CHAPTER XIII.

HOMOLOGIES.

Ir may seem to some of my readers that ] have wandered from my subject and forgotten the title of these articles, which purport to be a series of papers on "Methods of Study in Natural History." But some idea of the progress of Natural History, of its growth as a science, of the gradual evolving of general principles out of a chaotic mass of facts, is a better aid to the student than direct instruction upon special modes of investigation; and it is with the intention of presenting the study of Natural History from this point of view that I have chosen my title.

I have endeavored thus far to show how scientific facts have been systematized so as to form a classification that daily grows more true to Nature, in proportion as its errors are corrected by a more intimate acquaintance with the facts; but I will now attempt a more difficult task, and try to give some idea of the mental process by which facts are transformed into scientific truth. I fear that the subject may seem very dry to my read

ers, and I would again ask their indulgence for details absolutely essential to my purpose, but which would indeed be very wearisome, did they not lead us up to an intelligent and most significant interpretation of their meaning.

I should be glad to contribute my share towards removing the idea that science is the mere amassing of facts. It is true that scientific results grow out of facts, but not till they have been fertilized by thought. The facts must be collected, but their mere accumulation will never advance the sum of human knowledge by one step; it is the comparison of facts and their transformation into ideas that lead to a deeper insight into the significance of Nature. Stringing words together in incoherent succession does not make an intelligible sentence; facts are the words of God, and we may heap them together endlessly, but they will teach us little or nothing till we place them in their true relations, and recognize the thought that binds them together as a consistent whole.

I have spoken of the plans that lie at the foundation of all the variety of the Animal Kingdom as so many structural ideas which must have had an intellectual existence in the Creative Conception independently of any special material expression of them. Difficult though it be to present these plans as pure abstract formulæ, distinct from the animals that represent

them, I would nevertheless attempt to do it, in order to show how the countless forms of animal life have been generalized into the few grand, but simple intellectual conceptions on which all the past populations of the earth as well as the present creation are founded. In such attempts to divest the thought of its material expression, especially when that expression is multiplied in such thousand-fold variety of form and color, our familiarity with living animals is almost an obstacle to our success. For I shall hardly be able to allude to the formula of the Radiates, for instance, the abstract idea that includes all the structural possibilities of that division of the Animal Kingdom,—without recalling to my readers a Polyp or a Jelly-Fish, a Sea-Urchin or a Star-Fish. Neither can I present the structural elements of the Mollusk plan, without reminding them of an Oyster or a Clam, a Snail or a CuttleFish, or of the Articulate plan, without calling up at once the form of a Worm, a Lobster, or an Insect, or of the Vertebrate plan, without giving it the special character of Fish, Reptile, Bird, or Mammal. Yet I insist that all living beings are but the different modes of expressing these formulæ, and that all animals have, within the limits of their own branch of the Animal Kingdom, the same structural elements, though each branch is entirely distinct. If this be true,

and if these organic formulæ have the precision of mathematical formulæ, with which I have compared them, they should be susceptible of the same tests.

The mathematician proves the identity of propositions that have the same mathematical value and significance by their convertibility. If they have the same mathematical quantities, it must be possible to transform them, one into another, without changing anything that is essential in either. The problem before us is of the same character. If, for instance, all Radiates, be they Sea-Anemones, Jelly-Fishes, Star-Fishes, or SeaUrchins, are only various modes of expressing the same organic formula, each having the sum of all its structural elements, it should be possible to demonstrate that they are reciprocally convertible. This is actually the case, and I hope to be able to convince my readers that it is no fanciful theory, but may be demonstrated as clearly as the problems of the geometer. The naturalist has his mathematics, as well as the geometer and the astronomer; and if the mathematics of the Animal Kingdom have a greater flexibility than those of the positive sciences, and are therefore not so easily resolved into their invariable elements, it is because they have the freedom and pliability of life, and evade our efforts to bring all their external variety within the limits of the same structu

ral law which nevertheless controls and includes them all.

I wish that I could take as the illustration of this statement animals with whose structure the least scientific of my readers might be presumed to be familiar; but such a comparison of the Vertebrates, showing the identity and relation of structural elements throughout the Branch, or even in any one of its Classes, would be too extensive and complicated, and I must resort to the Radiates, that branch of the Animal Kingdom which, though less generally known, has the simplest structural elements.

I will take, then, for the further illustration of my subject, the Radiates, and especially the class of Echinoderms, Star-Fishes, Sea-Urchins, and the like, both in the fossil and the living types; and though some special description of these animals is absolutely essential, I will beg my readers to remember that the general idea, and not its special manifestations, is the thing I am aiming at, and that, if we analyze the special parts characteristic of these different groups, it is only that we may resolve them back again into the structural plan that includes them all.

I have already in a previous article named the different Orders of this Class in their relative rank, and have compared the standing of the living ones, according to the greater or less compli