CYCLES 117 



and reversing alternate signs, and plotting. Such curves have shown 

 extensive 14-year cycles and half-sunspot cycles. However, on testing 

 rainfall records for such period, the weight of evidence favors a broken 

 or variable cycle of some 28 months (Douglass, 1915; Clough, 1924). 



CYCLES IN TREE-GROWTH 



CYCLE RELIABILITY 



Definitions — The value of a record of the past is its service for the 

 future, and prediction becomes possible as repetition is recognized. 

 Repetition may come at irregular intervals, in which case it may be 

 wholly accidental; or it may come at nearly equal intervals, in which 

 case it constitutes a cycle; or it may come at exactly equal intervals, 

 in which case it can be called a true period. 



Short variations — In studying variations of weather and trees, 

 the first characteristic observed is the great number of short varia- 

 tions. These are usually interpreted as accidental and without sig- 

 nificance, for if any large number of annual values be drawn by lot 

 and plotted, we shall find in the curve a maximum number of 2-year 

 periods, a lesser number of 3-year periods, and so on in decreasing 

 rate, all of which, of course, are accidental. So the weather at any 

 one locality is full of small variations which it is useless to work 

 on at the start. Such variations remind one of waves on water. We 

 can picture a combination of land outline and winds which would 

 produce an exceedingly complex wave system, but we could probably 

 determine the origin of each. We do not get the same bird's-eye view 

 in the distribution of weather and we have to class small variations 

 as accidental in the sense that they are far too complex to disclose 

 their origins at present. But while these variations are now of no 

 value in weather prediction, their existence does not prevent the 

 existence of certain short-period variations buried in them which are 

 not accidental and whose origins are worth tracing. 



Long variations — Accidental and illusive periods decrease in 

 probability as the length of the period under test increases. Many 

 accidental 2-year and 3-year periods have been found, and even one 

 11-year period in numbers drawn by lot, but 20-year periods or over 

 have proved extremely rare in accidental sequences. Therefore, in 

 the analyses which follow, periods under 10 years have been given 

 little weight unless extraordinarily prominent, and as the length of 

 period advanced from 10 to 20 years and beyond, more and more 

 reliability has been credited to any evidence of periodic variation. 



Criterion of reliability — A criterion for judging the reliability of 

 cycles has been suggested which for simple reasons has not yet received 

 extensive use. It is applied by taking all the values in a curve con- 



