126 CLIMATIC CYCLES AND TREE GROWTH 



four or five of five years show no sunspot records at all. (See pages 68 and 

 69.) In the 1400's and 1500's, before the dearth, the Hellmann cycle is well 

 developed in the Arizona pines and appears weakly in the sequoias. An 

 11-year cycle reappeared in good form after 1760. 



During the dearth the Arizona trees show a 10-year cycle; four sequoias, 

 which generally show pronounced 11-year cycles, really give a 10-year cycle, 

 which according to Schulman is 10.5 years followed by 9.7 years, giving an 

 average close to 10. Many sequoias show cycles at 8.5 and about 14 years. 

 A long hemlock record in Vermont gives 20 and 28 years with probable half 

 values at 10 and 14 (see vol. II, Plate 9). 



Summary — In summarizing the cyclograms of Plate 22, we observe that 

 they show the Hellmann cycle by double horizontal rows repeated four or five 

 times. The fainter row, which is visible in most of these patterns, means that 

 the 11-year cycle is cut into two parts by an additional crest, usually slightly 

 non-symmetrical either in spacing or amplitude. The earlier diagrams, 

 mostly foreign, show the Hellmann doubling less well developed than the 

 American curves, and one remembers that the German trees follow the sunspot 

 cycle mostly without the second crest. In the later diagrams the similarity to 

 the sunspot cyclogram using inverted minima (1) is very evident. This comes 

 not merely in the two lines of crests in 11+ years but also in the secondary 

 double-crested cycle at 14 and 7 years. Note especially the agreement of this 

 secondary cycle in trees with the well-marked 14-year and 7-year lines in the 

 sunspot numbers (with inverted minima) in 1. This shows well in all the 

 American trees. Considered historically the dominant cycle, 11 years, 

 varies in similar manner in the trees and the sun. The minor cycles, 8£ and 

 14 years, are generally present in each. The presence of these cycles in the 

 sun is shown independently by cyclogram process and by Schuster's periodo- 

 gram, as appears in figure 55. 



LONGER CYCLES 



Early analysis (by inspection) of the Flagstaff 500-year tree records 

 (1909) gave a cycle of about 21 years since 1700. This has remained very 

 prominent in the last 200 years of Arizona tree growth. In various curves 

 of cycle intensity (periodograms) a considerable crest from 19 to 22 has been 

 evident. There has always been uncertainty regarding the real length of 

 this cycle. A series of integrations at 18, 19, 20, 21, and 22 years, in figure 

 16, gives 20 years as a good average value of its length. The best mean values 

 from 1700 to 1920 were sent to Dinsmore Alter, who subjected them to 

 periodogram analysis in a rapid and skilful mathematical attack. His cor- 

 relation periodogram of this sequence is given in figure 53, which shows a 

 strong crest at something over 20-years lag, with further conspicuous crests 

 of about 40- and 80- and 120-year lags. This indicates a 40-year cycle and 

 probably one of 20 years. A cyclogram made of the same data is represented 

 in Plate 16B, which shows at once that this 20-year cycle is composite during 

 this 220-year interval. Through the first one-third, a cycle of about 23 



