The chemical method (taking chemistry as a type of the sciences like optics, electricity, &c.) is a revelation of a different state of affairs. The elements of things are here seen to be unique and incomparable; yet in each there is a latent sympathy ready to break out when the proper occasion arrives. Bring two things together, and their affinity suddenly, in the proper circumstances, leads to their complete fusion: a product arises which, when formed, hardly betrays its origin and composition. In a way this is the converse of the mechanical or mathematical method. In it was no fusion, no inner mixture: each part after composition lay beside the other, and their union was only in the ideas of the onlooker. It was mere juxtaposition still,--though now closer: an abnormally keen eye would still have been able to descry the dividing lines and measure the gaps. At least mere mechanical physics tends so to conceive it. Here, on the contrary, there is union--but only at the moment of fusion: once that is accomplished, the result is apparently simple, and bears no suggestion of being a compound. In the mechanical union the result is exactly equal to the sum of the elements which go to make it: in the chemical there is something positively new, something, i. e., of which the premises gave no indication and made no promise.
Either of these methods,--of these conceptions of existence--works well in a certain region. But both of them only do their work on a certain hypothesis, or with a certain abstraction. The mechanical method supposes that objects are all qualitatively alike, differing only in quantity or weight: all therefore entirely comparable with each other, and capable of being substituted for each other in an equation. Where this assumption holds good, the method of addition and division, the method of the calculus does its work[2]. The chemical method works on another assumption,--the assumption of a number of qualitatively-differenced elements, of elements which also are, so to speak, set on edge against some, and ready to leap into the arms of others. If the observer in the first case had the game entirely in his own hand,--could build up and separate at his pleasure, could determine results _a priori_: he is here baffled by the unexpected, and can only wait and watch to learn _a posteriori_ the behaviour of the bodies possessed of this occult and non-predictable affinity. At the best he can only formulate what he observes, try to classify it, ascertain any common principles running through it, any serial recurrences, or the like: and that is all that chemical philosophy can achieve. Chemical affinity--the fact that certain elements combine in certain ways, and refuse to enter into certain alliances--is a great fact: but to _a priori_ reasoning or abstract syllogising it is an entire inexplicability, one of the accidents in the universe which must be reckoned with, but cannot be understood.