446 



EDWIN CARLETON MacDOWELL 



where the parents were not of the same bristle grade. In gen- 

 eration 52 the means of the offspring fluctuate markedly; in 

 spite of this, a straight line seems to be the best representation 

 of their theoretical distribution. In generation 53, which 

 includes a much larger number of parental grades, as well as 

 nearly seven times as many offspring, the means are more uni- 

 form and more nearly approximate the theoretical straight line. 

 The means at the extremes of the line are connected by dotted 

 lines because they include only one fraternity each. The actual 

 equations used in plotting the regression straight lines are as 

 follows : 



Generation 52 S = 3.540709-0.0824 P 



Generation 53 D = 4.823057-0.0932 P 



S = grade of sons 



D = grade of daughters 



P = grade of parents 



The regression straight line make it strikingly evident that 

 higher parents do not have higher offspring. In generation 52 

 the regression straight lines are strikingly inclined toward the 

 base line, indicating a reversed relation, namely, that the higher 

 parents produced lower offspring. In a smaller degree the 

 same thing is true of generation 53. The correlation coefficients 

 are as follows: 



"WTien the flies are averaged in groups according to the grades 

 of their grandparents, the lines shown in figure 8 are obtained. 

 The high means corresponding to grandparental grade 5| strongly 

 emphasize a tendency for successive points between grades 4 

 and 5| to rise. But this mean depends upon a single pair of 

 flies and includes a smaller number of grandchildren than any 

 other mean in this group. If this point is omitted, the remain- 

 ing means assume the appearance of random distribution about 

 the regression lines. These regression straight lines are nearly 

 parallel with the base line; for granddaughters it is slightly 

 descending; for grandsons it is slightly ascending. The actual 

 regression equations are as follows: 



