NA TURE 



261 



^mi" 



THLiRSDAY, MARCH ^, 1922. 



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Cycles in the Yield of Crops. 



'EARLY five-and-twenty years have elapsed since 

 Sir Arthur Schuster, by devising the orderly and 

 comparatively brief process known as the " periodogram 

 method/' gave a great stimulus to the investigation of 

 periodicities in natural phenomena. Solar and mag- 

 netic phenomena provided the first fields of apphcation, 

 and meteorological data have since been attacked by 

 many investigators. It seems fitting that crops, which 

 are so largely dependent on the weather, should be 

 submitted to the same test. 



In the course of last year Prof. H. L. Moore, of 

 Columbia University, published a series of three articles 

 in the American Quarterly Journal of Economics, which 

 may be briefly summarised as indicating that, in the 

 periodogram for periods of three to twelve years, there 

 is a marked maximum at eight years in the cycles of 

 a number of crops and corresponding cycles in the pro- 

 duction of the raw materials of industry. This 

 periodicity appears to correspond to what is known 

 as the " economic cycle " in trade, and it is suggested 

 that the periodicity in crops is the generating cycle of 

 the whole movement — a movement which is very clearly 

 reflected in prices. Prof. Moore's data refer, for the 

 most part, to the years 1882-1918 only, with the ex- 

 ception of Sauerbeck's data for prices in this country, 

 which are available from 1818, and of wheat prices in 

 England, which are utilised for the years 1870-1916. 

 To the latter part of his third article we return briefly 

 below. 



In the meantime, in an article published in the 



British Economic Journal for March 1920, Sir William 



Beveridge suggested, on evidence which, to many 



readers, did not seem at all adequate, the existence of 



NO. 2731, VOL. 109] 



a period " between 15*2 and i5'4 years." In the same 

 journal for December 1921, a further paper was pub- 

 lished in which the original conclusion is completely 

 vindicated. By the aid of overlapping data as to wheat 

 prices in a large number of places in Great Britain, 

 France, Germany, and the Netherlands, an index- 

 number of wheat prices for Western Europe is con- 

 structed running from 1500 to 1869. The index-num- 

 ber for each year is then expressed as a percentage of 

 the mean of the thirty-one years surrounding it, and 

 the results are submitted to periodogram analysis over 

 the three centuries 1 545-1844, for periods running 

 from two years to thirty-six. Data are also given 

 separately for 1 545-1 694 and 1 695-1 844. 



For the whole 300 years and for the last 150 years 

 the greatest intensity, taking only integral periods, is 

 at fifteen years, the maximum being well marked ; for 

 the earlier 150 years the intensity at 15 (70) is slightly 

 exceeded by the intensity at 11 (76), 13 (80), and 18 

 (73). Testing fractional periods on the series as a 

 whole, the intensity at 15 (47) is raised to 82 at 15^, 

 and to 80 at 15 J. The dominant period appears, 

 therefore, to be fairly closely 15-3. 



But, Sir WiUiam Beveridge suggests in an interesting 

 analysis that follows, the period thus found is probably 

 not a real one — i.e. is not the period that exists in the 

 operative cause, the weather. If a certain cycle exists 

 in the weather tending to give, say, abnormally heavy- 

 rain at its maximum, it will nevertheless not have any 

 adverse influence on the harvest unless the maximum 

 and its accompanying deluge fall within the Hmited 

 period of year during which the crop is growings 

 Hence what will be observed in the crop is not neces- 

 sarily the period of the weather cycle, but the period 

 in which its maximum tends to recur during the critical 

 months. We have not space to follow the author's 

 reasoning in detail, but it is suggested that there are 

 at least two weather cycles operating, if not four — 

 (a) with a period of approximately 4*37 years (30-6/7), 

 which corresponds to a cycle identified by Sir Arthur 

 Schuster in sunspots ; (b) with a period of about 5*11 

 years (30'6/6), which has been found in temperature 

 and rainfall records ; and two of less certainty, {c) 

 with a period of 2-74 years (30'6/ii), and {d) with a 

 period of 3-71 years, both of which also appear to have 

 been identified in meteorological or astronomical data. 



The period observed, it is argued, arises from a 

 temporary compounding of the effects of these four 

 cycles. All four " are due to return to a maximum 

 phase between February and September 1923," and 

 this may mean an exceptionally bad year for harvests 

 in Europe. "In the excessively improbable event of 

 my arithmetical analysis being complete and accurate 

 in every particular," Sir William Beveridge continues 



