inference. The detection of the difference saves us, indeed, from false inference, because so far as difference exists, inference is impossible. But classification consists in detecting resemblances of all degrees of generality, and ascertaining exactly how far such resemblances extend, while assigning precisely the points at which difference begins. It enables us, then, to generalise, and make inferences where it is possible, and it saves us at the same time from going too far. A full classification constitutes a complete record of all our knowledge of the objects or events classified, and the limits of exact knowledge are identical with the limits of classification.
It must by no means be supposed that every group of natural objects will be found capable of rigorous classification. There may be substances which vary by insensible degrees, consisting, for instance, in varying mixtures of simpler substances. Granite is a mixture of quartz, felspar, and mica, but there are hardly two specimens in which the proportions of these three constituents are alike, and it would be impossible to lay down definitions of distinct species of granite without finding an infinite variety of intermediate species. The only true classification of granites, then, would be founded on the proportions of the constituents present, and a chemical or microscopic analysis would be requisite, in order that we might assign a specimen to its true position in the series. Granites vary, again, by insensible degrees, as regards the magnitude of the crystals of felspar and mica. Precisely similar remarks might be made concerning the classification of other plutonic rocks, such as syenite, basalt, pumice-stone, lava.
The nature of a ray of homogeneous light is strictly defined, either by its place in the spectrum or by the corresponding wave-length, but a ray of mixed light admits of no simple classification; any of the infinitely numerous rays of the continuous spectrum may be present or absent, or present in various intensities, so that we can only class and define a mixed colour by defining the intensity and wave-length of each ray of homogeneous light which is present in it. Complete spectroscopic analysis and the determination of the intensity of every part of the spectrum yielded by a mixed ray is requisite for its accurate classification. Nearly the same may be said of complex sounds. A simple sound undulation, if we could meet with such a sound, would admit of precise and exhaustive classification as regards pitch, the length of wave, or the number of waves reaching the ear per second being a sufficient criterion. But almost all ordinary sounds, even those of musical instruments, consist of complex aggregates of undulations of different pitches, and in order to classify the sound we should have to measure the intensities of each of the constituent sounds, a work which has been partially accomplished by Helmholtz, as regards the vowel sounds. The different tones of voice distinctive of different individuals must also be due to the intermixture of minute waves of various pitch, which are yet quite beyond the range of experimental investigation. We cannot, then, at present attempt to classify the different kinds or timbres of sound.
The difficulties of classification are still greater when a varying phenomenon cannot be shown to be a mixture of simpler phenomena. If we attempt to classify tastes, we may rudely group them according as they are sweet, bitter, saline, alkaline, acid, astringent or fiery; but it is evident that these groups are bounded by no sharp lines of definition. Tastes of mixed or intermediate character may exist almost ad infinitum, and what is still more troublesome, the tastes clearly united within one class may differ more or less from each other, without our being able to arrange them in subordinate genera and species. The same remarks may be made concerning the classification of odours, which may be roughly grouped according to