The simplest possible case of inference, perhaps, occurs in the use of a *pattern*, *example*, or, as it is commonly called, a *sample*. To prove the exact similarity of two portions of commodity, we need not bring one portion beside the other. It is sufficient that we take a sample which exactly represents the texture, appearance, and general nature of one portion, and according as this sample agrees or not with the other, so will the two portions of commodity agree or differ. Whatever is true as regards the colour, texture, density, material of the sample will be true of the goods themselves. In such cases likeness of quality is the condition of inference. Exactly the same mode of reasoning holds true of magnitude and figure. To compare the sizes of two objects, we need not lay them beside each other. A staff, string, or other kind of measure may be employed to represent the length of one object, and according as it agrees or not with the other, so must the two objects agree or differ. In this case the proxy or sample represents length; but the fact that lengths can be added and multiplied renders it unnecessary that the proxy should always be as large as the object. Any standard of convenient size, such as a common foot-rule, may be made the medium of comparison. The height of a church in one town may be carried to that in another, and objects existing immovably at opposite sides of the earth may be vicariously measured against each other. We obviously employ the axiom that whatever is true of a thing as regards its length, is true of its equal. To every other simple phenomenon in nature the same principle of substitution is applicable. We may compare weights, densities, degrees of hardness, and degrees of all other qualities, in like manner. To ascertain whether two sounds are in unison we need not compare them directly, but a third sound may be the go-between. If a tuning-fork is in unison with the middle C of York Minster organ, and we afterwards find it to be in unison with the same note of the organ in Westminster Abbey, then it follows that the two organs are tuned in unison. The rule of inference now is, that what is true of the tuning-fork as regards the tone or pitch of its sound, is true of any sound in unison with it. The skilful employment of this substitutive process enables us to make measurements beyond the powers of our senses. No one can count the vibrations, for instance, of an organ-pipe. But we can construct an instrument called the *siren*, so that, while producing a sound of any pitch, it shall register the number of vibrations constituting the sound. Adjusting the sound of the siren in unison with an organ-pipe, we measure indirectly the number of vibrations belonging to a sound of that pitch. To measure a sound of the same pitch is as good as to measure the sound itself.