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.