172 FROM NEBULA TO NEBULA 



from underneath, and should tend to level, not to aug- 

 ment its height. The Newtonians, however, in their 

 vaunted wisdom, picture the attraction of the satellite as 

 turning the curve of the earth, as round a pulley, and lay- 

 ing a prehensile hand upon the tide and hauling it for- 

 ward by main force. 



Newton's idea of how the tides are formed, namely, 

 by the drawing away of the nearer waters from the ker- 

 nel, and the latter in turn from the rearward waters, con- 

 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 1-10260 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 



