266. In this passage it will be seen that Hume virtually yields the point as regards number. When he is told of the thousandth or ten thousandth part of a grain of sand he has ‘a distinct idea of these numbers and of their different proportions,’ though to this idea no distinct ‘image’ corresponds; in other words, though the idea is not a copy of any impression. It is of such parts _as parts of the grain of sand_--as parts of a ‘compound impression’--that he can form no idea, and for the reason given in the sequel, that they are less than any possible impression, less than the ‘minimum visibile.’ This, it would seem, is a fixed quantity. That which is the least possible impression once is so always. Telescopes and microscopes do not alter it, but present it under conditions under which it could not be presented to the naked eye. Their effect, according to Hume, could not be to render that visible which existed unseen before, nor to reveal parts in that which previously had, though it seemed not to have, them--that would imply that an impression was ‘an image of something distinct and external’--but either to present a simple impression of sight where previously there was none or to substitute a compound impression for one that was simple. [1] It is then because all divisibility is supposed to be into impressions, _i.e._ into feelings, and because there are conditions under which every feeling disappears, that an infinite divisibility is pronounced impossible. But the question is whether a finite divisibility into feelings is not just as impossible as an infinite one. Just as for the reasons stated above [2] a ‘compound feeling’ is impossible, so is the division of a compound into feelings. Undoubtedly if the ‘minimum visibile’ were a feeling it would not be divisible, but for the same reason it would not be a quantity. But if it is not a quantity, with what meaning is it called a minimum, and how can a quantity be supposed to be made up of such ‘visibilia’ as have themselves no quantity? In truth the ‘minimum visibile’ is not a feeling at all but a felt thing, conceived under attributes of quantity; in particular, as the term ‘minimum’ implies, under a relation of proportion to other quantities of which, if expressed numerically, Hume himself, according to the admission above noticed, would have to confess there was an idea which was an image of no impression. That which thought thus presents to itself as a thing doubtless has been a feeling; but, as thus presented, it is already other than and independent of feeling. With a step backward or a turn of the head, the feeling may cease, ‘the spot of ink may vanish;’ but the thing does not therefore cease to be a thing or to have quantity, which implies the possibility of continuous division.