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