1877.] The Rev. S. Haughton on Physical Geology. 



541 



If a be the angular velocity of the earth's rotation, 

 (t> = o)t. 



and 



dv= — ^ sin 2(p d(j>, 



v = — cos 20. 

 4w 



(14) 



89 



Eemembering that the earth's attraction upon the moon is ^qqqq ft. 



per sec, we have 



3 x 89 x 86400 



4u> 4x60x10000x2tt 



= 1*53 ft. per sec. 



If AC be the line joining the earth and moon, the relative velocity of 

 the tide will be zero at the points e, f, g,h; the maximum easterly velo- 



city will occur at A and C, and the maximum westerly velocity at B 

 and D *. If r were constant these velocities would be equal and opposite, 

 and the earth's rotation would not be affected by them ; or, in other words, 

 there would be no Residual Tidal Current ; but since in reality the axis 

 BD exceeds the axis AC by some feet, the greatest westerly velocities 

 will exceed the greatest easterly velocities, and thence will result a 

 balance of tidal current retarding the earth's rotation and lengthening 

 the day. 



If b, a denote the lesser and greater semiaxes of the disturbed water 

 surface, and 



a — i 

 a 



* From /to g, and from h to e, the water is moving faster than the earth , and from 

 g to h, and from e to /, the water is moving slower than the earth. 



