. It is
moved by a weight, and there is a wheel which revolves through a
small angle round its axis, at short intervals, presenting to the eye
successively a series of numbers engraved on its divided
circumference.

"Let the figures thus seen, be the series 1, 2, 3, 4, 5, &c. &c., of
natural numbers, each of which exceeds its immediate antecedent by
unity.

"Now, reader," says Mr Babbage, "let me ask you how long you will
have counted before you are firmly convinced that the engine has been
so adjusted that it will continue, whilst its motion is maintained,
to produce the same series of natural numbers. Some minds are so
constituted, that after passing the first hundred terms they will be
satisfied that they are acquainted with the law. After seeing five
hundred terms, few will doubt; and after the fifty thousandth term,
the propensity to believe that the succeeding term will be fifty
thousand and one, will be almost irresistible. That term _will_ be
fifty thousand and one, and the same regular succession will
continue; the five millionth, and the fifty millionth term will still
appear in their expected order, and one unbroken chain of natural
numbers will pass before your eyes from _one_ up to _one hundred
million_.

"True to the vast induction which has been made the next succeeding
term will be one hundred million and one; but the next number
presented by the rim of the wheel, instead of being, one hundred
million and two, is one hundred million _ten thousand_ and two. The
law changes."

The illustration is carried through a page or two more, but we have quoted
all that is essential.

Mr Babbage makes a very useless parade here of his calculating machine. A
common household clock that strikes the hours, would illustrate all that
his machine can possibly illustrate. If the reader seat himself before
that homely piece of mechanism, he will hear it _tick_ for sixty minutes,
when the _law of the machine_ will change, and it will _strike_.

In a scientific point of view it is absurd to talk about the _law of his
machine_. His machine partakes only of the laws of mechanics, which, we
presume, are as constant there as elsewhere. Our only definition of law
is, a sequence that is constant; deny its constancy, and you deny it to be
law; it is a mere contradiction in terms to speak of a law th