decisions can be made on a substantially consistent basis, the comparison between the relative duration of the prosperous and depressed phases of the cycles will not be compromised.' What the table indicates is that in this period of 36 years the prosperous phases averaged somewhat longer than the depressed phases.

Similar averages showing the relative duration of prosperity and depression for particular countries and periods are given in Table 7. To get comparable results it has been necessary both to take periods which comprise whole cycles, and to make these periods as nearly synchronous as may be. For the results in any one country vary considerably from one period to another. For example, the English and American averages come out in three different periods as follows:

As a guide to future expectations, the averages which include the years of the great war seem less significant than the averages which we have for longer periods of time in five countries, or than the averages for 17 countries in the period from about 1890 to 1913.

The wide differences between the averages for the countries at the bottom and the top of the list in Table 7 show how much business conditions are affected by political turmoil and stability. Brazil, China, Russia and South Africa had grave troubles in the period for which we have compiled their annals, and Austria suffered from her proximity to the Balkan volcanoes. The other figures speak for themselves. But we should remember that the figures for each country speak that country's language. Swedish prosperity may differ from Canadian prosperity-the comparison made is between the prosperous and the depressed phases of Swedish cycles in one case, and between the prosperous and the depressed phases of Canadian cycles in the other case. It is risky to say that one of these countries has been more prosperous than the other, even in the period here covered. And it is easy to conceive that any country might change its ranking in such a list radically within a decade or two.

'Chart VI, below, shows for every cycle the quarters and years which Dr. Thorp has taken as marking off revival and recession.

TABLE 7

RELATIVE DURATION OF THE PROSPEROUS AND DEPRESSED PHASES IN THE BUSINESS CYCLES OF SEVENTEEN COUNTRIES DURING VARIOUS PERIODS

One of the main reasons why these ratios of years of prosperity to years of depression are unstable is revealed by a further analysis of the long records for England and the United States. From various index numbers of prices, it is known that the long-period trend of the wholesale price level changed direction four times in the 130 years, 1790 to 1920. The turning points came at nearly the same dates in this country and England, save that our greenback prices reached their highest point just before the end of the Civil War in 1865, whereas in gold-standard nations prices continued to rise until

1873. Thus we have in both countries five periods of alternately declining and advancing price trends. From 1790 to 1814 wholesale prices rose unsteadily; from 1814 to 1849 wholesale prices declined unsteadily; from 1849 to 1865 in the United States and to 1873 in England wholesale prices rose unsteadily; from 1865 in the United States and 1873 in England prices declined unsteadily until 1896; from 1896 to 1920 they rose unsteadily. For the periods thus marked off, Dr. Thorp has obtained the following ratios of years of prosperity to years of depression:

TABLE 8

RELATIVE DURATION OF THE PROSPEROUS AND THE DEPRESSED PHASES OF BUSINESS CYCLES IN PERIODS OF RISING AND DECLINING TRENDS OF WHOLESALE PRICES: ENGLAND AND THE UNITED STATES, 1790-1925

These results are so uniform and so striking as to leave little doubt that the secular trend of the wholesale price level is a factor of great moment in determining the characteristics of business cycles. That is no novel conclusion; but Dr. Thorp's data lend it new force and precision.

A final point established by study of the relative duration of the prosperous and the depressed phases of business cycles is that the very long cycles usually owe their length primarily to prolongation of depression. Among the 166 cycles we have measured there are 17 which lasted 9 years or more. The average of all our observations, it will be remembered, is 5.2 years. Dr. Thorp has made a special examination of these long cycles to determine when the revivals occurred, and how long were the periods of declining and of increasing activity. His results appear in Table 9.

Whereas the most inclusive average in Table 7 gives a ratio of 1.14 years of prosperity per year of depression, the present table gives a ratio of 0.79. In 11 of the 17 cycles the phase of depression

is longer than the phase of prosperity. The longest period of prosperity found is 72 months; the longest periods of depression run 72, 76 and 100 months. Finally, the average phase of depression in these long cycles is nearly a year longer than the average phase of prosperity.

TABLE 9

RELATIVE DURATION OF PHASES OF DEPRESSION AND PHASES OF PROSPERITY IN BUSINESS CYCLES LASTING NINE YEARS OR MORE

1. Our measurements of the intervals between recessions do not bear precisely upon the obsolescent debate concerning the periodicity of crises. But measurements made from the annals upon the old plan would be as fatal to the hypothesis of periodicity as the measurements which we prefer. Indeed, counting from crisis to crisis would make the limits within which cycles vary even wider than does counting from recession to recession. The longest cycle shown by our annals -the Italian case of 1888-1900-would be extended from 12 to 19 years if we skipped the mild recession of 1900 and passed on to the

crisis of 1907. Perhaps still longer cycles might be found, were this method of counting systematically applied to all countries. Nor could the extension of the range in one direction be compensated by reduction at the other end of the scale. The shortest cycle could not be prolonged beyond two or three years, except by such violent procedures as telescoping the American panics of 1837 and 1839 into a single crisis.

Nor can we confirm the ingenious suggestion made by Professor H. S. Jevons and Mr. Joseph Kitchin, that long cycles are multiples of two or three short ones.1 Were such the case, and were the short cycles 3% or 32 years long as these writers suppose, one would expect our frequency diagrams to show modes, primary or secondary, at 3, 7, and 10, or 11 years. None of them do so. There are diagrams with modes, pronounced or faint, at 3 and 7 years, and 4 and 8 years. But there are also diagrams with modes, pronounced or faint, at 3 and 4 years; 3 and 5 years; 3 and 6 years; 3 and 8 years; 3, 4, 6, and 8 years; 3, 5, and 7 years; 3, 5, and 10 years; 3, 6, and 10 years; 4 and 5 years; 4 and 6 years; 5 and 7 years, etc. More significant is the fact that as the size of the samples increases the minor modes tend to disappear, instead of tending to grow clearer. In the most inclusive sample of all (Figure R of Chart IV), there are no secondary modes.

While few if any recent writers maintain the hypothesis of periodicity in any form, many of them do give some average figure to represent the duration typical of business cycles. Such averages are adequate for certain purposes. But our results show that no average can suggest the facts about the duration of cycles which are most. significant for theory and practice.

2. If there is any regularity in the sequence of cycles of different lengths, we have failed to find it. Chart III, which represents the duration of cycles taken in chronological order, shows the hazard of attempting to forecast how long the next cycle will last in any of our countries. Neither modal length, nor the duration of the preceding cycle is a safe guide.

3. A semblance of regularity does appear, however, when we disregard chronological sequence and group our observations in frequency tables. And the regularity becomes more marked as the size

'See Herbert Stanley Jevons, The Sun's Heat and Solar Activity, London, 1910, and Joseph Kitchin, "Cycles and Trends in Economic Factors," Review of Economic Statistics, January, 1923, Preliminary vol. v, pp. 10-16.