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



y is positive, or the liquid flowing westward, this force acts 

 eastward, and vice versa.', so that its sign is always opposite to 



that of y. It will therefore be expressed by — / - y. Hence 



X= — fi sin 2© —f-yi 



also Z = — g. 



Therefore, neglecting the small products, and substituting for 



-j- and -y- the values lately found, the equations are reduced to 



sldp . u a 2 cly , N 



)ld P _ _ « z d 2 y m 



Integrating (2), and taking the integral from to z, we 

 obtain 



.*. differentiating with respect to x, and neglecting the small 

 products, 



1 dp __ dy a?K d?ij 



pd7v~ 9 Zv + 'Y"dx i ' 



If there should be a floating crust of any kind capable of 

 adapting itself freely to the wave, the pressure arising from 

 this cause must be added to p ; but it disappears when diffe- 

 rentiated. 



Hence, putting aco for a, and equating the values of - -j-, 



the differential equation to the wave-surface is 



,a , / a 2 \ 1 dy , u 2 k d z y . a 



Assume 



y = A. cos 2w — B sin 2g>, 



.-. y = ^/A r +W cos (2a> + 28), 



tan 28=?. 

 And we find />«« 



tan 28= ~ -; . . . (3) 



where 



(r& 



