Febkl'ABY 8, 1895.] 



SCIENCE. 



145 



liar work of Newton to state these laws so 

 clearly and fully that the lapvse of two cen- 

 turies has suggested little, if any, improve- 

 ment. 



What, then, are these laws, you may en- 

 ((uire ? Let me turn them into the ^•ernacu- 

 lar. The first two assert that matter never 

 starts off on a journey without solicitation ; 

 having once started it never changes its 

 speed or direction unless forced to do so ; 

 when put to this extremity, it shows perfect 

 impartiality to every deflecting force ; and 

 linally, it never stops unless arrested. Add 

 to these the obvious fact that action and re- 

 action are equal and opposite, and we have 

 a body of doctrine which, simple as it may 

 seem, appears to l)e coextensive with the 

 material universe. It must be admitted, of 

 course, that a mere comprehension of these 

 laws does not suflice to make a mechani- 

 cian. Between these stepping stones and 

 the table-land from which Newton looked 

 out on the order of nature there is a long 

 and steep ascent ; but whoso would scale 

 the heights must go by waj' of these step- 

 ping stones. 



The law of gi-avitation, though commonly 

 considered the greatest of Newton's achieve- 

 ments, is, in reality, far less worthy of dis- 

 tinction than his foundation for mechanics. 

 Its chief merit lay in the clear perception 

 of the application of the law to the smallest 

 particles of matter, for the mere notion of 

 gravitation l)etween finite masses was fa- 

 miliar to his contemporaries ; in fact, accord- 

 ing to Newton's own statement, the law of 

 inverse squares as applicable to such masses 

 was within the reach of any mathematician 

 some years before the publication of the 

 I'r'iitcipia. 



A matter of the greatest importance in 

 the historj- of Newton's work relates not so 

 much to the substance as to the form of it. 

 It is now known that the grand results 

 bnmght (mt in his I'rincipia were reached 

 chietlv bv means of his calculus, or fluxions. 



as he called it, a contribution to science 

 hardly less important than either of his 

 others. But the fi\shion of his day did not 

 favor reasoning h\ means of infinitesimals, 

 tho.se mysterious increments and decre- 

 ments which the learned and eloquent Bish- 

 op Berkeley a half century later called 

 * the ghosts of departed «iuantities.' The 

 fa.shion, or rather prejudice, of Newton's 

 daj^ was strongly in favor of geometrical 

 reasoning ; and it would seem that he 

 felt constrained to translate the results to 

 which his calculus led him into geometrical 

 language. It was desirable, he thought, 

 that the system of the heavens should i)e 

 founded on good geometry. Subsequent 

 history shows that this course was an ill- 

 judged one. The geometrical method of 

 the I'rincipia renders it cumbersome, prolix, 

 and on the whole rather repulsive to the 

 modern reader; and the only justification 

 which appears at all adequate for the ex- 

 clusive adoption of this method, lies in the 

 fact that his fellow countrymen would not 

 have readily appreciated the more elegant 

 and vastly more comprehensive analytical 

 method. The result was very unfavorable 

 to the growth of mechanical science in his 

 own country. The seed he sowed took root 

 on the continent and has ever since grown 

 J[)est in French and German .soil. Accord- 

 ing to Prof. Glaisher, in an address deliv- 

 ered by him at the celebration of tlie 20(»th 

 anniversary of the publication of Newton's 

 great work, " the geometrical form of the 

 I'rincipia exercised a disastrous influence 

 over mathematical studies at Cambridge 

 T^niversity for nearly a century and a half, 

 by giving rise to a mistaken idea of the re- 

 lative power of analytical and geometrical 

 processes." 



Readers of Knglisb mathematical text 

 l)ooks and treatises can hardly fail to notice 

 that the bias they show for gcometncal 

 methods, and especially for the formal, 

 Euclidean mode of presentation, in which 



