"The law which seemed to govern this series fails at the one hundred million and second term. That term is larger than we expected by ten thousand. The next term is larger than was anticipated by thirty thousand. If we still continue to observe the numbers presented by the wheel, we shall find that for a hundred, or even for a thousand terms, they continue to follow the new law relating to the triangular numbers; but after watching them for twenty-seven hundred and sixty-one terms, we find that this law fails in the case of the twenty-seven hundred and sixty-second term. If we continue to observe, another law then comes into action. This will continue through fourteen hundred and thirty terms, when a new law is again introduced, which extends over about nine hundred and fifty terms; and this, too, like all its predecessors, fails, and gives place to other laws, which appear at different intervals. It is also possible so to arrange the engine, that at any periods, however remote, the first law shall be interrupted for one or more times, and be superseded by any other laws, after which the original law shall be again produced, and no other deviation shall ever take place. "Now, it must be remarked that the law that each number presented by the engine is greater by unity than the preceding number, which law the observer had deduced from an induction of a hundred million of instances, was not the true law that regulated its action; and that the occurrence of the number one hundred million ten thousand and two at the one hundred million and second term was as necessary a consequence of the original adjustment as was the regular succession of any one of the intermediate numbers to its immediate antecedent. The same remark applies to the next apparent deviation from the new law, which was founded on an induction of two thousand seven hundred and sixty-one terms; and to all the succeeding laws, with this limitation only, that whilst their consecutive introduction at various definite intervals is a necessary consequence of the mechanical structure of the engine, our knowledge of analysis does not yet enable us to predict the periods at which the more distant laws will be introduced."--_Ninth Bridgewater Treatise._