H. L. RiETz 
115 
0—2-5 yearf? 
2 '5 — 3-5 years 
3-5 — 4-5 years 
4-5— 
Total under 
4-5 years 
Cows in milk 
618 
494 
430 
1416 
1542 
Number in Advanced Registry 
413 
346 
269 
620 
1028 
n 
0-67 
0-70 
0-63 
0-44 
0-67 
With these estimates for /u„ = n/iV, we can obtain a for various classes of cows 
from data in Table I. 
(a) Value of a for mature cows. 
1^/= 14-90 - 12 00 = 2-90, 
/z„ = 0-44, 
/i' = 0151, 
<r = 3-89. 
(b) Value of a for immature cows. For immature cows the requirements 
increase uniformly with age from two years old to five years old according to the 
relation 
y — VQ x + 4<, 
where x is age in years and y is production in pounds. If the total frequency 
surface with respect to age and production is 
^ =f{^> y) 
the selected portion is separated from the rest of the surface by the plane 
7/ =z= I'G a; + 4. The theory for obtaining the constants of the total surface from 
such a portion of it has not, so far as I am aware, been developed. Perhaps it can 
be developed, without great difficulty, for the normal surface, but our distribution 
as to age is so far from normal that I think a method of dealing with arrays of the 
correlation table will give more reliable results than to assume the distribution 
normal. 
(c) Goivs under 2'25 years. For cows two years old or under, the requirement 
is 7'2 and for one 2'25 years old it is 7'6. For this small range in age we shall 
accept the requirement for age 2125, that is 7*4, as locating the stump of the tail. 
From the combination of arrays in Table I., for cows under 2'25, 
S = 1-48, and m = 9-33, 
/.o = 1 = 0-67, 
h' = - 0-44, 
zV = 9-33 -7-4 = 1-93, 
a = 1-90. 
15—2 
