^{page 111 note *} The fact that this is also the value of n for which u_n is a maximum seems to be a coincidence arising from the special character of the Example.

^{page 113 note *} This ignores a profit of u_t if x dies in the tth year before y. There is a similar contingent profit of a year's income involved tacitly in Tappenden's formula for a uniform reversionary life interest, loc. cit., p. 24. This margin, with others arising from (1) payment of the sum assured on the death of x instead of at the end of the year of his death, (2) neglect of the proportion of income payable in the year of y's death and the year of x's death, may be taken into account in fixing g and j.

^{page 115 note *} Assuming, of course, that the estimated income will be realized, as must be assumed in all purchases of life interests.

^{page 115 note †} It being assumed that u is decreasing, the arithmetic mean of the u's over a term of years would have a smaller value, over that term, than would the varying u's, so the adoption of the constant average would be on the safe side.