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ORIGIN OF SPECIES.

Caerleon, North Wales, June 19, 1869.

I am much obliged to your Correspondent¹ of June 5 for having pointed out a great error in my 'Origin of Species,' on the possible rate of increase of the elephant. I inquired from the late Dr. Falconer with respect to the age of breeding, &c., and understated the data obtained from him, with the intention, vain as it has proved, of not exaggerating the result. Finding that the calculation was difficult, I applied to a good arithmetician; but he did not know any formula by which a result could easily be obtained; and he now informs me that I then applied to some Cambridge mathematician. Who this was I cannot remember, and therefore cannot find out how the error arose. From the many familiar instances of rapid geometrical increase, I confess that, if the answer had been thirty or sixty million elephants, I should not have felt much surprise; but I ought not to have relied so implicitly on my mathematical friend. I have misled your Correspondent by using language which implies that the elephant produces a pair of young at each birth; but the calculation by this assumption is rendered easier and the result but little different. A friend has extended your Correspondent's calculation to a further period of years. Commencing with a pair of elephants, at the age of thirty, and assuming that they would in each generation survive ten years after the last period of breeding—namely, when ninety years old—there would be, after a period of 750 to 760 years (instead of after 500 years, as I stated in 'The Origin of Species'), considerably more than fifteen million elephants alive, namely, 18,803,080. At the next succeeding period of 780 to 790 years there would be alive no less than 34,584,256 elephants.

CHARLES DARWIN.

¹ Ponderer 1869. In Origin p. 64 Darwin wrote:

The elephant is reckoned to be the slowest breeder of all known animals, and I have taken some pains to estimate its probable minimum rate of natural increase: it will be under the mark to assume that it breeds when thirty years old, and goes on breeding till ninety years old, bringing forth three pair of young in this interval; if this be so, at the end of the fifth century there would be alive fifteen million elephants, descended from the first pair.

'Ponderer objected that there would be '85,524 elephants, less the number that would have died by reason of their age.' See Correspondence vol. 17, p. 274.

'Ponderer's letter is given below:

Darwins Elephants.—In the last edition of Mr. Darwin's 'Origin of Species,' he makes the following statement (chap, iii., page 74, line 18):— "The elephant is reckoned the slowest breeder of all known animals, and I have taken some pains to estimate its probable minimum state of natural increase. It will be under the mark to assume that it begins breeding when thirty years old, and goes on breeding till ninety years old, bringing forth three pair of young in this interval. If this be so, at the end of the fifth century there would be alive fifteen million elephants descended from the first pair." Perhaps some of your readers will be able to enlighten my dull intellect as to the process of reasoning by which this result is obtained. According to Mr. Darwin's theory, each pair brings forth a pair when it is thirty, when it is sixty, and when it is ninety. Hence if there be one pair in the first year, there will be one pair born in the thirtieth year; these two pairs will produce two pairs in the sixtieth year, and these four will produce four pairs in the ninetieth. After that we have only to add the numbers born in the three preceding periods to find out how many are born in each period; because after they have attained the age of ninety years they cease to breed. This method of reasoning gives the number of pairs born in each period of thirty years as 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1,705,3,136,5,768,10,609, 19,513; the last number being born in the period commencing with the five hundred and tenth year. Therefore the number of elephants alive at that time would be 42,762 pairs, that is, 85,524 elephants, less the number that would have died by reason of their age. But Mr. Darwin says that there would be fifteen millions. On what does he base his calculation?

PONDERER.