THE TIDES 99 



templates, as its vital feature, an actual physical dis- 

 placement of all three in the line of the moon's radius 

 vector. Let us see just what such possible displacements 

 would mathematically amount to and whether or not they 

 measure up to the requirements. 



According to the principle of gravitation, any object, 

 for example an apple, falling earthward, attracts as much 

 at it is attracted, for, viewed from either end, the tractive 

 tension is identically the same. This does not signify, 

 however, that in coming together earth and apple will 

 meet half way, but rather that they will traverse dis- 

 tances inversely proportional to the square roots of their 

 masses. A while back, we saw that the moon has been 

 computed to fall 1-19 of an inch per second. Since, how- 

 ever, she is only 1-81 of the earth's size, the latter 

 should theoretically fall moonward only 1-171 of an inch 

 in the same brief period. This computation, be it noted, 

 is based on the original law of the inverse squares, which 

 Newton repudiates in favor of his improvised rule of in- 

 verse cubes. Adopting his rule, we shall have to reduce 

 our already small fraction by multiplying the denomina- 

 tor by 60 (the moon's distance being 60 times the earth's 

 radius), whence we derive the quantity 1-10,260 of an 

 inch as the measure of the lunar tidal deflection of the 

 earth per second. But this quantity, again, must be 

 halved, for the reason that there are hypothetically two 

 tides, fore and aft, each of which must be allowed an 

 equal share of the provided space, yielding us only 

 1-20,520 of an inch for each. Summing it all up, Newton's 

 conception contemplates that the moon by drawing the 

 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- 



