DR GEORGE WILSON ON THE FINITE DIVISIBILITY OF MATTER. 85 
Wo.L.astTov, 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 will 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 mutually 
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 light 
on the question, whether or not it may contain an infinite number of mutually in- 
different, or mutually attractive ones. 
WOoOLLASTON’S argument, then, supplies no decision of the question of the divisi- 
bility ofmatter. That problem still presents the same twofold aspect of difficulty 
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 will not 
prove unacceptable to its members. WHEWELL’s reasoning cannot be appreciated 
by those who are ignorant of mathematics; and the views of Porsson 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 
grounds, which can be understood by every one, and which, so far as I am aware, 
VOL. XVI. PART I. Y 
