ALTER: RAINFALL AND SUxY-SPOT PERIODS. 25 



of maximum of each of the cycles of the sun spots will always fall 

 in one phase of the suspected rainfall variation and also each 

 minimum in one. Wolfer's values of maxima and minima are un- 

 certain by a month or so, and therefore in the first paper the 

 placing of them within one phase from the mean was considered as 

 a perfect check in determining the months to be averaged or re- 

 peated. When there was a greater error than this in determining 

 the position of a maximum or a minimum it meant that there was 

 a slight error in the curve and that it was necessary to apply a 

 slight adjustment factor to the values of the period taken from it. 

 In no case did I have a large factor to apply, thereby showing that 

 the curve as constructed was approximately correct. Indications 

 from the work explained above were that the period taken from it 

 could be relied upon to within three or four months, and that such 

 errors as did occur were canceled in most cases by ones of opposite 

 sign before adjustment had become serious. 



I did not realize at the time that readers might think this discrep- 

 ancy purposely made by me in order to better my results. To avoid 

 this objection I have, in this paper, made the Wolf-Wolfer epochs 

 fall exactly in the same phase each cycle. The phase in which the 

 sun-spot maximum falls has been numbered 1 and that in which 

 minimum falls 8. For 1913 Wolfer has published two dates of sun- 

 spot minimum, first May, and later August. I used the former in 

 the first paper before seeing his later work. The sun-spot curve 

 seems to me to indicate May, or even an earlier epoch, correct. 

 Wolfer's later epoch may, therefore, be a typographical error, and I 

 have continued to use May. Since a short period locates its epochs 

 of maxima and minima more exactly than a long one, it will be pos- 

 sible later, if the existence of the short rainfall period be admitted, 

 to revise the Wolf-Wolfer epochs from the rainfall data. Such a 

 gain in accuracy would mean much in an investigation of the sun- 

 spot periodicity. 



Table 3 shows which months I have averaged and repeated in the 

 analysis of the rainfall data of each country investigated. It is 

 probably useless to emphasize that there was no change in this table 

 for any of the countries under consideration. At first thought the 

 results of table 3 and of figure 1 are startling. However, an inspec- 

 tion of the much greater changes in the period which have persisted 

 through entire cycles during the last 115 years, namely, from 88 to 

 205 months, shows that these variations through short periods of 

 time are to be expected. Moreover, there is no way to draw a curve 



