PLANETARY MOTIONS 41 



"projectiles fired horizontally reach the earth simultane- 

 ously with other objects like them dropped from the same 

 height", a rule that only Newtonians disregard. 



Let us reduce the argument to mathematical form: 

 According both to theory and observation, the moon 

 at perigee has always exactly the same momentum. Con- 

 sidering, then, two successive perigees, let M represent 

 the Moon's momentum at the time of the first perigee, 

 and M' that which she has at the time of the second, and 

 we have, 



M=M' 



Again, by general consent the centripetal and centrifugal 

 forces are equal, which fact we may express, for one lun- 

 ation, thus : 



C= C' 



But astronomers inform us that the momentum, M, of 

 the moon supplies the centrifugal force, consequently, on 

 this theory, the momentum of the moon at the second 

 perigee must be M-C' ; substituting which in place of M' 

 in the first equation, we get, 



M=M C' 



whence, C'=Q 



and, since C=C' C=Q 



Reductio ad absurdum: There are no central forces: 

 gravitation is a myth! (V. p. 4.) 



You may be curious to learn how scientists try to 

 overcome this seeming impasse. Very characteristically ! 

 Herbert Spencer, innocently aided by Huxley, about the 

 year 1860, invented the euphonious phrase, "persistence 

 of force." This expression, primarily intended for use 

 in physics as an improvement on the phrase, " conser- 

 vation of energy", quickly commended itself to the astro- 

 nomical profession as an excellent substitute for Newton's 

 word "inertia." This word inertia, in fact, has fallen 

 of late so much into disfavor that seldom does the eye 

 meet it in modern books on astronomy. Persistence = 

 inertia! First, we are expected to concede the exist- 

 ence of uncaused motions t and now we are being unctu- 



