26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. I46 



phases, the groups of the same Wolf number will be approximately 

 of nearly the same form of distribution, and amplitude of intensity, 

 and may be combined. But if combined, the individual phases must 

 not be lost sight of. So when six columns of means are averaged to 

 yield one general mean, the columns must be shifted bodily upward 

 or downward to be as nearly as possible in the same phase. We use 

 symbols, ok, fm, |n, to indicate shifts. Then the general mean column 

 of the six numbers must be shifted back to the original phase rela- 

 tions of its individual members when tabulated for the summation to 

 make up a forecast. 



Beyond 15-1/6 months period, practically every period when 

 plotted betrays confusion, for shorter harmonic periods override the 

 period sought. This requires what is by far the most arduous com- 

 putation of all. After the electronically prepared tables are received 

 from Mr. Wexler they must be treated as was seen in figure 18 to 

 clear the overriding shorter harmonics away. It is sometimes difficult 

 to decide which submultiples are present until after one or two futile 

 trials. Such repeated trials with periods 54 to 91 months in length 

 are very tedious. 



The combination of 6 member columns into a general mean, as we 

 do for periods less than 15-1/6 months, will best be understood by 

 a numerical example. The letters a, b, c denote, respectively, data 

 of January- April ; May- August; September-December. Subscripts 

 1 and 2 with them mean first and second halves of the records. 

 As expected, these columns are not in the same phase. The signs, 

 ok, ^, and |, show how much the columns must be moved up or 

 down bodily to be brought into the best posture for uniform phases. 

 When the mean percentage departures from normal in the final 

 column of table 5 are used in the summation for prediction, the 

 columns marked "ok" are to be replaced by the general mean column 

 without shifting. The general mean values are to be lowered 2 months 



