ON THE FIGURES OF. PLATE XXI. 
REMARKS 
‘THE CAUDAL QUANTITY IS COMPARED WITH EACH QUANTITY IN THE SAME INCREASING SERIES. 
ee OR Oss, or the subtraction of elementary parts, has no limit on this side of total annihilation. 
Any whole quantity, however oreat may be its proper dimensions, will consequently, when submitted 
to the operations of metamorphosis, be varied from its original self, through all gradations of change which 
can occur between the extremes of plus and minus. Variety is infinite, because the law of its creation is 
one of infinite ovadation. When from any given integer this law of metamorphosis subtracts an infinitesimal 
part, therewith may be said to commence the line of species or variety, and this lme extends itself till 
_ metamorphosis which first subtracted an infinitesimal from the integer, may degrade the integer to an 
infinitesimal at last. The law of species follows the law of subtraction not only through the rational numbers 
or quantities of decreasing series, but also through the irrational numbers ; and therefore it is that we say 
any search which will be made for the limit of special variety, must be irrational also, for it is located 
an nthilo. 
The archetype or plus sum of form is limited. 
On the other hand, we find that the law of increase, or addition, is bounded by certain limits. 
The integer of number is, like the integer of space, an 
unknown quantity. But form, or the measurable ens and created embodiment of a thing which has its 
counterparts in Nature, must have limits. 
The thing which comparative osteologists name as unity, must 
have limits, and those limits must be a whole structural entirety. 
The smallest proportional of series which can be referred 
to a part of the archetype quantity standing also in the 
same series, must be a proportional metamorphosed from 
its own archetype... Thus, as we find that, in the serial 
spinal axis, the last caudal ossicle stands in the line 
common to all the centrums, so therefore as it holds series 
with the centrum of the thoracic archetype, it must be a 
- proportional of its own archetype which may be considered 
equal to that of the thorax. 
This assertion may at first sight appear to be a mere 
stretch of imagination. But it is a fact that natural truth 
far outstretches even the imagination, and we only for the 
first time discover the truth when we progress with nature 
through her easy law of gradation passing from plus to 
minus by those slight shades of variation which are scarcely 
discernible between the adjoining quantities, but which 
become fully obvious as a sum total when competed by 
the extremes. 
The plus and minus quantities of the serial spinal axis 
are instanced in the thoracic archetype and the last caudal 
bone. Between the sternal thoracic quantity or plus and 
-the next proportional of such a plus, viz., the asternal 
thoracic quantity, the variation is but slight. Between 
the last thoracic quantity, or twelfth costo-vertebral form, 
and the first lumbar vertebra, the variation is also slight. 
So, in like manner, but a very slight variation marks the 
penultimate and ultimate caudal bones. But when we 
hold in comparison the sternal thoracic archetype with the 
last caudal ossicle, its fellow of series, then it is that we 
marvel at the extremes of variation. This variation, how- 
ever, is only one of proportioning, metamorphosis or sub- 
traction, and hence if we interpret the caudal ossicle to 
be aserial proportional of such an archetype as that stand- 
ing in the thorax, we believe that reason is not sinned 
against any more than if we say 99 subtracted from the 
100 integer would leave behind the unit of such integer ; 
a—b=c and ¢+b=a. 
All the opposite figures are the same as those repre- 
sented in Plate XX. We have called them all the propor- 
tionals of B’, the thoracic archetype quantity with which 
they hold serial order, and so likewise does fig. I” the caudal 
ossicle which we have referred to the centrums of all those 
forms. 
As all the forms A’ C’ D’ E’ are but the varied propor- 
tionals of such as: B’, so may fig. EF’ be referred to them | 
as proportionals, and to B’ as the archetype. 
