^{page 10 note *} Since writing this paper, my attention has been called by a friend 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 which 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, the errors so introduced may not improbably act on the opposite side to that which they were introduced to favour.“

^{page 15 note *} If S denote the sum resulting from the addition of the true premiums per cent., taken at the ages 21, 22, 23, 24, &c., to 65, and if it be proposed to increase them one third, then and the total annual contribution to extra contingencies, irrespective of commission, will always be equal to (total sum assured).