REMARKS 
ON THE FIGURES OF PLATE LIII. 
ENTITIES OF DISTINCT SPECIES ARE SEVERALLY PRODUCED UNDER THE OPERATION OF THE LAWS OF 
SERIES AND SYMMETRY. 
INITY, when contrasted with infinity, manifests, through this mode of comparison, the law which operates 
for the creation of finite entities; and lends interpretation algo to the creations of finite uniform 
serieses themselves. very finite line of serial uniform creations in organic nature terminates by one or 
other of the following modes, viz.: either by the cycle and some of its modifications, or by the 
graduated scale caused by the subtraction, metamorphosis, or increation of quantity proper to the plus 
units of series. Hyery finite right line is composed of a series of uniform points: the genetic point 
is equal and homologous with the terminal point of such line; and its finity is owing to increation, 
a process which may be said to be the cause of its finity, for as much as we may ourselves produce 
it of greater dimensions, or even conceive it possible that by a simple extension it may be produced 
to infinity. But the line is, in nature, created finite, and increation is the cause of its finity. Every 
quantity standing in the same serial order is represented by every point of that serial line. The plus 
unit of every series will, if repeated as plus ad infinitum, extend series ad infinitum. We can - 
This 
finity of a serial order produced in right lines is effected by the graduated metamorphosis of serial 
fancy this, even though we find that all serial creations are actually rendered finite in Nature. 
quantity ; and the series, whichever it may be, presents itself in plus and, minus variety, the vanishing 
point or termination bearing the same ratio to the plus unit from which it has been metamorphosed, 
as a — 6 bears tow + 6; and thus we have the serial line of plus quantities 9, 9, 9,9, 9, 9, 9, 9,9, 
proportionally degraded to the converging series 9, 8, 7, 6, 5, 4,3, 2, 1, &c. 
The repetition of form, which is creative of symmetrical 
and serial homology, produces an entire figure whose 
character is an aggregate of similar elements. The series 
of quantities which constitute the entire structural form 
takes order similar to an arithmetic series of proportions 
and progressions. The series may present itself in simple 
linear order of equal plus quantities, or those quantities 
may be graduatedly proportioned from extreme plus to 
extreme minus. As an example of the first arrangement 
we may view 9, 9,9, 9,9, 9,9, 9,9; and as an example of the 
second, 9, 8,7, 6,5, 4, 3,2, 1. Both these varieties of series, 
regarded as structural designs, may again vary the general 
character of their serial forms in very many ways; as; for 
example, the series may remain as linear, or it may be 
afterwards curved upon itself, spirally twisted upon itself, 
circular, or radiated. 
Fig. A describes the carapace of a species of Chelonia. 
Its general figure is symmetrical, and its several elemental 
pieces are serially arranged from 1 to 5, and from 6 to 9. 
Fig. B, the plastrum of the same animal, is also sym- 
metrical, and its pieces are laid in serial order from 1 to 6. 
Fig. C, a Scutella dentata, is symmetrical, and its pieces 
take the serial order from 1 to 6, and from 5 to 1. 
Fig. D, another form of Scutella, is symmetrical, and 
having its pieces, 1, 2, 3, serially homologous. 
Fig. H, a Chiton Goodallii, is symmetrical, and its pieces 
are laid in serial order from 1 to 9. 
Fig. F, a star-fish, is symmetrical, with its rays serially 
ordered; each ray, from its base to apex, showing a 
graduated order of proportional tesselated structure, plus 
at the base, minus at the apex. 
Fig. G represents the section of a convoluted shell, each 
volute, from the small internal one to the outermost, being 
a repetition of the other. ‘The series from 1 to 4 is rolled 
upon itself, and describes the progressive stages of the 
animal development from minus to plus form. 
Fig. H is a section of a spiral shell, describing the serial 
order of development from 1 to 11. 
