The existence of differences of form introduces a new problem, the problem of diversity. There are only a few possible combinations of the principal organs, but as you get down to less important parts the possible scope of variation is greatly increased, and most of the possible variations do exist. Nature seems prodigal of form, of form which needs not to be useful in order to exist. "It needs only to be possible, i.e., of such a character that it does not destroy the harmony of the whole."[54] We seize here the relation of the principle of the adaptedness of parts to the problem of the variety of form. The former is in a sense a regulative and conservative principle which lays down limits beyond which variation may not stray. In itself it is not a fountain of change; there must be another cause of change. This thought is of great importance for theories of descent.

Cuvier has no theory to account for the variety of form: he contents himself with a classification. There are two main ways of classifying forms; you may classify according to single organs or according to the totality of organs. By the first method you can have as many classifications as you have organs, and the classifications will not necessarily coincide. Thus you can divide animals according to their organs of digestion into two classes, those in which the alimentary canal is a sac with one opening (zoophytes) and those in which the canal has two openings,[55] a curious forestalment, in the rough, of the modern division of Metazoa into Cœlentera and Cœlomata.

It is only by taking single organs that you can arrange animals into long series, and you will have as many series as you take organs. Only in this way can you form any Échelle des êtres or graded series; and you can get even this kind of gradation only within each of the big groups formed on a common plan of structure; you can never grade, for example, from Invertebrates to Vertebrates through intermediate forms[56] (which is perfectly true, in spite of Amphioxus and Balanoglossus!).

In the Règne Animal Cuvier restricts the application of the idea of the Échelle within even narrower limits, refusing to admit its validity within the bounds of the vertebrate phylum, or even within the vertebrate classes. This seems, however, to refer to a seriation of whole organisms and not of organs, so that the possibility of a seriation of organs within a class is not denied. Cuvier was, above all, a positive spirit, and he looked askance at all speculation which went beyond the facts. "The pretended scale of beings," he wrote, "is only an erroneous application to the totality of creation of partial observations, which have validity only when confined to the sphere within which they were made."[57] This remark, which is after all only just, perfectly expresses Cuvier's attitude to the transcendental theories, and was probably a protest against the sweeping generalisations of his colleague, Etienne Geoffroy St Hilaire.

A true classification should be based upon the comparison of all organs, but all organs are not of equal value for classification, nor are all the variations of each organ equally important. In estimating the value of variations more stress should be laid on function than on form, for only those variations are important which affect the mode of functioning. These are the principles on which Cuvier bases the classification of animals given in the Leçons, Article V., "Division des animaux d'après l'ensemble de leur organisation." The scheme of classification actually given in the Leçons recalls curiously that of Aristotle, for there is the same broad division into Vertebrates, with red blood, and Invertebrates, almost all with white blood. Nine classes altogether are distinguished—Mammals, Birds, Reptiles, Fishes, Molluscs, Crustacea, Insects, Worms, Zoophytes (including Echinoderms and Cœlenterates).

A maturer theory and practice of classification is given in the Règne Animal of seventeen years later. Here the principle of the subordination of characters (which seems to have been first explicitly stated by the younger de Jussieu in his Genera Plantarum, 1789,[58]) is more clearly recognised. The properties or peculiarities of structure which have the greatest number of relations of incompatibility and coexistence, and therefore influence the whole in the greatest degree, are the important or dominating characters, to which the others must be subordinated in classification. These dominant characters are also the most constant.[59] In deciding which characters are the most important Cuvier makes use of his fundamental classification of functions and organs into two main sets. "The heart and the organs of circulation are a kind of centre for the vegetative functions, as the brain and the spinal cord are for the animal functions."[60] These two organ-systems vary in harmony, and their characters must form the basis for the delimitation of the great groups. Judged by this standard there are four principal types of form,[61] of which all the others are but modifications. These four types are Vertebrates, Molluscs, Articulates, and Radiates. The first three have bilateral, the last has radial symmetry. Vertebrates and Molluscs have blood-vessels, but Articulates show a functional transition from the blood-vessel to the tracheal system. Radiates approach the homogeneity of plants; they appear to lack a distinct nervous system and sense organs, and the lowest of them show only a homogeneous pulp which is mobile and sensitive. All four classes are principally distinguished from one another by the broad structural relations of their neuromuscular system, of the organs of the animal functions. Vertebrates have a spinal cord and brain, an internal skeleton built on a definite plan, with an axis and appendages; in Molluscs the muscles are attached to the skin and the shell, and the nervous system consists of separate masses; Articulates have a hard external skeleton and jointed limbs, and their nervous system consists of two long ventral cords; Radiates have ill-defined nervous and muscular systems, and in their lowest forms possess the animal functions without the animal organs.

This well-rounded classification of animal forms is in a sense the crown of Cuvier's work, for the principle of the subordination of characters, in the interpretation which he gives to it, is a direct application of his principle of functional correlation. Each of the great groups is built upon one plan. The idea of the unity of plan has become for Cuvier a commonplace of his thought, and it is tacitly recognised in all his anatomical work. But he never takes it as a hard-and-fast principle which must at all costs be imposed upon the facts.

Cuvier has become known as the greatest champion of the fixity of species, but it is not often recognised that his attitude to this problem is at least as scientific as that of the evolutionists of his own and later times. No doubt he became dogmatic in his rejection of evolution-theory, but he was on sure ground in maintaining that the evolutionists of his day went beyond their facts. He considered that certain forms (species) have reproduced themselves from the origin of things without exceeding the limits of variation. His definition of a species was, "the individuals descended from one another or from common parents, together with those that resemble them as much as they resemble one another."[62] "These forms are neither produced nor do they change of themselves; life presupposes their existence, for it cannot arise save in organisations ready prepared for it."[63]

He based his rejection of all theories of descent upon the absence of definite evidence for evolution. If species have gradually changed, he argued, one ought to find traces of these gradual modifications.[64] Palæontology does not furnish such traces. Again, the limits of variation, even under domestication, are narrow, and the most extreme variation does not fundamentally alter the specific type. Thus the dog has varied perhaps most of all, in size, in shape, in colour. "But throughout all these variations the relations of the bones remain the same, and the form of the teeth never changes to an appreciable extent; at most there are some individuals in which an additional false molar develops on one side or the other."[65] This second objection is the objection of the morphologist. It would be an interesting study to compare Cuvier's views on variation with those of Darwin, who was essentially a systematist.

Cuvier's first objection was of course determined to some extent by the imperfection of the palæontological knowledge of his time. But even at the present day the objection has a certain force, for although we have definite evidence of many serial transformations of one species into another along a single line, for example, Neumayr's Paludina series, yet at any one geological level the species, the lines of descent, are all distinct from one another.[66]