12 BULLETIN 1300, U. S. DEPARTMENT OF AGRICULTURE 
relation which, however, would add little to the statement above that 
these two quantities have followed opposite trends for wholly unre- 
lated reasons. 
The objective of the present study is to find the extent to which 
annual fluctuations in pork supply are determined by the two fac- 
tors, slaughter and weight. To accomplish this an estimate of the 
long-time trend and measurement of annual fluctuations from the 
trend must be made. In the present case a slight positive correla- 
tion between average live weight and pork production is found, as 
is, of course, to be expected. 
A thoroughly satisfactory method of estimating the trend is some- 
what difficult to find. One method is to take as the trend the aver- 
age for a certain number of years before and after each successive 
date. To get a satisfactory trend in this way would probably re- 
quire the average of at least nine years. The method breaks down 
for the first and last four years of the period, which seriously cuts 
down the data available. Another method is to fit some mathemati- 
cal curve. The choice of such a curve is, however, purely arbitrary. 
The only measure of its success is the judgment of the eye. It has 
seemed best, therefore, to fit the trend by eye in the first place, using 
lines which change in curvature only gradually and not more than 
four or five times in the 45 years under consideration. Each graph 
was plotted twice. The trend was drawn in by eye, wholly inde- 
pendently in the two cases. The two estimates never differed greatly. 
The average between them was adopted as a final estimate and is 
shown in dotted lines in the figures. The deviations from the trend 
were then read off from the graphs and reduced to a scale of to 9 
for convenience in calculating the correlations. 
THE CORRELATIONS 
In many cases it is desirable to know not only the relation between 
two variables in the same year but also the relations one or more 
years apart. Most of the variables have thus been correlated with 
each, other over a period of five years. Most of the hog variables, 
for example, have been correlated with the corn variables of the 
same year, the following year, and the first, second, and third pre- 
ceding years. 
The correlations have been calculated with the help of card punch- 
ing, sorting, and tabulating machines. The cards which were used 
have 42 available columns, each of which can be used for one vari- 
able. In order, however, to obtain correlations between each vari- 
able and five successive years of another, as described above, it is 
necessary to use three columns for each variable, one column for 
each of three successive years. This has been done for the four corn 
variables (acreage, yield, crop, and price) and eight of the hog vari- 
ables (western slaughter, weight, pork, and cost for both summer 
and winter). The total western and total eastern slaughter and the 
January 1 farm price have been punched for only two successive 
years each. All the possible correlations among these 42 variables 
have been calculated. Those for which records were not available 
back to 1870 have been correlated with the others for as great a 
period as possible. The means and standard deviation are shown in 
Table 2. The correlations are shown in Tables 3 to 6. 
