294 M^ P. S. Girard on Navigable Canals, 



• • • (B+s)'^-' >'-^"~^+nB+s) 5 



making this height equal to the draft of water t„ or t of the 

 boats which ascend and descend, or 



we hall have 



t„-\-x-h. B x\ 



' X -VB+Sy ' 

 and therefore 

 n=log. (t,,-{-x — h) 



1 B 



B+S. 



This is the number of double passages after which the 

 height of water in the level B will have become precisely 

 equal to the draft of water of the boats, and will therefore 

 cease to be navigable, if it has received no new supply of 

 water. 



Hitherto we have examined only the passage of the boats 

 by a single lock, in considering the lower level as invariable, 

 which is a very special case We shall now consider the 

 question in a more general point of view, by supposing a 

 series of levels B B^ B, „ &;c. separated one from the oth- 

 er by locks E^ E, E ,/E,, &;c., of which the lifts are respec- 

 tively x f x\i x\,, x'\s &IC., and determine the rise of water on 

 any one of these levels by the successive descent of a certain 

 number of boats of an equal draft D of water. 



Let v'l u' II u' III u'\^,, &ic. represent the increased height of 

 the levels B, B/, B^,, Bj, &tc. by the descent of the first boat 

 through all the locks ; 



u'\ u' u" III m',,. &c., the increased height of the same 

 levels by the descent of the second boat ; 



?/", u'^',1 W" III u"'\y, &1C., the increase by the descent of the 

 third, &c. 



So that the upper index will designate the numecical or- 

 der of the boat in the series, and the lower one the rank of 

 the lock in the canal, counting from the summit level; each 

 of these quantities 



