In a strict sense it means a whole of quantity, that is, a whole considered as made up by the addition of parts of the same kind, as a foot is made up of twelve inches. In this sense the whole is the sum of the parts. And even in this sense the whole is represented within every part by an identity of quality that runs through them all. Otherwise there would be nothing to earmark them as belonging to the particular whole or kind of whole in question. Parts of length make up a whole of length, parts of weight a whole of weight, parts of intensity a whole of intensity, in so far as a whole of intensity is quantitative, which is not a perfectly easy question. Wholes like these are “_Sums_” or “_Totals_”. The relation of whole to part in this sense is a very simple case of the relation of differences in an identity, but for that very reason is not the easiest case to appreciate. The relation is so simple that it is apt to pass unnoticed, and in dealing with numerical computation we are apt to forget that in application to any concrete problem the numbers must be numbers of something having a common quality, and that the nature of this something may affect the result as related to real fact, though not as a conclusion from pure {55} numerical premisses. In a whole of pure number the indifference of parts to whole reaches its maximum. The unit remains absolutely the same, into whatever total of addition it may enter. In a whole of differentiated members, such as a square, all this begins to be different. A side in a square possesses, by the fact of being a side, very different relations and properties from those of a straight line conceived in isolation. In this case the whole is not made up merely by adding the parts together. It is a geometrical whole, and its parts are combined according to a special form of necessity which is rooted in the nature of space. Speaking generally, the point is that parts must occupy certain perfectly definite places as regards each other. You cannot make a square by merely adding three right angles to one, nor by taking a given straight line and adding three more equal straight lines to its length. You must construct in a definite way so as to fulfil definite conditions. The identity shows itself in the different elements which make it up, not as a mere repeated quality, but as a property of contributing, each part in a distinctive way, to the nature of the whole. Such an identity is not a mere total or sum, though I imagine that its relations can be fully expressed in terms of quantity, certain differentiated objects or conceptions being given (_e.g._ line and angle).