2 REMARKS ON THE FIGURES OF PLATE LIy. 
proportional of a plus skeleton form which is uniformity 
and the archetype. 
The integer 9 contains the proportionals 8, 7, 6, 5, 4, 3, 2, 
1, therefore, each of those proportionals may be interpreted 
as a proportional of the integer 9; this integer being the 
whole quantity. Now, if we disintegrate the proportionals 
of the full quantity 9, and place them in progressive series, 
thus, 1, 2, 3, 4, 5, 6, 7, 8, 9, it must be understood that each 
of these digital numbers (now separate and isolated) still is 
a proportional of the integer 9, and consequently when we 
compare those proportional quantities with each other, 
although we by no means can name them as equals, yet it 
is most true that each of them refers to the-one whole 
quantity or 9 from which they have been separated. And so, 
when we view the series of proportions 1, 2, 3, 4, 5, 6,7, 8,9, 
we consider them severally in relation to the integer 9; 
for 1 is a proportional of 9, so is 2 another proportional of 
9, and so of all the other quantities contained in 9. 
integer 9 is archetype of its own series of proportionals, 
and those proportionals can never be accounted uniform 
unless under the idea of equating them with the integer 
which is the common quantity to which all refer. One is 
not equal to two, nor is two equal to the integer nine; but 
14+8=9,and2+7=9,consequently 9-8=1, and 9—7=2. 
Fig. G represents a thoracic skeleton series. Its serial 
quantities are all costo-vertebral from first to last, the units 
of this series manifesting no other variety than that of pro- 
portioning from archetype quantity ; thus units 1, 2, and 3, 
are simply minus quantities compared to units 4, 5, 6, 7, 
&c. The common median.line cleaves all the serial quan- 
tities in order, from occiput to unit marked 61. And 
those units are simply repetitions of form throughout the 
entire series. 
Fig. H is a skeleton axis, which, when its units are 
numerically compared to those of fig. G, manifests no other 
variety than that of minus compared to plus. The first 7 
units of series in fig. G are costo-vertebral plus quantities. 
The first 7 units of series in fig. H are vertebral minus 
quantities, being simply minus as to costal structure. 
Again, in fig. G we find that the next 12 units of series 
succeeding unit 7 are also costo-vertebral and plus, when on 
turning to fig. H we find that the like plus forms are 
persistent for it also. In fig. G again we see that all the 
units of series which succeed unit 19 are persistent in their 
plus quantity; but when we seek for the like numerical 
quantities in fig. H, we find them to be minus. 
Fig. Gis an archetype series of plus costo-vertebral origi- 
nals. Fig. H is aserial structure proportioned or-metamor- 
phosed from such an archetypeas fig.G. It is possible to 
subtract quantity from fig. G so as to equate it with fig. H. 
It is also possible to fill up im idea that quantity which is 
lost to fig. H, so as to equate it with fig. G, and this can 
only happen because fig. H has been proportioned from 
such another form of archetype quantity as fig. G. The 
comparison, therefore, which is to be held between figs. G 
and H, can lead to nothing worth knowing if it be not the 
interpretation that the original or archetype quantity from 
which fig. H has been proportioned is fig. G. 
Now fig. I resembles fig. H both in general form and 
The. 
quantity ; and, therefore, we say, that if ever we are to 
appreciate the natural law of formation which created fig. 
I, it must be by understanding that fig. I has been also 
proportioned from the original or archetype quantity fig. G. 
We name figs. I and H to be homologous forms, because 
they contain forms of equal quantity and proportion. But 
when we further compare figs. I and H with fig. G, we | 
then are obliged to name the latter a plus archetype, and 
the former the minus proportionals of such plus arche- 
types; therefore, fig. G is unity, and figs. I and H are 
proportional varieties or species of such a unity. 
Metamorphosis or subtraction of quantity is that natural 
process by which fig. H has been proportioned from fig. G. 
The same process, no doubt, has fashioned the mammalian 
form fig. I from the archetype quantity fig. G. Or if it 
be doubted that fig. G is archetype of fig. I and fig. H, 
then let us ask ourselves the question, to what other goal 
of interpretation is the science of comparison promising to 
lead the anatomical reasoner ? 
If anatomical science be ever destined to reveal the law 
of unity im variety, as governing the development of 
animal form, let it determine well first of all between the 
rational and irrational, and when it turns to the com- 
parison of the opposite figures, let its first duty be to 
separate the impossible from the possible, let it under- 
stand that it is impossible to demonstrate a whole quantity 
in a part, or fig. G, in either fig. I or fig. H; whereas it 
is on the other hand possible to demonstrate the part m 
the whole quantity, or figs. I and H in fig. G. 
We have drawn through fig. G various secant lines 
indicating the Imes of metamorphosis and symmetry. 
The median line marked m, diyides the whole serial form 
from occiput to the 6lst unit of series, and would thus 
bisect the whole serial order of quantities, which in’ the 
Ophidian skeleton amounts to some hundreds, reckoning 
from occiput to the extreme caudal unit. The same line 
of median cleavage m, divides the serial proportional 
quantities of figs. I and H. It passes through fig. I from 
unit 1 to the ultimate caudal proportional marked 56, 
and through fig. H from unit 1 to unit 61, all the serial 
quantities of fig. H being evidently proportionals of such 
as the thoracic quantities of the same figure, or such as 
unit 61 of the same. 
The superior diagonal or oblique lines d s, of fig. G, 
indicate the law of proportioning, which creates minus 
quantities immediately succeeding the occiput. The same 
lines d s, of figs. I and H, point to the cervical creation or 
minus proportioning of the 7 uppermost units of series: 
those units, which are now vertebral quantities, and 
marked 1, 2,3,4,5,6,7, manifest no other difference to 
those of the thoracic region of figs. I and H, or to the 
cervical region of fig. G marked 1, 2, 3,4, 5,6, 7, than that 
of minus to plus. 
The inferior diagonal or oblique lines d 2, of fig. G meet 
each other at the median line of unit 61, and indicate the 
law of proportioning minus from plus quantities by the 
simple rule of metamorphosis, obliteration, or subtraction 
of all those parts of the serial costo-vertebral units which 
stand outside of those lines. Thus, supposing this sub- 
