of one class of substances so often used in our syllogistic examples; "Element" of another class, of which the former class is part. Reasoning has been plausibly represented to consist in affirming of the parts of a class whatever may be affirmed of the whole. Every law of nature which we arrive at enables us to classify together a number of facts, and it would hardly be too much to define logic as the theory of classification.

Here we deal, however, with that more conscious and distinct arrangement of objects or notions, which is especially employed in the natural sciences, such as Botany, Zoology, Mineralogy and Palæontology.

The derivation of the word class is somewhat curious. In ancient Rome it was the practice to summon the whole people together at certain periods, and this ceremony was known as a clãsis, from the Greek kλáσis, or Kλños, derived from kaλéw, to call together. Servius Tullius is said to have divided the people into six orders, according to the amount of tribute they could pay, and these orders were not unnaturally called the classes of the people. Hence the name came by degrees to be applied to any organized body of people, such as an army; thence it was transferred to a fleet of vessels as marshalled in a fixed order, and was finally extended by analogy to any collection of objects carefully arranged. When, however, we now speak of the lower or higher classes of the people it is curious that we are restoring the word very nearly to its original meaning.

Classification may perhaps be best defined as the arrangement of things, or our notions of them, according to their resemblances or identities. Every class should so be constituted as to contain objects exactly resembling each other in certain definite qualities, which are stated in the definition of the class. The more numerous and extensive the resemblances which are thus indicated by

any system of classes, the more perfect and useful must that system be considered.

Mr Mill thus describes his view of the meaning— "Classification is a contrivance for the best possible ordering of the ideas of objects in our minds; for causing the ideas to accompany or succeed one another in such a way as shall give us the greatest command over our knowledge already acquired, and lead most directly to the acquisition of more. The general problem of classification, in reference to these purposes, may be stated as follows: To provide that things shall be thought of in such groups, and those groups in such an order, as will best conduce to the remembrance, and to the ascertainment of their laws."

A collection of objects may generally be classified in an indefinite number of ways. Any quality which is possessed by some and not by others may be taken as the first difference, and the groups thus distinguished may be subdivided in succession by any other qualities taken at will. Thus a library of books might be arranged, (1) according to their size, (2) according to the language in which they are written, (3) according to the alphabetic order of their authors' names, (4) according to their subjects; and in various other ways. In large libraries and in catalogues such modes of arrangement are adopted and variously combined. Each different arrangement presents some peculiar convenience, and that mode must be selected which best meets the especial purpose of the library or catalogue. The population of a kingdom, again, may be classified in an almost endless number of ways with regard to different purposes or sciences. The population of the United Kingdom may be divided according to their place of birth, as English, Welsh, Scotch, Irish, colonial-born, and aliens. The ethnographer would divide them into Anglo-Saxons, Cymri, Gaels, Picts,

Scandinavians, &c. The statist arranges them according to age; to condition, as married, unmarried, widowed, &c.; to state of body, as able, incapacitated, blind, imbecile. The political economist regards the innumerable trades which are carried on, and classifies them in a complex manner. The lawyer again treats every one as a minor, an adult, a feme sole, a feme couverte, a guardian, ward, trustee, felon, and so on.

In the natural world, again, we may make various classifications. Plants may be arranged according to the country from which they are derived; the kind of place or habitat in which they flourish; the time they live, as annual, biennial, perennial; their size, as herbs, shrubs, trees; their properties, as esculents, drugs, or poisons: all these are distinct from the classifications which the botanist devises to represent the natural affinities or relationships of plants. It is thus evident that in making a classification we have no one fixed method which can be ascertained by rule, but that an indefinite number of choices or alternatives are usually open to us. Logic cannot in such cases do much; and it is really the work of the special sciences to investigate the character of the classification required. All that logic can do is to point out certain general requirements and principles.

The first requisite of a good classification is, that it shall be appropriate to the purpose in hand; that is to say, the points of resemblance selected to form the leading classes shall be those of importance to the practical use of the classification. All those things must be arranged together which require to be treated alike, and those things must be separated which require to be treated separately. Thus a lawyer has no need to classify persons according to the counties of England they were born in, because the law is the same independently of counties; but so far as a Scotchman, a Manx man, or an alien, is

under different laws from the English born man, we shall require to classify them apart. A gardener is quite right in classifying plants as annuals, biennials, perennials; as herbs, shrubs, trees; as evergreen and deciduous; or according to the soil, temperature and other circumstances which affect them, because these are points which must guide him in treating some differently from others.

Another and, in a scientific point of view, the most important requisite of a good classification, is that it shall enable the greatest possible number of general assertions to be made. This is the criterion, as stated by Dr Whewell, which distinguishes a natural from an artificial system of classification, and we must carefully dwell upon its meaning. It will be apparent that a good classification is more than a mere orderly arrangement; it involves a process of induction which will bring to light all the more general relations which exist between the things classified. An arrangement of books will generally be artificial; the octavo volumes will not have any common character except being of an octavo size. An alphabetical arrangement of names again is exceedingly appropriate and convenient to many purposes, but is artificial because it allows of few or no general assertions. We cannot make any general assertion whatever about persons because their names happen to begin with an A or a B, a P or a W. Even those who agree in bearing the name Smith or Taylor or Robinson might be submitted to the inductive method of agreement without the discovery of any common circumstance which could be stated in a general proposition or law. It is true that if we investigated the antecedents of the Evanses and Joneses we should find them nearly all to be Welsh, and the Campbells to be Scotch, and those who bear a very peculiar name would often be found to descend from common ancestors. So far even an alphabetic arrangement embodies something

that is natural in it, and enables general assertions to be made. Hardly any arrangement can be made, in fact, which will not indicate some vestiges of important relations and resemblances; but what we want is a system which will reveal all the most important general truths.

For this purpose we must select as the ground of union those characters which carry with them most other characters. In Lesson XII. we considered the proprium as a quality which belongs to the whole of a class without forming part of the definition of the class. Now we ought to frame the definition of a class that it may contain as few characters as possible, but that as many other characters, properties, or propria, as possible, shall be attributable to the things contained in the class. Every one can see, for instance, that animals form one great group of beings, which have many characters in common, and that plants form another group. Animals have sensation, voluntary motion, consume carbonaceous food, and evolve carbonic acid, possess a stomach, and produce fat. Plants are devoid of sensation and voluntary motion, produce carbonaceous tissue, absorb carbonic acid, and evolve oxygen, possess no stomach, and produce starch. At one time it might have been thought that almost any of the characters named was a sufficient mark of the group to which a being belonged. Whatever had a stomach, was an animal; whatever had not, was a plant; whatever produced starch or evolved oxygen was called a plant; whatever absorbed oxygen or produced fat was an animal. To the present day these statements remain generally true, so that we may make assertions in the form of the proposition U, that "all animals are all beings that evolve carbonic acid, and all plants are all beings that absorb carbonic acid." But in reality the exceptions are many, and increasing research makes it continually more apparent that there is no definite line to be drawn