A STUDY OF CORRELATIONS AMONG TERRESTRIAL TEMPERATURES. 



377 



Beginning with the first five-day term, we now multiply ao into each of the fol- 

 lowing five departures, and write their products in a horizontal line. A new period 

 is then begun with aj of the preceding term so that the departure which appears as 

 ai in the first line becomes ao in the second, after which it is not used. Thus each 

 individual departure enters into six consecutive periods. 



It does not seem necessary to encumber the work by giving the individual depar- 

 tures, 2376 in number, in detail. The following commencement of the table Will show 

 how the individual products were formed. 



It being usual to designate the ten-day terms of each month as a, h, and c, we 

 designate the five-day terms as Hi, a.,, hi, etc. 



The column ao of the table gives the five-day departures of the normal temperature 

 as determined from the records of the Weather Bureau. The method by which the 

 six products in each line are formed will be readily seen, as the factors are all given 

 for the first two lines, and can be readily understood for the lines following. 



Instead of showing at once the sum total, the addition has been grouped, the 

 period of 33 years being divided into terms of 5 years each, except the last, which 

 includes only 3 years. The results of the separate summations are as follows : 



In the bottom line of the table are given the coefficients of correlation found x. 

 by dividing the several sums of the products in the last five columns by the sums ao'^. 



The values of x thus found may be regarded as non-periodic. Were there any 

 tendency toward a recurrence at the end of 25 days there should be a marked increase 

 in the values of the 4th and 5th products, because the 5th corresponds to a completion 



