GENERATING ECONOMIC CYCLES By the same AUTHOR Economic Cycles: Their Law and Cause Laws of Wages Forecasting the Yield and the Price op Cotton GENERATING ECONOMIC CYCLES BY HENRY LUDWELL MOORE PROFESSOR OF POLITICAL ECONOMY IN COLUMBIA UNIVERSITY "To this the King replied, that he who worried so anxiously about the end of a piece of work would never make a beginning in anything." Benvenuto Cellini. Nrm f nrk THE MACMILLAN COMPANY 1923 All rights reserved COPTRIOHT, 1923, By the MACMILLAN COMPANY Set up and electrotyped. Published July, 1923. Printed in the United States of America 372 i F23i, TO THE MEMORY OF MY FATHER CONTENTS Preface CHAPTER I PAGE ix INTRODUCTION A Clue to the Economic Maze .... Three Types of Contemporary Theories of Cycles Method and Results ..... Reservations ....... 1 2 5 11 CHAPTER n GENERATING CYCLES OF PRODUCTS AND PRICES The Correlation of Crop Yields and Crop Prices ... 18 Generating Cycles of Products ..... 24 The Derived Cycles of Prices ...... 26 Cycles in the Products of Mines ..... 28 Cycles in the Production of the Raw Materials of Manufacture 32 CHAPTER III GENERATING CYCLES REFLECTED IN A CENTURY OF PRICES Data and Method . An Analysis of a Century- of Prices Crop Cycles as Generating Cycles 42 47 55 CHAPTER IV THE ORIGIN OF THE EIGHT-YEAR GENERATING CYCLE Economic Cycles ..... Meteorological Cycles .... The Cause of the Eight- Year Generating Cycle 70 76 88 viii Contents CHAPTER V THE EIGHT-YEAR GENERATING CYCLE IN RELATION TO ITS PHYSICAL CAUSE PAGE Recent Theories of the Sun ...... 104 Influence of the New Physics . . . . . .111 The Role of Venus 121 PREFACE Among the rare books in the hbrary where I am writmg there is a first edition of Gahleo's treatise Dialogo sopra i due massimi sistemi del mondo, Tolemaico e Copernicano. This was the work that brought him before the Roman Inquisition. By the Holy Office he was convicted ''of beheving and holding the doctrines — false and contrary to the Holy and Divine Scriptures — that the Sun is the centre of the world, and that it does not move from east to west, and that the Earth does move and is not the centre of the w^orld; also that an opinion can be held and supported as probable after it has been declared and decreed contrarj^ to the Holy Scriptures," and he was required by the Holy Office to "abjure, curse, and detest the aforesaid errors." Intolerance of unwonted views was not limited to the Holy Office. Galileo himself could close the windows of his mind and vent his critical scorn upon an adven- turous colleague. In the fourth chapter of his fatal book there is a discussion of the theory of terrestrial tides which was the occasion of Galileo's treating with disdain the suggestion of Kepler that the tides are dependent upon the attraction of the Moon. To Galileo this seemed an explanation by an appeal to "occult Qualities and to such like vain Imaginations, that are so far from being, or being possible to be Causes of the Tide that on the contrary, the Tide is the cause of them, that is, of bringing them into the brains X Preface more apt for loquacity and ostentation than for the speculation and discovering of the more abstruse secrets of Nature; which kind of people, before they can be brought to pronounce that wise, ingenious, and modest sentence, I know it not, suffer to escape from their mouths and pens all manner of extravagancies." And he added : ' ' But amongst all the famous men that have philosophated upon this admirable effect of Nature, I wonder more at Kepler than any of the rest, who being of a free and piercing wit, and having the motion ascribed to the Earth before him, hath for all that given ear and assent to the Moon's predominancy over the Water, and to the occult properties, and such like trifles." ^ As far as it went Kepler's theory was undoubtedly correct and Galileo's ingenious attribution of the tides to a combination of complex motions of the Earth was incontestably wrong. And certainly Kepler was not to be blamed for the vagueness of his theory considering that it was expressed two centuries before the composi- tion of the Mecanique Celeste, at a time when it was impossible for him to know the theory of gravitation, to become acquainted with the necessary mathematical tools of research, or to command the indispensable tidal observations. We who are concerned with economic cycles — the tides in the affairs of men — may learn much from the subsequent history and theory of terrestrial tides. The theory of their cause passed from the stage of a promis- ing speculation to that of a well-ordered working hypothesis when it took the rigid mathematical form 1 The translation by Thomas Salisbury, 1661, pp. 406-407, 422. Preface xi in which it appears in the Mecanique Celeste; it passed to the stage of tested, working theory after tidal ob- servations upon a vast scale had been collected, sub- mitted to analysis, and the results found to be in agreement with the tidal theory; the method of research was statistical, and the mathematical instrument was the hannonic analysis; the course of progress in tidal forecasting was to isolate the primary cycles and then to approximate more accurate measurements by com- bining primary changes with minor disturbances; the primary cycles were shown to be the effects of cosmical causes, and these causes were not discredited when their effects were not immediately discernible over one-half of the Earth; the phases of lag and lead and the complication of cosmical causes with general ter- restrial and local causes were found to give an increas- ingly accurate account of the observed phenomena. These features in the theory and history of tides will probably be found to have their counterparts in the theory and history of economic cycles. Will the theory of the cosmical origin of generating cycles, like Kepler's theory of the cosmical origin of terrestrial tides, incur the scorn of eminent critics and receive an adequate development only after two hundred years? GENERATING ECONOMIC CYCLES GENERATING ECONOMIC CYCLES CHAPTER I INTRODUCTION An ancient fable teaches the wisdom of provid- ing one's self with a clue before going into an unex- plored labyrinth. We are in search of regular causes of economic fluctuations and before entering the tangled maze of changes, we wish to profit by the wisdom of the ancient myth and take with us a clue to the intricate disorder A Clue to the Economic Maze Such a clue to the general course of regular economic changes in the United States and to the causes in which they originate is given by the rhythmic changes in the weather. Figure 1 describes three fundamental general facts which, considering the dependence of agriculture upon the weather, suggest an originating source of economic regularities and may not wisely be ignored in a theory of economic cycles. The three facts re- vealed by Figure 1 are these: (1) The annual rainfall in the United States con- sidered as a unit fluctuated in clearly defined eight-year cycles during the forty years for which we have data, from 1881 to 1921; 2 Generating Economic Cycles (2) The rainfall of the Ohio Valley fluctuated in clearly defined eight-year cycles during the seventy-two years from 1839 to 1910; (3) The cycles in the Ohio Valley were congruent with those in the United States considered as a unit. The course of rainfall before 1839, when there were no meteorological records in the middle and western portions of the United States, may be a subject of dis- pute, and one may have individual doubts as to the course of rainfall in the unrealized future. But the revelations of the existing record of eighty-three years describe a sequence of regular natural changes of such magnitude and of such economic importance that the observant explorer in quest of economic regularities will not ignore their suggestiveness. They supply a clue to the intricate economic disorder. Three Types of Contemporary Theories of Cycles Wlien the theory of economic cycles is completely worked out and the critical stages in its development are reviewed, there wdll be a grateful recognition of the helpfulness of Cournot's distinction between secular, cyclical, and random causes of change. This classifica- tion is an essential preliminary to a wise choice of methods of investigation, and there must be a marked difference in theories of cycles according to the degree in which the necessity of the segregation of causes is realized and methods appropriate to the three types of causes are devised. The degree in which these exigencies are recognized Introduction Smoothed DEPARTURL5 OF Annual RAiNfAuiNTHE uniteoStatesasaLInit 1882 1890 1898 1906 1914 1922 ANNUAL Rainfall in the Ohio Valley 1842 1650 1666 1874 1882 1690 1906 1914 1922 Figure 1 Cycles in the annual rainfall of the Ohio Valley and in the annual rainfall of the United States as a unit. Cycles in the United States: y = — 1.99 + 0.86 sin (45°« + 42° 50'), origin at 1881; Cycles in the Ohio Valley: y = 41.19 + 4.13 sin (45°« + 310° 41'), origin at 1S39. and met is a source of difference between three types of contemporary theories of cycles : In the first type there is a refusal to define the term, economic or business cycle, otherwise than as a vague general rhytlim, a series of changes which returns at an 4 Generating Economic Cycles unspecified time upon itself. The treatment is not concerned with the academic segregation of causes nor with the pedantries of mathematical formulae. No measures of correlated changes are carried out, and no definite clear-cut theory of cyclical causes is offered. Somehow, somewhen, some of the indices of business rise or fall, and somehow, somewhen, some other indices may follow. The possibility of forecasting is hinted, but in the best examples of this point of view there is prudent restraint in particularizing. In the second of the typical current discussions of cycles there is a full realization of the need of separating causes and of seeking appropriate mathematical meth- ods, but it introduces two embarrassing compromises: First, it proceeds upon the assumption that there are no known methods by which cyclical effects may be separated from random effects and accordingly at- tempts to treat as a whole the joint effect of cyclical and random causes; Secondly, it arbitrarily defines the combined effect as 'Hhe cycle." ''The cycle," in this method of treatment, is the residue of the total effect under investigation after the secular trend has been eliminated. There is no further analysis of this residual quantity for the purpose of seeing whether it may not be composed, in part, of constituent cycles with separate causes, but it is forthwith used — and used often with success — as a means of practical forecasting. The third typical theory of cycles assumes as its point of departure the necessity of segregating causes and the use of methods to decompose total effects into Introduction 5 secular, cyclical, and random elements. The term cycle is mathematically defined with definite period, amplitude, and phase. The primary object of the theory is not to forecast but to establish the existence of real cycles and to trace the causes of the specifically cyclical elements in the total of economic changes. It distinguishes between a rational forecast and an empir- ical forecast. No rational forecast can be made until the manner of change in the various constituents of the full cause is discovered and their measured interrelations are known. Empirical forecasts of value may be made, and are made, from the known routine in the sequence of economic changes. Method and Results If the third type of theory with regard to the nature of cjTles is allowed, then one is confronted with the problem of finding a method of detennining whether a series of observations contains real cycles. Several technical methods, to which reference will be made in the following chapters, have been devised for this pur- pose; but without entering upon technicalities we may see that from the point of view of forecasting and con- trolling economic changes, the importance of a cycle is dependent upon its amplitude. A cycle may be real and yet practically negligible if its recurrent effects are small. This very practical consideration suggests the method to adopt in order to discover significant cycles. It is obvious that whatever may be the mathematical justification of the procedure it is practically important to know which cycle will show the largest amplitude in 6 Generating Economic Cycles the given data, and this may be ascertained by finding the ampHtudes of trial cycles with periods between limits that will be determined by the problem" in hand. Suppose, for example, we wished to know what cycle with period between three and twelve years would give Figure 2 The periodogram of annual rainfall in the Ohio Valley, 1839-1910. the largest amplitude in the annual rainfall of the Ohio Valley for the interval of seventy- two years from 1839 to 1910. The results of the computation according to the method that has just been sketched are graphed in Figure 2. On the horizontal line the lengths of the various trial periods are measured, and on the corre- sponding perpendicular lines are plotted the squares of Introduction 7 the respective amplitudes. It is clear from Figure 2 that the cycle with a jieriod in the neighborhood of eight years is by far the most important. The graph is given in Figure 1. The mean annual rainfall in the Ohio Valley is 41.19 inches, and the amplitude of the eight-year cycle is 4.13 inches. The range of the eight-year cycle, which is twice its amplitude, is 8.26 inches or twentj^ per cent of the annual rainfall. The tremendous importance of much smaller variations in precipitation is being increasingly emphasized by the findings of the growing science of agricultural meteorol- ogy. The cyclical regularity in the variations of the rain- fall in the Ohio Valley for the seventy-two years from 1839 to 1910 was first announced ^ in 1914, and as the computations rested upon the records of only three stations, Cincinnati, Portsmouth, and Marietta, there was a very reasonable skepticism as to the reality of the eight-3'ear cycle. One might concede that the measure- ments of rainfall at the three stations show the eight- year cycle for nine consecutive periods in the seventy- two years, and yet deny the economic importance of the cycle on the ground that no evidence has been sub- mitted to show its presence in the whole of the United States. This perfectly legitimate objection must be met, and we shall attempt to meet it by conducting an independent inquiry that will serve as a severe test of the reality and generality of the eight-year cycle. We shall use all available data for the whole of the United States; we shall start with no prejudice with regard to ^ Economic Cycles: Their Law and Cause, 1914. The data are given in that work, p. 32. 8 Generating Economic Cycles the existence of a cycle of definite period ; we shall sim- ply inquire, if there be an important cycle with period between three and twelve years, what the length is; and then we shall compare the findings with those that were obtained for the Ohio Valley. In 1922 Professor Alfred J. Henry of the United States Weather Bureau pubhshed ^ an article which for the first time supplied rainfall data relating to the United States as a unit. Professor Henry's object was to show that there is no ground whatever for the recent claim that rainfall in the United States follows the eleven-year sun-spot cycle, and he sought to make his criticism as convincing as possible by arraying against the sun-spot argument the vast material collected by the Weather Bureau. The records that were utilized by Professor Henry were drawn from about two hundred individual Weather Bureau stations grouped into twenty climatic districts embracing the whole of the United States. ^ 1 Monthly Weather Review, March, 1922, p. 130. 2 These details Professor Henry gave me in a letter of December 29, 1922. After Professor Henry puljiished his article he discovered that a number of errors had crept into his data and computations and he very kindly sent to me, in December, 1922, his corrected table of rainfall departures for the forty years from 1881 to 1921. In Table I of the Appendix to this chapter are listed Professor Henry's original data as they appeared in the Monthly Weather Review, March, 1922, p. 130, and his corrected data as they were sent to me in December, 1922. In both cases Professor Henry smoothed the raw data by means of the formula 6 = ]4, {a -\- 2h -{- c) where h was the value of the middle year in each consecutive series of three years. The curve in Figure 1 for the rainfall in the whole of the United States was computed from Professor Henry's corrected data. The curve that was published in my paper on "An Eight- Year Rainfall Cycle," which appeared in the Monthly Weather Review, July, 1922, was based upon Professor Henry's uncorrected figures and fitted the data slightly better than the curve that is given in Figure 1. Introduction 9 If, now, we analyse Professor Henry's data ^ — which run from 1881 to 1920 — with a view to discovering whether there are important cycles in the rainfall of the United States as a miit, we obtain these smprising results : 1 00 LU § 080 . f— ( 1 Q. A s / j t 060 / \ a: / \ (- / 1 1 ■ / \ O / \ a 0.4-0 / \ < / \ 3 / 1 cr / \ CO / \ 0.20 -^7^ \/\^ 2 4 6 8 10 12 Length of the Cycle inI Years Figure 3 The periodogram of annual rainfall departures in the United States as a unit. 1881-1920. (1) Figure 3 shows that if there is an important real cycle within the limits of three and twelve years in the rainfall of the United States as a unit, its period is about eight years; (2) Figure 1 shows that when the equation to the eight-year rainfall cycle in the United States is 1 The data are given in Table I of the Appendix to this chapter. The figures in the column marked "Corrected Data" were used in the computation. 10 Generating Economic Cycles computed its maxima are, within the limits of the errors of observation, coincident with the maxima of the eight-year rainfall cycle in the Ohio Valley, which, in 1914, was found to have persisted throughout nine consecutive periods; (3) The amplitude of the eight-year cycle in the United States is relatively so large that it ac- counts for 42 per cent of the total variabiUty of the annual rainfall. This result is obtained by taking the ratio of the amplitude of the eight- year cycle to the mean of the annual rainfall departures irrespective of their signs. These meteorological facts raise important questions in the extremes of the hierarchy of the sciences. If the regularities that have been observed are not accidental they are probably cosmical in origin, and one of the leading questions they suggest relates to the astronomic and physical agents by means of which they may be produced. The fourth and fifth of the following chap- ters enter into the details of this question. While solar physics must be looked to for an explana- tion of the weather regularities, the regularities them- selves are the starting point of the economist's inquiry into cyclical economic changes. He wishes to know whether the observed cyclical recurrence of rainfall with its large amplitude may not originate agricultural cycles which, in turn, generate the cycles of production and the cycles of prices mth which the economist is more immediately concerned. The second, third, and fourth of the ensuing chapters treat of the details of this economic problem. Introduction 11 Reservations The primary purpose of this Essay is to show that a known natural cause originates an agricultural cycle which in turn generates other economic cycles. The perturbations in the ultimate cycles are not discussed, and these perturbations will doubtless be traced in part to natural, and, in part, to psychical and social origins. Because one element of the weather, rainfall, has been seized upon and its effects have been tracked into re- mote regions, it does not follow that temperature,^ sun- shine, and wind are regarded as negligible. Because a natural eight-year cycle has been isolated is no reason for denying the possible existence of other natural cycles, major or minor. Because some regularities in economic changes have been shown to originate in natural causes, it would be most unphilosophic to claun that the effects of the known regular causes may not be partially or totally offset by the effects of other causes, natural or social, regular or fortuitous. The object has been to find one cause and to follow its effects into their ultunate ramifications. However ingenious may be the mathematical meth- ods that are used to isolate periodicities, there will always be a healthy skepticism as to the reality of the cycles unless true causes are adduced. Mere empirical regularities are always suspect. While, therefore, in the quest of cycles, I have always tried to scrutinize the data by means of impartial mathematical devices, I have not remained content with empirical results but ^ Forecasting the Yield and the Price of Cotton, 1917. 12 Generating Economic Cycles have pressed on in search of real causes. The pursuit has led into meteorology, astronomy, and solar physics, where I may possibly have gone astray. But whatever uncertainties may be felt with regard to these adven- tures into natural science, they should not weigh against the theory of the origin of economic cycles in natural causes. The linking of astronomic, meteorological, agricultural, and economic causes places the whole discussion upon a rational, rather than upon an em- pirical, basis. There are uncertainties in respect to several links, but with the accumulation of weather data meteorologists are facing with an open mind the problem of periodicities; and with the startling dis- coveries in electricity and magnetism, solar physicists are advancing revolutionary views regarding the Sun's radiation, the interrelations of the planets, and the nature of the interplanetary medium. APPENDIX TABLE I. — Annc.\l Rainfall in the United States as a Unit Departures Smoothed by the Formula b = }i(a+2b + c) Professor Henry's smoothed departures Year Professor Henry's smoothed departures Year Original data Inches Corrected data Inches Original data Inches Corrected data Inches 1881 +0.4 +0.4 1901 —2.1 —2.1 1882 +0.2 +0.2 1902 —2.0 —2.0 1883 ±0.0 ±0.0 1903 —2.5 —2.5 1884 +0.4 +0.4 1904 —2.6 —2.6 1885 —0.4 —0.4 1905 —1.0 —1.0 1886 —2.7 —2.7 1906 —0.4 —0.4 1887 —3.2 —3.2 1907 —1.6 —1.6 1888 —2.1 —2.1 1908 —1.8 —1.8 1889 —2.0 —2.0 1909 —2.4 —2.4 1890 —2.4 —2.4 1910 —3.8 —3.8 1891 —1.3 —2.3 1911 —2.6 —2.6 1892 —2.5 —2.5 1912 —1.1 —1.1 1893 —3.1 —3.1 1913 —1.8 —2.3 1894 —3.5 —3.5 1914 —1.9 —1.9 1895 —3.2 —3.2 1915 —1.5 —1.5 1896 —2.1 —2.1 1916 —3.2 —2.9 1897 —1.6 —1.6 1917 —4.7 —4.7 1898 —2.1 —2.1 1918 —3.4 —3.4 1899 —2.2 —2.2 1919 —1.5 —1.5 1900 —2.0 —1.8 1920 —0.9 —1.4 CHAPTER II GENERATING CYCLES OF PRODUCTS AND PRICES i Summary The major features of economic cycles are traceable to three primary laws: (1) the law of the generating cycle of raw materials, which is due to a non-economic cause; (2) the law of demand for raw materials, in consequence of which the generating cycle of products originates a derived cycle of prices for raw materials; and (3) the law of competitive price, according to which the prices of finished goods in an open market tend to correspond with the cost of production. A TELLING advance was made in the theory of eco- nomic dynamics when crises were proved to be phases of economic cycles. The spectacular features of crises — panics, bankruptcies, collapse of prices, unemploy- ment of labor, and subsequent general depression of business — had for some time attracted attention and ehcited innumerable theories as to their cause. A gen- eral characteristic of these theories was the citing of detached, non-recurring events as the separate cause of each isolated crisis. A war, a failure of some conspicu- ous establishment, an election, or a bad harvest were among the supposed causes. With the development of the theory of cycles the well-marked stages of pros- perity, crisis, decline, and depression were described and shown to be parts of a general rhythm of industry. This more ample view of the vicissitudes of business ^ This chapter was first published, substantially in its present form, in the Quarterly Journal of Economics, February, 1921. Generating Cycles of Products and Prices 15 suggested that if the rhythm as a whole could be traced to a single cause, the foundation would be laid for long- range forecasting and would, perhaps, lead to the con- trol of economic changes in the interest of the social good. The buoyant, expectant hope which stimulated the early searchers for a single, persistent cause of cycles is shared by few recent investigators. On the contrary, there is flat denial of the existence of any marked regu- larity or periodicity in the phenomena; attempts at explanation by means of a few causes are regarded as obsolete ; and while recognition is made of the existence of the cycle with its separate phases, there is, in many cases, a reversion to the method of alleging isolated, separate explanations for each critical point in the several phases. The present inquiry takes up the abandoned search for a single explanation of the entire rhythm and its constituent parts. Two accomplished investigators, Professor Aftalion,^ and Professor Bresciani-Turroni, - have pointed out that the average length of cycles, since 1857, has been in the neighborhood of eight years. That fact is sufficient reason for asking why cycles are, on the average, about eight years in length, and whether this loose periodicity may not have as its origin a periodically recurring cause. Professor Mitchell, in his masterly Business Cycles, has given another fact of critical significance, namely, the supreme importance in each phase of the cycle of the volume and prices of raw materials. In ' Albert Aftalion, Lcs Crises periodiques de sur production, vol. i, p. v, vol. ii, pp. 32, 33, and passim. ^ Costantino Bresciani-Turroni, Le Variazioni cicliche del prezzi, p. 57. 16 Generating Economic Cycles his description of ''How Prosperity Breeds a Crisis" he has made an illuminating statement which is here quoted at length. I have taken the liberty of italicizing several sentences: "... The cost of materials exceeds wages in every one of the leading branches of manufacture, and in a majority of cases is over twice as large. Indeed, on the average it makes practically two-thirds of the total outlay. If wares for re-sale be substituted for materials, this proportion must run far higher in wholesale stores, while in retail shops it cannot be much lower than in factories on the average and may well be considerably higher. Even the trans- portation companies and enterprises in the extrac- tive industries have to buy vast quantities of current supplies. Hence an increase in the cost of materials, wares, or supplies is often an increase in the largest single item of expense, and always an increase in an important item. The relative fluctuations in the prices of those commodities which are bought and of those which are sold are therefore of great, in many cases of decisive, importance in determining profits. " Concerning these relative fluctuations, our definite information consists of index-numbers for raw ma- terials, partially manufactured products, and fin- ished goods; also for the same commodities at whole- sale and at retail. Now this statistical evidence points to the conclusion that what must be taken as buying prices creep up on selling prices during a period of prosperitj^ Of course this movement . . . threatens a reduction of profits. Generating Cycles of Products and Prices 17 '' While a difficulty of this character seems to ba en- countered in most branches of business it is likely to become pecidiarly acute in those manufacturing in- dustries ivhich use animal and farm products as their leading raw materials. For, following up a suggestion of Sombart's, we have found that these classes of products are more erratic m their price fluctuations than are the products of mines and forests. Hence an uncommonly large .speculative risk must be borne, or insured against, in such branches of trade as meat packing, flour milling, cotton spinning, woollen weaving, tanning, etc. Of course this risk exists during all phases of the business cycle, but it is aug- mented in prosperity by the necessity of carrying larger stocks of raw materials. The census indicates that more than three-fourths of all the 'materials pur- chased in the raw state' by American factories in 1900 belonged to this class which is pecidiarly unstable in priced ^ Now may it not be that the physical yield of the farms, which supplied more than three-fourths of all the raw materials of American factories in 1900, is itself a 1 W. C. Mitchell, Business Cycles, pp. 481, 482. To the above state- ment Professor Mitchell appends the following note, p. 482, note 10. "The sources of raw materials are given as follows: From farms $1,941,000,000 " forests 119,000,000 " mines 320,000,000 " the sea 10,000,000 " all sources $2,490,000,000 Twelfth Census of the United States, Manufactures, Part I, p. cxxxv." There is a slight error in the above value "from all sources." The aggregate sum is .S2, 390,000,000, and this would make the proportion contributed by the farms 81.2 per cent. 18 Generating Economic Cycles periodically varying magnitude that will produce a corresponding rhythm in the prices of raw materials and the prices of products derived therefrom? Is it not possible that this same periodicity may be of such length as to approximate the average length of cycles which has been noted by Professor Aftalion and Pro- fessor Bresciani-Turroni? If we discover this periodicity in the yield of farm products, we shall make a distinction between generat- ing economic cycles and derived economic cycles. Generating economic cycles will then be economic cycles which have their origin in non-economic causes and are themselves the originating source of derived economic cycles. If the varying yield of the crops has its origin in a periodic meteorological cause, it will itself be peri- odic and will generate periodic sequences in the whole of the dependent economic changes. If the existence of such a generating cycle is established, there will be no need, in treating the phases of economic cycles, to seek separate explanations for their existence. The phases of the generating cycles will themselves originate corresponding phases in the dependent, derived cycles. The Correlation of Crop Yields and Crop Prices From the point of view of the value of the product, our crops ranked, in 1919, in the following order: corn, wheat, cotton, hay, oats, potatoes. These six crops, in 1919, contributed 70.8 per cent of the value of the multitudinous crops produced by our farms. The aggregate value of all the crops produced in 1919 was, Generating Cycles of Products and Prices 19 according to the estimate ^ of the Secretary of Agricul- ture, $15,873,000,000, and of this aggregate amount the above six products contributed $11,238,536,000. The records of the yields and prices of these six crops from 1882 give the statistical material of which use is made in the subsequent investigation. As the American production in case of all six of these conmiodities is only a part of the world supply, our first inquiry will be whether, notwithstanding this fact, the domestic prices are inmiediately related to the domestic yield. Furthermore, as we wish to eliminate the varying factor of changing acreage, our inquiry will take the fonn of ascertaining whether the domestic prices of these several crops are immediately related to the respective yields per acre. In order to secure a certain degree of comparability in the graphs, the raw figures - of yield and the corre- sponding December fann price were, for each crop, converted into index numbers in which the average yield and the average price for the years 1890-99 were taken as the respective bases. The graphs of these index numbers of yield and prices are given in Figures 4, 5, 6. In each of the six graphs of yield and the six graphs of prices the statistics show a secular trend which must be ascertained as a preliminary to the work of finding the relation between the variations in jdeld and the varia- tions in prices. In each of the twelve curves the secular trend was obtained by fitting a curve of the type y = a+hx-{- cx~ + dx^ ^ Yearbook of the Department of Agriculture, 1919, p. 17. ^ The raw figures of yield per acre and December farm prices were taken from the Yearbooks of the Department of Agriculture. 20 Generating Economic Cycles Figure 4 Secular trends in the index numbers of the yield and price of corn and wheat. Corn: Yield, y = 103.9 + .838x — .0032x2 — .002,233x', origin at 1899; Price, y = 102.4 + 1.690x + .2275^2 _ .001,288x3, origin at 1897. Wheat: Yield, y = 102.1 + .952x — .0004x2 — .OOl.lOlx^, origin at 1899; Price, y = 99.2 + 1.057x + .1780x2 - .005,570x3, origin at 1897. to the data, and the resulting equations were found to be those that are given in the descriptions of Figures 4, 5, and 6. The origins of the equations are different in the two graphs, because the crops are taken from Generating Cycles of Products and Prices 21 IMOEX Of THE Yield Of Oms A62 1^86 16:90 16^ 1^98 IS(Oa I9.06 I9.10 19.14 1910 pa 16,66 ie.90 IB,9A 16,90 19,02 l9,Ofe I9,>0 I9,IA Index of the Price or Hay Figure 0 Secular trends ia the index numbers of the yield and price of oata and hay. Oats: Yield, y = 105.7 + .805j + .02.JSx2 — .000,038x5, origin at 1899; Price, y = 100.6 + 1.700j; + .1692^2 — .005,271j3, origin at 1897. Hay: Yield, y = 104.9 + l.l.iGj; - .0049x2 _ .001,816x', origin at 1899; Price, y = 103.1 + l.GOGx + .1882x2 - .004,042x', origin at 1897. 1880 to 1918, and the prices, owing to the abnormal fluctuations during the war, only from 1880 to 1914. The next step in the inquiry is to determine whether the percentage variations of the yields of the sev- 22 Generating Economic Cycles Index or the Yield of Potatoes 16,62 I902 1906 Index or the Price or Potatoes Figure 6 Secular trends in the index numbers of the yield and price of potatoes and cotton. Potatoes: Yield, y = 108.2 + 1.992x + .0179x2 _ .004,435x3, origin at 1899; Price, y = 101.6 + 1.612x + .0921x2 — .OOG.lOlx', origin at 1S97. Cotton: Yield, y = 101.2 + .548x - .0.331x2 — .001,901x3, origin at 1899; Price, y = 111.0 + 2.688x + .1667x2 — .009,536x5, origin at 1897. eral crops from their respective secular trends are related to the corresponding percentage variations of prices from the respective secular trends of prices. The method of investigation will be made clearer Generating Cycles of Products and Prices 23 by an illustration. The equation descriptive of the secular trend in the yield of corn was found to be y = 103.9 + m^x - .0032.1;^ — .002,233a;3 with origin at 1899. The graph of this equation is the smooth cur\'e in the upper part of Figure 4. The equation descriptive of the secular trend of the De- cember farm price of corn was found to be y = 102.4+ 1.690a; + .2275x2 - .001,288x3 with origin at 1897, the graph of which is also given in Figure 4. The percentage deviations from the secular trend of the actual yield per acre for the separate years from 1880 to 1914 were computed, and these percentage deviations were then correlated with the corresponding percentage deviations of the actual prices from the price secular trend. Table I in the Appendix, which refers to corn, gi\'es an illustration of the computations. Similar calculations were made for the remaining five crops, and the coefficients of correlation between the corresponding percentage deviations, for the years 1880-1914, were computed. The resulting coefficients were these : Corn r= — .78 Wheat r = - .23 Cotton r — — .45 Hay r= - .68 Oats 7- = _ .67 Potatoes r = — .90 Notwithstanding the fact that the American produc- tion of these crops is only a part of the world supply, there is an inverse relation between the percentage de\'iations of the yield per acre of our crops and the percentage deviations of the corresponding prices. 24 Generating Economic Cycles Generating Cycles of Products We have just established an inverse relation between the yield per acre of each of the six representative crops and their respective prices. If now we can show that the combined yield of the crops is periodic, there will be excellent reason for believing that their combined prices will be periodic and that the prices of commodi- ties produced from farm materials will tend to show the same well-defined rhythm. Our immediate prob- lem, therefore, is to discover whether there is a periodic cycle in the combined yield of the six representative crops. To go forward with the work w^e needed to compute an index munber of the combined yield of the represen- tative crops. In treating the preceding question as to the correlation of the yield of the several crops with their respective prices, we computed, in each case, the percentage deviations of the yield per acre from the secular trend. For our present purpose of finding whether the combined yield of the six crops tends to run in cycles, the percentage deviations of the yield of the several crops for each year of the record, from 1882 to 1918, were added. The resulting figures, which are given in Table II of the Appendix, constitute our index numbers of the yield per acre of the six crops. In the attempt to learn whether, during the interval under investigation, the yield of the crops was cyclical and periodic, the periodogram of the yield was com- puted and the graph was drawn. The results of the computation are given in Table III of the Appendix, and the graph appears at the top of Figure 7. The Generating Cycles of Products and Prices 25 AOO. 300 200 ^ 100. 200 150 . 100 so CROPS Coal and iron Raw Materims 2 4 6 6 THE LENQtH Of THE CYCLE IN YEARS Figure 7 Periodograms of crops, coal and iron, and raw materials of manufacture. periodogram shows that if there is a periodicity be- tween three and twelve years in the data, its most probable length is in the neighborhood of eight years. When the probable cycle of eight years is computed, its maxima are found to occur, approximately, at 1882, 1890, 1898, 1906, 1914. The graph of the eight-year 26 Generating Economic Cycles cycle is given in the lower part of Figure 8. This out- come of the calculations* is gratifying because of its consonance with results that have already been ob- tained. Other investigations '^ have shown that there are eight-year cycles with maxima approximately at 1882, 1890, 1898, 1906, 1914 in the annual rainfall of the United States as a unit, in the annual rainfall of the Ohio Valley, the May and June rainfall of the Dakotas, and in the yield of wheat, oats, and barley in the Da- kotas, the United States, the United Kingdom, and France. The Derived Cycle of Prices An index number of the combined yield of the six crops was devised, as we have just described, by simi- ming the percentage deviations of the yields from their respective secular trends. To carry the inquiry beyond the stage that was reached in the last section an index number of the combined prices of the six crops was con- structed by summing, for each year, the percentage deviations of the prices of the several crops from the respective secular trends of prices. The data are given in Table IV of the Appendix. These two index nmn- bers — the index of the combined yield and the index of the combined prices — supplied the material for the next stage in the problem, namely, to ascertain the degree of relation between the variations in the index 1 "Forecasting the Crops of the Dakotas," Political Science Quarterly, June, 1919, pp. 228, 229 "Crop Cycles in the United Kingdom and in the United States," Journal of the Royal Statistical Society, May, 1919. "Crop Cycles in the United Kingdom and in France," ibid.. May, 1920. "An Eight- Year Rainfall Cycle," Monthly Weather Review, July, 1922. Generating Cycles of Products and Prices 27 ACTUAL Index NUMMRS OF Prico ■ FoREOkST iNO£x NuMWRsor Prices GENERATiNa Cycles of yield per acre Derived Cycles or Prices Figure 8 Upper part : Actual index numbera of prices of the six representative crops and the index numbers of prices forecast from the index numbers of the yield per acre by means of the formula 2/ = — 1.295x — .02. Lower part: Generating cycles of the yield per acre of the crops, y =1.6 + 20.0 sin (45°< + 109°), origin at 1882; Derived cycles of prices of the crops computed from the generating cycles of jneld by means of the formula, y = - 1.2951 — .02. of the combined yield and the index of the combined prices. The coefficient of correlation between these two variables is r = — .69, and the equation expressing their relation is y = —1.295a: -.02 28 Generating Economic Cycles where x = the index of the yield and y = the index of prices. This close relation indicates that the eight-year cycle in the yield per acre of the crops tends to generate an eight-year cycle in the prices of the products. Figure 8 shows, in its upper half, the course of the index number of actual prices and the course of the theoretical index when y = - 1.295X - .02 is used as a forecasting formula. The lower half of Figure 8 shows the generating eight-year cycle in the yield per acre of the crops and the derived eight-year cycle in the prices of the crops. The equation of the generating cycle of products was obtained in the preced- ing section. The derived cycle of prices was computed from the generating cycle of products by means of the formula connecting the variations of the combined yield with the variations of the combined prices. y= - 1.295a; - .02 Cycles in the Products of Mines We have noted that according to the census of 1900, the values of raw materials used in manufactures were as follows: from farms, $1,941,000,000; from forests, $119,000,000; from mines $320,000,000; from the sea, $10,000,000. Of the aggregate value of these materials, 81.2 per cent was supplied by the farms; 5.0 per cent by the forests; 13.4 per cent by the mines; and 0.4 per cent by the sea. We have already shown that the yield of the leading fann crops moves in well-defined cycles which generate corresponding cycles of agricultural Generating Cycles of Products and Prices 29 prices. The leading crops upon which the computation was based supplied 70 per cent of the total value of American crops in 1919 and are therefore sufficiently representative of the yield and prices of fanii products. Next to the farms, according to the above figures, the mines furnish the most important source of materials for manufactures. The farms and the mines together supplied, in 1900,' 94.6 per cent of the value of the raw materials used in American factories. Does the pro- duction of minerals move in cycles? The most important minerals for the use of manufac- tures and transportation are coal and iron, and in our further inquiry these two minerals will be regarded as being representative of the products of the mines just as the six crops — corn, wheat, oats, hay, cotton, and potatoes — were treated as being representative of the products of the farm. In preparing the statistics of the production of coal and pig iron with a \dew to ascertaining whether there is any periodicity in their production, the procedure was smiilar to that which was followed in the case of the yield of the crops. The raw figures ^ of production were first reduced to index numbers in which the mean pro- duction for 1890-99 was placed as equal to 100. The graphs of the index numbers of production are given in Figure 9. Because of the enonnous and irregular in- crease in the production of both coal and iron in the in- terval under investigation, 1881-1913, the description of the secular trends by means of single equations requires the use of a slightly more complex curve than * The figures were taken from the Slalislical Abstract of the United States, 1915, pp. 689, 690. 30 Generating Economic Cycles the one employed in the treatment of the yield and prices of farm products. In the latter case a parabola of the type y = a -{■ bx -{- cx^ -\- dx^ was found to give a satisfactory fit. But in the descrip- tion of the secular trends in the production of coal and iron an additional term was added to the above equa- tion, and a parabola of the fourth order y = a+hx-\- ex- + dx^ + ex^ was fitted to the data. The graphs in Figure 9 show the secular trend of both coal and iron, and the correspond- ing equations are given in the legend descriptive of Figure 9. After the secular trend of coal and the secular trend of iron were ascertained, the percentage deviations of the production of each commodity in the years from 1882- 1913 were computed. These percentage deviations were then combined into an index number of the devia- tions in the production of coal and iron by summing the percentage deviations for each year. The data are given in Table V of the Appendix. Because of the abnormal demand for coal and iron during the war the figures were not extended beyond 1913. If now the index numbers of the deviations in the production of coal and iron from 1882 to 1913 are scrutinized with a view to discovering periodicities, we find that the periodogram takes the shape that is pictured in the second curve in Figure 7. The data are given in Table III of the Appendix. It is obvious from the periodogram that if there are real cycles in the production of coal and iron, the most Generating Cycles of Products and Prices 31 310 , 200 iNDtx Numbers or the Production or Com y 250 IN THE United States AvtRAGC Production fob i690- i899. ioo J ■yf 220 // A/ 190 J'^ 160 ^^ ISO y"'^ lOO ^__^^..-;=^^ 70 ^ 40 1662 1666 1690 169a 1698 1902 1906 1910 1914 310 J 280 Index Numbers or the production or Pig iron ^ \A 250 IN THE United States / AvtR»e[ Production roa 1690-1899 • IOO / j Yf 220 190 ry/l V 160 y^ V 130 y^ 100 /^^,^y\^,^^i^y 70 _^ff=:i^ ^"^^ 4.0 1662 leee ie90 i894 isse 1902 1906 1910 1914 Figure 9 Secular trends in the index numbers of the production of coal and pig iron in the United States. Coal: y = 114.1 + 7.777j + .4131j;-' _ .ooojolx' — .000,8141x', origin at 1897; Pig Iron: y = 119.4 + 9.199j + .4110x2— .002,501x3 _ .ooo,7239j<, origin at 1897. probable are in the neighborhood of eight and eleven or twelve years in length, but in the present paper we shall confine the discussion to the eight-year cycle. When 32 Generating Economic Cycles the equation to the eight-year cycle is computed, the maxima are found to occur approximately at 1882, 1890, 1898, 1906, 1914. And if the eight-year cycle in the production of coal and iron is graphed and com- pared with the graph of the eight-year cycle in the yield of the crops, the coal and iron curve is found to lag about three-tenths of a year behind the curve for the crop yield. The graphs are given at the top of Figure 10. Cycles in the Production of the Raw Materials of Manufacture The production of the farms and the mines taken separately tends to run in eight-year cycles, the cycles of the raw materials from the mines inclining to lag a few months behind the cycles in the yield of the crops. The farms and the mines together supphed, in 1900, 95 per cent of the raw materials of American factories, and, consequently, their joint production affords both an adequate measure of the changes in the volume of raw materials and a valuable index of the changes in the physical volume of trade. Is there any regularity in the joint production of the farms and the mines? In the same manner in which we constructed an index nimiber of the yield of the crops and an index number of the production of coal and iron, we made an index nxmiber of the raw materials of manufacture. The per- centage deviations of the jdeld of the crops and the percentage deviations of the production of coal and iron were summed, and the aggregate percentage deviations were regarded as the index numbers of the production of raw materials. The data are given in Tables II and V of the Appendix. Generating Cycles of Products and Prices 33 When the index numbers of raw materials from 1882 to 1913 were scrutinized for the purpose of discovering periodicities, it was found that the periodogram took the shape of the bottom curve in Figure 7 showing that Eight-Year Cycles in Crops Ekjht-Year Cycles in Coal and Iron Eight -Year Cycles in Raw Materials Figure 10 Cycles in the yield of the crops, the production of coal and iron, and the produc- tion of the raw materials of manufacture. Crops: y = 20.0 sin (io'l + 109°), origin at 1882; Coal and Iron: y = 11.0 sin (45°< + 93°), origin at 1882; Raw Materials: y = 30.3 sin (45°< + 103°), origin at 1882. if there is a cycle in the production of raw materials of manufacture in the United States, its probable length is about eight years. The computations referring to the periodogram are given in Table III of the Appendix. If the eight-year cycle in the production of the raw mate- 34 Generating Economic Cycles rials of manufacture is computed, its maxima will occur, approximately, at 1882, 1890, 1898, 1906, 1914, and the graph of the cycle will run in the manner de- scribed in the bottom curve of Figure 10. There are two observations with regard to the theory of economic cycles that need to be emphasized by frequent repetition . The first was made by Professor Aftalion, the second by Rodbertus. After estimating the average length of cycles since 1857 at approxmiately eight years, Professor Aftahon stated that the essential problem in the theory of eco- nomic cycles is to discover the cause of the rhythm. '^L'observation du rythme de la production generale fait . . . seulement comprendre la survenance d'une hausse, puis d'une baisse generale des prix, Fexistence d'un rythme. EUe ne nous donne pas Fexphcation de la duree de cette hausse ni de cette baisse, de la duree des phases du rythme." ^ In one of the briefer essays of Rodbertus, ''Physio- kratie und Anthropokratie," - the initiator of the social- ist theory of business cycles stresses the importance of discovering the natural cause of the economic rhythm in order that society may set about adjusting itself in the light of the acquired knowledge. He draws the distinction between the rule of nature — Physioki'atie — and the rule of man — Anthropokratie. Quesnay and Adam Smith and their followers, according to Rodber- tus, regarded the problems of social science primarily ^Albert Aftalion, Les Crises periodiques de surproduction, vol. ii, pp. 41, 42. * Rodbertus- Jagetzow, Briefe und Social politische Aufsdtze. Generating Cycles of Products and Prices 35 from the point of view of physical science and were led to the maxim "laissez alter et laissez passer; le monde va de lui-memcy By contrast Rodbertus would empha- size the great possibilities of social progress through the intervention of the state and the utilization of natural laws for social purposes. With regard to the specific problem of economic cycles, the natural law and cause of the rhythm must be discovered and then utilized by society for its own ends. ''Sich un Staatsleben Natur- gesetzen zu unterwerfen, heisst, sich des 'Gottlichen' im JMenschen begeben, heisst, von socialen Organismen, muthwillig in Krankheit und Tod gehen. Nach ewigen, eh'rnen Grossen Gesetzen Mtissen wir Alle Uns'res Daseins Kreise voUenden. Nur allein der Mensch Vermag das Unmogliche; Er unterscheidet, Wahlet und richtct; Er allein darf Alles Irrende, Schweifende Nutzlich verbinden." Goethe: Das Gottliche. APPENDIX TABLE I. — Correlation op the Percentage Deviations op the Price of Corn with the Percentage Deviations of the Yield PER Acre op Corn Year Index number of the yield of corn General trend of the yield of corn Percentage deviation from the trend Index number of the price of com General trend of the price of corn Percentage deviation from the trend 1880 114 102 + 11.8 115 146 -21.2 1881 77 101 -23.8 184 139 +32.4 1882 102 100 + 2.0 141 133 + 6.0 1883 94 99 - 5.1 123 127 - 3.1 1884 107 98 + 9.2 103 122 -15.6 1885 110 98 + 12.2 95 117 -18.8 1886 91 97 - 6.2 106 113 - 6.2 1887 83 97 -14.4 129 110 + 17.3 1888 109 97 +12.4 99 107 - 7.5 1889 112 97 + 15.5 82 104 -21.2 1890 86 98 -12.2 147 102 +44.1 1891 112 98 + 14.3 118 101 + 16.8 1892 96 99 - 3.0 114 100 + 14.0 1893 93 99 - 6.1 106 99 + 7.1 1894 80 100 -20.0 132 99 +33.3 1895 109 101 + 7.9 73 100 -27.0 1896 117 101 + 15.8 62 101 -38.6 1897 99 102 - 2.9 76 102 -25.5 1898 103 103 0.0 83 104 -20.2 1899 105 104 + 1.0 88 107 -17.8 1900 105 105 0,0 103 109 - 5.5 1901 69 106 -34.9 175 113 +54.9 1902 111 106 + 4.7 117 116 + 0.9 1903 106 107 - 0.9 123 120 + 2.5 1904 111 108 + 2.8 128 125 + 2.4 1905 120 108 + 11.1 119 130 - 8.5 1906 126 109 + 15.6 116 135 -14.1 1907 108 109 - 0.9 150 141 + 6.4 1908 109 110 - 0.9 176 147 + 19.7 1909 106 110 - 3.6 168 153 + 9.8 1910 115 110 + 4.5 139 160 -13.1 1911 99 110 -10.0 179 167 + 7.2 1912 121 109 + 11.0 141 175 -19.4 1913 96 109 -11.9 200 182 + 9.1 1914 107 108 - 0.9 187 191 - 2.1 Appendix 37 TABLE II. — Index Numbers op the Yield per Acre of Six Crops Year Percentage deviations from the respective trends of the index numbers of yield per acre Combined index number Corn Wheat Oats Potatoes Hay Cotton 1882 + 2.4 +12.9 + 1.1 + 1.0 + 2.9 + 8.7 +29.0 1883 - 4,7 - 3.7 + 7.7 + 19.2 + 14.6 — 3.3 +29.8 1884 + 9.2 + 7.8 + 5.0 + 15.5 + 8.8 - 9.8 +36.5 1885 + 12.5 -14.1 + 5.7 + 5.2 - 3.8 — 3.3 + 2.2 1886 - 6.3 + 2.0 + 1.1 + 1.1 - 2.0 — 1.1 - 5.2 1887 -14.1 - 0.9 - 2.9 -22.1 - 7.0 + 6.4 -40.6 1888 + 12.1 - 9.6 - 0.8 + 10.6 + 1.4 + 4.3 + 18.0 1889 + 15.0 + 4.4 + 4.3 + 6.3 + 4.7 - 8.5 +26.2 1890 -12.1 -10.8 -25.0 -23.2 - 2.1 + 6.3 -66.9 1891 + 14.2 +22.0 + 9.4 +27.1 - 2.9 + 1.0 +70.8 1892 - 2.7 + 5.9 — 8.1 -17.5 - 4.9 +17.7 - 9.6 1893 - 5.8 -10.6 — 12.3 - 6.1 + 6.0 -16.5 -45.3 1894 -19.4 + 2.6 - 8.6 -18.2 -10.1 + 8.2 -45.5 1895 + 8.1 + 5.5 + 9.8 +29.7 -17.4 -15.2 +20.5 1896 + 15.4 - 5.4 - 5.2 +15.5 + 5.5 + 1.0 +26.8 1897 - 3.3 + 1.3 - 0.4 -19.2 + 8.9 - 1.0 -13.7 1898 - 0.2 + 14.5 + 3.3 - 7.5 + 16.8 +17.8 +44.7 1899 + 1.1 - 8.7 + 9.1 + 12.0 + 2.0 - 2.0 + 13.5 1900 + 0.3 - 9.6 + 6.1 - 4.5 - 5.7 + 2.9 -10.5 1901 -34.4 + 9.2 - 8.3 -24.1 - 6.7 - 9.8 -74.1 1902 + 4.6 + 4.7 +21.6 + 9.6 + 8.2 - 1.1 +47.6 1903 - 1.2 - 7.7 - 0.8 - 5.2 + 10.0 - 8.7 -13.6 1904 + 3.3 -11.2 + 11.0 +22.0 + 7.5 + 7.8 +40.4 1905 + 10.3 + 2.0 + 16.5 - 5.8 + 8.0 - 1.9 +29.1 1906 + 15.4 + 8.3 + 5.8 + 9.0 - 6.1 + 6.8 +39.2 1907 - 1.6 - 2.8 -20.5 + 0.8 + 0.1 - 4.9 -28.9 1908 - 0.8 - 3.5 -17.0 - 9.7 + 4.1 + 2.9 -24.0 1909 - 3.6 + 8.3 - 0.6 + 10.4 - 3.4 -17.8 - 6.7 1910 + 4.6 - 5.1 + 2.6 - 3.2 - 8.0 - 8.9 -18.0 1911 - 9.5 -15.1 -21.8 -17.3 -23.2 +12.0 -74.9 1912 + 10.9 + 7.6 +18.5 + 16.5 - 1.5 + 5.1 +57.1 1913 -11.9 + 2.6 - 8.5 - 7.1 -12.4 + 2.1 -35.2 1914 - 1.0 + 11.7 - 8.1 + 13.4 - 4.7 + 18.9 +30.2 1915 + 8.9 +14.3 + 15.4 - OS + 11.9 - 2.1 +47.6 1916 - 4.8 -18.6 - 9.2 -16.0 + 9.2 - 6.6 -46.0 1917 + 4.0 - 5.2 + 8.9 + 5.6 + 0.7 - 3.4 + 10.6 1918 - 3.7 + 4.4 + 1.6 + 2.5 - 9.2 - 2.3 - 6.7 38 Generating Economic Cycles TABLE III. — Periodograms of the Index Numbers op the Yield PER Acre of the Crops, the Production of Coal and Iron, AND THE Production of the Raw Materials of Manufacture Length of the Square of the amplitude cycle (years) Crops Coal and iron Raw materials 3 148.65 14.12 182.17 4 41.15 42.37 110.64 5 67.18 24.41 5.92 6 65.20 13.13 11.45 7 319.21 21.03 725.32 8 401.24 120.41 919.26 9 123.92 70.41 170.32 10 155.16 87.49 16.42 11 129.95 176.26 211.03 12 54.31 237.70 368.68 Appendix 39 TABLE IV. — Index Numbers op the December Farm Prices of Six Crops Year Percentage deviations from the respective trends of the index numbers of the December farm prices Combined index number Corn Wheat Oats Potatoes Hay Cotton 1882 + 6.0 - 4.9 + 3.1 - 2.5 - 4.5 - 5.7 - 8.5 1883 - 3.1 + 3.0 - 4.8 -22.8 -15.7 0.0 - 43.4 1884 -15.6 -22.7 -16.0 -25.5 -12.3 + 6.4 - 85.7 1885 -18.8 - 3.3 - 9.6 -12.3 - 2.6 + 2.5 - 44.1 1886 - 6.2 -10.3 - 1.8 - 5.8 - 1.8 + 2.6 - 23.3 1887 + 17.3 - 7.1 + 2.8 +40.6 +20.2 + 11.8 + 85.6 1888 - 7.5 +31.5 - 2.9 -15.2 + 8.5 + 14.9 + 29.3 1889 -21.2 + 1.9 -18.8 -24.5 -11.5 + 17.1 - 57.0 1890 +44.1 +25.5 +54.5 +62.9 + 1.0 +20.1 +208.1 1891 + 16.8 +26.7 +15.3 -23.7 + 6.0 + 1.0 + 42.1 1892 + 14.0 - 4.0 + 16.5 +41.2 + 8.0 +16.5 + 92.2 1893 + 7.1 -16.3 + 9.3 +26.8 + 14.0 - 2.9 + 38.0 1894 +33.3 -23.5 +20.6 +13.3 +12.0 -36.2 + 19.5 1895 -27.0 -20.4 +26.5 -44.4 + 9.0 + 3.8 -105.5 1896 -38.6 + 13.3 -32.3 -41.0 -15.7 -11.0 -125.3 1897 -25.5 +25.3 -24.7 +11.8 -15.5 -12.6 - 41.2 1898 -20.2 -11.0 - 9.8 -16.5 -24.8 -27.2 -109.5 1899 -17.8 -12.7 -14.3 -22.9 -11.2 -13.7 - 92.6 1900 - 5.5 - 8.7 -13.1 -15.9 + 6.4 + 10.8 - 26.0 1901 +54.9 -10.4 +30.9 +45.9 +15.9 -18.5 + 118.7 1902 + 0.9. -11.1 - 2.7 -11.7 + 2.6 -13.4 - 35.4 1903 + 2.5 - 4.5 + 6.0 + 13.3 0.0 +16.0 + 33.3 1904 + 2.4 +24.8 - 5.0 -18.3 - 7.3 - 3.7 - 7.1 1905 - 8.5 - 1.7 -13.9 + 9.4 -11.8 + 13.8 - 12.7 1906 -14.1 -14.3 - 9.5 -10.9 + 3.8 - 2.1 - 47.1 1907 + 6.4 + 9.8 +23.3 + 5.8 + 13.3 + 4.1 + 62.7 1908 + 19.7 + 13.6 +27.8 +20.5 -15.1 -14.9 + 51.6 1909 + 9.8 + 18.0 + 6.6 - 9.7 - 4.2 +33.1 + 53.6 1910 -13.1 + 3.8 -11.4 - 7.2 + 7.4 +33.3 + 12.8 1911 + 7.2 0.0 + 13.3 +32.8 +22.9 -17.4 + 58.8 1912 -19.4 -14.7 -21.2 -16.7 - 1.3 + 9.6 - 63.7 1913 + 9.9 -12.2 - 6.0 +13.5 + 0.6 + 12.0 + 17.8 1914 - 2.1 + 7.1 + 3.9 -19.8 -12.0 -37.3 - 60.2 40 Generating Economic Cycles TABLE V. — Index Numbers of Coal and Pig Iron Year Percentage deviations from secular trend Combined index numbers Coal Iron 1882 + 1.9 + 6.5 + 8.4 1883 + 5.3 - 2.0 + 3.3 1884 + 3.3 -18.5 -15.2 1885 -10.8 -25.9 -36.7 1886 -13.2 0.0 -13.2 1887 - 2.9 + 7.8 + 4.9 1888 + 6.8 + 3.0 + 9.8 1889 - 1.3 + 15.7 + 14.4 1890 + 5.1 +32.4 • +37.5 1891 + 8.6 + 11.4 +20.0 1892 + 10.6 + 16.7 +27.3 1893 + 6.7 -14.6 - 7.9 1894 - 5.3 -26.0 -31.3 1895 + 1.0 - 1.9 - 0.9 1896 - 6.5 -17.1 -23.6 1897 - 8.8 -13.4 -22.2 1898 - 5.7 - 2.3 - 8.0 1899 + 0.8 + 4.3 + 5.1 1900 0.0 - 2.7 - 2.7 1901 + 0.7 + 4.9 + 5.6 1902 - 3.7 + 9.1 + 5.4 1903 + 6.9 + 2.7 + 9.6 1904 - 2.1 -12.4 -14.5 1905 + 3.0 + 14.4 + 17.4 1906 + 1.9 + 18.3 +20.2 1907 +11.6 + 13,6 +25.2 1908 - 8.4 -33.6 -42.0 1909 - 3.6 + 2.2 - 1.4 1910 + 0.8 + 3.5 + 4.3 1911 - 4.4 -13.9 -18.3 1912 - 0.4 + 4.3 + 3.9 1913 + 3.1 + 5.4 + 8.5 CHAPTER III GENERATING CYCLES REFLECTED IN A CENTURY OF PRICES 1 Summary Cycles of approximately eight years ia the jdeld per acre of British crops have probably recurred in a continuous series during the last one hmidred and sixty years. In consequence of the law of demand, these crop cjTles have generated corresponding cycles in the prices of food and of organic raw materials. In conformity with the law of competitive price, the cycles in the prices of food and of raw materials should have been followed by corresponding cycles in the prices of manufactured commodities. As a matter of fact, the analysis of Sauerbeck's index numbers of general wholesale prices reveals real cycles of approximately eight years in which the originating, generating crop cycles are reflected throughout the century for which the Sauerbeck index numbers have been computed. The principal results of the investigation appear in the graphs of Figures 15 and 16. In the preceding chapter I drew a distinction be- tween generating economic cycles and derived economic cycles. Generating economic cycles were described as economic cycles that have their origin in non-economic causes and become the originating som*ce of derived economic cycles. A careful scrutiny of American agricultural statistics revealed the existence of an eight- year generating cycle in the yield per acre of the leading American crops, and this generating cycle of products ^ This chapter was first published, substantially in its present from, in the Qvarlerly Journal of Economics, August, 1921. 42 Generating Economic Cycles was found to originate a derived cycle of agricultural prices. American manufactures, according to the cen- sus of 1900, obtained about 80 per cent of their raw materials from the farms, and as the prices of manu- factured comm.odities tend to adjust themselves to the cost of production, it was argued that the eight-year cycles in the prices of farm, products tended to induce derivative cycles in the prices of manufactured com- modities. The major features of economic cycles were regarded as being traceable to three primary laws: (1) the law of the generating cycle of raw mate- rials, which is due to a non-economic cause; (2) the law of demand for raw materials, in con- sequence of which the generating cycle of products originates a derived cycle of prices for raw materials; and (3) the law of competitive price, according to which prices of finished goods in an open market tend to correspond with the cost of production. The inquiry is now carried a stage further. An analysis is made of the history of prices in Great Britain, for a century, and the results are considered with reference to their dependence upon generating agricultural cycles and with regard to their bearing upon the economic theory of cycles. Data and Method The data for the first part of the investigation are the Sauerbeck index numbers of general wholesale prices for the interval between the Napoleonic wars and the Great War. This record from 1818 to 1913, which Generating Cycles in a Century of Prices 43 is a summary description of economic history during a century of unparalleled development between two world-wide catastrophes, supplies unique material for an inductive quest of economic regularities. The method used in the inquiry is Fourier's Theorem as it has been developed for statistical purposes by Professor Schuster and Professor Turner. The Savilian Professor of Astronomy at Oxford, Professor Turner, has said that "apart from the plane- tary motions periodicities in nature are seldom clear- cut." ^ As we shall attempt to estabhsh certain economic cycles and to trace their cause to periodicities in nature, the part of wisdom would seem to be to profit by the experience of natural scientists who have dealt with the problem of isolating natural periodicities. It is well known that Fourier's celebrated theorem y = Ao-{- aiCOfikt-\- a2Cos2kt-\- . . . + bi sin kt + 62 sin 2kt + . . . if carried out to a sufficient number of terms will repro- duce almost any type of graph. Tliis equation may be expressed also in the form y = Ao + Ai sin {kt -f eO + A2 sin i2kt + 62) + . . . When the parameters of this equation are determined from statistical data the question arises as to the signifi- cance of the several terms in the Fourier series. Do the successive terms in the sine series correspond to real periodicities in nature, or are they merely formal terms the summation of which will give the observed 1 H. H. Turner, Tables for Facilitating the Use of Harmonic Analysis, p. 44. 44 Generating Economic Cycles values of the original data? If, for example, a high value were obtained for one of the A-coefficients in the sine series, what warrant would there be for assuming that the particular sine term of which the given A was the coefficient would be significant of a real recurring periodicity? This problem was considered by Professor Schuster in his theory of the periodogram.^ According to Profes- sor Schuster, "the periodogram may be said to put the statistical material in a fonn in which it may be most readily discussed, but there may be always cases in which the interpretation is difficult. ... I do not, of course, claim to have first introduced the application of Fourier's Theorem to the discovery of hidden periodicities. . . . The process is sufficiently obvious to have been frequently introduced, but it has generally been assumed that each maximum in the amplitude of a harmonic term corresponded to a true periodicity. What distinguishes the method which I am endeavour- ing to introduce from that of others, is the discussion of the natural variability of the Fourier coefficients according to the theory of probability, independently of any periodic cause which may have influenced the phenomenon." ^ 1 The fundamental memoirs of Professor Schuster are: "On the Investigation of Hidden Periodicities with Application to a Supposed 26 Day Period of Meteorological Phenomena," Terrestrial Magnetism, for March, 1898; "The Periodogram of IMagnetic Declina- tion as Obtained from the Records of the Greenwich Observatory during the Years 1871-1895," Cambridge Philosophical Society Transactions, vol. 18, 1899; "On the Periodicity of Sunspots," Philosophical Transac- tions of the Royal Society of London, A, vol. 206, 1906. 2 "On the Periodicities of Sunspots," Philosophical Transactions, A, vol. 206, pp. 71, 72. Generating Cycles in a Century of Prices 45 The first step in the Schuster method of isolating true periodicities by the method of the periodogram consists in arranging the data of the statistical series into groups of different lengths and then computing the values of the coefficients of the sine tenns appropriate to the different groups. The required lengths and closeness of the groups are discussed * by Professor Schuster, and he further shows how the probability of the reality of any assumed cycle is dependent upon the magnitude of the coefficient of its correspond- ing harmonic in the periodogram. In brief, the prob- ability of the reality of an assumed cycle is shown to be dependent upon the relative size of A - where A is the coefficient of the sine term descriptive of the assumed cycle. Professor Turner's method, which he has called the method of Fourier Sequence,^ is based upon Professor Schuster's method of the periodogram. The device may be illustrated by the problem in connection with which the method of Fourier Sequence was developed. In 1913, when Professor Turner published his essays, a fairly good record of sunspots existed for a period of 156 years. His problem was to determine whether there 1 See particularly "On the Periodicities of Sunspots," Philosophical Transactions, A, vol. 206, p. 71. 2 The fundamental memoirs of Professor Turner are "On the Har- monic Analj'sis of Wolf's Sun-spot Numbers, With Special Reference to Mr. Kimura's Paper," Monthly Notices of the Royal Astro?iomical Society, May, 1913; "On the PJxpression of Sunspot Periodicity as a Fourier Sequence, and on the General Use of a Fourier Sequence in Similar Problems," i6id., 1913 (Supplement); " Further Remarks on the Expression of Sun-spot Periodicity as a Fourier Sequence," ibid., November, 1913. 46 Generating Economic Cycles was ground for believing that there were real periodic- ities in the sunspot data, and if so, to ascertain their approximate lengths. The same problem had been considered by Professor Schuster wdth the aid of the method of the periodogram, but, according to Professor Turner, the Schuster method was needlessly complex, involving an unnecessary amount of computation. An adequate solution was thought to be obtained if a Fourier series were computed for the whole series of data, and the several terms of the series were investi- gated more in detail according as the magnitudes and signs of the coefficients of the several terms indi- cated the possible presence of a real cycle. In order to carry out this idea, Professor Turner computed for the 156 years of sunspot data the harmonics for the periods of the following number of years: 156, 156/2, 156/3 . . . 156/54. The principal advantage claimed by Professor Turner for the method of Fourier Sequence is this: The development of the Fourier Sequence is (1) Necessary. — "Since each term of the Fourier Sequence is independent of every other, it can- not be inferred from any other. Hence we must at least calculate all these terms." ^ (2) Sufficient. — "If we desire to know to what ex- tent any periodicity intermediate between two of those directly tabulated is represented in the observations . . . we are able to deduce this information from the sequence." - 1 "On the Expression of Sun-spot Periodicity as a Fourier Sequence," Monthly Notices of the Royal Astronomical Society, 1913, p. 715. ^Ibid., p. 715. Generating Cycles in a Century of Prices 47 An Analysis of a Century of Prices As a preliminary step our investigation will follow the method of Professor Turner in the analysis of Sauerbeck's index numbers of general wholesale prices. Sauerbeck's index numbers of general wholesale prices from 1818 to 1913 are recorded in Table I of the Appendix and are graphed in Figure 11. The graph shows quite clearly that the mean value of the items in the early part of the series is higher than the mean value during the latter part, and we are, therefore, confronted with the question as to what shall be done about the secular trend of the figures. Any hypothesis that might be made as to the type of curve to represent the secular trend would, to a degree, be an arbitrary hypothesis, and my decision has been to make no supposition as to the secular trend, but to proceed with the computation of the Fourier tenns from the crude index numbers. In support of this decision these two considerations are offered: 1. It is known that each term of a Fourier sequence is independent of the other tenns, and there is, therefore, a probability that when a Fourier series is fitted to the statistical data covering a considerable length of time, the early tenns of the series will make an allowance for the secular trend which will be independent of the later terms. ^ Figures 11, 12, 13, 14 show the reasonable- 1 Cf . Schuster, "The Periodogram of Magnetic Dedination," p. 113. "Table . . . clearly shows the effects of secular variation, and we must consider in how far it is necessary to take any notice of this variation. If our observations extended over an indefinite time, Fourier's analysis would itself perfonn all that is required, and each period would be totally independent of all others." 48 Generating Economic Cycles ness of this assumption. An ample description of these graphs will be given later on. 2. The authority of Professor Schuster is against the early elimination of the secular trend before the Fourier terms are computed: ''Very considerable labor has sometimes been spent in eliminating secular variations and other known periodicities before the hidden periodicities are searched for. We may reasonably ask the question, what object is thereby gained? It is one of the great advantages of Fourier's analysis that each of its terms is independent of the others; and if we wish to determine any particular coefficient it is imnecessary to begin by eliminatmg the others. The analysis itself performs that process in the best possible way, if the coefficients are obtained by arithmetical calculations. . . . The general rule may be given, that it is the best to eliminate as few variations as possible, and to carry out the elimination at as late a stage of the computation as possible." ^ For these reasons we have computed the Fourier terms directly from the index numbers in the raw state. The results of the computation are given in Table II of the Appendix. The headings of the table will be understood from an examination of Fourier's series when it is expressed in the following two forms: (1) y = Ao -\- ai cos kt-\-a2 cos 2kt-i- . . . + bi sin kt + &2 sin 2kt + • • . {2)y = Ao + Ai sin {kt + eO + A^ sin i2kt + 62) + • . . The amplitudes of the terms in (2) — the ^-coeffi- cients— are obtained from the corresponding coeffi- 1 "On the Investigation of Hidden Periodicities," p. 34. Cf. also p. 38. Generating Cycles in a Century of Prices 49 cients in (1) by means of the foraiula A = \/ d'+h'-. Aq is equal to the mean value of the 96 index numbers. The lengths of the periods in the second colunm of Table II are obtained by di\'iding 96, which is the number of years of obser\'ations recorded in the Sauer- beck index numbers, by the consecutive integers that are given in the first column. The constant k in the fomiulae (1) and (2), which does not appear in Table II, oprvo is equal to -^ = 3° 45'. The constants e in (2) do not occur in Table II, but their values may be obtained from the corresponding values of a and h in (1) by the relation tan e = t. 6 We shall now consider the conclusions that may be drawn from the data of Table II and we shall begin with the last column which gives the values of A-. If we let the eye run down the last colmnn, it will note that at four places the values of A ^ assume special importance — for the periods of 96 years, 48 years, 24 to 16 years, and 8.7 to 7.4 years. A moment ago when the question of eliminating the secular trend was under consideration, the decision was reached to permit the early terms of the Fourier series to pro\dde for the secular trend rather than to adjust the raw figures of the observation ac- cording to a more or less arbitrary assumption as to the type of curve which might be appropriate to repre- sent the trend. It now seems reasonable to conclude that the large values of yl^ at 96 years and 48 years, and possibly those between 24 and 16 years, are caused by the general trend of the figures. Inasmuch as the first of these covers the whole range of the observations and 50 Generating Economic Cycles the second, one-half of the range, one would certainly not be justified in holding that they represent real recurrent cycles. Figures 11 and 12 depict these two Fourier constituents of the price curve. Figure 11 also shows the curve that is obtained by combining the mean of the Sauerbeck index numbers with the 96-year Fourier constituent. Likewise Figure 12 gives the compound curve made up of the mean of the Sauer- beck index numbers and the 96-year and 48-year Fourier constituents. With two of the four important values of J. ^ in Table II accounted for, the possibility of real cycles in the 96-years record is limited to the remaining two epochs between 24 and 16 years and between 8.7 and 7.4 years. The mean of the limiting values of the latter 8 7+74 period is — =8.0 years, and the limits of the other period are respectively twice and three times this mean value. The value of ^ ^ in Table II corresponding to a period of exactly 8 years is small, but if the com- putation had been confined to the interval 1857-1913 its value would have been 7.95. Thus far the argument as to the existence of real periods has been based upon the size of A - which is the criterion used by Professor Schuster. An additional criterion has been offered by Professor Turner. In his fundamental memoir ^ he has pointed out that when a striking periodicity is present, there is a tendency for the signs of a and h to change between consecutive 1 H. H. Turner, "On the Expression of Sun-spot Periodicity as a Fourier Sequence," Monthly Notices of the Royal Astronomical Society, 1913, p. 716. Cf. also, pp. 722, 723. Generating Cycles in a Century of Prices 51 Fourier constituents. Table II shows that not only are the values of ^- large for the period between 24 and 16 years, and for the period between 8.7 and 7.4 years, but that in both instances there is a change of sign in either a or 6. Considering that in a record of 96 years a possible cycle of about 16 years could occur six times and one of about 8 years could occur twelve times, this analysis of a century of prices seems to warrant the conclusion that there may be a real cycle of prices between 16 and 24 years in length, and that there is a large probability of the existence of a real cycle in the neighborhood of 8 years. As the argument proceeds we shall have strong additional reason for believing that the indicated eight-year cycle in the Sauerbeck index numbers of wholesale prices is a real cycle with an assignable cause. Certainly the Fourier analysis indicates that if there is a real cycle in the 96 years of the Sauerbeck observations, its most probable value is in the neighbor- hood of eight years. In order to isolate and exhibit the cycles of approxi- mately eight years the graphs of Figures 13, 14, 15 have been computed and drawn. Figure 13 shows the Fourier constituent of 19.2 years — which, according to Table II, is one of the most important constituents — and the compound curve that results from combining the mean of the Sauerbeck observations with the Fourier constituents of 96, 48, and 19.2 years. Figure 14 depicts the 16-year Fourier constituent and the compound curve made up of the mean value of the Sauerbeck nmnbers and the 96-, 48-, 19.2- and 16-year Fourier constituents. A re\dew of Figures 11, 12, 13, 14 52 Generating Economic Cycles Figure 11. Sauerbeck's index numbers of general wholesale prices. Equation to the upper smooth curve: y = 88.6 + 11.2 sin {?^~ t + 342°), origin at 1818. Figure 12. Sauerbeck's index numbers of general wholesale prices. Equation to the upper smooth curve: y = 88.6 + 11.2 sin (?_?_?_ t + 342°) + o ^ ^ 13.8 sin (3_6_0. I + 55°), origin at 1818. Generating Cycles in a Century of Prices 53 Fourier consiitucnt or 19 2 YtARs Figure 13. Sauerbeck's index numbers of general wholesale prices. Equation to the upper smooth curve: y = 88.6 + 11.2 sin (-—*- t + 342°) + 13.8 sin (3 c CI c| o 3 o COlQO ^ CO n 1^ "1 W ■s + c T)< »» ■a C3 ■* °o| CO + ttto u f/l ^, "1 d S .3 -S P-, 2 + t col is 64 Generating Economic Cycles and the phase of the eight-year cycle is the mean of the go _i_ 92° phases of the two cycles = 50° 30'. It will be seen from Figure 16 that the eight-year cycles in the cen- tury of Sauerbeck's index numbers were approximately synchronous with the corresponding cycles in the indi- cated yield per acre of the British crops. The eight- year cycle in the crops is proved to have persisted throughout nearly the whole period of 159 years from 1760 to 1918 (the investigation of the American crops was carried through 1918) or for an interval of twenty cycles of eight years in length. This generating eight- year cycle in the crops induced derived cycles of prices which are reflected and verified in the century of Sauer- beck index numbers of general wholesale prices. APPENDIX TABLE I. — Sauerbeck's Index Numbers of General Wholesale Prices Year Index Number Year Index Number Year Index Number Year Index Number 1818 142 1842 91 1866 102 1890 72 1819 121 1843 83 1867 100 1891 72 1820 112 1844 84 1868 99 1892 68 1821 106 1845 87 1869 98 1893 68 1822 101 1846 89 1870 96 1894 63 1823 103 1847 95 1871 100 1895 62 1824 106 1848 78 1872 109 1896 61 1825 117 1849 74 1873 111 1897 62 1826 100 1850 77 1874 102 1898 64 1827 97 1851 75 1875 96 1899 68 1828 97 1852 78 1876 95 1900 75 1829 93 1853 95 1877 94 1901 70 1830 91 1854 102 1878 87 1902 69 1831 92 1855 101 1879 83 1903 69 1832 89 1856 101 1880 88 1904 70 1833 91 1857 105 1881 85 1905 72 1834 90 1858 91 1882 84 1906 77 1835 92 1859 94 1883 82 1907 80 1836 102 1860 99 1884 76 1908 73 1837 94 1861 98 1885 72 1909 74 1838 99 1862 101 1886 69 1910 78 1839 103 1863 103 1887 68 1911 80 1840 103 1864 105 1888 70 1912 85 1841 100 1865 101 1889 72 1913 85 66 Generating Economic Cycles TABLE II. — Results op Fourier Analysis of Sauerbeck's Index Numbers of General Wholesale Prices. 1818-1913 Di- visor Period in Years a b A= Di- visor 13 Period in Years a b A2 1 96.0 — 3.^46 + 10.60 124.42 7.4 +3.12 — .11 9.74 2 48.0 + 11.27 + 7.96 190.40 14 6.9 +2.12 + 1.77 7.62 3 32.0 + 1.08 + .76 1.73 15 6.4 + .61 + .17 .41 4 24.0 + 2.95 + .70 9.17 16 6.0 + 1.67 + .29 2.86 5 19.2 4- 4.18 + 3.28 28.23 17 5.6 + .88 + .72 1.30 6 16.0 — 1.08 + 3.46 13.13 18 5.3 + .59 +2.03 4.48 7 13.7 + .78 + .76 1.19 19 5.0 + .04 + .66 .44 8 12.0 + 1.85 + .73 3.95 20 4.8 + .29 + .75 .65 9 10.7 + 1.18 — .02 1.40 21 4.6 + 1.38 + .48 2.14 10 9.6 + 2.00 — .92 4.86 22 4.4 + .03 + 1.64 2.68 11 8.7 + .61 + 3.76 14.52 23 4.2 + .80 + .63 1.03 12 8.0 + 1.36 — .51 2.12 24 4.0 + .30 — .10 .10 Appendix 67 TABLE III. — Residuals of Sauerbeck's Index Numbers OF General Wholesale Prices Year Residual Year Residual Year Residual Year Residual 181S +42.4 1842 — 1.2 1866 + 3.9 1890 + 7.7 1819 + 17.7 1843 — 5.7 1867 + 1.2 1891 + 8.5 1820 + 5.5 1844 — 0.9 1868 — 1.0 1892 + 5.2 1821 — 2.6 1845 + 5.3 1869 — 3.2 1893 + 5.2 1822 — 8.4 1846 + 9.7 1870 — 6.6 1894 — 0.5 1823 — 6.3 1847 + 17.0 1871 — 2.8 1895 — 2.4 1824 — 1.7 1848 + 0.2 1872 + 5.9 1896 — 4.7 1825 + 11.6 1849 — 4.8 1873 + 8.2 1897 — 5.3 182G — 2.4 1850 — 4.1 1874 + 0.3 1898 — 5.0 1827 — 2.4 1851 — 9.0 1875 — 4.3 1899 — 2.5 1828 + 0.4 1852 — 9.5 1876 — 3.3 1900 + 3.2 1829 — 1.3 1853 + 3.7 1877 — 1.9 1901 — 2.9 1830 — 1.8 1854 + 7.3 1878 — 6.3 1902 — 4.5 1831 — 0.4 1855 + 2.5 1879 — 7.5 1903 — 4.7 1832 — 3.6 1856 + 1.0 1880 + 0.5 1904 — 4.1 1833 — 2.8 1857 + 3.6 1881 + 0.3 1905 — 2.4 1834 — 5.6 1858 —10.9 1882 + 2.0 1906 + 2.1 1835 — 5.3 1859 — 7.9 1883 + 2.7 1907 + 4.1 1836 + 3.0 1860 — 2.1 1884 — 0.7 1908 — 4.4 1837 — 6.2 1861 — 2.2 1885 — 2.4 1909 — 5.8 1838 — 1.5 18(52 + 1.8 1886 — 2.9 1910 — 4.8 1839 + 3.2 1863 + 4.8 1887 — 1.7 1911 — 6.5 1840 + 4.9 1864 + 7.2 1888 + 2.3 1912 — 5.7 1841 + 4.5 1865 + 3.3 1889 + 6 1 1913 —10.2 68 Generating Economic Cycles TABLE IV. — Poynting Index Numbers of the Price of Wheat Per Quarter in England from 1760 to 1875. Mio = Ten- Year Average of the Absolute Prices of Wheat M4 = Four- Year Average of the Absolute Prices of Wheat Year Poynting Index M4/MJ0 Year Poynting Index M4/M,o Year Poynting Index M4/M10 Year Poynting Index M4/M10 1760 ■ 82.3 1789 106.0 1818 116.6 1847 111.6 1761 82.2 1790 98.5 1819 103.5 1848 103.6 1762 92.1 1791 90.0 1820 87.9 1849 84.2 1763 98.1 1792 87.1 1821 82.6 1850 75.9 1764 101.8 1793 98.1 1822 86.2 1851 78.0 1765 111.6 1794 110.7 1823 95.0 1852 94.8 1766 112.9 1795 102.3 1824 103.3 1853 112.9 1767 104.8 1796 91.9 1825 105.0 1854 126.4 1768 101.4 1797 86.4 1826 101.7 1855 124.6 1769 94.3 1798 97.0 1827 98.6 1856 108.5 1770 93.3 1799 117.4 1828 100.9 1857 92.2 1771 100.2 1800 121.1 1829 107.0 1858 86.8 1772 107.7 1801 117.8 1830 111.7 1859 91.4 1773 110.7 1802 98.4 1831 107.8 1860 103.0 1774 105.3 1803 85.7 1832 100.2 1861 107.7 1775 103.8 1804 85.7 1833 87.6 1862 99.2 1776 98.3 1805 91.3 1834 82.3 1863 88.8 1777 90.5 1806 99.7 1835 83.3 1864 85.3 1778 88.9 1807 95.4 1836 91.9 1865 96.2 1779 89.2 1808 97.6 1837 105.8 1866 107.2 1780 93.9 1809 101.7 1838 114.2 1867 110.0 1781 104.8 1810 116.8 1839 117.0 1868 105.8 1782 113.6 1811 120.3 1840 111.4 1869 99.3 1783 111.0 1812 108.8 1841 101.5 1870 95.5 1784 101.7 1813 100.3 1842 92.9 1871 101.0 1785 91.6 1814 89.8 1843 89.4 1872 106.5 1786 89.1 1815 90.0 1844 92.4 1873 104.7 1787 95.3 1816 97.8 1845 106.1 1874 96.4 1788 104.2 1817 111.3 1846 111.1 1875 99.8 CHAPTER IV THE ORIGIN OF THE EIGHT-YEAR GENERATING CYCLE 1 Summary The persistence of the eight-year generating cycle in England for one hundred and sixty years; the congruence of the eight-year crop cycles in England, France, and the United States; the persistence of the eight-year meteorological cycles, and their congruence in Europe and America; the congruence of the economic and meteoro- logical cycles — -these uniformities and agreements suggest that their cause must be sought in a cosmical cycle. The probable cause is the planet Venus in its eight-yearly periodic motion with respect to the Earth and the Sun. Generating economic cycles are to be described as economic cycles that have their origin in non-economic causes and become the originating source of derived economic cycles. The theory of generating cycles em- braces three fundamental inquiries: first, as to the existence of generating cycles, their length, amplitudes and phases; second, as to the ways in which the generat- ing cycles work out their rhythmic effects in remote parts of economic life; and third, as to the cause of generating cycles. In previous chapters I have dealt with the first and second of these divisions. We must now attempt to place the cause of the eight-year generating cycle. ^This chapter was first published, sul)staiitially in its present form, in the Quarterly Journal of Economics, November, 1921. 70 Generating Economic Cycles Economic Cycles If index niunbers of the annual yield per acre of American crops are plotted for a considerable period, from 1882 to the present tune, for example, the graph will be a composite of three types of changes — secular, cyclical, and random — which were long ago classified and described by Cournot. In Chapter II, I eliminated the secular changes in the yield per acre of the six Crops 1 400 1 300 1 < ^ 200 K ° IOC \ / ^ \ a. < a 1 1 1 1 1 1 2 4 6 S 10 12 The Length of the Cycle in Years FiouBE 17. Periodogram of the yield per acre of American crops. leading crops in American agriculture, and then formed index numbers of their percentage deviations from the respective secular trends. The series of index numbers was then scrutinized with a view to finding evidence of a real, recurring cycle, and Figure 17 shows that of all possible cycles between three and twelve years in the index numbers of the yield per acre of the crops, the most probable length is in the neighborhood of eight years. If an eight-year cycle is fitted, by the method of least squares, to the index numbers of yield, the maxima of the repeated cycle fall, approxunately, Origin of Eight-Year Generating Cycle 71 The Dakotas France FiorRE 18. Cycles in the yield of wheat, oats, and barley in the Dakotas, the United States, the United Kingdom, and France. The Dakotas: y = 3.20 sin (l|Ji°' + 93" 50'), origin at 1882; The United States: y = 2.49 sia (Mi^^ + 111" 27'), origin at 1882; The United Kingdom: y = 3.02 sin (3.6£°4 + 142° 0'), origin at 1884; France: y = 2.17 sin (5.|2.°« +292° 56'), origin at 1879. 72' Generating Economic Cycles at 1882, 1890, 1898, 1906, 1914. In other studies ^ refer- ring to the Dakotas, the United States, the United Kingdom, and France, the eight-year cycles were iso- lated and were found to be practically synchronous in these countries. Figure 18 shows the graph descriptive of the eight-year cycles in the yield of wheat, oats, and barley. With the existence of an international cycle in the yield of the crops firmly established, an obvious corol- lary suggested that according to the law of demand — in consequence of which the price tends to fall with an increase in the supply of the commodity — there should be a derived eight-year cycle in the prices of farm products. Accordingly, the law of demand for the six representative American crops was ascertained, and the derived cycle of prices of farm products was computed from the established eight-year cycles in the yield of the crops. The results are presented in Figure 19, together with a comparison between the actual index numbers of prices and the forecast indices of prices. After ascertaining that the prices of agricultural products do actually vary inversely with the yield in a definite, predictable way, it became possible to sub- ject the theory of the existence of generating cycles of crops to a severe critical test. If the prices of agricul- tural commodities do vary inversely with the yield, and if there is a real cycle of eight years in the yield of the crops, then the record of prices throughout a long inter- 1 "Crop-Cycles in the United Kingdom and in the United States," Journal of the Royal Statistical Society, May, 1919; "Crop-Cycles in the United Kingdom and in France," ibid., May, 1920; "Forecasting the Crops of the Dakotas," Political Science Quarterly, June, 1920, partic- ularly pp. 228, 229. Origin of Eight-Year Generating Cycle 73 ACTUAL Index NUMKM Of PRICE5 ToRecAST iNDtx NuM6tRS OF Prices generatin8 cycles of yield per acre Derived Cycles of prices Figure 19 Upper part: Actual index numbers of prices of the six representative crops and the index numbers of prices forecast from the index numbers of the yield per acre by means of the formula V = - 1.295x - .02. Lower part: Generating cycles of the yield per acre of the crops, J/ = 1.6 + 20.0 sin (45°< + 109°), origin at 1SS2; Derived cycles of prices of the crops compute 1 from the generating cycles of yield by means of the formula, y = — 1.295j; - .02. val should reveal the existence of the eight-year generat- ing cycle of crops. Moreover, if the generating cycle is a persistent, real cycle, then the cycle of yield per acre that is revealed indirectly by the record of prices throughout a long interval should be the same as the cycle that is obtained directly from the more recent 74 Generating Economic Cycles official estimates of the actual yield per acre. Figure 20 shows not only that the record of prices in England from 1760 to 1875 exhibits a clear-cut cycle of eight years in the yield per acre, but also that the cycle is continuous with the eight-year cycle which is estab- lished directly from the official estimates of the crop yields since 1884. The theory of the generating cycle also requires that the movement of general prices should follow the rhythmic changes in the yield of agricultural products. As nearly all foods are derived either directly or in- directly from the farms, and as eighty per cent of the raw materials of manufactures — according to the United States census of 1900 — are organic raw materials produced on the famis, the movement of general prices should reflect the rhythm in the yield of the crops. The theory of the relation between the generating cycles of crops and the movement of general prices was subjected to a searching empirical test. Sauer- beck's index numbers of general prices, covering the interval of nearly a century between the Napoleonic wars and the Great War, were examined by means of Fourier analysis with a view to discovering real periodicities. The analysis showed that if there were a sequence of real cycles in the century of prices in England, the most probable length of the constituent cycle was approximately eight years. When this cycle of general prices was computed and plotted, its graph was found to be practically congruent with the graph of the yield of wheat determined indirectly from the record of wheat prices from 1760 to 1875, and practic- ally congruent with the graph of the cycles in the Origin of Eight-Year Generating Cycle 75 » 3 o> 2 2 tD|oO ^ col + r cl " mix 0> «| is o a I-) 76 Generating Economic Cycles yield of the crops determined directly from the official estimates of the annual yield of the crops since 1884. The graphs are given in Figure. 20. Meteorological Cycles In 1919 the Carnegie Institution published Climatic Cycles and Tree-Growth, by A. E. Douglass. With the hope of throwing some light on the periodic activity of the sun, Professor Douglass, by training and profession an astronomer, undertook this laborious and valuable investigation of the variation in the size of the rings of trees, which, he assmned, was a consequence of me- teorological changes having their origin in solar activity. He selected for his first studies yellow pines taken from the forests of northern Arizona. As there is, for the most part, a scant and variable rainfall throughout the state. Professor Douglass assumed as a working theory (1) that the growth of pines in that rpgion depends largely upon the available water; (2) that the rings of the pines measure the growth of the trees; (3) that the rings form a measure of annual precipitation. The rainfall of Arizona is extremely variable from station to station. ''Storms come from the Pacific coast and rain occurs a day or so later than in southern California. Spring and autumn are the dry seasons, and the warmest time of the year is usually in June, just before the summer rains begin. The summer rains occur in July and August and often come in 'spells ' that last a week or two, with thunderstorms in the afternoons or at night, followed by clear mornings. Unlike the winter storms, the summer rains are local Origin of Eight-Year Generating Cycle 77 and apt to be torrential in character, with heavy run- off." The San Francisco Peaks, about ten miles north of Flagstaff, ^'illustrate how meteorological data may vary in rugged localities. The west slopes of these mountains are exposed to the westerly stonns and have an immense snowfall. Springs abound, and all favor- able localities are taken up as ranches. East of the mountain, however, the land is dry and barren, and long distances intervene between watering places. . . . Ina very rugged country like that about Prescott similar differences between east and west mountain slopes must constantly occur." The longest meteorological record in the Arizona pine forest was begun at ^Miipple Barracks, near Pres- cott, in 1867, and then continued at Prescott, which has an elevation of about 5200 feet. With the variability of rainfall from station to station which we have just noted, and with the change of the meteorological obser- vation from WTiipple Barracks to Prescott, one would scarcely expect any normality to be revealed in this particular rainfall record. An examination of Figure 21 is, nevertheless, surprisingly suggestive. The top graph^ shows the relation between the annual rainfall and the growth of pines near Prescott. The growth seems to show a secular trend downwards and for that reason, in seeking the degree of relation between the annual rainfall and the annual growth, I have computed the correlation between their first differences. The measure of this relation is r = .56, which shows that there is an unmistakable relation between the rainfall and the growth of pines in this region. ^ The top graph is taken from Professor Douglass' work, p. 29. 78 Generating Economic Cycles Is the rainfall itself subject to law? In the lower part of Figure 21 an eight-year cycle is fitted to the annual rainfall data, and we find that the maxima occur at 1866, 1874, 1882, 1890, 1898, 1906— which makes the Prescott rainfall, during this interval, synchronous RAINFALL IN INCHES 2B OROWTH in MlLLlMETEHS r^ :s li S 5 20 J 16 S 12 1 8 V ^ A V ^ .^ A ' t-' 24 2 20 1 16 i z 12 ^ 08 1 4 - V 04 ia66 1670 I87d 1676 1862 1666 1890 1694 1696 1902 1906 Eight Year Rainfall Cycle 26 » f", 24 a |20 S 16 i 12 z J e A \ V /^ A 1666 1670 1674 1676 1682 1686 1690 1694 16« 1902 1906 Figure 21. Cycles in the rainfall and in the growth of pines near Prescott, Arizona. Equation to the rainfall cycle, y = 16.9 + 3.2 sin (3.|£.°f + 127° 12'), origin at 1867. with the crop cycles in the United States, in the United Kingdom, and in France. Gratifying as this result is, I should not attach importance to it — because of the meteorological record being made up of observations at two different stations in a country in which the rainfall is notoriously variable from station to station — but for its relation to what is about to be described. Flagstaff, in Arizona, is about 67 miles north of Prescott. From the magnificent pine forests about Flagstaff Professor Douglass was able to obtain cuttings from trees which supplied him with a continuous history Origin of Eight-Year Generating Cycle 79 of rings for 500 3Tars. Referring to these Flagstaff pines, Professor Douglass makes these statements as to the cyclical variations in their growth: ''The interval from 1830 to the present time divides . . . fairly well in (a period) of 7.3 years" (p. 108). As to the whole record of 500 years, he says, "a 7-year period is also frequently observed" (p. 101). In Table 8 (p. 108) Professor Douglass indicates that this cycle of approxi- RESIOUALJ OF5AUER&eCK'5 INDEX NUMBERS. WOKEN UHI Cycles or Prices, smooth curve. Cycles OF Qrowth. dmhidcurvc. -... Figure 29. Cycles in the residuals of Sauerbeck's index numbers of general wholesale prices in England and in the growth of pines near Flagstaff, Arizona. Equation to the cycle of prices, : j/ = 3.1 sin (|-^**3- t + 92°), origin at 1818; Equation to the cycle of growth, : y = .05 sin (2- ^'^ <+ 137° 57'), origin at 1818. raately 7.3 years has been continuous since 1817. By an odd coincidence Sauerbeck's index numbers of gen- eral prices in England begin just one year later, in 1818. In the analysis of the Sauerbeck numbers we found that the eight-year cycle was the mean of two cycles, one of about 8.7 and the other of about 7.38 years. In Figure 22 the smooth graph records the 7.38-year cycle in Sauerbeck's index numbers, and the dashed graph,' ^ The data to which the cycle was fitted covered the 88 years from 1818 to 1905 and were taken from Professor Douglass' work, p 113. 80 Generating Economic Cycles the Douglass 7.3-year cycle in the Arizona pines. The two graphs, considering the errors in the estimated lengths of the cycles, are practically congruent, and from 1867 to 1910 the Douglass 7.3-year cycles in tree growth at Flagstaff run well with the eight-year cycles in the rainfall at Prescott. The close relation between meteorological cycles and crop cycles is infonningly illustrated in the crops of the spring-wheat area in the United States. In 1916, among the states of the United States, North Dakota ranked first in the production of spring wheat, second in the production of barley, and seventh in the production of oats; and to these three crops, in 1918, seventy per cent of its crop area was devoted. The semi-arid region of the United States begins to the west of the one-hundredth meridian, and this meridian divides nearly in two the state of North Dakota. The average precipitation does not greatly exceed the minimum essential for vegetation, and, consequently, we find a close correlation between the crop yield and the rainfall of the critical months, which are May and June. The correlation coefficients ^ between the rain- fall of May and June and the yield of the crops are, for wheat, r =.66; for oats, r =.79; and for barley, r =.73. With this close relation between rainfall and crop yields established for this very important, semi-arid agricultural region, one is again led to inquire whether the rainfall itself is not subject to law.^ The rainfall ^ "Forecasting the Crops of the Dakotas," Political Science Quarterly, June, 1920, p. 219. ^ This question I have treated in a paper on "Forecasting the Crops of the Dakotas," Political Science Quarterly, June, 1920. Origin of Eight-Year Generating Cycle 81 records of North Dakota and South Dakota, for May and June, from 1882 to 1918 were searched for evidence of periodicity between the hmits of three and twelve years, and the result indicated that, if there is a real cycle of rainfall for May and June in these two repre- sentative states its most, probable value is in the neigh- borhood of eight years. When an eight-year cycle is fitted to the rainfall data, the maxima occur, approxi- mately, at 1882, 1890, 1898, 1906, 1914, and are prac- tically synchronous with the dates of the maxima of rainfall of Prescott, Arizona, the growth of pines in Arizona, and the maxmia of the international crop cycles in the United States, in the United Kingdom, and in France, The graph of the Dakota rainfall is given in Figure 23. Starting from the hypothesis that American economic activity is largely dependent in its ebb and flow upon the prosperity of the agricultural Middle West, I sought, in an early study ^ of meteorological cycles, to discover a periodicity in the rainfall of the Mississippi Valley. As the meteorological records were much longer for the Ohio Valley than for the states further west, the rainfall of the Ohio Valley was made the basis of the first ex- amination. The method employed was a test of the possible presence of cycles between the limits of three and thirty-three years, and the evidence was unmistak- able. If there is a real cycle of rainfall in the Ohio Valley its most probable length is about eight years and its maxima are approximately synchronous with the maxima of the May and June rainfall of the Dakotas, the annual rainfall of Prescott, Arizona, the growth 1 Economic Cycles: Their Law and Cause, 1914. 82 Generating Economic Cycles of pines in Arizona, and the international crop cycles to which we have so frequently referred. The graph is given in Figure 23. Monthly Rainfall in the Dakotas. m*y*nd junc ANNUAL Rainfall in the Ohio Valley Figure 23. Cycles in the rainfall of the Dakotas, of the Ohio Valley, and of Illinois. Dakota cycle: y = 3.09 + 0.45 sin (^|.^°< + 84° 39'), origin at 1882; Ohio cycle: y = 41.2 + 4.13 sin (1|A°< + 310° 41'), origin at 1839; Illinois cycle: y = 38.5 + 3.05 sin (MiL°< + 241° 52'), origin at 1870. At the time of the publication of the essay Economic Cycles, 1914, Illinois was regarded as our leading cereal-producing state, ranking first in the production of corn and second in the production of oats. Rainfall records for many stations in that state w^re available Origin of Eight-Year Generating Cycle 83 for a period of 41 years, from 1870 to 1910. The corre- lation between the rainfall in the Ohio Valley and the rainfall of Illinois was r = .60, and the eight-year cycle in the Ohio Valley rainfall was repeated in an eight-year cycle in the rainfall of Illinois. The graph is likewise given in Figure 23. In October, 1920, H. W. Clough of the United States Weather Bureau published in the Monthly Weather Review an article on ''An Approximate Seven- Year Period in Terrestrial Weather, with Solar Correlation." From this paper I make use of two facts: the first re- fers to atmospheric pressure at Toronto, in Canada, and at St. Louis, in the United States. In Mr. Clough 's paper a graph is given of atmospheric pressure at To- ronto from about 1843 to 1911, and a similar graph is given for the pressure at St. Louis from about 1874 to about 1917. An inspection of these shows (1) that for the interval covered by the two graphs, they are approx- imately congruent ; (2) that the maxima occur, approxi- mately at 1850, 1858, 1866, 1874, 1882, 1890, 1898, 1914, and are therefore synchronous with the eco- nomic and meteorological cycles already examined. The other fact that I take from Mr. Clough 's paper refers to atmospheric pressure in Europe. "Mauer {Archives des Sci. Phys. Nat., Geneva, May, 1918) called attention to a well-marked periodicity of seven to eight years in the winter pressure in Central Europe, with maxima as follows: 1818-19, 1827-28, 1835-36, 1843-44, 1850-51, 1857-58, 1865-66, 1873-74, 1881-82, 1889-90, 1897-98, 1904-05, 1912-13." If now the dates of the maxima in Mauer's European 84 Generating Economic Cycles pressures are compared with Clough's in America, it will be seen (1) that they are approximately synchro- nous; (2) that the common interval between the maxima is about eight years; (3) that they are approximately synchronous with the maxima of the crop cycles in the United States, in the United Kingdom, and in France; (4) that they are approximately synchronous with the cycles in Sauerbeck's index numbers from 1818 to 1914. The next evidence of meteorological cycles is found in an official publication by the United States Weather Bureau. In 1901 the United States took "the lead in reducing its barometric observations to a standard system." ^ The work was conducted by Professor F. H. Bigelow and included "a reexamination of the various elevations, the local and instrumental errors, the re- duction of the station pressures to a homogeneous sys- tem, and the preparation of noraial tables and charts of pressure, temperature, and vapor pressure at sea level and at the 3,500 foot and 10,000 foot planes." ^ This monumental work bears the title Report on the Barom- etry of the United States, Canada, and the West Indies, and constitutes volume II of the Report of the Chief of the United States Weather Bureau, 1900, 1901. After the completion of this Report with the reduced and standardized material, it became possible for the first time to combine the many thousands of observa- tions that had been made in the United States since the beginning, in about 1870, of the systematic work of official weather observation. The tremendous impor- ^ Prefatory note in vol. ii of Report of the Chief of the Weather Bureau, 1900, 1901. 2 Report of the Chief of the Weather Bureau, 1900-01, vol. i, p. 12. Origin of Eight-Year Generating Cycle 85 tance of this great increase in the utihzable meteoro- logical observations is shown in what is, I think, the most pregnant conclusion of Professor Bigelow's Report. I shall quote that conclusion at length and invite par- ticular attention to a few sentences which I have put in italics. The table referred to in the quotation is one in which the final mean pressures for the whole of the United States and for the several constituent large sections are presented. In detail, the barometric pres- sure series upon which the generalization was based were obtained from the following sections: North Atlantic, South Atlantic, Lake Region, Pacific, West Gulf, North Plateau, South Plateau, and from the records of these regions all combined into a general mean. The pregnant quotation is now given: " We are at once struck by the remarkable fact, which constitutes an important discovery in baro- metric science, that the secular variations of the ba- rometer from year to year are by no means acci- dental but a phenomenon of definite proportions. In looking over the tables it is seen that for certain years the barometric reading is persistently lower than the average of the series, and for certain other years it remains higher than the average. This fact is indicated, generally, by each station in the group, most conspicuously for the year 1878. The residuals of that year are persistently minus, about -0.050 inch for each station in every group for the entire United States; for the year 1883 they are as persistently plus, about +0.020 inch. This constitutes a range of 0.070 inch, and when we consider that the annual 86 Generating Economic Cycles range in the barometer, due to the change of the eun in latitude from +23° to -23°, causing the change in the seasons, the difference between winter and summer, is shown by Table 54 to be about 0.100 inch, we conclude that we are dealing with a phenome- non which at times is seven-tenths of the annual depar- ture in its intensity. The fact is that the barometric pressure is sometimes maintained higher than the average throughout the entire year over a large continental area in middle latitudes, and that it often equals at least half as much as the influences of the sun's action on the atmosphere by departing 23 degrees in latitude from the equator; in other years the pressure is kept lower than the average by a similar amount. The years of maximum pressure are 1874-75, 1882-3, 1890, 1896-7, with an interval of about 8 years between them successively; the years of minimum pressure are 1878, 1884-5, 189S, also having an interval of about 8 years. ..." " In seeking for the causes of this phenomenon, I confess that it has been difficult to assign one which is satisfactory. It cannot be a wave motion because the duration of each wave is too long to admit of anything resembling propagation. One suspects that there may be a tilting of the atmosphere from one continent to another, or from one hemisphere to the other, but when we consider the rapid mo- tion of the upper strata of the atmosphere, it does not appear how it can so far deviate from its usual paths as to leave an entire continent lower or higher than the average for so long a time. One may also suspect purely cosmical causes due to the Origin of Eight-Year Generating Cycle 87 variable solar output; indeed, these barometric vari- ations do closely follow the variations in the sun- spot frequency and the other products of the sun's variable activity. From 1873 to 1890 there is a remarkable agreement between these two classes of phenomena, hut if the pressure period is 8 years and the sunspot period 1 1 years that connection cannot he complete in its nature. It is evident that we shall be obliged to prosecute this study yet further by constructing similar barometric tables for other countries, in each hemisphere, and also that it will be well to include in our research some account of the temperature, the vapor tension, and the magnetic and electric fields of the atmosphere before attempting any further remarks on the subject. . . . " Finally, it is evident that for the United States we can now correlate the years which have similar secular variations, as 1878, 1885, and 1893, and study them clmiatologically to see if there are any marked and prevailing features which charac- terize them. It is clear that this discussion opens to us for the first time the prospect of a scientific hasis for seasonal forecasts, certainly so if it should prove to be the case that the maximum-pressure years differ distinctly from the minimum-pressure years in their seasonal character, for in the event of our happening on a maximimi year we could then pre- dict the feature due to a falling barometer, or, if we are in a minimmn year, to a rising barometer, at least for one or two years ahead." ^ 1 Report of the Chief of the WeaUier Bureau, 1900, 1901, vol. ii, pp. 1004, 1005. 88 Generating Economic Cycles Upon the preceding passages I make these notes: (1) As far back as 1901 the United States Weather Bureau isolated a cycle in the barometric pressure of the United States; (2) That cycle was an eight-year cycle which was synchronous with the cycles in economics and meteorol- ogy to which constant reference has been made in this essay ; (3) Professor Bigelow regarded the isolation of the cycle as "an important discovery in barometric science," the discussion of which ''opens to us for the first time the prospect of a scientific basis for seasonal forecasts"; (4) Professor Bigelow suspected a cosmical cause of the phenomenon, but known solar periodicities failed to satisfy the conditions: ''if the pressure period is 8 years and the sun-spot period is 11 years that connec- tion cannot be complete in its nature." What is the cosmical cause of the eight-year cycle? ^ The Cause of the Eight-Year Generating Cycle Is there a cosmical cycle of approximately eight years in length, the effects of which upon the Earth might account for the observed nieteorological cycles? Let us divide this question into two and ask (1) is there a cosmical cycle of eight years in length which is syn- chronous with the observed meteorological cycles? (2) is there reason for believing that the cosmical cycle ^This chapter was first printed in 1921. Since then I have shown that the annual rainfall in the United States as a unit, according to the records of about two hundred stations, passes through the same eight- year cycle. See the discussion in Chapter I. Origin of Eight-Year Generating Cycle 89 is accompanied with a synchronously varying force that could produce the observed meteorological cycles? The first question may be answered definitely and positively: there is a cosmical cycle of about eight years that is synchronous with the economic and me- teorological cycles the existence of which has already been estabHshed. Perhaps the best way to approach its description is to consider these facts : the maximum visibility of Venus is produced by its greatest phase, its greatest elonga- tion from the sun, and the clearness of our atmosphere, and that maximiun tends to recur at intervals of eight years, ''Venus passe tous les huit ans par ses periodes de plus grand eclat (1889-1897-1905-1913). Elle est alors si brillante qu'elle porte ombre comme un petit clair de lune, et il est facile de s'en assurer soit en se pla^ant dans une piece obscure, soit en marchant devant un mur a la campagne. On peut la distinguer en plein jour, a I'oeil nu, non seulement avant le coucher du soleil, mais a midi meme, lorsque Ton salt ou elle est. Aucune etoile ni aucune planete n'atteint un eclat comparable a celui-la." ^ Here is an eight-year cycle in which the dates of maxima are a little in advance of our economic and meteorological cycle. It is not the cycle that we want, but it is closely related to the one for which we are in search. Before passing to a detailed consideration of the Venus cycle a prejudice must be noted and, if possible, removed. In suggesting that the variability in the brilliance of Venus may have some possible relation to terrestrial affairs one is reminded at once of the 1 Camille Flanunarion, Reves eloiles, pp. 132, 133. 90 Generating Economic Cycles disdainful attitude of Laplace: ''Venus surpasse en clarte les autres planetes et les etoiles ; elle est quelque- fois si brillante, qu'on la voit en plein jour, a la vue simple. Ce phenomene, qui revient assez souvent, ne manque jamais d'exciter une vive surprise; et le vul- gaire, dans sa credule ignorance, le suppose toujours lie aux evenements contemporains les plus remar- quables." ^ Now with regard to this remark, the sub- stance of which is repeated by others in pamphlets and treatises, these comments should be made : (1) Laplace's scorn was directed towards the prog- nosticators who encouraged the belief that particular, isolated events were predictable from the aspect of Venus. (2) Until many years after the death of Laplace, economic and meteorological observations had not been carried sufficiently far to admit of the isolation of long- time cycles showing mean results which could be asso- ciated with cosmical variations. (3) Many physicists and astronomers of unques- tioned sanity and proven ability have attempted to discover the effect of Venus upon the position and fre- quency of sunspots. If that is not a visionary inquiry when Venus is nearly three times further from the Sun than it is from the Earth, the consideration of the pos- sible effects of that planet upon the weather of the Earth should not be regarded as a preposterous under- taking. Returning now to the question of the periodicity in the motion of Venus with respect to the Earth let us first recall that the relative distances of the Earth and 1 Laplace, Exposilion du systems du monde, Livre premier, chap. v. Origin of Eight-Year Generating Cycle 91 Venus from the Sun are as 1000 to 723; that the orbits of both planets are nearly circular; and that in size, Venus of all the planets most nearly approaches the Earth, its diameter being 7630 miles as compared with the 7918 miles of the Earth. Let Figure 24 represent the orbits of Venus and the Earth, the orbits being assumed, for the sake of sim- plicity, to be circles. At this stage no account is taken of the inclination of the plane of the orbit of Venus, which will be considered later on. The following simple description of when and where the two planets are in conjunction is given by R. A. Proctor in his Transits of Venus: " Imagine that a straight pointer from the Sun to Venus, extending to the Earth's orbit, Hke the line SVE, is carried round S as a central pivot by the motion of the planet Venus. Then whenever this pointer comes up to the Earth, the three bodies — Sun, Earth, and Venus — are in conjunction. Now, Venus travels with a mean motion of 96' 7".8 per day around the Sun (completing a revolution in 224.701 days), while the Earth travels with a mean motion of 59' 8".3 (completing a revolution in 365.257 days); so that in each mean solar day Venus gains, on the average, 36' 59".5 upon the Earth. This is the rate at which our imaginary pointer, starting from a position such as SVE, sweeps onwards from the advancing Earth, so as to again reach the Earth by overtaking it, just as the minute-hand of a clock, after being in conjunction with the hour-hand, passes on towards its next conjimction, with the excess of its motion over the hour-hand. We have 92 Generating Economic Cycles only, then, to ask how long it will take the pointer, with its mean daily gain of 36' 59". 5, to gain one complete circuit, to have the interval in time between successive conjunctions of the Earth and Venus — Figure 24. Illustration of the conjunctions of the Earth and Venus. in other words, there will be just as many days in this interval as the number of times 36' 59".5 is contained in 360°, or, reducing both to seconds, as 2219.5 is contained in 1,296,000. The division . . . gives us 583.9 days. " Our Venus-carried pointer thus takes 583.9 days in overtaking the Earth. This is more than a year by about 218.6 days, in which period, with her mean motion of 59' 8". 3 per day, the Earth travels round nearly 215^ degrees. Now, 216 degrees would be | of a complete circuit. We see, then, that the next conjunction-line must be set almost exactly | of the way round from SVE, or in the position SViEi; the next will have the position SV2E2 ; the third will have the position SV3E3; the fourth, the position SV4E4; and the fifth will be close up to SVE, in the position SV5E5, about 2| degrees behind SVE. Origin of Eight-Year Generating Cycle 93 '* Since the interval between isach conjunction is about a year and three-fifths, the whole time occupied before the position SV5E5 is reached by the conjunc- tion-line will be five times 1| years, or 8 years, less the short interval corresponding to the Earth's motion over the arc E5E. We see, then, how it comes to pass that an interval of eight years brings round nearly the same circumstances as at the beginning of the interval, and why, therefore, when a transit has occurred, another may occur eight years later. . . . " And now let us consider the effect of the inclina- tion of the orbit of Venus to that of the Earth, still, for the sake of simplicity, lea\'ing out of account the slight eccentricity of the orbits. "If EE', VV (Figure 25), represent the two orbits, ^ and M be the place of the Earth at the autumnal equinox, then the line EE' represents the intersection of the two orbit-planes; and if, as before, we regard the plane of the paper as containing the orbit EE', then the part V'vV of the path of Venus is to be regarded as slightly above, the part Vv'V as slightly below, the plane of the paper. Accordingly the end of the pointer which we have supposed Venus to carry round the Sun, passes above the semi- circle E'eE and below the semi-circle Ee'E'. And suppos- ing this pointer to be of the length SE, so that its end appreciably travels round Ee'E'e (except for the displacement below and above the plane of this * In the description of Figure 25 I have altered slightly Proctor's lettering so as to correspond with the use I shall make of the reasoning later on. Proctor starts with the transit of 1631 while I begin with that of 1761. 94 Generating Economic Cycles orbit), it is easy to calculate how much above or below the level Ee'E'e the end of the pointer runs. When in the direction SE or SE', of course the Venus-carried pointer has its extremity on the Earth's path; when in direction Sve or Sv'e', at right angles to EE', the end of the pointer is at its farthest from Figure 25. The transit regions (pp' and qq') in the Earth's orbit. the plane Ee'E'e. The inclination of the orbit of Venus being about 3° 23y, and the distance Se (the Earth's distance from the Sun) being about 91,430,000 miles, ^ it is easily calculated that the extremity of the pointer passes above e and below e' at a distance of about 5,409,000 miles. At any other point as P or P', the end is above or below by an amount less than 5,409,000 miles in the same degree that PM or P'M is less than eS, or e'S (PMP' being drawn square to EE')-" 1 Proctor's work, Transits of Venus, was published in 1875. Since that date the mean distance of the Earth from the Sun has been as- certained to be about 92,900,000 miles. The difference between Proc- tor's figures and the real distance affects the accuracy of his subsequent calculations. Origin of Eight-Year Generating Cycle 95 By means of this theorem Proctor computes that the length of the transit regions pp', qq' is about 3° 28'. Figure 26 will facilitate the discussion of the eight- year cycle of Venus in its relation to the Earth and the Sun. In 1761 and in 1769 there were June transits of Venus and in 1874 and 1882 there were December transits. Let us assume that at the 1761 transit the Earth and Venus stood in their orbits at the points E and V. Then according to the reasoning which has just been traversed the next inferior conjunctions of Venus and the Earth were at EiVi, E2V2, E3V3, E4V4, E0V5. The conjunction at E5V5 was just 2° 22' behind the point at which Venus and the Earth stood eight years before, and as E5 fell within the transit region there was a June transit in 1769. Now just as the fifth conjunction E5 was 2° 22' behind E, so the sixth conjunction occurred 2° 22' behind Ei; the seventh, 2° 22' behind E2; the eighth, 2° 22' behind E3; the ninth, 2° 22' behind E4; and the tenth, 2° 22' behind E5. In case of all five of the conjunction regions, there were inferior conjunctions 2° 22' behind the points of con- junction which occurred eight years previously. The sequence is followed out in Figure 26 to the 81st conjunction. If now we consider the two transit regions pp', qq', we observe that the recession of the conjunction lines at the rate of 2° 22' in eight years caused the conjunc- tions in the region VE to recede from the transit region pp', and those in the region ViEi to approach the transit region qq'. The distance of Ei from E is about 215^° and the distance of the transit region qq' from the transit region pp' is 180°. As the transit region is 96 Generating Economic Cycles itself about 3° 28', it is obvious that the distance of Ei from the transit region is about 34°; and as the conjunc- tions in the region Ei approach the transit region qq' at the rate of 2° 22' every eight years while the conjunc- tions in the region pp' recede at the rate of 2° 22' every Figure 26. The regression of the conjunction lines of Venus and the Earth. eight years, it is clear that a conjunction must occur within 17° of either the pp' or the qq' transit region every eight years. It is this eight-yearly conjunction in the neighborhood of the transit regions which is syn- chronous with the eight-yearly terrestrial phenomena that we have already described. This eight-yearly cycle is the Venus cycle for which we have been in search. Origin of Eight-Year Generating Cycle 97 Up to this point no account has been taken of the small eccentricities in the orbits of the Earth and Venus and of the unequal motions of the planets in the differ- ent parts of their orbits. The consequences of these facts are so well known that they have been calculated/ and it is sufficient for our purpose to observe that the eight-year sequence in the transit regions — the Venus cycle — still persists when the eccentricities of the orbits and the varying motions of the planets are taken into consideration. We see, therefore, that in 1761 and again in 1769 the Earth, Venus, and the Sun were in a straight line in the transit region pp' ; they were again in a straight line in 1874 and 1882 in the transit region qq'. Between the limiting dates 1761 and 1882, at intervals of approxi- mately eight years, the Earth, Venus, and the Sun, in this sequence, made their nearest approach to being in a straight line. After 1882 until the date of the next transit in 2004, the Earth, Venus and the Sun will make this maximum approach to a straight line, in this sequence, at intervals of approximately eight years. Now the longest record we have of economic cycles is given in Figure 20, which is the record of the crops in England. That invaluable sequence runs from 1760 to 1914. The maxima of the crop cycles occurred at 1762 and at intervals of eight years thereafter. The Venus cycle had maxima in June, 1761, and approximately eight years thereafter, so that at intervals of eight years before and after the dates of the last transits in December, 1874, and 1882, the maxima of the economic, meteorological, and Venus cycles were congruent. ^ Proctor, Transits oj Venus, pp. 111-118. 98 Generating Economic Cycles We come now to the second part of our question: is there reason for beUeving that the Venus cycle is accom- panied with a synchronously varying force which could produce the observed meteorological cycles? Here our point of departure is a comparatively recent discovery of great importance relating to the period of rotation of Venus upon its axis. From the observations of some faint markings sup- posedly on the surface of Venus, Domenico Cassini of Bologna in 1666-67 inferred that the period of rotation was about twenty-three hours. J. J. Cassini, in 1740, gave a more exact estimate of twenty-three hours and twenty minutes. Schroeter, in 1789, fixed the period at twenty-three hours and twenty-one minutes, and De Vico, in 1839-41, carried the spurious accuracy to twenty-three hours, twenty-one minutes, and twenty- two seconds. So the matter remained until 1890, when Schiaparelli announced his surprising discovery, Schiaparelli made the innovation of conducting his observations by day, as near to noon as possible, when Venus would be highest and its own glare reduced by the brilliant midday sky. From a long series of careful observations he concluded that the period of rotation of Venus upon its axis could be nothing like twenty- four hours, but must lie between six and nine months and very probably agreed exactly with its period of revolution around the Sun, which is, approximately, 225 days. In 1896 the question was made the subject of research by Percival Lowell with the assistance of an accom- plished staff, at his observatory in the clear air of Flag- staff, Arizona. The markings noted by Schiaparelli Origin of Eight-Year Generating Cycle 99 upon which he based his conclusions as to the long pe- riod of rotation were verified at the Lowell Observatory, and in addition new markings were discovered and pho- tographed. ''By watching them assiduously it was pos- sible to note that no change in position occurred in them, first through an interval of five hours, then through one of days, then of weeks. Care was taken to guard against illusion. It thus became evident that they bore always the same relation to the illuminated portion of the disk. This illuminated part, then, never changed. In other words, the planet turned always the same face to the Sun. The fact lay beyond a doubt, though of course not beyond a doubter." ^ Thirteen years after these first discoveries Professor Lowell re- peated, in 1909, the account of his early work and then said ''the years that have passed since these observa- tions were made have brought corroboration of them. Several observers at Flagstaff have seen and drawn them and added discoveries of their own." ^ The conclusion that the period of rotation of Venus upon its axis is the same as its period of revolution around the Sun was reached by Schiaparelli and Lowell from telescopic observations. There was, of course, the possibility, though not the probability, that both observers had been misled by visual errors. But no such deception could occur with the spectroscope, and to make sure of his ground Lowell installed at his observa- tory a spectroscopic equiqm.ent. The investigator was Dr. Slipher, the present Director of the Lowell Observa- tory. The accuracy with which Dr. Slipher could de- 1 Percival Lowell, The Evolution of World, pp. 77-79. ^ Ibid., p. 79. 100 Generating Economic Cycles termine the rotation period of a planet by means of spectrograms was tested by his spectroscopic approxi- mation of the well known periods of rotation of Mars and Jupiter. The rotation period of Mars is known to be 24^ 37"^ 23'.66. Dr. Slipher determined its period from spectrograms within an hour of the true time. The rotation period of Jupiter is 9*" 50°^.4. Dr. Slipher found the rotation period from spectrograms to be 9*^ 50*^, or within a minute of the exact tune. Wlien, in an exactly similar manner, he made his observation of Venus, the spectrograms showed that the rotation period must exceed three months, which meant that so slow a rota- tion as three months was beyond the power of Dr. Slipher's spectroscope to disclose.^ 1 Lowell, The Evolution of Worlds, pp. 83-89. The reasoning of the next chapter will show that the theory of perturbation by Venus will stand even if the period of the planet's rotation on its axis is not coincident with the period of revolution about the Sun. Nevertheless I wish to add opinions of experts confirmatory of the statement in the text: (a) "Dr. W. W. Campbell, Director of the Lick Observatory . . . states : ' We have given some attention to the spectrographic velocities of the east and west edges of the planet Venus, but we have written very little on the subject. Our results seem to point to a long period of rotation; at least several days in length and possibly a period coin- cident with the revolution period around the Sun.' " Popular Astron- omy, March, 1922, p. 139. (b) "It may be remarked that when the observations are corrected for the systematic displacements to the violet discussed above, the difference between morning and evening series, viewed in the light of the probable error of observations, is not of an order that would indicate a divergence from the assumed parallax or a rate of rotation higher than that found by Slipher." "On Systematic Displacement of Lines in Spectra of Venus." By Charles E. St. John and Seth B. Nicholson. Contribution from the Mount Wilson Observatory, No. 208, p. 9. (c) "By the use of Barnet 'Ultra Rapid' plates hypersensitised with ammonia it has been possible to photograph Venus spectra with a very narrow slit, and these are the finest plates hitherto obtained. They give no evidence of an inclination of the lines due to a rotation Origin of Eight-Year Generating Cycle 101 Lowell regarded Dr. Slipher's spectrogram report as confiiinatory of Schiaparelli's conclusion and his own that Venus rotates on its axis in the same time that it revolves around the Sun, turning always the same side to the source of light and heat. The bearing of this discovery upon the theory of the effect of Venus upon terrestrial meteorological cycles we shall approach by considering the following quota- tion from Lowell: ''That Venus turns on her axis in the same time that she revolves about the Sun, in conse- quence of which she turns always the same face to him, must cause a state of things of which we can form but faint conception, from any earthly analogy. One face baked for countless aeons, and still baking, backed by one chilled by everlasting night, while both are still surrounded by air, must produce indraughts from the cold to the hot side of tremendous power. A funnel-like rise must take place in the centre of the illuminated hemisphere, and the partial vacuum thus formed would be filled by air drawn from its periphery which, in its turn, would draw from the regions of the night side. Such winds would sweep the surface as they entered, be- coming less superficial as they advanced, and the marks of their inrush might well be discernible even at the dis- tance we are off." ^ The last part of this quotation is perhaps hyperbole. I am very far from wishing to suggest that the winds of Venus may be directly responsible for the periodicity in terrestrial weather. Our question is this : is there of the planet when the terminator is placed normal to the slit." Annual Report of the Director of Kodaikanal and Madras Observatories for 1920, p. 2. 1 The Evolution of Worlds, pp. 80-82. 102 Generating Economic Cycles reason for believing that the Venus cycle is accom- panied with a synchronously varying force which could produce the terrestrial meteorological cycles? .The con- sequence of the long rotation period of Venus with the one face always turned towards the Sun is that the planet is in a constant state of violent meteorological commotion on a vast scale; and this planet, which is about the size of the Earth, thrusts itself at intervals of eight years almost exactly in the direct path of radia- tion from the Sun to the Earth. Is it not probable that the storm-racked planet creates a disturbance in the interplanetary medium which affects the Sun's radia- tion on its way to the Earth? If that is the case, then the cause of the eight-year generating cycle is the planet Venus in its eight-yearly periodic motion with respect to the Earth and the Sun. CHAPTER V THE EIGHT-\^AR GENERATING CYCLE IN RELATION TO ITS PHYSICAL CAUSE "You ask a rational question, and answering to the Objection, I say: That although Astronomy in the courses of many ages hath made a great progress in discovering the constitution and motions of the Celestial bodies, yet is it not hitherto arrived at that height, but that very many things remain undecided, and haply many others also undiscovered." — Galileo. "Dans revolution du systeme du monde, les forces electriques et magnetiques semblent jouer un role comparable a celui de la force de gravitation." — Kr. Birkeland. The preceding chapter closed with the suggestion that the eight-yearly interposition of Venus between the Sun and the Earth may be responsible for the eight- year generating cycle. Reasons were given for assum- ing that Venus may be in a state of vast meteorologi- cal conmiotion, and the conjecture was offered that her interposition between the Sun and the Earth produces a disturbance in the interplanetary mediiun which af- fects the solar radiation on its way to the Earth. WTien this theory was first advanced a distinguished man of science wrote me that the eight-year cycles appeared to be established but the alleged cause was "hard to digest" for the reason that one could not conceive how Venus might produce the effect. The criticism recalls the attitude of Galileo when he as- 104 Generating Economic Cycles sailed the theory that the Moon might be responsible for certain terrestrial tides: "To say . . . that the motion of the Earth meeting with the motion of the Lunar Orb, the concurrence of them occasioneth the Ebbing and Flowing, is absolute vanity . . . because it is not exprest, nor seen how it should so happen. . . ." ^ The object of the present chapter is to show how Venus may produce the cyclical effect. We shall approach the explanation by considering certain im- portant recent discoveries in Solar Physics. Recent Theories of the Sun Solar Physics may be said to have had its beginning in 1610 when Gahleo's discovery of sunspots intro- duced the idea of variability in the Sun. It became a science with clear-cut aims in consequence of the per- tinacity of a German amateur, Herr Heinrich Schwabe of Dessau. Schwabe's discovery of the sunspot cycle not only has a direct bearing upon the theory of the Sun's activity, to which reference will be made later on, but falling as it does within the realm of the most exact of the sciences, its history cannot fail to give courage to economists engaged in the study of perio- dicities in notoriously inexact data. Schwabe began his work in 1826. His observatory was a small apartment at the top of his dwelling and his instruments were two small telescopes with low powers. His method of observation is described^ ^ Galileo: The Systeme of the WorW. in Four Dialogues Translation by Thomas Salisbury, pp. 421-422. 2 "Address delivered by the President, M. J. Johnson, Esq., on pre- senting the Medal of the Society to M. Schwabe." Monthly Notices of the Royal Astronomical Society, vol. xvii, pp. 126-132. Eight-Year Cycle in Relation to Physical Cause 105 by his English contemporary, Mr. Manuel Johnson, President of the Royal Astronomical Society: "His plan is to note by a number each spot in the order of its appearance, carrying on his nota- tion from the first to the last spot in each year. He reckons an isolated spot or a cluster of spots where there is no visible separation between their penum- brae, as one group. 'Hence,' he observes, 'the num- ber of spots will depend in a great measure on the excellence of the telescope; and it often happens that the clusters of many hundred, nay, of many thousand spots, will be designated by one number only, just as a single isolated spot will be. So great, however, is the Sun's tendency to present his spots in the form of clusters, that observers will in the course of a year, assuredly not find any great dif- ference between their numbers and mine.' But he particularly impresses his reader that he attaches importance not so much on the absolute number of groups, as on the ratio which obtains between them in different years." For ten years Schwabe's daily countings of the sun- spots were published annually in the Astronomische Nachrichten apparently without attracting any atten- tion. In 1838 he grouped his annual observations for the period 1826-1837 but forebore to indicate a periodicity, and his researches were still ignored by his fellow astronomers. For five more years he con- tinued to publish his records annually when in 1843 he made the announcement of periodicity in his data. 106 Generating Economic Cycles But even then his work received no recognition. Not until 1851, when Alexander Humboldt mentioned in his Cosmos the discovery by Schwabe, did the theory of periodicity in sunspots receive the attention of professional astronomers. In 1857, the Royal Astro- nomical Society made official recognition of Schwabe's heroic courage, patience, and labor by bestowing upon him its highest honor. In presenting the gold medal of the Astronomical Society to Herr Schwabe, President Johnson called attention to the discouraging atmosphere in which the discoverer entered upon his observations. The opin- ions of his predecessors who had studied the appearance of sunspots were apparently unanimous as to the law- lessness of their occurrence and as to the inutility of observing them. According to the astronomer Long, ''Solar spots observe no regularity in their shape, magnitude, number, or in the time of their appearance or continuance." Lalande corroborated this opinion, ''Les apparitions des taches du Soleil n'ont rien de regulier," and Delambre added the weight of his au- thority to the prevailing view. "II est vrai qu'elles (sunspots) sont plus curieuses que vraiment utiles." Mr. Johnson proceeded to characterize the discovery in these words : ''The result of his investigation . . . has been to establish with a degree of probability almost amounting to certainty, that the solar spots pass through the phases of maximum and minimum frequency, and vice versa, in a period not very different from ten years." "Twelve years, as I have said, he spent to satisfy him- self— six more to satisfy, and still thirteen more to Eight-Year Cycle in Relation to Physical Cause 107 convince, mankind. For thirty years never has the Sun exhibited his disk above the horizon of Dessau without being confronted by Schwabe's unperturb- able telescope, and that appears to have happened on the average about 300 days a year. So, supposing that he observed but once a day, he made 9000 observations, in the course of which he discovered about 4700 groups. This is, I beheve, an instance of devoted persistence unsurpassed in the annals of astronomy. The energy of one man has revealed a phenomenon that had eluded even the suspicion of astronomers for 200 years!" Let us for a moment look more closely into Schwabe's methods and results : (1) Length of his observations. He began his ob- servations in 1826 and announced in 1843 his discovery of a periodicit}^ of ten years. His observations of 18 years covered not quite two full periods of the phenome- non. (2) Variability of the period. At the time Schwabe's discovery received official recognition, February, 1857, his observations covered just thirty years, or, assimiing the period to be ten years, the length of three cycles. In the very act of praising his work President Johnson was prompted to say, "the exact period Schwabe does not pretend to have determined. That it is liable to perturbation is evident. During twenty-seven years of the series, the results were extremely regular; during the last three years they have shown symptoms of disturbance. The epoch of minimum which consistently with earlier indications should have happened in 1853, did not occur until 1856." (3) Other coexistent cycles. As far as I am aware he 108 Generating Economic Cycles made no attempt to establish the existence of other cycles than the one of a supposed ten-year period. (4) The cause of the cycle. The discoverer of the sunspot cycle did not advance a theory as to the cause of the cycle. For this statement we have the authority of the President of the Astronomical Society: "Schwabe has not entered into speculation as to the nature and origin of sunspots." (5) The method of measuring the length of the cycle. Schwabe was not embarrassed with three of the most difficult problems in the mathematical theory of cycles : the problem of distinguishing between real and spurious cycles ; the problem of separating compound cycles into their constituent elements ; and the problem of measur- ing the exact length of a cycle. Nevertheless "the outcome of Schwabe's work was the first step in the whole series of discoveries which have gradually built up the modern science of Solar Physics." 1 The first momentous consequence of Schwabe's discovery was the perception of an entirely new form of action by the Sun upon the Earth. Until Schwabe's time all theories of solar action proceeded upon the assumption that the Sun could affect the Earth in only three ways — through gravitation, through heat, or through light. But with the estabhshment of the cychcal variation of sunspots and with the accumula- tion of observations bearing upon the variations of the magnetic needle, it was a natural step to compare these two forms of oscillation. In 1852 Sir Edward Sabine 1 H. H. Turner, Astronomical Discovery, p. 157, also p. 176. Eight-Year Cycle in Relation to Physical Cause 109 announced the discovery of the synchronism between the sunspot cycles and the frequency of terrestrial magnetic storms. His findings were quickly confirmed by Wolf and Gautier, and subsequent observations have strengthened the theory of the essential concord- ance of the sunspot cycle and the cycles of terrestrial magnetic variations. But how can the Sun at a dis- tance of 93 millions of miles affect the state of terres- trial magnetism? The investigations which have the solution of this problem in view are among the most stimulating of contemporary inquiries and, as will appear later on, they have a direct bearing upon our meteorological problem. After one series of terrestrial phenomena had been showTi to be in direct accord with the sunspot cycle, it was inevitable that a host of alert investigators should set about discovering other agreements. For some time it had been known that the aurora bore- alis and magnetic disturbances were associated phenom- ena, and about 1819 Arago had added materially to the measured e\'idence of their relation. With Sabine's proof of the synchronism of the sunspots and magnetic storms, it was only a corollary that the aurorae should vary with the sunspot cycle. To Wolf, of Zurich, credit is usually given for the detailed proof of the coincidence. Economists are familiar with Sir William Herschel's speculation^ in 1801 on the possible relation of sun- 1 " Observations tending to investigate the Nature of the Sun, in order to find the Causes or Symptoms of its Variable Emission 110 Generating Economic Cycles spots to the crops through variations of the weather. He assumed that the variation in the number of the sunspots was probably accompanied with a varia- tion in the amount of heat received upon the Earth which would be manifested in a quickened or blighted vegetation. Indeed, he made the first attempt, as far as I am aware, to establish a relation between changes in the number of sunspots and changes in the price of wheat. Necessarily his pioneer undertaking could be only suggestive because of the lack of data, but since Schwabe's time there has been unremitting effort to show correlation between the sunspots and changes in the terrestrial weather.^ W. S. Jevons, as every economist knows, attempted to work out the Herschel theory of the synchronism of sunspots and the yield of the crops. His heroic honesty in confessing his failure in his study of Euro- pean data is not so commonly known. Assuming that the true length of the cycle in trade was eleven years — the true length of the principal sunspot cycle at the time of the publication of Jevons' essay had been shown to be approximately eleven years — Jevons arranged the prices of English crops during the 13th and 14th centuries in series of eleven years, and without making any statement as to whether the cycles of sunspots were congruent with the cycles of the crops, he advanced the theory of an eleven year cycle in the prices of farm of Light and Heat; with Remarks on the Use that may possibly be drawn from solar Observations." Philosophical Transactions of the Royal Society of London, 1801, pp. 265 to 318. Particularly pp. 313-318. 1 For a vast amount of data, see The Computer's Handbook, published by the English Meteorological Office, 1919. Eight-Year Cycle in Relation to Physical Cause 111 crops, the cause of which is connected with the cause of the eleven-year cycle of the sunspots. In a subsequent essay he published this confession : ^ "In 1875 I made a laborious reduction of the data contained in Professor Thorold Rogers' admirable History of Agriculture and Prices in England from the Year 1259. I then believed that I had discovered the solar period in the prices of corn and various agricul- tural commodities, and accordingly read a paper to that effect at the British Association at Bristol. Sub- sequent inquiry, however, seemed to show that periods of three, five, seven, nine, or even thirteen years would agree with Professor Rogers' data just as well as a period of eleven years; in disgust at this result I with- drew the paper from further publication." Influence of the New Physics In the seventies of the last century the researches of Sir William Crookes on the discharge of electricity through gases initiated a course of inquiry which has led to results that dominate both contemporary phys- ics and contemporary astronomy. By improving de- vices for exhausting the contents of discharge tubes he was able to obtain much nearer approaches to vacua than had previously been possible and he was conse- quently able to conduct, under much more favorable circumstances, experiments on the effects of electrical discharges in rarefied media. In Figure 27 there is an outline sketch of the simplest type of discharge tube. Platinum wires to conduct 1 Investigations in Currency and Finance, p. 225. 112 Generating Economic Cycles the electric current are sealed into the glass of the tube, forming electrodes at the points A and C. The end of the wire where the current enters the tube, A, is the anode, and the other end, C, where the current makes its exit is the cathode. The electrodes are usually tipped with some substance, such as alimiinium, that + r POSITIVE COLUMH WITH STRIAE 1 fARADAY DARK SPACE 1 NEGATIVE GLOW CRC DAP r OKES K CE pffiE^=^-=»^^ ^^ 1 ^ A V. J c Figure 27. A simple discharge tube. does not easily volatilize under an electric discharge. The degree of vacuum that is obtained is measured by the pressure of the gas within the tube. Under the conditions of ordinary pressure, air and other gases are among the best insulators of electricity. But when a highly rarefied gas is confined within a discharge tube and the electric tension between the electrodes is great, the gas becomes a conductor and reveals the remarkable phenomena that have led to the recent views as to the nature of electricity. If, for example, a tube with anode and cathode about twelve inches apart is filled with air at ordinary pressure, no spark will pass between the electrodes even when the tension is comparatively high. When, however, the pressure is reduced to about one millimetre of mercury, a glow appears at the two electrodes, the positive glow being greater than the glow at the Eight-Year Cycle in Relation to Physical Cause 113 cathode, and the space between the two glows remains dark. When the gas is still further rarefied the glow near the cathode begins to change, leaving a light close to the cathode, — the cathode glow — which is separated by a dark space — the Crookes' dark space — from the other part of the original cathode light which is now called the negati\'e glow. The relatively dark space between the negative glow and the glow at the anode is the Faraday dark space. The positive glow, or positive column, breaks up into a series of bright and dark striae at right angles to the line between the anode and the cathode. With still further reduction of the pressure of the gas the negative glow and the Crookes' dark space fill more and more of the tube, and the posi- tive column correspondingly decreases. Streamers of bluish light, called cathode rays, are seen to start out perpendicularly from the cathode. If the exhaustion of the gas is carried still further the Crookes' dark space apparently fills the entire tube, and the walls of the tube become fluorescent, particularly w^here the cathode rays impinge, the color of the fluorescence varying according to the composition of the glass of the tube. Crookes' researches were concerned primarily with the properties of the cathode light. The cathode rays apparently started perpendicularly from the cathode, producing fluorescence upon the walls of the tube where they impinged. His experiments led him to the con- clusion that these streamers originated on the metal surface of the negative electrode and were a new mani- festation of matter. He called it radiant matter. Many 114 Generating Economic Cycles of his critics, most of whom were scandaHzed by his postulating a new form of matter, inferred from the luminescent effect of the rays that they must be some form of wave motion in the ether analogous to ultra- violet light. The controversy as to the nature of the cathode rays lasted nearly twenty years until Sir J. J. Thomson, in 1895, following the lead of Perrin, proved that they are not ethereal waves but negatively electrified particles with definite mass. The experiments of Pro- fessor Thomson not only were conclusive with respect to the nature of the cathode rays but were suggestive of epoch-making views with regard to the theory of electricity and the constitution of the atom. The characteristics of cathode rays w^hich, for our purpose, should be specified are these: (1) Cathode rays originate at the cathode of the discharge tube and proceed in straight lines perpendicular to the cathode. The rays will take this direction, noiTnal from the cathode, no matter where the anode may be placed. (2) They light up a fluorescent screen when they fail upon it. (3) They are composed of negatively electrified particles. (4) They may be deflected from their path by a magnetic or an electrostatic field. The experunental proof is suggested by the preceding characteristics. As the cathode rays light up a fluorescent screen the deflecti- bility of the rays by a magnet or by an Eight-Year Cycle in Relation to Physical Cause 115 electrically charged body may be observed, under proper conditions, by the movement of the light upon the screen when the rays are subjected to a magnetic or an electro- static influence. The very great importance for our purpose of the magnetic and electric deflectibility of these rays will be pointed out later on. (5) They ionize gases through which they pass and consequently render the gases conductors of electricity. We have seen that cathode rays are com- posed of negatively charged particles which have recently been called electrons. The theory of ionization by the cathode rays is that the passage of the rays separates the gas into molecules which because of the acti\dty of the rays have individually gained or lost one or more electrons. These mole- cules, which in this state are known as gaseous ions, become carriers of electric current. (6) The gaseous ions produced by cathode rays may become nuclei for the condensation of water vapor. Sir J. J. Thomson's treatise was not the only piece of epoch-making research that grew out of the investigation of cathode rays. In Germany, at the University of Wiirzburg, Professor Roentgen, in 1895, was at work upon the problem of cathode rays when he made the discovery of the rays, subsequently called X-rays or Roentgen rays, which were ahnost immediately put to 116 Generating Economic Cycles spectacular as well as humane uses in the practice of medicine. The cathode rays had been observed to produce luminiscence when they impinged upon the walls of the Crookes' tube. Roentgen showed that the rays which he discovered originated at the point where the cathode rays coUided with a solid substance. Later researches showed that X-rays are produced under the best circumstances when a definite surface to receive the cathode rays — the anti-cathode — is pre- pared of polished metals. The view which is at present generally accepted as to the nature of the X-rays was first advanced by Sir George Gabriel Stokes. He suggested that they are electro-magnetic waves having their origin in the oscillation of the electrical charge upon the cathode particle when the particle is brought to a sudden stop by striking a solid substance. The principal characteristics of X-rays that we need to consider are these : (1) The X-rays originate at the spot in which cathode rays strike a solid substance. (2) They light up a fluorescent screen. (3) They are not deflected in a magnetic field. (4) They produce an ionization of gases through which they pass. (5) The gaseous ions may become nuclei for the condensation of water vapor. The cathode rays, as we have seen, are negatively charged particles moving normally from the cathode. If an obstacle, say a metal Maltese cross, is placed in the path of the cathode rays, two shadows of the cross Eight-Year Cycle in Relation to Physical Cause 117 will appear: one directly opposite the cathode on the wall of the tube and the other on the cathode itself. The shadow on the wall is explained by the intercepting of the cathode rays which would otherwise produce a fluorescence on the wall. . The shadow on the cathode is due to the intercepting of positively charged mole- cules mo\'ing in the direction of the cathode. These are the positive or anode rays: (1) The positive rays are positively charged mole- cules of the gas in the discharge tube stream- ing in the direction of the cathode. (2) They light up a fluorescent screen. (3) The size of the positively charged molecules is comparable with the size of the molecules of the gas, and they are much larger than the negatively charged particles in the cathode stream. The mass of the electrons is only about 1 /1800th of that of a hydrogen atom, while its radius is only about 1/50, 000th that of an atom. (4) The positive ra^^s are deflected both by a mag- netic and an electrostatic field. (5) They produce ionization of gases through which they pass. (6) The gaseous ions may become nuclei for the condensation of water vapor. - There is a principle in physics known as the prin- ciple of reversibility which has been the means of a number of important discoveries. If a set of forces can produce an observed change, it is in order, accord- 118 Generating Economic Cycles ing to the principle of reversibility, to inquire whether the converse relation may not hold true. If, for ex- ample, an electric current can produce a magnet, it is reasonable to suppose, as Faraday showed, that a mag- net can produce an electric current. After the observa- tion was made that cathode rays, positive rays, and Roentgen rays illuminate a fluorescent screen, the principle of reversibihty obviously suggested that those substances which make good screens may pos- sibly emit rays that are similar to the positive, cathode, and Roentgen rays. Henri Becquerel was one of the first to enter this field which has been so successfully exploited by Pro- fessor and Madame Curie and Professor Rutherford. The history of researches into radio-activity is recent and well-known. The central discovery, however, needs to be connected with what has been said about the radiations attending the discharge of electricity in rarefied gases. Three principal kinds of rays, known respectively as a-, jS-, and 7-rays, have been derived from radio-active substances, and these rays have their analogues in the radiations of the discharge tube. The a-rays are positively electrified and resemble in general characteristics the positive rays of the dis- charge tube. The jS-rays are negatively electrified and resemble cathode rays. The 7-rays resemble the Roentgen rays. These discoveries in electricity and in the nature of matter have produced a veritable renaissance in astro- nomical speculation. " La decouverte des electrons et le succes croissant dc la conception corpusculaire de Eight-Year Cycle in Relation to Physical Cause 119 I'electricite a . . . fait fairc dc grands progres k nos connaissances sur Ic Soleil ot celles-ci paraissent aujourd'hui, commc la Physique ontiere, dominees par cette nouvelle maniere d'cnvisager les phenomenes." ^ In the next section we shall give attention to some of these more recent astronomic theories in as far as they throw light upon changes in terrestrial meteo- rology which may be attributed to Venus. We shall, however, carry much more to the discussion if we bear in mind : (1) that nearly all forms of the rays we have con- sidered are electrically charged and are de- flectible by electric and magnetic fields; (2) that all of the rays produce ionization of gases; (3) that the gaseous ions may become nuclei for the condensation of water vapor. Nearly half a century ago experiments by CouUer in France (1875) and by Aitken in Great Britain (1880-1881) revealed the importance of dust particles in the formation of clouds and the precipitaion of water vapor as rain. In their experiments upon air saturated with water vapor, clouds were formed, or not formed, under the same degree of saturation, according as dust was present or absent. The dust particles sup- plied the necessary nuclei for the condensation of the vapor. The recent theory of ionization by radiation has added greatly to our knowledge of the process of cloud 1 Bosler: "Sur les relations des orages magnetiques et des phenomenes solaires." Annales de I'Observatoire d' Astronomie Physique de Paris, Tome V, 1912, p. 7. 120 Generating Economic Cycles fonnation. Nuclei are essential, but they may be sup- plied, and are supplied, not only by dust particles but by the gaseous ions that result from the action of the many kinds of rays which have already been described. Indeed the objective existence of the gaseous ions was disputed by many physicists until their reality was placed beyond doubt by experiments in which pre- cisely their capacity to act as nuclei for condensation of water vapor was employed to make their presence visible. C. T. R. Wilson, who devised the experiments, succeeded in obtaining actual photographs of rain- droplets formed about the ions along the tracks of the various types of rays discharging in vapor-saturated air. Wilson's experunents on the ionization of gases and the condensation of water vapor were reported in 1911 and 1912. It was in the line of progress from his early conclusions to turn his attention to the problem of the relation of rainfall to electrical variations in the at- mosphere. Accordingly we find this statement in the Annual Report of the University of Cambridge for 1919, in the section referring to the work of C. T. R. Wilson at the Solar Physics Observatory: ^ ''The results obtained in these investigations have suggested a theory which both accounts for many of the more important phenomena of thunderstonns, and relates them to those of fine weather atmos- pheric electricity and terrestrial magnetism." - ^Quoted by Bauer: "Some of the Chief Problems in Terrestrial Magnetism and Electricity," Proceedings in the National Academy of Sciences, 1920, vol. 6, pp. 575-576. 2 There is an ample account of Wilson's researches upon this topic in a paper, "Investigations on Lightning Discharges and on the Electric Eight-Year Cycle in Relallon to Physical Cause 121 The Role of Venus If Venus affects terrestrial weather it may obviously do so either directly through magnetic or electrostatic influence upon the Earth, or indirectly through mag- netic or electrostatic influence^ upon solar radiation on its way to the Earth. Both hypotheses imply that Venus is a seat of electrical activity. We shall first consider the evidence for this assumption. Professor Hale, a resourceful and cautious investiga- tor, has expressed the opinion "that every star, and probably every planet, is also a magnet, as the Earth has been known to be since the days of Gilbert's De Magnete," ~ and in 1921 Dr. Bauer, whose rare knowl- edge of contemporary thought is well known, has sum- marized in a sentence his view of the tendency of recent investigation: ''That there are other bonds of union than those of gravitation — electrical in their nature — between the Earth, the sister planets, and our parent Sun, by means of which cosmic forces responsible for electric and magnetic effects are conveyed, is be- coming increasingly evident." ^ These authoritative opinions would probably justify Field of Thunderstonns, " Philosophical Transactions of the Royal Society of London, Series A, vol. 221, March, 1921, pp. 73-115. 1 By the above statement I do not mean to limit to this kind of influence the possibility of disturbance by Venus. If, for example, Venus should be a source of radio-activity it could produce an effect upon the Earth directly through radiation and indirectly by altering the electric conductivity of the interplanetary medium. 2 Hale, The New Heavens, p. 70. ' Bauer, "Measures of the Electric and Magnetic Activity of the Sun and the Earth, and Interrelations," Terrestrial Magnetism and AtmoS' pheric Electricity, May and June, 1921, p. 42. 122 Generating Economic Cycles one in proceeding upon the hypothesis that Venus is a magnetic field, but it is well to add to them such direct observations as I have been able to find. The first observation relates to the significance of a disturbance in the solar corona produced by the prox- imity of Venus. As long ago as 1885 Sir William Huggins in his classical address before the Royal Society, "On the Corona of the Sun," defended the view that the corona is electrical in origin. A few years earlier, in 1881, Goldstein advanced the idea of the Sun's emitting cathode rays and even suggested that, perhaps, the key to the Sun's influence upon the electrical and magnetic phenomena of the Earth might be found in these negatively charged solar rays. The two concep- tions were combined in an account of the solar corona by Deslandres. According to his theory the character- istic features of the solar corona are explained by as- suming that the cosmical dust particles of the corona are each enveloped in a gaseous atmosphere rendered luminous by the phosphoresence produced by the cathode rays discharged from the Sun. If now there is evidence- that Venus produces a perturbation of the electrified solar corona, then the hypothesis which attributes to the planet a magnetic or electrical field becomes more worthy of being enter- tained. Sir William Huggins in the address to which reference has been made refers to the coronal per- turbation by Venus : ''Hitherto in our discussion of the forces which may be active in the corona we have taken account Eight-Year Cycle in Relation to Physical Cause 123 only of the influence of electrical changes which take place upon the Sun. Now these changes at the Sun make themselves felt upon the Earth; we may then well suppose, with a high degree of probability, that the Earth, and especially the near planets Venus and Mercury exert an influence on the electrified and attenuated matter of the corona." "We know nothing of the electric distribution on Venus and Mercury, but it seems more than probable that these bodies as well as the meteor swaims nearer the Sun have an influence in determining the mode of out- flow of the electrified coronal matter in the direction in which they happen to be. The influence may be one of attraction, giving rise to coronal extension or rays from the corona, or to repulsion, in which case we might have what appears to us a rift directed towards the body. "We have not sufficient data to furnish certain information on this point, but it may be of interest to quote the following sentence from Mr. Trouvelot's Report of the Eclipse of 1878: — 'There is a fact con- nected with this eclipse, which, if not due to a sin- gular coincidence, would seem to point to some attractive action of the planets on the solar atmos- phere (corona). On the day of the eclipse Mercury and Venus were in ahiiost opposite points of their orbits, with the Sun between them and ahnost on a line with them, while the Earth on the same day was in a part of its orbit which formed the apex of an equilateral triangle having for base the line joining Mercury and Venus. Knowing this, it is perhaps singular, and anyhow very remarkable, to see that 124 Generating Economic Cycles the eastern wing of the corona was directed on a straight Hne to Mercury, while the western ap- pendage was directed on a straight hne to Venus. The coincidence was still greater. As in regard to the Sun, the two planets were not exactly on the same line. Mercury being a httle to the North while Venus was a little to the South of the ecliptic, the solar appendages have shown the same peculiarity, their axes being a little inclined to each other. I may say that the inclination of the axes of the coronal extensions on the sides of the Sun may be seen in the photographs of the eclipse. It should be stated that Professor Newcomb, who observed the coronal extension towards Venus says, 'I tried to judge whether the western one (ray) pointed towards the planet Venus then plainly visible near the horizon. The direction was apparently very slightly below the planet.' Professor Newcomb's words seem to show that he did not make allowance for refraction, which would make the planet when near the horizon appear sensibly higher than its true place." ^ The second observation supporting the hypothesis that Venus is a magnetic field relates to the significance of the disturbance of a comet by the proximity of Venus. Here, as in the case of the solar corona, the increasing knowledge of electrical forces has supplied fruitful hypotheses where hitherto little progress had 1 The Bakerian Lecture. — "On the Corona of the Sun," by Sir WilHam Huggins, D. C. L., L. L. D., F. R. S. Proceedings of the Royal Society of London, vol. xxxix, 1885, pp. 130, 131. Eight-Year Cycle in Relation to Physical Cause 125 been made in understanding the phenomena. A corol- lary of Maxwell's electro-magnetic theory of light was that light must exert pressure. The idea was seized upon by Arrhenius as a clue to the explanation of comets' tails. He assmned that negatively charged small bodies are driven off from the Sun under the influence of light-pressure, and are electrically dis- charged in the gases surrounding the comet thereby causing the characteristic shape and glow of the comet's tail.^ Birkeland, in his theory of comets' tails, substituted cathode rays or streams of electrons for Arrhenius' negatively charged small bodies.- Deslandres, Bernard, and B osier rendered still more probable the hypothesis of the cathode rays by their spectroscopic studies of Morehouse's comet in 1908, in which they showed the resemblance of the comet's radiation to that of cathode rays in a Crookes' tube.^ 1 "Eine andere Schwierigkeit bieteii die Gase der Kometen insofern, als sie leuchten, wenn sie in einer Entfernung von der Sonne sind, wo die Temperatur nicht wohl hoher sein kann als auf dem heissesten Punkte des Mondes. Dies zeigt, dass wahrscheinlichervveise elek- trische Vorgange hier vor sich gehen. Dies kann durch die Theorie erkliirt werden, wenn man anninimt, dass von der Sonne nach alien Seiten negativ geladene kleine Korper ausgestrahlt werden. Diese treffen den Kometen und bewirken da Entladungen, welche die Gase zum Gliihen bringen. Arrhenius, Lehrbuch der Kosmischen Physik, 1903, p. 204. 2 "Arrhenius has also, as we know, maintained a similar theory, only that instead of electric corpuscle-rays of the kind here considered, he imagines rays of electrically-charged atoms, moving under the in- fluence of light-pressure." Birkeland, The Norwegian Aurora Polaris Expedition, 1902-1903, p. 631. 3 "Dans un ordre d'idees bien different, mais egalement en faveur de la theorie cathodique, on pent encore relever un fait interessant: le spectre de la queue de certaines cometes, et plus particulierement de la comete Morehouse (1908 c ), s'est montre identique a celui que 126 Generating Economic Cycles Now whether one accepts the theory of Arrhenius, or of Birkeland, or of Deslandres the tails of comets are electrical in nature and should show a distortion in the presence of a magnetic or an electric field. The follow- ing incident, therefore, has a bearing upon the hypothe- sis as to the magnetic field of Venus: In 1910 when Halley's ''comet passed near Venus . . . the tail . . . broke up, as if a result of the near approach to the planet." ^ The observations of Halley's Comet in 1910 throw light upon another aspect of our problem. Venus, according to the Director of the Lowell Observatory, seemed to break up the tail of the comet when the comet approached the planet. If now it can be shown that the comet in its approach to the Earth affected terrestrial meteorological conditions, there would seem to follow two probable conclusions: (1) that terrestrial weather is affected by the electro-magnetic condition of neighboring celestial bodies; and, (2) that Venus by in- fluencing the magnetic field between neighboring bodies and the Earth may affect the Earth's weather. Two observations will be cited. The first is from Kr. Birke- land, the Norwegian physicist: Je mentionnerai . . . quelques observations faites le printemps dernier a mon observatoire, sur le pic de Halde, pres de Bossekof, au moment du passage de la comete de Halley. On constata qu'apres de violents orages magnetiques, il certains gas presentent sous Taction du rayonnement cathodique." Bosler: "Sur les relations des orages magnetiques et des phenomenes solaires." Annales de l' Observatoire d' Astronomie Physique de Paris, 1912, pp. 8-9. 1 V. M. Slipher, "The Spectrum of Halley's Comet in 1910 as Ob- served at Lowell Observatory," Lowell Observatory Bulletin, No. 52, p. 15. Eight-Year Cycle in Relation to Physical Cause 127 pouvait produire une forte ionisation do Tatmosphere, de telle sorte que la conductibilite specifique electrique de celle-ci etait a certains moments 200 fois plus grande que la nonnale. L'atmosphere, au sommet de la montagne, avait une conductibilite telle qa'on aurait pu croire qu'il y a\'ait du radium dans la voisinage des appareils. Nous nous trouvons ici en face d'une decouverte sans doute tres importante, ear on a ainsi trouve une liaison electrique entre les phenomenes magnetiques de la terre et les phenomenes meteorologiques. L'ionisation prononcee de l'atmosphere influe en effet sur la formation des nuages et sur I'etat electrique de la terre." ' The next fact is taken from an address given in Leipzig by Augusto Rhigi, of Bologna. Referring to the work of his assistants in the observa- tions in Bologna, at the passage of Halley's comet, Rhigi says: "Die Herren, die in jener Nacht in meinem Institute Wache hielten, um die verschiedenen Mes- sungen auszufiihren, konnten ferner eine Konden- sation von Wasserdampf von ungewohnlicher Menge feststellen, die sich aus der Gegenwart vieler lonen, und besonders negativer lonen, erklaren lasst." ^ We have thus far considered the influence of Venus upon the solar corona and upon the tail of Halley's comet as tending to estabhsh the hypothesis that 1 Kr. Birkeland, "Orages magnetiques et aurores polaires," Archives des sciences physiques et naturelles de Geneve. Qua tri erne jieriode, t. xxxii — Aout, 1911. 2 Augusto Rhigi, Kometen und Elektronen, Leipzig, 1911. Akademische Verlagsgesellschaft M. B. H., p. GO, 128 Generating Economic Cycles Venus is a magnetic or an electric field. Our next piece of evidence strengthens this hypothesis and at the same time increases the probability of a direct electro-magnetic action of Venus upon the Earth. In 1911 Professor Arthur Schuster published a paper on "The Influence of Planets on the Formation of Sun-Spots." ^ Assuming that whatever planetary in- fluence might exist, Jupiter, Venus, and Mercury would be likely to be most efficient, he sought to discover whether the formation of sunspots was in any way dependent upon the position of these planets with respect to the Sun. He interpreted his results in the light of the theory of probability, seeking thereby to elmiinate chance associations. Our interest centers in this conclusion, namely, ''if we take each planet separately ... it is seen that only in the case of Venus do the numbers help to establish a real con- nection." 2 In the same year, 1911, F. J. M. Stratton, Assistant in Astrophysics, at Cambridge Observatory, dealt with the same problem in a paper "On Possible Phase-rela- tions between the Planets and Sun-spot Phenomena." ^ Using a slightly different method and confining his study to Jupiter and Venus, he reviewed the work of Professor Schuster. He reached the general conclusion "that the case for planetary effects on sun-spot phenom- ena is 'not proven' " (p. 26). But there was a notable qualification: "A careful study of the detailed figures underlying the tables in this paper leaves the author ^ Proceedings of the Royal Society of London, Series A, vol. 85, 1911, pp. 309-323. 2 Ibid., p. 317. ^ Monthly Notices of the Royal Astronomical Society, vol. 72, pp. 9-26, Eight-Year Cycle in Relation to Physical Cause 129 unable to support the theory of a real planetary effect. Only in the case of the 3 h. maximmn for Venus . . . does the mequality continue strongly throughout the series of observations " (p. 14). Resorting to the theory of probability to determine whether this apparent effect of Venus is a real effect, he concluded: "In general practice a de\dation from the mean of less than three times the standard de\'iation is regarded as ascribable to fluctuations of sampling" (p. 14). "The standard deviation for the Venus spot-birth is 9.7. A residual of 30 in the figures for 3 h. does, according to the above criterion, call for explanation. Dr. Schuster suggests a planetary effect. To the present writer the evidence seems so uncertain that he prefers to suspend judgment mitil more figures are available " (p. 15). The net result, for our purpose, of Mr. Stratton's review of Professor Schuster's work is that he finds the same formal indication of an effect on the part of Venus. Professor Schuster, reasoning from probabilities, re- gards the effect as real while Mr. Stratton, admitting the very great probability in favor of a real effect, prefers to suspend judgment until more figures are avail- able. If the Venus effect is real, then there is need of ex- plaining how it is produced. One of the theories ad- vanced by Professor Schuster is that the solar perturba- tion may be due to an electrostatic influence on the part of the planets, and he assumed that the planetary electrostatic influence would hardly diminish more rapidly than according to the inverse third power of the distance from the Sun. At this point Professor Schuster's argument respect- 130 Generating Economic Cycles ing planetary influence upon the Sun and his finding with regard to the effect produced upon the Sun by Venus touch very closely the fundamental theory that Venus exerts an electro-magnetic influence upon the Earth either directly, or indirectly, through its effect upon solar radiation on the way to the Earth. The distance of Venus from the Sun is to the distance of the Earth from the Sun as .723 to 1.000. At the time of inferior conjunction the distance, on the average, of Venus from the Sun is to its distance from the Earth as .723 is to .27". Consequently, if we assume with Professor Schuster that the electrostatic influence di- minishes with the inverse cube of the distance, then at the time of inferior conjunction, the influence of Venus upon the Earth should be nearly eighteen times as great as its influence upon the Sun. The evidence already submitted would seem to war- rant the hypothesis that Venus is a seat of a magnetic or an electric field. ^ Furthennore, Professor Schuster's argmnent that Venus may produce an electrostatic influence upon the Sun would seem to tell with even 1 Reference may be made to an undertaking to estimate the direct influence of the planets upon the declination of the magnetic needle. According to Ernst Leyst, there is a measurable influence, and one of his conclusions is that the degree of effect is dependent in each case upon the distance of the planet from the Earth and its position with resj^ect to the Earth and the Sun. "Die Erdnilhe der Planeten bewirkt also ein Anwachsen der westlichen Declination und die grossere Entfernung der Planeten von der Erde, zur Zeit der Conjunction der ausseren Planeten und der oberen Conjunction der Venus bewirkt eine Abnahme der westlichen Declination." ' ErnstLeyst: "IJber den Magnetismus der Planeten," Repertorium fur Meteorologie, Bd. xvii. No. 1, St. Petersburg, 1894, p. 20. Leyst's results have been criticised as being inconclusive. Eight-Year Cycle in Relation to Physical Cause 131 greater strength in favor of the direct action of Venus upon the atmosphere of the Earth. We shall now con- sider the possibility of an indirect effect of Venus through the perturbation of radiation from the Sun to the Earth. E\Tn before the discovery of electrons and the formulation of the corpuscular theory of electricity, the synchronism in the variations of the magnetic needle with the frequency of sunspots had caused many to hold to a direct electric or magnetic action of the Sun upon the Earth. But how could the action be achieved at the distance of ninety-three millions of miles? The mystery has not yet been cleared up, but the investigations looking to its solution, as is usual in such cases, have been most fruitful in other dis- coveries. Laboratory experiments had already established that the propagation of electrons is facilitated by ex- treme rarification of gases; that very hot bodies give off electrons ; that the electrons proceed normally from the cathode; and that the position of the anode does not affect the course of the cathode rays. It was therefore an almost obvious step to assume that the Sun, being in- tensely hot, gives off negatively charged particles that are gathered in by the planets along their respective magnetic lines of force. ^ ^ As an illustration of the hypotheses to which this fructifying con- ception led we have in compact form Sir Oliver Lodge's speculations: "The Earth is in fact a target exposed to cathode rays, or rather to electrons, emitted by a hot body, viz., the Sun. The Sun is evidently intensely radio-active; and the result of its discharge of electrons into the approximate vacuum of its immediate neighborhood is not unlikely to be the appearance known as the corona. The gradual accumulation of negative electricity by the Earth is a natural consequence of this 132 Generating Economic Cycles One of the very first to take this step was the physi- cist, Kr. Birkeland, of Christiania, whose primary objectives were the cause of magnetic storms and the origin of terrestrial magnetism. Holding as a working hypothesis that magnetic storms are probably traceable to solar bombardment by means of electric corpuscles, he laid the foundation of his work in an elaborate collection of observations relating to the aurora borealis and simultaneous variations in the magnetic needle. By a very rare combination of experimental ingenuity and speculative fertility he extended his electrical theory of cosmical phenomena to the solar corona, the zodiacal light, comets' tails, and Saturn's rings. To throw new light upon his theories he spent a fortune in building observatories in the far north, equipping sail- ing vessels, and organizing scientific expeditions in which he personally suffered the contrasting hardships and dangers of life within the arctic circle and within the tropics, in the Soudan. Whatever may be the even- tual estimate of his theories, his collection of material^ electron bombardment extending to greater distances across space, where no residual matter exists; and the fact that the torrent of particles constitutes an electric current of fair strength gives an easy explanation of one class of electric storms; these storms having long been known, by the method of concomitant variations, to be connected with sun- spots and aurorae. The electric nuclei, when they form ions, would also serve as centers of condensation of atmospheric water vapour at high altitudes, and so be liable to affect the rainfall. Moreover, the fact that water vapour condenses more readily on negative than on posi- tive ions, seems to furnish us with one explanation of atmospheric electricity; for a fall of rain would bring down with it a negative charge, and would leave the upper regions positively electrified with respect to the Earth's surface: and this agrees with the known sign of the normal field of electric force in the atmosphere." Lodge, Electrons or the Nature and Properties of Negative Electricity, pp. 168-169. 1 The Norwegian Aurora Polaris Expedition, 1902-1903. Eight-Year Cycle in Relation to Physical Cause 133 will be of incalculable value in the solution of the problems that interested him, and the contemplation of his courage in thought and expression and his de- votion to science will always produce an emotional elevation. In the theories of Birkeland cathode rays, or /5-rays, play an unportant role. It is to these negative particles which are shot off by the Sun and gathered in by the Earth along its magnetic lines of force that he attrib- uted the aurora borealis and the simultaneous varia- tions in the magnetic needle. For a while Birkeland 's theory stood a chance of wide acceptance, but doubt was created by the dissent of his pupil Vegard and his mathe- matical colleague Carl Stormer both of whom had at first accepted his explanations but later attributed the phenomena to a-particles. He was fortunate, however, in the character of the men who opposed him, and in view of what has just been said about Birkeland 's personality, his love for science and his unswerving fidelity in its pursuit, one cannot fail to have a lively satisfaction in the most recent utterance of his critics. Both Vegard and Stormer have modified their dissent- ing views and have taken a position much nearer Birkeland's original hypothesis: "Dans son dernier ouvrage publie pendant la re- daction definitive du present memoire, M. Vegard a abandonne sa theorie, que les aurores sont causees par des rayons a; en effet, en etudiant la distribution de la lumiere le long des rayons auroraux, il arrive a la con- clusion que cette distribution ne pent pas etre explique par sa theorie; il faut supposer que I'aurore est causee par des rayons cathodiques, des rayons |3 ou bien 134 Generating Economic Cycles par des rayons positifs tres deviables par le ma- gnetisme." ^ Vegard then, according to Stormer, not only abandons his own view but leans toward the Birkeland theory which attributes the phenomena to the negatively charged rays. As for himself, Stormer says: "De la discussion . . . dans le Terrestrial Magne- tism, je tirai ... la conclusion suivante: * il semble comma demontre que I'aurore etait due a des cor- puscles charges d'electricite positive.' MM. Kr. Birkeland et Vegard ont critique cette conclusion, et le plus prudent sera probablement de ne pas pren- dre une resolution definitive avant d 'avoir a dis- position une serie de pareilles observations. En effet, on ne sait pas encore le role exact joue dans un pareil phenomene par des courants terrestres ou par des courants corpusculaires en dehors de I'atmo- sphere." ^ But we have seen that whether the rays be negative or positive, a-rays or jS-rays, they are deflectible by either an electrostatic or a magnetic field. Further- more, as we have learned, C. T. R. Wilson has proved experimentally that the gaseous ions produced by ioniz- ing radiation may become nuclei for the condensation of water vapor and has suggested that important phe- nomena of thunderstorms may be related to variations ^ Carl Stormer, Rapport sur une expedition d'aurores boreales a Bossekop et Store Korsnes pendant le printemps de I'annee 1913. Kristiania, 1921, p. 158. 2 lUd., p. 64. Eight-Year Cycle in Relation to Physical Cause 135 in atmospheric electricity. Birkeland also, as I have remarked in the account of Halley's comet, attempted to connect meteorological phenomena with variations in the supply of ionizing cathode rays. It would seem ob\aous, therefore, that if Venus is the source either of a magnetic or an electrostatic field, its approach to, and recession from, the line of radiation from the Sun t6 the Earth and its interposition in the direct line of radiation must produce disturbances in terrestrial meteorology. If that be true, then, since the conjunc- tions of the Sun, Venus, and the Earth are periodically reproduced, meteorological disturbances should tend to show the same recurrent cycles. The reasons for assuming that Venus may be the seat of a magnetic field have already been given. Likewise the proofs of the defiectibility of the ionizing rays have been reported. Supposing that Venus carries a mag- netic field comparable in intensity with that of the Earth, what ground is there for believing that the trajectories of the corpuscles shot from the Sun would be so altered by the magnetic field of Venus as to affect materially the electric phenomena of the Earth? For- tunately we have the very best authority for making a positive statement. After Birkeland advanced his hypothesis that the aurora borealis is due to cathode rays emanating from the Sun and taking a course in the Earth's atmosphere that is determined by terrestrial magnetic lines of force, Stormer undertook to subject the theory to a mathe- matical treatment. His primary problem was to devise mathematical ways of computing the probable trajec- tories of the electric corpuscles starting from the Sun 136 Generating Economic Cycles and approaching the magnetic field of the Earth. It can readily be understood that the mathematical prob- lem was difficult to formulate and the arithmetical computations were extremely laborious. As is usual in complicated mathematical problems, Stormer was compelled to proceed by first simplifying his hy- pothesis and then adding, one by one, the actual com- plicating circumstances. His first assumption ignored the perturbations due to the magnetic fields of the inner planets Mercury and Venus, which perturbations would of course vary not only with the strength of the respec- tive magnetic fields of the planets, but also with their relative positions and velocities with respect to the Sun and the Earth. From^ the nature of his equations Stormer came to a conclusion of critical importance in the theory of the influence of Venus upon the radiation of the Sun to the Earth: ''The trajectories . . . give a good idea of what enoniious perturbations the planets Mercury and Venus will have on the movement of the electric corpuscles from the Sun to the Earth, if these planets are surrounded by a magnetic field of about the same strength as the magnetic field of the Earth." ^ Thus far the argument has tended to show reason for believing the periodic configurations of the Sun, Venus, and the Earth to be a periodic source of terres- trial meteorological cycles. The criticism may be made with some fairness that if such an effect exists it should have been observed by scientists long ago. The reply to the criticism would take this form : 1 Carl Stormer: "On the trajectories of electric corpuscles in space under the influence of terrestrial magnetism, applied to the aurora borealis and to magnetic disturbances." Archiv for Mathematik og Naturvidenskab, B. XXVIII, nr. 2, p. 35. Eight-Year Cycle in Relation to Physical Cause 137 (1) The significance of the newer theories of electric- ity as a means of explaining the mode of action of the Sun upon the Earth is only be- ginning to be realized. As an indication of progress I should note, in addition to what has already been said, the new view as to the nature of the inter- planetary medium. In 1896 when J. J, Thomson and Roentgen were extending the researches of Crookes, Schuster raised the important question as to whether the inter- planetary medium could transmit an electric current : ''Speculative theories on the magnetic and electric relationship between the Sun and Earth lack all solid basis until we can give an answer to the question, whether inter- planetary space is to be considered an elec- tric conductor or not." ^ A quarter of a century later, in 1921, Dr. Bauer could make this reply: " . . . the evidences are getting stronger and stronger that interplanetary space, as the result of solar radiations and emanations, may indeed be an electric conductor, the possibility of which Schuster suggested." ^ (2) Even now there is no adequate provision for the observations of the essential phenomena. 1 Terrestrial Magnetism, vol. 1, 1896. Quoted jjy Dr. Bauer: "Meas- ures of the Electric and Magnetic Activity of the Sun and the Earth, and Interrelations." Terrestrial Magnetism, March and June, 1921, p. 37. - Bauer, Ibid., p. 38. 138 Generating Economic Cycles For example, it seems almost incredible that there should be no wide systematic observation of such an important known electrical effect as earth-currents. "As far as known, there has been but one observ- atory in recent years where systematic earth-current observations have been made, namely, at the Observatio del Ebro, Tortosa, Spain, where a very valuable series has been obtained from 1910-1920." Dr. Bauer, from whom this quotation is made, was compelled to add, "unfortunately the series was interrupted on January 1, 1921, because of defective earth-plates; it is much hoped that the defects will soon be remedied and the series continued." ^ (3) The subject has been placed under a kind of scientific taboo. It has been regarded as the special domain of charlatans and as- trologers. The biographer of Sir Isaac Newton, Sir David Brewster, illustrates the complacent assurance, if not the arrogance, of an influen- tial school of writers. Kepler had said, "I have seen the state of the atmosphere ahnost uniformly disturbed as often as the planets are in conjunction, and in the other con- figurations so celebrated among astrologers. ^ Bauer: "Some Results of Recent Earth-Current Observations and Relations with Solar Activity, Terrestrial Magnetism, and At- mospheric Electricity." Terrestrial Magnetism and Atmospheric Electricity, March and June, 1922, p. 2 and p. 2 note 3. Eight-Year Cycle in Relation to Physical Cause 139 I have noticed its tranquil state either when there are none or few such aspects, or when they are transitory and of short duration.'' The comment by Brewster, who died in 1868, mirrored the view of his contemporaries: "Had Kepler been able to examine these hasty and erroneous deductions by long-con- tinued observation, he would soon have found that the coincidence which he did observe was merely accidental, and he would have cheerfully acknowledged it. Speculations of this kind, however, are from their very nature, less subject to a rigorous scrutinj^; and a long series of observations is necessary either to establish or to overturn them. The industry of modern observers has now sup- plied the defect, and there is no point in science more certain than that the Sun, Moon, and planets do not exercise any in- fluence on the general state of our atmos- phere." ^ (4) At least one competent astronomer has had the courage to enter the field, and in a singular manner his results bear out the thesis of this chapter as to the influence of Venus. In July, 1922, a friendly astronomer gave me the following reference, A. Nodon : Essai d'Astrometeorologie, and I received from France a copy of the work in October, 1922. There is a Preface by M. G. Bigourdan, ^ Sir David Brewster, Martyrs of Science, pp. 241-242. 140 Generating Economic Cycles Membre de 1' Institut et du Bureau de Longi- tudes, in whicli he says ''Get essai d^Astrome- teorologie, et de ses applications a la prevision du temps, interessera done tous ceux qui, de pres ou de loin, s'occupent de Meteorolo- gie. II peut meme presenter une veritable valeur pratique, et constituer une concep- tion feconde pour I'avenir. Aussi TAuteur merite de vifs remerciments pour ses perseve- rantes recherches, qui doivent apporter a la Meteorologie une aide efficace." ^ The extremely important quotation that I am about to make is a summary of his results, and its singularity consists not only in its neat confirmation of what has been said as to the influence of Venus, but in these facts — that of all the planets he considered, Venus alone 1 M. Nodon's professional accomplishments and associations are indicated in the title-page description of his work: Essai D'Astrometeorologie et ses applications a la prevision du temps par Albert Nodon Officier de I'lnstruction publique Docteur es Sciences Ingenieur-Chimiste Ex-adjoint a I'Observatoire d'Astronomie physique de Paris Membre correspondant de I'Academie royale des Sciences de Barcelone President de la Societe astronomique de Bordeaux. The book was published in 1920, in Paris, by Gauthier-Villars et Cie. Eight-Year Cycle in Relation to Physical Cause 141 should be particularly specified in his results; and of all possible configurations with respect to the Sun and the Earth, the period of approach to, and reces- sion from, conjunction should be singled out as being of most importance. "Une etude comparative des divers tableaux que nous avons precedemment passes en revue, fait apparaitre des liens etroits entre les troubles solaires, les grandes perturbations de I'atmosphere, les troubles electriques et magnetiques, les depressions generales, les sismes, la direction des vents, la pluie, le mauvais temps et le beau temps, dans les divers points du globe. Notre attention a ete d'autre part, attiree par les actions dependantes des positions relatives des planetes in- ferieures par rapport au Soleil, en particulier pendant les quadratures heliocentriques de la Terre et de Venus. Ces actions paraissent etre accrues pendant les epoques de syzygies." "Bref, il semble exister une etrange concordance entre la resultante des quadratures heliocentrique 6 9 , le nombre des centres actifs du soleil, les cyclones, les ondes de depression et les sismes! Cette concordance est-elle fortuite, ou bien resulte-t-elle de cause a effet?" ^ ' Nodon: Essai D' Astrometeorologie, pp. 57, 172. BOSTON UNIVERSITY 1 17n DlSbS TEb3 Do not remove charge slip from this pocket if slip is lost please return book directly to a circulation staff member. FREDERICK S. PARDEE MANAGEMENT LIBRARY BOSTON UNIVERSITY LIBRARIES 595 COMMONWEALTH AVENUE BOSTON, .\L\ 02215