446 ATOM. 



i* known to us seem to have discussed the ideas of number and of continuous 



magnitude, of space and time, of matter and motion, with a native power of 



thought which haa probably never been surpassed. Their actual knowledge, 



however, and their scientific experience were necessarily limited, because in tin ii 



dar* the records of human thought were only beginning to accumulate. It is 



probable that the first exact notions of quantity were founded on the considera- 



n of number. It is by the help of numbers that concrete quantities are 



practically measured and calculated. Now, number is discontinuous. We pass 



from one numU'r to the next per WM//I. The magnitudes, on the other hand, 



which we meet with in geometry, are essentially continuous. The attempt to 



apply numerical methods to the comparison of geometrical quantities led to the 



doctrine of incommensurables, and to that of the infinite divisibility of space. 



Mtitnwhilr, the same considerations had not been applied to time, so that in 



the days of Zeno of Elea time was still regarded as made up of a finite number 



Miim-nts." while space was confessed to be divisible without limit. This 



was the state of opinion when the celebrated arguments against the possibility 



..f in<>tin. of which that of Achilles and the tortoise is a specimen, were 



propounded by Zeno, and such, apparently, continued to be the state of opinion 



till Aristotle pointed out that time is divisible without limit, in precisely the 



aame sense that space is. And the slowness of the development of scientific 



ideas may be estimated from the fact that Bayle does not see any force in 



this statement of Aristotle, but continues to admire the paradox of Zeno. 



(Bayle's Dictionary, art. "Zeno".) Thus the direction of true scientific progress 



was for many ages towards the recognition of the infinite divisibility of space 



and time. 



It was easy to attempt to apply similar arguments to matter. If matter 

 is extended and fills space, the same mental operation by which we recognise 

 tin- divisibility of space may be applied, in imagination at least, to the matter 

 which occupies space. From this point of view the atomic doctrine might be 

 regarded as a relic of the old numerical way of conceiving magnitude, and the 

 opposite doctrine of the infinite divisibility of matter might appear for a time 

 the most scientific. The atomists, on the other hand, asserted very strongly 

 th- distinction between matter and space. The atoms, they said, do not fill 

 up the universe; there are void spaces between them. If it were not so, 

 Lucretius u-lls us, there could be no motion, for the atom which gives way 

 first must have some empty place to move into. 



