2 SMITHSONIAN MISCF-LLANEOUS COLLECTIONS VOt.. 95 



publish a statement of my reduction of them from the point of view 

 of the 23-year cycle. 



In the first place, the range of tree-ring widths is very great. 

 After 1800, the widths as measured averaged several times as great as 

 from 1544 to 1720. Hence for a fair comparison I thought it neces- 

 sary to first approximately reduce all the data to a common scale'. 

 That such a reduction might not introduce a deformation of any 

 23-ycar cycle, I made the reductions at intervals which were in every 

 case multiples of 23 years after 1544. The factors employed were 

 as follows : 



Interval I544-I7_'7 1728-1796 1797-1842 1843-present 



Reduction Factor i.o 0.8 0.4 0.3 



With these changes the resulting mean tree-ring widths from 

 Professor Lyon's measm-ements for h^airlee, \"ermont, are as shown 

 in table i . 



The values are arranged in 17 successive cycles of 23 years each. 

 At the head of each column stands the first year of the cycle, so that 

 the dates corresponding to all values may readily be obtained. 



It was soon noted that every fourth cycle, the ist, 5th, 9th, 13th, 

 and 17th, differed decidedly in type from the average form of the 

 others. This is but to say, of course, that there is a pronounced 

 92-year cycle in the tree-ring widths. It was noted, too, that five of 

 the cycles, some belonging to the group just mentioned, some to the 

 majority group, were partly intermediate between this type and the 

 prevailing type of the 23-year cycle fixed In' the remaining twelve 

 cycles. These of intermediate type are the 2d, 7th, 9th, loth, and 13th. 

 Columns 18, 19, and 20 of the table give the mean forms of the 

 three types just described. They are shown graphically in figure i, 

 C, A, B. 



The range in widths of the prevailing mean form is about 50 

 percent, and that of the 92-year type about 70 percent, as based in 

 each case on the smallest mean values. A large difference in average 

 widths also distinguishes the two types. The average width for the 

 mean of the five cycles (curve C) is 0.41 and that of the mean of the 

 twelve (curve A) is 0.50, a range of 22 percent. 



I have also sought to discover a periodicity of 46 years in the tree- 

 ring widths for Fairlee. For this purpose the values were arranged in 

 eight columns of 46 successive years each. The last column ends 

 with the year 1911. It was soon noted that the columns alternately 

 revealed forms of contrasting types. In figure i, D, E, I show the mean 

 form of the odd-numbered 46-year cycles in the lower curve, and the 



