It is impossible to examine the details of some of the so-called artificial systems of classification of plants, without finding that many of the classes are natural in character. Thus in Tournefort’s arrangement, depending almost entirely on the formation of the corolla, we find the natural orders of the Labiatæ, Cruciferæ, Rosaceæ, Umbelliferæ, Liliaceæ, and Papilionaceæ, recognised in his 4th, 5th, 6th, 7th, 9th, and 10th classes. Many of the classes in Linnæus’ celebrated sexual system also approximate to natural classes.
Correlation of Properties.
Habits and usages of language are apt to lead us into the error of imagining that when we employ different words we always mean different things. In introducing the subject of classification nominally I was careful to draw the reader’s attention to the fact that all reasoning and all operations of scientific method really involve classification, though we are accustomed to use the name in some cases and not in others. The name correlation requires to be used with the same qualification. Things are correlated (con, relata) when they are so related or bound to each other that where one is the other is, and where one is not the other is not. Throughout this work we have then been dealing with correlations. In geometry the occurrence of three equal angles in a triangle is correlated with the existence of three equal sides; in physics gravity is correlated with inertia; in botany exogenous growth is correlated with the possession of two cotyledons, or the production of flowers with that of spiral vessels. Wherever a proposition of the form A = B is true there correlation exists. But it is in the classificatory sciences especially that the word correlation has been employed.
We find it stated that in the class Mammalia the possession of two occipital condyles, with a well-ossified basi-occipital, is correlated with the possession of mandibles, each ramus of which is composed of a single piece of bone, articulated with the squamosal element of the skull, and also with the possession of mammæ and non-nucleated red blood-corpuscles. Professor Huxley remarks[564] that this statement of the character of the class mammalia is something more than an arbitrary definition; it is a statement of a law of correlation or co-existence of animal structures, from which most important conclusions are deducible. It involves a generalisation to the effect that in nature the structures mentioned are always found associated together. This amounts to saying that the formation of the class mammalia involves an act of inductive discovery, and results in the establishment of certain empirical laws of nature. Professor Huxley has excellently expressed the mode in which discoveries of this kind enable naturalists to make deductions or predictions with considerable confidence, but he has also pointed out that such inferences are likely from time to time to prove mistaken. I will quote his own words:
“If a fragmentary fossil be discovered, consisting of no more than a ramus of a mandible, and that part of the skull with which it articulated, a knowledge of this law may enable the palæontologist to affirm, with great confidence, that the animal of which it formed a part suckled its young, and had non-nucleated red blood-corpuscles; and to predict that should the back part of that skull be discovered, it will exhibit two occipital condyles and a well-ossified basi-occipital bone.
“Deductions of this kind, such as that made by Cuvier in the famous case of the fossil opossum of Montmartre, have often been verified, and are well calculated to impress the vulgar imagination; so that they have taken rank as the triumphs of the anatomist. But it should carefully be borne in mind, that, like all merely empirical laws, which rest upon a comparatively narrow observational basis, the reasoning from them may at any time break down. If Cuvier, for example, had had to do with a fossil Thylacinus instead of a fossil Opossum, he would not have found the marsupial bones, though the inflected angle of the jaw would have been obvious enough. And so, though, practically, any one who met with a characteristically mammalian jaw would be justified in expecting to find the characteristically mammalian occiput associated with it; yet, he would be a bold man indeed, who should strictly assert the belief which is implied in this expectation, viz., that at no period of the world’s history did animals exist which combined a mammalian occiput with a reptilian jaw, or vice versâ.”
One of the most distinct and remarkable instances of correlation in the animal world is that which occurs in ruminating animals, and which could not be better stated than in the following extract from the classical work of Cuvier:[565]
“I doubt if any one would have divined, if untaught by observation, that all ruminants have the foot cleft, and that they alone have it. I doubt if any one would have divined that there are frontal horns only in this class: that those among them which have sharp canines for the most part lack horns.
“However, since these relations are constant, they must have some sufficient cause; but since we are ignorant of it, we must make good the defect of the theory by means of observation: it enables us to establish empirical laws which become almost as certain as rational laws when they rest on sufficiently repeated observations; so that now whoso sees merely the print of a cleft foot may conclude that the animal which left this impression ruminated, and this conclusion is as certain as any other in physics or morals. This footprint alone then, yields, to him who observes it, the form of the teeth, the form of the jaws, the form of the vertebræ, the form of all the bones of the legs, of the thighs, of the shoulders, and of the pelvis of the animal which has passed by: it is a surer mark than all those of Zadig.”
We meet with a good instance of the purely empirical correlation of circumstances when we classify the planets according to their densities and periods of axial rotation.[566] If we examine a table specifying the usual astronomical elements of the solar system, we find that four planets resemble each other very closely in the period of axial rotation, and the same four planets are all found to have high densities, thus:—