To the Athenæum   19 June 1869

I am much obliged to your Correspondent of June 5 for having pointed out a great error in my ‘Origin of Species,’ on the possible rate of increase of the elephant.² 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.³ 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.⁴ 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, 18,803,080.⁵ At the next succeeding period of 780 to 790 years there would be alive no less than 34,584,256 elephants.

Charles Darwin.