28 Economic Cycles: Their Law and Cause 



reference to these data would be to compute the 

 periodogram in the same manner in which it was com- 

 puted in the case of the Ohio Valley data, and then com- 

 pare the periodograms. But this method has not been 

 followed. A less direct, and far less laborious, process 

 has been adopted. We know from the Ohio data that 

 there are two cycles of rainfall, a 33 years cycle and an 8 

 years cycle, and we know, furthermore, that when the 

 curve for rainfall in the Ohio Valley is computed for the 

 33 years and 8 years periods and their semiharmonics, a 

 good fit to the data is obtained. The questions that are 

 asked with reference to the Illinois data are these: 

 If we assume the existence of a 33 years period and an 

 8 years period in the Illinois rainfall data, will the 

 rainfall curve fit the Illinois data as well as the Ohio 

 curve fits the Ohio data? Will the Illinois curve re- 

 produce the characteristic features of the Ohio curve? 

 A presumption in favor of an affirmative answer to 

 these questions is suggested by the fact that the correla- 

 tion between the annual rainfall in the Ohio Valley and 

 the annual rainfall in the state of Illinois is r=6.00. 

 The graph of the curve of rainfall in Illinois is given 

 in Figure 7. Its equation is 



y =38.53 +3.03 sin (|^+325 35' \+ 1.87 sin &+ 194° 55') 



+3.05 sin (^*+241° 52') + 1.12 sin ^p+232°26'Y 



the origin being at 1870. The root-mean-square devia- 



but in no year were fewer than seven records obtainable while for a 

 large proportion of the years the thirty records were complete. 



