28 THE TIDES. 



Multiplying by the number of seconds in 100,000 years 

 (about 3 billions), we obtain ^j- nearly. 



Now, the velocity of the earth's surface at the equator 

 relatively to the moon is about 1470 ; the angular velocity 

 1470 



, . 

 therefore is 



r 

 I earth's velocity 



If the earth's velocity is diminished in this propor- 

 tion, the length of the lunar day will be increased by 



89432 



/ seconds = nearly T96 / seconds. To find the 



effect on the actual (solar) day we must take the angular 



velocity = - , when the last fraction will become .,.,, ,., / 

 r 47151 ' 



or, approximately, 1.836 seconds. The solar tide need 

 not here be taken into account since its effect on the pro- 

 minences due to the moon is alternately positive and 

 negative. If the displacement instead of being 45 is 

 = then the elevation will be (as a first approximation) 

 e sin 28 and the retardation l*7/sin 2$ seconds. 



Now, in the case supposed, /is exceedingly small, the 

 friction being ultimately that of water on water. Hence we 

 conclude that in an unobstructed equatorial canal the 

 effect of the moon's attraction on the tidal prominences in 

 retarding the rotation would be quite insignificant, even 

 on the supposition above adopted, that the place of high 

 water is 45 before quadratures. If this place were affected 

 only by friction, the displacement could never reach 45, 

 for tan 28 = 7000 /and /must be less than unity. The 



