In a short paper read before the Institute at the early part of this year, after alluding to the erroneous methods commonly adopted for the determination and division of surplus in Life Assurance Companies, I intimated my intention to investigate the nature and character of those methods, and to endeavour to demonstrate the mischievous and injurious consequences resulting from them. In the present paper I propose to commence this undertaking, trusting that the undeniable importance of the subject will be considered a sufficient apology for my somewhat frequent introduction of it at these meetings.

The merits and demerits of the present mode of assessing the Property and Income Tax have been so frequently made the subject of popular discussion, and are in themselves questions of such national importance, that I feel no apology to be necessary for again bringing the subject under the notice of the Institute of Actuaries.

A valuable paper on the inequitable operation of this tax was, some time ago, read before the Institute by Mr. Jellicoe; and, more recently, an elaborate and important contribution on the same subject was brought by Mr. Farr under the notice of the Statistical Society of London, which paper has given rise to a lengthened and very interesting discussion. An exceedingly temperate and able pamphlet has also been recently published by Mr. John G. Hubbard, the Deputy Governor of the Bank of England, in which that gentleman has discussed, with very considerable ability, the views of Mr. Warburton, and has, in my opinion, very effectually exposed their absurdity.

It is a well-known feature in the advancement of learning, that the more knowledge becomes prevalent, the less positive do opinions become. Not only in theology does the staggering demand of “What is truth ?” assail us, but we meet with the same impregnable question in all the pursuits of literature and science, obliging us to admit that the truth of yesterday is not always the truth of to-day, and that to-morrow may still be about to offer us some third form.

The older class of writers felt no such difficulty. They conceived they were in possession of certain abstract truths or data that might be considered as fundamental axioms, and that by these axioms might all conclusions whatsoever be tried.

Let a1, a2 . . an be the reciprocals of the roots of the expression 1 − s1x+s2x2 − . . ±sn−1xn−1∓snxn, which call ϕx. We have then ϕx = (1 −a1x) (1 −a2x) . . . (1 −anx), from which the following series of values may be readily deduced, the Σ implying the sum of all the instances of the form placed under it, so that each expression is a symmetrical function of a1, a2 . . an.

The sign is positive when p is even, and negative when p is odd. A single term of the pth expression contains p factors of the form a, and n–p factors of the form 1 – a; and the expression itself is the sum of every term which can be so constructed.

It was hardly to be expected but that an attempt to demonstrate the inconveniences arising from daily increasing competition in the business of life assurance should meet with resistance and reprobation. The large number of persons interested in novel undertakings of the character in question would naturally feel themselves aggrieved at statements which went to prove that such undertakings were mischievous because they could not be successful, and which sought to demonstrate their hopelessness of success by an expose of their actual condition; on the other hand, it is not much to be wondered at, that minds familiar only with a state of affairs so wholly different should regard with anxiety and alarm a succession of enterprises threatening not merely to encroach on their own field of operation, but, by a series of failures, to bring all alike into general suspicion and discredit. As in most other controversies, much allowance is to be made on either side. The interests of the two parties are probably not altogether antagonistic, but they can scarcely fail to come into serious collision unless placed under more carefully devised regulations than at present exist.

V. The life assurance branch of the General Assurance Company (Assicurazioni Generali Austro Italiche) in Trieste was established in 1834 as a separate branch of business of this Company, which also undertakes fire and marine assurance; and its operations extend not only to all Austria and Germany, but also to other European countries, and especially to Italy. It is a purely Proprietary Company, the assured receiving no part of the profits of the Company. The security for the fulfilment of the Company's engagements is a share capital of two millions gulden (£200,000), in 2000 shares of 1000 gulden (£100) each, of which 10 per cent. is paid up. One half of the capital is specially set apart for the guarantee of the life and annuity business. The Company offers to the public the choice of a great variety in the modes of assurance. Assurances for the whole life, for fixed periods of years, of sums deferred for a given time—assurances of the sum payable either in case of death or on attaining a given age—survivorships, the last with the return of premiums in case of the life against which the assurance is made dying first—as well as endowments and life annuities—are granted. As in other established Companies, by far the greater part of the business consists of the single assurances for the whole life, and the other modes are resorted to but seldom. The premiums appear to be computed on some peculiar data, or a table not generally recognized.