ANALYSIS OF TERRESTRIAL RECORDS 83 



Prescott ring growth to rainfall and have found it rather general in that 

 relation in the Pueblo Area. I answered that it had been noticed and that 

 it would probably be found stronger in the maxima of tree growth than in 

 the minima. So he segregated the measures of the general Flagstaff area 

 mean curve, FAM, 1780 to 1921, one of the curves already tested for correla- 

 tion periodogram, into four successive groups extending from the highest 

 value to the lowest and obtained the correlation coefficient between successive 

 years for each group separately. The coefficients were as follows: 



Mean value r r/<r r 



Highest 25 p. ct 1.30 0.42 3.2 



Second " .89 .23 1.7 



Third " .67 -.09 .66 



Lowest " .40 .10 .71 



In the highest and lowest groups the correlation was carried backwards 

 to the preceding value with this result: 



Highest 25 p. ct 1.14 0.41 3.1 



Lowest " .58 -.12 .86 



He concluded that there is a certainly real positive correlation with the 

 succeeding value in the highest one-fourth of the data and a quite probable 

 correlation in the second highest 25 per cent of the data. The rest show what 

 we should expect from accidental values within the chosen sample. 



The reverse problem, that is, the correlation with the preceding value 

 shows, as far as carried, the same result as the forward test. Hence he 

 regarded this as evidence that an unusually good growth strongly indicates 

 a reserve for the following year and also that the preceding year was good. 

 In other words a favorable condition this year can not give the best growth 

 this year if the tree was weakened last year. 



Triangle Tests — These are tests for the purpose of distinguishing between 

 random and natural sequences. Three curves are prepared, one giving the 

 original data and the other two showing the same set of values drawn by lot. 

 Attempts were made to select the genuine record from the random records 

 by some obvious character in it. Some twenty different growth curves 

 averaging 150 to 175 terms (yearly values) in length were tried and in every 

 case correct selection was made. This success, we recognize, was due to 

 conservation in these natural sequences. 



Two basic methods of choice were used: smoothing and periodogram 

 methods. In trying to pick out the genuine from two random curves by 

 the first of these methods, each sequence is smoothed by longer and longer 

 running means ; the one that most reluctantly becomes a straight line is likely 

 to be the genuine. In this treatment we observed a significance in another 

 character: namely, that natural sequences, the longer they are, show longer 

 and longer cycles 1 (fig. 34). 



1 If a number of group curves are tested at the same time, many of the genuine can 

 be picked out from the group by similarity of appearance, for they cross-identify and 

 the random sequences do not. 



