s variations, all occurring together,
is an improbability of the same kind. If we suppose that any single
variation occurs on the average once in _m_ times, the probability of {53}
that variation occurring in any individual will be

1/_m_;

and suppose that _x_ variations must concur in order to make an
improvement, then the probability of the necessary variations all occurring
together will be

1/_m_^x.

Now suppose, what I think a moderate proposition, that the value of _m_ is
1,000, and the value of _x_ is 10, then

1/_m_^x = 1/1000^{10} = 1/10^{30}.

A number about ten thousand times as great as the number of waves of light
that have fallen on the earth since historical time began. And it is to be
further observed, that no improvement will give its possessor a _certainty_
of surviving and leaving offspring, but only an _extra chance_, the value
of which it is quite impossible to estimate." This difficulty is, as Mr.
Murphy points out, greatly intensified by the undoubted fact that the
wonderfully complex structure has been arrived at quite independently in
beasts on the one hand and in cuttle-fishes on the other; while creatures
of the insect and crab division present us with a third and quite
separately developed complexity.

As to the ear, it would take up too much space to describe its internal
structure;[42] it must suffice to say that in its interior there is an
immense series of minute rod-like bodies, termed _fibres of Corti_, having
the appearance of a key-board, and each fibre being connected with a
filament of the auditory nerve, these nerves being like strings to be
struck by the keys, _i.e._ by the fibres of Corti. Moreover, this apparatus
is supposed to be a key-board in function as well as in appearance, the{54}
vibration of each one fibre giving rise, it is believed, to the sensation
of one particular tone, and combinations of such vibrations producing
chords. It is by the action of this complex organ then, that all the
wonderful intricacy and beauty of Beethoven and Mozart come, most probably,
to be perceived and appreciated.

Now it can hardly be contended that the preservation of any race of men in
the struggle for life ever depended on such an extreme delicacy and
refinement of the internal ear,--a perfection only exercised in the
enjoyment and appreciation of the most perfect musical performances. How,
then, could either the minute incipient stages, or the final perfecting
touche