sidered." On account of their convenience for some purposes, we easily and thoughtlessly fall into the habit of using level net premium reserves for purposes for which they are far from ideal.

The position is taken in the textbook to which reference is made that there is a "borrowing from reserve" both in the various forms of preliminary-term valuations and under select and ultimate valuations, but that there is a difference between the two in that what is borrowed under the select and ultimate method will never have to be repaid because the mortality which would require it will never occur.

To my mind, the methods are much better described, in a brief way, by saying that the definition of legal reserve has undergone changes in different states and countries so as to allow certain deviations from the level net premium reserve. It is the purpose of such changes to adapt valuations to the principle that each policyholder is to pay the expense of putting his policy on the books of the company, and to meet very practical conditions that are almost sure to confront any successful new company.

Under full preliminary-term valuations the purposes are accomplished by making the first year's insurance term insurance, thus releasing for expenses the difference between the net premium for one year and the gross premium. In the case of ordinary life and twenty payment life, this difference is approximately the amount required for initial expenses. For higher priced policies, this difference becomes so large that some kind of limitation of the preliminary-term plan is desirable. It is the theory of the modified preliminary-term valuations that a proper measure for initial expenses is the loading under an ordinary life policy, with full preliminary-term method of valuation, and that therefore a higher priced policy such as a twenty year endowment policy may appropriately be preliminary-term only to the extent of an ordinary life policy. More precisely, it is held that for a policy with annual premiums greater than an ordinary life policy, the net premiums shall be formed by making such a level addition to the net premiums for ordinary life, with full preliminary-term valuation, as will cause the policy to be paid-up or mature according to the terms of the contract. The chief effect of the preliminaryterm method is simply that the policyholder contributes a much greater loading in the first year and a less amount of loading in

D. P. Fackler, Trans. Actuarial Soc. America, vol. VIII, p. 79; cf., M. M. Dawson, Journal Institute of Actuaries, vol. 42 (1904), p. 438.

subsequent years than under the level net premium method of valuation. It is the theory of the select and ultimate valuations that proper reserves may be obtained from a select and ultimate table where the select table reflects the experience, in a sort of approximate way, of the companies with persons who recently passed a medical examination for life insurance; but the annual premium used in the calculation of reserves by the prospective method is based on the corresponding ultimate table. This gives a first year terminal reserve much smaller than if the annual premium were based on the select table as are the other quantities that enter the valuation. The chief effect of this scheme of valuation is similar to that under preliminary-term valuations in that the policyholder contributes much more to loading the first year than under a level net premium valuation, even if part of the loading is nominally designated as a saving in mortality.

The methods are thus not well described as processes of borrowing from reserve. They are much better described as methods under which the reserve is adjusted to meet the conditions of obtaining new business; and, at the same time, is maintained at such a value as will insure the fulfilment of the contracts by the company.

In illustrating one of the objections which is brought against preliminary-term methods, there occurs the following statement: "Should the holder of an ordinary life insurance policy valued on the preliminary-term plan die at any time before age 96 the company will not have entirely replenished the reserve borrowed for the purpose of writing its policy and the deficiency must be made up from funds which should be diverted to other uses." For con-' trast one may well consider the impression obtained from this statement and from the following by the leader of actuarial thought in America during much of his active life: "The use of this system of Dr. Sprague (preliminary-term system) was advocated by me five years ago provided it could be made legal. If it could be made legal and if the reduction in reserves on other forms could be assimilated to the reduction on the ordinary life plan, I should have nothing but praise for that system."

In considering the first of these two statements, we may give a simple illustration that shows how the operation of preliminaryterm valuations may have the opposite effect by obviating the

necessity of diverting funds to somewhat questionable purposes. Suppose an ideal case under the American Experience Table of mortality in which each of 100,000 persons of age 35 takes an ordinary life policy to operate with preliminary-term valuations. Let $21.75 be the gross premium per thousand, and $8.65 be the net term premium for this one year. Under the table, the number of deaths of the year is 895 and the interest on $865,000 is such that $895,000 is available at the end of the year to pay all the death claims. Moreover, the difference between $21.75 and $8.65 or $13.10 is available on each policy for acquisition expenses. This is reasonably near what is required under present American methods of writing business, and there has been no borrowing from the funds of the company. Suppose, on the other hand, that these policies had been written on the level net premium valuation basis; then there would be no such amount as $13.10 available from the new entrant and there would be a really significant borrowing from funds belonging to the group of older members, not only for the expenses on the policies of the 895 that die during the year, but also for the expense of the policies of the survivors of the 100,000 insured. This illustration shows clearly that in a large way the preliminary-term method obviates the necessity of borrowing the funds of the older policyholders to write new business. The holding of modified preliminary-term reserves instead of level net premium reserves does not mean that there is a deficiency in adequate reserves. Indeed, there is not the least evidence that, on behalf of the 100,000 persons used in my illustration, a company with insurance on the preliminary-term plan would have to borrow anything from the time the insurance is taken until the last claim is paid. The same statement would hold under the select and ultimate method, if the assumed saving in mortality is experienced.

In all the discussion of this subject, the effective criticism on the one side is not against the modified preliminary-term valuations, but on the danger of carrying modifications too far. On the other side, it is held as pointed out by the distinguished English actuary, Mr. George King, as an objection to the select and ultimate method that "it would be very difficult to change the table to be used in the valuation when valuing by the select and ultimate method, because that would disturb everything." Of course, in theory there is possible infinite variation of the select

Journal of the Institute of Actuaries, vol. 42 (1908), p. 454.

and ultimate method by a change in the percentages of ultimate rates used to get select rates. But it is difficult to make the changes in practice. Again, Mr. King, who seemed to favor the preliminary-term method in preference to the select and ultimate method, stated as his principal objection1o to the select and ultimate method that the allowance for new business depended, not on the cost of the new business, but upon the table of mortality used in the valuation.

To summarize, the question as to which is the better of the two methods is not a one-sided question, as would appear from the textbook whose criticisms we have considered. It does not seem from what has been written and from somewhat intimate personal knowledge of the operation of these methods that either one has a clear advantage over the other. It does seem rather that with a strict adherence to modified preliminary-term valuations, and with the present practice under the select and ultimate method, the evidence is not good that the differences between the two exceed the effect of the somewhat arbitrary factors that enter into these valuations. On the one side, it is important to guard against carrying too far the allowances in preliminary-term valuations by modifications to standards that differ much from modifications to the ordinary life policy; and, on the other side, it is important to make more convenient the way to changes in the select and ultimate standard as soon as experience can be used to show that changes are desirable.

University of Illinois. 10 Loc. cit., p. 453.

H. L. RIETZ.

REVIEWS AND NEW BOOKS

General Works, Theory and Its History

NEW BOOKS

BOGARDUS, E. S. Introduction to sociology.

(Los Angeles: Univ.

Southern California Press. 1917. Pp. 343. $1.50.)

ELLIOT, H. Herbert Spencer. Makers of the nineteenth century, edited by Basil Williams. (London: Constable. 1917. Pp. vi, 330. 6s.)

ELLWOOD, C. A. An introduction to social psychology. (New York: Appleton. 1917. Pp. xii, 343. $2.)

This is a restatement as a textbook of the author's Sociology in its Psychological Aspects. The author has succeeded in outlining the leading phases of his subject and has arranged his discussion helpfully in its sequence, subdivisions, and references. The repetition sometimes seems monotonous but is probably needed in such a text. There is a catholicity about the author's thinking that will be a wholesome corrective for one-sidedness in teacher or students; there is not only a willingness to see strength as well as weakness in divergent opinions but also a desire to gain the strength of each in some inclusive conception. The style is easy, so easy, in fact, that the student may be lulled into agreement rather than aroused to argument, and may respond to the pleasant flow of ideas by drifting with the current.

The real limitation of the book for teaching purposes is its abstractness. The author probably realizes his desire to "avoid, as far as possible, an overspecialized scientific terminology"; but his illustrations are so few and so brief that the discussion is almost like a succession of conclusions about unknown facts, as far as the student is concerned. Certainly the richness of the author's observation and reading has supplied him with actual social situations to interpret and vitalize his conclusions. Then, why not give the student at least some concrete base on which to stand? If the teacher of the parallel reading can supply sufficient illustrative material, the present text can well serve to guide and strengthen the course; but, if not, the text may evoke confidence in the student without understanding.

The first chapter is devoted to definitions and methods and the second and third chapters to the organic background and the interrelations of human and social evolution. Then follow discussions of the unifying influences in society, the continuity of these influences from generation to generation, and their change under normal and under abnormal conditions. The next chapters expand previous statements into detailed analyses of instinct and intelligence, imitation and suggestion, and sympathy in the social life. The author's success in combining different opinions is specially shown in his final chapters on the contributions of government, religion, morality, education, etc., to social order and on the varied