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dates and also the per cents. of property possessed by the several classes. An objection to such procedure is that the uppermost class has no upper boundary, though this criticism is met in part where per cents. of amount of property as well as of numbers of owners are used. To be complete, the scheme should also include a class without property; classes should be of comparatively small range. But there still remains the fundamental objection that such classes, as they have been used, are bounded by absolute and fixed amounts, while concentration is a fact of relation. The boundaries of the classes should themselves be relative numbers, and should change with the per capita of the total amount of fortunes. If wealth classes are to be employed, the dividing lines should be at multiples of some sort of an average.*

The essence of the following attempt to interpret statistics relating to concentration of wealth is its use of thoroughly relative criteria. Another important difference from usual methods of treatment consists in keeping this question as to concentration of wealth separate from the other and larger question. as to the character and tendency of the distribution of incomes, including thus incomes from labor. Special attention is given also to the peak of the pyramid of fortunes. One reason for this-in addition to the peculiar interest of that aspect of the question which relates to the growth of great fortunes-is the difficulties met in trying to obtain tolerable statistics of small properties, as distinguished from small incomes.

To test for a tendency to concentration of wealth, probate and inheritance statistics are the best available material. There is an assumption involved in the use of such material. But it is a fair assumption that any considerable influence affecting the degree of concentration of wealth among the living will soon affect in the same direction the distribution of property in the estates of deceased persons. In other words, the errors are constant and do not affect tests of tendency.

For an extended discussion of this rather technical subject of the method of measuring concentration of wealth, the reader is referred to articles by Messrs. Lorenz, Holmes, and Watkins, Publications American Statistical Association, Nos. 70, 71, 72.

The best evidence we have for the United States bearing on the question under consideration is certain probate statistics compiled by the Massachusetts Bureau of Statistics of Labor. Following are the important primary tables:—

PROBATES IN MASSACHUSETTS: NUMBER AND AMOUNTS, AND THEIR PERCENTAGE DISTRIBUTION, 1829-31.*

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PROBATES IN MASSACHUSETTS: NUMBER AND AMOUNTS, AND THEIR PERCENTAGE DIS

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* The absolute numbers are from the Twenty-fifth Annual Report of the Bureau of Statistics of Labor, Massachusetts, 1894, p. 265.

† Ibid., p. 267.

PROBATES IN MASSACHUSETTS: NUMBER AND AMOUNTS, AND THEIR PERCENTAGE DISTRIBUTION, 1879-81.*

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The absolute numbers are from the Twenty-fifth Annual Report of the Bureau of Statistics of Labor, Massachusetts, 1894, p. 267.

+ Ibid., p. 267.

In these statistics there is exhibited a notable tendency to an increased number of the larger fortunes. There were two estates of over half a million probated in the earliest threeyear period, and 30 such probated sixty years later. Meanwhile population had increased 267 per cent. The estates above $100,000 were 11 in number in the earliest period, and 244 in the latest. The wealth of the community certainly did not increase at such a rate. The greatest growth of riches, but chiefly in numbers of moderate fortunes, appears to have occurred in the thirty years preceding the Civil War. In the latest decade covered there appears a tendency to reverse the process. For the latest period there is a decline in the relative number of half-million dollar estates probated. The tendency to concentration doubtless began to produce marked effects earlier in Massachusetts than elsewhere, owing to its leadership in manufactures and its lack of capacity for agricultural expansion. Hence the tendency may well have worked itself out by 1880.

But let us consider these figures in their proper relation to the growth of per capita wealth. According to the United States Census, the "true valuation" of real and personal property in Massachusetts for several decades past was follows:

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The per capita wealth of the State thus declined noticeably between 1880 and 1890. The two sets of figures, probate and census, are in general agreement as regards the indication that the relatively large number of estates of half a million or more in 1880 was in part but an expression of the greater per capita wealth of the State in that and in the immediately preceding years, as compared with ten years later and with twenty years.

earlier. If a thorough relative test were applied, the year 1880 would probably not stand out so prominently in this matter of concentration of wealth as it does when one uses fixed class boundaries or any method which involves definition of the large fortune absolutely.

If the character of the actual statistics permitted the plotting of a practicable curve indicating relative quantities (that is, percentages), comparison of the course of such curves for different sets of data would immediately indicate to the eye which set was characterized by greater concentration.* The pyramid of fortunes, however, is of such a nature as not to lend itself readily to such diagramming. It is significant of prevailing inequality that the attempt to construct the curves fails because of the disproportion between the flattened base of the pyramid and the elongated peak. The curves resemble a capital L with enormously elongated arms and so little thickness of the different parts that the eye can form no judgment of quantitative relations. This is explained by the fact that the curve of the distribution of property is hyperbolic in its general characteristics.† Quantities arranged in something like a hyperbolic series do not lend themselves readily to ordinary graphic representation.

But a hyperbola is very easily represented graphically if one will plot the logarithms of the numbers instead of the numbers themselves. Just what the degree of difference is between two series of numbers so compared is not obvious, at any rate

This is Mr. Lorenz's proposed method in the article referred to above. It is significant that Mr. Lorenz uses hypothetical figures, and thus fails to perceive the limited practical value of the particular species of graphic method that he prefers. The value of my comment in this discussion is subject to a similar qualification.

† If the statistics dealt with were not concentrated upon round numbers, the hyperbolic nature of the distribution of estates would find expression in the position of the arithmetic average of the estates within each class; that is, it should in each case be near the geometrical mean between the limits of the class. The Massachusetts statistics conform to this rule almost without exception. The British statistics almost as regularly do not conform to it; that is, the arithmetic average of the estates within the class is usually considerably above the arithmetic mean between the approximate boundaries of the class. The difference is explained by the fact that the estates at the round number which marks the lower limit of the class are included in it in the Massachusetts figures and the upper limit is exclusive; while in the British figures the lower limit is exclusive, and the upper limit inclusive, and especially the lower limit marks the transition to a higher tax rate.

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