CORRELATED VARIABILITY. 57 



Galtoii ('97) has shown that an individual inherits not only 

 from his parents, but also from his grandparents, great-grand- 

 parents, and so on. The heritage from his 2 parents together 

 is, 011 the average, 50$ or i of the whole ; from the 4 grand- 

 parents 25# or J ; from the 8 great-grandparents 12. 5# or ; 



from the nth ancestral generation of the whole ; the total 



heritage adding up 100#. This law has been generalized by 

 Pearson ('98) as follows : 



where hi = average abmodality of fraternity. 

 CT O = standard deviation of fraternity. 

 <TI , cr, . . . <T 8 = standard deviation of mid-parent of 

 1st, 2d ... th ancestral generation. 

 A?i = abmodality of mid-parent of 1st ancestral genera- 



tion. 

 &a, k* . , . k a = abmodality of mid-parent of 2d, 3d 



. . . sth ancestral generation. 



The abmodality of the mid-parent of any degree of ancestry 

 may be taken as the average abmodality of all the contributory 

 ancestors of that generation. 



MENDEL'S LAW OF ALTERNATIVE INHERITANCE. 



In 1865 Georg Mendel published an account of his experi- 

 ments in Plant Hybridization and reached the following laws, 

 which 'have been abundantly confirmed in certain experi- 

 ments. 



First Case. The two parents differ in one character (the 

 antagonistic peculiarity) case of monohybrids. 



Of the two antagonistic peculiarities the cross exhibits 

 only one; and it exhibits it completely, so as not to be dis- 

 tinguishable in this regard from one of the parents. Inter- 

 mediate conditions do not occur [in alternative heritage]. 



2. In the formation of the pollen and the egg-cell the two 

 antagonistic peculiarities are segregated; so that each ripe 

 germ-cell carries only one of these peculiarities. 



