NEWTON'S THEORY OF PLANETARY MOTIONS 77 



the orbit will be a parabola or hyperbola ; and that if the 

 velocity be deficient, the result will be an ellipse, broad or 

 narrow, according to the degree of such deficiency; but 

 that in no event can the circulating body fall in. When 

 you come to scrutinize their argument closely, however, 

 you will discover that they assume the tangentiality of 

 direction at each and every point of the moon's orbit as 

 a pure gratuity, for which they neither vouchsafe ex- 

 planation, nor even concede the need of it. Newton, in- 

 deed, escaped this difficulty by boldly invoking Divine or- 

 dination in the placing of the moon exactly on the line of 

 her predestined orbit, imparting to her the precise 

 velocity requisite to offset the earth's gravity, and es- 

 tablishing with infinitesimal nicety her tangential motion ; 

 but this Aid, we have seen, his followers voluntarily re- 

 nounce, non constat they offer us nothing to take its 

 place. Be the orbit the shape of any conic section it may, 

 Newtonian theory is compelled to postulate motion tan- 

 gential to it at every point from the very beginning, else 

 the body in question must, even in accordance with New- 

 tonian premises, either escape from the central attraction 

 or fall toward it, as the case may be. Further, even 

 granting tangentiality of motion as a "natural" phe- 

 nomenon ' ' demanding explanation only as mere existence 

 does", the most trifling excess of velocity, or the least 

 diminution in the force of the centripetal attraction, or 

 the slightest outward displacement of the body would, 

 under the premises, mean its inevitable escape into space ; 

 while the antitheses of these, or of any one of them, would 

 mean the prompt collapse of the whole system. I reit- 

 erate, Newtonian theory throws absolutely no light what- 

 ever on how the moon acquired her tangential motion in 

 the outset, how she preserves it, how she acquired her 

 original velocity, how this was, and remains, so mirac- 

 ulously adapted to the intensity of the earth's gravity, or 

 how all these remarkable adjustments managed to come 

 into existence simultaneously, as the theory presupposes. 

 Let us reduce the argument to mathematical form: 

 According both to theory and observation, the moon 



