PLANETARY MOTIONS 47 



gravity, but by poor marksmanship, or something else 

 less understandable, she misses the earth that is calling 

 her, falls around it, and again away. As to the two miles 

 she falls by gravity, they furthermore tell us, she doesn't 

 fall this distance after all, because she comes no nearer ! 



It is one of the ludicrous fictions of astronomers that 

 the moon, having once gotten started in her tangent, is 

 continually falling beyond the limits of the earth and 

 therefore can never actually alight, but must continue cir- 

 culating round and round the planet indefinitely. At 

 perigee, for instance, the moon's velocity, they say, is 

 such that it shoots the body so far beyond the earth, and 

 with such force, as to fire her clear out to apogee, where 

 gravity finally regains the upper hand and compels her 

 return. On this return journey, they proceed, the moon 

 is so strongly attracted toward the center of gravity of 

 the earth as to cause her to acquire thereby so much 

 momental velocity as to enable her to foil the attraction 

 to which she owes that velocity, and at perigee to swing 

 clear of the snare ! To see how well the principle works 

 out in terrestrial practice, try it out with a ball attached 

 to a rubber string and see whether the contraction of the 

 elastic will let the ball play any such tricks without the 

 flinging motion of your hand to aid. The notion that the 

 moon can fall beyond the earth is in itself very silly, for, 

 wherever it may be in its orbit, it is always over the very 

 center of the earth and is being incessantly drawn toward 

 that point. 



To "elucidate" this matter in a way "intelligible to 

 non-mathematical minds, ' ' Dr. Newcomb, in his Popular 

 Astronomy (p. 77) says: 



To the mathematician the passage from the gravitation of an 

 apple to that of the moon is quite simple ; but the non-mathemat- 

 ical reader may not, at first sight, see how the moon can be con- 

 stantly falling towards the earth without ever becoming any 

 nearer. The following illustration will make the matter clear: 

 Any one can understand the law of falling bodies, by which a 

 body falls sixteen feet the first second, three times that distance 

 the next, five times the third, and so on. If, in place of falling, 

 the body be projected horizontally, like a cannon-ball, for ex- 

 ample, it will fall sixteen feet out of the straight line in which it 



