RLF 
 
 SB 
 
 
 CO 
 C\J 
 
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LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 I 
 
 Class 
 
Institute of Hctuartes. 
 
 MESSENGER PRIZE ESSAY 
 
 ON 
 
 FRIENDLY SOCIETIES 
 
 
 BY 
 
 GEORGE F. HARDY, 
 
 FELLOW t OF THE INSTITUTE OK ACTUARIES. 
 
 Published by the Authority of The Institute of Actuaries. 
 
 LONDON : 
 
 CHARLES AND EDWIN LAYTON, 
 56, FARRINGDON STREET, E.G. 
 
 Price 2s. 
 
institute of 
 
 MESSENGER PRIZE ESSAY 
 
 FRIENDLY SOCIETIES, 
 
 BY 
 
 GEORGE F. HARDY, 
 
 FELLOW OF THE INSTITUTE OF ACTUARIES. 
 
 Published by the Authority of The Institute of Actuaries. 
 
 LONDON: 
 
 CHARLES AND EDWIN LAYTON, 
 56, FARRINGDON STREET, E.G. 
 
1VH3N33 
 
 INDEX. 
 
 PAGE 
 
 Conditions of the Competition Hi 
 
 Historical Sketch 1 
 
 Existing Societies 11 
 
 Friendly Societies in Foreign Countries 19 
 
 Application of Actuarial Principles and Data to the Various Classes of 
 
 Societies 26 
 
 Sickness Tables Existing Data 37 
 
 Valuation of Friendly Societies 49 
 
 Financial Effect of Changes in the Rates of Sickness and Mortality ... 63 
 
 Secessions 68 
 
 Fluctuations in Death and Sickness Rates 77 
 
 Tables . 86 
 
Ill 
 
 SYLLABUS OF THE MESSENGER PRIZES, 1886. 
 
 SUBJECT FRIENDLY SOCIE 
 
 THE COUNCIL of THE INSTITUTE OF ACTUARIES, in an announce- 
 ment contained in the January 1887 number of the Journal, 
 stated that they had resolved to offer a Prize of 50 to the 
 Author of the best Essay upon this subject, and a further sum 
 of 25 to the Author of the second best Essay, or divided 
 between two or more Essayists, if and as the Adjudicators 
 might recommend. 
 
 The Council, without restricting Candidates in the treat- 
 ment of the subject, thought it desirable to make the 
 following suggestions as to what the Essay should include : 
 
 "1. A brief historical sketch of the Friendly Society system in this 
 country, including a short account of the salient features of the legislation 
 on the subject, particularly that of recent years. Reference is invited also 
 to the Friendly Societies, and to the legislation relating thereto, in other 
 countries. 
 
 " 2. A description of the various classes of Friendly Societies at the 
 present time, including the affiliated orders, such as the Manchester Unity 
 of Oddfellows, the Ancient Order of Foresters, &c. It is desirable that the 
 description should include a classification of societies in respect of the nature 
 of the benefits assured to the members, and the manner in which those 
 benefits are paid for whether by fixed periodic contributions, by levies to 
 meet current claims, by levies of fixed amount on the happening of certain 
 events, &c. including also the cases where societies are subsidized from 
 extraneous sources. 
 
 " 3. An enquiry into the applicability of actuarial principles and data to 
 the various classes of societies, both in respect to the benefits assured and 
 the methods in use with regard to payments for those benefits. 
 
 " In this section should also be included : (a) an investigation into 
 the proper methods of keeping accurate records of the experience 
 
 1201 
 
IV 
 
 of societies, and of obtaining therefrom the necessary data for 
 actuarial purposes ; (b) a critical account of well-known existing 
 data, and an enquiry as to how far they may be made use of for 
 the purposes of particular societies ; (c) an exact enquiry into the 
 effect of secessions in the various classes of societies, and the 
 manner in which, and extent to which, secessions should be 
 introduced into valuations of their contracts and in dealing 
 with this question, the treatment of negative values should 
 receive careful consideration ; (c?) an examination of the relative 
 effect of rates of mortality and rates of sick pay in determining 
 the values of sick-pay benefits in other words, how far the 
 rates of sick-pay benefit will be interfered with by a light or 
 heavy mortality ; (e) an enquiry as to the number under risk in 
 various classes of societies necessary to render probable a steady 
 experience, particular attention being given to the difference 
 (if any) in this respect between societies granting death benefits 
 only and those granting sick-pay or accident benefits, with or 
 without death benefits. And, where practicable, statistics should 
 be furnished bearing upon the various points under discussion. 
 
 " The Essays may, inter alia, indicate such changes in the existing 
 practice of societies, or in the existing legislation and accompanying executive 
 arrangements, as seem to the writer desirable and in dealing with this part 
 of the subject a comparison is invited between the legislation relating to 
 Friendly Societies and that affecting ordinary life insurance companies." 
 
 "CONDITIONS OF THE COMPETITION. 
 
 " 1. That the Competition be open to all Members of the Institute, with the 
 exception of past or present members of Council. 
 
 " 2. That the Essays be sent in to the President of the Institute before or on 
 31 December 1887. 
 
 " (If Essays are written in a foreign language they should be accompanied 
 by a literal English translation.) 
 
 " 3. That the names of the Competitors be sent in under seal, with a Motto corres- 
 ponding to one to be prefixed to the Essay ; the Motto and Essay not to be 
 in the handwriting of the Competitor. 
 
 " 4. That the Essay or Essays to which a Prize may be awarded be the property of 
 the Institute. 
 
 " 5. That a Prize or Prizes be only awarded if the Adjudicators shall consider an 
 Essay or Essays to be worthy of the distinction. 
 
 " 6. That unsuccessful Essays be returned, on application at the Institute, with the 
 corresponding envelopes unopened/' 
 
[Printed by the Authority of The Institute of Actuaries.'] 
 
 MESSENGER PRIZE ESSAY 
 
 FRIENDLY SOCIETIES 
 
 BY 
 
 GEORGE F. HARDY, 
 
 FELLOW OF THE INSTITUTE OF ACTUARIES. 
 
 HISTORICAL SKETCH. 
 
 Early Times. ^ considering the origin and development of the 
 friendly society system, it is necessary to recognize 
 the twofold purpose that these institutions have fulfilled. In the 
 view of the actuary they are merely associations for the mutual 
 assurance of certain benefits, generally in the case of the sickness 
 or death of any of the members. This, however, represents only 
 one side, and that by far the most recent, of the work of these 
 institutions. A not less prominent and much older feature is to 
 be found in the opportunities for social intercourse, companion- 
 ship, and mutual help, which such associations naturally afford 
 wants common to man in every state of society, and as old as 
 civilization itself. Hence, from the earliest times, small com- 
 munities have existed, drawn together by the common interests, 
 tastes, or pursuits of the members, such communities being 
 
2 Friendly Societies. 
 
 originally purely social in character, subsequently charitable and 
 mutually protective, and only in recent times financial. 
 
 Institutions very closely agreeing, in many of their charac- 
 teristics, with the friendly societies of the present day, date from 
 a very remote period. Mr. Tompkins, in his essay on the 
 Friendly Societies of Antiquity, has shown that they existed 
 among both Greek and Roman communities before the Christian 
 era, and that, besides meeting for religious observances, they 
 possessed funds which were employed to provide funerals and to 
 assist members in needy circumstances, although there is no 
 evidence of the grant of benefits in cases of sickness. The con- 
 necting links between these early societies and those of modern 
 times are difficult to trace; nor is it necessary to suppose that 
 the latter are merely a development of the former. The history 
 of the friendly society movement in our own country has been 
 very ably sketched by Dr. Hasbach, of Leipsic (Das Englishe 
 Arbeiterver sicker ungswes en Leipsic, 1883), of whose work I have 
 availed myself to some extent in the following short sketch. The 
 Rev. J. Frome Wilkinson's work on the same subject contains also 
 much useful information, more especially in relation to the rise of 
 the affiliated orders. 
 
 Prior to the 13th century, aid was generally dispensed to the 
 necessitous by the Church. Being the central and only receiver 
 of contributions for this purpose, and the sole dispenser of relief, 
 its charitable functions covered the same kind of wants that our 
 friendly societies deal with at the present time. These functions 
 were to feed and clothe the destitute, to visit the sick, to house 
 the homeless, to liberate prisoners, and to bury the dead in its 
 own words, vito, poto, cibo, redimo, tego, colligo, condo. Such 
 duties did not remain merely voluntary. Grants, tithes, bequests, 
 &c., gradually increasing the property of the Church, imposed at 
 the same time the tacitly understood obligation to satisfy the 
 wants of the poor, and at a later period we find the obligatory 
 nature of the duties of the Church to the poor emphasized and 
 confirmed by various legislative enactments, such as the Act 9 of 
 Edward I, and Act 15 of Richard II, and others. 
 
 In the 13th and 14th centuries, a great social change 
 Centuries. took place. Agricultural serfdom was gradually 
 
 The Guilds. . _ . r 
 
 breaking up, industries began to develop, and a 
 general tendency was manifested by society to forsake the 
 socialistic order of things. As regards the relief of the poor, 
 the first effect of the change was the taking over of part 
 
'. 
 
 or THE 
 UNIVERSITY ) 
 
 Friendly Societies. .<^^ 
 
 of the functions hitherto performed by the Church by smaller 
 communities of persons, each community, or guild, as they 
 were called, having a more or less distinct and well-defined 
 object. These guilds undertook, though usually as an object 
 of secondary importance, the distribution of relief amongst 
 their members, constituting them the first friendly societies 
 in this country of which we have any clear information. They 
 appear to have flourished up to the time of the Reformation, 
 and most of them had, according to Mr. Toulmin Smith, 
 particular provisions for the optional relief, by way of charity, 
 of those members of the guild who were in want. The 
 Guild of St. Katherine, Aldersgate (and many others), contained 
 stipulations in its statutes decreeing support to brethren in case 
 of poverty, old age, damage by fire or water, by thieves or 
 sickness. Others undertook special tasks, apart from their general 
 charity. The Guild of Garlekhith of St. Leonard's, Lynn, of the 
 Smiths of Chesterfield, and others, gave relief in case of any of 
 their members being cast into prison. The Guild of the Palmers 
 provided dowries for women, and others, too numerous to mention, 
 gave relief in a vast variety of cases. The following paragraph in 
 the statutes of the Guild of Smiths of Chesterfield is of great 
 interest: "When a brother is ill and needs relief, then he shall 
 " receive half a dime daily ; when brethren fall into poverty, then 
 " they shall go singly, on certain days, into the houses of their 
 " brethren, where each one shall be received civilly, and he shall 
 " obtain whatsoever he may need in the shape of food and clothing, 
 " as if he were the master of the house himself ; and he shall also 
 " receive half a dime, like those who are ill, and then he shall go 
 " his way in peace." It is to these guilds that we must look, 
 rather than the protective trade guilds which then existed, for 
 the progenitors of our modern friendly societies. As to their 
 financial basis, we find that in some cases the contributions were 
 equal ; in others they varied according to the wealth of the 
 member, each contributing as much as he could to the common 
 fund, not distinctly for his own benefit, but for the benefit of the 
 members generally, or the community at large. 
 Period of the ^he P ei *i 0( l of the Reformation was another era of 
 Reformation. change in the direction of self-assertion and self-help, 
 and the general tendency affected the guilds quite as much, 
 perhaps, as the change from Catholicism to Protestantism. In the 
 15th century they began to decay. Corruption and abuses were not 
 uncommon amongst them, as in the convents and other religious 
 
 A 2 
 
4 Friendly Societies. 
 
 foundations. This state of things culminated in the 16th century 
 in the passing of Acts 27, 31, and 37 of Henry VIII, and 1 of 
 Edward VI, which enabled the king to confiscate the property of 
 both guilds and monasteries ; and although Parliament laboriously 
 stated that special commissioners should have power to confirm 
 those guilds in the possession and enjoyment of their property 
 which devoted it to useful and charitable purposes, and that it 
 was only sought to suppress institutions cultivating religious 
 superstitions and corrupt practices, very few of the guilds were 
 spared. 
 
 In the 16th and 17th centuries some of these 
 institutions which had survived the preceding period, 
 and still retained sufficient cohesion, were reformed, whilst many 
 new societies were started, embodying some of the features of the 
 guilds, but in conformity with more modern ideas. As the 
 organization of the trade guilds, following the general tendency 
 of the times, gradually changed, the various trade societies, 
 having vastly increased in numbers and become more democratic, 
 re-united themselves into aid societies, which combined in them- 
 selves some of the characteristics both of the religious and the 
 trade guilds. The relief and economic system of these societies, 
 moreover, underwent a radical change, in the direction of requiring 
 fixed contributions to be made by the members for the grant of 
 specific benefits. As an illustration of the financial basis of such 
 societies, it may be interesting to note that in one society the 
 subscriptions were 2d. weekly, to provide for benefits, during 
 sickness, of 65. weekly for the first year, and 3s. 6d. per week for 
 the remainder of illness, while a levy of 6d. per member was made 
 at each death. 
 
 About the beginning of the 18th century a movement arose 
 in the Guild of Masons which exercised a great influence in 
 stimulating the rapid growth of friendly societies. By the 
 introduction of mystic rites and observances, and by other changes 
 which need not be detailed here, the Guild of the craft of Masonry 
 was transformed into the order of Freemasons. Members of the 
 aristocracy joined the new and highly successful order, while the 
 mystery with which they surrounded their transactions took the 
 public fancy, and created desire in other societies to imitate them. 
 The Odd Fellows are known to have existed shortly after this 
 period, though in a form having little or nothing in common with 
 their modern development, the oldest lodges being practically 
 social clubs. 
 
Friendly Societies. 5 
 
 The friendly societies existing at the close of the 
 
 Number and . * , . ., 
 
 class of eighteenth century appear to have been very similar 
 
 in the nature of their operations to those of the 
 present day. It is difficult to estimate, with any degree of 
 certainty, the number of societies or their aggregate member- 
 ship, but there is good reason for believing that they were 
 at least as numerous in proportion to population as at the 
 present day. Sir P. Colquhoun, in 1796, estimated the number 
 of societies in London at 600, with a membership of 70,000, 
 while Sir F. M. Eden, five years later, considered that the 
 whole kingdom might number 7,200 societies, with a mem- 
 bership of over 600,000. The amount of the sick pay 
 allowed seems somewhat larger in proportion to wages than now, 
 6s., 8s., and 10s. a week being common sums ; while the modern 
 system, now all but universal, of reducing the sickness allowance 
 in cases of prolonged illness, appears to have been at this date 
 rare, although, in some cases, the allowance ceased after a specified 
 period of 13, 20, or 26 weeks of illness, and in others provision 
 was made for the superannuation of members at a reduced 
 rate of pay. 
 
 The influence of occupation upon health about which so 
 much has since been written, but which is still largely an un- 
 solved problem was not unrecognized. In Gloucester, we find 
 societies who excluded workers in white lead, miners, and others ; 
 and similar precautions were not uncommon. Societies confining 
 their membership to distinct trades or classes were relatively more 
 numerous than at the present day, and naturally so when it is 
 considered to what an extent the present friendly society system has 
 grown from such trade societies. The propriety of limiting the 
 age at entry was very generally recognized, and endeavours were 
 often made to secure the permanency of societies by making the 
 amount of the benefit depend upon the funds in hand. The 
 provision for death benefits by means of levies upon the members 
 at each death no doubt a method of great antiquity was also 
 common, while in many societies pensions to the widows of 
 members took the place of the now customary funeral allowances. 
 It was very usual for societies at this period to limit their 
 membership 101, 81, and in some cases 51 or 41 members, was 
 made the limit of a society : though what superstition lay in the 
 use of these numbers it is impossible to say. 
 
 The rules of the societies, as in earlier times, almost always 
 
6 Friendly Societies. 
 
 exercised a paternal care over the morals and even the opinions of 
 the members. 
 
 Defects of The friendly society system on the whole worked well, 
 System, k ut ft j^j manv defects which became increasingly 
 
 apparent. The societies having no legal status, were open to 
 fraud and corrupt practices, no prosecution being possible except 
 in the names of all the members, the societies being regarded at 
 law as partnerships. The uniform premiums did not answer 
 well ; as members grew old, younger men did not care to join, 
 and bankruptcy often resulted. There was also too much feasting 
 by members at the expense of the funds. 
 
 Nevertheless, while the State poor laws, which, in 1572, had 
 replaced the administration of charitable funds by the Church, had 
 proved to a large extent a failure, voluntary efforts had succeeded, 
 in spite of disadvantages, in nursing and gradually extending over 
 the country that system of friendly societies, to a larger extension 
 of which many looked for a removal of the evils created by the 
 poor laws. While some reformers favoured the continuance of 
 the voluntary system under the control of the parishes, others 
 advocated compulsory and universal State insurance. Defoe, in 
 his essay on Projects, had, as early as 1697, recommended the 
 establishment of pension offices in each parish. Francis Maseres, 
 in 1772, formulated a scheme for establishing life annuities in 
 parishes for the benefit of the industrious poor, an idea which, in 
 the following year, was embodied in a Bill passed by the Commons 
 but thrown out by the Lords ; while about the same time various 
 projects for compulsory State insurance were also before the 
 public. 
 
 In 1787 Gilbert originated the idea of requiring each society 
 to be registered in order to obtain legal protection ; and it was 
 his proposals undoubtedly which induced the framing and passing 
 of the highly important Act of 1793, which practically settled the 
 struggle between compulsion and voluntaryism in favour of the 
 latter system. 
 
 The Act of 1793 marked a new era in the history of 
 friendly societies. Their legal position before the 
 Act, and the various abuses that resulted from it, have already 
 been referred to. The Act remedied these abuses by establishing 
 some supervision and some safeguards as to the management. It 
 required, for example, the submission of rules, and alterations of 
 rules, to the justices at Quarter Sessions, who had power to confirm 
 them or not at discretion. The objects of the society were to be 
 
Friendly Societies. 7 
 
 specified, and a dissolution could only take place with the consent 
 of the justices. On the other hand, certain privileges were con- 
 ferred upon the societies. They might appoint officers; trustees or 
 treasurers might give a hond to the clerk of the peace ; free -appli- 
 cation was allowed to the Court of Chancery to compel trustees to 
 account for moneys, and a first claim was given on their estates. 
 The power was also conferred to allow of disputes being settled by 
 arbitration. The Act was extended in 1795 for the benefit of 
 societies existing prior to 1793, and in 1796 an Act embodying 
 similar provisions was passed by the Irish Parliament. The extent 
 to which the Act was utilized differed very much in various parts 
 of the country. On the whole, probably more than 50 per-cent of 
 the societies availed themselves of its provisions. Very many, how- 
 ever, were much frightened by the new legislation, and in a large 
 number of cases societies were dissolved. 
 
 It is not easy to systematize the various efforts made by the 
 Legislature to control or to encourage, as the case might be, the 
 friendly society movement between 1793 and the great Act of 
 1875. All of these attempts were necessarily in the nature of 
 experiments, and were generally without any common plan. 
 
 The Acts of 1803 and 1809 can scarcely be said to have been 
 important. In 1818, however, a Bill was introduced providing 
 for the appointment of five public valuers in the language of 
 the Bill, "persons skilled in arithmetical calculations" to whom 
 tables and rules might be submitted at fixed fees. The fear of 
 Government interference, however, which was so common among 
 members of friendly societies, caused this provision to be struck 
 out of the Act of the following year (1819). This 
 Act provided, however, that rules and tables of all 
 future societies should both be confirmed by the justices at Quarter 
 Sessions ; and, moreover, contained the important provision that 
 such justices should not confirm or allow any table of payments 
 or benefits, or any rules dependent upon or connected with the 
 calculations thereof, until it shall have been made to appear to 
 such justices that the said tables and rules are such as have been 
 approved of by two persons at least, known to be professional 
 actuaries or persons skilled in calculation, as fit and proper 
 according to the most correct calculation of which the nature of 
 the case will admit. In the same way, dissolution could only take 
 place with the consent of the trustees and under the certificate of 
 two actuaries. Several provisions were made as to the investments 
 of societies, permitting funds to be placed in savings banks, in the 
 
I 
 
 8 Friendly Societies. 
 
 Bank of England, on debentures, in the public funds or real 
 security. Investments in savings banks, to the extent of 300, 
 were permitted nine years later, by the Act of 1828. 
 
 The Act of 1829 contained several provisions of 
 
 Act of 1829. 
 
 Previous Acts considerable importance. By this Act, nearly all 
 previous legislation relating to friendly societies 
 was repealed, and the law consolidated. The Act allowed 
 any number of persons to form a society and to make rules, 
 provided that these latter should declare the purpose of the 
 society, and that they should be submitted to a barrister or to the 
 Lord Advocate for certification. When so certified, they were to 
 be confirmed by the justices at sessions and to be deposited with 
 the clerk of the peace. By the 6th section of the Act it was 
 provided that the justices should not certify the rules unless they 
 were satisfied with the tables proposed to be employed. The 
 rules, when entered and deposited, were binding on the members, 
 and could only be altered at a general meeting of the society, the 
 place of such meeting being specified in the rules. Societies were 
 allowed to appoint committees of management, whose powers were 
 to be declared in the rules, and who were controllable by the 
 members. Treasurers or trustees were to lay out any surplus 
 contributions, to render accounts, and pay over balances, while 
 the priority of claim upon the estates of such trustees was 
 continued. Provision was also made for the payment of sums 
 not exceeding 20, where members died intestate, to persons 
 appearing to be next of kin. Societies were to make annual 
 audits and statements of the funds to the members; and a 
 dissolution could only take place when agreed upon by five-sixths 
 of the members and all persons entitled to relief. Minors were 
 allowed to become members, and to act as such. 
 o,uin uenniai Perhaps the most important provision in the Act 
 returns. however, was that requiring quinquennial returns ot 
 
 sickness and mortality to be made to the clerk of the peace, by 
 whom they were to be transmitted to the Secretary of State, and 
 laid before Parliament ; all societies neglecting to make such 
 returns losing the privileges of the Act. The Act embraced all 
 existing and future societies, the former, if enrolled, being 
 required to conform within three years (a period, however, which 
 was subsequently extended) to the provision for quinquennial 
 returns of sickness and mortality. The object was stated clearly 
 in the Act to be the collection of data by which tables of the 
 payments and allowances dependent on the duration of sickness 
 
Friendly Societies. 9 
 
 and probability of human life may be constructed, " the present 
 existing data of these subjects having been found imperfect and 
 insufficient/' The form of return was to state, among other 
 things, each member's occupation, date of birth, of admission into 
 the society, and of becoming free to benefit, with the number of 
 weeks' pay received in each of the five years on account of sickness 
 and of superannuation. A new feature of the Act was the absence 
 of any limit as to the sum which a society might insure on the 
 death of a member, one effect of which was the enrolment of 
 various societies which were, strictly speaking, insurance societies 
 as the Clergy Mutual which added the business of sickness 
 assurance to that of an ordinary mutual life office. 
 
 By the Act of 1834, the powers of the justices to 
 
 Act of 1834. J .. . , , . . , . , *Y i, 
 
 decline to certify the rules, in cases m which they might 
 deem the tables insufficient, was withdrawn, as also was the priority 
 of claim by societies upon the effects of trustees and others. The 
 purposes for which societies might be formed, however, were 
 somewhat extended, and were stated to be " for the mutual relief 
 " and maintenance of all and every the members thereof, their 
 " wives, children, relations, or nominees, in sickness, infancy, 
 " advanced age, widowhood, or at any other natural state or 
 " contingency whereof the occurrence is susceptible of calculation 
 " by average, or for any other purpose which is not illegal." It 
 was carefully provided, however, that for any such general 
 purposes, not being "natural contingencies", the contributions 
 should be kept distinct and separate, or that the charges for 
 these benefits should be defrayed by levies upon the members. 
 The quinquennial returns were continued. The Act of 
 1846 imposed a penalty for failure to forward these 
 returns, and appointed a salaried registrar, who was only to 
 register rules when tables were certified by an actuary. 
 
 The Act of 1850 required this certificate in respect of annuity 
 tables only, and limited the amount of benefits, especially in the 
 case of children's assurances, allowed investments with National 
 Debt Commissioners at a fixed rate of interest of 2d. per-cent per 
 diem, and allowed branches to register. This year was memorable 
 on account of the founding of the well-known Royal Liver Friendly 
 Society, which within 20 years reached a membership of over 
 half-a-million. 
 
 Most of the features of the recent legislation were continued 
 by the Acts of 1855, 1858, &c., the position of friendly societies 
 remaining very much the same down to the important legislative 
 
10 Friendly Societies. 
 
 enactment of 1875. This was preceded by the Royal Commission 
 of 1870, the result of whose labours is embodied in four 
 successive reports of the utmost value to every student of the 
 friendly society system. 
 
 Act of 1875 "^ * s on ^ P oss ible to give a brief outline of the 
 changes effected by the great Act of 1875, by which 
 societies are now governed. By this Act the law relating to 
 friendly societies was both consolidated and amended. 
 
 The following provisions of the new Act may be mentioned as 
 among the most important : 
 
 The maintenance of the voluntary principle, as respects 
 registration and the actuarial certification of tables. 
 
 The continuance of the quinquennial and annual returns. 
 
 The limitation of benefits, especially for infants' assurances, 
 this provision also applying to industrial assurance 
 companies. 
 
 The authorizing of the Treasury to issue regulations from 
 time to time, and the power conferred on the registrars 
 to appoint inspectors, when duly requested to enquire 
 into the management of societies, and call general 
 meetings of the members. 
 
 The compulsory valuation of all registered societies every 
 five years, and the provision for the appointment of 
 public valuers by the Treasury, who might undertake 
 such valuations. 
 
 The reconstruction of the Registry Office, resulting in the 
 appointment of an actuary to the Registry. 
 
 The Act on the whole was drawn with great care, and upon 
 undoubtedly sound principles. A few amending Acts of no 
 great importance, have been passed since. The third of these 
 dispenses with the quinquennial returns of sickness and mortality 
 which had gradually accumulated a mass of data more than 
 ample for the purpose for which they were collected. These 
 materials have for some time been undergoing complete exami- 
 nation and analysis at the able hands of the actuary to the 
 Registry. The results of the analysis, from the improved form in 
 which the returns have been made, and the care that has been 
 taken to eliminate doubtful returns, may be expected to throw 
 much light upon the rates of sickness prevailing among the 
 
Friendly Societies. 11 
 
 friendly societies of this country, and at the same time solve some 
 of the important questions (such as the duration of sickness, for 
 example) which have hitherto been left in some obscurity. 
 
 EXISTING SOCIETIES. 
 The friendly societies of the present time are not more 
 
 Classification. J \ 
 
 remarkable on account of their number than in respect 
 of the great variety to be found in their constitution and mode 
 of working, and minute as is the classification adopted by the 
 Commission of 1875, it is very doubtful if it is absolutely 
 comprehensive. Such a classification of societies may be viewed 
 from two stand-points either as regards their method of manage- 
 ment and the scope of their operations, or in respect of the 
 benefits granted and the method in which those benefits are 
 provided for. The classification of the Commission of 1870 
 proceeds mainly upon the former basis. In what follows I have 
 endeavoured to combine both these points of view. As may be 
 supposed, however, there is considerable difficulty in drawing a 
 hard and fast line between some of the classes enumerated. 
 
 1. Local Friendly Societies (in town or country), independent 
 as to management, and usually granting benefits in cases of 
 sickness and death (occasionally with medical attendance), form 
 the most ancient, as well as one of the most interesting, of 
 existing classes of societies. They abound in every town, and in 
 almost every considerable village, throughout the country, and, 
 notwithstanding the recent rapid growth of the affiliated orders, 
 constitute a very large proportion of the registered societies. 
 
 They may be subdivided into: 
 
 (a) Societies having uniform contributions and benefits 
 for all ages of entry, the limits of which vary con- 
 siderably. An entrance fee, increasing with the age 
 at entry, is the usual and quite inadequate substitute 
 for a graduated scale of contributions. There is 
 usually no special restriction as to the occupations 
 from which the members may be drawn, which are, 
 in general, those prevailing in the district. Where 
 these are mainly of one class, the society will approxi- 
 mate to the particular trade societies referred to 
 under (d). 
 
 The vast bulk of these local societies are in a more or 
 less unsound financial position, the contributions 
 
12 Friendly Societies. 
 
 being generally not more than adequate at the lowest 
 ages at entry. Some cases, however, might be cited, 
 in which such societies have been extremely well 
 conducted and have been very successful. A 
 remarkably interesting group of such cases occurs 
 in the small societies principally in East London, 
 which appear to have been founded by the original 
 French Protestant refugees, about 1685 and subse- 
 quently. 
 
 (b) Societies similar to the last named, in which the 
 
 funeral benefits are met wholly or in part by levies. 
 
 (c) Societies having a graduated scale of contribution, in 
 
 most cases adopted under actuarial advice, or in 
 imitation of other societies that have taken that 
 step. 
 
 (d) Societies confined to particular trades (whether rigidly 
 
 so by virtue of the society's constitution, or practically 
 so in consequence of the locality and prevalent occu- 
 pation of the inhabitants, is of little moment from an 
 actuarial point of view). These societies are extremely 
 numerous, but the nature of their benefits and general 
 working differ but little from that of the ordinary 
 local society. They are of interest to the actuary as 
 affording examples of societies to which the ordinary 
 table of sickness and mortality cannot be generally 
 applied. 
 
 2. Large General Societies, whose membership extends over a 
 large area, although the management is usually in one location. 
 These societies may or may not have agents, whose duty is to 
 obtain new members and collect subscriptions. 
 
 As typical societies of this class may be mentioned the 
 London Friendly Institution (established in 1824), the Royal 
 Standard (four years later), the Royal Oak Benefit Society (in 
 1837), the United Kingdom, and the Hearts of Oak. Some of 
 these societies have agents; others, as the Royal Standard and 
 the Hearts of Oak, dispense with this aid outside London, the 
 members remitting their contributions and receiving benefits by 
 Post Office Orders. This latter system tends, naturally, to 
 economy of management, and in the latter of these societies the 
 expenses amount to only about 6 per-cent of the total expenditure. 
 
Friendly Societies. 13 
 
 Societies of this class have, almost invariably, extensive graduated 
 tables of contributions, and benefits are generally guided by 
 actuarial advice, and, on the whole, their financial position is 
 satisfactory. 
 
 3. Patronized County and District Societies form a special 
 class as regards management, which rests wholly, or in great part, 
 in the hands of the honorary members. The societies are usually 
 spread over a considerable area, mainly in rural districts, and 
 although their experience has varied considerably, they have, on 
 the whole, been well and successfully managed. It has been 
 said that their constitution does not enlist so strong a feeling in 
 their members against imposition, and hence it is often difficult 
 to keep down the sickness claims to within a reasonable amount. 
 Whilst this may be to some extent the case, much of the excessive 
 sickness, especially the heavy claims for reduced allowances at the 
 older ages, is doubtless to be attributed to the class of occupations 
 generally followed by the members, which is largely agricultural. 
 
 4. The Affiliated Orders represent the most popular and 
 growing section of friendly societies. The Manchester Unity and 
 the Ancient Order of Foresters each number over half-a-million 
 of members, spread throughout the whole of the country, and 
 their numbers are constantly and rapidly increasing. The various 
 branches are generally independent in respect of sick pay, but 
 mutually dependent in the limits of each district as to the liability 
 for funeral allowances ; while the districts again are independent 
 of each other financially, but unite for legislative purposes. In 
 addition to the sickness funds belonging to each lodge or court, 
 there is usually a district burial fund, which is kept up by equal 
 levies for each member in the district, irrespective of age; and, 
 in some orders, general funds common to the whole order, as the 
 general funeral fund and the annuity fund of the Nottingham 
 Odd Fellows, and the funeral fund of the Derby Midland Odd 
 Fellows. In many districts, again, widow and orphan funds 
 provide a fixed sum to the widow, and a smaller sum on account 
 of each child of a deceased member. These funds are, in many 
 instances, it is to be feared, insolvent. There is, of course, 
 no mutual responsibility between the several branches of the 
 affiliated orders. The average size of the lodges is small, averaging, 
 in the Manchester Unity and the Ancient Order of Foresters, a 
 little over 100 per lodge. 
 
 The extent of the various orders in this country will be seen, 
 from the following approximate statement, to be very great, and 
 
14 
 
 Friendly Societies. 
 
 there is no doubt that they are at the present time spreading 
 rapidly : 
 
 TABLE I. Affiliated Orders in the United Kingdom (1886). 
 
 Order 
 
 Members 
 
 Funds 
 
 
 
 
 
 Ancient Order of Foresters 
 
 582,000 
 
 3,342,000 
 
 Manchester Unity of Odd Fellows 
 
 542,000 
 
 5,053,000 
 
 Grand United Order of Odd Fellows 
 
 83,000 
 
 273,000 
 
 Six Orders of over 40,000 members 
 
 316,000 
 
 1,100,000 
 
 Ten Orders of over 10,000 members 
 
 160,000 
 
 608,000 
 
 Smaller Orders (estimated) 
 
 70,000 
 
 170,000 
 
 Juvenile Societies (estimated) . 
 
 150,000 
 
 150,000 
 
 TOTALS .... 
 
 1,903,000 
 
 10,696,000 
 
 
 
 
 5. Dividing Societies, an important class of society as to 
 numbers, and especially numerous in Scotland, but of little 
 interest to the actuary. The plan of these societies is to receive 
 certain fixed annual contributions from the members, out of which 
 all sickness claims for the year are paid, together with the expenses 
 of management, while any surplus that may exist at the end of the 
 year is returned to the contributing members, in some cases 
 wholly, in others after a deduction has been made for the purpose 
 of starting the new year's transactions. Since all the members 
 pay an equal contribution, irrespective of age, great difficulties 
 must attend the progress of these societies, and it is only in very 
 exceptional cases that they can last for many years. Their chief 
 difficulty is with prolonged sickness, and it is very usual to avoid 
 the payment of superannuation by advancing either the whole or 
 part of the anticipated death benefit and excluding the member. 
 It is worthy of note that the principle on which these societies are 
 conducted is very similar to the American mutual assessment 
 scheme of insurance. The stoppage of these societies is usually 
 brought about by the failure to obtain the constant influx of new 
 members at the younger ages, upon which they must depend to 
 keep down the average sickness rate. 
 
 6. Deposit Societies, which, like dividing societies, can scarcely 
 come within the cognizance of the actuary, being rather savings' 
 banks than friendly societies. In the language of Mr. Best, 
 who may be said to be the originator of this class of society : 
 " A member's money is and remains his own under his own 
 
Friendly Societies. 15 
 
 " control, under such limitations only as are necessary for the 
 " protection of all." 
 
 7. The large Collecting Burial Societies form a very important 
 class of societies, differing totally in character from any of the 
 preceding classes. In the aggregate, they probably include nearly 
 a million and a half members, an extent of membership nearly equal 
 to that of the affiliated orders. The largest societies are general 
 in their character, their business extending over the whole of the 
 kingdom. Some few include sickness benefits in their operations, 
 but this part of the business has never been successful, from the 
 extreme difficulty of working sickness business over a large area. 
 Nearly all the largest societies are located in the big towns, such 
 as Liverpool, Manchester, and Glasgow. The largest society of 
 all, the Royal Liver, has a membership equal to that of the 
 Manchester Unity, though of course with much smaller funds. 
 The whole business of these societies usually consists of insuring 
 small sums by weekly payments, an immense proportion of the 
 insurances being on the lives of infants. The premiums are 
 collected weekly by the agents of the society, which necessarily 
 makes the ratio of expenditure very heavy. In this respect they 
 approximate very closely to the industrial assurance companies ; 
 indeed, in the class of business undertaken, and in the general 
 management of the societies, there is scarcely any distinction to 
 be drawn. Of their financial position, on the whole, it is difficult 
 to speak with certainty, though the larger societies are probably 
 solvent. 
 
 8. Annuity Societies form a class entirely distinct from the 
 ordinary type of friendly society. They are generally of old 
 standing, very few now being registered, perhaps on account of 
 the requirement of an actuarial certificate. They, however, 
 exist in some numbers in the West of England. The funds of 
 these societies are naturally very large in proportion to their 
 membership. 
 
 9. Subsidized Societies, among which the large railway 
 funds form an important element. These are, of course, of com- 
 paratively modern growth, but they have now become very general. 
 In most cases membership is compulsory, and, in addition to the 
 contributions made by members, they are frequently supported by 
 a subsidy of a fixed amount per annum from the company; 
 notwithstanding this extraneous assistance, however, many of the 
 funds are in an unsatisfactory financial position. In addition to 
 providing for sickness benefits, an important feature of these 
 
16 Friendly Societies. 
 
 societies is the provision for retiring allowances. The experience 
 of the societies, in respect of both mortality and sickness, is 
 often very different from that of ordinary friendly societies. 
 
 Most of the railway societies have dropped out of registry 
 owing to the companies having taken powers under their special 
 Acts for regulating the provident funds attached to them. The 
 system of compulsory membership, which is common to these 
 societies, lends a certain stability to their operations, as the 
 distribution by age of the members probably varies very little 
 from year to year. The same feature is found in many of the 
 societies attached to collieries, iron works, and large factories. 
 These societies, existing amongst widely different classes of occu- 
 pation, have special interest for the actuary, and the experience 
 derived from their working is calculated to throw considerable 
 light on the laws of sickness and mortality as affected by 
 occupation ; many being limited to callings of more than ordinary 
 risk, such as those of fishermen, pilots, and so on, in addition to 
 those of miners and railway servants already mentioned. 
 
 10. Societies of Females also form a special class by themselves. 
 In some cases females are admitted as members in ordinary 
 friendly societies, but it is doubtful whether this plan has worked 
 satisfactorily, as, in many cases, the rates of sickness among the 
 female portion of the society have been heavier than among 
 the remaining members. There are several orders composed 
 exclusively of females, and constituted on the same principle as 
 the larger affiliated orders. The benefits frequently differ from 
 those in male societies, and usually include allowances on 
 confinements. 
 
 It is difficult to estimate exactly the numbers of 
 
 Number and . t i 
 
 Financial even the registered societies, but they may probably 
 
 Registered be put down at something like 25,000. of which 
 
 Societies. ' ' 
 
 more than one-hall are branches or the various 
 affiliated orders. The aggregate membership of these societies, 
 when the large burial societies are included, probably exceeds 
 4,000,000. The materials do not as yet exist for forming a just 
 opinion as to the financial position of the societies as a whole. 
 In the paper read before the Statistical Society, 21 April 1885, 
 Mr. E. W. Brabrook, Assistant Registrar of Friendly Societies, 
 gives a table showing approximately the results of the valuations 
 recorded during the five years ending 31 December 1880. 
 According to this estimate, the aggregate valuation balance sheet 
 of the 6,567 societies valued would be as follows : 
 
Friendly Societies. 
 
 17 
 
 TABLE 2. Aggregate Balance Sheet of 6,567 Societies. 
 
 LIABILITIES. 
 
 Present value of benefits . 33,405,152 
 
 Other liabilities . . 3,030,582 
 
 Surplus (in 1,537 societies) 885,382 
 
 37,321,116 
 
 ASSETS. 
 
 
 8,380,851 
 
 Amount of funds . 
 
 Present value of contribu- 
 tions .... 23,066,592 
 
 Other assets . . . 717,857 
 
 Deficiency (in 5,030 so- 
 cieties) . 5,155,816 
 
 37,321,116 
 
 The Colonies. 
 
 It is not possible to draw any very decided conclusions from 
 these figures, from the uncertainty attaching to the large number 
 of valuations made by unskilled valuers. They probably roughly 
 indicate, however, the financial position of the societies as a whole, 
 as it would be brought out by a general valuation upon the basis 
 of the Manchester Unity experience, at about 3J per-cent interest. 
 While the proportion of the net deficiency to funds is undoubtedly 
 large, it is the opinion of those best qualified to judge, that the 
 financial position of the societies generally is annually improving, 
 not so much, perhaps, by the progress of individual societies, as 
 by the gradual dying out of the unfit and their replacement by 
 their sounder and better-managed rivals. 
 
 During recent years friendly societies have taken con- 
 siderable hold in the various colonies, and especially 
 in Australia. Branches of the various affiliated orders constitute 
 the great bulk of these societies, the Manchester Unity of Odd 
 Fellows having been in existence in the Australian colony since 
 1840. 
 
 The duties which in this country are vested in the Registry 
 Office are, in Victoria, divided between the registrars and the 
 Government statist. In the Report of 1884, some very interesting 
 particulars are given as to the valuations received up to the end of 
 that year. In all, 660 societies, comprising 43,000 members, had 
 made valuations : less than one-fourth showed a surplus, and the 
 remainder a deficiency the net deficiency for the whole being 
 about J300,000. As compared with the Manchester Unity 
 experience, it is stated that the actual mortality in the societies 
 had been less than the expectation by 9 per-cent, but the sickness 
 was greater by 2 per-cent, while the withdrawals had been almost 
 three times more numerous. Thirty-one parent societies were in 
 existence at the close of 1884, comprising 788 branches and 
 59,000 members, showing an increase of 4,000 on the previous 
 
18 
 
 Friendly Societies. 
 
 year. The income of the societies amounted to 228,000, the 
 expenditure to 183,000, and the total funds to about 570,000, 
 invested at an average rate of 5Jth per-cent. This high rate of 
 interest must have an important bearing on the financial position 
 of the societies, although there seems little probability that it will 
 be permanently maintained. 
 
 In New Zealand, the affiliated orders also appear to be fairly 
 numerous, and to constitute nearly the entire bulk of the societies 
 there existing, the Manchester Unity and the Ancient Order of 
 Foresters taking the lead. At the close of 1883 there were 243 
 societies, including lodges, with a membership of 19,000, and 
 funds of 230,000, an average of a little over 12 per member. 
 The societies are small, averaging between 70 and 80 members. 
 Mr. Edmund Mason, the registrar, furnishes, in his report, some 
 very interesting particulars as to the rate of mortality and sickness 
 prevailing. The following is an extract from his table relating to 
 the experience of the New Zealand societies for the ten years, 
 1873 to 1882 : 
 
 TABLE 3. Experience of New Zealand Friendly Societies. 
 
 
 Percentage of Members 
 Sick per Annum 
 
 Weeks' Sickness per 
 Annum per Member 
 
 Deaths per 1,000 per 
 Annum 
 
 Members 
 
 New 
 Zealand, 
 1873-82 
 
 A.O.F. 
 
 1871-75 
 
 New 
 Zealand, 
 1873-82 
 
 A.O.P. 
 
 1871-75 
 
 New 
 Zealand, 
 1873-82 
 
 A.O.F. 
 
 1871-75 
 
 20 to 25 
 
 12-69 
 
 21-5 
 
 0-55 
 
 0-82 
 
 4-18 
 
 7-43 
 
 25 30 
 
 11-72 
 
 21-6 
 
 0-60 
 
 0-85 
 
 4-71 
 
 7-29 
 
 30 35 
 
 13-38 
 
 22-3 
 
 0-73 
 
 0-97 
 
 5-28 
 
 8-86 
 
 35 40 
 
 14-77 
 
 23-4 
 
 1-01 
 
 1-15 
 
 7-04 
 
 10-92 
 
 40 45 
 
 15-21 
 
 25-0 
 
 1-17 
 
 1-37 
 
 10-70 
 
 12-84 
 
 45 50 
 
 15-40 
 
 26-9 
 
 1-33 
 
 1-71 
 
 9-90 
 
 16-58 
 
 He rightly recognizes, however, that the statistics of the New 
 Zealand societies are not yet sufficient as a basis of calculation 
 for contributions. It will be seen that, as is the case with the 
 Victoria societies, the sickness rates are, throughout, higher than 
 in the English tables, while the mortality is considerably lower. 
 The financial effect of this feature, however, will be much more 
 than counteracted, for many years to come, by the high rate of 
 interest at which the funds are invested, which is stated to 
 amount to over 6 per-cent. By the Act of 1878, annual returns 
 of sickness and mortality are required, the cost of which is 
 defrayed by the Government. 
 
Friendly Societies. 19 
 
 Generally societies in the colony are governed by the Act of 
 1877, and the Governor's Regulations issued under it, which 
 closely approximate to our own Acts of 1875 and 1876, and to the 
 Treasury Regulations, except that some of the duties performed 
 by the English Registry Office are, in New Zealand, divided 
 between the registrar and the revising barrister. One very 
 important provision of the Act secures that every valuer shall be 
 approved by the Governor, and another provides for the absolute 
 separation of the management and benefit funds. 
 
 In New South Wales, Queensland, and South Australia, the 
 position of the societies is very similar to that in Victoria and 
 New Zealand. 
 
 FRIENDLY SOCIETIES IN FOREIGN COUNTRIES. 
 
 In no part of the Continent has the friendly society 
 system taken root so extensively as it has in this 
 country, and, so far as can be ascertained, the system is not 
 only less extensive, but, on the whole, less ancient. Government 
 patronage and control is carried out to a much greater extent than 
 here, and much of the legislation is of a character that would be 
 decidedly resented by the societies in this country. 
 
 In France the societies seem to have taken their origin 
 mainly from religious associations or guilds rather than from 
 trade societies, as here. They appear to have existed extensively 
 amongst the French Protestants, as the refugees who came to 
 this country after 1685 introduced several, some of which 
 have been in existence down to quite recent times; but the 
 number of societies remained very limited until the middle of the 
 present century. In 1849 a committee was founded for the 
 encouragement of provident societies, which did very useful work 
 by making extensive inquiries into the then condition of societies 
 in France. One result from the labours of this committee was 
 the publication, by M. Hubbard, the secretary of the committee, 
 of a report, dealing not only with the condition of the societies as 
 a whole, but also containing an investigation into the sickness and 
 mortality experienced by 25 societies who responded to the 
 invitation to send in returns. The results of this investigation, 
 which have been made known to actuaries in this country 
 through the medium of Mr. Samuel Brown's paper (J.I. A., 
 v, 208), are of considerable interest. In many respects they are 
 similar to the experience obtained by the Highland Society 25 
 
 B 2 
 
20 -Friendly Societies. 
 
 years previously, the sickness being lighter than that shown by 
 any experience in this country. The experience was divided into 
 sickness claims and claims for infirmity, a distinction answering 
 nearly to bed-lying and walking pay in some of our own societies, 
 or perhaps better to the distinction made between sickness and 
 superannuation the reduction in the allowance for the latter 
 being very considerable. 
 
 After the establishment of a superior commission for the 
 encouragement and supervision of friendly societies in 1852, the 
 number of societies in France rapidly increased. By the decree 
 of that year they were divided into two classes approved societies 
 and allowed societies. The difference between the two classes of 
 society answers very nearly to that existing between registered 
 and unregistered societies in this country. Mr. Ludlow gives the 
 following list of privileges conferred by " approval " : 
 
 1. The right of "civil personality" (practically equivalent 
 
 to our "incorporation"), carrying with it the right 
 of taking immovable property on lease, of accepting 
 gifts and legacies (with the prefect's authority) up to 
 200, and by decree of the Council of State for higher 
 sums. 
 
 2. The occupation, rent free, of places of meeting, put at 
 
 their disposal by the communes. 
 
 3. Supply of the necessary books for their management and 
 
 accounts. 
 
 4. A reduction to one-third of funeral taxes. 
 
 5. Exemption (generally) from stamp duties. 
 
 6. Deposit of funds, without limit, with the " Caisse des 
 
 Depots et consignations " at 4J per-cent interest, the 
 grant of life-annuities from the same office, and the 
 right of depositing up to 8,000 francs (320) in 
 savings banks, postal or other. 
 
 7. Contributions from the funds of the " Caisse des 
 
 Depots et consignations" in proportion to payments 
 in collective insurance in case of death. 
 
 8. Admission, at reduced rates, for convalescents in the 
 
 Department of the Seine in two municipal establish- 
 ments. 
 
 Honorary members form a special feature of the approved 
 societies. The management is mainly vested in them, an important 
 
Friendly Societies. 21 
 
 post in these societies being that of president, who, in all cases, 
 is appointed by the Government, the wishes of the members of 
 the society being, of course, considered. In carrying out the 
 rules, however, all propositions are submitted to discussion and to 
 the votes of general meetings. 
 
 The difficulty of providing for sick claims and superannuation 
 at the older ages, which has been so seriously felt in societies in 
 our own country, was also in existence among the French societies. 
 Among the old societies the pension fund, generally, rested on 
 an unsound basis, offering benefits to the members which there 
 was no prospect of their ever receiving. An important change 
 in this respect was made by the decree of 1852 already referred 
 to, which substituted for the old system of pension funds the 
 power of taking a certain portion of the reserve fund, especially 
 the contributions of honorary members, with a view of assisting 
 the aged and infirm. In the case of approved societies, this 
 portion of their funds is placed at the caisse aforesaid. Accounts 
 are opened in the name of each society which pays in, and the 
 interest of the moneys is distributed in the shape of annuities 
 among the aged members, who are chosen by a general meeting, 
 and who have been at least 10 years in the society. At the death 
 of these members the capital of the pensions is returned to the 
 society and used again in the same manner for the benefit of the 
 other members. 
 
 The average magnitude of the societies appears to be quite 
 equal to that of the English ; reduction in the rate of pay after six, 
 nine, or twelve months, is now almost invariable, and, as already 
 intimated, is very considerable; and in addition to members who 
 are permanently invalided, there are regular pensioners whose 
 benefits date from a certain fixed age, and who receive similarly 
 reduced amounts. 
 
 Since the period at which friendly societies in France first 
 became directly encouraged and patronized by Government, their 
 numbers have rapidly increased. In 1884, the total number of 
 societies was 7,743, of which 5,570 were approved. Of these 
 latter, 3,956 consisted solely of men, 1,452 of men and women, 
 and 162 of women only. The number of members in approved 
 societies was stated to be 928,788, and in authorized or 
 allowed societies 319,123. The funds of the approved societies 
 amounted to about 3,860,000, and of allowed societies to 
 1,050,000, in addition to investments for annuities belonging 
 to approved societies only, and amounting to some 2,170,COO, 
 
22 Friendly Societies. 
 
 making a total for all societies of something over 7,000,000 
 sterling. This, although a large sum, is much below the amount 
 standing to the credit of English societies. 
 
 Friendly societies in France still appear to be without any 
 trustworthy guide in the way of sickness and mortality tables 
 deduced from their own general experience ; but there is no doubt 
 that their financial position, as in our own country, has greatly 
 improved during the latter part of the present century. 
 
 There is in Belgium only one legally recognized 
 class of friendly societies, answering to the approved 
 societies in France, but the unrecognized societies exist in large 
 numbers, and many of these, unlike the unregistered societies 
 in our own country, furnish returns to the Commission, which 
 takes the place of our Registry Office. From the report of 
 M. Duepetiaux, a member of the Central Statistical Commission, 
 in 1852, it would seem that the origin of many of the Belgian 
 societies is very ancient, and their organization of great variety. 
 It appears that there were then only 211 "societies of mutual 
 aid " existing in Belgium, numbering 24,300 members. 
 
 Societies are regulated by the law of 3 April 1851, which 
 authorizes their recognition by Government; such recognized 
 societies enjoying the following advantages : The power to sue 
 or be sued; exemption from stamp duties and registration fees 
 of all deeds; power to receive donations or legacies of personal 
 property; and other less important privileges. 
 
 The number of societies in Belgium does not appear to have 
 been increased materially during the 30 years that have elapsed 
 since the law of 1851. At the close of 1882, according to the 
 report of the Permanent Commission of Friendly Societies, there 
 were 191 recognized societies, with about 30,000 benefit and 
 4,000 honorary members, while there were 77 non-recognized 
 societies which had forwarded reports, with a membership 
 amounting to 23,000. It is stated, however, that in addition 
 to these, the mining population had special societies, with an 
 aggregate of over 104,000 members. 
 
 The average contributions in the recognized societies amount 
 to about 9s. per member, and in the non-recognized about 12s.; 
 and the average sickness benefit to about Is. 2d. in the former, 
 and Is. in the latter class per day. 
 
 The practice of valuations appears to be unknown, and no 
 attempt has been made to investigate the experience of the 
 
Friendly Societies. 23 
 
 societies as to sickness or mortality.* It is stated, however, as 
 a result of experience, that the monthly contribution should be 
 equivalent, or nearly so, to the daily pay in sickness; and it 
 appears that the Commission does not recommend for recog- 
 nition societies whose contributions it considers insufficient. 
 Dividing societies are not recognized. 
 
 In addition to the friendly societies, properly so-called, there 
 exist provident societies for the assistance of sick or disabled 
 workmen, their wives and children, whose operations are much 
 more varied than those of the friendly societies. Thus, provident 
 funds have been founded for miners, servants on the State 
 railways, fishermen, pilots and sailors. Of these the most 
 important are, perhaps, the miners' funds, which provide pensions 
 either for life or for shorter periods. The life pensions are allotted 
 to workmen who may be permanently disabled, to the widows, and, 
 in some cases, the parents or grandparents of workmen who have 
 perished by accidents in the mine the temporary pensions being 
 granted to the infant children, or orphans of such miners, and 
 ceasing when the children attain the age of 12 years. The funds 
 are derived from the following sources: A deduction from the 
 wages of the miners, varying from a half to one per-cent ; a 
 similar contribution from the proprietors of the mines ; allowances 
 granted by the Government or the province, in addition to interest 
 on capital gifts and legacies. The assistance on the part of the 
 proprietors is voluntary. 
 
 So far back as 1838, a fund was established for workmen 
 employed on the State railways, which is supported by a deduction 
 of about 2 per-cent from the wages of the men, and which grants 
 assistance to sick members varying from one-half to three-quarters 
 of their wages, or to the whole wages in case of wounds received 
 in the service, a graduated scale of benefits being in force, 
 dependent upon the extent of the family of the injured man. 
 
 The objects of the German friendly societies are, by 
 the Act of April 1876, confined to relief in sickness 
 or convalescence, medical aid, and allowances to the families of 
 deceased members which take the place of the death benefits usual 
 in our own societies. It is provided that the rules shall contain no 
 provision not connected with the objects of the society, and there 
 are provisions for quinquennial valuations, returns of sickness and 
 
 * The report for 1859, however, gives the rate of sickness among the 
 members, from 18 to 50 years of age, as 6'81 days, a result stated to be midway 
 between the French and English experience. 
 
4 Friendly Societies. 
 
 mortality, and balance sheets, very similar to our own. The 
 leading differences are that the amount of Government interference 
 is considerably greater, and many points, in this country left to the 
 discretion of societies, are, in Germany, fixed by law. For example, 
 the period after which a member becomes free to benefit must 
 not exceed 13 weeks, while the right to relief exists for a similar 
 period after withdrawal or exclusion. The same period is fixed as 
 the minimum duration of relief, should sickness continue so long. 
 The limits between which the sickness benefit may vary are also 
 fixed, and depend upon the wages of the members, while societies 
 are not allowed to refuse the benefit for particular cases of 
 sickness. 
 
 All societies, whether recognized or not, are considered to be 
 under superintendence, and the authority appointed for this 
 purpose by the provincial government may inspect the books of 
 the societies, receive yearly statements, and give notices to 
 societies (entailing dissolution when disregarded) with respect to 
 arrears of contributions or benefits, illegal resolutions, &c., may 
 appoint liquidators, call general meetings when the committee of 
 management fails to do so, and impose fines for failure to forward 
 returns. 
 
 The higher administrative authority registers rules and receives 
 quinquennial returns of sickness and mortality, and valuations, 
 &c., and, in certain cases, subject to appeal, may order the closing 
 of the society. It is, moreover, the superintending authority for 
 all federations of societies, whose boards of direction sit within its 
 jurisdiction. 
 
 In the chief registrar's report for 1876 he makes the following 
 remarks upon the German legislation of that year : " It is not 
 " too much to say that, under such a weight of official oversight, 
 " any multiform development of our friendly societies would have 
 " been impossible. Yet these are the provisions relating to what 
 " may be termed the free societies. The fact must now be 
 " recalled that these form only one portion of the German system. 
 " According to the law of the 8th April, amending the ' Gewerbe 
 " Ordnung ', the formation of friendly societies may be ordered 
 " by local regulations. In this case, the communal authorities, 
 " after hearing the parties interested, appear to frame the rules 
 " of the society, and by local regulation it may be made com- 
 " pulsory on all working men aged 16 years and upwards to 
 " join it, unless already members of some registered society, and 
 " in like manner compulsory on all employers to advance the 
 
Friendly Societies. 25 
 
 " contributions of their workmen to the society so established by 
 " the commune, up to the amount of one half of their wages, and 
 " to subscribe themselves to the society, up to the amount of one 
 " half of the contributions of their workmen. The same powers as 
 ( ' those given to the communes are given also to ' larger communal 
 " unions.' " 
 
 In 1882 a law was passed rendering insurance against sickness 
 obligatory on all persons whose wages do not exceed 4s. a day, 
 employed in mines, factories, and some other undertakings, and 
 upon agricultural labourers when so determined by the district 
 authorities, two-thirds of the contributions being paid by the 
 workmen, and one-third by the employers, but the latter being 
 responsible for the whole. 
 
 From a Minute of the German Government which has just 
 appeared (November 1887) in the official papers, it seems to be 
 the intention to extend the existing legislation so as to cover 
 superannuation allowances for all persons of 70 or over, and for 
 all below that age who may become permanently unable to work. 
 Societies in Switzerland are very numerous in pro- 
 
 Switzerland. , J 
 
 portion to the population, and appear to be somewhat 
 similar to the German societies, the majority providing only for 
 sickness allowances, and not funeral benefits. The average 
 magnitude of the societies is very similar to that obtaining in 
 this country, ranging from about 100 to 120 members. In 
 1883 a proposal for compulsory insurance of the whole population, 
 for both sickness and burial, was made in the Great Council of 
 Basle by the Commission which had been appointed to consider 
 the subject, but was rejected. The Executive Council, however, 
 was directed to prepare measures for gratuitous burial and com- 
 pulsory sickness insurance in the case of the adult labouring 
 population. 
 
 The guild system common to nearly all European 
 
 Denmark. . ? -.. i T i / 
 
 societies, was, in Denmark, succeeded by one of 
 compulsory friendly societies, corresponding to that of the German 
 Zwangskassen. After the enactment of the Free Constitution 
 of 1849, however, it was considered unnecessary to maintain a 
 compulsory principle, and free friendly societies were allowed to 
 be established with the funds belonging to the compulsory ones. 
 Very few restrictions being imposed by the law on these societies, 
 a large number were founded, and, at the present time, out of a 
 population of 2,000,000, probably about 150,000 are members 
 of these societies. Affiliated orders like the English, do not 
 
26 
 
 Friendly Societies. 
 
 exist. The most recent statistics with respect to Danish societies 
 appear to be those contained in the publications of the Statistical 
 Bureau for 1885, and which give particulars of the operations of 
 the societies to the close of 1882. There were at that time 831 
 societies, with 115,000 ordinary members, and between 5,000 and 
 6,000 honorary members. The income of the societies amounted, 
 in the aggregate, to some 58,000, against an expenditure of 
 53,000, and the funds in hand to a total of 118,000 (about 
 two years' income), and during the five years had risen from about 
 17s. 9d. per member to 1. Os. 5d. 
 
 Attempts have recently been made to investigate the sickness 
 rate prevailing among the Danish societies, but it is stated that 
 the materials are scanty, and, it is feared, incorrect, while the 
 experience of different societies is extremely dissimilar. The 
 following table, however, may be found interesting, as giving a 
 comparison of the results obtained with the rates prevailing in the 
 Manchester Unity Society : 
 
 TABLE 4. Sickness Hate in Danish Societies. 
 
 
 DANISH SOCIETIES (1878-82) 
 
 Manchester Unity 
 
 Age 
 
 
 
 (R. T. & C.), 
 
 
 Rural and Town 
 
 Copenhagen 
 
 1866-70 
 
 20-29 
 
 48 
 
 75 
 
 78 
 
 30-39 
 
 54 
 
 94 
 
 98 
 
 40-49 
 
 77 
 
 1-06 
 
 1-44 
 
 50-59 
 
 93 
 
 1-61 
 
 2-59 
 
 60-69 
 
 1-37 
 
 2-16 
 
 5-58 
 
 APPLICATION OF ACTUARIAL PRINCIPLES AND DATA TO THE 
 VARIOUS CLASSES OF SOCIETIES. 
 
 Sickness 
 Benefits, 
 
 If the rate of sickness were uniform at all periods 
 of life, friendly society finance would be a very 
 simple matter, since societies might be conveniently carried on 
 upon the "dividing out" principle, the members being charged 
 an annual contribution slightly in excess of what experience had 
 shown was sufficient for the current claims, and a small sum being 
 kept in hand to cover fluctuations from year to year. Since, 
 however, liability to sickness increases, like the rate of mortality, 
 with the age of the individual, it is necessary to charge an annual 
 contribution which will be more than sufficient, in the first 
 instance, to meet the current sickness claims, allowing such 
 
Friendly Societies. 27 
 
 difference to accumulate in the hands of the society against the 
 period when the annual claims will, by reason of increasing age, 
 exceed the annual contribution. It is obvious that to fix this 
 contribution at a sum which shall be adequate in the long run to 
 provide for all the claims that will arise, without, at the same 
 time, making it unnecessarily heavy, and, further, to determine 
 from time to time how far the accumulations in the possession of 
 the society are sufficient for this purpose, the actuary must be in 
 a position to estimate, within fairly narrow limits, the amount of 
 the claims that will in future years be made by the members upon 
 the fund. The only basis upon which such an estimate is 
 possible is, of course, past experience, either of the particular 
 society, or, if this is not available or is insufficient, then of other 
 societies similarly constituted. 
 
 The application of actuarial principles to the financial 
 operations of friendly societies is, however, a problem of greater 
 difficulty than in the case of life assurance ; in the first place, 
 because the two elements of sickness and mortality are involved ; 
 and, secondly, from the more frequent deviation of the sickness 
 experience, from one cause or another, from the average type. 
 Hence, while as regards both the mathematical theory and the 
 data to which it can be applied, the science of life contingencies 
 may be now said to be nearly perfect, the extension of these 
 principles to the work of friendly societies is still in its infancy. 
 
 The possibility of applying the principle of averages 
 modifying upon which actuarial science is based to sickness 
 
 Sickness Rates. . . 
 
 assurances, is a question that can only be decided by 
 experience. In the case of life assurance, various reasons have 
 facilitated this process. The fact to be dealt with, that is to say, 
 the rate of mortality prevailing amongst a given class of lives, is 
 well defined, and depends mainly upon the one factor of age, 
 because although there may be disturbing causes, such as occupa- 
 tion, locality and the duration of the assurances, these are of minor 
 importance, and it has been possible in practice very largely to 
 disregard them. In the case of the average friendly society, 
 however, we have to deal with the further element of sickness, 
 which is much less easily defined than that of mortality. It may 
 have, for instance, a merely relative signification depending on the 
 nature of the occupation : sickness which would permanently 
 incapacitate the sufferer from following certain callings, being, as 
 regards other occupations, of little moment. Especially is this the 
 case at advanced ages, where the line between true sickness and mere 
 
28 Friendly Societies. 
 
 incapacity to follow occupation is not easily drawn. The rate of 
 sickness, as well as the actual cost of the allowances, may, more- 
 over, be very materially modified by the rules of the individual 
 society; by reductions in the allowances in continued sickness 
 or their final cessation after a definite term ; or by the length 
 of the period for which a member must be off the books before 
 being free again to claim full benefit; while there is the still 
 further element of imposition to which societies granting sickness 
 benefits, especially the large centralized societies, must necessarily 
 be open. 
 
 It may be pointed out, however, that the application of 
 actuarial principles to friendly societies does not necessarily 
 depend on the possibility of constructing tables of sickness which 
 shall accurately represent rates prevailing throughout the country, 
 or that shall be generally applicable to all societies. Where a 
 society has been actually in operation for any length of time, even 
 though its experience may differ very widely from the average, so 
 long as that experience has been uniform, the actuary may find 
 himself in possession of sufficient data from the actual records of 
 the society upon which to base estimates of future results. We 
 have, therefore, to consider two questions : in the first place, the 
 possibility of constructing tables of sickness which should be 
 generally applicable ; and, secondly, the extent to which past 
 experience of any given society may be expected to reproduce 
 itself in the future. Both of these points will be considered 
 later, but it may be stated here that experience has undoubtedly 
 shown that although the causes influencing the rates of sickness 
 in a given body of persons are more numerous and more effective 
 than in the case of mortality rates, nevertheless, whenever a group 
 of persons or of societies is sufficiently homogeneous, the 
 principle of averages will be found to apply as much in respect of 
 sickness as for deaths. 
 
 Collection of ^e ^ rs ^ important step in the construction of sickness 
 Data * tables, whether of a single society or a large group of 
 
 societies, is the collection of data, and, in order that this may be 
 trustworthy, accurate records of the experience of the society 
 must be kept, the ages of the members under observation in any 
 given year must be known, and the amount of sickness experienced 
 by each carefully tabulated. 
 
 The forms and books to be employed for this purpose will, of 
 course, vary to some extent with the magnitude and nature of the 
 society and with the object for which the data is to be employed. 
 
Friendly Societies. 29 
 
 If this object is to form part of a large general experience, to 
 include societies of various classes as to benefits and rules, forms 
 must be used which will be universally applicable, and which, 
 moreover, will give full information on many points which may be 
 taken for granted where the enquiry refers to a single society 
 only or to a group of perfectly similar institutions. Now that 
 the quinquennial returns of sickness and mortality have been 
 discontinued, it is these latter cases only that are in question. 
 Passing over the general register of members and of the cash 
 transactions of a society, it is necessary that a special register 
 should be kept of all the sickness claims made by the members in 
 each year, that these may be readily tabulated and analyzed when 
 required. This register may conveniently be in the following 
 form, which is only slightly modified from that recommended by 
 the "Actuarial Commission" (Report 1876). The date of the 
 commencement of sickness will enable an analysis to be made, as 
 provided for in the "Total" columns, but it is desirable that a 
 distinctive mark should show whether each sickness payment is at 
 the full or reduced rate. 
 
 Register of Sickness, 188 . 
 
 
 
 DAYS SICK, AND AMOUNTS PAID IN WEEK ENDING 
 
 
 Date of 
 Com- 
 
 January 7 
 
 January 14 
 
 Ite. 
 
 TOTAL 
 
 Name 
 
 mence- 
 
 
 
 
 
 
 ment of 
 
 
 
 
 
 
 
 
 
 Sickness 
 
 
 
 
 
 
 Time 
 
 Amount 
 
 
 
 Days 
 
 
 
 A + 
 
 &c 
 
 
 
 
 
 
 
 
 
 
 1st 6 
 Months 
 
 2nd 6 
 Months 
 
 After 
 
 1st 6 
 Months 
 
 2nd 6 
 Months 
 
 After 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 &c. 
 
 
 
 
 
 
 
 It is desirable that a ledger account should be kept of every 
 member's contributions and benefits. The form of this will vary 
 with the class of society, but it should contain at least the 
 following particulars : 
 
30 
 
 Friendly Societies. 
 
 Name, Occupation, & 
 
 e 
 
 
 
 Entered. 
 Became : 
 Date of 
 Age(n.b 
 
 
 Sicl 
 Sup 
 Dea 
 Wif 
 
 Allowances Contributions 
 ;ness 
 
 "ree 
 
 erannuation 
 th 
 
 
 birth 
 .d.) at 
 
 
 
 entry 
 
 
 e's deal 
 
 h 
 
 
 
 Date 
 
 CONTRIBUTIONS EECEIVED 
 
 Date 
 
 ALLOWANCES PAID 
 
 Sick. 
 
 Super- 
 ann. 
 
 Death 
 
 Mangt. 
 
 Fines 
 
 Total 
 
 Sickness or Superann. 
 
 Other 
 Payments 
 
 Weeks 
 
 At 
 
 Amount 
 
 
 
 
 
 
 
 
 
 
 
 
 
 In estimating the ages of the members for the purpose of 
 summarizing the experience, it will be found most convenient to 
 adopt such a system as will make the assumed years of age 
 coincident with the calendar year. This may be done by making 
 assumptions similar to those in the Institute of Actuaries' 
 Mortality Experience, namely, that the lives enter on the average 
 in the middle of the calendar year and in the middle of the year 
 of age, attaining their current age at entry (next birthday) at the 
 close of the year of entry. The following plan, however, will be 
 found on the whole more convenient. Let the particulars from 
 the sickness register be posted annually on to cards of the 
 following form, one of which should be prepared for every 
 member entering the society : 
 
Friendly Societies. 
 
 31 
 
 Nc 
 
 Ns 
 Date oj 
 
 i. 
 
 Occupa 
 
 SOCIETY. \. 
 
 ition 
 
 \ 
 
 imp 
 
 
 
 'Birth, 3 May 1848. 
 
 Entry, 7 August 1879. 
 
 Freedom, 7 February 1880. 
 
 Exit, 15 September 1884. 
 Mode of Exit Withdrawal. 
 
 Year 
 
 Nearest 
 Age on 
 1 January 
 
 SICKNESS 
 
 1st 6 Months 
 
 2nd 6 Months 
 
 After 12 Months 
 
 Weeks 
 
 Days 
 
 Weeks 
 
 Days 
 
 Weeks 
 
 Days 
 
 1880 
 1881 
 1882 
 1883 
 1884 
 
 32* 
 33 
 34 
 35 
 36* 
 
 1 
 26 
 
 4 
 
 -"5 
 
 "3 
 
 ... 
 
 ... 
 
 The ages given are those at the nearest birthday to 
 1 January in each year. In the above instance, the ages opposite 
 the years 1880 and 1884 (the years of freedom and withdrawal) 
 are marked with an asterisk to indicate that the member was 
 exposed to risk only for a fraction of those years. 
 
 These cards, which may be made to contain a record of 5 or 
 10 years' sickness, may be annually or quinquennially sorted and 
 summarized, according to the ages of the lives under observation, 
 the total number under observation at each age and the sickness 
 and deaths experienced being then scheduled. If this summary 
 be made separately for various ages at entry, it will be possible, 
 where desired, to investigate the effect of the duration of the 
 assurances upon the rates of sickness or mortality, while, combining 
 the facts for all ages at entry, we obtain the materials for con- 
 structing tables of sickness and mortality in their usual form. 
 The same assumptions should be made in respect to the numbers 
 at risk both for sickness and deaths, that is to say, any life dying 
 in a given year should be considered at risk for the whole of the 
 year. If this is not done we obtain a function which may be 
 termed, by analogy, the " central sickness rate ", or force of 
 
32 Friendly Societies. 
 
 sickness in the middle of the year. There is, of course, no 
 objection on principle to the employment of the functions of the 
 force of mortality and force of sickness. It will be found, 
 however, much more convenient to use the rates of mortality and 
 sickness as usually understood. 
 
 The numbers at risk at each age, the deaths, and the number 
 of weeks' sickness experienced, having been thus obtained, the 
 ratio of the latter numbers to the former will give the probability 
 of death within the year, usually termed the rate of mortality, 
 and the average number of weeks' sickness, which may similarly 
 be termed the rate of sickness, experienced by each individual. 
 Adjustment of Before these facts can be conveniently employed in the 
 Tables. construction of monetary tables, it is necessary that 
 
 they should undergo a process of adjustment, or, as some prefer 
 to term it, (c graduation ", in order that the irregularities incident 
 to all observations into which the element of probability enters 
 (however numerous the facts) may be removed. Much has been 
 written at various times on the subject of the adjustment of 
 mortality tables, the papers of Mr. Sprague, Mr. Woolhouse, and 
 Mr. J. A. Higham, in the Journal of the Institute of Actuaries, 
 being especially valuable. Mr. Sprague, who advocates the 
 graphic method of adjustment, has so completely described and 
 illustrated his system that it will be sufficient to refer the reader 
 to his original papers. 
 
 Mr. Woolhouse, who was the first to apply the theory of finite 
 differences to the problem of the graduation of mortality tables, 
 and Mr. Higham, 'who has improved upon Mr. Woolhouse's 
 methods and formulas, both take exception to the graphic method 
 on the ground of the possible variety in the results that may be 
 obtained by different operators, and upon the fact that it pre- 
 supposes a considerable degree of skill and judgment in the person 
 employing it. Without attempting to determine generally 
 between the merits of the two systems, it may be said, that while 
 the graphic method is, in some special cases perhaps, the only 
 method available, on the other hand, for the adjustment of 
 ordinary mortality and sickness tables, the use of formulas, such 
 as Mr. Woolhouse' s, Mr. Higham' s, or that given below, is not 
 open to any practical objection, and has an undoubted advantage 
 in respect of the ease and rapidity with which they can be applied, 
 and the certainty of the results attained. The formulas which 
 Mr. Higham has produced give very admirable results; to give 
 completeness, however, to the discussion of this portion of the 
 
Friendly Societies. 33 
 
 subject, I will add here a new formula, which I believe superior 
 both in smoothness and simplicity to any yet given. 
 
 In this formula, if the graduated value of the function be 
 represented by u x and the ungraduated by u x , 
 
 Its method of application in practice is as follows. Supposing the 
 graduated table is to commence at age 18, the unadjusted table 
 should be brought down to age 10 by inserting constant values for 
 the sickness and mortality rates from 10 to 18 (these may, in general, 
 be equal to the average values of these functions at the lowest 
 group of ages observed) . At the other extremity of the table, if, as 
 usually happens, the facts at the older ages are very small or are 
 not reliable, it will be necessary to make some arbitrary adjust- 
 ment, by inserting the rates from some suitable standard table, or 
 in the case of the sickness by assuming it to become chronic above 
 a selected age, remembering that the highest rate of sickness at any 
 
 age will be 52 ^j weeks per annum. The point at which this 
 
 should be done must, of course, depend entirely upon the 
 judgment of the actuary as to the character of the data. It is to 
 be noted that where the sickness is assumed to be chronic, the 
 rates for the earlier periods of sickness must be taken as zero. 
 For example, if, at age 85 and upwards, the rates of sickness are 
 taken at their maximum amount, 26(1 +p x ), then at age 86 and 
 upwards the rate for the 1st and 2nd 6 months of illness must be 
 taken as zero, and similarly the rates for the 2nd 12 months at 
 age 87 and upwards. 
 
 Having in this manner completed the whole series of rates to 
 be adjusted, the formula above given may be thus applied : 
 
 * This formula is not quite true to second differences, differing from the true 
 value of u x by one-twelfth of the central second difference. The error is, how- 
 ever, insignificant, being not greater in value than that due to the neglect of 
 fourth differences in all such formulas. The error might be corrected by taking 
 
 Q8u x instead of ~ in column (2), and by summing in 5's in columns (6), (7), 
 12 
 
 and (8) (see next page) ; but there would be no practical advantage as regards 
 accuracy, while the graduation would be less smooth. 
 
34 Friendly Societies. 
 
 1. Divide the rates of sickness or mortality by 12, cutting 
 
 down the decimals to leave two significant figures at 
 the young ages. 
 
 2. Sum these results in 3% putting the result opposite the 
 
 middle age. 
 
 3. From the last result subtract the sum of the two numbers 
 
 in col. (2) at ages two years older and younger. 
 
 4. Sum the last result in 4's. 
 
 5. 5's, cutting down the last figure. 
 
 6. jj 6's, which will give the finally 
 adjusted rates. 
 
 The form of the work will be as in the following table : 
 TABLE 5. Application of Graduation Formula. 
 
 Age 
 
 X 
 
 h^x 
 
 = w x 
 
 Sum in 
 3's 
 
 U>x-2 + Wx+Z 
 
 (3)-(4) 
 
 Sum in 
 4's 
 
 ^j- Sum in 
 5's 
 
 Sum in 
 6's 
 (Adjusted 
 Value) 
 
 (l) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 (8) 
 
 10 
 
 068 
 
 
 
 
 ... 
 
 
 
 1 
 
 68 
 
 204 
 
 
 
 ... 
 
 
 
 2 
 
 68 
 
 204 
 
 136 
 
 68 
 
 . . . 
 
 ,. 
 
 
 3 
 
 68 
 
 204 
 
 136 
 
 68 
 
 9*79 
 
 K 
 
 ... 
 
 4 
 
 68 
 
 204 
 
 136 
 
 68 
 
 Via 
 
 
 
 5 
 6 
 
 7 
 8 
 9 
 20 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 30 
 
 68 
 68 
 68 
 68 
 68 
 64 
 70 
 64 
 64 
 68 
 71 
 66 
 65 
 56 
 66 
 65 
 
 204 
 204 
 204 
 204 
 200 
 202 
 198 
 198 
 196 
 203 
 205 
 202 
 187 
 187 
 187 
 200 
 
 136 
 136 
 136 
 132 
 138 
 132 
 132 
 132 
 141 
 130 
 129 
 124 
 137 
 131 
 134 
 123 
 
 68 
 68 
 68 
 72 
 62 
 70 
 66 
 66 
 55 
 73 
 76 
 78 
 50 
 56 
 53 
 77 
 
 272 
 
 272 
 276 
 270 
 272 
 270 
 264 
 257 
 260 
 270 
 282 
 277 
 260 
 237 
 236 
 245 
 9fi1 
 
 136 
 136 
 136 
 135 
 133 
 132 
 132 
 133 
 135 
 135 
 133 
 129 
 126 
 124 
 126 
 
 808 
 804 
 801 
 800 
 800 
 800 
 797 
 791 
 782 
 773 
 
 1 
 2 
 
 69 
 67 
 
 201 
 212 
 
 142 
 140 
 
 59 
 
 72 
 
 29OX 
 
 276 
 
 ... 
 
 ... 
 
 3 
 
 76 
 
 218 
 
 150 
 
 68 
 
 ... 
 
 
 
 4 
 
 75 
 
 222 
 
 ... 
 
 
 
 
 
 5 
 
 81 
 
 
 ... 
 
 
 
 
 
 6 
 
 ... 
 
 ... 
 
 ... 
 
 
 
 
 ... 
 
Friendly Societies. 
 
 35 
 
 Upon the basis of the graduated rates of mortality and 
 sickness thus obtained a table corresponding to the usual form of 
 a mortality table should be constructed as follows : 
 
 
 
 
 NUMBER OF WEEKS' SICKNESS EXPERIENCED 
 
 Age 
 
 Number living 
 at Age x 
 
 Dying between 
 x and x + 1 
 
 BY l x PERSONS 
 
 
 
 
 
 
 
 1st 6 Months 
 
 2nd 6 Months 
 
 Remainder of 
 
 
 
 
 
 
 Sickness 
 
 x 
 
 = h 
 
 = d x 
 
 -faj 
 
 -lA 
 
 =**r 
 
 
 
 
 
 
 
 From these values will then be computed the values for the 
 ordinary form of commutation table, having, however, additional 
 columns for the computation of sickness benefits; such values 
 being calculated according to the formulas given below. The 
 usual function Na. may be usefully replaced by the continuous 
 function N a; =N a ; + iD a ., since the continuous values of annuities 
 and assurances are those almost invariably required for friendly 
 society calculations. The values of A^ and P^ may, of course, be 
 calculated from those of a x by means of Messrs. Rothery and 
 Ryan's Premium Conversion Tables now in the press. 
 
 By means of these commutation tables the value of sickness 
 benefits ceasing at certain ages and replaced by superannuation or 
 deferred annuities, may readily be calculated a point of considerable 
 importance, since at the old ages there is a great lack of accurate 
 information as to the rates of sickness prevailing ; and in the great 
 majority of cases, even where pensions are not provided for by the 
 rules of a society, it becomes necessary to treat the sickness above 
 a given age (for example, 70, 75, or 80) as though it were a pension 
 at the lowest rate of pay, assuming that every member would be 
 constantly upon the funds after these ages were attained. The 
 value of the annuities and the funeral benefits being also given 
 by such tables, there will thus be all the elements requisite to 
 construct a scale of the contributions or to value the liabilities of 
 a society. 
 
 ^ wu *l ^e desirable to present a brief system of notation 
 or s i c k ness benefits, based, as far as possible, upon that 
 now employed for life contingencies. 
 
 Notation and 
 Formulas. 
 
 c 2 
 
36 
 
 Friendly Societies. 
 
 &c. 
 
 3+ 
 
 average number of weeks' sickness experienced by each 
 
 individual between ages x and x+\. 
 rate of sickness at age x. 
 
 ,, during 1st 6 months of sickness. 
 
 4 + = 
 fe, 
 
 Izl 
 
 &c. 
 
 after 1st 
 2nd 
 
 number of weeks' sickness by l x persons between ages 
 x and #+1. 
 
 during 1st 6 months of sickness. 
 2nd 
 
 2nd 
 &c. 
 
 and subsequently. 
 &c. &c. 
 
 Hi = 
 
 = v*+Vzl + 
 &c. 
 
 Forming the quantities in the commutation 
 table for sickness benefits, answering to the 
 C x columns for annuities and assur- 
 
 ances respectively. 
 
 f Forming the quantities in the 
 commutation table for sickness 
 benefits answering to the N* 
 and Mj. columns for annuities 
 
 Land assurances respectively. 
 
 Ka- _( value of sickness benefit of l per week 
 Da? ~~ I throughout life. 
 
 Ki __ (value of sickness benefit of 1 per week during 
 Da? | 1st 6 months of illness. 
 
 KJ _ (value of sickness benefit of \ per week during 
 Da- ~~ I 2nd 6 months of illness. 
 
 K^ + __( value of sickness benefit of 1 per week after 
 D* ~~ | 2nd 6 months of illness. 
 
 A 
 
 &C. 
 
 = value of similar benefits ceasing at ages 70, 
 75, and 80 respectively. 
 
Friendly Societies. 37 
 
 Ps 1 Ps 2 &c.) 
 
 x [ x> 2 " [. = annual premiums payable throughout 
 
 P 7 o*a; ; Vj** j &c. j life for tne corresponding benefits 
 
 to S x , 7 oSx> &C. 
 
 70 Ps x -, 7oP4j 7<>P4; &c. = do., premiums and benefits ceasing 
 
 at age 70. 
 IV,, &c.] 
 
 P os x &c. > = corresponding annual premiums when paid con- 
 p^ ^ I tinuously through the year (say by weekly or 
 
 monthly instalments). 
 
 As an example of this notation, we may express the single 
 and annual premiums for a sickness benefit of 1 per week, with 
 reduction to half and quarter-pay after 6 and 12 months 
 respectively, replaced after age 70 by a pension of quarter-pay. 
 
 Value of sickness benefit of 
 1 per week 1st 6 months. 
 
 to age 70, with pension thereafter, 
 of 5s. per week for life. 
 
 (K-K r 2 ) + (KJ + -K? 
 
 Annual premium for same, payable ) _. ^ 
 
 r J f Denominator = N^ 
 weekly or monthly ) 
 
 or if ceasing at age 70 . . . Do. =N a? N 70 
 
 SICKNESS TABLES EXISTING DATA. 
 
 HI hiand earliest attempt to construct tables of sickness, 
 
 based upon the collected experience of friendly societies, 
 
 was that made by the Highland Society in 1820, the 
 results of which were published in 1824. The table is historically 
 interesting, and merits notice principally from the fact that it was 
 largely employed (with unfortunate results) between that date and 
 its withdrawal in 1851, when its unsafe character had become 
 apparent to its authors. The data were voluntarily contributed by 
 73 societies (out of a much larger number applied to) from the 
 various counties of Scotland, and were sufficiently extensive (up to 
 about 70 years of age) to afford a fair basis for a sickness table, 
 the number of years of life observed being over 104,000. 
 
38 Friendly Societies. 
 
 It was scarcely to be expected that a first attempt to produce 
 a table that should be generally applicable would prove entirely 
 successful, and subsequent experience speedily showed that the 
 table gave far too favourable a view of the sickness prevailing on 
 the average among the members of friendly societies. The cause 
 of the very low rate of sickness shown has been much discussed 
 by various authorities. It has been variously attributed to the 
 superior healthiness of the districts from which the returns were 
 collected, the inaccuracy of the data, and to the fact that many of 
 the members of the contributing societies did not claim in case of 
 illness (though an attempt appears to have been made to correct 
 the returns in this respect). In addition to these possible 
 explanations however, the following considerations seem to me to 
 go far towards reconciling the results with those of later investiga- 
 tions. In the first place, the returns were purely voluntary, and 
 were furnislied by a small proportion only of the societies applied 
 to ; many societies strongly objected to the enquiry, many were 
 indifferent, and still more had not kept their books in a form to 
 afford the desired information. Considering the marked differences 
 which will be shown to exist between the sickness experiences of 
 individual societies, it does not appear unlikely that a principle of 
 selection would work in the production of such voluntary returns 
 by which societies whose experience had been favourable would be 
 more likely to respond than where the sickness rates had been 
 above the average, and, further, that it would in general be the 
 best-managed societies alone who would be in possession of the 
 facts required. 
 
 The rates of sickness as given are, moreover, not fairly 
 represented in the resulting table, owing to the very unhappy 
 method of adjustment employed. The original returns gave the 
 numbers at risk and sickness in decennial groups of ages, 20-30, 
 30-40, &c. To obtain the sickness rates at individual ages, 
 these numbers might have been adjusted by some method similar 
 to that employed by Mr. Milne in dealing with the Carlisle 
 Table, and the numbers living and sickness experienced at each 
 age deduced, or the rate given by the decennial groups might 
 have been taken as that for the middle age of the group. The 
 method actually adopted was to make the average of the sickness 
 rates for ages 21, 22 ... 30 equal to the rate deduced from the 
 numbers exposed to risk between ages 20 and 30. This method 
 would only have been sound where the exposures were the same 
 at each age in the group, and at the older ages it greatly under- 
 
Friendly Societies. 39 
 
 estimated the true rate, to say nothing of the fact that the rates 
 entered against the ages 21, 22, 23, &c., were those properly 
 belonging to ages 20, 21, 22, &c. This erroneous method of 
 adjustment reduced the observed rates at the older ages by 
 fully 20 per-cent. Finally, all entrants and withdrawals were 
 estimated at risk for an entire year, materially affecting the 
 rates at the younger ages. I have made an estimate of the extent 
 to which the final sickness rates were affected by these causes, 
 and in Table 9 the third column gives what I believe to be a 
 fair approximation to the original facts. 
 
 The monetary tables were affected by another circumstance. 
 No investigation was made into the mortality experienced by the 
 societies, and in constructing the tables a mean between the 
 Northampton, Carlisle, and Swedish rates of mortality was 
 adopted. The inclusion of the first-named table probably resulted 
 in the rate of mortality being over-estimated, and, taken into 
 conjunction with the extremely low sickness rates observed, 
 rendered the resulting tables very unsafe. 
 
 Mr. Anseii's ^ n 1835 M F - Charles Ansell published his treatise 
 on friendly societies, containing tables based on the 
 experience of various societies for the five years 1823-27, embracing 
 about 5,000 members and about 24,000 years of life. The rates 
 of sickness observed were considerably higher than in the Highland 
 Society Tables, and at the early ages, up to age 35, they differed 
 but little from those of the Manchester Unity Tables (1866-70), 
 and from 35 to 65 were generally lower than the latter. 
 Mr. Ansell did not attempt to carry the sickness rates beyond 
 age 70, but for a considerable period prior to that age the data 
 were not sufficient to furnish trustworthy results. The rates were 
 obtained from the numbers at risk, the deaths and the sickness in 
 quinquennial groups of ages. Above age 70 the Northampton 
 rates of mortality were employed, a somewhat doubtful step. 
 Although the table was a great improvement upon that of the 
 Highland Society, and came much nearer to the experience of 
 average friendly societies, the number of societies constituting the 
 experience was too small for a table based upon them to be 
 generally applicable, and subsequent experience has shown that 
 the tables were unsafe for the large majority of societies. 
 
 As in the case of the Highland Tables, no attempt was made 
 to analyze the sickness in respect of duration, an important 
 enquiry in view of the nearly universal plan of reducing the 
 allowances in prolonged sickness. 
 
40 Friendly Societies. 
 
 In 1845 Mr. Nelson published extensive tables, based 
 
 Mr. Nelson's . . _ , ,, 
 
 Tables upon an analysis ot the Urovernment returns irom 
 
 1836 to 1840. The data left nothing to be desired 
 as regards extent, embracing 1,147,000 years of life, with a 
 considerable experience at the older ages. In these tables the 
 division of the experience into rural, town, and city districts, 
 which is common to all subsequent investigations, was, it is 
 believed, first made. Mr. Neison also investigated the rates of 
 sickness and mortality prevailing in various occupations, and he 
 separated the Scotch experience, in which the sickness rates up to 
 age 50 were considerably lower than those of English experience, 
 although the rates of mortality were throughout heavier. 
 
 The principal points to be noticed in these tables are the 
 very light rates of mortality recorded, and the heavy rates of 
 sickness, especially above age 65, the latter feature forming 
 a strong contrast, not only to the earlier tables of Mr. Ansell 
 and the Highland Society, but also to those deduced by 
 Mr. Finlaison from the Government returns 10 years later. 
 The divergences between these tables illustrate the difficulty of 
 distinguishing between sickness and superannuation at the older 
 ages. While, on the one hand, Mr. Finlaison's wish to exclude all 
 cases of superannuation no doubt resulted in the exclusion of a 
 considerable portion of chronic sickness, and rendered his tables 
 practically valueless for the average friendly society, on the other 
 hand, it may be shown, I think, from careful examination of the 
 figures upon which Mr. Neison's Table is based, that in many 
 cases allowances that were purely superannuation and not in any 
 sense sickness payments were included. If reference is made to 
 the summary of the facts of Mr. Neison' s experience, as given in 
 his Vital Statistics, it will be seen that in each of the three districts 
 rural, town, and city the quantity of sickness observed makes a 
 sudden bound, in the case of the two former at the commencement 
 of the group 65-69; and in the latter at 70-74. This increase is so 
 sudden that it evidently points, not to any real increase of the 
 sickness at these ages, but to the practice of many of the societies 
 included in Mr. Neison's returns of practically pensioning their 
 members at these ages whether sick or not. Hence, in societies 
 making allowances only in cases of actual sickness, they are 
 unnecessarily stringent. The very light mortality brought out in 
 this investigation resulted, together with the heavy sickness rates, 
 in a very high value for the single and annual sickness premiums, 
 the latter exceeding Mr. AnselPs values by 25 to 30 per-cent. 
 
Friendly Society 
 
 UNIVERSITY 
 
 or 
 
 41 
 
 From whatever cause, it would seem probable that the mortality 
 was under-estimated in Mr. Neison's Table, in the rural districts 
 especially, where the rates are lower than those given by the English 
 Life Table for ages five years younger. Mr. J. A. Higham has 
 suggested that this may have resulted from the immense number of 
 insurances that were discontinued, not as in the case of insurance 
 companies by the healthy and prudent, but by the unhealthy and 
 reckless. This explanation, however, seems scarcely sufficient, 
 and is contrary to later experience. It is possible that in some 
 cases, where societies insured for sickness only, some of the 
 deaths may have been returned as discontinuances, but no doubt 
 the explanation is to be found mainly in the uncertainty as to the 
 facts, not only as regards the actual number of deaths recorded, 
 but especially in respect of the ages returned. The ages of the 
 lives beyond 60 or 70 must have been in many cases a matter 
 of guess-work, and beyond age 80 the recorded rate of mortality 
 actually diminishes instead of increasing, which makes it extremely 
 probable that here at least the ages given were altogether erroneous 
 and, no doubt, greatly exaggerated. It may be of interest to give 
 here a comparison of the rates of mortality in Mr. Neison's rural 
 experience with those deduced from the experience of a large 
 rural society. 
 
 TABLE 6. Rural Mortality Experience. 
 
 
 MORTALITY PER-CENT 
 
 Ages 
 
 Essex Provident Society, 
 
 1876-80 
 
 Neison's Rural Districts, 1836-40 
 
 
 Rough 
 
 Adjusted 
 
 General 
 
 Labourers 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 15-19 
 
 oo 
 
 52 
 
 73 
 
 50 
 
 20-24 
 
 65 
 
 59 
 
 73 
 
 64 
 
 25-29 
 
 34 
 
 68 
 
 73 
 
 57 
 
 30-34 
 
 93 
 
 79 
 
 69 
 
 57 
 
 35-39 
 
 83 
 
 92 
 
 77 
 
 61 
 
 40-44 
 
 1-12 
 
 1-08 
 
 82 
 
 75 
 
 45-49 
 
 1-45 
 
 1-28 
 
 97 
 
 84 
 
 50-54 
 
 1-34 
 
 1-55 
 
 1-35 
 
 1-11 
 
 55-59 
 
 2-02 
 
 1-97 
 
 1-82 
 
 1-49 
 
 60-64 
 
 2-71 
 
 2-74 
 
 2-36 
 
 1-78 
 
 65-69 
 
 4-33 
 
 4-21 
 
 3-65 
 
 3-17 
 
 70-74 
 
 6-92 
 
 6-80 
 
 6-07 
 
 5-25 
 
 75-79 
 
 10-37 
 
 10-98 
 
 7-53 
 
 6-86 
 
 The differences in the rates in columns (3) and (5) are 
 instructive, but it is unnecessary to discuss them at length. 
 The fact that the mortality in the various districts observed by 
 
42 Friendly Societies. 
 
 Messrs. Nelson and Finlaison differ so greatly, although both were 
 deduced from a similar class of returns, throws a doubt upon the 
 trustworthiness of the facts in each case. 
 
 Mr. Finiaison's The next tables of importance are those of Mr. Fin- 
 Tabie (1846-50). i a i son ^ a l re ady alluded to. These were based on 
 the Government returns from 1846 to 1850. As already stated, 
 all cases of superannuation were excluded from this inquiry. 
 In Mr. Finiaison's own words (see Parliamentary Paper, 12 August 
 1854, page 7), " Nothing but sickness in the true sense of the 
 " word, that is, sickness incapacitating from labour and requiring 
 " constant medical treatment, and of limited duration, as dis- 
 " tinguished from chronic ailment and mere decrepitude, was 
 " considered to be sickness. For instance, slight paralysis, blind- 
 " ness, mental disorder, or senile infirmity was not included." 
 Had these cases been separately treated the results would have 
 been both interesting and valuable, but a great quantity of what, 
 in the majority of friendly societies, constitutes sickness at 
 the older ages being entirely disregarded, Mr. Finiaison's Tables 
 are necessarily unsuited to such societies. The sickness rates 
 in Mr. Finiaison's Tables are comparatively heavy at the younger 
 ages, where the exclusion of chronic sickness would have but little 
 effect. Up to age 40, for example, the rates are heavier than those 
 of the Manchester Unity, while above 50 they are very much lower, 
 nearly corresponding to the rates at five years younger. Below 
 age 50, moreover, the rates in rural, town, and city districts were 
 very nearly identical, differing in this respect from the results of 
 Mr. Neison's investigation. It should be stated, however, that 
 the city districts in Mr. Finiaison's classification included only 
 populations of over 65,000, as against populations of 30,000 in 
 Mr. Neison's. 
 
 Mr. Finlaison divided the experience, with reference to the 
 nature of the occupation of the lives observed, into light, heavy, 
 and general labour, including a special investigation into the 
 sickness rates prevailing amongst miners, mariners, railway ser- 
 vants, and painters. His results went to show that, so far as 
 that class of sickness is concerned with which he dealt, that is 
 to say, chiefly temporary sickness, the character of the labour is 
 of more importance than the locality from which the lives were 
 drawn, or the density of the population. He states that the only 
 practical difference in the distribution of sickness that could 
 be discovered was seen to turn on the amount of physical force 
 called out by the occupation of the contributors. It is doubtful, 
 however, whether this theory could be substantiated, if the chronic 
 
Friendly Societies. 43 
 
 sickness had been included. The sickness prevailing amongst 
 the female members of the societies was also dealt with and 
 the tables were accompanied by a complete system of monetary 
 values, based on a rate of interest of 3J per-cent. 
 
 Almost simultaneously with Mr. Finlaison's report, 
 Manchester the Manchester Unity of Odd Fellows made an investi- 
 
 Unity Tables. . * . . . , . 
 
 gation into the mortality and sickness experienced in 
 their society for the three years 1846 to 1848. A similar investi- 
 gation Avas made for the five years 1856 to I860, and again 10 
 years later for the period 1866 to 1870. The earlier tables were 
 doubtless much less accurate than the last ones, which have for 
 some years held the position of standard sickness tables.* 
 
 From the fact that the later returns, 1866 to 1870, are the 
 third series tabulated by the Manchester Unity, there is every 
 reason to believe that the data are, in the main, trustworthy, and 
 they have probably afforded the best series of observations with 
 which we have at present been furnished. The extreme difficulty 
 of obtaining an accurate record of facts relating to sickness 
 experience from average friendly societies is well known to all 
 actuaries, and there can be no doubt that the earlier returns 
 furnished to the Government in many cases abounded in errors, 
 but it is probable that greater reliance may be placed upon returns 
 obtained from the branches of an order such as the Manchester 
 Unity, especially where these have not been made for the first time. 
 
 The most important feature of the Manchester Unity 
 experience is the separation of the sickness claims made during 
 the 1st, 2nd, 3rd, and 4th periods of six months from the com- 
 mencement of illness. This analysis, which was common to the two 
 last investigations 1856-60 and 1866-70 was only carried out 
 approximately, however, owing to the absence of complete informa- 
 tion as to the date at which the cases of prolonged sickness claim 
 had commenced. So far as can be ascertained this date was taken 
 in practice as 1 January 1856 and 1866 respectively, whenever 
 the lives observed were sick at that date. The obvious effect of this 
 assumption is to exaggerate the proportion of sickness occurring 
 in the first six months of illness, and to diminish in like 
 
 *In the earlier returns numerous inaccuracies were apparent especially 
 is this the case with those of 1856 to 1860. For example, on reference to 
 Table 5 (p. 17), the numbers at risk at age 52 appear to have been put down at 
 7,443 instead of 6,443, and as a consequence the rates of death and sickness from 
 51 to 55 are under-estimated about 3 per-cent. A similar error occurs in Table 6 
 (p. 19), at age 50, where the numbers 6,180 should clearly read 5,180. Even as the 
 figures stand the rate of sickness given for this quinquennium is erroneous, the same 
 being the case also from 61 to 65, where the rate should be 5'950 instead of 
 4'625. These and other errors have affected the final Table, although the effect 
 on the financial results may have been small. 
 
44 Friendly Societies. 
 
 manner that relating to subsequent periods ; and the general 
 experience of actuaries will, I think, confirm the impression that 
 the Manchester Unity Tables do, as a matter of fact, considerably 
 under-estimate the relative amount of prolonged sickness in most 
 societies. The financial effect of the error is of course upon the 
 safe side. 
 
 The Ancient Order of Foresters have also published 
 Experience the results of an investigation into their sickness and 
 
 mortality experience for the five years 1871-5, made by 
 Mr. Neison, Junior, whose report and analysis of the experience 
 is very elaborate, and contains much interesting information. 
 The experience was very extensive, comprising 1,300,000 years of 
 life ; but there are manifest traces of the same exaggeration of the 
 ages in advanced life which has been noticed in the earlier data 
 of Mr. Neison, Senior, and which would suggest that at present 
 at least, the facts as to the mortality and sickness of the Ancient 
 Order of Foresters have not been obtained with the same accuracy 
 as in the Odd Fellows' experience. The distribution of the 
 experience into rural, town, and city, differed considerably from 
 the Manchester Unity, as the following table will show : 
 
 TABLE 7. Distribution of Data. 
 
 Odd Fellows Foresters 
 
 (1866-1870) (1871-1875) 
 
 Rural Districts . . . 222 per M. 324 per M. 
 Town 513 291 
 
 City 265 385 
 
 Total Experience . 1,000 1,000 
 
 Thus the Manchester Unity prevails principally in the smaller 
 towns, the Ancient Order of Foresters in the city and rural districts. 
 
 The same difficulty occurred in determining the exact propor- 
 tion of sickness falling in the first six months of illness as with 
 the Manchester Unity experience. Mr. Neison, however, by 
 means of certain supplementary returns and certain assumptions 
 as to cases of continuous sickness, succeeded in partially over- 
 coming this difficulty. 
 
 The aggregate sickness rate in the Foresters' experience is a 
 trifle higher than in the Manchester Unity, but the proportion of 
 prolonged sickness is considerably greater. 
 
 It is worth while to point out that the want of 
 
 Correction of i i i /> i 
 
 the sickness complete information as to the duration or sickness in 
 the various the Manchester Unity and the Foresters' (original) 
 returns, might have been practically overcome by 
 a simple correction. 
 
Friendly Societies. 
 
 45 
 
 Since all sickness recorded in the first half-year of the quin- 
 quennium was treated as belonging to the first six months of 
 sickness, it will be seen that, speaking generally, sickness returned 
 as belonging to the second and subsequent periods of sickness 
 would comprise only such as fell in the last four-and-a-half years 
 of the quinquennium; that returned as of the third and sub- 
 sequent periods would comprise only such as fell in the last four 
 years. 
 
 Hence, if we call the recorded rates of sickness in the three 
 periods a, b> c, and the true rates z l , z 2 , z 3+ ) and assume the 
 exposures to be equally distributed through the five years, we 
 should have 
 
 
 
 10 
 - 
 
 10 
 - 
 
 As a matter of fact, the exposures would not be equally 
 distributed; although the exact distribution would have been 
 easily ascertainable. If we assume that 7 per-cent of the 
 experience belonged to the first half-year, and 14'7 per-cent to 
 the first year (which will probably be near the truth), the 
 following table will show the resulting corrections to the rates of 
 sickness in the various periods : 
 
 TABLE 8. Manchester Unity Experience (1866-70). 
 
 
 RECORDED RATES OF SICKNESS 
 
 CORRECTED RATES 
 
 Ages 
 
 
 
 
 
 
 
 
 1st 
 
 2nd 
 
 After 
 
 1st 
 
 2nd 
 
 After 
 
 
 6 Months 
 
 6 Months 
 
 12 Months 
 
 6 Months 
 
 6 Months 
 
 12 Months 
 
 22 
 
 683 
 
 039 
 
 019 
 
 679 
 
 040 
 
 022 
 
 27 
 
 711 
 
 049 
 
 046 
 
 704 
 
 048 
 
 054 
 
 32 
 
 773 
 
 068 
 
 085 
 
 761 
 
 065 
 
 100 
 
 37 
 
 847 
 
 080 
 
 134 
 
 831 
 
 073 
 
 157 
 
 42 
 
 959 
 
 114 
 
 204 
 
 935 
 
 103 
 
 239 
 
 47 
 
 1-142 
 
 168 
 
 360 
 
 1-102 
 
 146 
 
 422 
 
 52 
 
 1-417 
 
 246 
 
 579 
 
 1-353 
 
 209 
 
 678 
 
 57 
 
 1-817 
 
 376 
 
 953 
 
 1-717 
 
 312 
 
 1-117 
 
 62 
 
 2-405 
 
 628 
 
 1-776 
 
 2-224 
 
 503 
 
 2-082 
 
 67 
 
 3-234 
 
 1-074 
 
 3-248 
 
 2-910 
 
 844 
 
 3-803 
 
 72 
 
 3-910 
 
 1-675 
 
 6-516 
 
 3-293 
 
 1-178 
 
 7-630 
 
 77 
 
 4-130 
 
 2-281 
 
 10-691 
 
 3-154 
 
 1-429 
 
 12-519 
 
46 
 
 Friendly Societies. 
 
 It is true the correction made does not show the full extent 
 of the error, as it takes no account of those cases of continued 
 sickness commencing in the first half-year of the quinquennium, 
 in which the member (on account of recent claims upon the 
 fund) was not entitled to draw full pay for the full period of six 
 months. These cases, however, would not be very numerous. 
 
 The following tables give in a concise form the means 
 
 Comparison of . ' L i 
 
 various sick- of comparison oi the rates of sickness and mortality 
 
 ness Tables, .. . i i i i i i 
 
 in the various tables that nave been referred to. 
 
 TABLE 9. Comparative Sickness Rates. 
 
 
 HIGHLAND 
 
 
 
 
 MANCHESTER UNITY 
 
 
 
 
 SOCIETY 
 
 Ansell, 
 
 Neisou, 
 
 Finlaison, 
 
 
 A.O.F. 
 
 A rrnct 
 
 Ages 
 
 A o 
 
 A o 17o-f i 
 
 1823-27 
 
 1836-40 
 
 1846-50 
 
 
 
 
 1871-75 
 
 Ages 
 
 
 AS 
 
 Given 
 
 AS JiiSll- 
 
 mated 
 
 
 
 
 1846-48 
 
 1856-60 
 
 1866-70 
 
 
 
 20-24 
 
 576 
 
 680 
 
 785 
 
 857 
 
 985 
 
 678 
 
 829 
 
 754 
 
 819 
 
 20-24 
 
 25-29 
 
 596 
 
 680 
 
 825 
 
 890 
 
 985 
 
 758 
 
 820 
 
 806 
 
 853 
 
 25-29 
 
 30-34 
 
 641 
 
 710 
 
 893 
 
 917 
 
 971 
 
 837 
 
 858 
 
 928 
 
 968 
 
 30-34 
 
 35-39 
 
 702 
 
 770 
 
 1-009 
 
 1-036 
 
 1-091 
 
 940 
 
 1-004 
 
 1-062 
 
 1-150 
 
 35-39 
 
 40-44 
 
 814 
 
 880 
 
 1-195 
 
 1-273 
 
 1-227 
 
 1-179 
 
 1-239 
 
 1-261 
 
 1-373 
 
 40-44 
 
 45-49 
 
 1-108 
 
 1-190 
 
 1-475 
 
 1-634 
 
 1-437 
 
 1-515 
 
 1-545 
 
 1-636 
 
 1-707 
 
 45-49 
 
 50-54 
 
 1-541 
 
 1-730 
 
 1-890 
 
 2-181 
 
 1-732 
 
 2-030 
 
 2-011 
 
 2'222 
 
 2-265 
 
 50-54 
 
 55-59 
 
 2-018 
 
 2-380 
 
 2-586 
 
 3-048 
 
 2-177 
 
 3-206 
 
 3-025 
 
 3-047 
 
 3-210 
 
 55-59 
 
 60-64 
 
 2-736 
 
 3-980 
 
 3-991 
 
 4-745 
 
 3-118 
 
 5-059 
 
 4-638 
 
 4-715 
 
 4-594 
 
 60-64 
 
 65-69 
 
 6-600 
 
 7-220 
 
 7-471 
 
 10-012 
 
 4-622 
 
 6-495 
 
 7-165 
 
 7-237 
 
 7-971 
 
 65-69 
 
 70-74 
 
 
 
 
 16-529 
 
 7-668 
 
 12-151 
 
 12-056 
 
 12-062 
 
 11-999 
 
 70-74 
 
 75-79 
 
 
 
 
 25-064 
 
 11-056 
 
 16-716 
 
 16-637 
 
 16-873 
 
 17-662 
 
 75-79 
 
 TABLE 10. Comparative Rates of Mortality (Per-cent). 
 
 
 TT;~I, 
 
 
 
 
 MANCHESTER UNITY 
 
 
 
 A craa 
 
 Jblign- 
 
 loT-1/1 
 
 Ansell, 
 
 Neison, 
 
 Finlaison, 
 
 
 A.O.F., 
 
 
 Ages 
 
 land. 
 
 1823-27 
 
 1836-40 
 
 1846-50 
 
 
 
 
 1871-75 
 
 Ages 
 
 
 Society 
 
 
 
 
 1846-48 
 
 1856-60 
 
 1866-70 
 
 
 
 20-24 
 
 
 679 
 
 667 
 
 748 
 
 740 
 
 758 
 
 643 
 
 743 
 
 20-24 
 
 25-29 
 
 
 989 
 
 726 
 
 729 
 
 790 
 
 748 
 
 762 
 
 729 
 
 25-29 
 
 30-34 
 
 
 1-143 
 
 774 
 
 796 
 
 870 
 
 834 
 
 818 
 
 886 
 
 30-34 
 
 35-39 
 
 d 
 
 1-788 
 
 875 
 
 893 
 
 916 
 
 991 
 
 977 
 
 1-092 
 
 35-39 
 
 40-44 
 
 o> 
 
 i 
 
 1-663 
 
 992 
 
 1-100 
 
 1-165 
 
 1-178 
 
 1-258 
 
 1-284 
 
 40-44 
 
 45-49 
 
 8 
 
 2-014 
 
 1-201 
 
 1-306 
 
 1-399 
 
 1-421 
 
 1-429 
 
 1-658 
 
 45-49 
 
 50-54 
 
 9 
 
 ft 
 
 2-290 
 
 1-567 
 
 1-636 
 
 1-861 
 
 1-795 
 
 1-905 
 
 2-045 
 
 50-54 
 
 55-59 
 
 49 
 
 Q 
 
 3-635 
 
 2-120 
 
 2-360 
 
 2-867 
 
 2-609 
 
 2-492 
 
 2-973 
 
 55-59 
 
 60-64 
 
 
 
 4-433 
 
 2-772 
 
 2-855 
 
 4-114 
 
 3-566 
 
 3-537 
 
 3-802 
 
 60-64 
 
 65-69 
 
 
 5-504 
 
 3-968 
 
 4-391 
 
 5-721 
 
 5-499 
 
 5-209 
 
 5-848 
 
 65-69 
 
 70-74 
 
 
 10-417 
 
 6-732 
 
 6-203 
 
 7-042 
 
 6-825 
 
 7-811 
 
 8-003 
 
 70-74 
 
 75-79 
 
 
 7-407 
 
 8-146 
 
 9-209 
 
 
 11-538 
 
 9-950 
 
 14-259 
 
 75-79 
 
 It will be observed that these results are quite as accordant in 
 respect of the sickness rates as in the case of the mortality rates. 
 
Friendly Societies. 47 
 
 When the various circumstances under which the data were 
 collected is taken into account, and the different methods of treat- 
 ment to which the facts were subjected, their agreement appears 
 more remarkable than their differences. If a comparison is made 
 of the Manchester Unity (1866-70), the Ancient Order of 
 Foresters (1871-75), and Mr. Neison's results (1836-40), the 
 three largest series of observations, the agreement in the sickness 
 rates up to age 65 is remarkable. If an average of the three 
 rates be taken, in only one case do any of the figures differ by 
 so much as 5 per-cent from this average. 
 
 It is well known that the effect of " selection", as it is 
 Selection" termed, upon the rates of mortality prevailing among 
 nes^^tes. assured lives is considerable, and it would seem natural 
 
 to suppose that a similar though less marked effect 
 would be produced by the same cause upon the rates of sickness : 
 less marked, because the selection is, on the whole, less strict, 
 and, further, cannot be expected to eliminate early sickness claims 
 to the same extent as early deaths. There are no data of any 
 extent available by which this question can be determined, and 
 the experience of individual societies no doubt differs as to this 
 point very considerably. In Mr. Neison's Report, Ancient Order 
 of Foresters' experience, 1871-75 (page 28), the effect of medical 
 selection is referred to in connection with a table showing the 
 percentage of members sick during the quinquennium out of 
 
 (fl) Those in the courts, 1 January 1871 ; 
 
 (b) Those who became "free" during the quinquennium. 
 
 From the smaller percentages in the second class Mr. Neison- 
 draws the conclusion that " for the first few years after admission 
 the medical selection employed is not without practical effect." It 
 is clear, however, that since the lives entering during the quin- 
 quennium are at risk for only about half the period of those 
 existing at its commencement, the comparison cannot legitimately 
 be made the basis of such conclusion. While the subject is not 
 perhaps of the first importance, the following table, comprising the 
 analyzed experience of eight societies of an average type, may be 
 found of interest as throwing some light upon this question. The 
 facts are not very numerous, but are sufficiently so to indicate 
 that recent selection does influence the sickness rates at the 
 various ages ; but to an extent which can scarcely be considered 
 important, or necessary to be taken into account in the calcula- 
 tion of contributions or in the valuation of societies. 
 
48 
 
 Friendly Societies. 
 
 4 
 I 
 
 1 
 
 '3 
 
 
 , 
 
 si 1 
 - 
 
 iif 
 
 M 
 
 iHrHr-lr-l<NCOcr I 
 
 i I rH i I <N 
 
 O5 O5 C5 
 i-H r-l 
 
 Ci CO J> rH 00 
 
 ^10 co >o i> :::::;:: co g 
 
 l> CO 
 
 a 
 
 O5 
 
 co * co r-i rH ::::::: co 
 
 
 
 CO O5 O O5 <M CO CO 
 
 M 
 
 oo - : 
 
 ua 10 cp cp J^ <N : : : ' : ' .' 
 
 i 
 
 1 
 w t^ 
 
 O 00 CO 00 00 rH 
 rH *? CO i I 
 
 <M O CO O 10 -rfl 
 O5 CO (M t I <M i I 
 
 *l 
 
 O5^O5^O5T?O5^O5Tj(O5-^O5 
 
 i-HCjiGqcoco^T|<ioiococoi>t> 
 
Friendly Societies. 49 
 
 VALUATION OF FRIENDLY SOCIETIES. 
 
 The object of a valuation is to estimate, as nearly as 
 possible, the present value of future payments to be 
 made by the society, on the one hand, in respect of the 
 benefits assured to the members for sickness or deaths; and by 
 the members on the other hand, in respect of the contributions 
 to be received from them ; and hence to determine what sum it is 
 necessary that the society should have in hand to be able eventually 
 to meet all the claims as they arise. It is, therefore, important 
 that the assumptions made in the valuation in respect of the rates 
 of mortality and sickness that will prevail, and not less important 
 the rate of interest at which the funds may be expected to improve, 
 shall be such as past experience shows may be made w 7 ith safety. 
 Such a valuation will only be useful as the future working of the 
 society may coincide with the assumptions upon which it is based, 
 and the first business of the actuary, therefore, will be to make 
 himself acquainted with the actual experience of the society whose 
 financial position he is investigating, that he may select the most 
 suitable basis upon which to frame his estimates. 
 
 In valuing the liabilities of life offices, a uniform standard of 
 mortality might, without much difficulty, be selected. No such 
 general standard of sickness can, however, be adopted for friendly 
 society valuations. 
 
 variety in Reference has already been made to the differences 
 existing in the sickness experience of individual 
 
 societies. With a view of illustrating this feature, the 
 following diagram has been made, exhibiting the variety of expe- 
 rience found amongst 129 societies, taken promiscuously. The basis 
 of the comparison was the ratio of the actual cost of the sickness 
 allowances during a given period (usually five or ten years), to the 
 estimated cost according to the Manchester Unity (1866-70) 
 experience and the rules of the society. These ratios are exhibited 
 as percentages on the left of the diagram, the length of the 
 parallelograms opposite being proportional to the number of 
 societies in which the ratio of actual cost to estimated cost fell 
 between the various limits shown. Thus, in 21 societies the cost 
 of the sickness was between 90 and 100 per-cent of the estimated 
 amount, and in 21 other societies between 100 and 110 per-cent. 
 In a number of cases the light sickness observed was traceable to 
 the nature of the society's rules, which, as will be seen later, may, 
 in various ways, keep down the rate of sickness claim. In other 
 cases, where the cost of sickness had been specially heavy, this 
 was found to be due to the nature of the members' occupations. 
 
50 
 
 Friendly Societies. 
 
 When these cases are excluded, there remain the 98 societies 
 shown in the last column of the diagram, and represented by the 
 parallelograms bounded by the heavy lines. 
 
 TABLE 12. Comparison of the Relative Cost of Sickness in 129 
 Societies with that shown ly the Manchester Unity Table. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 All 
 Societies 
 
 Excluding 
 Special 
 Rules or 
 Occupations 
 
 oU 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 4U 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 1 
 
 50 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 4 
 
 60 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 8 
 
 5 
 
 70 
 
 
 
 
 
 
 
 
 
 
 
 
 
 11 
 
 10 
 
 80 
 
 
 
 
 
 
 
 
 
 
 
 
 
 12 
 
 12 
 
 90 
 
 
 
 
 
 
 
 
 
 
 
 
 
 21 
 
 21 
 
 100 
 
 
 
 
 
 
 
 
 
 
 
 
 
 21 
 
 21 
 
 110 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 16 
 
 14 
 
 120 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7 
 
 4 
 
 loO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 3 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 1 
 
 loU 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 1 
 
 loU 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 
 . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 
 180 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 iu 
 
 
 
 
 
 
 
 
 
 
 
 
 
 [ 4 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 J 
 
 j 
 
 &LO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 &&\j 
 
 OOfl 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 129 
 
Friendly Societies. 51 
 
 The extent of data requisite to properly test the 
 
 Deviations . . r . ; 
 
 from standard experience of a society and to give a fair idea of the 
 sickness rates that may be expected to prevail in 
 the future is a question closely related to that to be presently 
 discussed namely, the extent of membership required to give 
 a steady experience. Usually the experience of five years' 
 working will be found to be sufficient, provided it is of an 
 average class, without any special features. If, however, the 
 society is small, or if, from the nature of the members' 
 occupations or from the rules governing the sickness allowances, 
 the experience presents special features which render a departure 
 from the standard tables necessary, it is desirable that the 
 period embraced should be at least 10 years. The simplest form 
 of exhibiting the sickness experience of a society is that of 
 comparing the actual sickness observed among the members 
 of different groups of ages and the estimated amount, according 
 to any standard table that may be employed. Such a comparison 
 will show whether the sickness is normal as to its aggregate 
 amount, as to its distribution at various periods through life, and 
 its division into full pay and reduced pay. Where deviation 
 from the standard table occurs, its cause and nature must be 
 examined. It may occasionally happen, especially in very small 
 societies, that such deviation is accidental. It may be caused, for 
 example, by a single member continuing sick during the period 
 under observation, thus producing a very high average rate of 
 sickness in that group of ages in which he is included. As to 
 how far deviations from the average table are to be considered 
 significant must of course depend upon their amount, relative to the 
 magnitude of the experience. Reference should be had to the 
 results obtained later in considering the question of sickness and 
 mortality fluctuations. 
 
 Occasionally a simple modification of the standard table, 
 such, for example, as an increased percentage on the sickness 
 rates at all ages, will meet the case. Where the values of the 
 sickness allowances by the standard table employed are available 
 for various rates of interest, and terminating at various ages, it is 
 possible to vary the table almost indefinitely, and thus obviate the 
 labour of calculating a special sickness table. Thus, provided 
 the society's mortality is well represented by the standard table, 
 it is possible to employ any rates of sickness that can be repre- 
 sented by constant or percentage additions to (or deductions 
 from) the standard rates e.g., suppose that the full-pay sickness 
 
 D 2 
 
52 Friendly Societies. 
 
 experienced by the society is nearly a constant of *5 weeks per 
 annum above the standard, and the reduced pay is well represented 
 through life by an addition of 20 per-cent at all ages, a valuation 
 would be first made by the standard table, the value of the 
 reduced pay (up to the " pension " age) increased by 20 per-cent, 
 and an addition of the value of an annuity of half the weekly 
 allowance added to the value of the full pay as brought out by 
 the table. When it is necessary, also, to vary the mortality rates, 
 this may be done either by a variation in the ages, or by a 
 constant addition to (or deduction from) the value of p x at all 
 ages, which, as is known, will affect the values of the annuities 
 and sickness benefits in precisely the same manner as a similar 
 change in the force of interest. Where a change is thus made in 
 the rates of mortality by a variation in the assumed ages, the 
 sickness rates must, of course, be represented in terms of the 
 rates at the new ages according to the standard table. 
 
 It may prove impossible by any such simple modifi- 
 
 Employmentof . J ' - u J J 1. 
 
 the society's cation to represent the observed facts. In such cases 
 it is necessary to base our valuation estimate on the 
 rates actually found to prevail in the society. In other words, 
 taking the observed experience as our basis, a sickness table must 
 be constructed to represent that experience, in the same way in 
 which the standard table itself was formed from the larger general 
 experience upon which it was based. Where a valuation is thus 
 based upon the actual experience of the society, care should be 
 taken to see that the experience has been tolerably uniform over 
 a series of years, and that the data are sufficient to justify 
 dependence upon the results. It is not sufficient to represent 
 merely the average experience of a decennium, or even a longer 
 period, unless it is known that there has been no marked 
 change in the character of the experience during that period. 
 Such a change may result from various causes, as, for example, 
 from a relaxation of the management, or from the introduction 
 of a class of lives more liable from their occupation to sickness 
 than those previously existing in the society; or a change may 
 even be caused by an alteration in the benefits granted, especially 
 by an increase in the allowances for prolonged sickness. 
 Cases may even occur in which it is impossible to employ the 
 same standard for all the members of a society. That is to say, we 
 cannot assume merely on the basis of the sickness experience that 
 the rates of sickness found to prevail at the different ages through 
 life during the period under observation will actually prevail at 
 
Friendly Societies. 
 
 53 
 
 these ages in the future. It may be useful to give an actual 
 illustration of this point. The following table represents the 
 experience of a small country society over a period of five years. 
 
 TABLE 13. Example of Non- Homogeneous Sickness Experience. 
 
 Ages At Risk 
 
 Estimated Cost 
 of Sick Pay 
 
 Actual Cost 
 
 Actual to each 
 100 expected 
 
 
 
 
 
 
 
 
 15-19 
 
 355 
 
 116-0 
 
 133-5 
 
 115 
 
 20-24 
 
 303 
 
 108-0 
 
 158-4 
 
 147 
 
 25-29 
 
 231 
 
 87-8 
 
 136-7 
 
 156 
 
 30-34 
 
 196 
 
 83-3 
 
 146-6 
 
 176 
 
 35-39 
 
 154 
 
 73-5 
 
 143-3 
 
 195 
 
 40-44 
 
 102 
 
 57-2 
 
 44-6 
 
 78 
 
 45-49 
 
 47 
 
 33-3 
 
 22-9 
 
 69 
 
 40-54 
 
 46 
 
 41-5 
 
 27-0 
 
 65 
 
 55-59 
 
 37 
 
 46-4 
 
 51-9 
 
 1 
 
 60 & upwards 
 
 14 
 
 25-5 
 
 6-8 
 
 ' 
 
 It will be seen by a comparison of the expected cost of sickness 
 with the actual cost, that the experience may be divided into two 
 parts, namely, that below age 40 and that above that age. In 
 the former group the sickness claims were more than 50 per-cent 
 in excess of the expected amount, while in the latter they 
 were exactly 25 per-cent below the expectation. An examination 
 of the cause of this break in the society's experience showed 
 that it was due to the introduction of a large number of new 
 members following hazardous occupations. It is clear that a 
 valuation proceeding on the assumption that the experience of the 
 past five years in respect of the sickness rates prevailing at the 
 various ages would be reproduced in the future, would have greatly 
 under-estimated the future liabilities of the society in respect of 
 the sickness allowances. The only safe method of procedure in 
 such a case is to divide a society into two classes, namely, those 
 subject to the normal rate of sickness, and a second class, formed 
 of those whose occupations render them liable to excessive sickness 
 rates. This same experience also affords an illustration of the 
 extent to which a single member may affect the character of the 
 experience. It will be seen that if the two groups of ages 30 to 
 39 be taken, the observed sickness claims in these groups exceeded 
 the expected amount by about .133; of this excess, however, 
 no less than 70 is due to sickness experienced by a single 
 member. 
 
54 
 
 Friendly Societies. 
 
 sickness Occasionally the distribution of sickness at various ages 
 claims modi- will be considerably affected by the nature of the rules 
 
 fied by Rules. .., . . J . * 
 
 modifying or limiting the sickness benefits, and it 
 may be of interest here to give some actual instances showing the 
 character of these modifications. The most common case occurs 
 where, in lieu of a reduction in the sickness rate in cases of pro- 
 longed sickness, the benefits for a certain time cease altogether. 
 In these cases it will generally be found that, notwithstanding the 
 fact that the society's rules do not recognize chronic sickness claim, 
 they cannot be entirely ignored in the valuation, as although the 
 member cannot be continuously upon the funds, he may neverthe- 
 less come on repeatedly at intervals. For example, a society 
 granting 10s. a week allowance during the first six months, 5s. 
 during the second, and no allowance thereafter, nevertheless, in the 
 case of continuous sickness, must after a certain period (generally 
 after 12 months from the cessation of the half-pay allowance) 
 permit the members to come again upon the funds, if sick, at full 
 pay, treating the case as a fresh case of illness. Hence, on the 
 average, in every two years a member who is permanently invalided 
 will be able to draw 26 weeks of full, and 26 weeks of half-pay, 
 and this would be equivalent to a permanently reduced allowance 
 of 3s. 9d. per week, and should be treated as such at a valuation. 
 It will, nevertheless, be found in practice that this cessation of the 
 sickness allowance after 12 months or some such period of claim 
 does, as a matter of fact, very materially reduce the aggregate 
 amount paid for sickness, especially at the older ages. 
 
 The following table represents the experience of a society in 
 which the distribution of the sickness at various ages has been 
 materially influenced by a rule permanently reducing the allow- 
 ance after a total of 52 weeks' claim had been made, with a further 
 reduction after a second period of 52 weeks. 
 
 TABLE 14. 
 Example of Effect of Permanent Reduction of Allowance. 
 
 Ages 
 
 At Risk 
 
 Estimated Cost of 
 Sickness, M.U. 
 Full Pay throughout 
 
 Actual Cost 
 
 Percentage 
 
 15-19 
 
 65 
 
 21 
 
 8 
 
 s 
 
 20-29 
 
 288 
 
 112 
 
 89 
 
 > 
 
 30-39 
 
 414 
 
 208 
 
 91 
 
 45 
 
 40-49 
 
 369 
 
 270 
 
 155 
 
 57 
 
 50-59 
 
 184 
 
 244 
 
 105 
 
 43 
 
 60-69 
 
 79 
 
 215 
 
 484 
 
 225 
 
 70-79 
 
 23 
 
 174 
 
 200 
 
 115 
 
Friendly Societies. 55 
 
 A comparison of the estimated amount of the sickness claims 
 at the various groups of ages with those actually paid will show 
 that the effect of this rule is mostly felt during middle life. The 
 sickness at the younger ages is nearly normal in its amount, but 
 after about age 30 there is evidently a tendency to postpone the 
 claims, with a view to avoiding the reduction in the allowances as 
 old age is approached. This effect continues to about age 60, 
 when there being probably a large number of cases in which the 
 full period of 52 weeks' pay has been drawn, and the reduction 
 actually effected in the allowance, the rate of claim rises very 
 rapidly, and at the older ages is considerably above the Manchester 
 Unity Table. This society represents a case in which the average 
 tables would be inapplicable, and where it would be necessary to 
 base the valuation estimate entirely upon the rates of claim that 
 had actually been experienced at the different ages. In such 
 cases it is clear that, with a limited experience, it must be diffi- 
 cult to forecast the future with any degree of certainty, there 
 being so many circumstances which may modify the society's 
 future experience. Consequently it is necessary to allow a 
 considerable margin over and above the rates actually observed if 
 our estimate is to be a safe one. 
 
 Beneats There are certain cases in which the ages of the 
 
 X2tionof th members cannot be taken as the basis of the valua- 
 MembersMp. j.-^ t k e S p ec i a l ru les of the society making the 
 duration of membership a more important element than age. As 
 a typical case may be mentioned a society in which the members 
 are divided into classes, according to the period of membership : 
 the first-class consisting of all who are insured under five years, 
 the second from 5 to 10 years, the third from 10 to 15, and so on, 
 the sickness allowance increasing each time a member is transferred 
 to a higher class. It is here evident that the cost of the sickness 
 claims amongst any group of members will depend rather on the 
 duration of their membership than upon their age. And since in 
 a small society a double classification would be impracticable, it is 
 necessary to treat all the members as entered at one average age, 
 and to base the observations upon years of insurance rather than 
 years of age. The same society has a rule which is not uncommon 
 among societies of this class, in which the funeral allowance 
 made to a member is modified by the sickness claims that have 
 been made upon the society. In this particular instance the 
 amount of funeral allowance increases, like that of the sickness 
 allowance, with the duration of membership to a maximum sum 
 
56 Friendly Societies. 
 
 of 10. If, however, any member had during his lifetime drawn 
 a larger sum in special sickness allowances than the contributions 
 he had paid to the society, the amount of his funeral benefit was 
 reduced to 4* ; while, on the other hand, members who had been 
 a sufficient time in the society and had not drawn more than a 
 certain sum for sickness claims during the period were allowed 
 15 at death. It is clear that rules of this kind make the 
 estimation of the future sickness and funeral benefits a matter of 
 considerable complexity. The difficulty, however, may be fairly 
 surmounted by assuming an average age at entry for each member, 
 as proposed above, classifying them according to the duration 
 of membership, investigating the average cost rather than the 
 average time of sickness for various periods of membership, and 
 in the case of the funeral claims determining the average amount 
 of the allowance when paid for the same periods, and treating the 
 benefit as a variable insurance. This modification of the funeral 
 benefit, increasing it by way of bonus where the sickness claims 
 have been small, or diminishing it where they have been exces- 
 sive, is by no means uncommon in practice, and will be found 
 generally to have a marked influence on the rates of sickness 
 claim. 
 
 In general the actual experience of any society will 
 Benefit in afford but little data upon which to estimate the 
 
 sickness rates at the most advanced ages. This is 
 a point of considerable importance at a valuation, since, although 
 the number of members in a given society at the older ages 
 may be very small, the value of the sickness claims that will 
 be made at these ages will always be found to represent a 
 considerable portion of the society's liabilities. What is true 
 of individual societies in respect of want of information as to 
 sickness claims in old age, is also true to some extent of all 
 the general sickness tables. Though many of these tables 
 profess to show the rates of sickness throughout life, the 
 data beyond about 70 or 75, certainly beyond age 80, is quite 
 untrustworthy. The ages of the members returned must be at 
 these periods of life very uncertain, and no doubt are in many 
 instances exaggerated. Even if this were not so it would be still 
 very hazardous to assume, in the case of any given society, that 
 any of the average tables would represent its experience to the end 
 of life. It is at these extreme ages that the sickness is most 
 difficult to distinguish from mere superannuation, and the rate of 
 claim will depend almost entirely on the management of the 
 
Friendly Societies. 57 
 
 society. The safest plan, therefore, appears to be that which is 
 generally followed by the most experienced actuaries, of assuming 
 that in extreme old age sickness will become practically chronic 
 and must be treated as a pension at the lowest rate of pay. The 
 age to be adopted must of course depend upon the nature of the 
 society's experience, but it should in no case be taken later than 
 age 80. Even where the experience of the society would appear 
 to justify such a step, the actuary cannot be certain that that 
 experience will remain uniform. The members now in the 
 society at these old ages may happen to be, on the whole, in 
 fairly comfortable circumstances, and may not make claims in 
 every case of sickness ; but it by no means follows that when the 
 present younger members reach the same ages a similar state of 
 things will exist. 
 
 This difficulty in determining the rates of sickness at the older 
 ages has led some actuaries to propose the abolition of sickness 
 benefits throughout life, and the substitution of sickness allowance 
 ceasing at age 65 or 70, to be then replaced by a pension at a 
 fixed rate of pay. While this would be a great improvement from 
 the point of view of the actuary, the proposed change does not 
 appear to be popular among the friendly societies themselves, 
 and there can be no objection to the sickness benefit continuing 
 throughout life, provided it is always treated in the manner 
 suggested. 
 
 With regard to the effect upon the value of the sickness 
 benefit of the age at which the pension is assumed to commence, 
 it will be sufficient to refer to the various tables appended to this 
 Essay. 
 
 valuation With respect to the funeral allowances, those payable 
 o^Fu^erai at the death of the member present no difficulty. 
 They are usually accompanied by an allowance at 
 the death of a member's wife, provided that she die during the 
 lifetime of her husband. For the purpose of accurately valuing 
 these, the ages of the wives should be known, but it is quite 
 sufficient in ordinary practice to assume the wives of the same 
 ages as the husbands, and subject to like rates of mortality. 
 Clearly, all members must be treated as married. It will be 
 generally found that the value of the allowances at the death of 
 the wives of the members, as given by the formula Aj x , or %A XX 
 when equal ages are assumed, may be taken at very nearly 
 f of the value of a similar allowance at the death of the 
 member. 
 
58 Friendly Societies. 
 
 Funeral allowances are occasionally continued to the 
 
 Widows' and ' ' * 
 
 Children's widows of deceased members on payment of a small 
 
 Allowances. . -, 
 
 contribution, commencing at the death of the member. 
 As this contribution is always less than the premium required 
 to provide for the benefit, the sum payable at the death of the 
 wife must be treated as an absolute assurance, and the annual 
 widows' contributions valued by the formula (a x a xx }. 
 
 In other societies payments are made on the death of the 
 children of the members who die under a certain age. In this 
 case it is obviously not sufficient to take into account the children 
 actually existing; provision must also be made for those who may be 
 born to existing members, and who may die during the lifetime of 
 their fathers before attaining the stated age. To estimate the pro- 
 vision necessary for such additional liability, it is best to consider 
 that at the birth of each child the society assumes a liability that may 
 be symbolically expressed, e.g., as 1 12 A \. x x (amount of the funeral 
 benefit); where x represents the age of the member at the birth of 
 his child. The above may be taken for practical purposes at a 
 constant value, using an average age for x. It will be quite near 
 enough in general to assume an average rate of mortality of, say, 
 1 per-cent for the life x taking ji 2 Aj :a; as equal to Aj : i2 at 1 per- 
 cent higher rate of interest. The average number of children 
 born annually to members of various ages being determined from 
 the experience of the society, the benefit resolves itself into a 
 variable annuity and may be readily valued. 
 
 Funeral The societies dealt with so far have been varieties of 
 
 lranch sin tne ordinary friendly society granting simply funeral 
 societies. anc [ sickness benefits. It remains to be noticed how 
 far the practical process of valuation needs to be modified to suit 
 other types of societies. 
 
 In the case of a branch of an affiliated order in which the 
 funeral benefits are re-assured with the district, since the 
 society is primarily liable the funeral benefit must be valued in 
 the usual manner, and, provided the district funeral fund is 
 solvent, credit may be taken for its re-assurance of the death 
 monies. The solvency of this fund is not always, however, easy 
 to determine. The whole question of district levies is at present 
 a burning one, and the maintenance of the district funds by means 
 of an equal contribution per member from all the branches of the 
 district, quite irrespective of their ages, is not only wrong in 
 theory but increasingly inconvenient in practice. Especially is 
 this so where the branches differ greatly as to the average age of 
 
Friendly Societies. 59 
 
 the members, in which case the younger branches may find them- 
 selves burdened with annual levies considerably in excess of the 
 premiums necessary to insure the whole of their funeral benefits. 
 Various methods have been proposed to remedy this inequality, 
 but the only sound one is to fix a contribution for each member, 
 graduated according to his age, which shall be sufficient to insure 
 his funeral benefit ; and to accumulate the surplus contributions 
 as a reserve fund. 
 
 Funeral ^ n tne case ^ an ordinary friendly society, where the 
 
 death benefits are partly met by levies upon the 
 members, the value of these latter may be computed by the 
 formulas I have demonstrated elsewhere (J.I.A., xxvi, 478), as 
 follows : 
 
 Value of a levy of 1 per member at each death in a society of 
 n members 
 
 Ditto at each death of a member's wife 
 
 n(n-\)~ 
 3 
 
 where x may be taken as the average age- of the members of the 
 society. Where the funeral benefit is alone assured and is 
 provided for by means of levies, great care must be used as to the 
 inclusion of negative values at the earlier ages, a point which will 
 be dealt with presently. 
 
 Burial ^ De l ar o e burial societies not involving considerations 
 
 of sickness do not present many special features that 
 it is important to consider here. In their general characteristics 
 they resemble closely the industrial assurance companies. The 
 children's assurances, which form so large a proportion of the 
 business, may, owing to the diminished benefit at the younger 
 ages when the mortality is heaviest, and its gradual increase as the 
 rate of mortality diminishes, be treated as temporary assurances 
 having no liability, provided that the valuer is satisfied that the 
 contribution in each year of age is adequate to meet the sums 
 assured at that age. 
 
 The mortality prevailing amongst the societies differs consider- 
 ably, mainly from difference of locality, but in most of the 
 larger societies it is higher than that of the population generally. 
 Hence an average table cannot be employed. Mr. Sprague's 
 analysis of the Royal Liver experience shows that the rate of 
 
60 
 
 Friendly Societies. 
 
 mortality is higher (and considerably so) among the newly-entered 
 than among those of the same age who have been longer assured. 
 This will be seen from an inspection of the following table, which 
 gives the rates of mortality, as deduced by Mr. Sprague, from the 
 Royal Liver experience, those of a comparatively small Lancashire 
 society, and those of the English Life Table (3). 
 
 TABLE 15. Comparative Rates of Mortality by the under- 
 mentioned Standards. 
 
 
 ROYAL LIVER EXPERIENCE 
 
 
 
 Ages 
 
 
 Darwen 
 Society 
 
 English Life 
 No. 3 
 
 At Entry 
 
 Assured 
 5 Years 
 
 Assured 
 10 Years 
 
 Ultimate 
 Bates 
 
 20 
 
 1-12 
 
 1-04 
 
 81 
 
 81 
 
 66 
 
 84 
 
 30 
 
 1-44 
 
 1-34 
 
 1-12 
 
 Mb 
 
 1-00 
 
 1-03 
 
 40 
 
 2-00 
 
 1-88 
 
 1-76 
 
 1-40 
 
 1-28 
 
 1-29 
 
 50 
 
 2-50 
 
 2-67 
 
 2-67 
 
 2-32 
 
 2-00 
 
 1-75 
 
 60 
 
 4-39 
 
 4-76 
 
 4-84 
 
 4-79 
 
 4-00 
 
 3-07 
 
 70 
 
 8-34 
 
 8-84 
 
 8-90 
 
 8-92 
 
 10-10 
 
 633 
 
 Subsidized 
 Societies. 
 
 The question of secessions in these societies will be dealt with 
 under that heading. 
 
 Subsidized societies present a special feature in respect 
 of the annual grant available, either fixed in amount, 
 as is usually the case, or varying with the membership of the society. 
 Where the subsidy takes the form of a fixed annual sum independent 
 of the number of members, it is usual to capitalize the payments, 
 but in doing so it seems desirable that any probable increase in the 
 membership of the society should be taken into account, as the 
 subsidy will thereby be rendered relatively less effective. This may 
 be conveniently done by capitalizing the sum at a higher rate of 
 interest than that assumed in the valuation. (It is clear that an 
 annual growth of the membership of a society enjoying a fixed 
 subsidy is financially equivalent to an annual diminution of the 
 subsidy.) 
 
 Female societies necessarily differ widely from ordinary 
 friendly societies. Their benefits almost invariably 
 include allowances during confinements, in addition generally to 
 funeral and sickness benefits. The confinement allowances may 
 generally be safely valued on the basis of the society's experience. 
 The benefit may be very conveniently and not inaccurately treated as 
 a temporary annuity, ceasing, say, at age 45, the amount of which 
 
 Societies of 
 Females. 
 
Friendly Societies. 61 
 
 may be taken as the average annual sum paid for confinements 
 divided by the number of members below that age. 
 Rate of With respect to the rate of interest to be assumed at a 
 
 interest. valuation the utmost care is needed. The tendency to 
 adopt a high rate is certainly one to be guarded against, and it 
 is to be remembered that the actual return made by the society 
 upon its funds is not in itself a sufficient guide. The nature and 
 solidity of the investments must also be looked to, and it may 
 generally be said that only when there is evidence that these are 
 of really sound character, and, at the same time, are remunerative, 
 will it be safe to adopt a rate above 3 or 3^ per-cent. Probably 
 the great bulk of societies in this country cannot anticipate with 
 any confidence a return of more than the lower of those rates. 
 
 It must be remembered that a change in the rate of interest 
 employed in the valuation will produce a much greater relative 
 effect in the case of a friendly society than in that of a life 
 assurance society; for, in the latter, an increased rate of interest, 
 while diminishing the estimated value of the liabilities, diminishes 
 also that of the assets, by giving a smaller net premium. In a 
 friendly society, where the gross premiums are almost invariably 
 valued, this compensating effect does not exist. 
 Net Premium -^ n tnose relatively few cases, where the contributions 
 valuations. h ave ^ een ca l cu l a ted by an actuary, and where the 
 society's experience has been well within the assumptions upon 
 which they have been based, both as regards rates of sickness and 
 rates of interest, the valuation may fairly be made upon the same 
 basis as that upon which the contributions were originally 
 computed. Indeed, this would be the natural and proper 
 method to adopt, leaving the same margins for contingencies 
 and future profits as were found desirable in the first instance. 
 Such a valuation will correspond to what is usually termed a net 
 premium valuation in insurance companies. 
 
 Where, as the result of a valuation, a deficiency is shown 
 to exist, it is of importance that suitable steps should be 
 taken to place the finances of the society upon a sound basis. This 
 may be done in various ways, either by increasing the contributions 
 by a reduction in the benefits granted, or by a combination of both 
 methods. The method employed, however, must be carefully con- 
 sidered with reference to the causes of the deficiency, so far as 
 these are ascertainable. These will generally be found to be either 
 inadequate contributions (usually in consequence of a uniform rate 
 
62 Friendly Societies. 
 
 having been charged for all ages at entry), excessive sickness rates 
 (which is, of course, practically the same thing, since the adequacy 
 of the contributions must be tested by the actual experience of the 
 society), or insufficient provision for management expenses. The 
 circumstances of societies vary so widely, that it is not possible to 
 lay down any very precise rules as to the best methods of 
 procedure in these cases; the principal point to be attended to 
 being that the burden of the readjustments made should fall upon 
 those members who are mainly responsible for the deficiency. 
 Where, for instance, the deficiency has arisen from insufficiency of 
 contributions, a uniform increase of these for all members, old 
 and new, would obviously be very unfair and ineffective besides, 
 seeing that it would create a mass of negative values at the 
 younger ages, which would be almost wholly lost by the with- 
 drawals that would immediately take place. It would be prefer- 
 able, in the first instance, to increase each member's contribution 
 to the sum which he should originally have paid (on the valuation 
 basis), having regard to his age at entry. If a re-valuation is now 
 made, the deficiency will be found to have been considerably reduced, 
 and, in the case of a young society, may even have practically 
 disappeared. The remaining deficiency may now be met by a 
 further increase in the contributions of the older members, in 
 proportion to the duration of membership, or by a corresponding 
 reduction in the benefits. 
 
 Where the deficiency is large, and the society an old one, it 
 will be found that no practicable increase to the contributions will 
 meet the case, and it is then necessary to have recourse to a 
 reduction in the benefits; and here the same principle of throwing 
 the loss upon those members who have created the deficiency 
 should be followed. Further reductions of the sickness allowance 
 in prolonged illness often prove the simplest mode of dealing with 
 such cases, as such reductions affect but slightly the recent 
 entrants at the younger ages, operating mainly by reducing the 
 heavy values of the benefit in old age. Where a deficiency has 
 arisen in part from abnormally heavy sickness rates, a decrease in 
 the allowances will usually be found to work in the direction of 
 reducing the rates in the future, and is thus doubly effective 
 financially. In some cases it unfortunately happens that the 
 deficiency has become so unmanageable that the only course open 
 to the actuary is to recommend that the society should take 
 advantage of the Act and submit to a dissolution. 
 
Friendly Societies. 63 
 
 In those cases in which a valuation shows a surplus 
 of assets over liabilities, it will generally be found 
 desirable to allow such surplus to remain, except in special cases. 
 Where the surplus is merely nominal, that is to say, bears only a 
 small proportion to the gross liabilities of the society, and might 
 disappear upon a comparatively slight change in the basis of 
 valuation, it should invariably be left untouched. In the few 
 cases in which there is a substantial surplus brought out, where 
 the valuation has been a stringent one, and comparison with 
 previous investigations shows the surplus to be a growing one, it 
 may be dealt with. The circumstances of individual societies 
 vary so greatly that no very precise directions can well be given 
 as to the best method of appropriating such surplus. Speaking 
 generally, however, cash distributions are to be avoided, and 
 perhaps the simplest and, in the end, most satisfactory method, 
 is to employ the surplus in reducing the members' future 
 contributions. The greatest care should be exercised in augmenting 
 the sickness allowances, especially those payable in continued 
 sickness, lest the rate of claim be thereby increased, and the 
 assumptions upon which the valuation has been based should fail 
 to work out in the future. 
 
 FINANCIAL EFFECT OF CHANGES IN THE RATES OF SICKNESS 
 AND MORTALITY. 
 
 Effect on the ^ will frequently happen that the same causes which 
 Sickness produce a change in the rate of sickness also affect the 
 mortality prevailing among the members of the 
 society. The result of such a change in the rate of mortality is 
 hardly less important than a change in the sickness rate, although 
 it may be easily overlooked, as its effect is entirely indirect. In 
 the first instance, indeed, a light rate of mortality appears to be 
 beneficial to the society, since a less sum is annually paid on 
 account of funeral benefits, and it is overlooked that in consequence 
 of the larger number of members surviving to the older ages, the 
 liability in respect of the future sickness is largely increased. 
 Especially is this the case in respect of the pension after 70, 75, 
 or 80, as the case may be, into which the allowance practically 
 resolves itself at this period of life. It is therefore important, in 
 considering the suitability of a table of sickness as the basis of a 
 valuation, to have regard, not only to the sickness prevailing in 
 the society, but also to the probable rate of mortality that may 
 be expected to obtain in the future. 
 
64 
 
 Friendly Societies. 
 
 With a view of illustrating the relative effect upon the financial 
 position of the society of a deviation from the standard tables 
 in respect both of sickness and mortality, tables which are 
 appended have been constructed on the assumptions that 
 
 The Mortality Rates are 
 
 The Sickness Rates are 
 
 Normal 
 Normal 
 Normal 
 20 per-cent above Standard 
 20 per-cent above Standard 
 20 per-cent below Standard 
 20 per-cent below Standard 
 20 per-cent below Standard 
 
 Normal 
 20 per-cent above Standard 
 20 per-cent below Standard 
 Normal 
 20 per-cent above Standard 
 Normal 
 20 per-cent above Standard 
 20 per-cent below Standard 
 
 These tables give the monetary values, reckoning interest at 
 3 per-cent, for the sickness benefits to ages 65, 70, 75, and 80, 
 with a pension afterwards at the reduced rate of pay, and also the 
 values of annuities and assurances, and are based upon the 
 Manchester Unity, and Ancient Order of Foresters' experience.* 
 
 A reference to the figures in these tables will show at once 
 the relative effects of changes in the rates of sickness or mortality, 
 on the full value of the sickness benefit at various ages. The 
 following shorter tables for three specimen ages will show very 
 clearly the relative value of the benefit under the varying 
 conditions named, the value when both mortality and sickness 
 are normal being taken at 1,000. It will be seen that when 
 the reduction in the allowance is to half-pay only, the effect 
 of the change in the mortality rates is relatively much greater, 
 but that the effect of the variations in the sickness rates is 
 somewhat less than when the reduction is to quarter-pay. 
 
 TABLE 16. Relative Value of Sickness Benefit (Reduction to 
 Quarter-Pay and Pension after 80) M. Z7. 3 per-cent. 
 
 
 AGE 22 
 
 AGE 42 
 
 AGE 62 
 
 Mortality 
 
 Sickness 
 
 Sickness 
 
 Sickness 
 
 
 Normal 
 
 + 20o/ 
 
 -200/0 
 
 Normal 
 
 + 200/0 
 
 -200/0 
 
 Normal 
 
 + 200/ 
 
 -200/0 
 
 Normal 
 
 1,000 
 
 1,190 
 
 810 
 
 1,000 
 
 1,185 
 
 815 
 
 1,000 
 
 1,170 
 
 830 
 
 + 200/ 
 
 904 
 
 1,080 
 
 728 
 
 890 
 
 1,059 
 
 721 
 
 877 
 
 1,021 
 
 733 
 
 -200/ 
 
 1,120 
 
 1,328 
 
 912 
 
 1,145 
 
 1,350 
 
 940 
 
 1,164 
 
 1,340 
 
 988 
 
 * Four-figure logarithms were employed in the construction of these tables. 
 
Friendly Societies. 
 
 65 
 
 TABLE 17. Relative Value of Sickness Benefit (Reduction to 
 Half-Pay and Pension after 80) M.U. 3 per-cent. 
 
 
 AGE 2-2 
 
 AGE 42 
 
 AGE 62 
 
 Mortality 
 
 Sickness 
 
 Sickness 
 
 Sickness 
 
 
 Normal 
 
 + 20% 
 
 -20% 
 
 Normal 
 
 + 200/0 
 
 -200/0 
 
 Normal 
 
 + 200/0 
 
 -200/0 
 
 Normal 
 
 1,000 
 
 1,185 
 
 815 
 
 1,000 
 
 1,178 
 
 822 
 
 1,000 
 
 1,169 
 
 831 
 
 + 20% 
 
 887 
 
 1,056 
 
 718 
 
 870 
 
 1,031 
 
 709 
 
 858 
 
 1,003 
 
 713 
 
 -200/0 
 
 1,124 
 
 1,328 
 
 920 
 
 1,176 
 
 1,372 
 
 980 
 
 1,196 
 
 1,370 
 
 1,022 
 
 TABLE 18. Relative Value of Sickness Benefit (Reduction to 
 Quarter-Pay and Pension after 80) A.O.F. 3 per-cent. 
 
 
 AGE 22 
 
 AGE 42 
 
 AGE 62 
 
 Mortality 
 
 Sickness 
 
 Sickness 
 
 Sickness 
 
 
 Normal 
 
 + 200/0 
 
 -200/0 
 
 Normal 
 
 + 200/o 
 
 -20% 
 
 Normal 
 
 + 200/ 
 
 -20% 
 
 Normal 
 
 1,000 
 
 1,192 
 
 808 
 
 1,000 
 
 1,186 
 
 814 
 
 1,000 
 
 1,171 
 
 829 
 
 + 20o/ 
 
 904 
 
 1,081 
 
 727 
 
 882 
 
 1,051 
 
 713 
 
 860 
 
 1,002 
 
 718 
 
 -200/ 
 
 1,116 
 
 1,328 
 
 910 
 
 1,146 
 
 1,351 
 
 941 
 
 1,163 
 
 1,349 
 
 977 
 
 TABLE 19. Relative Value of Sickness Benefit (Reduction to 
 Half-Pay and Pension after 80) A.O.F. 3 per-cent. 
 
 
 AGE 22 
 
 AGE 42 
 
 AGE 62 
 
 Mortality 
 
 Sickness 
 
 Sickness 
 
 Sickness 
 
 
 Normal 
 
 + 200/ -20% 
 
 Normal 
 
 + 200/0 
 
 -20% 
 
 Normal 
 
 + 200/0 
 
 -20% 
 
 Normal 
 
 1,000 
 
 1,186 
 
 814 
 
 1,000 
 
 1,179 
 
 821 
 
 1,000 
 
 1,160 
 
 840 
 
 + 20o/ 
 
 884 
 
 1,054 
 
 714 
 
 860 
 
 1,022 
 
 698 
 
 837 
 
 983 
 
 657 
 
 -20o/ 
 
 1,151 
 
 1,357 
 
 945 
 
 1,180 
 
 1,379 
 
 981 
 
 1,197 
 
 1,372 
 
 1,022 
 
 The effect upon the sickness values of any change 
 the Net in the assumed rate of mortality will be partly com- 
 
 pensated at a valuation by the effect on the value 
 of the contributions and death benefits ; hence these tables do 
 not exhibit the net result of such variations in practice. AVith 
 a view of showing more precisely how far the financial position 
 
66 
 
 Friendly Societies. 
 
 of an average Society would be affected by the supposed changes 
 in the sickness and mortality rates respectively, the following table 
 has been calculated. Upon certain assumptions as to ages at 
 entry and rates of secession and mortality (based on the Ancient 
 Order of Foresters' experience), a model society was constructed, 
 with the following supposed benefits : 
 
 Sickness Allowance 
 
 Funeral Allowance 
 
 
 
 Annual Contribution 
 
 12. per week 1st 6 months. 
 
 6s. 2nd 
 
 35. thereafter. 
 10 at death of member. 
 
 5 member's wife. 
 
 1 per member. 
 
 The table shows the results of a valuation of societies of 20, 40, 
 and 60 years' standing by the Manchester Unity Table, 3 per-cent 
 interest, under the various conditions described. 
 
 TABLE 20. 
 
 Net Liability of a Society of 1,000 Members M. U. 3 per-cent. 
 (Benefits and Contributions as described.) 
 
 
 AGE OF SOCIETY 20 YEARS 
 
 AGE OF SOCIETY 40 YEARS 
 
 AGE OF SOCIETY 60 YEARS 
 
 Mortality 
 
 Sickness 
 
 Sickness 
 
 Sickness 
 
 
 Normal 
 
 + 200/0 
 
 -200/ 
 
 Normal 
 
 + 20o/ 
 
 -200/0 
 
 Normal 
 
 + 20o/ 
 
 -20o/ 
 
 Normal 
 
 15,745 
 
 21,078 
 
 .10,412 
 
 23,434 
 
 29,182 
 
 17,686 
 
 26,321 
 
 32,081 
 
 20,561 
 
 + 20% 
 
 12,916 
 
 18,019 
 
 7,813 
 
 19,945 
 
 25,156 
 
 14,734 
 
 22,533 
 
 27,816 
 
 17,250 
 
 -200/0 
 
 18,924 
 
 24,605 
 
 13,243 
 
 27,343 
 
 33,655 
 
 21,032 
 
 30,695 
 
 37,058 
 
 24,331 
 
 LOW Mortality ^ combination of a low rate of mortality and a high 
 sfcknessRates ra ^ e ^ sickness is by no means unusual, especially 
 combined. among rural societies, and in this case it is highly 
 dangerous to ignore the effect of the former element. It may be 
 of interest here to give an actual case where this combination of 
 high sickness rate and low mortality occurred. The table below 
 represents the experience of five years of a large country society ; 
 and it will be seen from an inspection of the figures that the sick- 
 ness rates, especially in respect of reduced pay and at the more 
 advanced periods of life, are much above the average amount, 
 while the number of deaths in the society during the five years 
 was considerably below the expected numbers, as estimated by 
 either the Manchester Unity or the Ancient Order of Foresters' 
 experience. 
 
Friendly Societies. 
 
 67 
 
 1 
 
 rHO(MOOOO 
 
 09 9 t-4 9 el ei 
 
 p-l O 04 fH 
 
 l> T? CC? CO CO r-T 
 rH CO O CO 
 
 CO 00 
 
 rH i * ? J 
 
 4>* (M ^ 
 
 I 
 
 Is 
 
 I 
 
 * 
 
 O>i (OO 
 
 N O CD 
 
 CO lO 
 
 COi I 
 O 00 
 
 S 
 
 i 
 
 i 
 
 co" c T? 
 
 rH CO CO 
 
 00" CO" N CO 
 
 M-- 
 
 s^ 
 
 00 rH CO t>* rH 
 
 c<f uj CD" i> co 
 
 5 
 
68 Friendly Societies. 
 
 In this particular case the valuation of the society by the Man- 
 chester Unity Table without modification would have resulted in a 
 net liability of J96,500. If, on the other hand, effect is given to the 
 heavier rate of sickness found to prevail, the mortality still being 
 assumed to be normal, the liability is increased to \ 14,500; while 
 finally, a valuation based upon the actual rates of sickness and 
 mortality observed during the five years brought out a net 
 liability of 128,500. The difference between these last two items 
 will show the extent to which the financial position of the society 
 was affected by the light rate of mortality. 
 
 SECESSIONS. 
 
 Secessions in ^- n ^6 valuation of a Friendly Society it is usually 
 Friend\ nary assumed that the contract of the society by which it 
 society. undertakes to pay certain benefits, in case of sickness 
 
 or death, to the assured, in consideration of certain weekly or 
 monthly contributions made by him, will be terminated only by 
 the death of the member. In practice, however, many more 
 members may leave the society by voluntary withdrawal than by 
 death, and since these withdrawals are not provided for in the 
 ordinary tables of the values of sickness and funeral benefits, it 
 is important to consider their effect upon the finances of the 
 society ; the more so, that very erroneous views often exist upon 
 this subject among those connected with friendly societies. 
 
 By the withdrawal of any member the society, on the one 
 hand, is released from a liability in respect of the benefits assured 
 to that member, and on the other hand it loses an asset in the 
 shape of the present value of his future contributions. Whether, 
 therefore, a loss or profit will result, will depend on the relative 
 value of such future benefits and contributions. To take the most 
 common instance of a friendly society charging the same contri- 
 butions for all ages at entry : where such contribution is any- 
 where near sufficient to meet the benefits assured, it is clear that 
 the younger entrants must pay at an unnecessarily high rate. In 
 the cases of such members the present value of their future con- 
 tributions at the time of entering the society will be greater than 
 the value of the benefits assured to them ; and this would continue 
 to be the case until such members reached the age at which the 
 average contribution was just sufficient to provide for the benefits. 
 Until such time the withdrawal of any of these members would 
 result in a loss to the society, but at those ages at which the value 
 
Friendly Societies. 
 
 69 
 
 of the benefits exceeded the value of the contributions, in other 
 words, where there is a liability attaching to the assurance, the 
 secession of members will in theory relieve the society of such 
 liability. 
 
 class of Lives ^ ^ oes no ^ follow, however, that in practice such with- 
 withdrawing. drawals w iH be of any great benefit. The members 
 comprising a friendly society must necessarily differ greatly amongst 
 themselves as to their relative health or liability to sickness ; and 
 although, for the purposes of valuation, each case is treated as an 
 average one, that is to say, every member is considered to be in 
 ordinary health, this will not actually be the case. It may be 
 presumed that the healthier members of a society would be more 
 likely to withdraw than those more liable to make sickness claims 
 upon the fund ; and statistics prove clearly that this is the case. 
 In Mr. Neison's report on the mortality and sickness experience 
 of the Ancient Order of Foresters, 1871 to 1875, a table is given 
 showing the number of withdrawals amongst the members who 
 during the five years made no claims for sickness, and amongst 
 the members who made claims during the same period. The 
 following abstract will show at various ages the proportion of 
 members in either class withdrawing from the society ; and it 
 will be seen that the rate of withdrawals among those whom we 
 may term the healthy members is very heavy, as compared with 
 the rate prevailing amongst those who had made sickness claims. 
 
 TABLE 22. A.O.F. Experience (1871-75). Rates of Secession 
 
 per-cent. 
 
 
 Amongst Members 
 
 Amongst Members 
 
 Ages 
 
 not Claiming 
 Sickness Benefits 
 
 Claiming 
 Sickness Benefits 
 
 
 during the 5 Years 
 
 during the 5 Years 
 
 20-24 
 
 15-50 
 
 3-28 
 
 25-29 
 
 11-03 
 
 2-76 
 
 30-34 
 
 7-66 
 
 1-99 
 
 35-39 
 
 5-20 
 
 1-40 
 
 40-44 
 
 3-06 
 
 97 
 
 45-49 
 
 1-68 
 
 68 
 
 50-54 
 
 1-03 
 
 40 
 
 55-59 
 
 52 
 
 32 
 
 From this it would appear that the actual gain to the society's 
 finances resulting from withdrawals is less in practice than calcu- 
 lation would show one effect of the withdrawal of healthy 
 
70 
 
 Friendly Societies. 
 
 I 
 
 
 
 H 
 
 
 A 
 
 S 
 
 
 GO 
 
 o to o o S 
 
 rH rH <N CO 5< 
 
 * * 1 
 
 rH 
 CO 
 
 
 
 ""H 
 
 rH 
 
 
 ! 
 
 1 
 
 rH rH rH rH 
 
 
 
 * 
 
 O G^l 00 00 O O5 to 00 W CO 
 
 
 
 |1 
 
 CO O tO CO O rH rH t ; : 
 CO CO ^J* CO rH CO (M 
 
 
 35 to 44 
 
 1 
 
 g 
 
 10 to <? CO rH os <M : ; ; 
 
 H 
 
 
 1 
 
 CJOOOOOOOOOClCO^rH 
 rH (N 
 
 1 
 
 
 sl 
 
 COCOt-tOCOCOCOCDtO 
 
 
 
 *s, 
 
 rH 
 
 
 J 
 
 5 
 
 OOCOCOCiC5<MOOI>CO ; 
 CD Tjl CO <M rH CO 
 
 
 
 2 
 
 1 1 i 1 i g g 1 1 1 
 
 
 
 4 
 
 (MrHrHCOptpr-igS^ t 
 rH r- 1 rH 
 
 
 Under 25 
 
 Withdrew 
 
 rH 
 
 
 
 At Risk 
 
 00 t> CO O "^T <M O5 l> 00 ^ 
 
 
 Year 
 of 
 Membership 
 
 
 a 
 
 2 r5 ^ i \ 
 rHNCO^tO^^^^I 
 
 rH rH (M 2 
 CO 
 
Friendly Societies. 
 
 71 
 
 members being to increase the average sickness rates prevailing 
 in the society. 
 
 In considering the extent to which a society's 
 as to Age and liabilities will be relieved by withdrawals, the age at 
 
 which such withdrawals take place is a factor of con- 
 siderable importance. It may be laid down as a general principle 
 that the heaviest rates of withdrawal will be amongst the younger 
 members of the society, and amongst those who have most recently 
 joined. In other words, secessions on the whole occur mainly at 
 the insuring ages where the members have been insured for a brief 
 period only, and where, in consequence, the liability in respect of 
 their insurances is comparatively small. In illustration of this 
 point, I have prepared Table 23, based upon a somewhat limited 
 experience, but sufficient to indicate approximately the law of 
 secessions in an average friendly society. 
 
 [TABLE 23, see preceding page.~\ 
 
 If we adopt a somewhat broader grouping, as in the following 
 smaller table, the law of the figures is still better brought out. 
 
 TABLE 24. Rates of Secession per-cent. 
 
 
 AGES AT ENTRY 
 
 Years 
 
 
 Assured 
 
 
 
 
 Under 25 
 
 Over 25 
 
 1- 2 
 
 11-2 
 
 in 
 
 3- 5 
 
 8-7 
 
 7-7 
 
 6-10 
 
 5-5 
 
 3-3 
 
 11-20 
 
 2-6 
 
 1-4 
 
 21-30 
 
 1-4 -5 
 
 31 and over 
 
 ... 
 
 Where a uniform contribution is payable by all the members, 
 which, on the whole, is the most common case, the duration of the 
 assurances in the case of those seceding will not be important 
 except so far as it affects their ages. Where the contributions differ 
 with the age it will not be sufficient to consider merely the ages at 
 which withdrawals take place. Nearly all tables professing to show 
 the effect of secessions have hitherto considered only this question 
 of age, and not that of the duration of assurance, and the effect of 
 this is greatly to exaggerate the effect of such secessions. 
 
 If we consider a group of members of a given age who have 
 entered at various times, and consequently are paying various rates 
 
72 Friendly Societies. 
 
 of contribution, while such a group may be subject to an observed 
 average rate of withdrawal, the actual rate prevailing amongst the 
 different members of a group will differ very considerably. In 
 the case of the members recently assured the rate will be very 
 heavy, but the corresponding financial effect will not be in pro- 
 portion to this high rate in consequence of the smallness of the 
 liability of the society with reference to those members. The real 
 relief from secessions will arise from amongst such members of 
 the group who, having been assured for several years, and their 
 assurances having thus attained a positive value, may nevertheless 
 withdraw from the society. But the rate of withdrawal amongst 
 this portion of the group will be very much below the average of 
 the whole group. Consequently, to treat all the members at 
 the given age as subject to one constant rate will considerably 
 exaggerate the financial effect of such withdrawals. Hence it would 
 be quite unsafe to employ tables similar to those of Mr. Neison 
 and Mr. Ratcliffe based on the Ancient Order of Foresters and 
 Manchester Unity experiences. 
 
 Effect of new Another point of practical importance is the extent to 
 Sadejuate* which the effect of withdrawals is counteracted by that 
 
 Contributions. /> * i i /> / 
 
 of new entrants. A very large proportion of societies 
 unfortunately grant benefits out of proportion to the contributions 
 received, and in these societies the value of such benefits is from 
 the outset greater than the value of the contributions payable by the 
 member; and every new member, although he may for some years 
 add to the funds of the society, in reality increases the society's 
 liability from the moment that he joins it. If, therefore, effect is 
 given to the influence of withdrawals, it is equally important that 
 account should be taken of the increased liability produced by 
 new entrants. 
 
 I have made an estimate upon the basis of the Ancient Order 
 of Foresters' rates of entry and secession (1871-75), and find 
 that, assuming benefits of 125. per week (with reduction to 
 quarter-pay) in sickness, 10 at death of member, and 5 at 
 death of wife, annual contribution 1, in an average lodge of 
 300 members, the net liability at a valuation being 2,271, the 
 society's liabilities would during five years 
 
 Be diminished by secessions . . 330 
 Increased by new entrants . . 454 
 
 Net loss . . . . 124 
 Or about 25 per annum. 
 
Friendly Societies. 
 
 73 
 
 Secessions in 
 
 Collecting 
 
 Societies. 
 
 In ordinary friendly societies, secessions practically 
 cease at about ages 55 to 60, but in some societies 
 this is not the case. Notably in the large collecting 
 societies, whether assurances for sick pay are granted or the 
 business confined exclusively to death benefits, the effect of collect- 
 ing weekly or monthly, as the case may be, the small contributions 
 payable by the members is to create a large number of withdrawals 
 at almost all ages throughout life. The experience of the largest of 
 such societies, the Royal Liver, has been analyzed by Mr. Sprague, 
 who has deduced from the records of the society for the five years, 
 1874-78, the following table, giving the adjusted rates of secession 
 for various ages at entry and various durations of membership. 
 
 TABLE 25. Hates of Secession per-cent in Royal Liver Society, 
 1874-78 (Sprague). 
 
 
 AGE AT ENTRY 
 
 Years 
 
 
 
 
 Assured 
 
 
 
 
 
 
 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 
 
 22-91 
 
 23-87 
 
 22-61 
 
 21-22 
 
 19-22 
 
 14-95 
 
 11-71 
 
 5 
 
 5-97 
 
 6-36 
 
 5-44 
 
 3-83 
 
 3-06 
 
 2-77 
 
 2-02 
 
 10 
 
 3-96 
 
 3-50 
 
 2-66 
 
 1-85 
 
 1-45 
 
 1-60 
 
 I'll 
 
 15 
 
 3-80 
 
 2-83 
 
 1-39 
 
 1-21 
 
 1-17 
 
 1-14 
 
 
 20 
 
 3-41 
 
 1-89 
 
 1-20 
 
 1-M 
 
 1-16 
 
 I'll 
 
 
 30 
 
 1-89 
 
 1-20 
 
 1-M 
 
 1-16 
 
 I'll 
 
 
 
 40 
 
 1-20 
 
 1-18 
 
 1-16 
 
 1-11 
 
 ... 
 
 
 
 50 
 
 I'M 
 
 1-16 
 
 1-11 
 
 ... 
 
 
 
 
 60 
 
 1-16 1-11 
 
 
 
 
 
 
 70 
 
 I'll | ... 
 
 
 ... 
 
 ... 
 
 ... 
 
 
 This table shows that to the oldest age withdrawals take 
 place ; but that while, immediately after entry, the rate of 
 withdrawal is extremely high, amounting at the younger ages to 
 upwards of 20 per-cent in the first year, it rapidly diminishes 
 with the duration of assurance, and finally, when such duration 
 exceeds 15 or 20 years, it reaches a minimum value of about 
 1 per-cent. The financial effect of such a rate of withdrawal 
 must be very considerable, when it is remembered that a constant 
 rate of secession of 1 per-cent per annum at all ages is equivalent 
 in its effect to an increase of 1 per-cent in the rate of interest. 
 A practical advantage gained by a society from the heavy 
 rates of secession during the first year of assurance should not 
 be lost sight of. By means of the large proportion of the first 
 year's contribution which is usually available for management 
 
74 Friendly Societies. 
 
 purposes, the fund by means of which the society is enabled 
 to keep together its agency organization is largely augmented. 
 There is also this distinction between a large collecting society 
 and an ordinary friendly society or branch, that in the former 
 case the rate of withdrawal will be a comparatively stable 
 quantity. It will be a rate in the first place depending upon 
 an average of an enormous number of cases spread over a 
 large area, and subject to comparatively constant influences; 
 and while circumstances may arise to considerably increase the 
 rate of secession in such a society, either owing to disputes in the 
 management or doubts as to its stability, there will always be, 
 under the most favourable circumstances, a certain minimum rate 
 below which the withdrawals will not fall. This can scarcely be 
 said to be the case in a simple friendly society where, on the one 
 hand, there is every inducement to the members to keep up their 
 contributions, and, on the other hand, the numbers in the society 
 can scarcely afford a sufficient basis upon which to estimate with 
 any certainty the rates of withdrawal that may in future be 
 expected. In such a society, while the rates of sickness and 
 mortality may be comparatively stable, notwithstanding the small- 
 ness of its membership, the rate of withdrawal may be subject to 
 very violent fluctuations. 
 
 There is another class of society in which secessions 
 
 Secessions in 
 
 subsidized stand on yet a different basis namely, that class of 
 subsidized societies, such as the large railway servants' 
 funds, or the funds belonging to large firms or works where 
 membership is compulsory. In these cases withdrawal from the 
 employment of the firm generally means withdrawal from the 
 society, and from the fact that during employment membership is 
 compulsory, the rate of withdrawal at different ages really becomes 
 a rate of retirement from employment, and does not depend so 
 much upon the voluntary action of the members as upon 
 circumstances which are beyond his control. In these cases it is 
 clear that the rate at which the members withdraw at the different 
 ages is a factor that may be ascertained with some degree of 
 approximation, and also some amount of confidence as to the 
 working out of a similar experience in the future. 
 
 In considering the manner and extent to which the 
 
 allowed for in element of withdrawals should be taken account of 
 
 at a valuation, effect must be given to all these 
 
 various considerations. In the first place, the experience of 
 
 the society must be sufficiently extensive to afford trustworthy 
 
Friendly fif 
 
 data as to the rate of withdrawal that has^pfe?fRfea : first, as to 
 the various ages throughout life; secondly, as modified by the 
 duration of assurance ; thirdly, it must be clear from the 
 nature and relation of the benefits to the contributions that 
 the relief afforded to the society by the withdrawal of members 
 is not practically destroyed by the introduction of fresh members, 
 entailing fresh liabilities; fourthly, the experience of the 
 society must have been sufficiently steady to give confidence in 
 similar results in the future. It will generally be found that 
 very few of these conditions are fulfilled in the case of an 
 ordinary friendly society. As a rule the membership is much 
 too limited to afford sufficient basis for the future calculation 
 of such an uncertain quantity as the number of members 
 seceding at different ages. Still less will it admit of further 
 analysis in respect of duration of assurance, and consequently, 
 whatever may be said in theory as to the propriety of taking 
 account of secessions in the valuation of such a society, the 
 practical difficulty will always remain that there are no reliable 
 data upon which their effect can be calculated. Where the 
 membership of a society, however, is sufficiently large, and where 
 the experience in respect of secessions has been steady, there can 
 be no objection in principle to allowing for the effect of such 
 secessions at the valuation. But, in order that this effect may not 
 be greatly exaggerated, it is important that a more minute analysis 
 should be made of the withdrawals than that of proceeding 
 merely upon the basis of age. It is necessary that tables should 
 be framed showing the various ages at entry, the rate of with- 
 drawal that has prevailed at the different durations of the 
 assurances, and the valuation of the liability to the society must 
 be conducted on this basis, all members of given ages at entry 
 being treated separately. In the majority of societies where the 
 membership is large, it will be found that the effect of such seces- 
 sions is not material, in consequence of their absolute cessation 
 before the older ages are reached, and it is only in such societies 
 as the burial and collecting societies that its effect becomes 
 important. 
 
 Negative ^ n conjunction with the question of secessions must 
 Values. k e considered that of negative values. These arise, as 
 
 has already been explained, mainly in such societies as have one 
 uniform rate of contribution for all ages at entry, from the value 
 of the contributions at certain ages exceeding that of the benefits. 
 In these cases, the withdrawal of the member entails an absolute 
 
76 Friendly Societies. 
 
 loss upon the society, and this loss can only be effectually 
 guarded against either by excluding such members entirely from 
 the valuation, or simply by valuing their future contributions at 
 a sum not exceeding the value of the benefits. In other words, 
 these negative values must be excluded in the valuations, otherwise 
 the insurances appear as assets in lieu of liabilities assets which 
 may be lost at any time by the voluntary withdrawal of the members 
 in question. The cases in which it would appear to be safe to include 
 a proportion of such negative values are, first, the large collecting 
 societies where the vast numbers of members involved may make it 
 possible to count with some degree of certainty upon a proportion 
 of the negative values being actually realized ; and, secondly, in 
 those cases where membership of the society is compulsory, and 
 where, consequently, the payment of the future contributions is 
 assured. In order to eliminate all cases of negative values at a 
 valuation, the safest plan is to calculate the contributions required 
 to provide for the benefits at each age, and to examine the schedules 
 prepared for the valuation, and in all cases where the contribution 
 actually payable exceeds the calculated amount, to value only the 
 latter. 
 
 There are two special cases which may present some 
 values in difficulty, namely, levy societies and societies of females. 
 As regards the former, where, as is usually the case, 
 the levies are only a part of the contributions, the simplest method 
 of excluding negative values is as follows : at the younger ages, 
 where alone these values will appear, the value of the future levies to 
 be paid by any given member may be taken as equal to (w l)Aij,; 
 those to be paid by the remaining members at his death (n I)Al JX ; 
 together =(n I)A xy , where y is the age of the member, x the 
 average age of remaining members, n the number in the society. 
 This value will, of course, increase with the age of y ; and making 
 the reserve values (apart from the levies) equal at all ages to this 
 minimum value, all negative values are necessarily excluded. 
 
 Where the levies are the sole contributions paid by the 
 members, the following method must be adopted. Having made 
 a valuation of the sums assured at each age in the usual manner, 
 a table must be formed, showing, for each age, 
 
 Value of the sums assured at that age and upwards = 2 A^ 
 Number of members . . . . = n 
 
 Average age of members . . . . . x 
 
Friendly Societies. 77 
 
 If the amount of the levy be K per member, the net liability in 
 respect of the members at age y and over will then be 
 
 . 
 
 K 
 
 and by selecting the age y, so that the highest value of this 
 expression may be obtained, all negative values will be ipso facto 
 excluded, but not otherwise. 
 
 in Female I n ^ e case ^ f ema ^ e societies, the negative values do 
 not necessarily appear at the youngest ages. In such a 
 society, for instance, there maybe a funeral allowance at the death of 
 the member, the husband, and children, besides allowances at con- 
 finements. The liability in respect of the member's and husband's 
 deaths is at first small, but increases with the age of the member; 
 on the other hand, the prospective liability in respect of confine- 
 ments and children's deaths is heaviest at the younger ages. In 
 consequence of this feature, the contributions at the younger ages 
 may be too small in fact, not covering the current risk but 
 more than sufficient in middle life (say from 35 to 55), giving, at 
 these ages, negative values for the liability. In order to effectually 
 exclude all negative values from the valuation of a society of this 
 description, it is not enough to strike out all that appear upon the 
 face of the valuation, the prospective negative values must also be 
 taken account of. This may be best done by treating the 
 contracts at the younger ages (up to age 35 in the case supposed) 
 as temporary assurances, ceasing at the age at which the negative 
 values first appear. 
 
 FLUCTUATIONS IN DEATH AND SICKNESS RATES. 
 
 Theory of The calculations of the actuary are all made on the 
 Fluctuations. assum ption that certain average results will work out ; 
 and such expected results, being based upon those already 
 observed during a series of years, it is important to know how 
 far the assumption of a like experience in the future may be 
 trusted. Three main causes tend to produce fluctuations from 
 year to year in the sickness or mortality experience of a society: 
 1. Exceptionally healthy or unhealthy years, affecting all societies 
 alike. 2. Changes in the management of the society, involving 
 greater strictness or laxity in the conduct of the business. 3. The 
 limited number of the members under observation, producing 
 purely accidental fluctuations. Of these causes, the first is 
 unimportant, the second is not susceptible of calculation, the 
 
78 Friendly Societies. 
 
 third being the only one of which the actuary can take cognizance. 
 Even in the largest societies there will be fluctuations from the 
 average experience of an accidental nature, and these fluctuations 
 will, as a matter of fact, be larger in actual magnitude than in 
 a smaller society. The idea that in a very large number of cases 
 individual fluctuations are completely balanced, and so entirely 
 destroyed, is quite erroneous. The actual deviations from the 
 most probable result will be greater the larger the number of 
 cases, but, on the other hand, the proportion which such deviations 
 bear to the average or expected result is smaller. The theory 
 of such deviations has been discussed at length by writers on 
 probability, and where simple cases of probabilities are concerned 
 is well known. 
 
 It may be shown that if n lives are exposed to risk for 
 to Mortality a year, the probability of death being in each case q, 
 
 the average or " expected" number of deaths being 
 consequently nq ( = m, say), then, in a series of such observations, 
 the average deviation from this mean result will be very nearly 
 -f. \/nq(l q)j which again (seeing that the factor \/l q is 
 nearly unity for all but the extreme ages) may be approximately 
 written + -f v/numDer of expected deaths.* This result we may 
 conveniently call the " probable error" of the observations, 
 although this phrase is already used by mathematicians with a 
 somewhat different meaning. It follows from this relation that 
 if we have a series of observations at various ages, in which the 
 expected deaths are respectively m ly m 2 , m 3 , . . . m n , and the 
 probable errors a lf a^, a 3 , . . . a n (where a r = ^\im^ y then the 
 probable error, when the whole of the results are combined, will 
 
 be \/a\ + al + al ... +<. This result agrees, as would be 
 expected, with what is known as the " Theory of errors of 
 observation." 
 
 If, now, we consider a table of mortality experience, showing 
 at each age the number exposed to risk and the numbers dying, 
 it is clear that the rates of mortality deduced from these numbers 
 will be affected by the accidental errors of which we are speaking, 
 and to which are due the irregularities of all unadjusted tables. 
 These irregularities, however, may be reduced by some process of 
 graduation, when the probable errors in the resulting rates will be 
 correspondingly smaller; and if the formula of graduation be 
 known, an expression can be found for the mean deviation of the 
 
 * Sec the demonstration I have given of the formula in J.I.A., xxvii, 214. 
 
Friendly Societies. 79 
 
 adjusted and unadjusted results. For example, if the formula of 
 
 graduation, given on page 33, be employed, we have the 
 following expression for this deviation : 
 
 u-u= 
 
 Now, if we suppose each of the unadjusted values of u x in the 
 above expression to be affected with the same probable error, + a, 
 then the probable error of the successive terms on the right of the 
 
 . . 96 22 22 17 
 equation will be, respectively, j20, 19Q^ l2Q a ' 120^ ' 
 
 and the probable error of their sum will be found by taking the 
 square root of the sum of the squares of these quantities 
 
 = - - a, or Q a nearly. Hence, in a table adjusted by this 
 120 8 
 
 formula, the theory shows us that the average difference between 
 the adjusted and unadjusted number of deaths at each age should 
 be 
 
 - x = A/adjusted number of deaths 
 o o 
 
 = '7 ^adjusted number of deaths. 
 
 If Mr. Woolhouse's formula had been used, the coefficient would 
 be nearly identical, namely, "706; and it will be found, generally, 
 that, for all practicable formulas of adjustment, the differences of 
 the adjusted and unadjusted deaths will be very nearly 
 
 \/-|- adjusted number of deaths. 
 
 Having arrived at this result from theory alone, we are now 
 in a position to test it by an application to actual facts. This is 
 done in the following table, which shows, for the three divisions 
 (rural, town, and city) of the Foresters' experience (1871-75), the 
 average deviations between the actual and adjusted deaths in 
 various groups of ages, and the computed deviations according to 
 the formula just given. It will be observed that the average 
 difference in each of the three divisions is small, and when the 
 whole is combined we have the following results : 
 
 Average of observed deviations = 6'85 
 computed = 6*90 
 
80 
 
 Friendly Societies. 
 
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Friendly Societies. 81 
 
 We may take it, therefore, that a comparison of theory and 
 observation confirms the formula given at the commencement of 
 this section, and that in any given society, if the expected (or 
 average) annual deaths = m, the average deviation from this mean 
 number will be about 4- v/m, or f >/5w in each quinquennium. 
 If it is required that the average fluctuations shall not exceed 
 10 per-cent of the deaths in each quinquennium, we must 
 have 
 
 4 5m 
 
 which gives m > 12'8 ; that is to say, for a society's mortality 
 experience to attain this degree of uniformity there must be at 
 least an average of 64 deaths in the quinquennium. This may 
 be taken as equivalent to a membership of about 1,000. 
 
 In the case of sickness, however, the question is more 
 to sickness complicated. It would naturally be supposed that the 
 
 fluctuations would be less as regards the sickness than 
 in the case of deaths, from the fact that the attacks of sickness 
 are much more numerous than the deaths. Experience proves that 
 this view is correct. Numberless small societies of 50 or 60 
 members contrive to carry on their operations from year to year, 
 with, on the whole, a fairly steady experience in respect of 
 sickness claims, which, did they grant death benefits alone, would 
 be in considerable and constant danger from the smallness of 
 their numbers. It is to be noted that the sickness claims in a 
 society are liable to causes of fluctuation which do not affect the 
 mortality experience. For example, there are cases of imposition 
 which it is very difficult to entirely eliminate, but which scarcely 
 affect the mortality experience. There may be insufficient super- 
 vision maintained in cases of prolonged sickness, and it is 
 mainly in respect of these cases that such small societies run 
 into risk. This risk, moreover, in respect of heavy claims for 
 superannuation, will be greater or less according to the extent 
 to which the benefit is reduced under these circumstances. If, 
 for example, a member can draw half- pay for an indefinite period 
 of sickness, it is clear that the finances of the society will be 
 affected by such prolonged claim to a much greater extent than 
 where only quarter-pay is allowed e.g., a society of fifty 
 members, contributing annually 1 to the funds and receiving a 
 sickness benefit amounting to 105. full pay, might, by the 
 prolonged illness of a single member, be subject to a drain of 13 
 
82 Friendly Societies. 
 
 per annum upwards of a quarter of the society's entire income. 
 If, however, the sickness claim in such cases was reduced to 
 quarter-pay, the annual loss would be only half the sum named. 
 It is evidently important therefore, that in small societies adequate 
 provision should be made for the reduction of the sickness claims 
 whenever they become chronic. Where the total amount that can 
 be drawn by any member is limited the danger arising from such 
 cases is, of course, avoided. 
 
 The fluctuations arising in the sickness experience of societies 
 cannot be dealt with theoretically in the same manner as mortality 
 fluctuations, since it is not merely the probability of sickness that 
 is involved, but also the varying durations of illness. It is 
 necessary, therefore, to proceed in the inverse order and to employ 
 the observed deviations between the adjusted and unadjusted 
 sickness claims at various ages to obtain a general expression for 
 such fluctuations. The following table exhibits the results for 
 the same experience as that dealt with in the table of mortality 
 fluctuations given above : 
 
 [TABLE 27, see page 83.] 
 
 An analysis of these results shows that the mean differences 
 observed between the adjusted and unadjusted numbers are, on 
 the average, nearly equal to \ -/average number of weeks' sickness. 
 Allowing for the effect of the graduation formula in the same 
 manner as in the case of the mortality experience, this would 
 correspond to a probable error in the number of weeks' sickness 
 observed of 2 \/expected number of weeks' sickness. Thus, in a 
 society experiencing an average of about 5,000 weeks' sickness 
 each year the probable error or average annual fluctuation would 
 be 2 v/ 5,000 weeks =140 weeks nearly. 
 
Friendly Societies. 
 
 83 
 
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84 
 
 Friendly Societies. 
 
 The following table gives an illustration of the differences 
 between the actual sickness claims during five successive years, 
 in a large society of 5,500 members, and the estimated claims 
 based upon the adjusted rates deduced from the society's 
 experience for the period. 
 
 TABLE 28. Actual and Estimated Sickness. 
 
 Year 
 
 Actual Weeks' 
 Sickness 
 
 Estimated 
 Weeks' Sickness 
 
 Deviation from 
 Estimated 
 or Average 
 Amount 
 
 1876 
 
 1877 
 1878 
 1879 
 1880 
 
 17,694 
 17,310 
 
 17,580 
 18,795 
 
 18,774 
 
 17,487 
 17,723 
 18,002 
 18,490 
 18,943 
 
 207 
 413 
 422 
 305 
 169 
 
 Average 
 
 18,031 
 
 18,109 
 
 284 
 
 As computed by the above formula, the average deviation 
 should be 2\/18109 = 269, very nearly in accordance with the 
 observed amount. 
 
 To come to still smaller bodies, a society of 100 members, 
 having say an annual average of about 120 weeks' sickness, may 
 expect annual fluctuations to the extent, on the average, of about 
 -^th of the annual claims ; or in a period of five years about 45 
 weeks out of a total of 600 weeks; hence, in such a society a 
 "margin" equal to about 10 per-cent of the contributions would 
 probably be sufficient to cover all contingencies. To produce an 
 experience as steady as this, a society granting death benefits 
 alone would require a membership of about 1,000. 
 
 Where sickness and death benefits are combined in the 
 same society the danger from fluctuations is lessened, 
 for the reason that the financial effect of each death 
 that takes place is to release the society from a liability in respect 
 of future sickness claims, which will generally be greater than 
 that incurred in respect of the funeral allowance. Hence, the 
 plan of making a group of lodges and courts interdependent as 
 regards their death payments, although from some points of view 
 desirable, does not rest upon any actuarial basis, and does not 
 
 sickness 
 
 bmed. 
 
Friendly Societies. 85 
 
 give additional stability to the individual societies. Theory goes 
 to show that even small sickness societies of from 50 to 100 
 members may (always assuming careful management) attain a 
 condition of permanency, and practical experience largely confirms 
 this view. 
 
 As regards the present position and prospects of friendly 
 societies, the principle of affiliation, which is daily becoming 
 more popular, must have a beneficial influence upon the system 
 as a whole, by fostering a spirit of emulation in the various orders, 
 diffusing information, and affording the officials of the various 
 branches opportunities for acquiring a wider experience, and by 
 encouraging judicious supervision, especially in the matter of 
 valuations. The benefits that accrue to the affiliated societies in 
 these respects (in spite of various defects in the system still to be 
 overcome), and the gradual improvement in their position, must, 
 by the force of competition, spread to other societies, which must 
 otherwise in the struggle for existence go down before their more 
 vigorous rivals. Seeing that this is the natural tendency of things 
 at this moment, and that the Act of 1875, as now administered, is 
 gradually achieving what it was intended to do, namely, the 
 improvement of the financial position of the societies, it would 
 appear to be undesirable to attempt any drastic alteration in the 
 principles upon which existing legislation is based. 
 
 The basis of the Acts regulating life assurance companies 
 is publicity. Each company must show the public clearly what 
 its transactions have been, in what manner and upon what 
 assumptions its valuation estimates have been based, and what is 
 the result of those estimates ; and it is very doubtful whether any 
 better principle can be applied to friendly societies. 
 
86 
 
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Friendly Societies. 
 
 87 
 
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Friendly Societies. 
 
 89 
 
 TABLE 32. M. U. Experience. Sate of Mortality Increased by 20 
 
 per-cent. Values of Sick Benefit (1 per week Full 
 
 Pay). 3 per-cent. 
 
 
 RATE OF SICKNESS INCREASED BY 20 PER-CENT 
 
 Age 
 
 X 
 
 Half-pay after 12 Months, and Pension 
 of Half-pay after Age 
 
 Half-pay after 6 Months, Quarter- 
 pay after 12 Months, and Pension 
 of Quarter-pay after Age 
 
 
 65 
 
 70 
 
 75 
 
 80 
 
 65 
 
 70 
 
 75 
 
 80 
 
 22 
 
 54-71 
 
 45-59 
 
 41-34 
 
 39-87 
 
 39'12 
 
 35-51 
 
 34-07 
 
 33-69 
 
 27 
 
 61-08 
 
 50-09 
 
 44-96 
 
 43-15 
 
 42-44 
 
 38-10 
 
 36-37 
 
 35-89 
 
 32 
 
 68-82 
 
 55-46 
 
 49-20 
 
 47-02 
 
 46'44 
 
 41-16 
 
 39-04 
 
 38-47 
 
 37 
 
 78-01 
 
 61-65 
 
 53-99 
 
 51-34 
 
 51-05 
 
 44-59 
 
 41-98 
 
 41-30 
 
 42 
 
 89-45 
 
 69-19 
 
 59-72 
 
 56-44 
 
 56-64 
 
 45-65 
 
 45-44 
 
 44-59 
 
 47 
 
 103-42 
 
 78-02 
 
 66-14 
 
 61-98 
 
 63-19 
 
 53-17 
 
 49-13 
 
 48-04 
 
 52 
 
 121-10 
 
 88-51 
 
 73-34 
 
 68-00 
 
 7094 
 
 58-09 
 
 52-96 
 
 51-56 
 
 57 
 
 144-50 
 
 101-54 
 
 81-46 
 
 74-47 
 
 80-55 
 
 62-60 
 
 56-79 
 
 54-96 
 
 62 
 
 178-50 
 
 118-80 
 
 90-83 
 
 81-07 
 
 93-45 
 
 69-88 
 
 60-90 
 
 57-83 
 
 67 
 
 190-90 
 
 143-80 
 
 101-68 
 
 86-97 
 
 95-43 
 
 77-35 
 
 63-07 
 
 59-23 
 
 72 
 
 150-30 
 
 150-30 
 
 115-20 
 
 90-19 
 
 75-15 
 
 75-15 
 
 63-83 
 
 57-25 
 
 77 
 
 117-30 
 
 117-30 
 
 117-30 
 
 93-94 
 
 58-65 
 
 58-65 
 
 58-65 
 
 53-11 
 
90 
 
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Friendly Societies. 
 
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Friendly Societies. 
 
 95 
 
 TABLE 38. A.O.F. Eate of Mortality Increased by 20 per-cent. 
 Value of Sick Benefit (1 per week Full Pay}. S per-cent. 
 
 
 RATE OF SICKNESS INCREASED BY 20 PER -CENT 
 
 Age 
 
 X 
 
 Half-pay after 12 Months, and Pension 
 of Half-pay after Age 
 
 Half-pay after 6 Months, Quarter- 
 pay after 12 Months, and Pension 
 of Quarter-pay after Age 
 
 
 65 
 
 70 
 
 75 
 
 80 
 
 65 
 
 70 
 
 75 
 
 80 
 
 22 
 
 52-45 
 
 44-20 
 
 40-40 
 
 38-98 
 
 38-28 
 
 34-99 
 
 33-65 
 
 33-26 
 
 27 
 
 58-23 
 
 48-23 
 
 43-60 
 
 41-91 
 
 41-22 
 
 37-22 
 
 35-61 
 
 35-13 
 
 32 
 
 6507 
 
 52-90 
 
 47-32 
 
 45-21 
 
 44-68 
 
 39-82 
 
 37-87 
 
 38-26 
 
 37 
 
 73-37 
 
 58-45 
 
 51-56 
 
 48-97 
 
 48-75 
 
 42-80 
 
 40-36 
 
 39-65 
 
 42 
 
 83-64 
 
 65-03 
 
 56-46 
 
 53-23 
 
 53-60 
 
 46-16 
 
 43-14 
 
 42-25 
 
 47 
 
 96-38 
 
 72-85 
 
 62-05 
 
 57-94 
 
 59-29 
 
 49-88 
 
 46-10 
 
 44-93 
 
 52 
 
 113-23 
 
 82-72 
 
 68-72 
 
 63-41 
 
 66-52 
 
 54-33 
 
 49-42 
 
 47-92 
 
 57 
 
 136-03 
 
 95-12 
 
 76-27 
 
 69-13 
 
 75-67 
 
 59-31 
 
 52-70 
 
 50-68 
 
 62 
 
 170-42 
 
 112-61 
 
 86-00 
 
 75-92 
 
 89-09 
 
 65-97 
 
 56-64 
 
 53-80 
 
 67 
 
 184-34 
 
 138-22 
 
 97-25 
 
 81-76 
 
 92-17 
 
 74-19 
 
 59-81 
 
 55-45 
 
 72 
 
 148-20 
 
 148-20 
 
 112-81 
 
 85-29 
 
 74-10 
 
 74-10 
 
 62-25 
 
 54-47 
 
 77 
 
 116-22 
 
 116-22 
 
 116-22 
 
 86-92 
 
 58-11 
 
 58-11 
 
 58-11 
 
 49-87 
 
96 
 
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Friendly Societies. 
 
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LONDON : 
 
 PRINTED BY CHAHLES AND EDWIN LAYTON, 
 FARR1NGDON STREET, K.C. 
 
 
. 
 
 OVERDUE. 
 
 LD 21-lOOm-8,'34 
 
YC 23316"