purpose, are never identical, though it may be no difference could be detected in them apart from that relation to this peculiar purpose. Relatively to the system of intelligent purposes which realises itself through the circumstances, every situation is, properly speaking, unique. Now, if we consider the methods by which the uniformities called “laws” of nature are actually formulated, we may see ground to conclude that they may one and all be uniformities of the approximate non-exact type. In many cases, if not all, these uniformities have manifestly been obtained by statistical methods. Thus, for example, when it is said that all the atoms of a given chemical element are absolutely alike, _e.g._, that every atom of oxygen has the atomic weight 16, there is absolutely no valid ground for regarding this uniformity as actually realised without deviation in individual cases. If the atom should prove, as it may, to be no more than a convenient device of our own, useful for computing the behaviour of sensible masses but with no real existence of its own, it is of course evident that there can be no question of the real conformity of individual cases to the law. But even if there really are indivisible bodies answering to our conception of atoms, still we have to remember that we have no means of dealing with the individual atom directly. We infer its properties indirectly from the behaviour of the sensible masses with which we can deal more directly. Hence, at most, the statement that the atom of oxygen has a certain weight means no more than that we can for our practical purposes disregard any possible individual divergences from this value. The oxygen atoms, if they really exist, might actually fluctuate in individual atomic weight about an average; yet, so long as we cannot deal with them individually but only in bulk, these fluctuations, if only sufficiently small, would produce no appreciable effect on our results, and would therefore properly be treated in our science as non-existent. Conceivably, then, such chemical uniformities may afford no safer ground for precise statements about the weight of the individual atom, than anthropological statistics do for precise statement about the actual height, weight, or expectation of life of an individual man. And we can readily see that a non-human observer with senses incapable of perceiving the individual differences between one man and another, might be led from the apparent uniformity of behaviour exhibited by large collections of human beings to the same sort of conclusions which we are tempted to make about atoms.[133]