ie a lens) 
REMARKS ON THE FIGURES OF PLATE XXIX. 
THE NUMERICAL ENTIRE LENGTH OF EACH MAMMALIAN SERIAL AXIS VARIES LIKE THE NUMERICAL LENGTH 
ai By OF ANY REGION OF THOSE AXES. 
UMBER is serial and illimitable. The laws of proportions and progressions are likewise illimitable. 
The mammal spinal series being one of proportional quantities, is also seen to be variable, both 
as to serial number and serial proportioning. Uniformity as to existing quantity cannot therefore be 
said to characterise the mammalian axes either generally or individually contemplated. If two or more 
skeleton serieses are seen to vary, so likewise is the one skeleton series seen to vary. If neither the 
entire numerical length of series or any one of its regional divisions be produced of set and fixed 
number for a plurality of animals in the same class or the same species, the same may be said with 
regard to the individuals for it evinces through its several phases of development a variation from minus 
to plus quantity. Uniformity, absolute and unexceptional, characterises the series of integers written 
fase 9, 9; 9, 9,9, 9, and if these be extended ad cnfinitum, still they will maintain their linear uniform 
meaning.” To imagine this serial lme of infimite uniformity, is also to create the ideas of its possible 
saan’ proportional variety, for if the creation of 9 may be serially succeeded by 9 to infinity, so 
may the infinity of this series be infinitely varied by the subtraction of 9, and hence we can conceive 
any proportional length of such a series. Such are the varieties or proportional serial lengths which 
vary all skeleton serieses from occiput to caudex. But as the number 9 is an integer, and will if repeated 
in series produce a uniform series of integers, so will the costo-vertebral quantity as a whole produce, 
when repeated in series, the plus uniform order of such structures from origin to termination of the 
line. The mammalian serial axis is not thus produced, because metamorphosis, or the subtraction of 
quantity, has (under the eye and government of design) reduced one region of such an oon plus 
series to cervical fitness, another region to lumbar character, and another region to the extreme 
degradation of caudal quantity, while the thoracic series persists in its original plus quantity. The 
serial costo-vertebral quantities, like the serial integers, 9, 9, 9, &c., are subjected to the law of proportioning, 
and thus original plus uniformity is struck proportionally various, according to the required design. 
Hitherto we have only compared the human skeleton axis 
to itself, and so far as we have proceeded we have seen 
that the serial order of the units constituting the human 
spine proves those units to vary amongst themselves, simply 
as plus and minus quantities. But the main object of this 
comparison was to have it understood that each of the 
minus or vertebral units had been metamorphosed from 
their own plus costo-vertebral quantities, and under those 
ideas we have sought to interpret the occurrence of such 
creations as cervical and lumbar ribs. 
The framework of man is comparable to that of the 
lower animals. We have only to anatomise this fact in 
order to know it, and to know also that the law of Nature 
is one and the same in the creation of all animal beings, 
the only difference between them as corporeal structures 
being that which exists between plus and minus quan- 
tities. 
Animal bodies are one and all products of the same law - 
of development. A Newton, a Leibnitz, a Geoffroy, or a 
Cuvier, could not deny that their own corporeal frame- 
