2 26 GENETICS: R. PEARL Proc. N. A. S. 
if a bull's daughters are on the average poorer milkers, or poorer in the 
quality of their milk, than the dams from which they came, then the bull 
is exercising a harmful effect upon the breed. On the other hand, if a 
bull's daughters are on the average measurably better than the dams from 
which they came, in productive qualities, then that bull is exercising a 
beneficial effect on the breed. Stated specifically, if represents the 
milk production of a daughter of a given bull, and the milk produc- 
tion of the dam of this daughter, then the measure of this bull's transmit- 
ting qualities for milk production in respect of this pair would be : 
Sire's transmitting power = — D^. 
If the daughter's production is more than the dam's the sign will be plus. 
Insofar as one daughter-dam pair is indicative the bull is increasing the 
production of his daughters and consequently improving the breed. If 
the daughter's production is less than her dam's the sign will be minus. 
The bull is consequently insofar detrimental to the breed. By the summa- 
tion of these plus and minus differences with regard to sign, the amount 
and sign of this summed quantity gives the measure of what he did for all 
his daughters, and dividing by the number of daughter-dam pairs gives 
a measure of the mean or average effect of this sire on the breed. 
Being convinced that this reasoning was sound, and that if carried out 
thoroughly the consequences would be bound in the long run to be of in- 
calculable, but great, practical economic value to mankind, the writer 
inaugurated in his laboratory at the Maine Experiment Station the pro- 
ject of determining the transmitting power as above defined, of every bull 
in the Jersey breed recorded up to 1916 as having two or more daughters 
whose milk-producing qualities were known, as well as the producing 
abilities of the dam. This project involved a very large amount of labor 
and was interrupted by the war, but has now been finished and will shortly 
be published.^ It is the purpose of the present paper to give a brief ac- 
count of the scope of the work and some of its chief results. 
A prerequisite to the comparison of daughter and dam production was 
an accurate method of correction for change of milk and fat production 
with age. Considerable study has been given this problem. I showed 
in 1914^ that the equation relating milk flow to age in dairy cattle was of 
the form 
y = a -\- hx -\- cx^ -\- d log x. 
Since that time these curves have been w^orked out in my laboratory for 
all the principle dairy breeds, chiefly by Miner, Gowen, Patterson, and 
myself. The curve for annual milk production in the Jersey breed is 
y = 4586.50 -f 307.55x - 12.65x2 -f- 2216.62 log x 
where y denotes milk production in one year in pounds, and x denotes 
age in years. How closely this equation agrees with the observed facts is 
shown in figure 1. 
