Besides these doctrines of Special Homology by which the bones of all vertebrates are referred to their corresponding bones in the human skeleton, and of General Homology, by which the bones are referred to the parts of vertebræ which they represent, Mr. Owen treats of Serial Homology, the recognition of the same elements throughout the series of segments of the same skeleton; as when we shew in what manner the arms correspond to the legs. And thus, he says, in the head also, the basioccipital, basisphenoid, presphenoid and vomer are 357 homotypes with the centrums of all succeeding vertebræ. The excoccipitals, alisphenoids, orbitosphenoids, and prefrontals, are homotypes with the neurapophyses of all the succeeding vertebræ. The paroccipitals, mactoids and postfrontals, with the transverse processes of all the succeeding vertebræ: and so on. Perhaps these examples may exemplify sufficiently for the general reader both Mr. Owen’s terminology, and the intimate manner in which it is connected with the widest generalizations to which anatomical philosophy has yet been led.
The same doctrine, that the history of the Language of a Science is the history of the Science, appears also in the recent progress of Chemistry; but we shall be better able to illustrate our Aphorism in this case by putting forward previously one or two other Aphorisms bearing upon the history of that Science.
Aphorism XXVI.
In the Terminology of Science it may be necessary to employ letters, numbers, and algebraical symbols.
1. Mineralogy.
I have already said, in [Aphorism XV.], that symbols have been found requisite as a part of the terminology of Mineralogy. The names proposed by Haüy, borrowed from the crystalline laws, were so inadequate and unsystematic that they could not be retained. He himself proposed a notation for crystalline forms, founded upon his principle of the derivation of such forms from a primitive form, by decrements, on its edges or its angles. To denote this derivation he took the first letters of the three syllables to mark the faces of the PriMiTive form, P, M, T; the vowels A, E, I, O to mark the angles; the consonants B, C, D, &c. to mark the edges; and numerical exponents, annexed in various positions to these letters, represented the law and manner of derivation. Thus when the primitive form was a cube, 1B represented the result of a derivation by a decrement of one row 358 on an edge; that is, a rhombic octahedron; and 1BP represented the combination of this octahedron with the primitive cube. In this way the pentagonal dodecahedron, produced by decrements of 2 to 1 on half the edges of the cube, was represented by B² ½C G² ²G
Not only, however, was the hypothesis of primitive forms and decrements untenable, but this notation was too unsystematic to stand long. And when Weiss and Mohs established the distinction of Systems of Crystallography[66], they naturally founded upon that distinction a notation for crystalline forms. Mohs had several followers; but his algebraical notation so barbarously violated all algebraical meaning, that it was not likely to last. Thus, from a primitive rhombohedron which he designated by R, he derived, by a certain process, a series of other rhombohedrons, which he denoted by R + 1, R + 2, R − 1, &c.; and then, by another mode of derivation from them, he obtained forms which he marked as (R + 2)², (R + 2)³, &c. In doing this he used the algebraical marks of addition and involution without the smallest ground; besides many other proposals no less transgressing mathematical analogy and simplicity.
[66] Hist. Ind. Sc. b. xv. c. 4.
But this notation might easily suggest a better. If we take a primitive form, we can generally, by two steps of derivation, each capable of numerical measure, obtain any possible face; and therefore any crystalline form bounded by such faces. Hence all that we need indicate in our crystalline laws is the primitive form, and two numerical exponents; and rejecting all superfluity in our symbols, instead of (R + 2)³ we might write 2 R 3. Nearly of this kind is the notation of Naumann. The systems of crystallization, the octahedral or tessular, the rhombic, and the prismatic, are marked by the letters O, R, P; and from these are derived, by certain laws, such symbols as
3 O ½, ∞ R 2, ½ P 2, 359