338 



SCIENTIFIC THOUGHT. 



masses, not only at a point on the surface of our earth, 

 where the force of gravity can be considered to be con- 

 stant, but all through the universe, where it varies with 

 the distances of the moving masses. 



The Newtonian formula of gravitation was not at once 



22. 



Gravitation 111-11 i> i 



not an accepted by philosophers as a correct statement or the 



ultimate r J r r 



property of facts of nature. 



matter. 



It appeared to limit the existence of 



1 The philosophy of Descartes, 

 which then reigned on the Con- 

 tinent, seemed in many ways to 

 hinder the acceptance of Newton's 

 doctrines. Descartes had taken a 

 great step in advance in philosophi- 

 cal teaching ; he had placed mathe- 

 matics at the head of his doctrine ; 

 he had opposed the older metaphy- 

 sical methods, and he had, through 

 his application of algebra to geo- 

 metry, made great progress towards 

 a mechanical description of phe- 

 nomena. But he had not separated 

 the description from the interpre- 

 tation of nature. Philosophy and 

 science remained united, the mathe- 

 matical formulae were only a new 

 kind of metaphysics, incapable with- 

 out observation of making any real 

 advance in the knowledge of nature. 

 The facts of geometry which are 

 required for an application of an- 

 alysis are the well-known axioms of 

 Euclid. An application of analysis 

 to dynamics requires a knowledge 

 of the laws or fundamental proper- 

 ties of motion. These were not 

 correctly and completely known to 

 Descartes ; Newton placed them at 

 the head of his mathematical phil- 

 osophy of nature. A further appli- 

 cation to physical phenomena re- 

 quired a knowledge of some general 

 physical fact : such was supplied by 

 Newton in the gravitation formula. 

 The laws of motion and gravitation 

 once admitted as facts, there was 

 plenty to do for mathematics. Not 

 so with Descartes. In his philoso- 



phy the basis of facts was too nar- 

 row and indefinite, and had to be 

 supplemented by metaphysical sup- 

 positions and deductions. The field 

 for mathematical reasoning not be- 

 ing sufficiently prepared and wide 

 enough, Descartes had speedily got 

 back again into metaphysical rea- 

 soning. In fact the doctrines of 

 Newton, in which mathematical and 

 philosophical deductions had for the 

 first time been successfully separ- 

 ated, encountered on the Continent 

 the doctrines of Descartes, in which 

 mathematical and philosophical de- 

 ductions were hopelessly mixed up. 

 On one point especially the two 

 views seemed to clash. Descartes 

 had by metaphysical considerations 

 tried to define what matter is. 

 Newton had postponed the answer 

 to this question, but had defined 

 mathematically two properties of 

 matter viz., inertia and gravita- 

 tion. Descartes' metaphysical con- 

 siderations had led to the concep- 

 tion that matter and extension were 

 identical, that space therefore could 

 not be empty. Newton, occupying 

 himself not with matter in the ab- 

 stract, but only with moving observ- 

 able matter, had established the 

 general law of gravitation, leaving 

 it undecided whether the apparent 

 vacuum existing between visible 

 bodies was really empty or full. 

 For the deductions from the law 

 of gravitation it might in the 

 first instance be considered empty. 

 Thus on this question about space 



