# From Edward Lacy Garbett to the Athenæum   29 June 1869

June 29, 1869.

Without pretending to an exact solution of Mr. Darwin’s elephant problem, I would submit that his first calculation must have been the truest, if, indeed, it made the rate of increase sufficiently high; for the period of doubling seems to me some where about 23 years, whereas his present estimate in the Athenæum, letting 18,803,080 become no more than 34,584,256 in 30 years, requires as much as 34 years for doubling.1

Remembering that if the births of the first generation extend through 60 years, those of the second will be spread over twice that period, those of the third over thrice, and so on, we shall find the births in the first three centuries as follows:—

 Total of Dates between No. born No. born No. born each which they in 1st in 2nd in 3rd generation. are born. century. century. century. 6 30 – 90 6 — — 18 60 - 180 6 12 — 54 90 - 270 3 30 21 162 120 - 360 — 54 67 486 150 – 450 — 81 162 1,458 180 – 540 — 81 405 4,374 210 – 630 — — 937 13,122 240 – 720 — — 1,640 39,366 270 – 810 — — 2,187 No. surviving each century 15 258 5,419

Now, as the first parents are not here counted, not surviving the first century, nor even their youngest calf living through the second, in the third at least the regular birth and death rates must be established. The number alive after two centuries, we see, is but 17 times that at the end of the first; while the number alive after three centuries is 21 times those surviving the second. But a 21-fold increase per century is doubling in every 22.7 years; for as Log. 31 is to 100, so is Log. 2 to 22.7. This rate will give in 5 centuries about 2,400,000 elephants, and in one more century 50,000,000. Even the second century’s 17-fold increase would approach Mr. Darwin’s first results. His present correction, therefore, allowing not even an 8-fold centurial increase, must, I think, involve some great error.

Edward L. Garbett

## Footnotes

See letter from Ponderer to the Athenæum, [before 5 June 1869] and n. 2, and letter to the Athenæum, 19 June 1869.

## Bibliography

Athenæum. 1844. A few words by way of comment on Miss Martineau’s statement. No. 896 (28 December): 1198–9.

## Summary

Calculations relating to the problem of the increase of elephants (see 6787).

## Letter details

Letter no.
DCP-LETT-6806F
From
Edward Lacy Garbett
To
Athenæum
Sent from