Rainfall and the Crops 37 



As the yield per acre of the various crops may show a 

 secular as well as a complex cyclical change, it will be 

 necessary, before their cyclical elements can be brought 

 into relation with the corresponding cyclical changes of 

 rainfall, to eliminate from the recorded course of the 

 yield per acre of the several crops the element of change 

 that is secular in character. 



The method that has been adopted here to effect the 

 elimination of the secular change is simple, but to secure 

 a first approximation, it is adequate. For a period of 

 time covered by the statistics, a change is regarded as a 

 secular change if, for the period of time taken as a 

 whole, the yield per acre of the crop shows a tendency 

 either to increase or to decrease. In order to determine 

 whether there is a secular change in the yield per acre, 

 for a certain period of time, the yield data are correlated 

 with time, and the existence or non-existence of a 

 secular change is inferred from the relative magnitudes 

 of the coefficient of correlation and its probable error. 

 If there be a secular change, the calculation of the 

 coefficient of correlation of the yield with time is then a 

 first-step toward the elimination of the secular element 

 by means of a regression equation in which the co- 

 efficient of correlation is a factor. 



The method may be illustrated by taking the history 

 of the yield per acre of corn. In Figure 9 the actual 

 yield per acre in Illinois is plotted for the period 1870- 

 1910. The straight line showing the secular trend of the 

 yield is the graph of the regression equation between 

 the yield per acre and time. The correlation of the 



