These implications latent in quantitative order or determination come out in mensuration. If quantitative or numerical precision is to have a real basis, it presupposes the existence of a qualitative atom or unit which shall be the Measure. Measure is therefore the truth and the unity of quantity and quality: each refers forward and backward to the other, and both lead up to or imply a modulus, or standard unit. Such a standard unit may seem, at first sight, to be a matter of arbitrary choice and imposition. There seems to be no ultimate reason for taking the foot or the cubit as unit of measurement: and if the original foot or cubit be the king's limb, it is easy to say that the whole thing is conventional and artificial. But it is evident on further reflection, first that the foot or the pace is the natural and primitive measurer of lengths of space for the human being, and secondly that the particular foot which is imposed as the measure is taken as being normal and typical. So too it is partly arbitrary choice which fixes upon the starting-point for the scale of temperatures: but here also the range from freezing-point to boiling-point of the commonest of liquids affords a sufficient standard from which naturally to carry on the scale above or below it. What happens is therefore that what is the rule, the standard,--we may also say, the test of being, is the natural mean or average. The measure presents itself as the permanent and regular proportion of quantity and quality. It is the amount or quantity at which things settle down in equilibrium and produce the quality or characteristic feature of the object. To say that Measure is the supreme category or the truth of being--of that superficial being which merely is--of the mere fact of perception--is to say that the prime or governing feature of reality, its obviously dominant characteristic in this sphere, is a self-imposing harmony and proportion. It naturally arranges itself--defines and describes itself in rhythmic series, in regular scales, in symmetrical schemes. All things are in geometrical proportion, self-defined and uniformly graded. Such a conception and category of reality may be said to be peculiarly Greek. The doctrine of the Mean is well known as a principle of their popular Ethics. But the Mean is an average which is regarded as a Normal,--a regular and permanent mode of being which is equivalent to a standard. The rule is given by the logic of facts and of nature. There is in it an apparent optimism--a belief that what is predominant and fundamental is right: a doctrine of immanent symmetry and order. The mere habitual custom is as such held to be the right and good. It is true, no doubt, that Protagoras came to point out that this Measure was not inherent in things, but came from Man, the measure of all things: and that the later philosophy had to show how the conception of reality should be re-construed, if the objectivity of Measure and symmetry in the