VARIATION AND HEREDITY 31 



revert to the type ; they show variations, but the varia- 

 tions bear no relation to those of their respective parents. 



If this result be substantiated, it will follow that 

 variations which are inherited must be derived from 

 ancestral differences. A true division of variations 

 into two classes essentially distinct would thus be made. 

 The real contrast is not between small variations and 

 large. It is probably true that large or discontinu- 

 ous variations can only be produced by ancestral 

 differences, but small ones may be either of ancestral 

 origin or of the fluctuational type which arises in pure 

 lines. The real distinction is between variations due to 

 ancestral differences, or mutations, and the accidental 

 variations or fluctuations which would appear, even were 

 we dealing with a "pure line." The ancestral varia- 

 tions, modified or unmodified, are transmitted to future 

 generations, the accidental variations are not. 



Whether or no these ideas be supported by further 

 research, the study of the transmission of the variations 

 actually found in a more or less homogeneous race is of 

 fundamental importance. If a parent differ from the 

 normal type of the race by a certain amount in a certain 

 direction, will his offspring also differ in that direction, 

 and to what amount ? 



A long series of statistical investigations by Karl 

 Pearson and others enables us to answer this question 

 with certainty. In a race, whether of men or of animals, 

 mating at random, on the average of large numbers, 

 the offspring will diverge from the mean in the same 

 direction as the diverging parent, and to approximately 

 half the amount. If the average stature of the men 

 of a race be 5 feet 8 inches, a man of 6 feet will exceed 



