Perhaps it will be found in the sequel, that classification is not only the beginning, but the culmination and the end, of human knowledge."

Classification Involving Induction.

The purpose of classification is the detection of the laws of nature. However much the process may in some cases be disguised, classification is not really distinct from the process of perfect induction, whereby we endeavour to ascertain the connexions existing between properties of the objects under treatment. There can be no use in placing an object in a class unless something more than the fact of being in the class is implied. If we arbitrarily formed a class of metals and placed therein a selection from the list of known metals made by ballot, we should have no reason to expect that the metals in question would resemble each other in any points except that they are metals, and have been selected by the ballot. But when chemists. select from the list the five metals, potassium, sodium, cæsium, rubidium, and lithium and call them the Alkaline metals, a great deal is implied in this classification. On comparing the qualities of these substances they are all found to combine very energetically with oxygen, to decompose water at all temperatures, and to form strongly basic oxides, which are highly soluble in water, yielding powerfully caustic and alkaline hydrates from which water cannot be expelled by heat. Their carbonates are also soluble in water, and each metal forms only one chloride. It may also be expected that each salt of one of the metals will correspond to a salt of each other metal, there being a general analogy between the compounds of these metals and their properties.

Now in forming this class of alkaline metals, we have done more than merely select a convenient order of statement. We have arrived at a discovery of certain empirical laws of nature, the probability being very considerable that a metal which exhibits some of the properties of alkaline metals will also possess the others. If we discovered another metal whose carbonate was soluble in water, and which energetically combined with water at all. temperatures, producing a strongly basic oxide, we should infer that it would form only a single chloride, and that

generally speaking, it would enter into a series of compounds corresponding to the salts of the other alkaline metals. The formation of this class of alkaline metals then, is no mere matter of convenience; it is an important and successful act of inductive discovery, enabling us to register many undoubted propositions as results of perfect induction, and to make a great number of inferences depending upon the principles of imperfect induction.

An excellent instance as to what classification can do, is found in Mr. Lockyer's researches on the sun. Wanting some guide as to what more elements to look for in the sun's photosphere, he prepared a classification of the elements according as they had or had not been traced in the sun, together with a detailed statement of the chief chemical characters of each element. He was then able to observe that the elements found in the sun were for the most part those forming stable compounds with oxygen. He then inferred that other elements forming stable oxides would probably exist in the sun, and he was rewarded by the discovery of five such metals. Here we have empirical and tentative classification leading to the detection of the correlation between existence in the sun, and the power of forming stable oxides and then leading by imperfect induction to the discovery of more coincidences between these properties.

Professor Huxley has defined the process of classification in the following terms. "By the classification of any series of objects, is meant the actual or ideal arrangement together of those which are like and the separation of those which are unlike; the purpose of this arrangement being to facilitate the operations of the mind in clearly conceiving and retaining in the memory the characters of the objects in question."

This statement is doubtless correct, so far as it goes, but it does not include all that Professor Huxley himself implicitly treats under classification. He is fully aware that deep correlations, or in other terms deep uniformities or laws of nature, will be disclosed by any well chosen and profound system of classification. I should therefore propose to

1 Proceedings of the Royal Society, November, 1873, vol. xxi. p. 512 2 Lectures on the Elements of Comparative Anatomy, 1864, p. L.

modify the above statement, as follows:-"By the classification of any series of objects, is meant the actual or ideal arrangement together of those which are like and the separation of those which are unlike, the purpose of this arrangement being, primarily, to disclose the correlations or laws of union of properties and circumstances, and, secondarily, to facilitate the operations of the mind in clearly conceiving and retaining in the memory the characters of the objects in question."

Multiplicity of Modes of Classification.

In approaching the question how any given group of objects may be best classified, let it be remarked that there must generally be an unlimited number of modes of classifying a group of objects. Misled, as we shall see, by the problem of classification in the natural sciences, philosophers seem to think that in each subject there must be one essentially natural system of classification which is to be selected, to the exclusion of all others. This erroneous notion probably arises also in part from the limited powers of thought and the inconvenient mechanical conditions under which we labour. If we arrange the books in a library catalogue, we must arrange them in some one order; if we compose a treatise on mineralogy, the minerals must be successively described in some one arrangement; if we treat such simple things as geometrical figures, they must be taken in some fixed order. We shall naturally select that arrangement which appears to be most convenient and instructive for our principal purpose. it does not follow that this method of arrangement possesses any exclusive excellence, and there will be usually many other possible arrangements, each valuable in its own way. A perfect intellect would not confine itself to one order of thought, but would simultaneously regard a group of objects as classified in all the ways of which they are capable. Thus the elements may be classified according to their atomicity into the groups of monads, dyads, triads, tetrads, pentads, and hexads, and this is probably the most instructive classification; but it does not prevent us from also classifying them according as they are metallic or nonmetallic, solid, liquid or gaseous at ordinary temperatures,

But

useful or useless, abundant or scarce, ferro-magnetic or diamagnetic, and so on.

Mineralogists have spent a great deal of labour in trying to discover the supposed natural system of classification for minerals. They have constantly encountered the difficulty that the chemical composition does not run together with the crystallographic form, and the various physical properties of the mineral. Substances identical in the forms of their crystals, especially those belonging to the first or cubical system of crystals, are often found to have no resemblance in chemical composition. The same substance, again, is occasionally found crystallised in two essentially different crystallographic forms; calcium carbonate, for instance, appearing as calc-spar and arragonite. The simple truth is that if we are unable to discover any correspondence, or, as we may call it, any correlation between the properties of minerals, we cannot make any one arrangement which will enable us to treat all these properties in a single system of classification. We must classify minerals in as many different ways as there are different groups of unrelated properties of sufficient importance. Even if, for the purpose of describing minerals successively in a treatise, we select one chief system, that, for instance, having regard to chemical composition, we ought mentally to regard the minerals as classified in all other useful modes.

Exactly the same may be said of the classification of plants. An immense number of different modes of classifying plants have been proposed at one time or other, an exhaustive account of which will be found in the article on classification in Rees' "Cyclopædia," or in the introduction to Lindley's "Vegetable Kingdom." There have been the Fructists, such as Cæsalpinus, Morison, Hermann, Boerhaave or Gaertner, who arranged plants according to the form of the fruit. The Corollists, Rivinus, Ludwig, and Tournefort, paid attention chiefly to the number and arrangement of the parts of the corolla. Magnol selected the calyx as the critical part, while Sauvage arranged plants according to their leaves; nor are these instances more than a small selection from the actual variety of modes of classification which have been tried. Of such attempts it may be said that every system will probably yield some information concerning the relations of plants, and it is only

after trying many modes that it is possible to approximate to the best.

Natural and Artificial Systems of Classification.

It has been usual to distinguish systems of classification as natural and artificial, those being called natural which seemed to express the order of existing things as determined by nature. Artificial methods of classification, on the other hand, included those formed for the mere convenience of men in remembering or treating natural objects.

The difference, as it is commonly regarded, has been well described by Ampére,1 as follows: "We can distinguish two kinds of classifications, the natural and the artificial. In the latter kind, some characters, arbitrarily chosen, serve to determine the place of each object; we abstract all other characters, and the objects are thus found to be brought near to or to be separated from each other, often in the most bizarre manner. In natural systems of classification, on the contrary, we employ concurrently all the characters essential to the objects with which we are occupied, discussing the importance of each of them; and the results of this labour are not adopted unless the objects which present the closest analogy are brought most near together, and the groups of the several orders which are formed from them are also approximated in proportion as they offer more similar characters. In this way it arises that there is always a kind of connexion, more or less marked, between each group and the group which follows it."

There is much, however, that is vague and logically false in this and other definitions which have been proposed by naturalists to express their notion of a natural system. We are not informed how the importance of a resemblance is to be determined, nor what is the measure of the closeness of analogy. Until all the words employed in a definition are made clear in meaning, the definition itself is worse than useless. Now if the views concerning classification here upheld are true, there can be no sharp

Essai sur la Philosophie des Sciences, p. 9.