As we have seen in the previous chapter, generalisation passes insensibly into reasoning by analogy, and the difference is one of degree. We are said to generalise when we view many objects as agreeing in a few properties, so that the resemblance is extensive rather than deep. When we have only a few objects of thought, but are able to discover many points of resemblance, we argue by analogy that the correspondence will be even deeper than appears. It may not be true that the words are always used in such distinct senses, and there is great vagueness in the employment of these and many logical terms; but if any clear discrimination can be drawn between generalisation and analogy, it is as indicated above.
It has been said, indeed, that analogy denotes not a resemblance between things, but between the relations of things. A pilot is a very different man from a prime minister, but he bears the same relation to a ship that the minister does to the state, so that we may analogically describe the prime minister as the pilot of the state. A man differs still more from a horse, nevertheless four men bear to three men the same relation as four horses bear to three horses. There is a real analogy between the tones of the Monochord, the Sages of Greece, and the Gates of Thebes, but it does not extend beyond the fact that they were all seven in number. Between the most discrete notions, as, for instance, those of time and space, analogy may exist, arising from the fact that the mathematical conditions of the lapse of time and of motion along a line are similar. There is no identity of nature between a word and the thing it signifies; the substance iron is a heavy solid, the word iron is either a momentary disturbance of the air, or a film of black pigment on white paper; but there is analogy between words and their significates. The substance iron is to the substance iron-carbonate, as the name iron is to the name iron-carbonate, when these names are used according to their scientific definitions. The whole structure of language and the whole utility of signs, marks, symbols, pictures, and representations of various kinds, rest upon analogy. I may hope perhaps to enter more fully upon this important subject at some future time, and to attempt to show how the invention of signs enables us to express, guide, and register our thoughts. It will be sufficient to observe here that the use of words constantly involves analogies of a subtle kind; we should often be at a loss how to describe a notion, were we not at liberty to employ in a metaphorical sense the name of anything sufficiently resembling it. There would be no expression for the sweetness of a melody, or the brilliancy of an harangue, unless it were furnished by the taste of honey and the brightness of a torch.
A cursory examination of the way in which we popularly use the word analogy, shows that it includes all degrees of resemblance or similarity. The analogy may consist only in similarity of number or ratio, or in like relations of time and space. It may also consist in simple resemblance between physical properties. We should not be using the word inconsistently with custom, if we said that there was an analogy between iron, nickel, and cobalt, manifested in the strength of their magnetic powers. There is a still more perfect analogy between iodine and chlorine; not that every property of iodine is identical with the corresponding property of chlorine; for then they would be one and the same kind of substance, and not two substances; but every property of iodine resembles in all but degree some property of chlorine. For almost every substance in which iodine forms a component, a corresponding substance may be discovered containing chlorine, so that we may confidently infer from the compounds of the one to the compounds of the other substance. Potassium iodide crystallises in cubes; therefore it is to be expected that potassium chloride will also crystallise in cubes. The science of chemistry as now developed rests almost entirely upon a careful and