CYCLOGRAM ANALYSIS 35 



to verify or deny certain changes in an 11-year cycle observed in a cyclogram. 

 In carrying out this integration, the 500-year curve was divided into blocks 

 of 57 or 68 years (or 69 years) and these intervals integrated at 11.4 years. 

 (The results are shown in figure 33 of Volume I, page 103. See also Scientific 

 Monthly, December 1933, page 491, fig. 12 and our fig. 52.) In this 

 manner certain resemblances between climatic cycles in tree-ring growth 

 and solar changes were first observed. 



This chrono-integration method of studying cycle history was then applied 

 to the long records of the giant sequoias in similar blocks of 57 or 68 years, 

 but no especial result was forthcoming. Integrations at 23 years, however, 

 brought results that seemed to show frequent division of 23 years into a small 

 number of integral parts. This in turn led to "overlapping integration" at 

 23 years, which has seemed the most successful method yet tried. In effect, 

 this process consists in taking running means of three 23-year intervals. 



The defect hitherto existing in this overlapping integration is that only 

 one cycle length is tested in a very long series of integrations and other cycle 

 lengths go untested. The difficulties of testing all cycle lengths as in common 

 cycle analysis have been overcome in a process called "lag" analysis (see 

 page 50). 



PLOTTING UNSTABLE AND MIXED CYCLES 



We shall find in a few pages that our analyzing instrument called the cy- 

 clograph (whose automatic pattern is the cyclogram), in its common visual 

 operation combines successive integration (by the moving mirror) with 

 chrono-integration (by retaining a time element in the pattern). This is 

 accomplished by an "optical correlation" (as named by Dr. Alter) combined 

 with a certain method of plotting unstable and mixed cycles. In showing a 

 procession of discontinuous or short-lived periods on common rectangular 

 coordinates, we have a time scale horizontal as usual and upon this we may 

 plot cycle lengths as ordinates, as in figure 17a. But this fails to show a 

 continuity that is characteristic of cycle sequences. If, however, we abandon 

 the ordinary use of an ordinate scale for cycle lengths and combine a polar 

 scale for cycle lengths with a horizontal time scale, we can show continuity 

 with instability and even the presence of additional fragmentary periods. 

 In this plot directions vary with cycle length as shown in figure 17b which 

 obviously presents an 11-year cycle from 1500 to 1650, a 10-year cycle thence 

 for a hundred years, and again an 11.4-year cycle from 1750 to 1900. There 

 is also expressed the presence of an 8^-year cycle in the early part of the 400 

 years and a 14-year cycle in the last hundred years. Thus we can see clearly 

 that a combination of polar and rectangular coordinates gives a facility in 

 expressing unstable and mixed cycles, of which we will make further use. 



CYCLOGRAM PRINCIPLE 



We find it more advantageous to make use of a method of plotting cycles 

 that does not involve two different systems of coordinates but which brings 

 the same effect in the plot. It can be developed easily by a series of very 



