42 ANNALS NEW YORK ACADEMY OF SCIENCES 



take yearly means, the groups of exceptionally cold or exceptionally hot 

 months are also eliminated, at lea^t to a certain extent. In fact, in a 

 yearly mean, of a normal value, the effect of a couple of abnormally cold 

 Tiionths may be balanced by a couple of very hot months, so that the 

 yearly mean of temperature may remain normal. 



The advantage of consecutive twelve mqnthly means* over the calendar 

 yearly means is that we can detect the effecf of some of the shorter waves 

 on a yearly mean, giving us at the same time the possibility of locating 

 seasonal anomalies. Likewise, if we take the consecutive means of groups 

 of yearly means we will disclose, easier than in any other way, the suc- 

 cessions of colder and warmer periods during various lengths of time. 



Admitting, for the pleionian variations, a period of from two to five 

 years as the unit of time, we will say that shorter climatic variations are 

 hra-chyclirone and those that are very much longer than these pleionian 

 variations are ma^roclione. Besides the ordinary pleions and antipleions 

 or thermomeions, therefore, we will have to speak of brachy pleions and 

 macropleions, of hrachymeions and macromeions. 



The curves of the following diagram (Fig. 1) may serve to explain 

 more clearly the difference between maeropleionian. pleionian and braehy- 

 pleionian waves. 



The first curve shows the succession of consecutive annual means for 

 Arequipa. A, B, C, D, are pleionian crests, preceded and followed by 

 antipleionian depressions. With the exception of the second depression, 

 which may have been accentuated by the presence of great quantities of 

 volcanic dust in the higher layers of our atmosphere,^ the depressions, as 

 well as the crests, show a striking tendency to decrease from 1901 to 1909. 



• 1 think that the expression "consecutive means" is just as comprehensilile as the 

 expression "overlapping means." "progressive means" or "moving averages." 



WiLLFORD I. Ki.NC in his "Elements of Statistics" (New York, 1912, p. 160), uses 

 exclusivel.v the term "moving average." 



As far baclv as 1841 Luke Howaro. "On a cycle of eighteen .vears . . ." (Philos. 

 Trans. Royal Soc. of Ixindon for 1S41. p. 277), utilized consecutive means and called 

 them "averages on successive cycles." 



H. H. Clayton, in his paper "A lately discovered meteorological cycle" (Am. Meteor. 

 Joum., Vol. 1. p. 130, 1884), used the perfectly comprehensive expression "means of 

 every twelve consecutive monthly means." 



' Many papers have been published recently, concerning the question of the influence 

 on meteorological conditions of volcanic dust, present in the higher layers of our atmos- 

 phere. Some information upon the effect of this cause on the observed variations of the 

 "solar constant" may be found in the following papers : 



C. G. Abbot: "Do volcanic explosions affect our climate?" (Nat. Ctnagr. Mag.. Vol. 

 24, p. 181. 1913.) C. G. Abbot: "The solar constant of radiation." (Trans. Inter- 

 nat. Union for co-op. in solar research. Vol. 3, p. 201. 1911.) C. G. Abbot, F. E. 

 PowLE and L. V. Ai-Drich : "The variation of the sun." ( .^stronomische Nachrichten, 

 Vol. 194, p. 431. 1913.) 



C. G. Abbot and F. E. Fowlk : "Volcanoes and climate." (Smithsonian Miscellaneous 

 Collections, Vol. 60, No. 29. 1913.) 



