A STUDY OF CORRELATIONS AMONG TERRESTRIAL TEMPERATURES. 



319 



time-correlation. The nature of the criterion will be most readily seen by the graphic 

 representations in Figures 1 and 2. Let Figure 1 represent an approximately har- 

 monic fluctuation. If the ordinate at represents the initial variable quantity, there 



3/2 p 



Fio. 1. 



will always be a rising phase between the points |P and P; say near the point ^ at f 

 of a period from 0. If our initial departure is near ^P, then we shall have a descend- 

 ing phase betweeen P and #P, which is f of a period further on. 



Now, imagine that the regular fluctuations thus represented have superimposed 

 upon them accidental deviations so large as to mask the harmonic chai'acter of the 

 fluctuations. Were these accidental deviations superimposed upon a harmonic motion 

 in a continuous succession of periods, they could be detected by continuing one system 

 of observations through a number of periods, because they would then be eliminated 

 from the mean. But we are supposing a case in which the period is itself disturbed. 



Fig. 2. 



What we therefore have to do is to take a number of starting points, numbered 0, 1, 

 2, etc., and continue the series from each so far as we deem it useful to do so. In these 

 several series the accidental deviations will still be eliminated, ultimately leaving in 

 the general mean a tendenc}'^ toward the harmonic phase as described. 



Such a case is shown in Figure 2. Here there is not evident to the eye any ten, 

 dency toward an exact period. But a study of the diagram shows that by measuring 

 off equidistant intervals to the points P, 2P, etc., the departure is, in the general mean 

 positive, Avhile at the middle points of the spaces it is, in the general mean, negative. 

 A criterion is thus offered by which any periodic tendency may be brought out. 



We shall now show the method of time-correlation by which not only a period of 



I 



