CYCLES 



123 



obvious similarity in cycle-length. The relations between phase 

 and zone have been described above in connection with smoothed 

 curves. The relations between cycle-length and zone are now under 

 consideration. 



Effect of combination on cycles — In a previous chapter the cycle 

 analysis of each group was given, some 42 groups. Here we have a 

 large number of widely scattered small units. The dominance of 

 certain cycles in these zones seems very significant. When we com- 

 bine the curves and use the mean curve for a homogeneous area, the 

 cycles in this general curve are reduced in number, giving a few 

 powerful ones and only traces of others. 



Present importance of small units — It is felt that the group is still 

 the important unit for analysis, and though more general combinations 

 are illuminating and helpful, the fundamental information is in the 

 group. 



CYCLES IN WESTERN ZONES 



Arcigram — In a periodogram the ordinates give the amplitudes of 

 the various periods in a given curve. In the summaries below the 

 ordinates give the number of occurrences of each cycle-length over a 

 given area, and for the present the word " arcigram" is used to refer 

 to this kind of a diagram. The distribution of cycle-lengths in the 

 three western zones is shown in figure 15. 



Derivation of ordinates — The number of groups in the three zones 

 is nearly the same: Arizona, 14; Rockies, 15; Coast, 13. In the first 

 plotting of figure 15, the ordinates consisted of the number of occur- 

 rences of cycles in each half unit of period; for example, those between 

 12.0 and 12.4 inclusive, and those within 12.5 and 12.9. But in the 

 original analyses three weights had been assigned, and in the curves in 

 figure 15 each occurrence is counted one, two, or three times as it was 

 assigned weight. This inclusion of weights made no essential change 

 in the curves. 



Western area cycles — The cycle occurrences in the three zones 

 were counted and plotted separately, and the important characteristic 

 appeared that the cycles are much the same in each, with somewhat 

 different emphasis. This similarity, as shown in the figure, is evidence 

 in favor of the approximate values here given, which appear to be very 

 nearly simple fractions of 34 or 35 years, as can be seen in the following 

 list: 



6.8 | 



7.6 (rare) T \ or 



8.6 i 



10.2 f 



11.2 to 11.7 i 



14.2 | 



17.2 £ 



20.5±1 for 



22.5 to 24.0 f 



25 + (rare) | 



28±1 ft 



31± (rare) f 



35± 1 



