CYCLES. 101 



storms. Rain is the controlling factor in these trees. The trees show a 

 double-crested 11.4-year period through nearly all the 500 years of 

 their record. This will be illustrated below. A 7-year period is also 

 frequently observed, and the combination of the 7-year and 11-year 

 periods may be the cause of these trees showing the double sunspot 

 period prominently through most of their record by interfering to 

 suppress alternate 11-year maxima. A triple sunspot period is very 

 evident in the last 200 years, but is practically lost in the preceding 

 300. The pines and sequoias agree in showing a long period of about 

 100 years. The record of the pines is not long enough to give it much 

 precision, and 120 years fits it more nearly. The 3,200 years of the 

 sequoias analyze best at 101 years. 



Illustrations of cycles Two methods of illustrating cycles in the 

 tree curves are used here. One is the usual method of showing the 

 plotted curves together with another curve indicating the cycle, so 

 that agreements and disagreements may be noted. To this method 

 also belongs the integrated or summated curve, which shows the mean 

 variation in the desired period. The other method is by aid of various 

 periodograph diagrams. These diagrams may similarly be divided 

 into the differential pattern, in which variations from the cycle at any 

 time may be noted, and the periodogram proper, which gives roughly 

 the mean form of the cycles in a considerable range of periods. This 

 form of presentation, being new and yet carrying more information 

 than the former, will be given with some explanation after the curves 

 themselves have been shown. 



The 11-year cycle. Only two tree records, the yellow pine and the 

 sequoia, extend back of the first telescopic observations of sunspots. 

 It is of peculiar interest to see whether the trees which carry the rainfall 

 record back so far with a comparatively high degree of accuracy show 

 the same cycle. In nearly all parts of the yellow-pine curve there are 

 suggestions of an 11-year cycle. By tracing this throughout the record, 

 the period is found to have a length of about 11.4 years, which is 

 sufficiently close to the length of the sunspot cycle to be considered 

 identical with it. This exact figure is not yet considered final, as future 

 intensive study of the short-period variations in the trees may throw 

 more light upon it. Taking 11.4 years as the probable length, the 

 average total variation is found to be some 16 per cent of the mean 

 growth. The period is generally double-crested with two well-developed 

 maxima and minima, but they are rarely symmetrical. During the 

 120 years from 1410 to 1530 it shows most remarkable regularity. 

 This feature, which was observed as soon as the smoothed curve was 

 examined, is shown in figure 32. The tree curve in this diagram has 

 been reduced to departures from its own mean and smoothed by Hann's 

 formula. The short period is immediately evident, even without the 

 5.7-year cycle plotted below. This bit of record in the yellow pines 



