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:25—“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 produced 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 potassium, 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, potassium is present whenever this precipitate can be produced by adding platinum chloride to a solution. The fine purple or violet colour which potassium salts 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 an 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 genus when we discover by observation that an object possesses a particular difference. 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 infinite classes with which the specimen in question does not agree.
Index Classifications.
Under classification we may include all arrangements of objects or names, which we make for saving labour in the discovery of an object. Even alphabetical indices are real classifications. No such arrangement can be of 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 arrangement.
Now the purpose of a catalogue is to discover the place in which an object is to be found; but the art of cataloguing involves logical considerations of some 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 will be best remembered by the first line of the piece, 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 impossible to