10 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 1 39 



pose I used about 790 monthly mean values of Washington precipita- 

 tion, all observed when Wolf sunspot numbers exceeded 20. These 

 values were smoothed by 3-month consecutive means, which of course 

 reduces the ranges of percentage departures from normal to about 

 two-thirds of their actual monthly values. Table 3 and figure 5 show 

 the results. 



Figure 5 clearly shows that a value of the master period between 

 273 and 275 months is definitely indicated. 



I have preferred 2y^ months rather than 275 months because it is 

 an integral multiple of the strong periods 7, 13, 39, and 91 months. 

 It cannot be much more than 1/3 percent from the true master period. 



Table 3. — Percentage amplitudes of proposed periods 

 271.2 105.7 103.4 T 02-5 100.7 100.9 96.3 97.3 97.9 98.0 97.7 9.4 



Period Ranges 



Months Percent 



27 



273.0 95.7 95.8 93.4 96.1 99.3 102.0 103.7 108.0 104.8 101.1 14.6 



27 

 275.0 109.8 102.4 103.3 99-3 95-4 92.9 96.2 97-6 98.8 104.5 16.9 



27 

 277.0 94.6 104.4 106.2 101.3 105.8 105.5 94-6 97-5 96.9 93-3 12.9 



27 



The subordinate periods. — Of the 27 periods used in forecasting, 

 12 exceed 15-1/6 months in length. Owing to arrangements used to 

 treat changes of phase, which will be described, 42 tabulations for 

 each city are made of these 12 periodicities. Almost without excep- 

 tion the curves representing these 42 tables betray overriding har- 

 monics of the period in question, from two to eight in number. These 

 overriders must be evaluated and eliminated before the period in 

 question stands free. 



I show in table 4 and figure 6 the treatment of one only of the four 

 tables representing the 39-month period in precipitation at Helena, 

 Mont. Eight tabulations of successive runs of this period over the 

 interval of years 1891 to 1917 give the mean values and average de- 

 viations from the mean in percentages of normal precipitation. Then 

 five harmonics of 39 months are successively removed, yielding the 

 smooth-curve deviations from 100 percent given in column S, and its 

 deviations from what remains after the five removals of harmonics. 

 In the final column of table 4, and the final smooth curve of figure 6, 

 we see the real periodicity of 39 months. The average deviation from 



