Cycles of Rainfall 7 



rainfall. If this assumption is true, it follows that, in 

 all probability, the course of rainfall in the Ohio Valley, 

 is cyclical, or a combination of cycles. 



In an inductive treatment of any form of rhythmic 

 or cyclical change it is necessary that the method 

 adopted shall satisfy two conditions: (1) It shall be 

 consistent with recognized mathematical processes; 

 (2) It shall afford means of testing the degree of proba- 

 bility that the results are not chance phenomena. 

 Unless the method rests clearly upon an approved 

 mathematical process, it is scarcely possible to say 

 whether the attained results may not be entirely formal ; 

 and unless the findings are tested for the degree of their 

 probability, there is no assurance that the adduced 

 cycle may not be a chance occurrence. The literature 

 in which rhythmic phenomena are treated in a statis- 

 tical way teems with fallacies and uncertainties that 

 illustrate the need of observing the above conditions; 

 for the method frequently adopted of smoothing the 

 data is so arbitrary that one is at a loss to know whether, 

 after all, the alleged periodicity may not, in fact, be due 

 to the process of smoothing; and, in addition, one is 

 left in doubt as to whether an indefinite number of 

 cycles other than the particular one adduced might not, 

 with equal or greater probability, be obtained from the 

 same data. 



The method that was employed to reach the results 

 of this chapter rests upon the analysis invented by 

 Joseph Fourier, 1 which is called, in English treatises, 



1 The most philosophic exposition of Fourier's theorem is in 



