A STUDY OF CORRKLATIONS AMONG TERRESTRIAL TEMPERATURES. 313 



in families. This method is applicable to fluctuations so irregular that no law, periodic 

 or otherwise, can be detected in their course. Periodicity is to be detected by other 

 methods, involving somewhat different principles, which will also be developed. 



In investigating the question it is well to consider in advance the general char- 

 acter of the fluctuations which may be expected. The first question to arise is : assum- 

 ing that the sun's activity, as determined by terrestrial observations, is subject to a 

 periodic change, what periods are the most likely ? The reply to this is that there 

 are only two periods which can be assigned in advance with any plausibility. One is 

 that of the sun-spots ; the other that of the sun's synodic rotation. The latter period 

 would arise if one hemisphere of the sun were occasionally at a higher temperature 

 than the other through two or more successive rotations. We must regard this as highly 

 probable if the solar radiation is subject to any change whatever. It is. in fact, rather 

 unlikely that any cause affecting the temperature of the solar envelope would act at 

 one and the same time over the whole of the photosphere. If a difference in the two 

 hemispheres were permanent, or even if it continued through large fractions of a year, 

 there would be no difficulty in detecting it. As a matter of fact, permanence is 

 scarcely to be expected, and it is in consequence difficult to distinguish between 

 irregular fluctuations and those having this origin. 



Granting that some region of the photosphere experienced a rise or fall of tem- 

 perature which continued through an entire rotation, the effect would be seen in a cor- 

 responding fluctuation in the general temperature of the earth. From what is known 

 of motions in the photosphere, it is clearly impossible that two different regions of the 

 solar photosphere at the same latitude and the same altitude can be permanently at 

 different temperatures. But even if the difference in question ordinarily continued 

 only through two or three months, there would be no difficulty in detecting the periodic 

 effect as special regions of the photosphere would successively be brought into view 

 by the sun's rotation. On the other hand, if the inequality of temperature did not 

 ordinarily continue through a single rotation, the effect could not be distinguished 

 from that of irregular fluctuations. 



The problem of determining whether there is any period in terrestrial temperature 

 corresponding to that of the solar spots is one of such simplicity that it need not be 

 dwelt upon in the present connection. It will be studied in the course of the present 

 paper. 



The really difficult problem is that of detecting with certainty irregular fluctua- 

 tions in the radiation. The difticulty arises from the fact just mentioned that the 

 fluctuations of temperature are everywhere determined by varying and accidental 

 meteorological causes, especially the motion of large bodies of air from one region to 



