We have proved that certain samples of aluminium have a specific gravity of 2·6, and then see a metal--of specific gravity unknown--which has all the other properties of aluminium: we may confidently infer that this metal also would, if tested, show a specific gravity of 2·6. For purposes of reason it may be necessary to compare things that cannot be brought physically together. When this happens we generally compare them in _idea_, or the idea of one with the other as object. When great accuracy is required and the idea--which is always rather vague--cannot be relied on, we have recourse to mediate comparison. _Standards_ are employed. These are manageable or portable objects with which principal things are separately compared by way of effecting indirectly a comparison between them. Standards can only mediate comparisons between _abstract_ properties, for if they contained all the concrete properties of the compared objects they would, by supposition, be as unmanageable as the latter. We have standards for length in rules, scales, tapes, chains; the balance is a standard for weight. There are also scales for pitch of sound, varieties of colour, degree of light, heat, atmospheric pressure, and probably some others for special purposes. Indirect comparison is not in itself inference; or if inference it is subordinate and preparatory to some more important conclusion. A coin is weighed and concluded to be _light_, but this is only a datum in determining the more important question whether it is a forged coin or not. XXIII--ASSOCIATION In this category we widen the attention so as to include several objects in one act of perception. The first result of this diffusion of attention is to lessen the brilliancy of objects. Our attention is a light which is intensified when narrowed and concentrated--enfeebled when dispersed over several objects. The observation of a group amounts practically to observing the objects in rapid succession. At a given moment we perceive only one thing well, or it may be only a small part of a thing, but we have a dull sense of other things adjacent, which we have just seen and may immediately see again in any order we please. That is all that is meant by perception of a group. To distinguish this category properly from the next we must consider the group of objects as divested of depth or distance outwards. It is to be regarded as a flat surface standing a few feet from us, the objects in it having absolutely the dimensions they appear to have. This is in fact their _real_ magnitude, for the supposed real magnitude is a matter of theory, and means the perceptual magnitude taken under certain conditions of observation. The real magnitude is constantly changing, so for practical convenience in determining size, etc., we refer all objects to one condition of observation--that in which they can be touched as well as seen.