ON THE STATISTICAL VIEW OF NATURE. 619 



regression, reversion to ancestral types, extinction of 

 families, effect of bias in marriage, mixture of in- 

 heritance, latent elements, and generally to prepare 

 the ground for the combined labours of the naturalist 

 and the statistician ; he was also able to put novel 

 problems to the mathematician. 



To understand this latter point we must realise the 



partly from his parents, partly 

 from his ancestry. In every pop- 

 ulation that intermarries freely, 

 when the genealogy of any man is 

 traced far backwards, his ancestry 

 will be found to consist of such 

 varied elements that they are 

 indistinguishable from a sample 

 taken at haphazard from the 

 general population." As to the 

 mathematical problem referred to, 

 it was submitted by Mr Galton in 

 a definite form to Mr J. D. H. 

 Dicksou, whose solution is given 

 in the appendix to 'Natural In- 

 heritance.' On this solution Mr 

 Galton remarks : " The problem 

 may not be difficult to an ac- 

 complished mathematician, but I 

 certainly never felt such a glow 

 of loyalty and respect towards the 

 sovereignty and wide sway of 

 mathematical analysis as when his 

 answer arrived, confirming, by pure 

 mathematical reasoning, my vari- 

 ous and laborious statistical con- 

 clusions with far more minuteness 

 than I had dared to hope, because 

 the data ran somewhat roughly, 

 and I had to smooth them with 

 tender caution. ... It is obvious 

 from this close accord of calcula- 

 tion with observation, that the law 

 of Error holds throughout with 

 sufficient precision to be of real 

 service, and that the various results 

 of my statistics are not casual and 

 disconnected determinations, but 

 strictly interdependent" (p. 202). 

 Another passage indicating how 

 much the inferences from the law 



of regression run contrary to 

 popular opinions on inheritance is 

 the following : " The law of Re- 

 gression tells heavily against the 

 full hereditary transmission of any 

 gift. Only a few out of many 

 children would be likely to differ 

 from mediocrity so widely as their 

 mid-parent, and still fewer would 

 differ as widely as the more excep- 

 tional of the two parents. The 

 more bountifully the parent is 

 gifted by nature, the more rare 

 will be his good fortune if he be- 

 gets a son who is as richly endowed 

 as himself, and still more so if he 

 has a son who is endowed yet more 

 largely. But the law is even- 

 handed ; it levies an equal succes- 

 sion - tax on the transmission of 

 badness as of goodness. If it dis- 

 courages the extravagant hopes of 

 a gifted parent that his children 

 will inherit all his powers, it no 

 less discountenances extravagant 

 fears that they will inherit all his 

 weakness and disease " (p. 106). 

 Prof. Karl Pearson ( ' The Grammar 

 of Science,' 2nd ed., p. 479) says 

 of the law of ancestral inheritance : 

 " If Darwinism be the true view 

 of evolution i.e., if we are to 

 describe evolution by natural selec- 

 tion combined with heredity then 

 the law which gives us definitely 

 and concisely the type of the off- 

 spring in terms of the ancestral 

 peculiarities, is at once the founda- 

 tion-stone of biology and the basis 

 upon which heredity becomes an 

 exact branch of science." 



