RELATION BETWEEN TERRESTRIAL AND SOLAR RECORDS 123 



indicates the double-crested nature of the cycle represented by C-C. In 

 fact, the slant downward to the right in patterns g and m as well as in h, i, 

 j, k, and 1, is caused by a double-crested 14-year cycle which, it is evident, 

 exists both in the tree records and in the sunspot numbers. The last pat- 

 tern, 1, is taken directly from the sunspot cycle itself with the minima in- 

 verted, which turns it into the Hellmann form. Thus the existence of a 

 Hellmann cycle in any pattern may be judged by its similarity to 1. 



The 11 -Year Cycle and Its Half Value, the Hellmann Cycle — These are so 

 commonly found merging into each other that they must be considered 

 together. The Hellmann cycle was first isolated in Arizona trees in 1908. 

 The full 11-year cycle was found in German and Swedish trees in 1912. 

 Plate 21 shows German trees (at Eberswalde) whose growth follows the sun- 

 spot cycle. Forest men in our country have suggested that these effects 

 are due to thinning the forests with characteristic German regularity. On a 

 recent visit there, I was assured by the supervisor of the forest in which the 

 trees grew, Dr. Wittich, that the forest is thinned every three years or so for 

 instruction purposes in the Forest School at Eberswalde. The variations 

 therefore are natural. 



Many tree groups show, since 1850, an 11-year cycle with two crests. 

 This cycle in actual length varies from 11.2 to 11.8 years, with perhaps the 

 commonest value at 11.4, which compares favorably with 11.35 years, the 

 average sunspot cycle length since the maximum of 1837. The two crests 

 are somewhat unequal in height and in spacing and in stability. In most cases 

 one crest comes near sunspot maximum and the other near sunspot minimum. 

 The one at maximum seems to be more stable than the one at minimum. 



A cycle that fits this description was found by Hellmann in 1906 in North 

 German rainfall; it is shown in figure 51: 2 (a). Though Hellmann had 

 little confidence in this relation to the solar cycle, it seems to be sufficiently 

 frequent in trees to justify using his name. The existence of this cycle and 

 the others mentioned below is based on the cyclogram patterns in Plate 22, 

 in which the letters correspond to the letters in figure 51. 



In Plate 22a and figure 51: 2(a), Hellmann's curve of German rainfall is 

 extended to 1920 by the Berlin rainfall record. 



In 1912-13 eighty North European trees were sampled. Several hundred 

 dates of maximum growth between 1850 and 1907 are collected in figure 

 51: 7(b) (and Plate 22b), which give the result of this single qualitative test 

 in a symmetrical Hellmann cycle. The only difference from Hellmann's 

 curve is in the greater relative height of the crest at maximum. This curve 

 has been reproduced in extended form in volume I, Climatic Cycles and Tree 

 Growth, page 78. The correlation coefficient between full curve and the 

 sunspot numbers is + 0.57 ± 0.07. Extended curves are used here as in 

 each case mentioned below. 



Figure 51: 9(c) represents a group of twelve trees from Dalarne, Sweden. 

 The mean curve of the twelve, between 1830 and 1907, based on 900 measures, 



