DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER. 85 



WoLLASTON, in truth, erred, in assuming that the self-dividing power pre- 

 sent in the atmosphere was able to divide, to the uttermost, the divisible mass 

 subjected to its action ; in taking for granted that the divisibility was co-ordinate 

 with the actual division, so that the latter was the exact index and measure of 

 the amount of the former. The fallacy of his argument will at once appear if the 

 latter be thrown into a syllogistic form. It wiU then run thus : — 



1. An atmosphere consisting of an infinite number of mutually repulsive par- 

 ticles, must be infinitely extended. 



2. But our atmosphere is not infinitely extended. 



3. Therefore our atmosphere does not consist of an infinite number of particles. 

 Whereas it should have been. 



Therefore our atmosphere does not consist of an infinite number of mutvally 

 repulsive particles. 



The premises fully warrant the conclusion that our atmosphere does not 

 consist of an infinite number of mutually repelling particles, but throw no hght 

 on the question, whether or not it may contain an infinite number of mutually in- 

 different, or nmhially attractive ones. 



"Wollaston's argument, then, supplies no decision of the question of the divisi- 

 bility of matter. That problem still presents the same twofold aspect of diflBculty 

 which it has ever exhibited. If we affirm that matter is infinitely divisible, we 

 assert the apparent contradiction, that a finite whole contains an infinite number 

 of parts. If, pressed by this difficulty, we seek to prove that the parts are as 

 finite as the whole they make up, we fail in our attempt. We can never exhibit 

 the finite factors of our finite whole ; and the so-called atom always proves as 

 divisible as the mass out of which it was extracted. Finity and infinity must both 

 be believed in ; but here, as in other departments of knowledge, we cannot re- 

 concile them. 



It seems surprising that fallacies so palpable as those we have been discuss- 

 ing, should not have been detected long ago by the able philosophers who have 

 noticed Wollaston's argument. It is especially singular, that Dumas, who holds 

 that, in the combination of gases, a division of the chemical equivalent frequently 

 occurs (so that he represents the latter as expressed physically by a group of 

 many molecules), should not have applied his views, as he could so easily have 

 done, to its full refutation. 



As it is, I trust that the discussion I have laid before the Society wiU not 

 prove unacceptable to its members. Whewell's reasoning cannot be appreciated 

 by those Avho are ignorant of mathematics ; and the views of Poisson and Dumas, 

 even should they be fully established, leave unconsidered the question of the in- 

 trinsic validity of Wollaston's conclusions. I am not without hopes, accordingly, 

 that a demonstration of a fallacy in the argument in question, on purely physical 

 gi-ounds, which can be understood by every one, and which, so far as I am aware, 



VOL. XVI. PART I. Y 



