Natural inheritance / by Francis Galton.

  • Galton, Francis, 1822-1911.
Date:
1889
Catalogue details

Licence: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

Credit: Natural inheritance / by Francis Galton. Source: Wellcome Collection.

    260/282 (page 244)
    246 NATURAL INHERITANCE. (a-\^bxY i.e. suppose that tr. —t\=-Q ^ ^ and so on. ^ ^ {a + b)^ ^ ^{a + bf ГПг оШ(. = , ^ I а + Ъ.тпг. 2 ® {a + by\ ^ Generally ^ | a + 5r-]^o | ^ {а + Ьу I ■ j {a + b)^[r ' J If, therefore, we wish to find the number of extinctions in any generation, we have only to take the number in the preceding generation, add it to the constant fraction — , raise the sum to the Ъ l'i power of q, and multiply by {а-\-Ьу With the aid of a table of logarithms, all this may be effected for a great number of generations in a very few minutes. It is by no means unlikely that when the true statistical data t^, etc., are ascertained, values of a, b, and q may be found, which shall render the terms of the expansion {a + bx^ approximately proportionate to the terms of (x). If this can be done^ we may approximate to the determination of the rapidity of extinction with very great ease, for any number of generations, however great. For example, it does not seem very unlikely that the value of q might be 5, while Ìq, might be *237, *396, 264, *088, *014, *001, or nearly, ^,3, -gj, 2V' io\)o* Should that be the case, we have, (x) = ^^ = _ and generally = Js | ^ + r-1^0 | 45 5 Thus we easily get for the number of extinctions in the first ten generations respectively. •237, *346, *410, -450, *477, *496, *510, *520, *527, *533. 1 I I 2 We observe the same law noticed above in the case of —— 3 viz., that while 237 names out of a thousand disappear in the first