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 

 genera/ 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 ^rs^ is the proposition, that 

 the Slim 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. 



Those 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 infinite 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 certain 

 than that matter is infinitely divisible in the sense in which the 

 writer of the article attempts to prove that it is not so. But there 

 is a sense in which the infinite divisibihty 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 fac- 

 ulties. 



