Cycles of Rainfall 21 



36 years. Moreover, the periods of 8 years and 33 

 years afford the most probable basis derivable from the 

 data upon which to reason both as to the future course 

 of rainfall in the Ohio Valley and as to the course of the 

 phenomena dependent upon rainfall. 



Assuming, then, that for the purpose in hand, the 33 

 years and 8 years periods are the most probable and 

 valuable, we turn to the consideration of the equation 

 to the graph giving the course of rainfall in the Ohio 

 Valley. 



The Equation to the Rainfall Curve 



It will be helpful to approach the algebraic descrip- 

 tion of the cyclical movement of rainfall in the Ohio 

 Valley, by observing how we obtain an increasingly 

 accurate account of the actual rainfall by superposing 

 the constituent cycles. We shall use, as an index of the 

 relative fit of the several curves, the root-mean-square 

 deviation of the observations from each curve. 



If, as a preliminary step, the raw data of the course 

 of annual rainfall are examined, it is found that the 

 mean annual rainfall in the Ohio Valley is 41.19 inches, 

 and the root-mean-square deviation about the mean is 

 $ = 6.70 inches. 



If the long 33 years cycle is considered by itself, it 

 appears that the root-mean-square deviation about the 

 33 years curve is S = 6.39 inches. The graph of the 

 33 years cycle is given in Figure 4. Its equation is 



y = 41.19 + 2.88 sin /^ / + 328° 7') , 



