NO. 10 SOLAR RADIATION AND WEATHER STUDIES ABBOT 69 



23 years, or a mutation of phase due to unknown causes. But the in- 

 dividual 23-year cycles in both the eighth century and the nineteenth 

 century show much similarity. Fortunately, they differ but little from 

 being in step with the important date 1819. This adds interest to the 

 apparent inversion of phase shown by cycles i, 2 ; 4, 5 ; and 5, 6 of 

 the early period. Figure 28 also includes five mean curves, each one 

 the mean of 138 years or six successive 23-year cycles. Finally curves 

 are given to represent the general mean forms of the 23-year cycle for 

 542 years and 690 years of observation, respectively. These latter 

 means are taken separately, because the 138-year period ending in 1424 

 seems to show a change of phase tending to approach the form of 

 cycles which prevailed from 1839 to 1884. 



The general result seems to be that the Nile, before its regulation 

 by British engineering works, showed plainly the influence of the 23- 

 year cycle. During the 690 years preceding 1424, the average range 

 of the low level during the 23-year cycle was about i meter. The 

 extreme range of the original values during any of those centuries 

 seldom exceeded 2^ meters, so that a very large part of it was due 

 to the 23-year cycle. Maxima and minima repeated themselves so 

 nearly in phase throughout the interval of 552 years from 735 to 1286 

 that the cycle can hardly differ by as much as i month from 23 years. 



22. A Test of the 23-YEAR Cycle in the Widths of Tree Rings 



In the appendices to his " Climatic Cycles and Tree Growth," Vol- 

 umes I and 2, A. E. Douglass gives many tables of measurements of the 

 widths of tree rings from many localities. In volume i, pp. 11 7- 123, 

 we find two records of Sequoia trees, the first of i to 4 trees extending 

 from 1306 B. C. to 251 B. C, the second of 11 trees extending from 

 274 B. C. to A. D. 1910. 



I have arranged most of these data in tables of 23 columns and 

 5 lines, each table covering 115 consecutive years. Each group of 

 trees just referred to gave the same general type of result, namely : 

 At the first part of each Douglass table, where the rings are wide, 

 there is a well-marked indication of a periodicity of 23 years, as de- 

 termined from my tables of 115 years' duration. But the amplitudes 

 of the curves diminish as time goes on. After two or three centuries, 

 when the rings become much narrower, the 23-year periodicity prac- 

 tically disappears. The same thing is also observed with the long 

 Flagstaff table, 1390-1911, found in volume i on page 113. 



Figure 29, which contains but a few examples of my results, illus- 

 trates the preceding statements. It seems but a reasonable considera- 



