216 Rev. 0. Fisher on the Effect upon the Ocean-tides 

 and 



... (*) = _«(*!). 



\cltj \dxJ 



Henceforth the brackets will be omitted. 



■ 

 " Q 



! 1 



I 



y 









1-f . 



- 



z ^^"^ 



v 



* t 



i 



71 



<r 



Let x be the mean level of the surface, 

 0' be the depth of the canal =k, 

 0M = x, 

 MP=y, 

 mZ = z. 

 Let w be the vertical velocity of the liquid at Z at the time 

 t, and in the time dt let the surface rise from P Q to It S. 



Then the volume of liquid which enters Q Z in the time dt 

 is 



v(k +y —z)dt + io dx dt ; 

 and that which goes out is 



v\K+y'-z)dt, 

 v' and y' being the values of v and y at x-\-dx, or 



v+ —'dx, &c. 



dx ' 



And their difference is SP, or 

 dy 



dt 



dx dt. 



Therefore, neglecting the products vy and v'i/ , we get 

 d v , \ dy 



It is obvious that when z — 0, then io = 0, and ■—• \ 



function of z ; whence the two relations, 

 dv _ dy 

 ~ K 'dx~dt' ' ' 



(1) 



