It is no reply to this to say, what is no doubt abstractedly true, that whatever is possible becomes probable, if only time enough be allowed.

There are improbabilities so great that the common sense of mankind treats them as impossibilities.

It is not, for instance, in the strictest sense of the word, impossible that a poem and a mathematical proposition should be obtained by the process of shaking letters out of a box; but it is improbable to a degree that cannot be distinguished from impossibility; and the improbability of obtaining an improvement in an organ by means of several spontaneous 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.