8 BULLETIN 504, U. S. DEPARTMENT OF AGEICULTUEE. 
two at a time, had been considered, they were taken three at a time, 
and finally all four were taken into account simultaneously. In 
all, 260 of the coefficients were computed. Some of them, however, 
are of little interest, and if this were simply a study of the data, 
and not also an exposition of the method used, the computation of 
some of them might have been omitted. 
In order to avoid needless repetition in the tables, the different 
factors are designated by letters as follows: Profit^/?, weight=w, 
value per hundredweight =#, value of feed per head=/, cost at wean- 
ing time=c, date of sale=c/, and the notation for the different coeffi- 
cients is the same as that used in the explanation of the theory, viz : 
r a i)>cd, etc, is the coefficient of correlation between a and b when c, d, 
etc., are taken into account. 
INTERPRETATION OF THE COEFFICIENTS. 
There are four factors, namely, initial cost, value of feed consumed, 
weight, and selling price, which determine almost entirely the profit 
or loss to the farmer in finishing cattle for market. In fattening 
baby beef animals, the weight of the calves and the value of feed 
consumed both depend, to a large extent, on their age when sold 
and the length of time they were on feed. Also the price per pound 
received for them is rather intimately connected with the date 
on which they were sold, prices having had a tendency to rise as the 
season advanced. The calves for which data were gathered were 
all born in the spring, went on feed in the fall or early winter, and 
were sold some time during the following year. Consequently, any 
one of the three factors, age, length of feeding period, and date of 
sale, is a very good measure of the other two, and on account of 
this only the date of sale has been considered. 
If the price per pound, value of feed, initial cost, and date of sale 
were constant, and if nothing else affected the profit, it would vary 
directly with the weight in every case and, according to the theory, 
the coefficient of correlation between the two should be +1. The 
coefficient, r pw . V f Cd , obtained here is +.97. Similarly, if all things 
were constant except value per hundredweight and profit, there 
would be perfect positive correlation between them. The net coeffi- 
cient, I'pv.wfcd* given in Table III is +.94. If all things were constant 
except the value of feed consumed we should expect a high negative 
correlation between it and profit, i. e., the calf that received the least 
feed would return the greatest profit. The net coefficient, r P f. WVC d, is 
—.98. Similarly, other things being equal, perfect negative correla- 
tion should exist between initial cost and profit. The net coefficient 
in this case, rpe-wn, is also —.98. An examination of the remainder 
of these net coefficients, which are the last ones given in the table, 
