Cycles of Rainfall 23 



the origin being at 1839. This curve traces in bold 

 outline the general course of rainfall. It gives the 

 ground-swell of the rainfall movement. 



If the 8 years cycle is superposed upon the 33 years 

 cycle, the root-mean-square deviation about the curve 

 becomes S = 5.66 inches. The graph of the combination 

 of these two curves is traced in Figure 5. Its equation is 



^ = 41.19 + 2.88sm(|^ + 328 o 7')+4.13sin(| r * + 310 o 41'), 



the origin being at 1839. A point of interest with regard 

 to the flow of the curve is the rapidity with which it 

 rises from the least minimum to the greatest maximum, 

 and the slowness with which it then descends to the 

 subsequent least minimum. 



If the 8 years cycle and its semiharmonic of 4 years 

 are combined with the 33 years cycle and its semi- 

 harmonic of 16.5 years, the root-mean-square deviation 

 about the compound curve becomes *S=5.29 inches. 

 The graph of the curve is given in Figure 6. Its equa- 

 tion is 



y = 4 1.19 + 2.88 sin (J^ +328° 7') + 2. 25 sin (|^ + 271° 42') 



+ 4.13 sin (^ t +310° 41') + 2. 14 sin (~ t + 180° 28') , 



the origin being at 1839. In this closer approximation 

 the characteristic rapid rise to a general maximum and 

 slow fall to a general minimum is reproduced. Another 

 characteristic is the longer interval that the curve 



