These figures are not exactly comparable for the successive periods covered. Those for 1838 relate only to personalty. The same is true of the figures for 1884-85 to 1888-89,* which are therefore comparable with those of 1838. Changes in the law in 1889, followed by simplification and systematization in 1894, extended the taxation so that realty is included in the figures of later date. As indicated in the tables above, there is a difference between the figures for the earlier periods and for the latest period used as regards the method of classification; that is, estates at the lower boundary of the class are included and those at the upper limit not in the former case, while the lower boundary of the class is exclusive and the upper inclusive in the latest figures. This does not affect the validity of the results of testing for concentration by the slant of logarithmic curves. In practice, it is true, the tendency to concentrate estimates on round numbers might make a slight difference in the reliability of the indication from a comparison of figures employing classifications differing in this respect.

The figures for the latest period include all realty, and are in every way the most reliable and complete. The ownership of realty in England is, for historical reasons, notoriously concentrated, and the appearance of greatest concentration at the latest date might be due only to the previous inadequacy of the picture. But such an argument leaves little room for much decentralization in the ownership of real estate. And comparison of the figures for the two earlier periods shows-even after making allowance for evident irregularity and inaccuracy of the figures for 1838-an unmistakable tendency to concentration in the ownership of personalty, which has probably not been

*Exactly what effect the qualification "exclusive of property assessed to corporation duty" would have, I am unable to say; but Giffen uses figures resulting from the identical tax laws as comparable with Porter's figures. See Journal of the Statistical Society, 1883, p. 614. The amount so exempted is inconsiderable.

† Bastable, "Finance," 556, ff. Spahr ("Distribution of Wealth," p. 16, ff.) is therefore mistaken in his assumption that the figures of 1892 are exclusively for personalty. Of the three sets of figures used, those for the latest period and for the intermediate period are net. Of the figures for 1838 Porter says (iii, p. 128), "The amounts are in many cases reduced by the payment of debts due from the deceased and by other charges upon their estates." Does this mean that the figures are not net?

completely reversed in the latest period. In the United States the evidence is clear for a much greater degree of concentration in the ownership of personalty than of realty, and there is likely to be no absolute inconsistency as regards economic conditions in New York and in Great Britain. The tendency of personalty, too, is the tendency of three-fourths of the wealth of Great Britain. The conclusion that there has been, on the whole, in the last half-century, a tendency to concentration in the ownership of wealth in the United Kingdom appears to be not presumptuous.†

An important question to be considered, however, before drawing any conclusion from the above figures is, What is the relation between the character of the distribution exhibited by a combination of two sets of figures and the character of the distribution of the original series thus added together? The addition in the present case is effected through the possessors of the two kinds of property being the same persons; that is, the people of the United Kingdom. If the distribution were in each case a mere chance distribution, and if there were thus no correlation between the causes of inequality in the two cases, the effect of summation would obviously be a levelling down of previously existing inequalities. Both of these suppositions, however, are contrary to fact in the case of the statistics before us. The inequalities are not the result of chance distribution, and the same set of forces which produces inequality in the ownership of the one kind of property produces the inequality in the other case. There is thus a positive correlation of the inequalities. Certainly, no negative correlation is to be expected, such as would make the inequalities cancel each other, implying that those who possess little personalty possess much realty and vice versa.

Suppose, then, that there is correlation between the in

*These facts are dealt with by the writer in a study of the economic causes of the growth of great fortunes recently published by the American Economic Association. See "The Growth of Large Fortunes," p. 49.

† Porter, in 1851 (Journal of the Statistical Society, p. 198), compiled figures which appear to show conclusively that there was no tendency to concentration in the ownership of personalty between 1833 and 1848.

equalities and that it is positive in its nature. Suppose, also, that the inequalities are about the same in each case, that is, that the shares in each case are corresponding proportions of the total amount distributed. Then, according to the mathematics applicable to this situation, if the positive correlation is perfect and if the inequalities are the same, the inequality resulting from summation will also be the same as the original inequalities. But, if the correlation be not quite perfect, the result of summation must be lessened inequality. If the inequality be greater in one case than in the other, and if the correlation be perfect, then the resulting inequality will be intermediate. But, if the correlation of the original inequalities is imperfect, the resulting inequality is likely to be less than either of these original inequalities, even though they differ considerably. This last is the case of the statistics of the United Kingdom with which we are dealing.

Though it is open to question, it may be that there is a greater inequality in the distribution of landed property in the figures for the United Kingdom than of personalty. Even so, summation of the two kinds of property would probably not produce an appearance of greater inequality than that exhibited in the distribution of the personalty by itself. The greater weight of personalty in the total of the wealth involved supports the inference that a possible greater concentration in the ownership of realty is probably not responsible for the difference between the latest figures and the others. It is highly probable, therefore, that the greater concentration at the later date is due to an actual tendency in that direction rather than to a difference in the inclusiveness of the statistics. If the appearance were the other way, the validity of an inference would be much more open to question.*

Recently counteracting factors may have been working to produce less concentration. The most recent American figures

* The period since the adoption of the present tax laws is so short that no good test of tendency on this basis is possible. The figures for the four years immediately preceding those for the latest period used, these two sets being exactly comparable, give a slant to a logarithmic curve practically indistinguishable from the latest plotted. But there were in proportion a few less estates over £1,000,000 in the later than in the earlier period.

used are, as we have seen, somewhat ambiguous. Exemptions under Schedule A of the British income tax, moreover, point to a decided gain in the ownership of income-producing property by persons with small incomes.*

On the face of the figures it appears that there is greater concentration in Great Britain than in Massachusetts, since the slant of the curves drawn to the same scales is slightly greater in the former case than in the latter. Any positive conclusion from such a comparison, however, is defeated by the different nature of the statistics used, the British figures being tax statistics and net, the Massachusetts figures being mere probate statistics, influenced by no motive to check underestimation of large estates or overestimation of small debtor estates. Since the direction of the errors is of a kind to invalidate the natural inference, no positive inference can be drawn.

For France neither estates nor incomes appear to have been classified in official publications, with reference to size, long enough to make them available to test the operation of a tendency to concentration. Succession statistics are of long standing, but have only recently been classified by size. The figures for 1903 and 1904 subjoined indicate considerably less present concentration of riches in France than in the United Kingdom or than in the older and industrialized portions of the United States. This is the general opinion as regards the sources and the distribution of French accumulations.

This point is developed by the writer in the study above mentioned at p. 137.

†The difference is great enough to warrant an inference, even though the statistics are not exactly comparable, especially as the differences are such as tend to conceal the difference, the British figures including inter vivos gifts and the American figures being not net.