It is probably evident that, if we want to get a comprehension of the life and concrete reality of things, neither of these methods will quite answer the purpose. With the first alone, if it could be universally carried out, the universe would be thoroughly explained: everything would be exactly equivalent to some sum or multiple of every other: there would be no mystery, nothing unique, and strictly individual. Given time, we could find a formula for every reality, and a predicate exactly fitted to any subject. Yet even mathematics has to confess the existence of irrationals, surds, infinite series, and the like. For our unities and standards are always arbitrary, artificial, and one-sided, and fall short of the subtlety of nature. Even our simpler types of surfaces--the circle and the square--remain irreducible to each other: and we only avoid the collision by the remark that practically and with any required amount of exactness the discrepancy between the two can be adjusted. If we turn to the chemical method, again, there is a nearer approach to actuality in the recognition of the presence of something more than mere composition and juxtaposition. It is not that there is something which is _not_ juxtaposition: but rather it is much _more than mere_ juxtaposition. There may be degrees of this something more: but it is only to a gross or abstract view that it is not present at all. Mere cohesion even shows a unity in things juxta-posed. Mere contact is contagious: it infects. 'When a violin has been played on frequently by a tyro,' says G. H. Lewes, 'its tone deteriorates, its molecules become re-arranged, so that one mode of vibration is more ready than another[3].' 'Toute impression,' he quotes from Delboeuf, 'laisse une certaine trace ineffaçable.' So-called chemical composition is only a conspicuous instance, with peculiarities, of this alteration in state produced by what, from the mechanical standpoint, are called inner molecular displacements. But to recognise a fact is one thing: to give its explanation is another. Yet, on the other hand, to recognise the fact is to note an important point which had been omitted by the mechanical construction of things. There the result could hardly be called new: it was exactly equal to its constituent elements: and the equation was transparent. And it was transparent because the whole process, analysis and synthesis, was not a work or process of the observed thing, but the work of the observing mind: it makes the (artificial) unities, numbers them, and adds them or subtracts. But with the chemical result, though it also is equal to its elements, there is something new. Water, no doubt, is oxygen and hydrogen, but here, at least, there is no doubt that the _plus_ sign unduly simplifies the relationship, and rather indicates or represents a nexus than accurately defines it. And yet, there is nothing in water which was not, in some--shall we say mysterious?--way, in the oxygen and the hydrogen.