Haughton — On the Effects of Limar and Solar Tides, S^'c. 607 



This small permanent residual tidal current acts in a direction 

 opposed to the earth's rotation, and lengthens the sidereal day. 

 Let us proceed to calculate its magnitude. 

 "We have 



~ 40o;oob' "^ ~ T' 



where T= 89,280, the number of seconds in a lunar day. 

 Hence 



h 89,280 ^^ „ 



= 0-01775 ft. per second. 



2co 477x400,000 



Residual Current = - 0-01776-— . 



If we suppose a circle described, with radius «, at the surface of this 

 circle e = 0, and if eo be the ellipticity of the tidal ellipse at the surface 

 of the water, all the layers of water lying between the ellipse and 

 cii'cle will leave a residual tidal current depending on the values of e, 

 which range from e = to e = cq. The whole water between the circle 

 and ellipse will therefore have a residual tidal current corresponding 



to e = 77 • The whole mass of water, taken for both sides of the ellipse, 



will be represented by 



where tv denotes the width of the equatorial canal, and <? the longer 

 semiaxis of the tidal ellipse. This mass may be written — 



m = TTwa^eo. 

 The retarding couple of the residual tidal current will therefore be — 



SG = - 0"01776 X — X TTWa^eo x a, 



where G represents the couple animating the whole earth ; or. 



