“The Institute has now fairly started on its new career of usefulness as an incorporated society.” Usefulness, then, in the admirable words of the Council on the 5th June last, is to be the ruling principle of the Institute's new and corporate life, as few, who are acquainted with what has been done with hut small opportunity, will deny it has been of its action in the past. But for its usefulness to be thorough, the Institute must be concerned with both the theoretical and practical sides of our profession in all its branches—recollecting as well its commercial basis as its mathematical speculations, considering its connection with medical and legal specialties, collecting data, comparing methods, proving uncertainties, destroying chimæras, teaching students and testing their acquirements, not to mention accumulating a library for reference and instruction—always advancing, suggesting, restraining, reforming.

A case arose about this time—the middle of the eighteenth century—which, as it illustrated some points in practice and an important principle in the law of Insurance, I will briefly review. It is the case of Cleeve v. Gascoigne. In June 1749, the defendant (Gascoigne) had applied to an Office-keeper, or Broker, to insure £1,600 for one year at 5 per-cent on the life of one Poulton, from whom the defendant had agreed to purchase an estate, whereof Poulton had the reversion in fee, and also an intervening interest for his own life.

It is a common thing to find in the reports of life assurance companies a statement to the effect that the actual deaths and claim payments have been under the expectation, or have represented a certain percentage of the expectation. The records of life assurance literature would appear to show that little attention has been given to the methods on which these comparisons are based, the only contribution to the Journal bearing directly on the point being a paper by Mr. G. M. Low (J.I.A., xviii, 195). But as the matter possesses a considerable and growing importance, the following note has been prepared with the object of suggesting a method by which such estimates may be computed according to a plan which seems reasonable and defensible on scientific grounds.

I have on various occasions stated that, in my opinion, the graphic method is the best one to employ in graduating a mortality table; and I have more than once had it in contemplation to explain fully the grounds for this opinion, describing the advantages of the graphic method, and the objections I see to the use of some other methods which are commonly employed. In order to do this satisfactorily, it is clearly essential to give a graduation of some mortality observations; and my attention having been again drawn to the subject by reading Mr. Higham's brief, but extremely interesting and suggestive paper, On the Graduation of Mortality Tables (J.I.A. xxv, 15), in which he speaks unfavourably of the graphic method, I think that an examination of his reasoning and results will furnish me with the most suitable opportunity I could have for stating my views on the whole subject.

I do not pretend that much which is original will be found in this paper. Previous writers, notably the late Sir J. W. Lubbock, and Messrs. Woolhouse, Sprague, and G. F. Hardy, have, so far as actuarial science is concerned, nearly exhausted the subject of Formulas of Approximate Summation; and from time to time examples have been given of the practical use of the formulas, which have indicated the great facilities they afford to computers. But something in the way of numerical illustration remains to be done in order to bring the formulas into more general use, and to supply that want is my present object.

Globe Insurance Company.—Early in the year 1799 a plan was laid before Mr. Pitt for forming a Chartered Insurance Office, for granting Insurance against Fire, and for Insurance of Lives; for buying and selling Annuities, and for receiving deposits from Friendly Societies, and the Industrial Classes: to be called the Globe or General Insurance Office. It was understood that the plan received that Minister's approval, and a Bill was introduced to Parliament embodying these objects. The measure encountered some opposition. In the first place, the Bank of England objected to the Deposit branch, and the clauses relating thereto were accordingly struck out. Then it was opposed by several of the Insurance Offices; but the Bill finally passed through both Houses, and received the Royal Assent.

Mr. T. B. Sprague, in his opening address delivered on the 30th November 1885, when he was President of this Institute, treated, in his usually full and exhaustive' manner, of the various theoretical doctrines current respecting Life Assurance. One of these, he said, “ seems to me to proceed upon the idea that life “ insurance is exclusively a contract of indemnity, the object of “ which is to indemnify the family of the life assured against the “ loss they will suffer if he should die prematurely, and be deprived “ of the opportunity he might otherwise have had of saving money “ and making a provision for those dependent upon him. Looking “ at the matter more practically, it may be held that life insurance “ is also a species of investment; in fact, that an ordinary life “ insurance policy contains elements both of indemnity and of “ investment. … If an indemnity only were desired, life “ insurance should logically cease at the age when the need for the “ indemnity has ceast; that is to say, when a man's working years “ are past, and he is no longer in a position to earn money by “ following his trade or profession. In fact, the logical conclusion is that all insurances should be term insurances expiring at “ about the age of 65.

The great importance of the subject of distribution of surplus, I think, no actuary would be inclined to dispute. With regard to the magnitude of the interests involved, I will content myself with referring to Mr. Hewat's paper, read before the Actuarial Society of Edinburgh on 8 January 1880, and of which an abstract is given in the Journal (xxii, 286–292). In this paper he stated that, from the Board of Trade Returns relating to seventy-seven offices, he found that £2,285,000 was, on the average, annually divided among the policyholders by way of bonuses. Of this sum he estimated that £890,000 arose from surplus premiums or loading, and £1,040,000 from surplus interest.

The important and laborious investigation of which we give the results in the following pages is the last serious contribution to statistical knowledge by Mons. Marco Besso, a Fellow of the Institute of Actuaries of some years' standing, and an insurance expert of wide experience and great repute throughout the continent. The paper was at first published in part in the Bulletin de l'Institute de Statistique, and a translation subsequently appeared in the German Annual Magazine of Herr Ehrensweig.

Though between the graphic method on the one hand, and Mr. Higham's on the other, the formula used by Mr. Woolhouse in graduating the Institute Tables seems to have lost something of its pre-eminence, it may be convenient to have on record a general expression for it, correct to third differences, derived as on pages 341 and 350 of the twenty-third volume of the Journal.

The state of the law in respect to Joint-Stock Companies, and associations for business purposes generally, remained in the same unsatisfactory condition which I have described in the previous section down to this time. Those great Insurance Associations, with millions of capital subscribed, in many cases, by the merchant princes of the land, for purposes admittedly the most beneficent, were simple partnerships, almost without legal recognition, except for purposes tending to their detriment or destruction. They could be attacked or pulled down by legal process readily enough; but they could only protect themselves against fraud, or recover their just debts by the most cumbersome of processes. What they had a right to expect, as institutions designed to aid largely in the accumulation of national wealth, was protection in carrying out their laudable designs; but of this they had not a vestige. Not only was every holder of stock in a proprietary company primarily and personally liable to his last shilling for the engagements of the partnership, but every policy-holder in a mutual society, being a member of, and therefore a partner in such society, was equally liable for all its engagements.