312 A STUDY OF CORRELATIONS AMONG TERRESTRIAL TEMPERATURES. 



Strong evidence on the affirmative side of the question was adduced by Langley, 

 in a discussion of bolometric measures of the sun's radiation in 1902-3, compared with 

 fluctuations in the general terrestrial temperature. During the year 1903 especially, 

 the bolometer showed well-marked periods during which there seemed to be a I'emark- 

 able diminution of intensity of the sun's radiation. On comparing these fluctuations 

 with those of the temperature in various regions of the globe, derived from the Deka- 

 denberichte of the Hamburg Seewarte, a seeming correspondence was shown between 

 the two classes of fluctuations. The relation was exhibited by curves, but was not 

 reduced to the form of an exact numerical relation with a determined probable error. 



Notwithstanding the volume of observation and investigation bearing on the sub- 

 ject, and generally supposed to point to the actual existence of fluctuations in the sun's 

 heat, the question cannot be regarded as settled until more precise numerical results 

 than any yet reached are worked out. The drawing of conclusions from any system of 

 direct measures of the sun's radiation, whether made by the bolometer or any other 

 instrument, is subject to the seemingly insurmountable difficulty that the variations 

 in the transparency and temperature of the atmosphere, especially in the higher 

 regions, which may materially affect the measures, cannot be accurately determined. 

 It is equally impossible to determine with precision the varying fraction of the heat 

 which may be intercepted by the atmosphere, and to eliminate the radiation of the 

 matter contained in the atmosphere itself The uncertainty arising from these ever- 

 varying causes might indeed be reduced indefinitely by comparing simultaneous ob- 

 servations at points so widely separated that no common atmospheric cause could 

 affect the measures at any two stations. But, so far as the writer is aware, no at- 

 tempt to organize such a series of determinations has yet been made. 



On the other hand, when it is proposed to detect fluctuations in the solar radia- 

 tion by observations of temperature, we meet with the difficulty that the temperature 

 is everywhere subject to fluctuations from local causes, especially the varying aerial 

 circulation, which it is impossible to determine, or to eliminate individually. Hence^ 

 in studying the fluctuations of temperature at any one place or in any one region, the 

 problem arises of distinguishing between those due to local causes, and those due to 

 changes in the oi'iginal source of heat. 



The purpose of the present work is to develop and apply the methods best adapted 

 to secure definite results, especially the methods of investigating correlations between 

 irregularly fluctuating quantities. The fundamental principle of this method is the 

 same as that applied by tlie author long ago in collaboration with E. S. Holden, in 

 discussing the question whether measvn-ed variations in the sun's apparent diameter 

 were real ; and, more recently, whether there existed any tendency toward unisexuality 



