108 
Heredity in Production of Butter Fat 
From a slightly different table, we calculated the correlation coefficient between 
age and production of butter fat by including cows up to 5*25 years old, and certain 
additional cows that entered the records on a milk test rather than on production 
of butter fat. This gave 
r = 0-688 ± 0-006. 
The correlation is thus slightly increased by including cows between 4-75 and 
5-25 years old, while the regression coefficient of production on age is slightly 
decreased. 
For the group under 4-75 years old, regression of production on age is 
r ^ = 0-6623 = ^'^Ol with a probable error of 0-021. 
For the group under 5-25 years, 
r ^ = 0-6879 = 1-819 with a probable error of 0-018. 
(Ta 1-026 ^ 
From the variability of arrays corresponding to different ages, we make the 
following observation : 
The coeffijcient of variability increases gradtially from youth to three years old, 
and then gradually decreases to maturity. This may he expressed roughly by 
saying that the coefficient of variability is greatest near the mean of the total 
period of growth. 
In reference to lack of " smoothness " in the frequency distribution with respect 
to age, it should be noted that at each of the ages 2-5, 3-5, 4-5, 5-5, 6*5, 7-5, 
9-5, 11-5 there are fewer variates than at the year marks between which each of 
them lies. For example, at 4*5 there are 284 while at 4 there are 498, and at 
5 years 312. This seems to show simply a decided tendency on the part of 
breeders to have their cows tested nearer the year marks than the half-year marks. 
Ages are given to the day. 
(4) Mature and immature Cotus. 
From the results on correlation between age and production, it appears that 
the data should be divided into two parts near the age of 4 years 9 months — the 
cows in one division being regarded as mature, and in the other division as 
immature. 
The important question at once suggests itself as to whether inheritance, as 
measured by the correlation coefficient, is the greater when offspring and parents 
are at the same stage in the period of growth or when they are mature. 
(a) Off spring and dams under four years old at time of test (Table II.). The 
table represents records when the offspring and dams differ by less than one year 
in age at time of their respective tests, and are less than four years old. Tabulated 
with the records of offspring in the Advanced Register are, in general, the most 
remarkable records of dams and granddams. To correlate records of offspring 
