Cycles of Rainfall 17 



y = F(t) = 41.19-3.13 cos y t + 2.69 sin ^ * 



= 41.19+4.13 sin (^ t + 310° 41'). 



The values of the terms a\, b\, A\ are respectively 

 (3.1339) 2 , (2.6938)-, (4. 1325) 2 , and these values are 

 given in the proper columns of Table II in the Ap- 

 pendix. In Figure 3, the values of A 2 for the several 

 periods are measured on the axis of ordinates. 



An examination of Figure 3 will illustrate the truth of 

 a statement advanced a moment ago. It is clear from 

 the course of the periodograph l that if one were to 

 take any period at random between the limits of 3 

 years and 36 years, he would in every case obtain a 

 finite value for the amplitude of the selected cycle ; and 

 if, by chance, selection should fall upon, say, 18, or 21, or 

 29, or 36 years, an argument might be made with some 

 degree of plausibility that a real cycle had been dis- 

 covered. But, in truth, the real significance of no one 

 cycle taken at random can be judged apart from its 

 place in the distribution of all the cycles that can be 

 derived from the data. 



This last point is of fundamental importance. The 

 only object of investigating cycles of rainfall or cycles of 

 economic phenomena is that the knowledge of the 



1 The terms periodograph and periodogram were coined by Pro- 

 fessor Schuster. 



The periodograph is the curve tracing the values of A 2 ; the 

 periodogram is the surface between the periodograph and the base 

 line giving the lengths of the periods. Schuster: "The Period- 

 ogram of Magnetic Declination," p. 108. 



