page 133 note * Supposing no bonuses to have been surrendered.

^{page 133 note †} Thus it will be seen that, as between policies on lives of different ages at entry, but of the same length of standing, the remark of Mr. , Jellicoe (Assurance Magazine, vol. iii, p. 191),Google Scholar with reference to No. 6 method, that “at each septennial division the same degree, or very nearly the same degree, of injustice is perpetrated as at the first,” confirmed, and, indeed, may be extended to all the other methods here spoken of.

page 135 note * Of course this la true only upon the supposition here made, that the policies are for an equal amount and have been an equal number of years in force since the previous valuation. The share of each contributor being represented by the well-known formula , it is evident that the ratio between the amounts so represented will not be affected by dividing the above expression by what, under such circumstances, will be the constant quantity .

Referring to this method, an able writer has remarked (see paper by Mr. Sprague, in Assurance Magazine, vol. vii, “On certain methods of dividing the surplus among the assured in a Life Assurance Company, and on the rates of premium that should be charged to render them equitable”), that, “although it is as equitable as any that could be devised, there seems to be one point in its working which is open to some objection—I mean, that, since the successive cash bonuses on each policy will be of about the same magnitude, supposing the state of the Company to remain the same, it follows that the successive reversionary bonuses will form a decreasing series, on account of the increasing age of the life assured. This, of course, is no objection to the theory of the method; but I think it will be admitted, that the public at large, who understand nothing of the theory of life assurance, expect that each reversionary bonus on their policies should be at least as large as the preceding one; and it will probably be thought an advantage if a method of division could be adopted which, while equitable to all parties and simple in its details, should at the same time satisfy the condition mentioned above.” The writer then proceeds to indicate two means by which these objects may be, to some extent, attained. The first is, “to distribute only a portion of the surplus that appears as the result of the valuation, and reserve the remainder to accumulate and to be divided at a future time among the survivors of those who have contributed towards it.” The second, and, as added, the more practicable one, is to regard the loading as the annual premium for an increasing assurance. In both these cases, however, the effect would be to give an advantage to those who live long, at the expense of those who die soon; and, however desirable it may be to satisfy public expectation, it does not seem to me to be possible for an Office to adopt a system calculated to yield reversionary bonuses of increasing amounts upon a policy, without some departure from the fundamental object of the Association.

page 139 note * Mr. Higham's “Mixed Mortality Lives from among whom the effect of selection has been exhausted.” Interest 3½ per cent.