NO. 3 SIXTY-YEAR WEATHER FORECASTS — ABBOT I3 



ber of repetitions has to be large to eliminate accidental influences, and 

 more especially to eliminate the influence of over 20 other periods on 

 the one being tabulated, I omit considering the time of the year in 

 periods from 20 to 50 months. Normally there are six tables of that 

 class. For the three still longer periods I omit considering the sunspot 

 frequency. Thus the tabulations involve 12X 13 + 6x4 + 3x2=: 186 

 tables for the synthesis of monthly precipitation. 



The next complication comes from the need to have many repeti- 

 tions, in order to eliminate interference effects of over 20 periods upon 

 the one being evaluated. If the 12 tables for periods of less than 20 

 months each stood alone, the repetitions w^ould be too few. As a com- 

 promise measure, I make the assumption that the tabulations at differ- 

 ent times of the year, and at different epochs before and after 1900, 

 would be nearly the same for a given period, except in phase. With 

 this assumption, I can combine six tables into one, merely altering the 

 phases of the separate tabulations into the most harmonious relation. 



1 then use the mean values representing these sixfold combinations as 

 the representatives for all occurrences of the periods being studied. 

 But I carefully restore the mean assemblies to the phases which each 

 of their six constituents had, as I tabulate the periods in my synthesis. 



To make all this clearer, I now give, in tables 4 and 5, and figure 8, 

 an actual tabulation for the ii;^-month period in St. Louis precipita- 

 tion. I use certain symbols which I will first explain. For the three 

 selected times of the year, and for before and after 1900, I use Oi &i Ci, 



02 bz C2, when sunspots > 20 "VVolf numbers, and Oi^ bx^ d^, 02^ ^2^ C2^ 

 when sunspots < 20 Wolf numbers. If, in tabulating, I move values 

 to bring all six determinations to harmonious phases, I use the symbols 

 o k, 4', 'f, to indicate if the phases are left alone, or moved later or 

 earlier. I add the numbers i, 2, 3, etc., as subscripts, to indicate the 

 number of lines of displacement. With these explanations given, table 

 4 shows a determination of "ai." Table 5 shows the assembly of the 

 six mean columns "ai ^2 &i ^2 ^i C2," which cover all times between 

 1854 and 1949 when Wolf sunspot numbers exceeded 20. Table 6 

 compares these "departures" of table 5 with similar ones derived for 

 Wolf numbers < 20. Table 7 shows the displacements of phases 

 made to harmonize in table 5, and those made to harmonize phases in 

 the corresponding table (not shown) dealing with all times from 1854 

 to 1939, when Wolf numbers < 20. These displacements must all be 

 restored when using the "Departure" columns for syntheses of precip- 

 itation. This step will appear, so far as it concerns a time when Wolf 

 numbers exceeded 20, if one examines figure i, an actual synthesis of 

 St. Louis precipitation, covering the years 1875 to 1879. 



