body were infinite in number, the parts of the whole would be equalled by the parts of the half, for in the infinite there can be no greater and less. In the infinite, as we have seen above, there is no difference between palms, digits, miles, between units and thousands, nor in the infinite time that has elapsed are there more months than years, more years than centuries. If any one set of these were less than the others it would be finite, and if one finite number may be applied to the whole, then the whole is finite.[420] The force of the Achilles dilemma was derived from the false idea that the _minimum_ of one kind had some relation to that of another kind, _e.g._ that of time to that of motion, that of impulsive force to that of the motion produced. A thing of one kind does not define or measure a thing of another, and the duration of one does not compare in the same sense with the duration of another. Parts of different things are only equivocally called parts, and _minima_ are _minima_ only according to their proper (and diverse) definitions; therefore one is not measured by another, except in a rough way, for practical purposes.[421] [Sidenote: The vacuum. Atoms spherical.] As the atoms come into contact with one another, not in all points of their surface, but in a definite number, it follows that there is a space between them, in the interstices; it was this thought which led Democritus to posit a vacuum.[422] The figure of the corporeal minimum must be spherical, for any mass which has projections can always be thought of as smaller, when these projections have been removed; and nature itself suggests this, by the gradual rounding off of substances through time, and the apparent roundness and smoothness of rough and jagged bodies when the observer is at a distance.[423] Diversity of forms of composite bodies results easily from spherical atoms, through differences in situation and order, differing amounts of vacuum and solid; but a simple vacuum with solid bodies is not sufficient,--there must be a certain matter through which the latter cohere together.[424] Although all other determinations may be abstracted from, figure at least must be predicated of the atoms; quantity cannot be asserted of that which is thought to be unfigured. These determinations of the minimum, though not given to sense, may nevertheless be made object of thought, by analogy or inference from the combinations of sensible _minima_ in larger composites, the same forms of aggregation being repeated in the higher which occur in the lower forms.[425]