STATISTICAL STUDIES, INDIAN DAIRY CATTLE                 83

this fact in his work, for according to him " there always are some very long
S. Ps. being associated with only moderately long lactations and these are often
excluded automatically from the data by the farmers selling the cow before she
conceived."

         There seemed little evidence, however, of this defect in our data, and it was,
therefore, thought that the value of r obtained from it would approximate more
nearly the true physiological relationship than the same of Sanders' or Ellinger's.
A correlation surface was therefore drawn between these two variables, a close study
of which revealed that whereas there appeared to be quite a high value of r bet-
ween the two variables, i.e., a high value of S. P. seemed to be generally asso-
ciated with a long lactation, there were good many cases where the S. P. had
been longer than the lactation length accompanying it, this being especially true
for very long S. Ps. This led the author to the belief that the length of lactation,
though generally governed by S. P., tended to a limit even though the length of
the S. P. be infinitely increased, and therefore the true relation between the two
variables is not linear in nature as given by Sanders, for on the basis of Sanders'
linear equations a cow once in milk will milk infinitely provided she is kept away
from the bull, and that the lactation length increases regularly at the rate of 10.5
weeks for every 100 days the date of service is deferred in first calvers. All these
beliefs are quite substantiated by the statistical constants given in Table XI and as
derived from the said correlation surface.

                           TABLE XI.

         Correlation of S. P. with lactation length.

         As expected the value of r is considerably lower than that of Sanders or Ellin-
ger, though it is still quite high and highly significant. The value of n is nearly
quite significantly higher than that of r , n—r being .066 ╤ .017 or 3.88 times
its P. E., and the value of n²—r² does not permit the use of linear equation to
describe the function. All this means that though the relation between these two