between animal and vegetable life. This, of course, is not a failure of logical science, but a fact of great significance concerning the things themselves.

In a classification of plants we meet again with most deep and natural distinctions between the great classes called Exogens, Endogens, and Acrogens. The latter have no true sexual flowers and seeds, are formed almost wholly of cellular tissue, and have an epidermis without cuticular pores. The former two classes have much in common; they have true flowers, woody tissue and cuticular pores, and hence may be united into one wider class, Vasculares. But exogens and endogens are also most strongly distinguished. Exogens have a stem or trunk consisting of distinct bark, pith, and wood in concentric layers, leaves with reticular veins, seeds with two seed-leaves and a naked radicle; generally speaking, too, the parts of the flower are some multiple of two or five in number. Endogens, on the contrary, have no distinct bark, pith, and wood, no concentric layers, leaves with parallel veins, seeds with one seed-leaf, and a radicle not naked; they have, too, the parts of the flower generally a multiple of three in number.

These are the very widest classes in what is called the natural system of botanical arrangement; but similar principles are observed in all its minor classes. The continual efforts of botanists are directed to bringing the great multitudes of plants together in species, genera, orders, classes, and in various intermediate groups, so that the members of each group shall have the greatest number of points of mutual resemblance and the fewest points of resemblance to members of other groups. Thus is best fulfilled the great purpose of classification, which reduces multiplicity to unity, and enables us to infer of all the other members of a class what we know of any one member, provided we distinguish properly between those

qualities which are likely or are known to belong to the class, and those which are peculiar to the individual. It is a necessary condition of correct classification, as remarked by Prof. Huxley, that the definition of a group shall hold exactly true of all members of the group, and not of the members of any other group. To carry out this condition in the natural sciences is, however, very difficult, because kinds of plants or animals are continually discovered which stand in an intermediate position between classes which would otherwise be well distinguished. Thus ferns much embarrass the fundamental division of plants, because though they have no true flowers, and in this and other respects agree with other acrogens, yet they have abundance of woody fibre, which would entitle them to rank with vasculares, the larger group of which exogens and endogens are the subdivisions.

It may be remarked that the progress of chemistry is rapidly rendering it a science of classification; and in fact the whole theory of chemical combination now depends on a correct grouping of elements and compounds. Dr Roscoe in his Lessons in Elementary Chemistry enumerates no less than eleven classes of metals, each class having a number of properties in common. Thus the metals of the alkalies, namely, Potassium, Sodium, Casium, Rubidium, Lithium, form a remarkably natural class. They are all soft, easily fusible, volatile at high temperatures; they combine with great force with oxygen, decompose water at all temperatures, forming oxides which are very soluble in water, and become powerfully caustic and alkaline bodies from which water cannot be expelled by heat. Their carbonates are soluble in water, and each metal forms only one compound with chlorine.

The metals of the alkaline earths, Calcium, Strontium, and Barium, also form a very natural class, distinguished by the fact that their carbonates are insoluble in pure

water, but soluble in water containing carbonic acid in solution. The gold class contains the rare or valuable metals Gold, Platinum, Palladium, Rhodium, Ruthenium, Iridium, and Osmium, which are not acted on by nitric acid, and can only be dissolved by chlorine or the mixture of acids called aqua regia. The oxides can be reduced or deoxidised by simply heating them.

Natural classifications give us the deepest resemblances and relations, and may lead us ultimately to a knowledge of the way in which the varieties of things are produced. They are, therefore, essential to a true science, and may almost be said to constitute the framework of the science. Yet it does not follow that they are appropriate for all purposes. When our purpose is merely to recognise the name of a chemical element, a plant or an animal, its character as defined in a natural system would give us little or no assistance. The chemist does not detect potassium by getting it into the state of metal, and trying whether it would decompose water. He merely observes which, among all the compounds of potassium, have the best marked and most peculiar characters; thus a compound of potassium, platinum, and chlorine is most distinctive or characteristic of the metal, and is generally used as a means of recognising it; but a fine violet colour which potash gives to the flame of a lamp was also used as an indication of its presence long before the spectroscope was introduced to analyse such colours. An artificial classification of the elements is thus necessary to the detection of substances, and accordingly in any book on chemical analysis will be found arrangements of the elements according to characters of very minor importance, but which are selected on account of the ease and certainty with which they can be observed.

In Botany, again, the natural system of classification is far from being well suited for determining the name of a

plant, because the classes are often defined by the form of minute parts of the seed, the arrangement of the seedvessel, and other parts which it is usually difficult or sometimes impossible to examine. Accordingly botanists usually arrange their genera and species in the order of the natural system, but contrive a sort of key or artificial arrangement, in which the most simple and apparent characters, often called characteristics, are employed for the discrimination of the plants. The best arrangement of this kind as regards British plants is to be found in Bentham's British Flora. In reality the celebrated Linnæan arrangement of plants was intended by its author to serve in this way. Linnæus was too profound a philosopher to suppose that the numbers of stamens and pistils usually expressed the real relationships of plants. Many of his classes were really natural classes, but the stamens and pistils were selected as the general guide to the classes and orders, as being very plain and evident marks.

Closely connected with the process of classification is that of abstraction. To abstract is to separate the qualities common to all individuals of a group from the peculiarities of each individual. The notion "triangle is the result of abstraction in so far as we can reason concerning triangles, without any regard to the particular size or shape of any one triangle. All classification implies abstraction, for in framing and defining the class I must separate the common qualities from the peculiarities. When I abstract, too, I form a general conception, or one which, generally speaking, embraces many objects. If, indeed, the quality abstracted is a peculiar property of the class, or one which belongs to the whole and not to any other objects, I may not increase the extent of the notion, so that Mr Herbert Spencer is, perhaps, right in holding that we can abstract without generalizing. We

often use this word generalization, and the process may be defined as inferring of a whole class what we know only of a part. Whenever we regard the qualities of a thing as not confined to that thing only but as extended to other objects; when, in fact, we consider a thing only as a member of a class, we are said to generalize. If, after studying the properties of the circle, we proceed to those of the ellipse, parabola and hyperbola, it is soon found that the circle is only one case of a whole class of curves called the conic sections, corresponding to equations of the second degree; and I generalize when I regard certain of the properties of the circle as shared by many other curves.

Dr Whewell added to the superabundance of terms to express the same processes when he introduced the expression Colligation of facts. Whenever two things are found to have similar properties so as to be placed in the same class they may be said to be connected together. We connect together the places of a planet as it moves round the sun, when we conceive them as points upon a common ellipse. Whenever we thus join together previously disconnected facts, by a suitable general notion or hypothesis, we are said to colligate them. Dr Whewell adds that the general conceptions employed must be (1) clear, and (2) appropriate; but it may well be questioned whether there is anything really different in these processes from the general process of natural classification which we have considered.