Infinite Divisibility of Matter: 57 



ther, that no finite quantity can contain an infinite number of 

 parts however small, and of course that matter is composed of 

 parts or atoms beyond which there can be no subdivision. 



Euler made use of a similar argument to establish the reverse 

 of these results, but his premises were unsound. He says, " who- 

 ever is disposed to deny this property of extension, (infinite divis- 

 ibility,) is under the necessity of maintaining that it is possible to 

 arrive at last to parts so minute as to be unsusceptible of any fur- 

 ther division, because they cease to have extension. Neverthelessj 

 all these particles taken together must reproduce the whole by the 

 division of which you acquired them, and as the quantity of each 

 would be nothing or cipher 0, a combination of ciphers would 

 produce quantity, which is manifestly absurd." Here i\\e petitio 

 princifii is easily perceptible, for he assumes that because there 

 are " parts so minute as to be unsusceptible of any further divi- 

 sion," therefore the " quantity of each would be nothing or ci- 

 pher." 



These observations may contain nothing new ; the arguments 

 may have been advanced by the followers of Wolff, who lost 

 themselves in a labyrinth of monads ; if it be so the writer having 

 never met with them may have been only repeating that which 

 has appealed to his own understanding with the force of mathe- 

 matical demonstration. 



Remarks by a Coadjutor. 



In the accompanying article, the writer makes two attempts to 

 disprove the infinite divisibility of matter. He first undertakes 

 to point out a case in which the supposition of infinite divisibil- 

 ity, as a property of extension, involves an absurdity. The case 

 may be stated thus. 



A B D E C 



r- 1 i — 



Let two bodies, A and B, begin at the same time to move along 

 the right line ABC, from A and B towards C ; let the distances 

 from A. to B, and from B to C, be each one mile ; and let the ve- 

 locity of A be two miles a minute, and that of B, half as great. 

 It is evident that at the end of a minute, A will overtake B, at the 

 point C. But it is said that while A moves from A to B, B moves 

 to D, a point midway between B and C ; and while A moves from 

 B to D, B moves from D to E ; and so on, ad infinitum ; and it 



Vol. XXXIX, No. 1.— April-June, 1840. 8 



