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During its 1969 session the Legislative Assembly of Alberta enacted a distribution formula for the future distribution of Alberta provincial legislative districts.' The Legislative Assembly acted upon the recommendation of a special bipartisan Committee of the Legislature established during the previous session, the function of which was to determine the most appropriate method of provincial legislative distribution for Alberta.2 The new scheme follows closely that used by Manitoba for provincial legislative distribution, namely the establishment of separate electoral quotas for urban and rural districts, with the urban electoral quota being a set number of voters above the rural quota. The task of delineating district boundaries is to be handled by an Electoral Boundaries Commission, semi-independent of the Legislative Assembly. The special Committee of the Legislature was set up initially to cope with the necessity of adjusting the representation in the legislature of Alberta's continually growing urban centres. The impetus for establishing this committee came mainly from the recognition on the part of the Social Credit government that it faced a possible distribution crisis over the locus of political power within the province if the present distribution scheme continued in existence. The demands for equal representation in the provincial legislature have stemmed from a growing awareness by interested civic groups, urban members of the legislature, and urban city councilmen of the increasing political and economic importance of the province's urban areas and the belief that urban needs were being ignored by a rurally dominated provincial legislature. This rural domination had been maintained throughout Alberta's history by the continuous over-representation of the rural provincial districts. Moreover, Alberta's urban leaders have been cognizant of successful attempts by American cities to achieve both federal and state apportionment based on a "one man, one vote" standard. During the course of formulating its recommendation the special committee received briefs from both urban and rural organizations. The rural view, which subsequently underlies the new redistribution scheme adopted by the legislature, is the traditional feeling among Alberta legislators towards distribution, namely, to overweight rural areas. This view appears to be a rationalization of Alberta's

In a recent paper in this journal, Gilmer and Morgan attempted to prove that there is equivalence among certain forms of education subsidy programs-flat grants, foundation programs, and equalized apportionment formulas. This paper demonstrates that the proof presented by Gilmer and Morgan does not support the conclusion that these subsidy programs are equivalent.

In 1907 I had the honour of reading before the Institute a paper dealing with the Comparative Bonuses under Whole-Life and Endowment Assurances, and therein I pointed out that the method of apportioning the expenses between the two classes had a considerable effect upon the rates of bonus, and in the discussion more than one speaker referred to the relative premiums as vitally affecting the conclusions to be drawn from any investigation. The solution of the first problem will, mortality apart, also give us the key to the rates of premium which an office should charge for Whole-Life and Endowment Assurances respectively. As the premiums are the foundation of our business it is of the utmost importance that an analysis of the expenses should be made periodically in order to ascertain the adequacy of the remuneration the office receives for the risks it undertakes. The question of the office premiums has been frequently discussed, but I do not think any paper has been submitted to this Institute in which an agreement has been shown between the loadings adopted in obtaining the office premiums and the actual expenses of the office. The object of the paper is to elicit the views of the profession upon this subject.The commission paid by the majority of offices is, for the principal classes of Assurance, usually a percentage of the sum assured on payment of the first annual premium and a percentage of the office renewal premiums. The loading required to provide for the commissions is therefore easily ascertained and requires no discussion.

The subject of this paper has on two previous occasions been brought before the Institute; namely, by Mr. Jellicoe on 26 November 1855, and by Mr. Baden on 27 March 1871. The former of these gentlemen stated that, at the time his paper was written, a great diversity of opinion existed among actuaries, as to the proper method to be adopted in advising upon the proportions in which a settld fund should be divided by mutual consent between the life tenant and the reversioner; and so far as can be judged from the discussion that followd the reading of the latter paper, a similar diversity still existed then. One point, however, was clearly establisht by the discussion, namely, that Mr. Baden was quite mistaken in supposing that, because Mr. Jellicoe's conclusions had not been publicly calld in question, therefore they wer generally accepted by members of the profession.

…the solutions given…are so various as to excite no little surprise and distrust in the minds of those unacquainted with the subject, under whose notice such solutions are brought.…a great deal of judgment and discretion must always be required from the actuary, and…it is not possible to lay down any general rule which shall altogether obviate such requirement.The quotations above are taken from a paper by Jellicoe (J.I.A.6, 61) which was discussed by this Institute in 1855. It is a salutary thought that there are no subsequent statements recorded in J.I.A. on the subject which seem to express so succinctly the two principal points which should always be borne in mind when the apportionment of a trust fund is under consideration. It must be stated immediately, however, that since 1855 problems of apportionment have been discussed only in 1871 (J.I.A.16, 269), 1873 (J.I.A.18, 77) and 1925 (J.I.A.56, 243); indeed, reversions and life interests have scarcely been mentioned in Institute discussions since 1935, when O. I'A. Thurston presented his paper on Death Duties (J.I.A.66, 369).

SynopsisThe paper records the growth in the number of apportionments of trust funds due to the passing of the “Trusts (Scotland) Act 1961”. It considers the problems, as they arise in Scotland, of allowing for the impact of taxation, both in determining the interests to be valued and in fixing the valuation rate of interest, and it is suggested that the same net rate of interest need not necessarily be appropriate for all the beneficiaries.Numerical examples are given of the effects on funds of varying size and investment content of various valuation assumptions, and the problem of disposing of the potential savings in taxation is discussed. The paper ends with a general section covering some practical points in the preparation of schemes to vary trust purposes.

If any excuse be wanting for once more bringing this question forward for your consideration, it is not because the question itself is unimportant. The frequency of the cases involving it upon which the opinion of actuaries is sought, and the magnitude of the interests concerned, will be allowed by all to furnish ample grounds for the utmost possible care and pains in determining the principles by which the advice given should be regulated. Upwards of 15 years have elapsed since Mr. Jellicoe's well-known paper on this subject was read before the Institute. How far the practice of actuaries has been influenced by the conclusions laid down in that paper I do not know; but from the fact that (so far as I am aware, at least,) the subject has not been reopened since, it would seem that these conclusions have been accepted by the profession, and that in the opinion of those most competent to form a judgment there is nothing more to be said about them. If this be so, I am afraid that I shall incur the suspicion of rashness when I say that the excuse I have to urge for reopening the question is, that the conclusions laid down by Mr. Jellicoe do not commend themselves to my mind as perfectly satisfactory. I propose very briefly to state my reasons for differing from him; and should I fail, as I well may, in convincing others of the correctness of my views, I shall be consoled by the reflection, that however firmly established, and apparently beyond discussion, any truth may be, it is a profitable thing for most, perhaps for all of us, if a rash sceptic now and then compels us to review the grounds of our confidence, and to restate to ourselves, if not to others, the reasons for the faith that is in us.

This paper is mainly concerned with the division of a trust fund between the beneficiaries, when an actuary is asked for a solution which, in his opinion, is fair to all parties concerned. It may be that the beneficiaries are all sui juris and form a closed class, in which case they approach the actuary as umpire, and adopt a passive role, at least until they have considered the implications of his recommendations. Alternatively, the actuary's report may be required to assist the Court to approve a scheme involving beneficiaries, e.g. infants, whom it is the Court's object to protect. In that case the actuary's role—as discussed later in the paper—is rather different, but it may still be necessary for him to state what in his judgment would be an impartial solution.

As a result of the I950 census, and as the Constitution undoubtedly intended, the matter of congressional apportionment and how it will affect the Eighty-third and succeeding Congresses is brought forcefully to our attention. Many writers have left the impression that there is much to be desired with respect to the formation within the states of districts which provide representation on a fair and equitable basis. It is the purpose of this paper to analyze what is being done and what will be done on congressional apportionment in the various states in order to comply with the legal requirements and the traditional standards that have been set up to provide such fair and equal representation. Although the territorial unit as a basis of representation is old in American history, it was not until 1842 that it became the legally prescribed manner of electing members of the House of Representatives. The legal requirement that districts be composed of contiguous territory first appeared in I842,1 but the requirement that districts also be compact did not become law until the Apportionment Act of 190o.2 These requirements have been omitted from apportionment acts since I9293 and no such requirements exist in federal law at the present time. In a message to the first session of the Eighty-second Congress on this subject, President Truman called for the reinstatement of these legal requirements that districts be made up of compact territory, but up to the present time this has not been done.4 A Committee on Congressional Reapportionment of the American Political Science Association also called for the reinstatement of these provisions and in addition stated the desirability of expressing "the standard of approximate equality among the districts with greater definiteness than hitherto."5 It is evident then that these standards are very much alive as factors to be considered in achieving fair representation in Congress. Since what is done in any one state may affect the nation as a whole in contributing to the existing balance of power in the House of Representatives, it has been thought desirable to examine the situation in each of the 48 states where the necessary information has been available. This paper could not be a detailed analysis of the factors which went into the districting arrangement which exists in each of * Ph.B., Northwestern University. '5 STAT. 491 (1842). 2 3I STAT. 733 (I90I). 46 STAT. 21, 26 (1929). 4DECENNIAL CENSUSES AND APPORTIONMENT OF REPRESENTATIVES IN CONGRESS (MESSAGE FROM THE PRESIDENT OF THE UNITED STATES), H. R. Doc. 36, 82d Cong., Ist Sess. (Jan. 9, 1951); 97 CONG. REC. 114 (I95I). 5 The Reapportionment of Congress (Report of the Committee on Congressional Reapportionment of the American Political Science Association), 45 AM. POL. ScI. REV. 153, I54 (1951).

IN VIEW of the fact that the International Committee on The Standardization of Disinfectants, appointed at the last meeting of the International Congress on Applied Chemistry, cannot meet this year, owing to the war, and that this may entail a further delay of three years, we desire to call attention to one or two points which have arisen since the publication of our paper on "Approved Technique of The Rideal-Walker Test," * and to submit the following suggestions as addenda to the paper referred to. First, in view of the difficulty experienced by some workers not familiar with the technique of the chemical laboratory, we sliggest that a burette, such as that described by Hermann W. Mahr, of the Board of Estimate and Apportionment, New York, pan be adopted in place of the dropping pipette. On the other hand, we know many workers who have a decided preference for the dropping pipette originally used by ourselve's and who do not see the necessity for changing this detail of the technique.

Recent years have witnessed a renewal of interest in the application of management science techniques to personal selling related problems. Some early applications are described in [2] [7]. Cloonan has employed simulation in examination of the salesman routing problem [3] [4]. Lodish, in CALLPLAN, has devised an interactive call planning system designed to assist sales management and/or salesmen in allocating sales call time more efficiently [6]. Armstrong has devised a system he labels SCHEDULE which estimates the value of calls on accounts [1]. Hess and Samuels have designed a computer based sales districting model which is an analogue of a legislative apportionment model [5]. The objective of this paper is to explore the nature of a call planning system entitled ALLOCATE. ALLOCATE was designed to be employed by upper sales management either as an input device for sales management decisions such as sales-territory-size, or as a vehicle for determining the effects of alternative call allocation strategies on territorial revenue over multiple time periods.

It is, perhaps, heresy to quarrel with an old adage. In line, however, with a current bit of philosophy that it is as expedient to be hanged for a sheep as for a lamb, this paper will take issue not with one old adage, but with two. There is a proverb that to be absent makes one conspicuous. Another holds that the absent are always guilty. We wish to take the ground, that neither of these is of necessity true. As it is an economic axiom that no progress can be made until there is a definition of terms, it is necessary, before going further, to understand that "the absent" under discussion are the industrial absent. And by "the industrial absent" are meant-Jones, the machinist, who does not come to work on Monday morning and Smith who loses half a day on Wednesday. By absence we do not mean labor turnover or unemployment. Absence is unquestionably a factor in labor turnover, but for our purpose the terms are by no means synonyms. Turnover is the broader term. It is said that a man's, or firm's, pocketbook is a vital organ. It would seem then that anything connected with the apportionment or outlay of the purse's contents would be known to its owner. But there are practically no figures obtainable on the exact cost of industrial absences. Moreover, as one firm admits, most estimates in this connection are not estimates at all; they are simply wild guesses. Closer estimates, however, may be made in an indirect way. For instance the L. Bamberger Company of Newark estimates that they have to employ 5 per cent more people than is absolutely necessary because of the factor of absence. The Dennison Manufacturing Company figures the average wage loss to be forty-two cents a week to each female factory worker, and forty-nine cents a week to each male factory worker, these figures based on the average weekly wage being paid at the time the study was made. The total wage loss is $50,000 a year. A concern in Detroit is spending $50,000 a month 140

This paper attempts to examine carefully the problem of determining a numerical measure which reflects the quality of the population apportionment in a legislative body. We desire a single index, an index which takes advantage of the available population data, and an index which is readily understood. It should be said that we are not concerned with the much more difficult problem of legislative districting—actually drawing district boundaries on a map—but concentrate our attention only on the quality of apportionment in the particular, but important, sense of population equality.In order to accomplish this purpose I review a number of increasingly complex possibilities and eventually arrive at a measure which superficially seems somewhat esoteric, but which turns out ultimately to be easily interpretable.It will be convenient to proceed heuristically with the development by carrying along a small concrete example. For this purpose, consider the six congressional districts of Connecticut.

This paper first examines three methods currently used for apportioning the costs of joint waste water treatment facilities among users. The methods are cost sharing based on the measure of pollution, cost sharing based on single plant costs with a rebate proportional to the measure of pollution, and cost sharing based on the separable costs remaining benefit method. Through the use of numerical and theoretical arguments it is demonstrated that often these methods do not provide an apportionment that satisfies all the people involved and that a potential participant may find it economically advantageous not to join the regional plan and may thereby force the adoption of a system that is, in total, more costly. These difficulties will frequently arise when any plan is subjected to the pressures of ‘free market‘ bargaining. Two additional methods relying on game-theoretic concepts are then introduced to deal with the problem. These methods, which are practical, can satisfactorily solve problems that are not tractable when other techniques are used. Also, the basically perverse characteristics of situations requiring cost sharing are demonstrated by using the bargaining methods to prove that some cost-sharing problems have no unique solutions and that others have no viable solution at all unless the regional authority can obtain a subsidy.

This paper presents the characteristics of the more important types of apportionment formulas. From the standpoint of effects of grants upon program or service aided, formulas are examined with reference to two criteria or conditions. A form of algebraic examination of formulas is presented which permits determination of characteristics of apportionment methods without numerical computations. This is done in terms of amount of grant, amount of local contribution, total program supported, rate of local effort, and relationship between central and local funds.

In a paper published some time back in the Journal of the Institute, an endeavour was made to show the true principles upon which the value of securities depending on an isolated human life should be determined. Discarding the methods once so generally practised, and in accordance with which such securities were confounded with those depending on the average duration of many lives, it was urged that they should be regarded in a distinct point of view, and as affording the means of investments to be made not subject to any contingency whatever, but as securing to the holder a given rate of interest so long as he retains them, and the return of the capital invested when such interest shall cease to be paid or to accrue.

This paper describes a systematic approach for apportioning the mean corrective times (Mct) of equipment, based upon a technique employing maintainability features, usage, and reliability data. Weight (K) factors are assigned commensurate with the eauipment's importance to the system's mission and the design features necessary to maintain the equipment within the customer's constraints. Each item of equipment is evaluated in accordance with apportioned reliability data and the degree of maintainability incorporated in the conceptual designs. The technique yields values that can be met by diligent application of maintainability principles during equipment design.

The main concern of this paper is with the limitations of techniques already commonly applied, and in the more promising points of application for new technology in navigation, surveillance and traffic control. In seeking the latter, some of the current trends in other fields, particularly aircraft design, are taken into account. Considerable emphasis is placed on the efficient use of land at airports, in view of the strength of feelings aroused in ‘the community’ by the questions of apportionment and exploitation of land resources.

Some three or four years ago, I submitted to the members of the Institute a few observations on the valuation of property held for life and in reversion, and on the due apportionment of it when questions arise between the life tenant and the owner of the fee. I was induced to bring this subject under the notice of the members from observing the great difference of opinion prevailing in regard to it generally, and especially in the discussions on the subject of church leases and of other property similarly circumstanced—in which discussions no sort of agreement appears to have been come to as to the true principles upon which the value of the interests of the several parties concerned should be estimated. In the paper in question, I endeavoured to point out some of these principles; and my object now is to enlarge somewhat on the arguments therein laid down, to show that the question at issue almost always resolves itself into one whether a property is to be bought or sold, to call attention to the vast difference in value which arises under the two conditions, and to point out the imperative character of the causes, from which this difference originates; finally, to urge the necessity of great care and circumspection in dealing with the questions submitted to us, so that all risk of confounding one of the conditions above referred to with the other may be avoided.

In 1961 the U. S. Supreme Court ruled that federal courts have jurisdiction cases concerning states' apportionment laws when there is a possible denial of rights guaranteed by the Fourteenth Amendment to the Constitution. Because of this decision, people in some states may for the first time have an opportunity to obtain equality of representation in state and federal legislatures. Reapportionment and redistricting are taking place, but what are the chances for obtaining and maintaining something approaching true equality? The changes may not be sufficient to upset the political power now held by minority political groups in these states, since there is still a possibility of gerrymandering. A scientific method of apportionment which includes automatic changes after every census has been accepted for the apportlonment of the U. S. House of Representatives. As a result it seems that the bitter congressional fights and power struggles and the resulting inequalities representation due to reapportionment have been reduced. But why stop there? Why not do the same for the process of districting? Resented in this paper is one possible scientific or impartial method of districting that the author believes would free, to a certain degree, the process of districting from power struggles and gerrymandering. The method can apply to either the U. S. House of Representatives or to state legislative chambers in states where apportionment is based on population.

MY attention has been called to a pamphlet published by Mr. W. H. Harrison, purporting to contain a correct account of the first founding of the British Association for the Advancement of Science. I am sure that Mr. Harrison, in common with such other readers of NATURE as take an interest in the affair, will be glad to hear my father speak for himself upon a matter which Mr. Harrison, with the amount of information at his disposal, could only treat of as a subject of speculation. The paper which I inclose was addressed to Sir Edward (then Colonel) Sabine; and I think I may claim for it that it is written with much clearness and impartiality. You may perhaps also consider the letter of importance at this moment, as pointing out what was the view taken in those early days of the proper functions of the Association. The wisdom of this view is abundantly evident now that science has been so widely popularised, and that little more of real work remains for the Association beyond the just apportionment of its funds for scientific purposes. In respect to the numerous scientific letters addressed to my father by Buckland, Murchison, Smith, Sedgwick, Scoresby, Humboldt, Wollaston, Davy, Sabine, Faraday, Brewster, Babbage, Prout, Herschel, Whewell, Forbes, Liebig, De la Beche, Lyell, and others, I hope some day to cause a selection of them to be produced, in a form which may be of interest, and perhaps of use to the public.

The theme of the political and partisan implications of state legislative apportionment poses a challenge simultaneously with the sounding of a warning tocsin. The challenge lies chiefly in the need to view the forest of states as a whole in terms of their representative system; the warning lies in the necessity of considering individual state situations as significant in making up the forest without becoming appalled by the character and particularities of the separate trees. ]Reapportionment long since has become a chronic problem within the American states. Like all chronic situations it has been subjected to much critical analysis; like many such conditions the lack of ready, facile solutions has been bewailed or shrugged off as mood and time have seemed to dictate. It is not the task of this paper to chronicle the individual symptoms of this chronic malaise or disease; what is called for is a discussion of the social, economic, and political results and significances of a presumably epidemic condition. IConsequently the concern in this article will not be with the details of state representative systems, nor will there be any treatment of the merits or shortcomings of those individual legislative setups. Certainly it will be necessary to mention such detail in order to evaluate and assess specific representative devices. There will not however be the repetition of constitutional or statutory provisions so vital to an exposition of the apportionment process at the level of the American states. Trite and banal as it may seem, the process of the apportionment of the members of the American state legislatures has political and partisan implications simply because these positions are representative and are also elective. Under those circumstances it would seem to be inevitable that there would be political significance at all stages of the apportionment process. Approximately 7,500 individuals constitute the total membership of all American state legislative bodies. As has been detailed in an earlier section of this symposium, they have been distributed throughout the separate states in such a way that the 43 in the single chamber of Nebraska represent the minimum elected in any state; at the other end of the scale are the 433 in the two chambers of New Hampshire. All of these legislators, let it be repeated, are elective in terms of their acquisition of

Several excellent cost-benefit analyses of programs under the Manpower Development and Training Act have been conducted and reported in the literature. However, little attention has thus far been directed to the method by which federal funds for these training programs are initially apportioned among the states. The major part of the funds for institutional and on-the-job training under Title II, Parts A and B, is made available through an apportionment formula based on criteria set forth in the Act. The present paper describes and evaluates the existing method of apportionment. It is shown that this method contains serious weaknesses which may reduce the effectiveness of the over-all program. Formulas designed to avoid these weaknesses are developed as examples of available alternatives. Using data for fiscal year 1968, the apportionment factors resulting from these alternatives are computed and compared with those resulting from the existing method.

This paper attempts to more accurately define the doctrine of equitable apportionment governing non-navigable use of international rivers so that practitioners of international law may more easily predict the results of future cases.

This paper has been prepared in response to the editor's request for "a review of the methods of congressional reapportionment addressed to the average citizen not versed in mathematics." I am glad to comply with the request because within the last forty years a small group of scholars have developed what I believe to be an erroneous mathematical analysis of the problem and have persuaded Congress in reliance on that analysis to displace a better method by a poorer one. The debate during that period has been of great value, however, because it has cleared up many obscure points and suggests that the time has come for a new, possibly a final, exposition of the century-old problem. The average citizen wants first some history of the question. That has been my own approach but one which of recent years has been neglected. The ad interim House of Representatives set up by the Constitution to serve until after the first census had only 65 members. This number was based on that of its predecessor, the unicameral Continental Congress, limited to 91 members, 7 for each of the 13 states. When the new Constitution took 26 away from that Congress to make the new Senate, 65 remained for the House. These were apportioned among the states according to whatever population figures were available. A House of only 65 members, however, was too small and before the first census it became evident that Congress would enlarge it up to the limit set by the Constitution, "not more than one for every thirty thousand." As the debate began, however, that limit was found to be ambiguous. Did it mean not more than one for every 30,000 in any state and so II2 in all, as the House claimed, or not more than one for every 30,000 in the country as a unit and so 120, as the Senate interpreted the phrase? The Senate won its long struggle with the House only to lose in the end when Washington vetoed the bill in its Senate form as unconstitutional. That veto, the first ever sent to Congress, established what is now called the method of rejected fractions, used until I840. The earliest apportionment bill as it left the House divided the population of each state by 30,000 and apportioned to it as many representatives as there were units in its quotient. Since the rejected remainders averaged about 15,000, a fraction *A.B. I884, A.M. 1888, LL.D. 1906, Amherst College; LL.B. 1887, Ph.D. 1891, Columbia University. Member of the New York bar. Professor of Economics and Statistics, Cornell University, since I892, now emeritus. Author, The Apportionment of Representatives (presidential address to the American Economic Association), 6 AM. ECON. REV. SUPP. 3-I6 (I916); The Recent Apportionment in New York State, 2 CORNELL L. Q. I (I916); The Role of Mathematics in Congressional Apportionment: A Reply, 4 SOCIOMETRY 283 (I941); The Apportionment Problem and the Size of the House: A Return to Webster, 35 CORNELL L. Q. 367 (1950); Methods of Apportioning Seats Among the States in the American House of Representatives, 3 INTERNATIONAL STATISTICAL CONFERENCES PROCEEDINGS, 1947 858 (I95I).