6 Economic Cycles: Their Law and Cause 



The Use of Fourier's Theorem 



A preliminary examination of the rainfall data of the 

 Ohio Valley leads to the conclusion that there is prob- 

 ably no secular trend to the data, that is to say, there 

 is probably no tendency of the rainfall to increase con- 

 tinuously or to decrease continuously with the flow of 

 time. It is true that when the amount of rainfall is 

 correlated with time, the coefficient of correlation is 

 r = — .227 ± .075, where the coefficient is three times its 

 probable error and is therefore suggestive of a decrease 

 in the amount of rainfall with the flow of time. More- 

 over, if a straight line is fitted to the data, the indicated 

 annual decrease in the rainfall is seven hundredths of 

 an inch. But these facts are no justification for hold- 

 ing to a secular decrease in the amount of annual 

 rainfall. For, in the first place, if there are cycles in 

 the amount of the rainfall, the low degree of the ob- 

 served correlation might be due to the data of rainfall 

 including incomplete cycles; in the second place, the 

 record is drawn from only three stations and because 

 of the limited number of stations might give an acciden- 

 tal, low degree of correlation between amount of rain- 

 fall and time; and in the third place, improvements 

 in the method of taking the observations might have 

 introduced changes that would account for the ob- 

 served small annual decrease in the amount of rain- 

 fall. In view of these considerations, it is probably 

 best to proceed with our problem on the assumption 

 that there is no secular trend in the amount of annual 



