scheme, the great composite family of plants, together with the closely approximate genus Jasione, are first separated from all other flowering plants by the compound character of their flowers. The remaining plants are subdivided according as the perianth is double or single. Since no plants are yet known in which the perianth can be said to have three or more distinct rings, this division becomes practically the same as one into double and notdouble. Flowers with a double perianth are next discriminated according as the corolla does or does not consist of one piece, according as the ovary is free or not-free, as it is simple or not simple, as the corolla is regular or irregular, and so on. On looking over this arrangement, it will be found that numerical discriminations often occur, the numbers of petals, stamens, capsules, or other parts being the criteria, in which cases, as already explained (vol. ii. p. 374), the actual exhibition of the bifid division would be tedious.

Linnæus appears to have been perfectly acquainted with the nature and uses of diagnostic classification, which he describes under the name of Synopsis, saying:'Synopsis tradit Divisiones arbitrarias, longiores aut breviores, plures aut pauciores: a Botanicis in genere non agnoscenda. Synopsis est dichotomia arbitraria, quæ instar viæ ad Botanicem ducit. Limites autem non determinat.'

The rules and tables drawn out by chemists to facilitate the discovery of the nature of a substance in qualitative analysis are usually arranged on the bifurcate method, and form excellent examples of diagnostic classification, the qualities of the substances employed in testing being in most cases merely characteristic properties of little importance in other respects. The chemist does not detect potassium by reducing it to the state of metallic potase Philosophia Botanica' (1770), § 154, p. 98.

C

sium, and then observing whether it has all the principal qualities belonging to potassium. He selects from among the whole number of compounds of potassium that salt, namely the compound of platinum tetra-chloride and potassium chloride, which has the most distinctive appearance, as it is comparatively insoluble and produces a peculiar yellow and highly crystalline precipitate. Accordingly whenever this precipitate can be produced by adding platinum chloride to a solution potassium is present. The fine purple or violet colour which potassium salts usually communicate to the blowpipe flame, had long been used as a characteristic mark. Some other elements were readily detected by the colouring of the blowpipe flame, barium giving a pale yellowish green, and salts of strontium a bright red. By the use of the spectroscope the coloured light given off by any incandescent vapour is made to give perfectly characteristic marks of the elements contained in the vapour.

Diagnosis seems to be identical with the process termed by the ancient logicians abscissio infiniti, the cutting off of the infinite or negative part of a classification when we discover by observation that an object possesses a particular property. At every step in a bifurcate division, some objects possessing the difference will fall into the affirmative part or species; all the remaining objects in the world fall into the negative part which will be infinite in extent. Diagnosis consists in the successive rejection from further notice of those almost infinite classes with which the specimen in question does not agree.

Index Classifications.

Under the general subject of classification we may certainly include all arrangements of objects or names, which we make for the purpose of saving labour in the

discovery of an object. Even such apparently trivial and arbitrary arrangements as alphabetical or other indices, are really classifications subject to all the principles of the subject. No such arrangement can be of any use unless it involves some correlation of circumstances, so that knowing one thing we learn another. If we merely arrange letters in the pigeon-holes of a secretaire we establish a correlation, for all letters in the first hole will be written by persons, for instance, whose names begin with A, and so on. Knowing then the initial letter of the writer's name we know also the place of the letter, and the labour of search is thus reduced to one twenty-sixth part of what it would be without any arrangement.

Now the purpose of a mere catalogue is to discover the place in which an object is to be found, but the art of cataloguing involves logical considerations of some interest and importance. We want to establish a correlation between the place of an object and some circumstance about the object which shall enable us readily to refer to it; this circumstance therefore should be that which will most readily dwell in the memory of the searcher. A piece of poetry, for instance, will be best remembered, in all probability, by the first line of the piece, according to the laws of the association of ideas, and the name of the author will be the next most definite circumstance; a catalogue of poetry should therefore be arranged alphabetically according to the first word of the piece, or the name of the author, or, still better, in both ways. It would be wholly absurd and impossible to arrange poems according to their subjects, so vague and mixed are these found to be when the attempt is made.

It is a matter of considerable literary importance to decide upon the best mode of cataloguing books, so that any required book in a library shall be most readily found. Books may be classified in a great number of D d

VOL. II.

ways, according to subject, language, date or lace of publication, size, the initial words of the book itself, of the title-page, the colophon, the author's name, the publisher's name, the printer's name, the character of the type, and so on. Every one of these modes of arrange ment may be useful, for we may happen to remember one circumstance about a book when we have forgotten all others; but as we cannot usually go to the expense of forming more than two or three indices at the most, we must of course select those circumstances for the basis of arrangement which will be likely to lead to the discovery of a book most surely. Many of the criteria mentioned are evidently inapplicable. The language in which a book is written is no doubt definite enough, but would afford no criterion for the classification of any large group of English books, or of those written in any one language. Classification by subjects would be an exceedingly useful method if it were practicable, but experience, or indeed a little reflection, shows it to be a logical absurdity. It is a very difficult matter to classify the sciences, so close and complicated are in many cases the relations between them. But with books the complication is infinitely greater, since the same book may treat successively of different sciences, or it may discuss a problem involving many entirely diverse principles and branches of knowledge. A good history of the steam engine will be antiquarian, so far as it traces out records of the earliest efforts at discovery; purely scientific, as regards the principles of thermodynamics involved ; technical, as regards the mechanical means of applying those principles; economical, as regards the industrial results of the invention; biographical, as regards the lives of the inventors. A history of Westminster Abbey might belong either to the history of architecture, the history of the church, or the history of England. If we

abandon the attempt to carry out an arrangement according to the natural classification of the sciences, and form comprehensive practical groups, we shall be continually perplexed by the occurrence of intermediate cases, and opinions will differ ad infinitum as to the details. If, to avoid the difficulty about Westminster Abbey, we form a class of books devoted to the History of Buildings, the question will then arise whether Stonehenge is a building, and if so, whether, cromlechs, mounds, or even monoliths are so. At the other end of the scale we shall be uncertain whether to include under the class History of Buildings, lighthouses, monuments, bridges, &c. In regard to purely literary works, rigorous classification is still less possible. The very same work may partake of the nature of poetry, biography, history, philosophy, or if we form a comprehensive class of Belles-Lettres, nobody can say exactly what does or does not come under the term.

My own experience entirely bears out the opinion of the late Professor De Morgan, that classification according to the name of the author is the only one practicable in a large library, and this method has been admirably carried out in the great Catalogue of the British Museum. The name of the author is the most precise circumstance concerning a book, which usually dwells in the memory. It is more nearly a characteristic of the book than anything else. In an alphabetical arrangement we have an exhaustive classification, including a place for every possible name. The following remarks of De Morgan seem therefore to be entirely correct. From much, almost daily use, of catalogues for many years, I am perfectly satisfied that a classed catalogue is more difficult to use than to make. It is one man's theory of the subdivision of knowledge, and the chances are against its suiting any other man. Even if all doubtful works were entered under several

d Philosophical Magazine,' 3rd Series (1845), vol. xxvi. p. 522.