REMARKS ON THE FIGURES OF PLATE X. 
THE MINUS PROPORTIONAL IS REFERRED TO THE PLUS QUANTITIES OF THE SAME SERIAL ORDER. 
HE comparison of two minus quantities, even though they be homologous elements, will teach nothing 
further than that they are identical. But the comparison of a minus quantity with a plus archetype 
invariably points to the law of their difference as to quantity. When we subtract eight from the integer 
nine, as thus, 9—8, we find the remainder to be 1, and so 9—8=1. Now this remainder one can be 
considered in two different modes: first, we may regard it as an irrelationary quantity ; secondly, as a 
quantity which relates to an integer. When we say 9—8=1, it is the same as saying that one is a 
fractional quantity of the integer nine, and thus it relates to nine. For reciprocally as 9—8=1, so 
1+8=9; thus one is a fractional of the quantity nine: and it is in this way that we here design to consider 
it. The comparison of the quantity one with such another quantity produces only the idea of equality. 
One added to one makes two, 1+1=2, and one subtracted from one leaves nothing, 1—1=0. But the 
comparison of one with the integer nine creates the idea that the latter quantity is plus eight to the 
former, and consequently that the former is minus eight to the latter ; consequently, also, that one is now a 
quantity isolated and per se, because eight units have been subtracted from the integer nine. 
It is thus 
that minus may be compared to plus, in the quantities taking serial order for the spinal axis. 
When we have once seen the figure of an archetype or 
entirety, we then never fail, when meeting with any single 
element left remaining after the metamorphosis of that 
archetype, to know the full form to which such element 
refers. 
We have seen already that all vertebre of series, 
reckoning from the occiput to the first sacral form, 
present the same elemental structures; and consequently 
that, notwithstanding some slight transitional modifi- 
cations, those vertebre were absolutely homologous. 
Thus A”, the cervical vertebra, is homologous with B”, or 
with C”’, or with D”, which is the same as saying that D” 
C’ B’ and A” were all identical with each other. 
Now it is very easy to understand, that if fitness 
demanded the modification or metamorphosis of any of 
those forms A” B”’C” or D”, it could obliterate one or 
more or all of their elemental structures, leaving either 
similar elements, persisting from each, or dissimilar ele- 
ments of each. All may be homologously metamorphosed 
to the spmous processes, or the centrums; or else the 
spimous process of one, the centrum of another, the neural 
arch of another, or the autogenous costal process of 
another, may be the only element left remaining after 
metamorphosis. We know, then, that since the part 
speaks of the whole, so any one of those elements proper 
to the vertebral whole or archetype must refer to that 
archetype and to no other figure. 
We say, therefore, that even though the form A” suf- 
fered metamorphosis in all its parts, down to the nucleary 
piece, marked a, of its centrum, such a piece, whilst still 
holding series with all other centrums of the vertebral 
range, must refer to the vertebral archetype from which 
it has been metamorphosed. If A” can suffer meta- 
morphosis down to the nucleus a, so likewise can B” or C” 
or D”. 
The form marked E’”” is the last caudal ossicle, and it 
is seen to hold series with all the centrums of all the 
vertebre ; consequently, if we here interpret it as a form 
reduced or metamorphosed from a vertebral archetype 
which was the exact counterpart of any other vertebra of 
series, then we believe that there can be no objection to 
the reading thus given of it. 
No one will hesitate for a moment in comparing B’”, 
the ultimate caudal bone, with H’”’, the penultimate caudal 
form, and wherefore, then, should any one object to com- 
paring it with KE”, with E’, with D’C’B” or A”. If KH” 
be reasonably interpreted as a proportional of H’’, so may 
it also be named the proportional of such a form as EH”, or 
HY, or D’C’B” or A”. 
Consequently we have referred fig. K’”” to all the ver- 
