d for the purpose of roofing over and protecting the cerebrum.

A very curious development was given to the vertebral theory by K. G.
Carus, who seems to have taken as his text a saying of Oken's, that the
whole skeleton is only a repeated vertebra.[158] His system is worthy of
some consideration, for he tries to work out a geometry of the
skeleton.[160]

His method of deduction is a good example of pure _Naturphilosophie_.
Life, he says, is the development of something determinate from
something indeterminate. A finite indeterminate thing, that is, a
liquid, must take a spherical form if it is to exist as an individual.
Hence the sphere is the prototype of every organic body. Development
takes place by antagonism, by polarity, typically by the division and
multiplication of the sphere. In the course of development the sphere
may change, by expansion into an egg-shaped body, or by contraction into
a crystalline form, the changes due to expansion being typical of living
things, those due to contraction being typical of dead. At the surface
of the primitive living sphere is developed the protective
_dermatoskeleton_, which naturally takes the shape of a hollow sphere;
round the digestive cavity which is formed in the living sphere is
developed the _splanchnoskeleton_; round the nervous system (which is,
as it were, the animal within the animal) is developed the
_neuroskeleton_. All skeletal formations belong to one or other of these
systems.

Carus defines his aim to be the discovery of the inner law which
presides over the formation of the skeleton throughout the animal
kingdom; he desires to know "how such and such a formation is realised
in virtue of the eternal laws of reason" (iii., p. 93). Here we touch
the kernel of _Naturphilosophie_--the search for rational laws which are
active in Nature; the discontent with merely empirical laws.

The thesis which Carus sustains is that all forms of skeleton, whether
of dermatoskeleton, splanchnoskeleton, or neuroskeleton, can be deduced
from the hollow sphere, which is the primary form of any skeleton
whatsoever (p. 95). That means, put empirically, that every skeleton can
be represented schematically by a number of hollow spheres, suitably
modified in shape, and suitably arranged. The chief modification in
shape exhibited by bones is one which is intermediate between the
organic and the crystalline series of modifications of the sphere. The
organic modifications are bound