of space, they stop at the confines of body; or if they carry them farther, they regard space as if it were nothing, because there is no body existing in it: but duration is never supposed void of some other real existence. And if names may direct our thoughts to the original of ideas, one may think, by the name duration, that the continuation of existence, with a kind of resistance to destructive force, and the continuation of solidity, were thought to have some analogy, and gave occasion to words so near of kin as durare and durum esse. Be that as it will, whoever pursues his own thoughts, will sometimes find them launch out beyond the extent of body into the infinity of space.

Time is to duration as place to expansion: they are so much of eternity and immensity as is distinguished from the rest, as it were, by land-marks. Rightly considered, they are nothing but ideas of determinate distances from certain known points: for duration and space being in themselves boundless and uniform, the order and position of things, without such settled points, would be lost in them.

Time and place, taken for determinate portions of infinite space and duration, have each of them a twofold acceptation.

1. Time is so much of infinite duration as is coexistent with the motions of the great bodies of the universe, and in this sense time begins and ends with the sensible world. Place likewise is that portion of infinite space which is possessed by the material world. Within these are measured and determined the time or duration, and the extension and place, of all corporeal beings.

2. Sometimes the word time' is applied to such other portions of infinite duration which we suppose equal to certain lengths of measured time. For if we should suppose the creation of angels was at the beginning of the Julian period, we should be understood, if we said, It is a longer time since the creation of

Locke.

F

angels than the creation of the world by 764 years.' We should thus mark out so much of that infinite duration as we supposed equal to 764 revolutions of the sun. And thus we sometimes speak of place beyond the confines of the world, when we consider so much of that space as is capable of receiving a body of any assigned dimensions.

Where and when' are questions belonging to all finite beings, and are measured from some known parts, or certain epochs. Without some such fixed periods or parts, the order of things would be lost to our understandings in the boundless ocean of duration and expansion, which in their full extent belong only to the Deity. And therefore we find our thoughts at a loss when we would consider them abstractedly, or as attributed to the Creator. But when applied to finite beings, the extension of any body is so much of space as that body takes up; and place is the position of any body considered at a certain distance from another. As the idea of the duration of any thing is the idea of that portion of infinite duration which passes during its existence, so the time when the thing existed is the idea of that space of duration, which passed between some known period, and the being of that thing.

Space and duration have a great conformity in this, viz. that though they are reckoned among our simple. ideas, yet it is the nature of both of them to consist of parts; but their parts being all of the same kind, hinder them not from having a place among our simple ideas. The mind cannot, as in number, come to an indivisible unit or idea, and conceive space without parts; it uses therefore the common measures of inches, feet, hours, days, as simple ideas of which larger ones are compounded. Every part of duration is duration, and every part of extension is extension, both capable of addition or division in infinitum. But the least portions of either of them, of which we have clear

and distinct ideas, may, perhaps, be fittest to be considered by us as the simple ideas of that kind out of which our complex modes of space, extension, and duration are made up.

Expansion and duration also agree, in that their parts are not separable, no, not even in thought. But there is this difference between them, that the ideas of length which we have of expansion are turned every way, but duration is but as it were the length of one straight line, and is the common measure of all existence. What spirits have to do with space we know not; but it is as hard to have an idea of any real being, with a perfect negation of all manner of expansion, as it is to have the idea of any real existence with a perfect negation of all manner of duration.

Duration is the idea we have of perishing distance, of which no two parts exist together; as expansion is the idea of distance, all whose parts exist together. And though we cannot conceive that any being possesses at once more than the present moment of duration, yet we can conceive the duration of the Almighty far different from that of man; because man comprehends not in his knowlege and power all past and future things; but God's infinite duration being accompanied with infinite knowlege, the past and the future are no more distant from his sight than the present. To conclude, expansion and duration do mutually embrace and comprehend each other, every part of space being in every part of duration, and every part of duration in every part of expansion.

CHAPTER XVI.

Of Number.

Amongst all the ideas we have, as there is none suggested to the mind by more ways, so there is none

more simple than that of unity: every thought of our mind brings this idea with it, for number applies itself to every thing that either doth exist or can be imagined. By repeating this idea, we come by the complex ideas of the modes of it; thus by putting twelve units together we have the complex idea of a dozen.

The simple modes of number are of all other the most distinct, two being as distinct from one as two hundred. This is not so in other simple modes; for who will undertake to find a difference between the white of this paper and that of the next degree to it?

The distinctness of each mode of number makes me think that demonstrations in numbers, if not more exact than in extension, are more determinate in their application, because the ideas of numbers are more distinguishable than in extension. Number 91 is as distinguishable from 90, to which it is the next excess, as it is from 9000; but in extension of lines, which appear of an equal length, one may be longer than the other by innumerable parts; nor can any one assign an angle which shall be the next biggest to a right

one.

By repeating the idea of a unit we make a collective idea, marked by the name two; and whoever can proceed, still adding one to the last collective idea, and give a name to it, may have ideas for collections of units as far as he has names for numbers, and memory to retain them. So that he who can add one to one and so to two, and go on taking distinct names to every progression, and again by subtracting, can retreat and lessen them, is capable of all the ideas of numbers within the compass of his language, though not of more; for without names and marks we cannot use numbers in reckoning, which being put together without a name, will be hardly kept from being a heap of confusion. This I think to be the reason why some Americans could not count to 1000, although

they could reckon very well to 20; because their language had no word to stand for 1000, and in order to express a great multitude, they would show the hairs of their head. The Tououpinambos had no names for numbers above 5; any number above that they made out by showing their fingers, and those of others who were present; and we ourselves might number farther than we do, would we but find out fit denominations. To show how much distinct names conduce to well reckoning, let us set the following figures as the marks of one number:

Nonilions. Octilions. Septilions. Sextilions. Quintilions. 623,137. 857,324.

Quatrilions.

432,147.

162,486.

345,896.

437,916.

The ordinary way of naming this number is the repeating of millions, of millions, of millions, &c. &c. in which way it will be hard to have any distinguishing notion of this number; but by giving every six figures a denomination, a great many more may be easily counted, and more plainly signified to others.

Thus children, either for want of names, or not having the faculty to collect scattered ideas into complex ones, do not begin to number very early, and they have clear conceptions of several other things before they can count 20. And some, through default of memory to retain the combinations, are not able all their life-time to reckon any moderate series of numbers for to reckon right it is required-1. that the mind distinguishes two ideas, which differ only by the addition or subtraction of a unit; 2. that it retain in memory the names of the several combinations in exact order, without which there will remain only the confused idea of multitude, but the ideas necessary to distinct numeration will not be attained.

This farther is observable in number, that the mind makes use of it in measuring all things, and our idea of