9 : REMARKS ON THE FIGURES OF PLATE XII. 
which, like Triangles placed base to base, is symmetrically 
cleavable by the line 2 perpendicularly, or by the line 1 
transversely. 
In fig. A” we see that the half of a vertebral form, 
repeated above and below, still produces the same form of 
entire quantity when we again repeat those halves by 
opposite halves. The vertebral structure, thus fashioned, 
becomes, like the square figure, symmetrically cleavable 
by either the perpendicular line 2 or the transverse line 1. 
This character of transverse and perpendicular sym- 
metrical cleavage, which attaches to cervical vertebral 
form, when doubled or repeated, as at A”, characterises 
likewise the dorsal vertebra, as seen at fig. B’, or the 
lumbar vertebra at C”, or the sacral vertebra at D”. 
The object which has been had in view, when drawing 
these forms, was to show, that, as the repetition of form 
produces a structural entirety, symmetrically cleavable 
from back to front, and from side to side, so may it be 
understood that the vertebral figure, which is only cleay- 
able into symmetrical sides by the antero-posterior 
diameter alone, is actually but as part of an archetype 
structure, which will hereafter show itself to be a form 
symmetrically cleavable in both directions, transversely 
and antero-posteriorly, like the circle, or the square, or 
triangles placed base to base. 
It is observed that Nature, in the creation of all first 
designs, stamps them with the character of unity or com- 
pleteness by the similarity of sides or faces, and that she 
leaves this character persistent for the forms until some 
disturbing cause, consequent to a first cause and necessary 
to a secondary adaptation of form for particular fitness 
and design, works some afterchange upon the figure of 
unity, and thus adds to it the cast of variety. 
variety may hence be regarded as a prime model subjected 
to modification. The creation of a first ens, and the 
Unity in 
modification of the same thing afterwards, is in fact a 
cause drawing after it an inevitable consequence, which is 
the suiting of a form to all external circumstance. It is 
most true that the animal form is indicative of its proper 
sphere in nature; for the wing of an eagle, the palm of a 
dolphin, and the foot of a lion, express the fact of unity 
in variety adapting itself to Nature, which is unity in 
variety also; and thus stands the relationship between the 
“natura naturata” and the “natura naturans,”’ both of 
which constitute a to way inseparable and circumvolved. 
Form, in its genesis, is cast orbicularly. The circle or 
the sphere is its primitive figure. The ovum is thus cast, 
and even the microcosm of its primitive cellular organism 
A sphere is the 
archetype of symmetry, and all those secondary forms 
displays a conglomeration of spheres. 
which Nature fashions from it are symmetrically pro- 
_duced. The cellular mass, the ovum constituted of it, the 
primitive being created of the same, are things of sym- 
metry, or the repetition and homology of sides. The 
embryo being itself symmetrical, traverses the matrix of 
symmetry, and its first act after the birth is to milk a 
homologue of the opposite organ; it lives by comparison, 
reasons by analogy, mates with its fellow, acts conformably 
with its kind, and its whole history is marked by the 
avoidance of all that is diverse or dissimilar to its own 
being in nature. The being, which is itself symmetrical, 
and the duplicate of its right side, allies itself to forms 
which most nearly resemble itself, and so the fixity of its 
species is the effect of its own first law—self-devotion. 
The form for ever turns towards its analogue, and the 
coincidence of analogues is the creation of Gemini, exactly 
as we see them in the opposite figures. 
The duplication of half is equal to the whole, just as the 
bisection of a whole is productive of its halves ; and so, the 
whole form being one constituted of relationary halves, it 
follows that when we meet with any separate half, we have 
only to repeat it in order to reproduce a whole quantity. 
In Nature, we always find that whole quantities are capable 
of bisection in any direction, but that.a half quantity or form 
is only to be bisected in certain directions. A sphere or circle 
may be rendered bipartite by any lines of section passing 
through their centres; but a hemisphere or a semicircle, 
though capable of being themselves subdivided into equal 
parts, do not admit of bisection in all directions; and the 
reason is, they are only half quantities. This character, 
which attaches to the semicircle, is one which characterises 
the vertebra also; and hence we infer that the vertebra, 
which, like the semicircle, is only bilaterally symmetric, 
is a half, or it may be a lesser quantity, of some complete 
figure, for we find that the duplication of itself, fig. A’, 
creates a whole quantity which we can bisect transversely 
and antero-posteriorly. 
Now it is true that when we view the semicircle, we also 
see the homologue of itself in itself, and this is equal to 
the knowledge of the whole circle, fig. A’. It is possible, 
therefore, to ascertain the dimensions of an entirety from 
an examination of its separate half, for we have only to 
make a duplicate of the half in order to re-establish the 
existence of the whole. It is even possible to reconstruct 
a whole from its fourth part, for the quadruplicate of the 
fourth is equalto the whole, see figs. A’A” A”. It is possible, 
therefore, to create the complete figure of circular symmetry 
(even if this figure were not already existing in nature) by 
imitating or repeating the quantity and form of its half 
twice, and its fourth four times. And it is also possible 
to reconstruct a complete vertebral form (complete, that 
is to say, so far as regards symmetrical cleavage by the 
transverse and antero-posterior lines of section,) by the 
repetition of its half twice, or its fourth quantity four 
times, as seen in the opposite figures. 
We see, therefore, that it is the character of a whole - 
form to be symmetrically cleavable into halves, and these 
again into fourths. This is the character of figs. A, B,.- 
C,and D. And also we find that the same lines which 
bisect the whole symmetrically both ways are not capable 
of again bisecting the half, except in one direction, viz., 
by the line 2. Furthermore, we see that the Imes 1 and 
2 are totally incapable of bisecting symmetrically the 
fourth part of figs. A, B, C, and D. Thus we discover, 
that, according to the degree of subdivision performed 
upon a whole, there is a graduated failure of symmetrical 
