NO, 8 HARMONIC PERIODS IN PRECIPITATION ABBOT 9 



open a direct path to foreknowledge of precipitation, that highly- 

 important variable in agriculture and water supply. 



This hope has now been realized by a combination of five discoveries 

 of the twentieth century. For more than 10 years now it has been 

 possible, with these five helps, to make useful forecasts longer than 

 one generation in advance. The discoveries referred to are as follows : 



1. Nearly a century of patiently continued weather records are 

 now available. They embrace many stations in all continents, and are 

 published in World Weather Records. 



2. Both the sun's radiation and the long-continued weather records 

 contain as many as 27 harmonic periods, exact submultiples of 273 

 months, of equal lengths in solar radiation and in weather. 



3. While solar variation varies in amplitude, its phases appear 

 constant. Weather phases, on the other hand, vary considerably as 

 conditions alter in the atmosphere. These phase shifts, which may be 

 as great as several months, differ with length of period, locality, time 

 of the year, sunspot frequency, and growth of population. These diffi- 

 culties require a large number of divisions to be made of the long 

 weather records. Indeed, 222 tables for each station are required, 

 as I have explained in previous publications. 



4. The invention and development of the electronic computer 

 makes it possible to handle the multiplication of phase diflFerences, and 

 any desirable smoothing of arrays of numbers in a few moments, 

 instead of years, as when I computed alone for St. Louis forecasts, 

 1854 through 1957. 



5. The introduction of the smoothing formula YQ{a + 2b+Ac + 



2d + e) is highly valuable. In it the value c has y^ as great weight as 



the four neighboring values combined. With an irregular variable, 



like precipitation, smoothing is necessary. But to avoid displacing 



phases by smoothing, it must avoid giving preponderant weight to 



values outside the central value. 



Before demonstrating more, it may not be superfluous to point out 



that with nearly 100 years of records available, they may fairly be 



used, not only for prediction but to test the validity of predictions 



when made. For if all records of A^ years be employed in a prediction, 



the monthly records of a single year cannot affect the prediction for 



12 

 that year by more than r^. That quantity diminishes proportionally 



with the increase of N and reaches the negligible value of 1 percent 

 when AT =100, 



