if no very startling results were apparent, was always of great value for study and example. One small statement had attracted his attention, viz., that the census schedule did not provide for a true enumeration of married couples, and that persons appeared as "married" who, for purposes of the legitimate birth-rate, would rank among the unmarried. He rather doubted if this were the case, and was inclined to think that there might be quite as much tendency for a child to be wrongly described as "legitimate" in the registrar's returns as for the woman to describe herself as "married" in the census returns.

Mr. BAILEY said he very much doubted how far the accuracy could be depended upon of the ages stated in these public documents, which is so essential for this investigation. Several years ago he had thought of endeavouring to get out a table of the rate of mortality at different ages and comparing it with Dr. Farr's English Life-table. He and a friend of his used for this purpose the families of the peerage, believing that there would be a sufficient number of that class to arrive at some general laws; because there you really had the dates of birth and marriage, the number of children and the ages of the children; and no correction whatever was required. He thought if someone would take the trouble to get an old Peerage, and use it for the objects of Dr. Dudfield's paper, they could take out as many cases as were required, and would get a sufficient number of facts which could be absolutely depended upon to arrive at certain definite results without the necessity of corrections.

Sir ATHELSTANE BAINES, in moving a vote of thanks to the author of the Paper, said that the labour involved in handling so great a mass of figures would be recognised by all, and Dr. Dudfield was entitled to credit, also, for confining himself as strictly as he had done, to the issues he set out with, defining, not yielding to the temptation of straying into the attractive questions which his figures suggested, outside those issues. The effect of postponing_marriage on the birth-rate had been estimated recently by the RegistrarGeneral of England at about 20 per cent. of the decrease in the last thirty years, whilst the average age of the married men had risen by about 3, and of the wives by about 4 years. The ages had been tabulated, he thought, in smaller groups by Mr. Kiær, of Christiania. But the question most prominently before the meeting was the merit of the hypothetical corrections applied by the author. He (the speaker) always regarded with admiration the discernment and moderation with which such selection had to be made, as it was one of the most difficult of statistical operations, and might, if not well managed, lead to results very different from those anticipated by the operator. He had not himself had experience in applying corrections to the birth returns of so ancient a date as those in question, but, so far as he could judge, the author had proceeded upon sound methods, and had made the most of the available material for his basis of calculation.

Dr. DUDFIELD in replying to the vote of thanks and to the discussion, expressed his appreciation of the kindly manner in which the Paper had been received. As he could not claim to be more than a very junior student of the statistical science, he had hesitated to bring the results of his work before the Society, as the end achieved had by no means fulfilled his expectations.

With reference to Mr. Yule's remarks, the only point to which he would allude was the peculiarity attaching the figures for 1891. The census results for that year differed in some (at present, to him,. unknown) manner from those of 1881 and 1901. To that cause. he attributed the departure from the general agreement with the results obtained by Mr. Yule and Drs. Newsholme and Stevenson. The line of enquiry taken by him (Dr. Dudfield) had been so distinct from that of those authors, that he had not endeavoured to ascertain, as Mr. Hooker desired, the effect of his own work on that of the authors mentioned. He was seeking a concrete estimate of the loss, or deficit, of births, not a relative measure of the change of rate. The whole of his calculations depended on an assumption of constant fertility, a point referred to by Mr. Rosenbaum. He thought that there was no reason to believe that the national fecundity had altered at all, but, undoubtedly, owing to postponement of marriage to later ages, that fecundity was not fully effective, and hence the apparent fertility was reduced. He believed that with a reversion to the principles and practices of the middle of the last century, the birth-rate would return to its former level.

Mr. Humphreys's objection to the use of the records of the first. year of registration was a valid one. If, however, the Scotch figures for 1855 were rejected, there remained no data at all for this country. As regards his correction figures for non-registration of births, his experience, as a medical officer of health, had convinced him that such non-registration was more common than generally suspected. It was in part due to fear of the operation of the Vaccination Acts, although the last shred of real compulsion had been removed from the Statute Book. Quite recently he had learned of the existence of popular delusion as to relief from registration. It was thought by some people that the holding of an inquest on a child, prior to registration of the birth, absolved the parents from all liability for such registration. He had also brought to the notice of the Registrar-General a number of births which were reported by midwives, but never registered. Under the most favourable conditions these observations could extend to only a comparatively small proportion of all the births in his district, but he had little doubt that the cases investigated formed a fair sample of the whole.

He should have liked to have included "specific " fertility-rates, namely, rates for each age of the mothers, as Körösi did for BudaPesth, but while the births in Scotland were available for that purpose, he doubted whether the ages of married women in single years could be obtained, except by laborious and costly tabulation. Graphic interpolation was, doubtless, possible, but the trustworthiness of results so obtained would be more than uncertain.

The small effect on the fertility produced by the introduction of husbands' ages was at first sight remarkable. Some explanation was to be found by contrasting the changes for each quinquennial period, when examined vertically (for fathers) and horizontally (for mothers). (See Appendix.) The maternal age was the principal factor affecting fertility. It appeared to him to be desirable that the mean ages should be determined for each H.W. Table, not only for married men and women en masse, but for wives at each (quinquennial) age of husbands, and vice versa. Similarly the mean ages required to be taken out for the H.W. table of marriages published annually.

The uniformity of the index-numbers in Table 13 was, he thought, largely due to the causes indicated by Mr. Yule. The numbers of the total population of married women, &c., were so large, and the corrections made, relatively, so small, that the general tendency of the former would inevitably discount the results of any convictions introduced.

The following were elected Fellows of the Society :—

Bailey, Frederick.

Furniss, Henry Sanderson, M.A. Drake, E. T., Government Statist of Webb, Augustus Duncan, B.Sc. Victoria.

A METHOD of ESTIMATING CAPITAL WEALTH from the ESTATE DUTY STATISTICS.

By BERNARD MALLET.

[Read before the Royal Statistical Society, 18th February, 1908. The Right Hon. Sir CHARLES W. DILKE, Bart., M.P., President, in the Chair.]

THE subject with which I propose to occupy your attention to-day is a very limited one, and I feel that a word of explanation, perhaps of apology, is due from me by way of preface. It was suggested to me by the discussion which arose in the paper by Mr. W. J. Harris and the Rev. K. A. Lake, read by Mr. Harris on the 18th December, 1906. That paper was an attempt to arrive at a valuation of the realized wealth of the United Kingdom, for which purpose, as regards the most important part of the capital wealth of the country, that in the hands of private individuals, he relied on the statistics derived from the death duties. English statisticians have led the world in calculations of this kind, more especially, owing to the facilities afforded by the early establishment of an income tax in this country, in calculations of the national income; and I need not remind members of the Society of the labours of inquirers like Mr. Dudley Baxter, Mr. Leone Levi, Sir Robert Giffen, and Mr. A. L. Bowley in this connection, which have enabled us to reach a reliable statistical approximation of the national income of the United Kingdom, together with some notion of its distribution among the various classes of the community, the income tax paying class, the manual labour class, and the class intermediate between the two. But I think Messrs. Harris and Lake, and Mr. Chiozza Money in his "Riches and Poverty" (in which the question of the distribution of wealth in the community was handled in a very interesting manner), were the first who have published estimates of the national capital or wealth based on the death duty figures which have been available since the institution of the estate duty in 1894 by Sir William Harcourt. Previous inquirers, like Sir Robert Giffen in his standard book on the "Growth of Capital," were obliged to rely on the income tax returns, capitalizing the income under the different schedules at a certain number of years' purchase, a method which involved almost insuperable difficulties in respect to Schedule D.

But an essential preliminary to any trustworthy inference from the annual returns of property passing under the estate duty is 1 Journal, vol. lxix, 1906, p. 709.

VOL. LXXI. PART I.

F

to discover a "multiplier" by which to calculate the amount of property owned by the living from the amount which comes under review in any particular years or series of years. No real agreement seems to have been arrived at among statisticians on this point; the discussion on Mr. Harris's paper indeed revealed the most startling differences of opinion, Mr. Harris giving the necessary multiplier at 29, which Mr. Coghlan combated as far too low, while Mr. A. H. Bailey raised it from 29 to 65, which, however, he reduced in his letter to the Journal (March, 1907, p. 130) to 55. Mr. C. Money, in "Riches and Poverty," assumed 30 as the multiplier. Finally, reference must be made to the discussion of this question before the Select Committee on the income tax in 1906, of which our President was Chairman. Mr. A. L. Bowley prepared for the Committee carefully thought out estimates of the distribution of income, and in one table, Appendix 2a of the Report (House of Commons, 365, 1906), comparing national capital as deduced from the estate duty statistics with income from income tax statistics, adopted 32 as the multiplier for the former, referring in his evidence to Lord Milner's hypothesis (made some years previously) that the figure might be 40 (Q. 1179 and 1180). Sir Henry Primrose stated that he had taken 30 in his own calculations, but admitted that the proper multiplier was a "very doubtful problem," in view of the various ratios, ranging between 30 and 40, which had been put forward. (Q. 28-31). To bring home the effect of such differences of opinion, I may mention that Mr. Harris, on the strength of his multiplier of 29, put the accumulated wealth of the country, judging from the value of the property which came under the cognizance of the Estate Duty Office in 1905-06, at 7,893,015,463!., while Mr. Bailey gave it as 14,776,560,000l. Between these two extreme limits there is room for the most disquieting discrepancies, and it is therefore a matter of some importance to ask whether they can in any way be explained, or whether any data exist for suggesting a multiplier which may be more generally accepted for these calculations.

It is somewhat remarkable that previous to the discussion I have referred to, no English statistician seems to have concerned himself with the question except Sir Robert Giffen, who many years ago suggested a possible figure but who, as far as I am aware, has not given any subsequent investigation to the matter. Those who, like Mr. Branford, have dealt with calculations of national wealth in foreign countries have used the figure 36 originally established for France by M. de Foville, the statistical pioneer on this question, and adopted by the Italian economist, Pantaleone (see "Journal