Unquestionably, what we ordinarily see of nature is calculated to impress a conviction that each species invariably produces its like. But I would here call attention to a remarkable illustration of natural law, which has been brought forward by Mr Babbage in his _Ninth Bridgewater Treatise_. The reader is requested to suppose himself seated before the calculating machine and observing it. 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 that changes.