tical workers yielded to the lure of "normality." They were eager to establish the "periodicity of crises," which was suggested by such crisis dates as 1815, 1825, 1836, 1847, 1857 and 1866. This desire warped their selection and treatment of data. Jevons had an admirably candid mind; yet in 1875, when the sun-spot cycle was supposed to last 11.1 years, he was able to get from Thorold Rogers' History of Agriculture and Prices in England a period of 11 years in price fluctuations, and when the sun-spot cycle was revised to 10.45 years he was able to make the average interval between English crises 10.466 years.1 To get this later result, Jevons purposely left out from his list of crises "a great commercial collapse in 1810-11 (which will not fit into the decennial series)"; he also omitted the crisis of 1873, and inserted a crisis in 1878, which other writers do not find.2

Jevons' way of reckoning the length of cycles by the intervals between crises, and of counting as crises periods of financial strain coming after booms, or recessions followed by long depressions, is still common among theoretical writers. The results they get are not in close agreement. Tugan-Baranovski takes 7 to 11 years as the limits of variation in the length of cycles and 10 years as the average duration. Bouniatian says that “under normal conditions" cycles last from 9 to 11 years, but adds that there is "a tendency toward a normal period of about 10 years". Cassel takes 1873, 1882, 1890, 1900, and 1907 as crisis years in Europe, and 1873, 1882, 1893, 1903, and 1907 as crisis years in the United States. Cassel himself strikes no average, but his dates give limits of 4 to 11 years and an average of 812 years. Lavington also accepts 8 years as the average duration.

Slightly different is the method of reckoning cycles by the intervals between depressions. Otto C. Lightner records 18 depressions in American business from 1808 to 1921, not counting "minor" cases, with intervals ranging from 3 to 12 years and averaging 6 years. George H. Hull, denying that depressions are periodic, counts 17 "industrial crises" in the United States from 1814 to 1907. His dates differ somewhat from Lightner's, having intervals ranging from 1 to 11 years, and averaging a little less than 6 years.

'Jevons withdrew his first paper from publication when he discovered "that periods of 3, 5, 7, 9, or even 13 years would agree with Professor Rogers' data just as well as a period of 11 years." See his Investigations in Currency and Finance, London, 1884, pp. 207, 225.

See the three papers on crises reprinted in Jevons' Investigations in Currency and Finance, especially pp. 200-203, 225, 233.

With these results may be given two others of the same order of magnitude, but reached by quite different methods. Pigou, using British unemployment returns and measuring intervals between both the crests and the troughs of the industrial waves, gets a trifle less than 8 years as his average length. Henry L. Moore also gets 8 years as the standard length both of "generating" and of "derived economic cycles", but gets it from periodigram analysis of time-series.1

Other statistical workers have recently reached quite different conclusions. Thus Professor W. L. Crum made a periodigram analysis of monthly interest rates upon commercial paper in New York from 1866 to 1922 and found (somewhat doubtful) evidence of a period of 39-40 months in their fluctuations. At the same time Mr. Joseph Kitchin, after analyzing bank clearings, interest rates, and wholesale prices in Great Britain and the United States from 1890 to 1922, suggested that the cyclical fluctuations of trade are composed of minor cycles averaging 40 months in length, and major cycles, which are aggregates of two or less often, of three minor cycles. Since the publication of these two papers in January, 1923, "the 40-month cycle" has enjoyed a considerable vogue among statisticians.

2. MEASUREMENTS BASED UPON THE ANNALS.

It is not necessary to examine narrowly the discrepancies among the results obtained by measuring the intervals between years of crisis or years of depression. They run back partly to differences in the countries and the periods covered, and partly to differences of opinion concerning the severity which entitles a particular disturbance to be called a true crisis or depression. Granted each author his own conception of what constitutes a cycle, his measurements are presumably correct for the land and period covered. By using the present annals, anyone so disposed might validate, and anyone so disposed might question any of the averages and limits of variations which have been derived in this way.

'See M. Tugan-Baranovski, Les Crises Industrielles en Angleterre, 1913, pp. 247, 248; M. Bouniatian, Les Crises Économiques, 1922, p. 42; G. Cassel, The Theory of Social Economy, 1924, p. 508; A. Aftalion, Les Crises Périodiques de Surproduction, 1913, vol. i, pp. 8-14; F. Lavington, The Trade Cycle, 1922, p. 14; O. C. Lightner, History of Business Depressions, 1922, table of contents; G. H. Hull, Industrial Depressions, 1911, pp. 54-57, and the chronological table, pp. 50, 51; A. C. Pigou, The Economics of Welfare, 1920, p. 804; Henry L. Moore, Generating Economic Cycles, 1923, pp. 15, 64.

See W. L. Crum, "Cycles of Rates on Commercial Paper," Review of Economic Statistics, January, 1923, preliminary vol. v, pp. 17-28; Joseph Kitchin, "Cycles and Trends in Economic Factors," the same, pp. 10-16.

But anyone who reads the annals closely, whatever the definition of crisis in his mind, will see that there is grave question regarding the unity of many of the 6-, or 8-, or 10-year cycles. Take as the simplest example Professor Cassel's list of crisis years in the United States: 1873, 1882, 1893, 1903 and 1907. One may argue that the annals justify these dates from Cassel's viewpoint. But the important point is that the cycle from 1882 to 1893 was punctuated by the recessions of 1888 and 1890, and that the cycle from 1893 to 1903 was punctuated by recessions both in 1896 and in 1900.

Now, the differences of opinion concerning the length of American cycles in this period turn less on the facts of business expansion and contraction than on what movements of expansion and contraction should be selected for treatment as business cycles. The older writers fastened upon the salient phenomena-severe crises and the rather long intervals between them-as requiring explanation. This tradition still rules in theoretical treatises. But as knowledge of business cycles grows, and as men seek to use this knowledge more effectively in interpreting current developments month by month, a more intensive treatment becomes both feasible and useful. Without denying the graver importance of the wider swings, we find ourselves involved much of the time in dealing with fluctuations of less amplitude, fluctuations which the theorists have passed over lightly. The same developments which make it wise to substitute the concept of recession for the concept of crisis make it wise to recognize the shorter segments into which the long swings are frequently divisible. This change reduces the typical duration of American cycles to roughly one-half of the estimate commonest among theoretical writers.

By way of illustration, we may compile from the American annals a list of recessions in the United States since 1790. In this list the recessions are characterized by phrases which indicate their severity, and leading features. Financial troubles occurring in the middle of depressions are not counted as recessions, but cases of this sort which have commonly been listed as crises are noted in the table. In the early years the business fortunes of the northern states alone are followed; sometimes conditions were quite different in the agricultural south and west. Since the annals seldom permit a precise dating,

Other cases of financial troubles while business was depressed occurred in 1797, 1819, 1842, and 1914.

of recessions, the duration of successive cycles is reckoned to the nearest whole year.

TABLE 1

BUSINESS RECESSIONS IN THE UNITED STATES AND APPROXIMATE DURATION OF BUSINESS

*The dates thus marked show the commonly accepted years of financial crises. Other dates frequently listed are 1819, a case of financial strain in a business depression, and 1890. The "rich man's panic" of 1903 is omitted in some lists.

To show the usual way of reckoning the length of cycles, the commonly accepted dates of crises in the United States are marked with asterisks. Anyone who checks these dates against those given in other books will find different ways of counting; for example, 18371839 is sometimes put down as a single crisis. But, taking the dates as marked, we have 14 cycles between 1796 and 1920, ranging from about 2 years (1837-39) to about 16 years (1857-1873) in length, and averaging 8 years. We can raise this average by omitting or combining some of the crises counted here, or reduce it by counting some

of the other recessions as crises. At best there is a considerable margin for admissible difference of opinion.

When we drop the effort to discriminate the degrees of severity among crises and count all recessions, this margin of uncertainty becomes narrower, though it does not vanish. It is easier to recognize a change of direction in business movements than it is to determine how serious a change for the worse has been. Yet, another compiler drawing off a list of recessions from the most detailed form of our annals might give a slightly different set of dates, and one who made a fresh set of annals from the original sources might increase these differences somewhat. The broad results, however, seem well assured.

Counting business cycles now as the intervals between recessions, noting the quarters in which the turns came, and reckoning to the nearest whole year, we get the following results:

1 cycle about 1 year long (1845-46)

In all we have 32 cycles in 127 years, which yields an average length of not quite 4 years. The commonest length is about three years; and two-thirds of the cases fall within the limits of three to five years. There is no indication that the average duration of business cycles is changing. There were 16 cycles in the first 64 years covered by the table (1796-1860) and 16 cycles in the following 63 years (18601923). Of 3-year cycles, there were five in the first period and five in the second.

These results may be compared with similar summaries from the other country for which we have annals covering 136 years. The dates given by Bouniatian, who has written a history of English crises, are starred to show the conventional view of cycle chronology. His 16 dates mark off 15 cycles in the 127 years from 1793 to 1920an average length of almost 812 years. If 1913 be added to the list