ko 
B’, are the projections of the autogenous piece a, just as 
the costa of B” is produced from the piece 4, to the mid 
sternal point d. 
Now, fig. C”, the lumbar vertebra, is seen to hold ele- 
mental pieces similar in form and equal in number to fig. B’ 
and fig. A”, which are the cervical and dorsal proportionals 
of the thoracic archetype B”’; and we find that the auto- 
genous elements 6 of fig. C’” occasionally traverse the circle 
towards the median point d, hence, simulating the character 
of fig. B”. It is for this reason that fig. C’” must be inter- 
preted as the proportional of such an archetype quantity 
as fig. B”. 
Fig. C’ is the last or twelfth thoracic quantity, and its 
floating costa marked a performs, in like manner, through 
some part of the circle towards the mid point d. Hence 
it is also to be accounted as a proportional of the archetype 
quantity equal to fig. B”.. 
Fig. B’ and fig. B’, therefore, mark the proportional 
transition from cervix to thorax ; whilst fig. C’ and fig. C” 
mark the proportional transition from thorax to the lum- 
bar spe. In the former transition, we discover minus 
to be succeeded by plus; whereas, in the latter transition, 
we see that plus has been metamorphosed to minus. This 
variation we believe to have occurred on the figures of 
originally homologous archetype quantities, such as fig. B”. 
In the duty, therefore, of interpreting Nature as she is, 
and not, as it were, recreating her and bending her design 
to suit with preconceived hypothesis, we apply ourselves 
to the study of her serial order, and find the quantities of 
These 
quantities, such as they are, manifest the fact that the 
minus figure is to be found in the plus figure, and, also, 
this to be arranged in plus and minus variety. 
that the plus figure may be subtracted from, and rendered 
equal to, the minus quantity. Hence, we say, that the 
minus quantity may, by addition of elemental structure, 
be equated with the plus quantity ; and if this be said to 
be a licence performed upon created series with too free a 
hand, we then, in reply, say that Nature herself is known to 
perform the same acts, and, therefore, that it is only a copy 
of natural precedent. For it is the truth, that fig. A’, the 
seventh cervical vertebra, is seen occasionally to equate itself 
with the plus amount of fig. B”, the first thoracic arche- 
type; and also that fig. C”’, the first lumbar vertebra, now 
and then actually equates itself to the proportions of fig. C’, 
the last thoracic quantity. Whereupon, we venture to ask 
the following question, as to what we are to understand of 
the word species as characterising fig. B’ from fig. B”, or 
fig. C” from fig. C’, when it is a living fact that fig. B’ is 
not itself fixedly, nor fig. C’ remaining itself persistently, 
even in the one serial order of human type? 
When we shall consider the facts of how minus quantity 
increases to plus, and how plus quantity decreases to minus, 
we then will acknowledge to a condition of development 
which can, with as little propriety of speech, admit the 
application of the word species (in the sense of absolute 
difformity) to plus or minus quantity, as the oscillations of 
a pendulum can suffer to be described as fixation. Eyvi- 
dently, therefore, if we would understand something of 
REMARKS ON THE FIGURES OF PLATE XVIII. - 
the comparable minus and plus figures, such as figs. B’ 
and B” or C” and C’, we should concentrate attention as 
well upon the law of their development as upon the things 
produced ; and just as when we contemplate the body 
itself, whilst oscillating through an arch, we inquire, at the 
same time, into the laws of its motion. If we name fig. 
B’ as one species compared to fig. B” as another, at the 
same time that we know the former is only minus and the 
latter plus, and also that minus grows to plus, just as- 
plus may be metamorphosed to minus, then we say that 
there is'as little substance in the word species, when ap- 
plied to characterise the permanent distinctness of these 
bodies, figs. B’ and B”, as there would be in applying the 
word species to characterise difformity between two or 
more radii of the same arch, when the motionary pendu- 
Jum, as one and the same thing, becomes each radius 
successively. 
Acknowledging, therefore, to the facts of the case, we 
say of fig. B’ that it is a minus quantity compared to fig. 
B”, a plus quantity, and that we find both these figures 
With this acknowledg- 
ment, which cannot be disputed, we shall next briefly 
consider the two following themes, viz., the law of species 
and the law of form. And first, let us.ask ourselves the 
question, to what end does the study of one and the other 
of those laws promise to lead us? Has the differential 
method of searching out the limits of species in osteology 
any end? This must be answered in the negative; for, 
not to mention the fact that it is a theme which stretches 
as far back into antiquity as when Hippocrates, stringing 
vertebree together, offered them, as indecipherable enigmas, 
to the Delphian God, and gave up, as a lost subject, the 
standing in the one serial order. 
pursuit of specific variety whose name was infinity; so let 
us here know plainly, that if, by the differential method, 
we continue to read fig. B’ as a species of fig. B’, we 
should also, at once, understand that fig. B’ becomes, by 
the like rule, a species to.each and all of its phasial pius 
conditions of infinitesimal additions of quantity, till we 
find it of the same plus cast as fig. B”, the whole quantity. 
And to this let it be added, that fig. B” is struck specifi- 
cally various to itself through all the phases of infinitesi- 
mal subtraction of quautity, till it represents the form of 
B’, a proportional quantity. For the plus figure becomes 
varied by subtraction as much as the minus figure is 
varied by addition. 
The differential method is a subject illimitable in all 
cases as well as that of comparative osteology; and it 
is, therefore, that the mind renounces it altogether, or 
sleeps over it, for this is the physiological fact which we 
always observe to be evinced by an audience when the 
lecturer, subdividing a point, annihilates the thing by the act. 
When we are told, that between the rational numbers 1 
and 2, there exists an infinity of irrational numbers, who 
then shall remain awake and interested for the demonstra- 
tion of the mean proportional of | and 2, or the root of 2, 
while we find that 1] is not sufficient, and 14 too much, 
from which, if we subtract 4, we shall have subtracted too 
much, and if +,, too little? If this be all necessary to the 
