REMARKS ON THE FIGURES OF PLATE XII. 
THE DUPLICATION OF A VERTEBRA CREATES A FIGURE OF BILATERAL AND ANTERO-POSTERIOR SYMMETRY. 
RGANISED beings, throughout the entire chain of animate nature, are developed symmetrically. The 
fossilized animal remains manifest the character of symmetry, and thus we see the law to prevail 
not only generally through existing nature, but even to have existed through the records of all time past. 
The duplex or bilateral form is one of self-centering, and the median line which ranges between both 
sides from end to end of the being, is that place of fluxion where duality becomes the azygos structure. 
The development of the animal form, from the primitive germinal trace to the adult completion of the 
process, continuously obeys the law of symmetry, and this so correctly, that a side of the animal represents 
its opposite in all respects not less truly than the one half of a perfect sphere imitates the other. But 
EN it be the general rule for all animal forms to present in bilateral symmetry, or the absolute 
homology of sides, we find that symmetry is a character not generally attaching to anterior and posterior 
faces. The vertebral figure also is thus characterised,—its dorsal face does not always represent its ventral 
face ; but then, as it is acknowledged that as yet we do not understand the typical or archetype vertebral 
quantity, so it would be premature and useless either to affirm or deny whether symmetry does or does not 
manifest itself on all sides or faces of this figure. It is quite evident that antero-posterior symmetry does 
not characterise the form which they call vertebra in the human skeleton axis, but then there is every 
reason to believe that this vertebral figure is not a whole quantity, and perhaps it is on this account 
that it presents to us in bizarre or eccentric shape. 
If a part tells of the whole quantity of which it is a 
part, so will the half still more potently speak of its coun- 
terpart; and thus complete, in idea, the whole form. 
Even when we meet with either the part or the half 
standing isolatedly, we cannot fail to sum up the ideas of 
the remainder which is lost, and thereby complete the 
archetype form of symmetry. In short, the rule of 
analogy is never absent from the mind, and this is proved 
by the fact, that the half of any quantity of form or 
number in nature is suggestive of its analogue, or else 
suggests nothing at all concerning truth. The half of an 
oak, cleft perpendicularly, the half of a sphere, cleft 
through its centre, or the half of a man, cleft through his 
median line, causes us to equate the half with the whole, 
and so to create, in imagination, the idea of the entire oak, 
or sphere, or human figure. All perfect forms, whether 
of inorganic or organic nature, are symmetrical. 
The repetition of any form whatever is productive of 
symmetry ; when we repeat a side, we produce a form of 
symmetrical sides or analogues, and when we repeat the 
symmetrical form, we produce a homologue. The repe- 
tition of form is productive of the Beautiful; for the 
symmetrical is the Beautiful, since it then becomes the 
intelligible. 
When we repeat the semicircle at fig. A’, or the triangle 
at fig. A”, or the semi-square at fig. A’, we then create 
the circle, the double triangles, and the square figure, and 
these forms are one and all symmetrically cleavable 
through the antero-posterior median line, 2, as well as 
bemg symmetrically cleavable through the transverse 
diameter, 1. The repetition of a vertebra, and the appli- 
cation of the centrum of one to the centrum of the other, 
produces in like manner a form which is symmetrically 
cleavable from back to front, and from side to side, as 
seen in the opposite figures. 
In fig. A’ we see that the vertebral form, repeated above 
as below, produces an entire structure, which, like the 
circle, is symmetrically cleavable either by the line 1 or 2. 
In fig. A”, again, we see that the vertebral form, 
repeated below as above, produces a structural entirety 
