WCP1602

[1]

Trichinopoly

13^th Sept[ember]1896

Sir

I hope you will pardon a stranger to you for pointing out what seems an error in the calculation of the rate of increase of a ^new species on Prof[essor] Romanes theory in Chap[ter]. VII of your "Darwinism."

Assuming that in a species consisting of 100,000 of each sex[,] 10 percent become infertile with the remainder you point out that the unions between members of the two varieties (which we may call A & B) will be 81000 & 1000 & that the number of their offspring surviving at the beginning of the next year will be 98780 & 1220 respectively. To find the proportion of their descendants in the next year you again divide 100,000 [2] in the ratio of the squares of these numbers, this omitting to notice that the 1220 may unite with the newly developed member of the A B variety. This omission would greatly modify the result but it is almost neutralized by the fact that the number of such recruits would not be 10,000 every year 1/10 of the offspring of the A variety, a number which constantly diminishes till equilibrium is attained. Thus, if the numbers of A & B at the beginning of a year be a & b of each sex respectively the number of their offspring would be a² : b². a²/10 must be taken from the former and added to the latter to obtain the proportion of the young at the end of the breeding season, and 100,000 must be divided in the [3] ratio of 9a²/10 : b² + a²/10 to obtain the number of survivors at the beginning of next year.

The annexed table shows that if this is the correct method of calculation the numbers of the physiological variety would amount to 11489 at the end of beginning of the sixth year after which no further increase would take place.

Again apologizing for troubling you.

Believe me | Yours faithfully | [illeg.] [signature]

A. R. Wallace Esq.

To Mess^rs Macmillan & Co.