380 A STUDY OF rORRELATTONS AMONG TERRESTRIAL TEMPERATURES. 



110 change sufficient to produce anij measurable effect upon terrestrial temperatures. The 

 only admissible changes are such as going through their period in 10 days or less, 

 would produce no effect upon 10-day mean departures. Whether any such fluctua- 

 tions exist, except those arising from the irregular changes of the spots and faculse, 

 is a question to be judged by the probabilities of the case. 



4.' There is a certain suspicion, but no conclusive evidence, of a tendency in the 

 terrestrial temperature to fluctuate in a period corresponding to that of the sun's 

 synodic rotation. If the fluctuations are real they affect our temperatures only a small 

 fraction of one tenth of a degree. 



5. To facilitate the criticism of the preceding conclusions, and their comparison 

 with those reached by other investigators, we must point out what may be considei'ed 

 a limitation upon their scope. A careful study of the statistical method developed in 

 § 4 Avill show that the primary intention is not to determine specific fluctuations, and 

 attribute them to changes in the sun's thermal radiation, but only to find a general 

 criterion for detei-mining whether, as a general rule, the fluctuations have any other 

 cause than the accumulation of accidental vicissitudes of temperature in the regions 

 studied. Repeating once more in a condensed form the fundamental principle itself; 

 when we determine the mean temperature of the globe by comparing the actual with 

 the normal temperature at a great number of places through a number of time-terms, 

 — we may determine the general world fluctuation by taking the mean of the depar- 

 tures in the separate regions during this term. This world-departure will have a certain 

 probable deviation, arising from the probable deviations of the individual departures, 

 the magnitude of which is easily computed. 



If the world-departures are in general markedly greater than this probable devia- 

 tion, we should have no difficulty in concluding that at the times of the greater depar- 

 tures the solar i-adiation was probably greater or less than the normal. Now the statis- 

 tical method here applied is not intended to solve this easy problem should it arise (which 

 it does not), but the more difficult one which arises when the actual departures do not 

 ordinarily exceed their probable value, and when therefore we must be in doubt as to 

 tlieir arising from a cosmical cause. No sound method of research will enable us to 

 formulate a conclusion on insufficient data, and the logically best method is that which 

 will enable us to formulate all the conclusions that can be drawn. In the present case 

 this is shown to be the probable value, during each time-term, of the square of a cer- 

 tain quantity tq expressive of the increment of the solar radiation during that term. 

 This quantity will have its probable accidental error, and therefore, if its objectively 

 true value is evanescent, may still come out with a certain value, which is then as likely 

 to be negative as positive. Having found this value through all the various terms, if 



