Hence we find that Dr. Price considered that out of a total of 10,000 deaths, 1300 or 13 percent were the deaths of persons who entered Northampton at age 20. The proportion given by the facts was 469 out of 4689 or 10 percent.

We can now without any difficulty deduce the Northampton Table, as will appear from the following tabular summary.

TABLE D.-Showing the process actually employed in the construction of the Northampton Table.

Note. The 1300 deducted in Col. 2 = 13 percent of annual deaths.

Why Dr. Price concluded that 13 percent of the total deaths were those of persons coming into Northampton at age 20 does not appear. The proportion taken in the first Northampton Table was, as we have seen, 12.1 percent, being neither more nor less than that given by the facts from Dr. Price's point of view; but the proportion given by the facts on which the Northampton Table is based is only 10 percent. Bearing in mind, however, the following passage of his work:-"If for a course of years there has been no sensible "increase or decrease in a place, the number of annual settlers "will be equal to the excess of the annual burials above the "annual births. If there is an increase, it will be greater than "this excess. If there is a decrease, it will be less" (7th edition, vol. ii, p. 76)—it would seem that he had reason to believe that an increase had taken place in the population of All Saints' parish in the course of the 46 years of observation, and that this increase was brought about by persons settling in Northampton at age 20. It is probable, therefore, that this was one of the reasons *The previous cols. are the same as in Table C.

which led him to consider 13 percent, instead of 10 percent, of the total deaths as arising from immigration at age 20.

This however, appears to be a very large percentage, almost incredibly large; for it is equivalent to saying that out of 5135 persons, in a town, of age 20, 1300, or more than 25 percent, are persons who have just settled in the town.

At the same time there are several singular coincidences which we may here point out. Thus for a complete century, i.e., from 1633 to 1734, we are told on p. 77, vol. ii, that in Breslau the annual medium of births was 1089, and of burials 1256, the difference being 13.3 percent of the burials. Again, in Norwich, for the 30 years, from 1740 to 1769, the corresponding numbers were 1057 and 1206, the difference being 12.4 percent of the latter. Another point worthy of notice is that according to the Northampton Table, if we take the total number living at all ages as 5136, being the number ascertained by enumeration, to be the population of Northampton in 1746, we get from the formula

Dr. Price tells us that for the 10 years, 1741 to 1750, being just about the time when the number of inhabitants was 5136, the average annual number of deaths at all ages was 197.5. A similar calculation to the above, taking the Northampton Table of the first three editions of Dr. Price's work, gives the average annual number of deaths as 197.8.

In conclusion, it may not be out of place to point out that various passages in the fourth and subsequent editions of Dr. Price's work have reference not to the Northampton Table as there given, but to the first Northampton Table constructed by him and given in the first three editions. This, no doubt, in great measure arose from the fact mentioned by Mr. F. Hendriks in his paper in vol. i of the Assurance Magazine, that Dr. Price was overburdened with business and ill when the 4th edition was published, and compelled to leave to others the preparation of a portion of the work. will, nevertheless, save trouble to those reading it to bear this always in mind.

It

The following summary of the discussion which followed the reading of the paper is abridged from the Insurance Record.

The PRESIDENT congratulated Mr. Sutton on the successful result of his investigation, which had enabled him to reconstruct Dr. Price's Northampton Table. That once famous table is gradually going out of use. It is now probably more useful for comparison than for office purposes. Nevertheless, anything relating to the Northampton Table must be of interest to members of the Institute.

Mr. A. H. BAILEY thought that the result of Mr. Sutton's researches into the Northampton Table was of considerable interest and value. He had taken the trouble to read and examine the early editions of Dr. Price's work, which are not readily accessible, and which probably had not been seen by Dr. Farr; and, in consequence, had been able to all intents and purposes to reconstruct the Northampton Table as it appears in our ordinary text-books, conformably with Dr. Price's own views; whereas Dr. Farr proceeded on certain conjectures as to what Dr. Price did. This must have been a work of some labour, and was creditable to Mr. Sutton's industry and acumen. But while it now appeared that Dr. Farr had not done sufficient justice to Dr. Price, so Mr. Sutton had, quite unintentionally, scarcely done sufficient justice to Dr. Farr. The paper by Dr. Farr in the Appendix to the Eighth Report of the Registrar General, is one of his most valuable contributions to our particular subject. Although, perhaps, Dr. Farr had not met with such success as Mr. Sutton in reconstructing the Northampton Table, he had proceeded one or two steps further. By researches into county histories, and books of that character, he showed sufficiently that so far from the population of the town of Northampton having been stationary during the 46 years over which Dr. Price's observations extended, it had been, as everybody now is well convinced, steadily increasing throughout that period. But he went further. From the materials in the Registrar General's office he constructed a table of the mortality of the parish of All Saints, Northampton, during the years 1838-44 inclusive, and also, from the same materials, a table founded on Dr. Price's hypothesis of stationary population. The former of these new tables corresponded sufficiently well with any of the standard tables of the present time; the second, constructed on the hypothesis of a stationary population, corresponded with Dr. Price's table, and therefore gave the strongest possible confirmatory evidence of the faultiness of the assumption on which Dr. Price's table was constructed. That is a curious instance of how needful it is, in investigations of all kinds, to stand out, above all things, for truth. Dr. Price was a strong politician, and held most decided opinions about the decadence of the kingdom, amongst other things, the decline of the population; and in this book of his there are some perfectly ludicrous observations to prove how the population was decreasing. There are two or three essays assigning various reasons for such a state of things. We now know that the very reverse was the case. It is still more remarkable that Dr. Price's biographer and admirer his nephew, Mr. Morgan, without the same excuse, fell into the same mistake. Any one who has read Mr. Morgan's reports to the Equitable Society knows that he was in the habit of keeping

records of how far the actual experience of the Equitable corresponded with the Northampton Table; and the errors of that table should have been apparent when, in stating these ratios, he found that the decrements between the ages of 20 and 30 were as 1 to 2, while the decrements between 60 and 80 were as 4 to 5. Nothing, however, apparently, would convince Mr. Morgan that anything was wrong in the Northampton Table, and in his comments in his works he "follows on the same side", as they say in the Court of Chancery, about the decadence of the population of this country. In one paragraph Dr. Price says:-"The reflection on these facts"- a variety of facts are given-"must be mortifying to this country (the richest upon earth), if it be indeed true that our population is declining. But we must comfort ourselves by considering that in this case value is of more consequence than number. 1st. the decrease of London. It is almost reckoned certain, till some other satisfactory reason can be given for a diminution since 1727, of more than 7,000 per annum in the registered burials, and near 2,000 in the registered births". He (Mr. Bailey) did not apprehend that at any time since the great fire there had been any decrease in the population of London. He observed that Mr. Sutton says in his paper, "Bearing in mind the enormous importance which the Northampton Table acquired, it is a conspicuous fact how comparatively little was thought of it by its author when he first published it". That may have been the case when it was first published, but the language of the later editions tells a different story. Dr. Price says in the sixth edition-and it is a passage often quoted-that certain new tables have been ordered to be calculated; and, after giving a catalogue of them, he proceeds :They have been calculated by Mr. Morgan with incredible care and industry, and are correct and complete to a degree never before attempted in any tables of this kind. They are to form the basis of the future business of the Society"—that is, the Equitable—" and must conduce much to its growing credit and usefulness". Again, They are all founded on a table of the probabilities of the duration of human life at Northampton, which will be inserted among the other tables in the second volume of this work. This table made a part of all the former editions of this work; but it is in the present edition much improved, and gives, I believe, more correctly than any other, the mean probabilities of the duration of human life, and therefore seems to be more proper than any other for general use". That is hardly consistent with attaching little importance to the table. And then, when consulted about certain alterations in the Equitable Society, Dr. Price, in recommending the Chester Table, says :"I had, in the introduction to Mr. Morgan's treatise, recommended to the Society the observations on human mortality at Chester; and I had procured a copy of them from Dr. Haygarth, the ingenious founder of them. But the Directors of the Society have judged very rightly that they carry the probabilities of life too high for their business. I have been enabled by them to make the Northampton Table of observations more complete". He thought that Dr. Price really did attach considerable importance to the Northampton Table, and thought it was more fit for the purposes of the Equitable Society than any other. Then, again, with regard to its use for the purpose

66

66

One

of Government life annuities. Mr. Sutton had said a great many things about what Pitt should have done. He (Mr. Bailey) apprehended that Prime Ministers in all ages are far too much occupied to attend to matters of detail, such as what table should be used for Government annuities. But the fact is that the Government life annuities commenced in 1808; and as Pitt died in 1806, he could have had but little to do with it. He thought the capital improvement the late Mr. Finlaison introduced into the Government annuities was not so much a substitution of tables, as pointing out that, for the purpose of life annuities, a distinction must be made between the sexes. As a matter of fact, the bulk of annuities are bought above the age of 60. [Mr. BADEN-The average is 64.] Now, for male lives, the Northampton Table differs from the table now in use for the purchase of Government annuities nowhere so much as one year's purchase. In the case of female lives, it is very different; and as the majority of annuities are purchased for female lives, it was a frightful mistake to use the Northampton Table, although it would not have been so bad for males. Mr. Sutton's paper is further of interest, because there is a great deal to be learnt from the use and misuse of the Northampton Table. He thought that table had been responsible for two great fallacies, which had exercised some considerable influence. of those is the supposed material improvement of the duration of human life in the last 100 years. He was not going to deny that some improvement had taken place, but he believed it was much less than was commonly supposed. When any modern observation of mortality has been compared with the Northampton Table, it has been supposed that the difference between the two is due mainly to the improvement in vitality; but it is now established that the Northampton Table never represented the true state of the case. The other fallacy is, that the Northampton Table is a safe one to use for life assurance purposes, because it represents too high a mortality. When the question was before the Equitable Society as to what table they should substitute for the London observations, and they selected the Northampton in preference to the Chester Table, no doubt what was in their minds was this, that the Northampton Table gave higher premiums than the Chester Table, which of course is the case; and when that was stated to them, it was considered sufficient. [The PRESIDENT-A good reason.] A good reason, but by no means the whole of the case, because there is another rather important matter, and that is the question of how the liabilities are to be estimated, which was not thought of at the time the Northampton Table was first adopted. If the Northampton Table were consistently wrong, there might have been something said for that; but such is not the case, for, as already stated, it is substantially correct above the age of 60; and under the age of 20, where, as Mr. Sutton has shown, it was most knocked about by Dr. Price, it has been of very little, if any, practical use whatever. From the age of 20 to about 50 is the period during which the Northampton Table is so erroneous. ordinary formula for the value of a policy is

The