40 CLIMATIC CYCLES AND TREE GROWTH 



expressing cycle length between 6 and 13 years. We may now interpolate 

 the particular slant shown by the sunspot maxima in figure 19a. By com- 

 paring it with our set of position angles just developed, we obtain an approxi- 

 mate solution of 11.4 years for the mean cycle length exhibited by the maxima 

 since 1833. 



Now on the same coordinate paper let us extend the plot of sunspot 

 numbers back to the maximum at about 1749 and see what is indicated by 

 the same method of solution. The plot is shown in figure 20 and we see that 

 the various maxima instead of being scattered at random do form a broken 

 line or a sequence of fragmentary straight lines. Since each straight line is 

 a temporary period, we can, I think, consider the maxima sufficiently in 

 straight lines to call this diagram a sequence of short-lived or discontinuous 

 periods. 



In our polar diagram of figure 19b made in the same coordinates, we have 

 an easy solution for the approximate cycle lengths shown by these lines. If 

 the polar plot is on transparent paper it is only necessary to superimpose it 

 and we find as follows : 



Cycle length from plot : Cycle length from time interval : 



1750-1790 9.7 years between 5 maxima 39/4 or 9.8 years 



1790-1830 14 between 4 maxima 42/3 or 14.0 



1830-1837 7 between 2 maxima 7 



1837-1930 11.5 between 9 maxima 91/8 or 11.4 



It will be noticed that by means of the half-tones, all the original data 

 may be represented in figure 19a and, if other cycles are present and suffi- 

 ciently conspicuous, they will constitute alignments in other directions as 

 indicated in 19b. It is evident that a given alignment does not necessarily 

 continue through the whole pattern. If, for example, a cycle did not exist 

 before some definite date but did exist after that date, we would find an align- 

 ment beginning at that time. (See Plate 16.) Thus we can study cycles or 

 periods equally well, whether permanent or fragmentary, provided there are 

 a sufficient number of repetitions. Thus the detection of the presence of a 

 cycle is necessarily obtained in its full and extended form and not from inte- 

 grations and the cycle must become evident in competition with a considerable 

 range of values on either side which, if there, show at the same time. So a 

 proper and careful selection of value can be made and the analysis is not in 

 any sense a special test for a single value. 



CYCLOGRAPH 



Cyclogram analysis can be performed by anyone who has the patience 

 to understand it. It has introduced new methods and results in cycle study, 

 for fragmentary and interrupted periods can be measured as well as permanent 

 ones. This gives a new and more efficient approach to climatic and sunspot 

 cycles. The automatic character of this analysis has made it extraordinarily 

 rapid. Thus five minutes at the cyclograph has often been enough to 



