314 A STUDY OF OOKRELATIONS AMONG TERRESTRIAL TEMPERATURES. 



another, and the varying presence of water in its various forms in the atmosphere. 

 Leaving out these disturbing causes it is very natural, when the temperature of a wide 

 region is markedly above or below the normal for a considerable period, to attribute 

 the condition to a change in the amount of heat received from the sun. The ques- 

 tion of the reality of this cause admits of an obvious test. A change in the sun's 

 radiation will necessarily affect every part of the earth. If therefore a change of tem- 

 perature in one region has this cause as a factor we may, accidental causes aside, 

 expect a similar change in every other region. The problem is thus reduced to that of 

 detecting a correlation between the fluctuations of several var3'ing quantities. 



Since the ordinary fluctuations of temperature are mainly due to local causes, we 

 may expect the average or general temperature of the entire globe to be sensibly con- 

 stant if the sun's radiation is invariable. To speak more precisely if, on any one day, 

 it is found that the temperature in every part of the earth is in the general average 

 above or below the normal, we might rationally attribute this result to the sun. We 

 thus see that a very obvious way of testing the constancy of the solar radiation is to 

 determine the deviation of the temperature from the normal on any one day over all 

 points of the globe, and form their mean. The fluctuations of this mean would rep- 

 resent those of the sun's radiation. 



It being impossible to extend observations over the entire globe we must accept 

 the results of observations made within regions at which observations of temperature are 

 actually available. But even then it would be an error to conclude that variations 

 in the general mean must be due to the sun or any other common cause. It is not 

 to be expected that the accidental deviations in different regions completely neutral- 

 ize each other. The question must therefore be open, after we have determined the 

 changes of mean temperature from time to time over the whole globe, whether the 

 mean fluctuations outstanding are purely accidental, or are due to changes in the 

 thermal energy received from the sun. A rigorous method of treating this question 

 will also be developed. 



It follows that, in order to reach a well-grounded conclusion, some criterion is 

 necessary to determine whether the changes in the general temperature of the globe 

 are due to changes in the solar radiation, or to accidental terrestrial causes. No cri- 

 terion which will decide this question in any individual case is possible, but there is a 

 criterion by which the average amount of the cosmical fluctuation, if it be appreciable, 

 can be determined. To show the simplest example of its application let the deviation 

 of the temperature from the normal be observed from day to day and from year to 

 year in two regions of the earth so widely separated that no common purely terrestrial 

 cause can affect the two places at the same time. Then, by the law of probabilities, 



