Jan. 31, 1889] 



NATURE 



333 



: oalt with difTerently in the tables compiled for publication. Of 

 ic tables at tlie author's command, he has chosen that given by 

 AI. Hubbard as being, in his judgment, the best representative 

 of the circumstances with which he is immediately concerned. 



We cannot, at this point, do better than compare M. 

 Hubbard's figures with those we are familiar with in England, 

 viz. those of the Manchester Unity of Oddfellows and the 

 Foresters. We give, then, the average number of days of sick- 

 ness per annum at each of the undermentioned ages, as shown 

 by the several tables specified. In the cases of the Oddfellows 

 and the Foresters, the total average sickness in the year is shown 

 in two parts — sickness within six months of its commencement. 

 and sickness counting only beyond this limit. The rules of 

 French Societies generally do not continue aid in money beyond 

 the term of six consecutive months, a large proportion of them 

 not beyond three. 



A glance at the above table affords sufficient evidence that the 

 author is right in his assertion that sickness tables present very 

 discordant results ; and we should be somewhat failing in our 

 duty if we did not utter a word of caution as to the use of M. 

 Hubbard's tables by unskilled persons, more especially so as the 

 author is inclined to advocate the continued payment of the 

 sickness allowance in prolonged sickness rather than its curtail- 

 ment. The experience of the Oddfellows and the Foresters may 

 not supply a suitable basis for the calculations of les Societh de 

 Secotirs mutueis ; but this experience is extensive, has been care- 

 fully tabulated by competent actuaries, and is, at least, worthy 

 the attention of anyone proclaiming, as our author does, the 

 narrowness of existing and available data. 



We have not the space to follow the author in detail through 

 the numerous rules and explanations given by him in connection 

 with the calculation of actuarial liabilities and kindred matters. 

 We must content ourselves with an examination of one only, and 

 that a simple one. We propose to consider the method recom- 

 mended for the calculation of the actuarial liability attaching to 

 the receipt of contributions on account of pensions. As an 

 example, the author takes the case of a member of 47 years of 

 age, who has contributed 10 francs a year since the age of 1 6, 

 and who is looking forward.to a pension of 294 francs 1 1 centimes 

 to commence at the age of 65. He then proceeds on the:^basis 

 of the Caisse des Retraites tables, substantially, as follows : — 



According to the second of the two tables, an annual contri- 

 bution of 10 francs, the first payment being made at age 47, 

 secures a pension, to commence at age 65, of 41 francs 35 cen- 

 times a year. Whilst, for the same annual contribution, the first 

 payment being made at age 16, the pension is one of 294 francs 1 1 

 centimes a year. The equivalent at age 47 of the earlier contribu- 

 tions (from age 16 to age 47) is, therefore, a pension amount- 

 ing to the difference of the two preceding ones, 252 francs 76 

 centimes a year. But, according to the first of the two tables, the 

 cost, at age 47, of a pension of 34 francs 53 centimes a year is 100 

 francs. It follows that the cost of a pension of I franc is 



^^ francs, and of 252 francs 76 centimes is ^ — ^ , t-f. 



34-53 34-53 



732 francs. 



We do not think the tables on which this calculation is based 

 are more convenient in form than those in general use, or that 

 they lend tliemselves more readily to a simple presentation of the 

 theory of the subject ; and we do not think the method of 

 arranging the calculation is any improvement upon that com- 

 monly adopted. Annuity tables intended as aids to arithmetical 

 computation are usually constructed to the unit of annuity, and 

 not to the unit, or ten, or hundred, of contribution or purchase 

 money. A common form of annuity table gives, for each year 

 of life, the present value of a temporary annuity, payable to one 



of certain ages, say to age 65, accompanied by the present value 

 of a deferred annuity to commence immediately thereupon, the 

 two present values added together giving the present value of a 

 life annuity to run during the whole of the annuitant's life. 

 The ordinary calculation, which may be called the method of 

 present values, then proceeds to estimate the liability of the 

 Society to provide the future benefit, on the one hand, and the 

 claim against the member to provide future contributions on the 

 other : — 



Present value, at age 47, of a pension of 294 francs 

 II centimes a year, after age 65, is the tabular 

 number (2-90) x 294*11 853 francs 



Present value of contribution of 10 francs, payable 

 from age 47 to age 65, is the tabular number 

 (i2*lo) X 10 121 francs 



Leaving the actuarial net liability as before 



732 francs 



The principle of present values which distinguishes the usual 

 method of calculating actuarial liabilities, is quite as easy for the 

 general public to understand as the inverted method of using 

 tables, proposed by M. de Lafitle ; indeed, easier, because of 

 the uniformity with which it is applicable to all cases of annuity, 

 assurance, or sickness contracts. M, de Lafitte himself makes 

 reference to it in explaining the calculation of sickness liabilities. 

 We are of opinion, however, that there is a still simpler way of 

 explaining to the general public the calculation of actuarial 

 liabilities than that depending on the principle of present values. 

 The latter looks to the future, the former to the past. The latter 

 is a prospective method of procedure, the former is sometimes 

 described as a retrospective method. It consists in imagining 

 a number of persons, equal to the number in the table of mor- 

 tality or sickness, to have actual existence, and to live and die 

 as indicated in the table of mortality, and to fall ill as indicated 

 in the table of sickness, and for the periods mentioned therein. 

 By supposing contributions to be received year by year from all 

 who live to pay them, and the various benefits to be paid out 

 as they accrue due, the amount of money remaining in hand, as 

 thus shown, is the sum that a Society of the tabular number of 

 members should have in hand, and therefore the amount also 

 of the Society's actuarial liability as required. For any other 

 number of members than that suggested by the table, the amount 

 of the actuarial liability would be proportional. 



We have confined our observations, in the main, to the subject 

 of actuarial liability, the use of tables of such liabilities, the 

 mortality and sickness experiences on which they are based, and 

 the principles on which they are explained, because the chief 

 object of the book is to deal with this subject and to popularize 

 it. There is, however, a chapter on the due, or fine, or fee, to 

 be- charged new members who join at other than the age for 

 which the rates of contribution are arranged ; another chapter 

 on raising the contributions of existing members to provide 

 increased benefits or to meet a deficiency ; another on the mission 

 and the proper sphere of Friendly Societies ; and others beside, 

 all affording excellent reading, and on which, had space per- 

 mitted, we should like to have said a few words ; but we must 

 conclude this notice. The author manifests an enthusiasm in the 

 work he has undertaken, has expended a great deal of time and 

 thought upon it, and evidently has the welfare of Friendly 

 Societies at heart. If one may judge of literary composition in 

 a language which is not one's own tongue, we should like to ex- 

 press the opinion that the author's writing is clear and attractive. 

 In his efforts to promote and encourage a wider knowledge of 

 the somewhat abstruse subject of actuarial liabilities or valuation 

 reserves, he has our very best wishes. 



JVA TERS POUTS IN THE HUGHLI. ^ 



ON Tuesday, the 4th instant, a fine waterspout was projected 

 from the level vapour-plane of a silvery-edged towering 

 cumulus cloud — or, as our American cousins would term it, a 

 "thunder-head"— over the western side of Kulpee anchorage, and 

 near the village of Jiggerkolly, which, by the aid of a good 

 telescope, showed well the downrush on the inside of the tube, 

 and its counterpart the whirling uprush on its outside, twisting 

 and coiling round and round against the watch-hands (face 

 upwards). 



' Reprinted frjm the EnjlishmtH of S;p'.eTiber 13, 1888. 



