280 Jb '. H. Bigeloiv — Studies on the General Circulation 



cosmical causes, such as the movement of the sun in declina- 

 tion, from 23° north latitude to 23° south latitude, due to the 

 annual motion of the earth about the sun, the rotation of the 

 sun on its axis, the aperiodic fluctuations of the solar radiation 

 due to its thermodynamic internal actions, which affect the 

 temperatures of the earth in small regions or as a whole. 

 These mean departures, T r , usually consist of long and short 

 fluctuations, and it is necessary to separate them in preliminary 

 studies, in order to obtain some idea of the kind of action 

 underlying the variations, with the purpose of finding out the 

 laws representing the physical processes involved. The most 

 convenient way is to take consecutive means for a selected 

 number, r s , of the available r time-terms. In the example the 

 consecutive years are 5 in number, and the 5-year means r s 



derived from t r 5 in succession are placed in the next 



column, that for 1873-1877 against 1875, that for 1871-1878 

 against 1876, the last being 1900-1905 against 1903. The 

 r s consecutive departures represent the long period term r 

 which is found in the rapidly changing system of departures 

 ^ rn . The short-period term is found by subtracting each t s 

 from T r in succession, so that the residuals, t t -t s , are short 

 period variations in the system of departures. Examples of the 

 use of this method can be found in the following papers : Bul- 

 letin R, The Daily Normal Temperature and Precipitation of 

 the United States ; Abstract of data, No. 3, The Annual Pre- 

 cipitation of the United States; this Journal, vol. xxv, p. 413, 

 May 1908, The Relation between the Meteorological Elements 

 of the United States and Solar Radiation. In the last paper 

 the data of the solar prominence frequency numbers and the 

 European horizontal magnetic force are treated in the same 

 way, and the data of the solar prominences here used are 

 extracted from it. The long-period consecutive means P s , for 

 5-year intervals, and the short-period residuals, P-P s , are 

 placed in Table 1 ; they are plotted together with the corre- 

 sponding temperature variations in fig. 1. An inspection of 

 these diagrams brings out clearly several features of the 

 problems of departures and residuals, which must be care- 

 fully considered in discussing the physical causes that produce 

 them. It is apparent that the long-period curves have a 

 similar synchronism, but that the temperatures seem to lag for 

 about two years behind the prominences during the interval 

 1877 to 1888, while the lag has apparently disappeared after 

 1888. In the short-period the same lag occurs in the first half 

 of the run, the crests being displaced in the temperatures 

 about two years to the right, while in the second part of the 

 curve the crests synchronize or become minor and irregular 



