G ALTON'S LAW OF INHERITANCE 209 



very complex results as regards the characters of the offspring, is 

 a sufficient explanation of the fact that many cases of hybridism 

 are at present incapable of interpretation in terms of the 

 Mendelian theory, and such cases cannot be legitimately used as 

 arguments against the validity of that theory. It is obviously 

 impossible to explain the results of any particular cross until we 

 have some knowledge, not only of the extremely complex con- 

 stitution of the parental germ plasm on both sides, but also of 

 the way in which the factors which meet in the zygote may be 

 expected to influence one another. 



Mendelian phenomena, of course, can occur only as a result 

 of crossing or hybridization at some stage or other of the 

 ancestral history, and it does not seem likely that such crossing 

 has had any very great influence upon the evolution of plants and 

 animals in a state of nature. In cases of monohybridism, as we 

 have seen above, the hybrid form in the course of a few generations 

 would probably be quite swamped by the numerical preponderance 

 of the pure extracted forms which have reverted to one or other 

 of the original parental types, the hybrid itself never being 

 permanently fixed. New and permanent combinations may, of 

 course, sometimes arise naturally through dihybridism, but they 

 would at first be produced in very small numbers and could only 

 be expected to survive in the struggle for existence if they 

 happened to possess some material advantage over the parent 

 forms. Thus it appears that in a state of nature the results of 

 hybridization tend to be automatically eliminated. 



Attention has frequently been called to the alleged discrepancy 

 between the results of the Mendelian experiments and those 

 obtained by the late Sir Francis Galton and others by statistical 

 methods based upon the quantitative estimation of characters in 

 a number of successive generations. As a result of his investiga- 

 tions Galton was able to formulate the following " Law " of 

 inheritance : " The two parents contribute between them on the 

 average one-half, or (0'5) of the total heritage of the offspring ; 

 the four grand-parents, one-quarter, or (0'5) 2 ; the eight great- 

 grandparents, one-eighth, or (0'5) 3 , and so on. Thus the sum 

 of the ancestral contributions is expressed by the series { (0'5) + 

 (0'5) 2 + (0'5) 3 , &c.}, which, being equal to 1, accounts for the 

 whole heritage." 1 



This series has been modified by Professor Karl Pearson for 



1 Proceedings of the Royal Society of London, Vol. LXI.. 1897. p. 402. 

 B. P 



