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 other general characters.
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. Every characteristic should enable us to assert a simple identity; if A is a characteristic, and B, viewed intensively, the class of objects of which it is the mark, then A = B ought to be true. The characteristic may consist either of a single quality or circumstance, or of a group 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 importance in the general economy of the animal, but because such variations are proved 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 discriminated accurately by their teeth, especially by the foremost molars and the hindmost pre-molars. Some teeth, indeed, are occasionally missing, so that zoologists prefer to trust to those characteristic teeth which are most constant,21 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 a boundary-line between the animal and vegetable kingdoms, and it may even be doubted whether a rigorous boundary can be established. The most fundamental and important difference of a vegetable as compared with an animal substance 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 been referred by some previous investigation, the object being to avail ourselves of the information relating to such an object which has been accumulated and recorded. It is obvious that this is a matter of great importance, for, unless we can recognise, from time to time, objects or substances which have been investigated, recorded discoveries would lose their value. Even a single investigator must have means of recording and systematising his observations of any large groups of objects like 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