PLANETARY MOTIONS 29 



in order to be a discoverer of the first order lie must be 

 just in his habits of mind and wholly devoted to the 

 truth." As long as mathematicians exclusively preempt 

 the field of astronomy and at the same time continue to 

 entertain such complacent sentiments regarding them- 

 selves, it will be vain to expect any radical reform within 

 their ranks, however much it may be needed. 



The expression, "figures don't lie", is the vulgar 

 equivalent of, "mathematics is an exact science." But 

 the figures we start with must be accurate, and no degree 

 of mathematical skill can bring out a correct result unless 

 they are. It is related of a certain noted bridge-archi- 

 tect, now deceased, that he bankrupted his concern by 

 neglecting, in one of his otherwise accurate estimates, the 

 little formality of multiplying his final result by two, 

 overlooking for the moment that every bridge must have 

 two sides. 



Now, the simple moral of this digression is, that New- 

 ton, in his attempt to solve the dynamical problems of the 

 universe, neglected to take into the reckoning several es- 

 sential factors in his problem (for the very good reason 

 that he did not know of their existence) hence his 

 theories and conclusions, if not absolutely worthless, are 

 at least amendable. He assumed that the solar system 

 was a universe unto itself, completely independent of and 

 dissociated from the stars in general. When, therefore, 

 he spoke of gravitation as being "universal", he misused 

 that adjective, inasmuch as he incongruously restricted 

 its application to what we know now is little more than a 

 molecule in the total universe of matter. In other words, 

 he took into consideration only the mutual attractions 

 within the system, but he did not take into account the 

 stupendous reactions upon that system arising out of the 

 attraction between it, on the one hand, and the rest of the 

 universe, on the other. Like the bridge architect, he 

 failed to multiply by two ! 



It seems wonderfully strange to me that, of all the 

 brilliant minds that have heretofore applied themselves 

 to the theory of astronomy since Newton, not one has so 



