338 



A STUDY OF rORKELATIONS AMOXG TERKERTKIAL TEMPERATURES. 



Table III. 

 GoeffiGients Expressing Observed Fludualions of Temperature through the Sunsiyot Periods 

 at Various Places or in Various Regions in the Form : At = x cos v -\-y sin v. 



Column TF gives approximately the integral part of the coefficient aa or hh. In 

 the case of observations extending through any integral number of periods these two 

 values would be the same. Practically they are alwaj's so nearly the same, approx- 

 imately half the number of years, that it was unnecessary to make any distinction 

 between them. In other words, the values of x and y may be regarded as always 

 of equal weight. 



Were the accidental fluctuations at the several stations equal in amount, IF would 

 be the weight to assign to each result. But, as a matter of course, different points and 

 different regions are subject to different mean fluctuations. The mean of the squares 

 of these fluctuations is shown in the column S". In a rigorous treatment by the 

 method of least squares the value of 2 should be derived from the residuals left when 

 the concluded values of the unknown quantities are substituted in the equation of 

 condition. But, for obvious reasons, we should not find the residuals from each spe- 

 cial solution, but by substituting the final values of the unknowns derived from the 

 com])ination of all the data. Even then the weight might frequently be illusory. 



