2 REMARKS ON THE FIGURES OF PLATE LII. 
arrangement of her products, but not so as to quantity. 
The law of serial and symmetrical homology is the same 
as the successional and lateral repetition of form ; and this 
law, subjected to the law of metamorphosis or the sub- 
traction of quantity, is that natural agency under which 
the shell of a nautilus, the painted head of the passion- 
flower, and the skeleton axis, are severally created. By 
this assertion we do not mean that these entities are 
uniform and identical to each other; the one is a series 
specifically distinct from the other two; they are plurally 
various because they are singularly various, but it is quite 
true that in the serial composite of each may be seen the 
repetition of the first unit of each. 
Fig. A represents the upper maxilla or rostrum of the 
Saw Fish (Squalus pristis); itis a symmetrical organ, and its 
dental apparatus is arranged in series; the one side is 
homologous with the other, and the first dental unit marked 
1, holds series with the other dental units, all of which 
are homologues. 
Fig. B, an articulate animal (Squilla Mantis), is 
symmetrical, and its dorsal scales are arranged in a sym- 
metrical series from 1 to 9. 
Fig. C describes the branch of a plant whose leaves are 
characterised by the arrangement called “ duplicato- 
pinnated,” its entire figure is symmetrically cleavable 
through the midrib, and its leaves are in serial order from 
1 to 4. 
Fig. D represents the trachea of the Golden-eyed Duck 
(Anas clangula). The tracheal rings are serially arranged, 
and the entire organ is symmetrical. 
Fig. E represents the tracheal organ of the Swan (Anas 
cygnus). It is symmetrical, and its rings are arranged in 
serial order. 
Fig. F shows the serial marginal arrangement of the 
pieces of the carapace of the extinct Glyptodon clavipes. 
‘From 1 to 6, from 25 to 40, and from 45 to 52, we see that 
the serial repetition of form holds together, and it is by 
the unerring rule of serial homology that the Paleonto- 
logist is enabled to restore lost quantity, such as that 
represented by the dotted forms between unit 6 and 25, 
as also between 40 and 45. The form marked f, is one of 
the tesselated pieces of the carapace of the extinct Glyp- 
todon ornatus. It is symmetrical, and its elements are 
arranged in circular series from 1 to 4. 
Fig. G shows the linear serial -order of the scales of the 
Lepidosteus. 
Fig. H represents the foot of a gallinaceous bird; on it 
we see the serial arrangement of the scales of the cuticular 
membrane. Homologous development or serial repetition 
of form may be traced from unit 20 to unit 2; and the 
next scale which succeeds unit 2 is the nail marked 1, 
which terminates the scaly series at the distal extremity 
of the toe. The horny spur is such another scaly ap- 
pendage, shielding the rudiment of a toe. 
Fig. I shows an arrangement of leaf termed ““pinnated 
with an odd leaf:” it has serial and symmetrical order. 
Fig. K is a form of leaf termed “interruptedly pinnated :” 
its general form is symmetrical, but its serial leaflets vary 
from plus to minus; between the plus leaflets 2, 3, 4, occur 
the minus proportionals, giving the serial order of forms 
an alternate variation of greater and lesser quantities. 
Fig. L describes a flower of the Linnzan class (Polygamia 
necessaria): it represents symmetry, and a serial repetition 
of petals arranged in a circle. 
Fig. M describes a flower of the Linnean class (Icosan- 
dria). The stamens are developed in a serial circular 
order, and the whole form is symmetrical. 
Fig. N shows the single stamen of the class of flower 
(Monandria.) It is a form of symmetry. 
Fig. O shows a symmetrical repetition of form in the 
stamens of the class (Diandria.) 
Fig. P represents a triplex repetition of stamens in the 
class (Triandria.) A stamen of one sideis repeated by a sta- 
men on the opposite side, the median stamen falling with 
the median line, which bisects the whole figure of symmetry. 
Fig. Q represents the class (Tetrandria) where the two 
stamens of one side are repeated on the opposite side, and 
symmetry results. 
Fig. R shows the character of the class (Dodecandria) 
in which the laws of serial and symmetrical homology 
still prevail. The same line which cleaves the centre of 
N passes also through the centres of O, P, Q, and R. 
The opposite figures have been drawn to illustrate the 
fact that nature in the creation of each serial entity per- 
forms her work by the repetition of form in imitation 
of a first quantity.* In this process, she may be said to act 
uniformly ; but though we have every reason to designate 
her according to this manifestation as a uniform operator, 
it by no means follows that all her products are samenesses. 
It is required, therefore, that we should define the line 
which separates her laws of uniformity and variety, as well 
as that line which separates those entities which are pro- 
duced in absolute specific diversity to one another.t To 
this end, and principally in reference to the subject in 
hand, we remark as follows: 
Every organic quantity which is constituted of a series 
of units, and amongst which we can discover no other 
condition of variety save that of quantity, may be 
numbered, and may -be said to have reference to some 
serial line of whole or plus forms.t This variety as 
to quantity can only have been produced by the law 
of degradation acting upon the line of plus serial 
* Laertius observes of Pythagoras that he made unity the principle of all things, and that hence arose duality. 
+ “ Now because we cannot be certain of the truth of any general proposition, unless we know the precise bounds and extent of the species 
its terms stand for, it is necessary we should know the essence of each species, which is that which constitutes and bounds it. Because, not knowing 
this real essence, we cannot know what is, or what is not of that species ; and consequently what may or may not with certainty be affirmed of it.” 
—Locke, Human Understanding— Universal Propositions, chap. vi., p. 145. 
{ It was a common opinion amongst the ancient Philosophers, that the species of things have to each other the nature and relation of 
numbers. Whatever reason there may he to object to this assertion, when applied to forms whose substrata, intimate essence, and outward character 
manifest no manner of analogy whatever, we need not stay to inquire. 
But it seems self-evident that the several pieces which, taking serial 
order in the same ens, constitute the whole and connected serial design of the same, have actually a numerical relation with one another. 
