December 30, 1922] 



NA TURE 



Weather Cycles in Relation to Agriculture and Industrial Fluctuations. 1 



WO years ago Sir William Beveridge was led 



T 



to investigate the problem of weather periodi- 

 city from a new point of view, or at least with 

 materials hitherto unused — using wheat prices in past 

 centuries as evidence of harvest yields and so of 

 the weather. The investigation falls into three stages, 

 namely : 



(1) Construction of an index of wheat price 

 fluctuation in Western Europe from 1550 to 1869, 

 the index showing the price in each of those 370 

 years as a percentage of the average price for 31 years 

 of which it is the centre. 



(2) Harmonic analysis of this index for about 

 300 years to 1850 in order to discover periodicity. 

 In this analysis all possible trial periods between 

 i\ and 84 years in length have been examined and 

 every apparent periodicity has been tested by 

 analysing separately the two halves of the sequence. 

 The result of the analysis is remarkable ; not one 

 or two but many distinct periodicities — thirteen or 

 more — are suggested, and the suggestions are con- 

 firmed in varying degrees by the discovery of similar 

 periodicities in meteorological records. In view of 

 all the evidence, two of the periods — of 5-1 years 

 (found independently by Capt. Brunt and Mr. J. 

 Baxendell), and 35-5 years (found by Dr. Bruckner 

 in 1890) — may be regarded as " certain," though not 

 necessarily the most important. Seven others, with 

 lengths 5-67, 9-75, 12-84, T 5' 2 3. T 9"9°, 54'°. and 68-o 

 years, are classed as " nearly certain " ; all of these 

 show more strongly than the Bruckner and many 

 of them more strongly than the Brunt-Baxendell 

 cycle. Four more periods of 3-41, 4-41, 5'96, and 

 8-05 years are " probable." There are six other 

 "possibilities" including an 1 1 -year period, corre- 

 sponding in phase and in instability as well as length 

 to the sun-spot period. 



(3) Comparison of deductions from this analysis 

 of wheat prices before 1850 with the actual rainfall 

 from 1 85 1 to 1 92 1 on the assumption that the 

 meteorological factor most uniformly adverse to 

 wheat in Western Europe is rain. 



For this purpose eleven out of the thirteen 

 " certain," " nearly certain," and " probable " cycles, 

 with the lengths and phases given by harmonic 

 analysis, have been drawn for the years 1851 to 1921 

 and combined by a simple graphic method. The 

 resulting " synthetic curve " shows a large measure 

 of agreement with the actual rainfall for those years ; 

 for the 55 years to 1905 the coefficient of correlation 

 is 0-38 or about five times its probable error. The 

 principal droughts of the last seventy years, including 

 that of 1921, are particularly well shown and so 

 foretold by the " synthetic curve." 



This investigation, it is submitted, establishes the 

 existence, importance, and persistence over more than 

 300 years, of definite periodicities in the yield of 

 European harvests, some or all of which must be 

 attributed to cycles in the weather. It opens up 

 the possibility of valuable forecasts of general condi- 

 tions. But no such forecasts either as to the year 

 1923 or any other year are now possible, and Sir 

 William Beveridge makes none. He claims for his 

 investigation nothing more than that it affords a 

 starting-point for more detailed studies ; his hope is 

 that competent meteorologists may be encouraged 

 once again and more hopefully to take up these 

 studies. 



Mr. R. A. Fisher suggested that a periodicity in 



1 Joint discussion of Section A (Mathematical and Physical Science), F 

 (Economic Science and Statistics), and M (Agriculture) of the British 

 Association at Hull on September 7. 



yields is not necessarily an indication of a periodicity 

 in weather since it may indicate merely a periodicitv 

 of economic conditions. For example, the amount 

 of a farmer's crop is affected by the state of the labour 

 market and the state of his own bank account. 

 Nevertheless, if any considerable and persistent 

 periodicity reallv exists in the weather, it would be 

 likely to affect the crops and hence their prices with 

 a similar periodicity. The crop data suitable for an 

 investigation of this kind should be obtained, however, 

 not under commercial but under experimental 

 conditions. The figures obtained at Rothamsted 

 differ from those of the Ministry of Agriculture. 

 Detailed examination of these figures and comparison 

 with rainfall records, indicates that rainfall apparently 

 accounts for 30-50 per cent, of the total variation 

 in crop. 



Examination of the distribution of the rainfall in 

 each year shows that slow changes in yields seem 

 to be affected only by (a) the total rainfall in the 

 year, and (b) the excess of summer and winter rain 

 over that in spring and autumn. Between the two 

 latter there is a striking difference. In total rainfall 

 there have been spells of wet and dry years, two 

 wet spells about 35 years apart. But these spells 

 can scarcely account for more than 10 per cent, of 

 the changes in the yields, though they may account 

 indirectly for a larger percentage, e.g. by favouring 

 weed infestation. A period of 70 years is not enough, 

 however, to determine periodicity ; in any case the 

 quantitative value of the spells is not great, probably 

 less than 7 per cent, of the variation in crop : 

 the remaining 93 per cent, appears to be quite 

 fortuitous. It is here that the weak point occurs 

 in any argument which would make the yield of 

 farm crops to be dependent on the weather. 



The change which variation in excess of winter 

 and summer rain over that of spring and autumn 

 causes is more interesting than that caused by total 

 rainfall. Examination of ten-year means reveals a 

 steady increase for the last 70 years with no sign 

 of slackening. The effect of an increase in December 

 rain on the wheat yield is rather striking ; on dunged 

 plots, for example, a loss of more than i|- bushels 

 per acre occurred. 



The general result of examining these weather 

 records is that in most features the succession of 

 seasons appears to be wholly fortuitous, and in all 

 features by far the larger part appears to be fortuitous. 

 The two cases in which distinct changes are noticeable 

 account for a very small proportion of the variation 

 in yield. It is of course not denied that any series 

 of values, however arbitrary, may be expressed by 

 Fourier's expansion as a number of harmonic 

 cycles ; but in the case of the weather, these cycles 

 will be for the most part of short duration, and 

 cannot be expected to reproduce themselves in the 

 series of crop yields. For given weather the crop 

 may be predicted with some accuracy, but Mr. 

 Fisher is of opinion that the crop cannot be predicted 

 even approximately without a detailed prediction of 

 the weather. 



Dr. Simpson remarked that meteorologists might 

 be divided into two classes, those who had discovered 

 a period and those who had not. The latter as a rule 

 did not believe in periodicity, while the former 

 generally believed only in the period they had 

 themselves discovered. He exhibited on the screen 

 a table showing 88 periods discovered by various 

 investigators in solar and meteorological phenomena. 

 These ranged from 1800 years to 2 hours, and he 

 directed attention to the fact that from such a large 



NO. 2774, VOL. IIO] 



