2, REMARKS ON THE FIGURES OF PLATE XXXI. 
be also named the structural minus proportionals of such 
an archetype as shall be found symmetrically produced as 
to back and front as well as side and side. We know that 
fig. D is a proportional of the thoracic plus quantity. 
We also know that figs. A and G, the cervical and lumbar 
vertebrae, are proportionals of the like quantities, for their. 
anomalous costal growth prove it. We also infer, from the 
general line of serial proportional quantities, that fig. K, 
the caudal centrum, is a proportional of the like thoracic 
If, then, fig. D be the proportional of the 
existing thoracic archetype, as seen in mammal skeletons, 
quantity. 
and this archetype itself be the proportional of some fuller 
quantity hereafter to be named, so may we conclude that 
figs. A, G, and K are also the proportionals of this same 
fuller quantity. 
But the present object is to prove that.in the mammal 
skeleton axis the thoracic quantity stands as the archetype 
of such a series. 
What figs. B and C explain in reference to fig. A, is also 
expressed by figs. EH and F of fig. D, and by figs. H and I 
of fig. G, and by L and M of fig. K. 
Now as we have before said that it is absolutely impos- 
sible for the anatomist to develope the idea of osteological 
unity or the whole quantity by any mode of measurement 
to which he subjects the actual condition of forms which 
he does not understand to be as proportional quantities, 
so must it also be evident that under this mode of 
comparison carried upon parts, he can never appreciate 
the full sum of design as fashioned by the hand of Nature. 
The osseous quantity, wherever it happens in series, fur- 
nishes a self-evident proof of its mechanical design ; but 
this is not all which comparative science demands in illus- 
tration of the law of form. The vertebral quantity is 
acknowledged to be a mechanical fitness, and the descrip- 
tive anatomist gives it a name accordingly; but the com- 
parative anatomist rejects that barren mode of contem- 
plating the ens, and after having filled the ear of scientific 
Europe with “the vertebral theory ” and absolute unifor- 
mity, he leads us only half way up the Parnassus height, 
and from thence he fires his poetic shafts into the thin ether 
of empyreal transcendency, and generalises upon an ideal 
figure which he calls “ typical,’ but which figure is still an 
unknown quantity, immeasurable, undefinable, an arbitrary 
rule, false in its application, vague, void, unfixed, unlimited, 
and changing with the law of metamorphosis as with the 
borrowed traits of colour, a form which is called unity or 
the vertebral type, but which may as well be called non- 
existence, forasmuch as it is nowhere to be found described 
upon the anatomical chart in fixed character, if it have any 
such character at all. 
The abstract term of unity can claim no relationship 
with the science of anatomy, unless as appended to the 
anatomical figure which may be demonstrated as an 
abstract. or whole quantity, and where is this demonstrable 
Is it to be seen in the form 
which we commonly term the vertebra? ‘It would be no 
less absurd to read it in the form which we ordinarily 
name the costa. And consequently, since it is not to be 
found in either the vertebral or the costal quantity sepa- 
whole quantity to be found? 
rately considered, the only resource which we have re- 
maining is to seek for it im the combined relationship of 
both these parts, which we hold to be naturally inseparable 
from each other. 
It is true that semicircles, though standing separately, 
still argue the existence of the whole quantity or circle, - 
and it is no less true that the vertebra and costal pair 
naturally cleave towards each other descriptively of a whole 
or entire design. Therefore when we meet with the 
separate semicircle (as this will imvariably describe its 
counterpart), so do we spontaneously create the presence 
of the entire circle, and it is even so with the separate 
vertebra or the separate rib, for we hold it to be impossible 
to know either one part or the other without knowing: 
their combined structural entirety. It is the measure of 
reason to compare all relationary parts for the sole purpose 
of ascertaining the span, capacity, and full meaning of the 
whole. The part has no meaning in itself considered 
separately from the other parts which furnish to it its 
proper character and function, for the character of the part 
is, that it is the part of a whole quantity, and the function 
of such part is one which it bears in common with all other 
parts naturally related to itself. The thoracic costa is 
without either character or function, except we read it in 
connexion with the dorsal vertebra, and this again is with- 
out character or function, except we consider it relatively 
to the coste. 
interpretation to each other, so do they naturally combine 
Since, therefore, these parts mutually lend 
to figure forth a whole design, and to this design we here 
give the name costo-vertebral, as being a whole quantity 
met with in the thoracic series of the skeleton figures of 
terrestrial animals. 
And while we measure the design and structural quan- 
tity of this costo-vertebral figure, we find that all those 
minus quantities which stand in serial order with it can be 
referred to some proportionals of it, and therefore it is that 
we call it plus unity, that is to say, the whole standard 
figure, such as we represent it in fig. D, performing the 
ventral circle. To fig. D, the thoracic costo-vertebral 
quantity, we refer fig. A, the cervical vertebra, either as it 
now presents in minus condition or as it occasionally 
presents with costal “anomalies.” To fig. D we also refer 
fig. G, the lumbar vertebra, either as it now stands in series, | 
or as it sometimes presents itself with costal “ anomalies.” 
And to fig. D we im like manner refer fig. K, as being a 
caudal proportional metamorphosed from such another plus 
quantity as fig. D.* We have drawn the ventral circle 
* “Nor is it easy, when such a difference arises, to settle the point, if the excess or diminution be not glaring. If we differ in opinion about 
two quantities, we can have recourse to a common measure, which may decide the question with the utmost exactness; and this, I take it, is 
what gives mathematical knowledge a greater certainty than the other. But in things whose excess is not judged by greater or smaller, as 
smoothness and roughness, hardness and softness, darkness and light, the shades of colours, all these are very easily distinguished when the 
difference is in any way considerable, but not when it is minute, for want of some common measures, which perhaps may neyer come to be 
discovered.” —Burke, Philosophical Enquiry into the Origin of our Ideas of the Sublime and Beautiful, \ntrod. on Taste. 
