not possessed completely by any other objects. Diagnosis, therefore, consists in comparing the qualities of a certain object with the definitions of a series of classes; the absence in the object of any one quality stated in the definition excludes it from the class thus defined; whereas, if we find every point of a definition exactly fulfilled in the specimen, we may at once assign it to the class in question. It is of course by no means certain that everything which has been affirmed of a class is true of all objects afterwards referred to the class; for this would be a case of imperfect inference, which is never more than matter of probability. A definition can only make known a finite number of the qualities of an object, and it always remains possible that objects agreeing in those assigned qualities will differ in others. An individual cannot be defined, and can only be made known by the exhibition of the individual itself, or by a material specimen exactly representing it. But this and other questions relating to definition must be treated when I am able to take up the subject of language in another work.
Diagnostic systems of classification should, as a general rule, be arranged on the bifurcate method explicitly. Any quality may be chosen which divides the whole group of objects into two distinct parts, and each part may be sub-divided successively by any prominent and well-marked circumstance which is present in a large part of the genus and not in the other. To refer an object to its proper place in such an arrangement we have only to note whether it does or does not possess the successive critical differentiæ. Dana devised a classification of this kind22 by which to refer a crystal to its place in the series of six or seven classes already described. If a crystal has all its edges modified alike or the angles replaced by three or six similar planes, it belongs to the monometric system; if not, we observe whether the number of similar planes at the extremity of the crystal is three or some multiple of three, in which case it is a crystal of the hexagonal system; and so we proceed with further successive discriminations. To ascertain the name of a mineral by examination with the blow-pipe, an arrangement more or less evidently on the bifurcate plan, has been laid down by Von Kobell.23 Minerals are divided according as they possess or do not possess metallic lustre; as they are fusible or not fusible, according as they do or do not on charcoal give a metallic bead, and so on.
Perhaps the best example to be found of an arrangement devised simply for the purpose of diagnosis, is Mr. George Bentham’s Analytical Key to the Natural Orders and Anomalous Genera of the British Flora, given in his Handbook of the British Flora.24 In this 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 sub-divided 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 not-double. 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 (p. 697), the actual