58 Infinite Divisibility of Matter. 
is hence inferred, that A can never overtake B, though moving 
with twice its velocity. But this is to lose sight of the fact, that 
the period from the commencement of motion, to the time when 
either of the bodies occupies the position of any point of division 
whatever, in the line BC, is less than a minute ; since at the end 
of a minute, both bodies must have arrived at C. All that can 
be determined by the above mode of viewing the case in ques- 
tion, is this; that A cannot overtake B in any time less than a 
minute. But the object was to prove that A can never overtake 
B; a proposition widely different from the former. 
An attempt is.made in the latter part of the article, to give a 
general demonstration against the infinite divisibility of matter. 
The proof rests on three assumptions, to which it is supposed 
that no objection can be made. The firs¢ is the proposition, that 
the sum of an infinite number of magnitudes, however small, is 
a magnitude infinitely great. This is far from being an admitted 
truth. Nothing is more common in mathematics than series hav- 
ing an infinite number of terms, and only a finite sum, though 
some of the terms are themselves of finite value. As the assump- 
tion in question is therefore groundless, it vitiates the subsequent 
reasoning in the article, and the result obtained by means of it 
must be inconclusive. 
hose who maintain that bodies or portions of space are capa 
ble of infinite division, regard the parts obtained by this division, 
as infinitely small; and they have no difficulty in supposing that 
the sum of an anfinite number of such parts may be only a finite 
quantity, the very quantity by the repeated divisions of which 
those parts were obtained. Hardly any thing can be more certaift 
than that matter is infinitely divisible in the sense in which the 
writer of the article attempts to prove that it isnotso. But there 
is a sense in which the infinite divisibility of matter is question- 
able. ‘The inquiry concerned in it, however, is one which seems 
not to lie within the range of finite, or at least of the human face 
ulties. 
