THE TIDES 173 



oceans on the near side away from the earth's kernel the 

 infinitesimal fraction of 1-20,520 of an inch per second, at 

 once creates and provides room for a tide 8% feet high, 

 or more than 2,000,000 times its own magnitude ! Doubt- 

 less some will retort that the tide is the work of a day and 

 not merely of a second. Very well, grant even this for the 

 sake of argument and say the effect is cumulative for a 

 full day and thereafter remains uniform. In a day there 

 are 86,400 seconds : multiply this number into 1-20,520 of 

 an inch and you get, even with this improvident conces- 

 sion, the paltry space of only 4% inches, or 22 times less 

 than what the case requires. For the tide to reach the 

 high altitude of 8% feet that Newton gave it, the tidal 

 force would have to accumulate for nearly a month ! To 

 my mind, however, it is quite as preposterous to suppose 

 such cumulativeness to take place for the period of a day 

 as for a year, and I hold that the tidal force and the tidal 

 effect are mutually commensurate from one second to 

 another, and that it is for each individual second to tell 

 its own tale. To get an idea of the woful inadequacy of 

 this ratio of 1 to 2,000,000, then, the reader may mentally 

 compare a tub of water to Niagara 's overflow in the space 

 of a full minute ! To just this extent does Newton 's hy- 

 pothesis fall short of the actual dynamical requirements. 

 In making his computations of the tidal heights, even 

 on his own theory, Newton committed two serious over- 

 sights. The first of these was in erroneously treating the 

 entire thickness of the equatorial ring as being centrifu- 

 galized instead of only one-half of it. The other half of 

 the ring is, of course, rightfully in place, being a part of 

 the original ideal spherical shape. For it should be plain 

 to any person of intelligence that subtracting a unit from 

 one of two equal quantities and adding that unit to the 

 other quantity will make a difference of two units, and not 

 merely of one. Accepting as correct the estimate of the 

 earth's polar diameter at 7,899 miles, and of the equatori- 

 al at 7,926 miles, given out by the National Geographi- 

 cal Society, the disparity between the two is 27 miles. 

 Were the earth molded into a perfect sphere, the terres- 



