138 Mr W. Fraser on the History and Cwistitutkrn of' 



By this table it will be perceived, that, with the advance of age, the mem- 

 bers (column 3.) are every year diminishing by death, and the sickness (col. 8.) 

 is every year increasing • ; hence, while the annual income (col. 4.) decreases, 

 the expenditure (col. 9.) increases. It will be likewise perceived, however, 

 that when 4 per cent, interest (col. 6.) is added to the contributions (col. 5.), 

 and also 4 per cent interest (col. 11.) to the distributions (col. 10.), and when 

 the total amount of the two latter (col. 12.) is deducted from the amount of 

 the two former (col. 7«)» a large balance (cols. 13. and 14.) will for many years 

 be left in favour of the surviving members ; — that this balance will accumulate 

 at first very rapidly, but afterwards more slowly until the age of 64, when it 

 will begin to decrease ; — that at the age of 71 (in the middle of which year of 

 age, both contributions and allowances for sickness were calculated to cease), 

 it will be wholly exhausted ;— and that then both the amount (col. 7.) of the 

 contribution with interest, and the amount (col. 11.) of the distribution, with 

 interest, will be found exactly to equal each other. 



This society, it has been stated, is supposed to have begun with 1005 mem- 

 bers, all at the commencement of their 21st year of age, or rather, owing to 

 the contributions and allowances being considered as payable at various times 

 in the year, with 1000 members, being the average number alive in the middle 

 of that year of age, and to have admitted no new entrants from its commence- 

 ment till its termination ; — circumstances, however, which are not likely ever 

 to occur in actual practice, and the conclusions may therefore perhaps at first 

 sight appear to be inapplicable to the operations of real societies. This large 

 number of members was assumed for the sake of avoiding the awkward and 

 unnatural appearance of fractional parts in the annual mortality, which would 

 necessarily have resulted, had a smaller number been taken ; and, with re- 

 gard to no new members being supposed to be admitted, it will be obvious 

 that it matters not whether the original entrants had remained the sole mem- 

 bers, or new ones been admitted at all ages, provided each new member of a 

 higher age than 21, had paid— either a sum equal to the stock which the ori- 

 ginal members had in the society, after defraying all their allowances, when 

 they arrived at his age, — or a single or increased annual contribution that 

 would ultimately amount to it, — or should have only been entitled to a lower 

 rate of allowance than the earlier entrant, making the same payment. 



For example, the standard annual contribution of the original members be- 

 ing L. 1, and the weekly sick allowance I^. 1 : : 7, when the society has been 

 ten years in existence, and these members have reached the middle of their 

 3l8t year of age, they would then have a total capital of L. 4701.025 (Table, 

 col. 13.) or X.. 5.2234 each (col. 14.), and this sum, it has been shewn, would, 

 along with their future contributions, be all required to defi*ay their future 

 allowances. Now, as a member just entering at that age, has, with a very 

 slight difference (owing to his being then in health which some of the first 

 members may not now be), the same chances of sickness and death in time to 

 come, with the original entrants still alive,— and as his future contributions 

 are of less value (col. 15.) while his future distributions are of more value 



* By this coliunn, the aggregate amount of sickness appears to be every year diminishing, from 

 the 21st to the 28th year of age, but although this is the case with regard to the society as a body, it 

 will be found, upon dividing the sickness by the number of members alive each year, not to be appli- 

 cable to them as individuals :— See the table of the Law of Sickness, with reference to an individual, 

 given in the Number of this Journal for July 1827. 



