60 CLIMATIC CYCLES AND TREE GROWTH 



0.206 per set and a standard deviation of the mean of 0.124. So the Bartels 

 ratio for this sequence is 1.6, which places it in the realm of reality; the maxi- 

 mum possible value is s/l or 2.65. His a becomes (1.6) 2 or 2.6. 



It has been suggested that we use the fraction of 1.6/2.7 or 0.59 as the 

 reliability index. But that seems undesirable because we are only using 

 two of the necessary three terms; the unity term has disappeared, and we 

 can not let it disappear because it varies with every different number of sets. 

 In the present case the unity in the same proportion would be 0.37. We 

 might take the logarithms of the three terms; they are 0, 0.20, and 0.43. 

 This gives us 0.47 as the index. For the present we should perhaps tell the 

 story by saying that in 7 repetitions of the cycle the QP factor is 2.6, which 

 is 0.37 of the continuous length 7. 



At this time the subject should not be carried further, but we note that 

 if and when the variations that we here class as random become assignable 

 terms in other cycles, the variations lose a portion of their random character 

 and the QP factor will more nearly reach N, the number of sets used. 1 



This process of Bartels' seems a very promising method of evaluating a 

 cycle. In his application of this process to the magnetic character figure C, 

 he uses the full series of data in his 378 sets of the cycle length, which implies 

 that the QP is not localized at the few places where it has been recognized 

 but lasts throughout the data as a general solar character. While we, on 

 the other hand, are trying to localize such characters and learn more about 

 them, we appreciate the high value of his result as it stands; it is analogous 

 to a first statement of mean annual rainfall of a new locality as compared to 

 the more detailed monthly values to come later. 



Bartels 1 Multiple Plot of the Magnetic Character Figure C — The writer 

 feels that Dr. Bartels had previously reached important results in a graphic 

 analysis of discontinuous periods in the magnetic character figure C contained 

 in his paper of 1932, Terrestrial-Magnetic Activity and its Relation to Solar 

 Phenomena (Terrestrial Magnetism and Atmospheric Electricity, vol. 37, 

 No. 1, pp. 1-52, March 1932). To use a term already employed by us, 

 his long chart of symbols showing the daily values is a multiple plot. 2 Like 

 our figure 14b, page 31, it corresponds in function to a summation table and 

 represents quantities by symbols that catch the eye. It thus has the quali- 

 ties of the plot mentioned and by the eye alone periods and discontinuities 

 may be read off from it as from a cyclogram. Without really naming it as 

 a form of analysis, Dr. Bartels has correctly used it as such. He derived 

 very important inferences from the diagram. He confirmed the persistence 

 in solar longitudes of magnetic source areas which he called M-areas, finding 

 them largely independent of sunspot activity. He quotes outstanding exam- 

 ples of long 27-day recurrences of disturbed days: 1910-11, 13 rotations; 

 1921-22, 14 rotations; 1929-31, 17 rotations. He makes some references to 

 activity at opposite longitudes on the sun (as if there were a 13.5-day period) 



1 The co-existence of other cycles may seriously affect the A.D. ratio. 



2 Chree and Stagg used a multiple plot in 1927; see Bibliography. 



