shall see, that all accurate processes of measurement depend. If for a weight in a scale of a balance we substitute another weight, and the equilibrium remains entirely unchanged, then the weights must be exactly equal. The general test of equality is substitution. Objects are equally bright when on replacing one by the other the eye perceives no difference. Objects are equal in dimensions when tested by the same gauge they fit in the same manner. Generally speaking, two objects are alike so far as when substituted one for another no alteration is produced, and vice versâ when alike no alteration is produced by the substitution.
The Propagating Power of Similarity.
The relation of similarity in all its degrees is reciprocal. So far as things are alike, either may be substituted for the other; and this may perhaps be considered the very meaning of the relation. But it is well worth notice that there is in similarity a peculiar power of extending itself among all the things which are similar. To render a number of things similar to each other we need only render them similar to one standard object. Each coin struck from a pair of dies not only resembles the matrix or original pattern from which the dies were struck, but resembles every other coin manufactured from the same original pattern. Among a million such coins there are not less than 499,999,500,000 pairs of coins resembling each other. Similars to the same are similars to all. It is one great advantage of printing that all copies of a document struck from the same type are necessarily identical each with each, and whatever is true of one copy will be true of every copy. Similarly, if fifty rows of pipes in an organ be tuned in perfect unison with one row, usually the Principal, they must be in unison with each other. Similarity can also reproduce or propagate itself ad infinitum: for if a number of tuning-forks be adjusted in perfect unison with one standard fork, all instruments tuned to any one fork will agree with any instrument tuned to any other fork. Standard measures of length, capacity, weight, or any other measurable quality, are propagated in the same manner. So far as copies of the original standard, or copies of copies, or copies again of those copies, are accurately executed, they must all agree each with every other.
It is the capability of mutual substitution which gives such great value to the modern methods of mechanical construction, according to which all the parts of a machine are exact facsimiles of a fixed pattern. The rifles used in the British army are constructed on the American interchangeable system, so that any part of any rifle can be substituted for the same part of another. A bullet fitting one rifle will fit all others of the same bore. Sir J. Whitworth has extended the same system to the screws and screw-bolts used in connecting together the parts of machines, by establishing a series of standard screws.
Anticipations of the Principle of Substitution.
In such a subject as logic it is hardly possible to put forth any opinions which have not been in some degree previously entertained. The germ at least of every doctrine will be found in earlier writers, and novelty must arise chiefly in the mode of harmonising and developing ideas. When I first employed the process and name of substitution in logic,14 I was led to do so from analogy with the familiar mathematical process of substituting for a symbol its value as given in an equation. In writing my first logical essay I had a most imperfect conception of the importance and generality of the process, and I described, as if they were of equal importance, a number of other laws which now seem to be but particular cases of the one general rule of substitution.
My second essay, “The Substitution of Similars,” was written shortly after I had become aware of the great simplification which may be effected by a proper application of the principle of substitution. I was not then