402 



Prof. Karl Pearson. 



Thus, on the basis of the law of ancestral heredity the case against 

 panmixia is even stronger than it appeared in my memoir on 

 heredity.* Assuming Mr. Galton's law of regression. I there showed 

 that panmixia was possible with a stable focus of regression, but that 

 the supporters of the consistent theory of panmixia must place that 

 focus of regression, in order that degeneration should be continuous, 

 in a position inconsistent with observed facts (p. 314). We now see 

 that with the law of ancestral heredity even this is not possible, a 

 race with six generations of selection will breed within 1*2 per cent, 

 of truth ever afterwards, unless the focus of regression instead of 

 being steady actually regredes. Of course there are many ways in 

 which this law may be modified. For example, fertility may be a 

 maximum with the average, say, of the unselected original population, 

 and after a selection it may remain correlated, having the lesser 

 values of the selected character more fertile than others. f Then, 

 of course, the stock would degenerate with panmixia. £ This would, 

 however, be reproductive selection, not panmixia in the ordinary 

 significance, reversing natural selection. We are far too ignorant at 

 present of the correlation of fertility with other characters to base 

 any sweeping principle like that of degeneration by panmixia upon 

 it. Our attitude at present can only be that there are no facts, and 

 that there is no workable theory of heredity yet discovered which 

 favours in any way degeneration by panmixia. 



(9) Taxation of Inheritance. — If we assume Mr. Galton's law of 

 ancestral heredity to be a limiting statement, we can at once from 

 our general formulas ascertain the influence of " taxing the inherit- 

 ance " in any other than Mr. Galton's form. He has, in fact, taxed 

 the inheritance (where by " inheritance " I understand deviation 

 from the mean of the general population, not actual size of the 

 character), 50 per cent, in each transmission. There may, however, 

 be two types of taxation, a general taxation on the individual 

 receipts and a special tax on each transmission — corresponding, so to 

 speak, to a duty paid by an individual on coming into receipt of the 

 entire ancestral property, and a stamp duty on each conveyance of an 

 individual ancestor's contribution. The first is represented by the 

 7 of our equation (x), and the second by the \/2/3. 



Mr. Galton, in his memoir on Basset hounds, has stated certain 

 conditions of the law of ancestral heredity, and be concludes (p. 403) 

 that his conditions are only fulfilled by the series 



* + (*>'+(*)*+.•- 

 * ' Phil. Trans.,' A, vol. 187, p. 308 et seq. 



f This is how I should at present account for the degeneration of pedigree 

 wheat. 



X Some influence of this kind is possibly sensible in highly civilised communi- 

 ties. See " Reproductive Selection," in my ' Chances of Death,' vol. 1, pp. 98 et seq. 



