page 62 note * Mr. King has pointed out that this method was not intended for valuation purposes, but was suggested by him simply for use in connection with the Valuation Returns to the Board of Trade, with the view of supplying sufficient information to enable an independent opinion to be formed as to the position of a company.

page 64 note * The value 1·085 for the ratio was actually fixed in the manner above mentioned, but it might have been determined approximately as follows. Let x be the mean valuation age and n the mean unexpired term, for the whole business, and t a term of years such that the bulk of the business in any group is included within a range of t years on either side of the mean valuation age for the group. Then r may be taken as approximately equal to Putting x=40, n=20. t=10, and making the calculations on the basis of the Text-Book graduation of the H^M experience (in order to avoid the disturbing effect of irregularities), with 3 per-cent interest, it will be found that r=1·083, and practically the same result will be obtained if t be taken = 5 or 7. Again, putting x = 45, n = 15, t=5,7, or 10, the resulting value of r varies from 1·085 to 1·083, agreeing closely with the former result. In practice, it is recommended that the constant c be taken for the common ratio—see paragraphs 18·20, also Mr. G. F. Hardy's remarks in the discussion.

page 71 note * An extended table of Z has been prepared and is appended to the Paper. It should be stated that the particular form here given to the function Z has been adopted (in accordance with a suggestion made to the Author) as an improvement on the form originally proposed in the Paper. It is assumed that the assurances are payable, and that the groups are arranged, as explained in paragraph 23: if this be not the case, the definition of M may have to be slightly modified, according to circumstances.

page 72 note * Making t and n indefinitely great, we have the case of a whole life assurance, and _n E _x vanishes, so that εΔV₀= εP.