e established
fact of the constant co-existence of two parts as proof of a
functional correlation between them.

Correlation is either a rational or an empirical principle, according
as we know or do not know the interdependence of function of which it
is the expression. Even when we apply the rational principle of
correlation it would be useless in our hands if we had not extensive
empirical knowledge; when we use an empirical rule of correlation we
depend entirely upon observation. "There are a great many cases,"
writes Cuvier,[49] "where our theoretical knowledge of the relations of
forms would not suffice, if it were not filled out by observation,"
that is to say, there are many cases of correlation not yet explicable
in terms of function. From a hoof you can deduce the main characters
of herbivores (with a certain amount of assistance from your empirical
knowledge of herbivores), but could you from a cloven hoof deduce that
the animal is a ruminant, unless you had observed the constancy of
relation, not directly explicable in terms of function, between cloven
hoofs and chewing the cud? Or could you deduce from the existence of
frontal horns that the animal ruminates? "Nevertheless, since these
relations are constant, they must necessarily have a sufficient cause;
but as we are ignorant of this cause, observation must supplement
theory; observation establishes empirical laws which become almost as
certain as the rational laws, when they are based upon a sufficient
number of observations.... But that there exist all the same hidden
reasons for all these relations is partly revealed by observation
itself, independently of general philosophy."[50] That is to say, even
correlations for which no explanation in terms of function can be
supplied are probably in reality functional correlations. This may, in
some cases, be inferred from the graded correspondence of two sets of
organs. For example, ungulates which do not ruminate, and have not a
cloven hoof, have a more perfect dentition and more bones in the foot
than the true cloven-hoofed ruminants. There is a correlation between
the state of development of the teeth and of the foot. This
correlation is a graded one, for camels, which have a more perfect
dentition than other ruminants, have also a bone more in their tarsus.
It seems probable, therefore, that there is some reason, that is, some
explanation in terms of function, for this case of correlation.

Nevertheless,