1922.] 



335 



of which records exist, in more or less complete form, for nearly 

 400 years, for a large number of places in western Europe. Now 

 it is well known that, at least before the development of an over- 

 seas trade in corn, the price at a given locality was high when 

 the harvest in that neighbourhood was scanty, and low when 

 the crop was abundant. Sir William Beveridge has examined 

 these data, and being struck by the appearance at regular 

 intervals of abnormally high prices — which may be assumed to 

 follow immediately on bad harvests — has conducted an exhaus- 

 tive investigation into the whole material.* 



Now although it is simple enough to combine several cycles 

 to form, so to speak, one compound cycle, and find out when 

 their cumulative influence is greatest or least, it is not so easy 

 to decompose the resultant compound cycle, which is all that we 

 have to work upon. Yet there are mathematical processes which 

 enable us to unravel the threads and disentangle the constituent 

 cycles. The arithmetical calculations are very heavy, but by the 

 use of methods known as " harmonic analysis " and the 

 " periodogram," Sir William Beveridge has succeeded in de- 

 tecting a large number of cycles. He finds, in fact, no less than 

 19 (possibly there may be more), with periods of revolution 

 ranging from 2 § to 68 years. The probability of their lval exist- 

 ence is in a large number of cases confirmed by the periods 

 agreeing, with quite reasonable accuracy, with cycles detected 

 by various meteorologists. 



The most striking of these cycles, i.e., the one emerging most 

 prominently from the calculations, is one of about 15 years; 

 and it is the more remarkable because an independent period of 

 this duration is not known to meteorologists. Sir William 

 Beveridge suggests, however, that it may be really a combination 

 of shorter cycles, the maximum intensity of all of whicIT would 

 coincide about every fifteenth or every thirtieth year. 



He also finds a cycle of 11 years, corresponding to the sun-spot 

 cycle. This one, however, does not persist throughout the whole 

 300 years, and the author thinks that the real period (also 

 emerging from his calculations) is one of not quite 5\ years, or 

 almost half 11. A cycle found with a period of 35} years also 

 corresponds well with that discovered by Bruckner as causing 

 a regular alternation of dry, warm periods with wet. cold ones. 



Sufficient records do not exist to enable the author to use data 

 prior to 1550, but the records of historical famines show (lint 



*" Wheat Prices and Rainfall in Western Europe.'" a paper read before 

 the Royal Statistical Society on 25th April, 1922. This is in substance a 

 sequel to an article by the same author on " Weather and I lam st Cycles," in 

 the Economic Journal for December, 1921. 



