoir whose level is invariable, whatever 

 may be the number of boats which enter it, we have u'= 

 0, ?/'=o, and, consequently, after the passage of any num- 

 ber (N) of boats ; 



j;',+a^„+^,„+i'ivH X +m',+k",+m"',+m,'' .... 



+ w>; 



wh- i..;e we see that after the passage of any number (N) 

 of boats in the cana), the sum of the primitive falls of all 

 the locks ic' ,-\-x' „-^ x' ,i,+Ur.. is increased only by the quan- 

 tity u'l-^-u" ,-{-v!" ,-\r, &c. which has been raised to the sum- 

 mit level. 



What we have sa'd of the lower level which terminates 

 the canal, will apply equally to any intermediate level 

 which is maintained at a constant height, by means of a 

 feeder, whatever mi^ht be the activity of the navigation. 



Thus we see that the rise of water in each level by the 

 passage of a certain number of boats through the locks 

 of a navigable canal, will depend on the superficial extent, 

 and on the rise and fall which separates them respective- 

 ly ; so that it might happen, (if we neglected the relation- 

 ship which necessarily exists between the extent of the 

 levels, the lift of the locks, and the rise of the surfaces) 

 that the rise would be very considerable in some and very 

 small in others, although the latter would require the in- 

 troduction of a much larger quantity of water than the for- 

 mer, to repair the losses occasioned by natural evaporation, 

 and filtration through the bottom and sides. 



If we suppose for example, that the canal be opened in 

 a homogeneous soil throughout its whole length, the losses 

 resulting from filtrations and evaporation, on any one of its 

 levels, will be proportionate to the extent of that level, that 

 is to say, a prism of water of a constant height, since we 

 suppose all the levels to be of equal breadth. 



This point established, it is evident that the elevations 

 u'l u'„ w',,, m'jv produced by the descent of the first boat, 



