proposed to put seven years on her life, which made a most insignificant difference in the premium, which he (Mr. Hardy) did not consider was at all an equivalent for running a risk of that nature. It was usual for medical men to have by them a table of the expectation of life; and if they thought a man would not live the period there set down, they took him at an age corresponding to the diminished expectancy. But surely if that were the measure of the greatest possible duration of his life, he ought to have been rated at an age where by the tables he could not live that term. What they should look to, was to see what effect it would have upon the premium; because, unless they had a large premium, an early death would hit the company very hard. One point the medical men attach great importance to is the early deaths of the parents; but as a large number of deaths occur in the prime of life, it is evident there are a large number of persons in existence whose parents could not have attained a very old age. With regard to some of the additions made in the case of the Medical Invalid, he had had the schedules of that company under his notice, and he found that some of the rated-up cases had reached to the extreme of life-one case at the commencement of the company, where the addition was 30 years.

Mr. HODGE asked Mr. Humphreys whether he knew what was the highest rate of addition-not the average rate-in each class.

Mr. HUMPHREYS replied that he had got the whole of the data. He knew there was one case in which an addition of 34 years was made.

Mr. PORTER asked Mr. Humphreys whether it had been the custom in the company he represented, in dealing with cases in which there was a slight deviation from the normal standard of health, to charge the extra premium for a number of years, say seven or fifteen, and then if the disease had not developed itself to revert to the ordinary premium. With regard to a remark made by Mr. Hodge as to the varying intensity of disease, and the consequent impossibility of comparing tables of diseased lives, he had heard of a curious instance of that. A child under the care of Dr. West was suffering from mesenteric disease; and it was said that if there was consumption in either of the parents, the child must have died.

Mr. BUNYON enquired of Mr. Humphreys whether he had investigated the particular mortality which occurred amongst the gout and hernia cases, because although, as had been more than once observed that evening, the individual cases were all marked in the ordinary practice according to the supposed intensity of the disease that existed, yet they knew that the common practice with insurance companies had been to charge so much for gout and so much for hernia. The old offices used to make an addition of 10 per-cent, and sometimes 111⁄2 per-cent, to the ordinary premium for gout. He should like to know, as a matter of curiosity, what was the additional rate of mortality in the particular cases which had been assumed to have something like a uniform intensity of disease. In cases of consumption and so on, it is impossible to fix any uniform premium; because, in one instance, a small addition will suffice, and in another, an addition of 35 years will not be enough to meet the risk.

Mr. HUMPHREYS said he had worked out each disease financially, but not as a separate mortality table.

Mr. HODGE enquired how the cases of hernia turned out?

Mr. HUMPHREYS said they turned out very successfully,—rather better in fact than the others. The average duration of the policies with regard to hernia was 12 years, and of each policy on the whole of the diseased lives, 10 years. The average of the policies on lives afflicted with gout was 10 years. The financial result followed some

what the same law.

The PRESIDENT remarked that he believed the old extra charge of 10 per-cent was fixed because the Equitable charged 11 per-cent.

Mr. MANLY wished to know whether in the different columns family history was included with personal history. He noticed in the family history column there were only 579 cases out of a total of 3,147, which appeared a very small number indeed.

Mr. HUMPHREYS said that in the family history column, which included cases of general want of robustness, a very small addition was required. There was often no actual disease, but the lives were not what could be called first-class.

Mr. MANLY said he did not know whether Mr. Humphreys had examined Mr. Meikle's investigations into the diseased lives amongst the ten Scottish offices, but he there divided the doubtful lives into two classes-personal history and family history; and if he (Mr. Manly) remembered rightly, Mr. Meikle found that amongst those who were rated-up for family history, there being no disease found in the individual, the mortality was very nearly the ordinary average; but that the mortality amongst the lives which were rated-up for some defect in the personal constitution, was so bad that the business was hardly worth having. [Mr. BAILEY remarked that there were not 500 deaths in those observations.] Mr. MANLY said he was aware of that, but still the fact was very striking, and it was most important that it should be followed out. It was very difficult to reject a man because his family might have a tendency to disease, he himself being in apparently good health. This was a subject which would, he thought, be worthy of consideration, and if Mr. Humphreys would take it in hand on a future occasion, it would be an acceptable addition to their knowledge of the subject, which is one of real practical importance.

Mr. BAILEY remarked that with regard to family history, when he insured in the Eagle many years ago, questions on that subject were never asked. It was quite a modern practice to enquire into family history.

The PRESIDENT, in proposing a vote of thanks to Mr. Humphreys for his valuable contribution to their transactions, expressed a hope that they might again have the pleasure of listening to him on this difficult but important subject.

Mr. HUMPHREYS said he was very much obliged to them for the attention they had given him on that occasion. With reference to Mr. Porter's question, he could not call to mind how many cases had been met by a limited number of payments. In a recent case it was arranged that the larger premium should extend over twelve payments, so that the whole of the premiums at the increased age should be paid

in eleven years, the insurance not to be paid till the death of the person insured. He was fully aware of the difficulties environing this matter which Mr. Macfadyen had brought to their notice; but he had placed before them the best materials he had at command, and he hoped they would be found of some practical value.

On the method of comparing the Expected with the Actual Experience of a Life Insurance Company, as regards the number of Deaths and amount of Claims. By GEORGE M. Low, F.F.A., of the English and Scottish Law Life Association, Edinburgh. THE business of Life Assurance is founded on the principle that the number of deaths which will occur among a large number of persons in a given time is not a matter dependent entirely on what is called chance; but is subject to a law of average so uniform in its operations, and so trustworthy as to its results, as to be capable of forming the basis of calculations on which the shareholder may stake his capital, and the assured the welfare of those for whom it is his duty to provide. Proceeding on this principle, tables of mortality have been constructed,-from data collected at different places and under a variety of circumstances, and tabulated and adjusted with various degrees of accuracy, which show, out of a given number of persons born, the number who survive each year of age, and the number who die at each age from year to year. From such tables, companies transacting the business of assurance calculate the rates of contribution to be required from their clients; and on the sufficiency of the rate of mortality founded on in any instance depends, of course, the sufficiency of the premiums which the company is to receive in consideration of its risks. It is therefore of great consequence that the company should ascertain from time to time how the rate of mortality actually experienced compares with that indicated by the table on which the calculations are founded, in order that there may be proper grounds for being satisfied that the basis is a correct one. For it is not sufficient that the mortality table founded on should be known to represent faithfully the death-rate prevailing among the general population, or even among assured lives generally. Every office has, in the peculiar nature of the benefits which it offers-the localities from which its business is drawn-the character and social position of its agents-the skill, and, it may be, the peculiar opinions of its medical officers and its executive - and, indeed, in an endless variety of circumstances-influences at work which tend to modify

in a greater or less degree the quality of the lives which come upon its books, and consequently the rate of mortality which it is likely to experience. Nor do these remarks apply to offices only in the earlier stages of their existence. It is well known that the value of some of the most popular tables is not equal at all ages; and it is not until a company has been in existence for a very considerable period that it is able to test, from its own experience, the trustworthiness of the table on which its calculations have been founded, as regards the later periods of life. The Carlisle Table, for instance, once almost universally popular, is now gradually being abandoned, mainly because the experience of the older offices has shown its untrustworthiness at the higher ages of assured life.

Another important use of the calculated mortality occurs in connection with the periodical investigations which are made into the affairs of companies with the view of ascertaining the amount of profit arising from their transactions. It is very desirable to know what portions of the total profit have been derived from interest, mortality, margins, or other sources. Now the only way in which the actuary can ascertain what portion of his surplus has arisen from the actual mortality experienced being lighter than that calculated upon-or to what extent the surplus has been encroached upon by mortality in excess of that provided for,-is by calculating the amount of the expected claims for the period over which the investigation extends, upon the basis of the mortality table from which the premiums were charged.

Having thus endeavoured to show the importance of the calculations to which this paper refers, I will now proceed to consider some of the methods which are adopted by offices for ascertaining the number and amount of their expected claims, and to inquire to what extent these methods appear to diverge from strict accuracy. But, first, it may be necessary to say that the word "expected" is here used, not in its literal sense, as implying something which is likely to happen, but in a sense resembling in some degree that in which the phrase "expectation of life" is used:-the "claims to be expected" being, not those which it is anticipated will actually emerge, but those which are provided for by the table of mortality employed. Of course, no one would "expect" this number actually to arise, any more than a man of, say, 30 would "expect" to survive exactly the number of years enjoyed on the average by persons of

his age.

In most offices such estimates as we are now to consider are made and recorded from year to year, so that the materials are

always at hand for instituting a comparison between the expected mortality and that which has been developing itself among the lives assured during the various stages of the company's progress; while in some offices it is only thought necessary to institute a strict inquiry into the results of mortality experience at the investigation periods; any intermediate estimates being merely approximate, and not relied upon as furnishing the materials for comparison with any great degree of accuracy. In the observations. which follow, I shall have in view primarily the first of these two systems, namely, that of estimating mortality from year to yearbut the same general principles are applicable to both cases; the quantities on which the calculations are founded being always the number of lives and the amount of sums assured which are exposed to the risk of mortality for one year at each age.

Of all the various circumstances which affect the chances of life and death in individual instances, that only of age is taken into account by assurance companies in their calculations; it being assumed that selected lives of the same age are equally exposed to the chances of mortality, and any deviation from the general standard of eligibility in particular cases being generally met by referring the life in question to a class in which the chances of death are greater—that is, by making an addition to the real age in calculating the premium to be charged for the risk. Hence it is, that in dealing with the whole number of lives upon the books of a company, it is only necessary to treat separately the numbers existing at the different ages; and as has been said, that in calculating the number of expected deaths, the quantities founded on are the numbers exposed to risk at each age. The first step in the calculation, therefore, is to collect together the numbers existing at the several ages, which is accomplished by recording each assurance under the year in which the policyholder was born; care being taken, of course, to eliminate duplicate policies, so that each life may only be reckoned once, no matter how many different assurances may depend upon its existence.

Having thus ascertained the numbers alive at the commencement of any particular year, nothing would remain to be done in order to arrive at the expected mortality for that year but to multiply these numbers by the respective rates of mortality at the various ages, were these numbers not subject to increase, and to diminution from other causes than the death of the parties. But some of the policies are likely to be allowed to drop, others to be surrendered, and the period for which others have been effected may expire before the close of the year; while, at most ages, new assurances