Rainfall and the Crops 51 



must be devised for measuring; the fluctuation in the 

 yield of the crops when the crops are taken all together ; 

 and (2) a method must be devised for combining the 

 rainfall of the critical periods of the growth of the 

 several crops. These two steps we shall now consider. 

 In regard to the first of these desiderata, it is clear 

 that the measure of the fluctuation of crops taken as a 

 whole should be based upon the best measure of the 

 fluctuation of the yield of the crops taken singly. More- 

 over, there is a general agreement that the standard 

 deviation of a frequency scheme is a good measure of 

 the scatter of the observations about their mean value. 

 A natural step, therefore, would be to assume that if 

 the observations form a series in time, a good rela- 

 tive measure of their fluctuations at different epochs is 

 afforded by the ratio of the deviations of the observa- 

 tions from their mean divided by the standard devia- 

 tion. For example, the mean yield of oats in Illinois, 

 for the period 1870 to 1910, was 31.4 bushels per acre, 

 and the standard deviation of the yield for the same 

 period of time was c = 5.2 bushels. The yield per acre 

 for the year 1910 was 38.0 bushels. If A be taken to rep- 

 resent the deviation of the yield of any year from the 

 mean yield of the whole period, then the A for 1910 was 

 38.0-31.4 = 6.6, and the fluctuation for 1910 was 



- = -^ = 1.27. Similarly, for the year 1908, when the 



<r 5.2 



A 



yield was 23.0 bushels, the fluctuation was, - =  1 .62. 



It happens that in the case of oats, there is no secular 

 trend to the yield, but when the secular trend exists, 



