ions
we find in the world they supposed to be occasioned by the bond of
harmony. "Since the principles of things are neither similar nor
congenerous, it is impossible for them to be brought into order except
by the intervention of harmony, whatever may have been the manner in
which it took place. Like and homogeneous things, indeed, would not
have required harmony; but, as to the dissimilar and unsymmetrical, such
must necessarily be held together by harmony if they are to be contained
in a world of order." In this manner they confused together the ideas of
number and harmony, regarding the world not only as a combination of
contraries, but as an orderly and harmonical combination thereof. To
particular numbers they therefore imputed great significance, asserting
that "there are seven chords or harmonies, seven pleiads, seven vowels,
and that certain parts of the bodies of animals change in the course of
seven years." They carried to an extreme the numerical doctrine,
assigning certain numbers as the representatives of a bird, a horse, a
man. This doctrine may be illustrated by facts familiar to chemists,
who, in like manner, attach significant numbers to the names of things.
Taking hydrogen as unity, 6 belongs to carbon, 8 to oxygen, 16 to
sulphur. Carrying those principles out, there is no substance,
elementary or compound, inorganic or organic, to which an expressive
number does not belong. Nay, even an archetypal form, as of man or any
other such composite structure, may thus possess a typical number, the
sum of the numbers of its constituent parts. It signifies nothing what
interpretation we give to these numbers, whether we regarded them as
atomic weights, or, declining the idea of atoms, consider them as the
representatives of force. As in the ancient philosophical doctrine, so
in modern science, the number is invariably connected with the name of a
thing, of whatever description the thing may be.

[Sidenote: Pythagorean physics and psychology.]

The grand standard of harmonical relation among the Pythagoreans was the
musical octave. Physical qualities, such as colour and tone, were
supposed to appertain to the surface of bodies. Of the elements they
enumerated five--earth, air, fire, water, and ether, connecting
therewith the fact that man has five organs of sense. Of the planets
they numbered five, which, together with the sun, moon, and earth, are
placed apart at distances determined by a musical law, and in