LACTATION YIELDS AS MEASURES OF A COW'S MILKING CAPACITY                 245

                         STANDARD DEVIATION = 1196/1-(.8763)²
The probable error, .6745 × standard deviation, works out at 389 lbs., which
means that 50 per cent. of the cows with 2,000 lbs. mean " corrected " yield for
1st 4 lactations, would be expected to have a maximum yield between 3,112 ╤ 389,
or 2,723 to 3,501 lbs.

Evidently the best method of study of the problem indicated above is the
method of correlation, which is here followed. As in the previous publication,
probable error rather than the standard error has been employed to gauge the
significance of a difference. A difference of less than 4 times the probable error has
been considered as having arisen from fluctuations of random sampling.

                                          RESULTS.
Table III gives the values of correlation co-efficients obtained for the variables
maximum " corrected " yield and milk yield with different successive lactations for
our data, though for the sake of comparison with our values those got by Gavin
with British Holsteins and Dairy Shorthorns [1913] for r between the " Revised
Maxima " with successive calves and maximum " Revised Maxima ", and by Tuff
with Norwegian red polled breed [1928] for r between the I and II calf yield and
the average milk yield by the adult animal are also given:—

                                          TABLE III.
                        Value of correlation co-efficient.

A study of Table III shows that the values of r with our data are definitely
higher than those given by Gavin or Tuff for their data ; furthermore, that the
value of r goes on increasing with successive lactation yields. For instance, for our
data, the value of r in the case of first lactation yield is + .5026 ╤.0362, though
in second it is +.6642 ╤ .0271—a difference of + .1616 ╤ .0452, which is very
nearly significant. There is not much difference in the value of r for II and III
calf yields, the value for the III calf yield being + .6666 ╤.0269, though the
value of r with the 4th calf is the highest, + .7745 ╤.0194, its difference from