Rainfall and the Crops 45 



the annual rainfall but also the rainfall of 

 any considerable part of the year. Or, more 

 concretely, that the annual rainfall and the 

 rainfall of any considerable part of the year 

 may be described by an equation of the form 



y = A o + A x sin U^ t + eA + A 2 sin l^t + eA 

 + a i sin (~^- t + yA + a, sin (~ t + 7/ 2 j , 



where the constants in the series may be differ- 

 ent for the several parts of the year. 



(2) That where the correlation between the yield per 



acre of a particular crop and the rainfall of its 

 critical season is high, the same general type 

 of equation will fit both groups of data, the 

 data of rainfall and the data of the yield per 

 acre of the crops. 



(3) That both of the preceding assumptions are 



greatly fortified if the compound curves de- 

 duced from the actual data of rainfall and 

 yield satisfy a reasonable test of fit to the data. 



The working out of the consequences of these as- 

 sumptions is exhibited in Figures 11, 12, 13, and the 

 equations descriptive of the several curves appear on 

 the corresponding Figures. 



To measure the degree of fit of the curves to their 

 respective data, we shall employ a coefficient K, which 

 may be described as the ratio of the arithmetical sum 

 of the deviations of the observations from the curve 



