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 1l-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 ecyeles.—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 ll-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 
