296 M. P. S. Girard on Navigable Canals. 



Itis evident that the volume of virater u',-\-u',i gained by 

 two levels B, and B,, has been taken from the following lev- 

 el B,,. 



But the volume of water gained by the level B,=BX/ * 

 that gained by the level B^^=B,X« j 



The level B,^, will therefore have undergone a depres- 

 sion 



~ B , 



Consequently the fall of the lock E^,, will have become 

 , (B,z^,+B,,^^,) 



The descent of the boat through this lock will occasion a 

 temporary rise of its level : 



S S (BX+B y„) 



^'.'-=B— ;s(^=<") + B~T^ B~ ' 



But we have 



, (ByH-B.M'J 



</.=<.- B~ 



Therefore 

 , S , (B,t/^+B,X») 



In the same manner we shall find 



S _ (BXrt?XrfB^y 



"'^~B,-,4S ^^~^''^''~" "(Biv+S) ' 



And, generally 



S , ^ B,<+B,i.V+B,,Mo,4- 



B(„ i)MVn-i) \ 



• ' ■ • (B(o-I-S) 7 



If we suppose the extent and rise of water in each of the 

 leve's which precedes the last B („), to be given quantities^ 

 the above equation expresses, as we see, the general rela- 

 tionship between the indeterminate quantities B („), u („) 

 and x'\n)' 



After the first boat shall have passed through all the lev- 

 els B, B„ B,„ , the falls of the locks E, E„ E,„ Eiv &c. 



