NEWTON'S THEORY OF PLANETARY MOTIONS 71 



stated before, the publication of his Principia for as much 

 as four decades. The oversight, futhermore, appears all 

 the greater when we remember with what assiduity 

 mathematicians have devoted themselves to the investiga- 

 tion of the purely academical and altogether speculative 

 "fourth dimension of space", the while remaining stone 

 blind to this genuine third dynamical dimension of the 

 real cosmos. To them, just as to Newton, the solar sys- 

 tem is, to all intents and purposes, a world of two dimen- 

 sions, in which the mutual attractions of the members 

 take place in a single plane, the plane of the ecliptic ; and 

 they seem never to have taken thought to look up or down 

 from that level in search of an extraneous motive power 

 acting transversely. The universe of Newton's concep- 

 tion lacked the dynamical dimension of THICKNESS. 



I trust that I have now said enough to convince the 

 unprejudiced reader that there is plenty of room for im- 

 provement in the theory of astronomy as now taught in 

 the schools, and to prepare his mind to receive new im- 

 pressions and reconsider past judgments. 



When, at the age of twenty-three, as the story goes, 

 Newton saw the apple fall, the thought that occurred to 

 him was not single but duplex. One phase of it was, 

 Does the force of gravitation extend as far as from the 

 earth to the moonf, and the other, If it does so extend, 

 then why does the moon not fall, but preserve its uniform 

 distance from age to age? Doubtless thousands of men be- 

 fore him had asked themselves the same queries, but 

 given them up as unanswerable conundrums. Newton, 

 however, did not. It occurred to him that, supposing the 

 moon at every mathematical point of her orbit to be di- 

 rected, with undiminishing velocity, tangentially forward, 

 she might still fall like the apple, but fall no farther than 

 just from the line of the tangent to the rim of the orbit. 

 The first time he made his calculation the result was so 

 far out that he gave up his hypothesis as unsound, and 

 charged his labors to profit and loss. Some years later, 

 however, as luck would have it, one of the chief data of 



