496 Prof. J. Lovering on the Mathematical and 



When Voltaire visited England in 1727 he saw at the univer- 

 sities the effect of Newton's revolutionary ideas in astronomy. 

 The mechanism of gravitation had exiled the fanciful vortices of 

 Descartes, which were still circulating on the continent. So 

 he wrote : — " A Frenchman who comes to London finds many 

 changes in philosophy as in other things : he left the world full ; 

 he finds it empty." The same comparison might be made now, 

 not so much between nationalities as between successive stages 

 of scientific development. At the beginning of this century the 

 universe was as empty as an exhausted receiver; now it has filled 

 up again. Nature's abhorrence of a vacuum has been resusci- 

 tated, though for other reasons than those which satisfied the 

 Aristotelians. It is the mathematicians, and not the metaphysi- 

 cians, who are now discussing the relative merits of the plenum 

 and the vacuum. Newton, in his third letter to Bentley, wrote 

 in this wise : — " That gravity should be innate, inherent and 

 essential to matter, so that one body may act upon another at 

 a distance, through a vacuum, without the mediation of any thing 

 else, by and through which their action and force may be con- 

 veyed from one to another, is to me so great an absurdity, that 

 I believe no man, who has in philosophical matters a competent 

 faculty of thinking, can ever fall into it." Roger Cotes, who 

 was Newton's successor in the chair of Mathematics and Natural 

 Philosophy at Cambridge, was only four years old when the first 

 edition of the Principia was issued ; and Newton outlived him 

 by ten years. The venerable teacher pronounced upon the 

 young mathematician, his pupil, these few but comprehensive 

 words of eulogy : — i{ If Cotes had lived, we should have known 

 something." The view taken of gravitation by Cotes was not 

 the same as that held by his master. He advocated the pro- 

 position that action at a distance must be accepted as one of the 

 primary qualities of matter, admitting of no further analysis. 

 It was objected by Hobbes and other metaphysicians, that it 

 was inconceivable that a body should act where it was not. All 

 our knowledge of mechanical forces is derived from the con- 

 scious effort we ourselves make in producing motion. As this 

 motion employs the machinery of contact, the force of gravita- 

 tion is wholly outside of all our experience. The advocates of 

 action at a distance reply that there is no real contact in any 

 case, that the difficulty is the same with the distance of mole- 

 cules as that of planets, that the mathematics are neither long- 

 sighted nor short-sighted, and that an explanation which suits 

 other forces is good enough for gravitation. 



Comte extricated himself from this embarrassment by excluding 

 causes altogether from his positive philosophy. He rejects the 

 word attraction as implying a false analogy, inconsistent with 



