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forbidden by the nature of space. A classification is essentially a mental not a material thing.

Discovery of Marks or Characteristics.

Although the chief purpose of classification is to disclose the deepest and most general resemblances of the objects classified, yet the practical value of any particular system will partly depend upon the ease with which we can refer an object to its proper class, and thus infer concerning it all that is known generally of that class. This operation of discovering to which class of a system a certain specimen or case belongs is generally called Diagnosis, a technical term very familiarly used by physicians, who constantly require to diagnose or determine the nature of the disease from which a patient is suffering. Now every class is defined by certain specified qualities or circumstances, the whole of which are present in every object contained in the class, and not all present in any object excluded from it. These defining circumstances ought to consist of the deepest and most important circumstances, by which we vaguely mean those probably forming the conditions with which the minor circumstances are correlated. But it will often happen that the so-called important points of an object are not those which can most readily be observed. Thus the two great classes of phanerogamous plants are defined respectively by the possession of two cotyledons or seed-leaves, and one cotyledon. But when a plant comes to our notice and we want to refer it to the right class, it will often happen that we have no seed at all to examine, in order to discover whether there be one seed-leaf or two in the germ. Even if we have a seed it will often be very small, and a careful dissection under the microscope will be requisite to ascertain the number of cotyledons. Occasionally the

examination of the germ would mislead us, for the cotyledons may be obsolete, as in Cuscuta, or united together, as in Clintonia. Botanists therefore seldom actually refer to the seed for such simple information. Certain other characters of a plant are closely correlated with the number of seed-leaves; thus monocotyledonous plants almost always possess leaves with parallel veins like those of grass, while dicotyledonous plants have leaves with reticulated veins like those of an oak leaf. In monocotyledonous plants, too, the parts of the flower are most often three or some multiple of three in number, while in dicotyledonous plants the numbers four and five and their multiples prevail. Botanists, therefore, by a glance at the leaves and flowers can almost certainly refer a plant to its right class, and can infer not only the number of cotyledons which would be found in the seed or young plant, but also the structure of the stem and the other general characters and relations of a dicotyledon or a monocotyledon.

Any conspicuous and easily discriminated property which we thus select for the purpose of deciding to which class an object belongs, may be called a characteristic. The logical conditions of a good characteristic mark are very simple, namely, that it should be possessed by all objects entering into a certain class, and by none others. The characteristic may consist either of a single quality or circumstance, or of a conjunction of such, provided that they all be constant and easily detected. Thus in the classification of mammals the teeth are of the greatest assistance, not because a slight variation in the number and form of the teeth is of any great importance in the general economy of the animal, but because such variations are found by empirical observation to coincide with most important differences in the general affinities. It is found that the minor classes and genera of mammals can be

registered and discriminated accurately by their teeth, especially by the foremost molars and the hindmost premolars. Some of the teeth, indeed, are occasionally missing, so that zoologists prefer to trust to those characteristic teeth which are most constant, and to infer from them not only the arrangement of the other teeth, but the whole conformation of the animal.

It is a very difficult matter to mark out any boundaryline between the animal and vegetable kingdoms, and it may even be doubted whether any rigorous division can be established. The most fundamental and important character of a vegetable structure probably consists in the absence of nitrogen from the constituent membranes. Supposing this to be the case, the difficulty arises that in examining minute organisms we cannot ascertain directly whether they contain nitrogen or not. Some minor but easily detected circumstance is therefore needed to discriminate between animals and vegetables, and this is furnished to some extent by the fact that the production of starch granules is restricted to the vegetable kingdom. Thus the Desmidiaceæ may be safely assigned to the vegetable kingdom, because they contain starch. But we must not employ this characteristic negatively; the Diatomaceæ are probably vegetables, though they do not produce starch.

Diagnostic Systems of Classification.

We have seen that diagnosis is the process of discovering the place in any system of classes, to which an object has already been referred by some previous investigation, the object being to avail ourselves of the information concerning such an object which has been already accumulated and recorded. It is obvious that this is a

y Owen, 'Essay on the Classification and Geographical Distribution of the Mammalia,' p. 20.

matter of the greatest importance, for, unless we can recognise, from time to time, objects or substances which have been before investigated, all recorded discoveries would lose their value. Even a single investigator must have some means of recording or systematizing his observations of any large number of objects like those furnished by the vegetable and animal kingdoms.

Now whenever a class has been properly formed, a definition must have been laid down, stating the qualities and circumstances possessed by all the objects which are intended to be included in the class, and not possessed completely by any other objects. Diagnosis, therefore, consists simply 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 a matter of probability. A definition can only make known a finite number of the properties of an object, so that it always remains possible that objects agreeing in those assigned properties will differ in other ones. 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 many other questions relating to definition must be treated if I am able to take up the general subject of language in another work.

Diagnostic systems of classification should, as a general rule, be arranged on the bifurcate method explicitly. Any property 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 wel marked circumstance which is present in a large part i the genus and not in the other. To refer an object to its proper place in such an arrangement we have only to Lete whether it does or does not possess the successive critial circumstances. Dana devised a classification of this kind1 by which to refer any 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 Kobella. Minerals are divided according as they possess or do not possess metallic lustre; as they are fusible (including under fusible substances those which are volatile) or not fusible in a determinate degree, according as they do or do not on charcoal give a metallic bead, and so on.

Perhaps the best example to be found of any arrangement simply devised for the purpose of diagnosis, is Mr. George Bentham's Analytical Key to the Natural Orders and Anamolous Genera of the British Flora,' given in his Handbook of the British Flora". In this

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z Dana's Mineralogy,' vol. i. p. 123. Quoted in Watts's Dictionary of Chemistry,' vol. ii. p. 166.

a Instructions for the Discrimination of Minerals by Simple Chemical Experiments,' by Franz von Kobell, translated from the German by R. C. Campbell, Glasgow, 1841.

b Edition of 1866, p. lxiii.

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