$16 ILLINOIS ACADEMY OF SCIENCE 
If the means of the parent groups and the means of the off- 
spring for these groups are reduced to the scale of 100 for the 
mean of the pure line (by multiplying by 65) we get the fol- 
lowing interesting series in which parental lengths are given 
above, and the means of the offspring below: 
Length of parents in mm.; 
scale, mean of race=100 
| | | | 
82.87| 92.62| 99.12|102.37]105.62|108.87|112.12! 
Mean length for offspring; 
scale, same as for parents. |116.00| 92.65 
88.20 We wa ace 
115.37|118.62]121.87|125.12]128.37|141.37 
98.02/101.01)104.91]113.23]103.25]122.85 
Although we note that two of the low parental groups have 
low means for offspring, and two of the high parental groups 
have unusually high means for offspring, yet one of the low 
parental groups has a high mean for offspring and three of 
the high parental groups have low means for offspring. The 
general disagreement of the two sets of figures is evident, 
hence we see the lack of correlation while the regression is 
made evident. 
Let us study further the regression found in the ten parental 
classes above the mean of the line. This can be done by the 
use Of common fractions. Let the amount of regression in 
each case be indicated by a fraction, the numerator being the 
difference between the mean of the parent class and the mean 
cf the offspring for this class, and the denominator the dif- 
ference between the mean of the parent class and the mean of 
the pure line. If the numerator is smaller than the denomin- 
ator the regression is not complete, if greater it is more than 
complete, if equal to the denominator it is just complete, If 
we do this we get the following series for the ten parental 
groups above the mean: 
5.78 +8.32+8.90+10.88+17.35+17.61+16.96+11.89+25.12+18.32 
ee ee ee 
2.37 5.62 8.87 12.12 15.37 18.62 21.87 25/12 28137 41137 
There being some regression in each case all of the frac- 
tions are positive. If we reduce the series to decimals we get: 
2.44, 1.48, 1.00, 0.89, 1.13, 0.94, 0.77, 0.47, 0.88, 0,45. 
Now then, if we add these fractions together and divide by 
their number we will get the average amount of regression, 
which if complete should give 1.00, The actual number which 
