l6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 139 



Hence for these longer periods there are about four divisions to a 

 period. The secular time segregation holds beyond 39 months, two 

 divisions each for four periods. 



The grouping just indicated leads to computing many tables for 

 each station: 



Up to 15-1/6 months, 15 X 12 = 180 tables 



Thence to 39 months, 8 X 4 = 32 tables 



Thence to 91 months, 4X2= 8 tables 



Total 220 tables 



Shifts of phases. — The numerous groups used for the shortest 15 

 periods leads to tabulations with so few columns that the mean values 

 of individual periods are of little weight. To remedy this defect, I 

 assume that the forms and amplitudes of periods up to 1 5-1/6 months 

 in length, and in the same grouping as regards Wolf numbers, will 

 be similar, though in different phase relations. I therefore make 

 superposed graphs of the six tables of one period for each of the two 

 stated conditions of sunspot activity. From inspection checked nu- 

 merically I am then able to shift the individual curves of the graphs 

 to the same phase relations. Then I take a mean for all six tables 

 and use that generalized mean in forecasting. But v/hen using it in 

 forecasting, I must shift back the generalized mean to the proper 

 phase, as will appear by an example later. Figure 8 gives an example 

 of these shiftings in phase. 



NOMENCLATURE, SYMBOLS, AND TIME 



As stated above, 27 periods, all aliquot parts of 273 months, are 

 to be used in the forecasts. But, as just stated, these are used in 

 several groups, depending on the length of the periods. Lags, depend- 

 ing on atmospheric conditions, dictated tabulations of 12 independent 

 groupings for the periods of shortest length, that is a lt b u c x , a 2 , b 2 , c 2 , 

 as tabulated for the period of 9-1/10 months of SS>20 in tables 5 

 and 6. Besides these, there are six tables a\, b\, c\, a' 2) b' 2 , c' 2) for 

 SS<20. However, for periods above 15- 1/6 months this extended 

 grouping brings too few columns into the tables to be capable of yield- 

 ing satisfactory mean values. Hence for periods 273/15 to 273/7, the 

 distinction between months of the year is dropped, thus reducing the 

 number of groupings from 12 to 4 for these 8 periods. For the re- 

 maining 4 periods, 45-1/2 to 91 months, the distinction SS>20 or 

 SS<20 is also dropped, reducing their groupings to 2. So there are 

 three different arrangements of assembly, as just explained (12X 15) 



