of the Royal Statistical Society," 1901, p. 383). The method favoured by those English statisticians who have dealt with the question has been to estimate the total wealth of the living from the wealth of those dying in a given year by the simple process of multiplying the latter figures by the ratio of living to dying persons. It is this method which Mr. Coghlan fell back upon when questioned before the Select Committee on Income Tax, 1906, failing the possibility of the more correct method which he suggested, and to which I shall recur. There being about 1 death in 45 among persons from 25 years of age upwards, he said, "I would assume, as "I believe Sir Robert Giffen assumed, that the wealth of the "country is forty-five times the value of the estates of deceased "persons." (Q. 1398). Mr. Bailey, with his figure of 55, adopted a similar method of calculation.

Mr. Coghlan, in a previous question (1394), himself suggested a criticism of this method, which seems to be fatal to it. The following table shows how the multiplier may be affected by the fact, of which the above assumption takes no account, that (as he expressed it)" the accumulated wealth of an individual increases with years, "and is usually greatest when a man dies." The figures of average property at the different ages at which death occurs are in this table purely imaginary :

:

The figures in the lines at top and bottom of the table that are arrived at otherwise than by summing the figures in the age-categories are enclosed in brackets. The figure 59'1 in the top line is the ratio of the total living to the total deaths per annum among persons of 20 and upwards, and the figure 31'6 in the bottom line is arrived at by dividing the property of the living (col. 6) by the property of the dying (col. 4).

Thus at the ages 25-35 it is assumed that the average wealth of those who died was 200l., this gives a total of 5,962,240l. as the property of the 29,8112 persons who died annually at those ages. Multiplying this by 174'5 (the number of living persons at the same age out of whom one death occurred) 1,040,000,000l. is found as the property of all living persons between 25 and 35. Treating each age-group in the same way, the total property of all who died annually is 125,872,040l., and the aggregate property of the living estimated for each group separately is 4,930,000,000l. on 39.2 times the property of the dying.

If we substitute for the figures in column 3 the following assumed amounts of average property at death in age-groups :-100, 150, 250, 350, 500, 700, 900, we shall get a total property at death of 164,379,570l., and an aggregate of property for the living of 9,715,000,000l., or 316 times the property of the dying.

Thus, if property is distributed among persons of different ages in one way, the true multiplier is 39'2; whereas, if it is distributed in another way, the ratio becomes 31.6. Another kind of distribution would give yet another ratio. The "crude" method makes 59°1 the multiplier in all cases impartially. That this ratio should be a possible constant in coexistence with an indefinite number of ratios derived from different degrees of property-possession is in itself an indication that it is not germane as a measure of the movement of property mortis causâ. If, as we shall see, the actual figures confirm the assumption that "accumulated wealth increases with "years," the method which Mr. Bailey adopted in his letter must therefore, I think, be discarded. It could only be correct if the average wealth of adults at all ages tended to be the same. But I shall return to this point.

The method adopted by foreign inquirers is to base the required multiplier on what is called the "duration of a generation." The tradition since the days of Herodotus has, as M. de Foville remarks, been to count three generations to a century, and the estimates which have been made by modern statisticians of the normal duration of a generation defined, not as the average length of life, but as the 66 average survival of children over their parents," does not differ widely from the traditional figure referred to. M. Adolphe Coste, in a valuable paper published in the "Journal de la Société de Statistique de Paris" (vol. 1899, p. 191-4), covers the whole ground of the French speculations on this subject. He shows by a simple equation (p. 191) that the average survival of children over their parents is equal to the age of the legitimate father (or of the natural mother) at the moment of the child's birth. If a father is 33 at his son's birth and dies at 60, the son inherits at

27 and enjoys the inheritance till 60. His survival has, therefore, been thirty-three years (60-27). Suppose that instead of the father dying at 60 he dies, say, at 50, would this change in the conditions shorten the term of the son's survivorship? The son would in that case be 17 at his father's death, and would survive thirty-three years, dying in his turn at 50. The conclusion is inevitable that the chief determining element in the length of a succession is the average age of the parents when the children are born. As M. Coste puts it: if P is the average age of the parent, M the and S the survival of the son, then

average age of death,

In France the age of parents at the birth of their children is known by the état civil, and it is therefore possible to calculate exactly the "duration of a generation" in this sense. Tonnier, in 1816, calculated it for Paris in this way at 33 31; Vacher, in 1882, on a wider basis, put it at 33'06. M. Victor Turquan, in 1896, found that the average of a male generation for 782-082 legitimate births was 34 years 1 month 6 days, and for a female generation for 73,809 illegitimate births 25 years 9 months. The proportional average between these legitimate and illegitimate births is equal to 33 37, which is equal to the "average survival." A variant of this calculation, and the one I find quoted by M. de Foville and Professor Coletti, is an earlier one made by M. Turquan in 1892, which gives the average age of fathers as 34 years 1 month 6 days, and mothers (legitimate births) 29 years 9 months 28 days, giving an average survival of children of nearly thirty-two years.

The same line of speculation is followed by Professor F. Coletti in an important series of articles in the "Riforma Sociale" for March, April, and June, 1907. This economist describes the methods and conclusions of French and other statisticians on the subject. He dismisses as "infantile," methods which rest on the length of a physical generation, and confines himself mainly to discussing the methods falling under two classes according as it is sought to establish the length of an hereditary generation:(1.) Directly by determining the mean survival of children over parents (de Foville), or:

(2.) Indirectly by determining the comparative age of the parents, i.e., their mean age at the birth of the children. Under the second head fall the investigations of MM. Coste and Turquan in France and M. Rümelin in Germany. The last mentioned takes the formula age of father at marriage + one year + half the difference of age between first born and last born, and thus gets the figures of

=

36 for Germany | 35 for England | 34 for France.

With reference to M. Coste's formula quoted above, Professor Coletti points out that it fails unless both the "comparative age of "the parents" and the "mean duration of life" are the same for the successive generations. The criticism is just because it is clear that, if the mean duration of life is undergoing a change, the heir will on an average outlive his predecessor by a corresponding period.

Taking this consideration into account, and working on the Italian figures of the duration of life, he gives a mean length of an hereditary generation in Italy as 32 years 3 months for 1882, and 34 years 11 months for 1901.

Finally, there is the "direct" method of M. de Foville. The following was this eminent statistician's original calculation which, though it is well known, should perhaps find a place in the present summary of various methods:

(a.) Average interval of transmissions inter vivos and
Mortis cuted (basis of French or intintas, 1819)

=

20 years.

(b.) Average interval between transmissions of rea)} = 45 years.

property inter vivos (French official calculation)

This means that in nine hundred years there are—

45 transmissions inter vivos and mortis causâ.

900

(a'.)

=

20

That is to say, transmissions mortis causâ occur on an average

Professor Coletti's criticism upon this is as follows:

The interval of twenty years (a) relates to all kinds of property, real and personal, whereas the interval of forty-five years (b) relates to real property only. Now it is known that transmissions of real property occur at longer intervals than do transmissions of personal property. Therefore, for real and personal property, the interval (b) should be something less than forty-five years, and the number of transmissions in nine hundred years more than 20(b).

It follows that the number of transmissions mortis causâ (a' – b') should be less than 25, and the interval between such transmissions more than 36.

Professor Coletti appears to think 36 is in itself a suspiciously high figure, and that a higher figure still would be a clear proof that M. de Foville's data were not reliable.

I may add that, in his most recent pronouncement, M. de Foville seems to have abandoned 36 as his multiplier, and to have adopted

M. Turquan's 1892 figure of 32 as that by which the annual devolution of property in France should be multiplied until it is found to be incorrect (see an article, on "La Richesse en France," in the "Revue Économique Internationale," 15th-20th April, 1906, p. 21). By so doing he seems to assume that the two methods are equivalent, whereas it would appear that M. de Foville's original method could hardly have aimed specifically at finding the length of a generation (which is M. Turquan's object), for in that case his inquiry would have been limited to the passing of property from parent to child. It aimed rather at discovering the average length of time during which a property owner holds property. In other words, he seems to have discarded a multiplier based on the average survivorship of heirs over their predecessors for what is not the same thing, viz., one based on the average survivorship of children over their parents.

Such, then, briefly described, are the chief results, so far as I have been able to trace them, of recent researches having for their object the discovery of the "duration of a generation" in modern communities. They seem to have arrived at the conclusion (based, however, on figures of the whole population, whether property owners or not) that the period of time between the date when an heir receives his inheritance and the date when he in his turn hands it on at his death to his heir may be put at from thirty-two to thirtysix years in Western Europe. But an obvious-though not, as we shall see, the most fundamental-difficulty arises when we seek to apply some such figure, as M. de Foville boldly does in his latest paper, as the multiplier for the annual devolution of property revealed by death duty statistics. For property passes, not only from father to son, but also collaterally from brother to brother, husband to wife, and so on.2 M. de Foville notices this difficulty, only to pass it over as unimportant. It would, of course, have the effect of reducing the multiplier of 32 or 36 (or whatever figure might be taken as that of the duration of a generation); but, at the time when Mr. Harris read his paper, in December, 1906, I was inclined to assume, though I had previously accepted 32 as

2 Some interesting figures, for what they may be worth, on this point (which is quite subsidiary to my main point) came out of the succession duty figures, to which reference is made later on. It was found in the 273 cases analysed, 252,000l., out of a total of 405,cool. capital, or 62 per cent., was left to lineals. In order to verify this, the amount of property on which legacy duty was paid in the four years 1875, 1876, 1877, and 1879 (before the I per cent. on legacies to lineals was abolished in 1880) has been made. The total amount of property on which duty was paid over the counter at Somerset House in these years was nearly 322,000,cool., and roughly, 60 per cent. went to lineals and 40 per cent. to other persons.