334 



SCIENTIFIC THOUGHT. 



two properties of the gravitation formula have been brought 

 out by a long line of investigations, carried on with the 

 view of substantiating or of refuting the formula. They 

 mark the development of whole sciences, the foundation 

 of quite novel branches of research. I propose briefly to 

 follow up these developments. 

 20. Common-sense has never had any difficulty in knowing 



Matter and . 



force mathe- what matter and force are, or in denning them for the 



matically 



.defined. purposes of practical life. But it took thousands of years 

 to find a definition of these quantities which could serve 

 as the basis of exact measurement, and permit calcula- 

 tions of results into which both factors entered in varying 



recent publications that attention 

 is sufficiently drawn to the fact 

 that very few mathematical for- 

 mulae in physics or chemistry are 

 more than approximations. The 

 law of gravitation is one of the few 

 mathematical expressions which, 

 besides being universal, have stood 

 the most rigorous tests as to accur- 

 acy. A most interesting attempt 

 to prove the inaccuracy of New- 

 ton's law was made, but speedily 

 abandoned, by Clairaut, one of 

 the earliest Newtonians in the old 

 Academy of Sciences. Clairaut 

 began about 1743 to study the 

 lunar theory in the light of New- 

 ton's system, which Madrin be- 

 fore him had already despaired 

 of reconciling with the facts of 

 observation. When he himself, 

 on calculating the annual motion 

 of the moon's apogee (or farthest 

 point in its orbit round the 

 earth), found only half the value 

 which observation furnished, he was 

 tempted in his communication to 

 the Academy of November 1747 to 

 suggest that the Newtonian for- 

 mula might require a correction for 

 great distances. This suggestion 

 was followed, as Lalande tells us, 



by a veritable scandal in the learned 

 world. Buffon, for purely meta- 

 physical reasons, objected to this 

 infringement of the simplicity of 

 the laws of the universe. The 

 opponents of Newton's system had 

 a short triumph, which however 

 was speedily reversed when Clair- 

 aut, putting a greater precision 

 into his calculations by taking 

 inequalities into account which he 

 had previously neglected, explained 

 to the Academy in May 1749 that 

 he had succeeded in reconciling the 

 movement of the moon's apogee 

 with the law of attraction accord- 

 ing to the inverse square of the 

 distance. From that time the 

 Newtonian theory, to which only 

 shortly before mathematicians like 

 Euler had been won over, reigned 

 supreme. See Lalande in the 4th 

 volume of Montucla's ' Histoire 

 des Mathe'matiques,' p. 67, &c. 

 Euler's merits in solving many 

 problems in physical astronomy were 

 so great that the Academy procur- 

 ed permission from Louis XV. to 

 receive him as a surnumlraire, the 

 eight places granted to external 

 members being all occupied. 



