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Show UI'"POTUX~tS OF THE DEVELOPMENT OJ' ~ox~ iJ !.arg·er than we expe.c~ed by 10,000. The next t.er.r£1 i~ ~argcr than was anticipated by 30,000, and ~he ~:!:t~~N .. 0f each term above what we had expected, founs ih•~ f{•Hr-wing table: 1.0,000 30,000 60,000 1.00,000 J f>O,OOO being, in fact, 1ihe series of triangular numbers,* each multiplied by 10,000. "If we now continue to observe the n~mbers presented by the wheel \Ve shall find that for a hundred, or even for a thousand terms, they continue to follow the new l.aw relating to the trjangular nurnbers; ~ut after .wa!ch1ng them for 27G1 terms, we find that th1s law fa1ls 1n the case of the 2762d term. . " If we continue to observe, we shall discover another Jaw then coming into action? which also is depende~t, b_ut in a different manner, on tnangular numbers. Th1s w1~l continue through about 1430 terms, when a new la\v 1s again introduce? whicl~ extends over abo~t 950 ter.ms, and thi~, too, llke all .Its predeces~01:s,. fa1b,. and gives place to other laws, which appear at different Intervals. "Now it mu~t be observed that the law that each number 11resented by the en:gine is greater by unz"ty than the preceding nu/tnber·, which law the o?s?rve~· 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 10~,0.00,002d term was as necessary a consequence of the ongtnal ad- • The numbflrs 1, 3, 6, 10, 15, 21, 28, &c., are formed by adding the successive terms of the series of natural numbers thus: I= 1 1X2= 3 1X'2X3= 6 . 1 X2X3X4= 10, &c. They are called tnan· gular numbers, because a number of points. correspond!ng to anJ t~rm cau always be placed jn the form of a tnangle ; for mstance- ... 1 3 6 Hi I THE VEGETA:SLE AND AN.tMAL KINGDOMS J()g J'ltstment, and might have been as fully foreknown at the cmnme'Y}'cc1nent, .as was the ·regul.a'r .st£ccession of any one o( the ·tntermed~ate nunybers to zts un1nediate antecedent. 1 he same remark app~Ies to the next apparent deviation from the new law, which was founded on an induction of ~76.1 terms, and also to the succeeding law, with this lim- 1tatwn only-that, whilst their consecutive introduction at various definite intervals, is a necessary consequence of the m~chanical structure of the engine, our knowledge of analys1s d.oes not enable us to predict the period.:s themselves at wh1eh the mo distant laws will be introduced" It is not d~fficult to appl.y the philosophy of this passage to. the questwn under consideration.. It must be borne in mmd that the gestation of a single organism is the work of but a few days, weeks, or months; but the gestation (so t? speak) of a whole creation is a matter probably involving enorfl!ous spaces of time. Suppose that an ephemeron, hovermg over a pool for its one April day of life were capable of observing the fry of the frog in the wate; below. In its aged afternoon, having seen no chano-e upon them f~r such a long time, it would be little qualified to conceive that the external branchire of these crea. tures were to decay, and be replaced tiy internal lungs th~t feet were to be developed, the tail erased, and th~ animal then to become a denizen of the land. Precisely such. may ~e our difficulty in conceiving that any of the apecies wh.Ich people. our earth is capable of advancing by gen~ratwn !o a higher type of being. Durmg the whole t:me which we call the historical era, the limits of species have been, !o or~inary ob.servation, rigidly adhered to. But the htstoncal era Is we know only a small portion of the entire age of our' globe. W~ do not know what may have happened during the ages which precede~ its comme~cement? as we do not know what may happen In ages yet In the distant future. All, therefore, that we .can properly inf~r f1:om the apparently invariable productiOn of like by l1ke Is, that such is the ordinarv procedure of nature in the time immediately passing be. .- fore our eyes.. M r: Babbage's il1 ustration powerfully sugges~ s that th1s ot:dmary procedure may be subordinate to a highet· law w luch only penn its it for a time, and in proncr season interrupts and changes it. We shall soon see tome philosophical evidence fer ibis very conclusion. It has been seen that, in the reproduction of the higher |