50 FKOM NEBULA TO NEBULA 



thus gravitates towards the sun is inversely as the square of the 

 mean distance of the planet. 



Only one more step is necessary. What sort of an orbit will 

 a planet describe if acted on by a force directed towards the sun, 

 and inversely as the square of the distance? A very simple 

 demonstration will show that, no matter what the law of force, if 

 it be constantly directed towards the sun, the radius- vector of the 

 planet will sweep over equal areas in equal times. And, con- 

 versely, it cannot sweep over equal areas in equal times if the 

 force acts in any other direction than that of the sun. Hence it 

 follows, from Kepler's second law, that the force is directed to- 

 wards the sun itself. 



In transcribing the geometrical figure given by New- 

 comb, I have taken the liberty of adding the dotted lines 

 and using final letters of the alphabet to designate new 

 points of reference. Let Z, then, represent the center of 

 the earth, Ze a radius vector of the moon (the projectile 

 body), and let the line exv be drawn parallel with CAZ. 



My first objection to this attempted explanation is 

 that Newcomb errs in disingenuously representing that 

 the satellite falls along a line paralleling CAZ, for it 

 does nothing of the sort. Instead, it falls continually to- 

 ward Z, the focus of attraction, according to Newton's 

 second law of motion, on which is based the so-called law 

 of areas, and which reads, ' ' change of motion is propor- 

 tional to the impressed force, and takes place in the direc- 

 tion of the straight line in which the force acts." As 

 Newcomb misrepresents it, the point of attraction is 

 pictured as though traveling along ZQ with exactly the 

 same velocity as the projectile was originally impelled 

 along CE, and as if the earth would be at the end of the 

 quadrant to greet the moon when she should arrive at that 

 point. Does he suppose the earth to have an astral body 

 which it can thus project out of its physical corpus, and so 

 prompt other cosmic bodies toward places where itself is 

 not? 



Plainly, the moon instead of dropping to x, therefore, 

 falls to y, and we have a repetition of the condition ex- 

 hibited in Fig. 1, in which it was shown that the velocity 

 of the moon, by the combination of the projectile force 

 with the centripetal attraction, is slowed proportionately 



