18 THE TIDES. 



Hence the component parallel to equator 



= - H cos lat. sin 2 (hour angle) 



(H being the greatest disturbing force). This is less than 

 the force in the equatorial canal in the proportion of cos 

 lat. : 1. But the velocity of rotation is less in the same 

 proportion ; hence the rise of the tide will be the same. If 

 this force were alone (that is, if the water moved in canals 



N 



M 



Fig. 6. 



parallel to the equator), the ocean in every circle of latitude 

 would take the form of an ellipse with its short axis towards 

 the moon. But these ellipses would not be similar unless 

 the depth of the sea varied as cos lat. 



The effect of the meridional component is of a different 

 kind. Its value is 



- H sin 2AM cos = - 2H cos AM sin AM cos 0. 

 But sin AM cos = sin AB cos MB, 



and cos AM = cos MB sin AB (as above). 



Therefore this component 



= -2H sin AB cos AB cos 2 MB 



= - H sin 2 lat. cos 2 (hour angle) 



77" 77" 



- sin 2 lat. + -^ sin 2 lat. cos 2 (hour angle). 



The mean value of this is the first term, the effect of which 

 is to cause a permanent accumulation at the equator. 



