of the sample increases, that is, as the number of independent observations upon the duration of business cycles becomes greater.

The regularity which emerges, consists, not in the preponderance of cycles of any given duration, but in the way in which cycles of different durations group themselves about their central tendency. The distribution is of a type found in many studies of biological and social phenomena. It is not symmetrical, but skewed positively. In all the groups into which we have divided the observations for analysis, the range runs farther above than below the arithmetic mean, and in two-thirds of the groups the crude mode is less than the arithmetic mean.

4. American cycles have a shorter average duration than those of any other country studied. The averages of 32 American and of 134 foreign measurements are 4.0 and 5.4 years respectively. The shortest average duration found in any foreign country is 4.3 years in Japan, where 7 cycles occurred in approximately the period covered by 10 American cycles. The American distribution shows a pronounced mode at 3 years; the most inclusive of the foreign distributions shows a rounded top with equal numbers of cases at 3 and 4 years, and no marked decline in numbers before 8 years.

The peculiarity of the American cycles cannot be due to the "newness" of the country; for Canadian, Australian, and South African cycles conform more closely to the European type. Nor have we reason to believe that in our American sources the standard of business reports concerning recessions is peculiar. Certainly the differences between the duration of American and English cycles shown by our annals since the 1870's are matched by corresponding differences between the American and English indexes of business activity, shown for these years in an earlier section. Our confidence in the American measurements is further confirmed by the fact that several statisticians, dealing with various time series, have called attention to the prominence of a 40-month cycle in American business fluctuations. While the annals support this statistical finding on the basis of descriptive materials, they start a new problem by indicating that the predominance of 3-year cycles in recent years has been confined to the United States.1

5. While our frequency distributions lack the symmetry of the

'Table 3 shows that France had a remarkable run of 3-year cycles in 1854-1876. Since the latter date, however, we find that in France only 1 cycle out of 7 has been so brief.

Gaussian normal curve, their form suggests fitting "a logarithmic normal curve; that is a Gaussian curve in which the successive units (standard deviations) of the horizontal scale are readjusted to distances having a constant ratio rather than a constant difference." 1 This experiment has been tried upon Figure R of Chart 4-the distriCHART V. Logarithmic Normal Curve Fitted by Davies' Method to the Frequency Distribution of 166 Observations upon the Duration of Business Cycles.

bution which includes all of our 166 observations. Chart V shows that the fit of the logarithmic normal curve to the data is on the whole rather close.2

From this fact we infer that, like other biological and social phenomena whose distributions are well described by some form of the

'See George R. Davies, "The Logarithmic Curve of Distribution," Journal of the American Statistical Association, December, 1925, vol. xx, pp. 467-480. Dr. Thorp has adopted Professor Davies' method in making the chart which follows.

"When the cycles now running in our 17 countries are ended, the new batch of observations promises to modify the distribution of Chart V somewhat. Five years have already elapsed since the latest recession in three of our countries, and six years in seven countries.

normal curve, the durations of business cycles may be regarded as the net resultants of a multitude of factors which are largely independent of each other. If there is any dominant factor or set of factors, which tends to produce cycles of uniform duration, its influence is greatly modified by a host of other factors combined in ways which vary endlessly. This conclusion has an important bearing upon the theory of business cycles and the methods by which that theory may be improved.

6. Regarding the relative duration of the several phases which make up business cycles, the annals yield certain fragmentary, but significant, results.

As we interpret them, the phases of recession and revival are relatively brief. Put together, they account for only one-quarter of the duration of business cycles on the average. Of the remaining three-quarters, the prosperous phase occupies a somewhat longer time than the phase of depression. But the ratio of months of prosperity to months of depression varies widely from country to country, and within any country it varies widely from cycle to cycle. Consequently, the average ratios approach stability only when long periods of time and many countries are included. Perhaps the most significant figures are those for the United States and England in 1790-1925, and for all our 17 countries in 1890-1913. These three results come out respectively 1.50, 1.11 and 1.08 years of prosperity per year of depression.

Both the English and the American records indicate that the relative duration of the prosperous and depressed phases of business cycles is dominated by the secular trend of wholesale prices. In the three periods of rising price trends since 1790, the prosperous phases of the cycles have been prolonged and the depressed phases have been relatively brief. In the three periods of declining price trends, the prosperous phases of the cycles have been relatively brief and the depressed phases prolonged. While the observations upon which these conclusions rest are subject to a margin of uncertainty in every cycle considered, random errors could hardly produce such uniform results as we find.

Finally, it appears that the depressed phases of business cycles are susceptible of greater prolongation than the prosperous phases. Whereas our averages including many cycles all show a slight preponderance of years of prosperity over years of depression, our long

cycles as a group show a marked preponderance of years of depression over years of prosperity.

In weighing the conclusions drawn in this section, one should bear in mind certain features of the data and methods used.

No selection or "adjustment" has been practiced upon the observations. The "abnormal cases"-if that phrase has an intelligible meaning are included with the "normal". Every reader of the annals will note how frequently foreign wars and domestic turmoil, harvest fluctuations, epidemics, floods and earthquakes have checked or reënforced the tides of business activity. A tendency toward alternations of prosperity and depression must have considerable constancy and energy to stamp its pattern upon economic history in a world where other factors of most unequal power are constantly present, and where one or other of these factors, singly or in combination, rises to dominance at irregular intervals.

Our measurements are based solely upon the intervals between recessions. It would be desirable to check the results by a second set, based on the intervals between revivals. We have not attempted such a check, because business commentators have paid less attention to the upward than to the downward turning points of business cycles. The materials for making the second set of measurements are less full and reliable than the materials we have exploited. If a second set as satisfactory as the first could be made, the frequency distributions it yielded would doubtless differ in numberless details from the frequency distributions here presented. But we have no reason to believe that the broad conclusions suggested by the new frequency distributions would run counter to the conclusions we have drawn.

The year is too large a unit for measuring business cycles. Our results have the crudity of an effort to ascertain the stature distribution of men, women and children from measurements made in feet. In statistical work with time series, it is often possible to substitute the more appropriate unit of a month. But such investigations of business fluctuations are confined to those narrow limits of time, place, and type of business for which elaborate numerical data have been collected. In a problem which requires a considerable array of cases to yield significant results, the cruder but more numerous measures afforded by business annals have their advantages. And the preceding comparison between the business annals and the business indexes for the United States and England favor the view that the results to

which the annals point would be supported by statistical analysis, did the numerical data cover a longer period.

VI. International Relationships Among Business Cycles.

1. OTHER PROBLEMS UPON WHICH THE ANNALS THROW LIGHT.

Despite their brevity, the running accounts found in the following chapters on business conditions in various countries can be made to throw light upon many aspects of business cycles besides their duration. For example, variations in the intensity of different periods of prosperity and depression, in the severity of successive recessions, and in the character of successive revivals are here revealed, though they are not expressed in quantitative terms. The relations between the intensity of business fluctuations and their duration also appear, as well as the relations between intensity in one phase of a cycle and intensity in succeeding phases. So, too, the annals afford many insights into the complexities of business expansion and contraction. Often they show what branches of trade led a certain movement and what branches lagged behind, what parts of a country benefited or suffered most in a given cycle. The exceedingly mixed relations between business conditions and agricultural fortunes receive much attention. In one sense every cycle is a unique historical episode; the annals bring out many of the idiosyncrasies of particular cases, as well as the features which recur in case after case.

All these are matters which one will notice upon casual reading, but about which one can learn much more by systematic comparisons of the annals for different countries and different times. In the treatise upon Business Cycles, which the National Bureau has under way, we plan to make continual use of this collection, which, as said at the outset, covers a period longer and an area wider than we can cover, save in the most fragmentary way, in our collection of statistical data.

The present introduction, then, falls far short of developing the full significance of the materials contained in later chapters. But there is one more problem which must be discussed, both because of its relation to the duration of business cycles, and because of its large significance.