ANALYSIS OF TERRESTRIAL RECORDS 



97 



preliminary results, subject to improvement but certainly showing at this 

 time some of the general facts. The summary in a frequency periodogram, 

 fig. 55, contains a significant generalization from these data. 



Evaluation of Cycles in the 42 Groups — The preceding lists contain the 

 results of analyses by Mr. Schulman of the 42 Western groups with special 

 attention given to the dates of beginning and ending of cycles. About 100 

 cycles which he had "underlined" form perhaps the basis of the list; under- 

 lining means 1 that they showed signs of special strength; approximately 175 

 apparently weak cycles in addition to those listed are here omitted. But 

 he has included some 40 cycles observed by the writer and reported in Volume 

 II (1928, Chapter VII). They have been observed by Mr. Schulman but 

 were not underlined. They are, he says, equivalent to a preferred set of 

 values without underline. 



12 13 14 15 



Years 



.16 17 13 19 20 21 22 23 24 25 



Fig. 41 — Frequency periodograms of 42 Groups : 



(a) obtained by two independent observers. 



(b) weak and strong cycles compared (as recorded by Schulman). 



The amplitudes listed were determined by the usual arithmetical summa- 

 tion process described in a previous chapter. By actual tests it was found 

 that amplitudes are not changed to any appreciable extent in that summation 

 by letting some rows run one unit beyond the other rows, as is necessary in 

 testing fractional periods (periods that are not integers: See Chapter II). 

 After plotting the summated curve, the amplitudes were measured on the 

 plots and the value quoted is essentially half the range from the lowest to 

 the highest point of the plotted and smoothed curve. The difficulty was 

 encountered that the curves were not always of simple and regular type. 

 Often there were secondary crests that are non-symmetrical so that the curve 

 can not be classed as a multiple. That is quite characteristic of natural 

 sequences. 



These summations have formed the basis of a study by Mr. Schulman of 

 the meaning of underlines in terms of certain statistical quantities. He finds 



1 See also pages 146 and 147. 



