This scale is then used for determining the index figure for the current month. For January, 1914, for example, the number of immigrants was 44,700. This evidently falls between + 20 and + 30 on the January scale for immigration. 41,040 corresponds to + 20 on that scale. Subtracting from 44,700, the difference is 3,660. The last figure is then divided by 379, which is the value of each degree on the scale. The quotient, 9.6, is added to + 20, giving an index of + 29.6 for immigration in January, 1914.

An index number is similarly worked out for each of the subjects, by finding the scale figure to which the actual figure for the month of January, 1914, corresponds. Each month in each year is handled in the same way.

For business failures, surplus reserves, and idle cars, inverted scales are used, since these subjects vary inversely with business conditions. But for surplus reserves, when the figures fall below a certain point, weakness rather than strength is indicated, hence, to quote Mr. Babson again, " below $5,000,000 this subject is put upon what we call a deficit scale, declining quickly to zero as the reserves are wiped out and reading 66 for a deficit of $50,000,000, as in November, 1907." Similarly "when money rates for the best commercial paper reach about 5 per cent an average occurring only in a period of excess loans the scale figures begin to work downward again, for the lack of confidence' shown by the high rate overshadows the ' excess of business' feature shown by a majority of other subjects. On this panic scale the index moves to - 60 rapidly when rates advance from 5 per cent to 8 per cent or above." Both of these scales are purely arbitrary adjustments.

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Having found the index for each of the subjects for a certain month these figures are averaged, giving double

weight to bank clearings, domestic money rates, and the stock market index. The final figure thus obtained is the index to business conditions. Before undertaking to examine the use which is made of this summary figure, let us make a critical examination of this method of securing index numbers.

In the first place, it is evident that the index numbers are in no sense percentages. Since the lowest point is not zero, they do not show even the percentage of the range above the lowest points. The index numbers depend upon this range and upon the location of the zero point. The question of whether or not 1903-04 can fairly be assumed to have been representative of normal conditions for all of these subjects is of minor importance. The heart of the problem is the method of determinating the range upon which the scale figures are based.

The use of the range between the highest and lowest figures for each month over a ten-year period as a base for the scale figures presupposes that there were no abnormally high and no abnormally low figures in any instance. If in any month one subject showed an exceptionally high figure because of extraordinary circumstances which did not affect the other subjects and which had no influence in other months, the range was thereby made abnormally wide. The scale figures and the index numbers determined from such a range are not properly comparable with those for other subjects and for other months. The range, in other words, may be said to have been placed at the mercy of the extraordinary events during this ten-year period. As a matter of fact, a little experimenting will show that the exclusion of a single high figure, using instead the one next in order, materially modifies the scale figures for any subject.

Take the liabilities of business failures, which showed as its high point $100,045,440 in October, 1907. The greatest force of the panic was then felt by that subject. Altho in the following months failures were heavier than prior to the panic, they by no means exceeded the averages for the respective months to anything like the same degree as in October. Consequently the scale for

liabilities of business failures for October is not fairly comparable with the failures scales for the other months. Again, as has already been shown, the approach and the effects of the crisis were not felt synchronously to the same degree by all the subjects. Domestic money rates, for example, reached their highest point in December, 1907, and security prices their highest point in September, 1906. A brief examination of the statistics for the other subjects will show that there was no such correlation in their fluctuations as to warrant the use of this method of establishing a common basis of comparison or to justify the averaging of the index numbers.

The summary index figure which is obtained by averaging the index figures for the twelve subjects does not, therefore, indicate the percentage of anything, nor does it show the percentage change from month to month. It merely gives the average of the figures obtained by the use of this questionable range-scale method.

The summary figure is obtained solely for making the Composite Plot. The theory which underlies the Composite Plot is that in business, as in the physical sciences, "action and reaction" are equal and that the summary index figure for the twelve subjects measures business

1 From the explanation which has been given of the "deficit scale " used for money rates when they rise above 5 per cent, the latter figure must have been taken as the maximum in fixing the scale. If this same plan were to be commonly followed, the scales would become entirely arbitrary, depending upon the judgment of the person who made them out.

action and reaction so accurately that we can foretell the amount of depression which will compensate for a preceding period of prosperity.

Tho the rythmic movement in trade cycles is not to be disputed, it is more than doubtful whether there is a law applicable to our ultra-complex economic life which causes an exact balancing of action and reaction. Some forces may tend to counterbalance each other at one time, and yet not at another. Furthermore there may

be long delays in the manifestations of the resultants of certain forces. And even granting that a definite law of this kind is at work, are the twelve subjects for which statistics are used by Mr. Babson so representative of all business conditions and forces that we can base hard and fast conclusions upon them? Are the statistics themselves so free from error that they can serve as exact measures? Is the method of reducing these statistics to a common basis so scientifically accurate that the final composite index number deserves confidence? It is obvious that each of these questions must be answered in the negative.

Finally, the Composite Plot itself is to be considered. To obtain this the summary index numbers are plotted as for an ordinary graph, with the additional provision of a line of "normal growth," the X-Y line. This X-Y line is an essential part of the Composite Plot, since some of the subjects tend to show an increase from year to year in consequence of the growth of the country. If it were not for the growth of the country, the curve plotted from the index numbers would fluctuate above and below a straight line parallel to the base line. The line of "normal growth," however, must move upward in order to show a proper balance.1

1 It should be noted that for five of the twelve subjects there is no normal growth, but only fluctuations around the constant level. Money rates, for instance, do not

necessarily increase with the growth of the country.

As the summary index numbers are plotted upon the chart, a part fall above the X-Y line and a part below. There develop, consequently, a series of areas bounded by this curve for summary index numbers and by the X-Y line. These areas alternate above and below that X-Y line. Those above are positive and represent action; those below are negative and represent reaction. Since action and reaction are to be equal, the positive and negative areas must be equal. They are not regular in depth or breadth but equal only in area. For a current month this Composite Plot is assumed to show the position in which the business world is with reference to the business cycle. From this Plot, it is assumed, one can judge how much positive or negative area can be expected to develop before a change sets in. The Plot does not indicate in any way whether this development is likely to be rapid or slow, whether the "reaction" will be sharp and quick or slow and long.

Obviously the relative size of the areas above and below the X-Y line depends upon where that line is placed. When this plot was first published, the X-Y line was straight. Its direction had been determined by carrying the Plot back over several years and drawing the line of normal growth in such a way that equal positive and negative areas would be shown.

Until January, 1913, the line continued to be straight, running diagonally at an angle of about ten degrees from the horizontal. Events, however, were causing unequal areas to develop and a readjustment was necessary. Modifications in the direction of the X-Y line were introduced, causing long, irregular fluctuations. Had the direction of the line remained unaltered, the appearance of the plot at the present time would be quite different. Now the direction of the X-Y line is changed as occasion requires. To quote from an ex

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