Mr. Lidstone has kindly communicated the following notes of corrections to his paper “On the Rationale of Formulæ for Graduation by Summation”, in the present volume of the Journal—

(i) (P. 108), 2nd line of par. 28, for “rates”, read “ratios.”

“Before proceeding to examine the different methods pursued “in the valuation of the liabilities of an office under its policies, “I will briefly state what appears to me to be the true principle “upon which the valuation should be based. On the establish-“ment of an office it is assumed, or ought to be, that a certain “table will exactly correspond with the mortality likely to prevail “among the persons whom they will insure; and that a certain “rate of interest (generally 3 per-cent) is what they may with “certainty depend upon realizing. Under these circumstances, “premiums calculated upon such data, increased by a small “addition sufficient to cover all expenses likely to be incurred, “are charged. We will leave out of consideration the addition “ made for bonus, as it is only charged to be returned again. “Suppose now that all these conditions are realized, and that “after a few years it is found that the mortality experienced “corresponds exactly with the table adopted; that the rate of “interest realized is exactly 3 per-cent; and that the additional “charge, technically called the loading, has exactly covered all “the expenses. How much ought the office to have in hand? “The answer naturally will be,—the total net premiums received “in each year, less the claims paid in that year, accumulated at “3 per-cent compound interest.