NEWTON'S THEORY OF PLANETARY MOTIONS 75 



ear motion OA and the drop AP. At P it is for an instant mov- 

 ing towards B, and the same process therefore carries it to Q ; in 

 the third second it gets to R; and so on: always falling, so to 

 speak, from its natural rectilinear path, towards the centre, but 

 never getting any nearer to the centre. 



The force with which it has thus to be constantly pulled in 

 towards the centre, or, which is the same thing, the force with 

 which it is tugging at whatever constraint it is that holds it in, is 



m v 



; where m is the mass of the particle, v its velocity, and r the 



radius of its circle of movement. This is the formula first given 

 by Huyghens for centrifugal force. 



But suppose that, for any reason whatsoever, as by 

 etheric or meteoric resistance, the moon's momentum 

 (which, may the reader bear in mind, remains, according to 

 Newtonian theory, altogether unexplained) should not 

 avail to carry her clear to A, but only to some point by 

 ever so little short of it, then the moon would inevitably 

 sink at P within the line of her orbit, that is, nearer to the 

 earth, w^here the latter 's attraction would become even 

 greater, absolutely and relatively, and consequently, dur- 

 ing the succeeding second, overmatch the tangential ve- 

 locity still more ; a process which could not be stayed and 

 would inevitably rapidly precipitate the moon upon our 

 heads. On the other hand, suppose the tangential veloc- 

 ity to be ever so slightly excessive, so that the moon in 

 its initial second of time could not at P drop clear to the 

 orbital line, then would the earth's attraction, relatively 

 and absolutely, acceleratingly decrease more and more, 

 and the moon would consequently escape irrecoverably 

 into space. 



So precarious an arrangement as this surely cannot 

 be the cosmic fact ! Newton, with his hypothesis of di- 

 vine agency, had a great tactical advantage over the pro- 

 ponents of spontaneous motions, who, no doubt, imagine 

 that their hypothesis covers the requirements as respon- 

 sively as his. But they are vastly mistaken. Were New- 

 ton here to answer us, he could consistently retort that 

 the Creator is omnipotent ; that it was within His power 

 to place the moon just where He pleased ; that He could at 



