22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 1 39 



of the second half. If a backcast were to be made to long ago, the 

 weights would of course.be reversed. 



At some chosen date all periods must be in the same phase and 

 preferably in zero phase. I chose 1957-0 as this zero date. To insure 

 that any particular period will be in zero phase with 1957-0 it is 

 necessary to compute ahead from the start at about the year 1870. 

 This may be done as follows. Take the period 8-3/1 1 months for 

 example. 



From 1870 to 1957, 87 years, there are 1,044 months. About 126 

 periods of 8-3/1 1 months would cover this interval. But a date must 

 be chosen which is an exact integral multiple of 8-3/1 1. The nearest 

 is that which gives 121 periods in the interim. Multiplying, we find 

 that 121 periods require 1,001 months, or 83 years 5 months. Sub- 



Table 8. — Repeated 8-3/ 11 months and round numbers 



1 8.2737 8 7 57-9089 8 



2 16.5454 9 8 66.1816 8 



3 24.8181 8 9 74-4543 8 



4 33.0908 8 10 82.7270 9 



5 41.3635 8 11 90.9997 8 



6 49.6362 9 



tracting these figures from 1957-0 we find 1873-7. Thus a suitable 

 starting point is August 1873. But it was assumed that the record 

 begins about 1870-0. If so, 43 months would be lost. One therefore 

 counts backward from 1873-7 five periods, and therefore begins with 

 March 1870. 



We now come to considering periods ending in fractions of a 

 month. We may make tables of accumulation for them. Again using 

 the period 8-3/1 1 months, table 8 results. 



For most of the periods of inexact months, tables to 91 months 

 suffice. But for such as 12-9/22, 13-13/20, 24-9/1 1 and 27-3/10 the 

 tables must be carried on to 273 months. 



RESULTS OF FORECASTS 



Having treated of most of the features of the method, the re- 

 mainder of this paper will disclose the results of these forecasts of 

 precipitation. As I have stated, I discovered discrepancies sometimes 

 as great as 10 percent between the published monthly normals and 

 new normals obtained by separating years when Wolf sunspot num- 

 bers are respectively above and below 20. As my new normals may 



