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. But 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,

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 Casalpinus, 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

1 Essai sur la Philosophie des Sciences, p. 9.

and precise distinction between natural and artificial systems. All arrangements which serve any purpose at all must be more or less natural, because, if closely enough scrutinised, they will involve more resemblances than those whereby the class was defined.

It is true that in the biological sciences there would be one arrangement of plants or animals which would be conspicuously instructive, and in a certain sense natural, if it could be attained, and it is that after which naturalists have been in reality striving for nearly two centuries, namely, that arrangement which would display the genealogical descent of every form from the original life germ. Those morphological resemblances upon which the classification of living beings is almost always based are inherited resemblances, and it is evident that descendants will usually resemble their parents and each other in a great many points.

I have said that a natural is distinguished from an arbitrary or artificial system only in degree. It will be found almost impossible to arrange objects according to any circumstance without finding that some correlation of other circumstances is thus made apparent. No arrangement could seem more arbitrary than the common alphabetical arrangement according to the initial letter of the name. But we cannot scrutinise a list of names of persons without noticing a predominance of Evans's and Jones's, under the letters E and J, and of names beginning with Mac under the letter M. The predominance is so great that we could not attribute it to chance, and inquiry would of course show that it arose from important facts concerning the nationality of the persons. It would appear that the Evans's and Jones's were of Welsh descent, and those whose names bear the prefix Mac of Keltic descent. With the nationality would be more or less strictly correlated many peculiarities of physical constitution, language, habits, or mental character. In other cases I have been interested in noticing the empirical inferences which are displayed in the most arbitrary arrangements. If a large register of the names of ships be examined it will often be found that a number of ships bearing the same name were built about the same time, a correlation due to the occurrence of some striking incident shortly previous

to the building of the ships. The age of ships or other structures is usually correlated with their general form, nature of materials, &c, so that ships of the same name will often resemble each other in many points.

It is impossible to examine the details of some of the so-called artificial systems of classification of plants, without finding that many of the classes are natural in character. Thus in Tournefort's arrangement, depending almost entirely on the formation of the corolla, we find the natural orders of the Labiata, Cruciferæ, Rosaceæ, Umbelliferæ, Liliacea, and Papilionaceæ, recognised in his 4th, 5th, 6th, 7th, 9th, and 1oth classes. Many of the classes in Linnæus' celebrated sexual system also approximate to natural classes.

Correlation of Properties.

Habits and usages of language are apt to lead us into the error of imagining that when we employ different words we always mean different things. In introducing the subject of classification nominally I was careful to draw the reader's attention to the fact that all reasoning and all operations of scientific method really involve classification, though we are accustomed to use the name in some cases and not in others. The name correlation requires to be used with the same qualification. Things are correlated (con, relata) when they are so related or bound to each other that where one is the other is, and where one is not the other is not. Throughout this work we have then been dealing with correlations. In geometry the occurrence of three equal angles in a triangle is correlated with the existence of three equal sides; in physics gravity is correlated with inertia ; in botany exogenous growth is correlated with the possession of two cotyledons, or the production of flowers with that of spiral vessels. Wherever a proposition of the form A = B is true there correlation exists. But it is in the classificatory sciences especially that the word correlation has been employed.

We find it stated that in the class Mammalia the possession of two occipital condyles, with a well-ossified basi-occipital, is correlated with the possession of mandibles, each ramus of which is composed of a single piece