18 American Statistical Association. 



values. Galton also paid some attention to this subject, and 

 Dr. Gulick mentioned it in a recent paper. Glancing over 

 the curves representing large series of measurements, it 

 strikes me that they conform to the laws of chance only in a 

 general way, and that considerable deviations are quite 

 frequent. It is necessary to consider the biological laws 

 underlying the phenomena under consideration. Assuming 

 that there is a uniform ancestral type in a certain district, 

 and that the conditions of life remain stable, we may expect 

 that the people representing its offspring will be grouped 

 around the type according to the laws of chance. Assum- 

 ing, however, that there were two distinct ancestral types in 

 adjoining districts, and that these types intermingled, we 

 cannot foretell what the distribution of forms among the 

 offspring will be. It may be that they represent an inter- 

 mediate type between the parental forms. Jn this case we 

 might expect to find them distributed according to the laws 

 of chance. But it may also be that we find them to have a 

 tendency to reproduce one or the other ancestral type, either 

 pure or slightly modified. In this case the resulting curve 

 would not conform to the laws of chance, and would show 

 an entirely different character. Tliere is considerable evi- 

 dence that the laws of inheritance are sucli tliat there exists 

 a tendency of reproducing ancestral traits, not of producing 

 new intermediate traits. Therefore, we may be prepared to 

 find considerable deviations from the laws of chance. It is 

 clear that, if intermixture does not result in producing an 

 intermediate type, an attempt to express the type by means of 

 an average of the existing forms will have no meaning what- 

 ever. The probable value would have just as little mean- 

 ing. If the two parental forms were entirely distinct and 

 reproduced without cliange, the most frequent values might 

 have a meaning, as the two forms would occur most fre- 

 quently. This, however, would depend upon many condi- 

 tions favorable to such a result : the proportion of the two 

 elements would have to be nearly equal, their difference 



