^{page 332 note *} This observation will apply with double force to instances in which no reserve is made beyond the amount so determined. For it must be carefully noted that the comparison here is with the liability indicated by a true table, and that it is invariably the practice to make a large addition to the amount of liability indicated in that way. Thus, after 20 years, the values of assurances by the Northampton 3 per cent, and Experience 4 per cent, tables are as follows:—

The latter being, in the aggregate, a good deal in excess of the former, although the rate of interest is higher. But the advocates of this method would, nevertheless, conside r a large additional reserve necessary, whereas those of the former would, as a general rule, contemplate no other than that here exhibited!

^{page 333 note *} Since writing this paper, my attention has been called by Mr. Peter Gray to the following observations made by Mr. Babbage in his evidence on Friendly Societies (Report, 1827, pp. 29, 30):—“If I am asked which tables I should wish to use in making any calculations relative to the poorer orders of society, I should state that my object would be to get such tables as exactly and perfectly represented those classes throughout all their ages; but it may be said that this is unsafe, and that others should be taken where the deaths are more numerous than those that really happen. My view in all cases is, let us get, as nearly as we can, the law of mortality of the class for which we want to calculate, and add to the prices computed from it some proportional part sufficient to insure the safety of the establishment whic h uses them. I strongly object to using tables giving a greater mortality than is expected to take place, a course which has sometimes been defended on the ground of safety to the establishment Safety is much more certainly secured by judging, as nearly as possible, the true risk, and adding an additional sum for security. If tables not representing the mortality of the class for whom they are designed are employed, every step in the reasonings that are deduced from them is liable to increased error; and if the calculations are at all complicated, th e errors so introduced may not improbably act on the opposite side to that which they were introduced to favour.”

^{page 336 note *} This is obviously unjust, as well as unmeaning! Whatever is paid over and above the premium for the risk is in the nature of a contribution to rent, taxes, salaries, &c. &c; and what more simple or equitable plan can be devised than the requiring the like annual contribution to these charges on account of each one hundred pound assurance? A member's policy does not entail greater expense on the Society because he happens to be older than another!

^{page 336 note †} See Professor Morgan's, De Essay on Probabilities, page 271.Google Scholar