CYCLE PROBLEM AND LONG-RANGE FORECASTING 139 



weight to the last few repetitions than to the preceding many? It is interest- 

 ing to note that we have developed a method of trying out questions of this 

 type; the results of such studies will be reserved for a future paper. 



The second question naturally is : What is the expectation of continuity 

 after a cycle is established as operating at the present time? When is one 

 of the cycles likely to stop and when is a new one likely to enter? In the 

 case of the sunspot cycle the data show that the intervals between maxima 

 more often than not remain within about 10 per cent of the last value. Hence 

 one of the most important features in our cycle lists (chapter V) is the 

 number of repetitions without material change. That we can be very 

 sure of and by simple methods we can increase our knowledge on that point. 



But actual plots (some of them made in 1927) indicate periodic recurrence 

 of certain cycles. Here is the line of most promising development of the 

 theory of climate, bearing upon the temporary cycles that we encounter. 

 That also must be reserved for a future paper. 



Cycles in the Pueblo Area — In picturing the situation for a limited area 

 we are taking the only possible course, and no attempt is made to extend 

 consideration outside the "Pueblo" area of northern Arizona and New Mexico 

 west of the Rio Grande Valley and reaching into the southern parts of Col- 

 orado and Utah. Having outlined our area we can consider the cycles found 

 there which, together, produce a prediction "mozaic." Considering each 

 cycle as a natural unit of some sort, we wish to take the combination of units 

 operating now and put each unit or cycle one step or cycle length forward. 

 This could be called the "a" stage in the treatment. The "b" stage means 

 weighting each cycle by ascertaining its average number of repetitions in 

 its previous appearances in the last 2000 years and giving it the proportionate 

 part of its average number that remain undone. The "c" stage of treatment 

 is an estimate of its tendency to disappear and its probability of return, 

 derived from the general study of cycle sequence or recurrence from long 

 chronologies. Treatment "d" considers it in relation to cycles of similar or 

 related length in solar phenomena. 



It will be appreciated that the above analysis of the prediction problem 

 represents the situation at the present moment. As time goes on and larger 

 areas of the earth are brought under this kind of study, a much better knowl- 

 edge will be reached of the activity of these cycles and the probability of 

 their continuance or recurrence. 



Application to Winter Rainfall of the Pueblo Area — Four or five cycles 

 stand out as more important in the Pueblo Area; 23 years; 19-20 years, one 

 near 14 years, the 1 1 .5-year cycle, and the 2-year cycle. As the unit in tree-ring 

 records is the year, we can not cover very satisfactorily lengths under 5.0 

 years; certain values between 1\ and Z\ years are derived from the 2-year 

 reversal interference test. (See page 89.) Without doubt still longer cycles 

 now under investigation are equally important in this problem. 



The 23-Year Cycle — A cycle of this length and of high amplitude was active 

 during the 18th century. Since then it seems to have given place to a shorter 

 one of 19 or 20 years. 



