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 structural
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.
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