the hundred million and second term. This term is larger than we expected, by 10,000. The next term is larger than was anticipated by 30,000, and the excess of each term above what we had expected forms the following table: 10,000 30,000 60,000 100,000 150,000 ::: ::: being, in fact, the series of triangular numbers,* each_multiplied by 10,000. "If we now 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 2761 terms, we find that this law fails in the case of the 2762d term. “If we continue to observe, we shall discover another law then coming into action, which also is dependent, but in a different manner, on triangular numbers. This will continue "The numbers 1, 3, 6, 10, 15, 21, 28, etc., are formed by adding the successive terms of the series of natural numbers thus: 1=1. 1+2=3. 1+2+3= 6. 1+2+3+4= 10, etc. They are called triangular numbers, because a number of points corresponding to any term can always be placed in the form of a triangle; for instance: through about 1340 terms, when a new law is again introduced, which extends over about 950 terms; and this too, like all its predecessors, fails, and gives place to other laws, which appear at different intervals. "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 instances, was not the true law that regulated its action; and that the occurrence of the number 100,010,002 at the 100,000,002d term was as necessary a consequence of the original adjustment, and might have been as fully foreknown at the commencement, 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 2761 terms, and also to the succeeding law; with this limitation only—that while their consecutive introduction at various definite intervals is a necessary consequence of the mechanical structure of the engine, our knowledge of analysis does not enable us to predict the periods themselves at which the more distant laws will be introduced. "Such are the facts which, by a certain adjustment of the Calculating Engine, would be presented to the observer. Now, let him imagine another engine, offering to him precisely the same figures in the same order of succession; but let it be necessary for the maker of that other engine, previously to each apparent change in the law, to make some new adjustment in the structure of the engine itself, in order to accomplish the ends proposed. The first engine must be susceptible of having embodied in its mechanical structure that more general law of which all the observed laws were but isolated portions a law so complicated that analysis itself, in its present state, can scarcely grasp the whole question. The second engine might be of far simpler contrivance; it must be capable of receiving the laws impressed upon it from without, but is incapable, by its own intrinsic structure, of changing, at definite periods, and in unlimited succession, those laws by which it acts. Which of these two engines would, in the reader's opinion, give the higher proof of skill in the contriver? He cannot for a moment hesitate in pronouncing that that on which, after its original adjustment, no superintendence was required, displayed far greater ingenuity than that which demanded, at every change in its law, the intervention of its contriver. "In turning our views from these simple consequences of the juxtaposition of a few wheels, it is impossible not to perceive the parallel reasoning, as applied to the mighty and far more complex phenomena of nature. To call into existence all the variety of vegetable forms, as they become fitted to exist, by the successive adaptations of their parent earth, is undoubtedly a high exertion of creative power. When a rich vegetation has covered the globe, to create animals adapted to that clothing, which, deriving nourishment from its luxuriance, shall gladden the face of nature, is not only a high but a benevolent exertion of creative power. To change, from time to time, after lengthened periods, the races which exist, as altered physical circumstances may render their abode more or less congenial to their habits, by allowing the natural extinction of some races, and by a new creation of others more fitted to supply the place previously abandoned, is still but the exercise of the same benevolent power. To cause an alteration in those physical circumstances - -to add to the comforts of the newly created animals-all these acts imply power of the same order, a perpetual and benevolent superintendence, to take advantage of altered circumstances, for the purpose of producing additional happiness. "But, to have foreseen, at the creation of matter and of mind, that a period would arrive when matter, assuming its prearranged combinations, would become susceptible of the support of vegetable forms; that these should in due time themselves supply the pabulum of animal existence; that successive races of giant forms or of microscopic beings should at appointed periods necessarily rise into existence, and as inevitably yield to decay; and that decay and death-the lot of each individual existence-should also act with equal power on the races which they constitute; that the extinction of every race should be as certain as the death of each individual; and the advent of new genera be as inevitable as the destruction of their predecessors; to have foreseen all these changes, and to have provided, by one comprehensive law, for all that should ever occur, either to the races themselves, to the individuals of which they are composed, or to the globe which they inhabit, manifests a degree of power and of knowledge of a far higher order."-BABBAGE. "By a different distribution of atoms in the primeval world a different series of living forms on this earth would have been produced. From the same causes, acting according to the same laws, the same results will follow; but from different causes, acting according to the same laws, different results will follow. So far as we can see, then, infinitely diverse living creatures might have been created consistently with the theory of evolution; and the precise reason why we have a backbone, two hands with opposable thumbs, an erect stature, a complex brain, about two hundred and twenty-three bones, and many other peculiarities, is only to be found in the original act of creation. I do not, any less than Paley, believe that the eye of man manifests design. I believe that the eye was gradually developed, and we can in fact trace its gradual development from the first germ of a nerve affected by lightrays in some simple zoophyte. In proportion as the eye became a more accurate instrument of vision it enabled its pos sessor the better to escape destruction, but the ultimate result must have been contained in the aggregate of the causes, and these causes, as far as we can see, were subject to the arbitrary choice of the Creator."-JEVONS. "Doubtless there is in nature some invariably acting mechanism, such that from certain fixed conditions an invariable result always emerges. But we, with our finite minds and short experience, can never penetrate the mystery of those existences which embody the Will of the Creator, and evolve it throughout time. We are in the position of spectators who witness the productions of a complicated machine, but are not allowed to examine its intimate structure. We learn what does happen and what does appear, but if we ask for the reason, the answer would involve an infinite depth of mystery. The simplest bit of matter, or the most trivial incident, such as the stroke of two billiard-balls, offers infinitely more to learn than ever the human intellect can fathom. The word cause covers just as much untold meaning as any of the words substance, matter, thought, existence.”—JEVONS. NOTE TO CHAPTER VIII. The "How" we more and more comprehend; the "Why" remains as much a mystery as in the beginning of science. Thus, Tyndall, in his lectures on "Sound," explains the mechanism of the ear, and how when sound-waves act upon or are propelled against the tympanic membrane, "this is thrown into vibration, its motion is transmitted to the ends of the auditory nerve, and afterward along the nerve to the brain, where the vibrations are translated into sound." This is an admirably clear explanation of "How" the sound-waves reach the brain; it gives us the mechanics of the phenomenon; but Mr. Tyndall adds: "How it is [he really means Why] the motion of the nervous matter can thus excite the con |