Neither can I present the structural elements of the Mollusk
plan, without reminding them of an Oyster or a Clam, a Snail or a
Cuttle-Fish,--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 formulae, 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 formulae have the precision of mathematical
formulae, 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 Sea-Urchins, 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.
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