Twelve years have now elapst since the Married Women's Property Act, 1870, gave legislative sanction to the principle that a married man may effect a policy for the benefit of his wife and children, in such a way that the policy will be effectually settled upon them, notwithstanding his subsequent insolvency. I believe that the facilities thus afforded by the Legislature have been greatly appreciated by some classes of the community,—both by the lower middle classes who usually make no settlement upon their marriage, and by professional and mercantile men who have desired to supplement the provisions they made upon marriage, and to settle a portion of their accumulated savings so as to be secured to their families in the event of unforeseen reverses overtaking them.

This principle has since been extended to Scotland. In England the provision was included in an Act dealing generally with the rights and liabilities of married women; but in Scotland the law relating to married women is fundamentally different from that in England, and it was therefore thought better that the provision should be made by a short Act dealing only with this matter, which Act is printed in the Journal for July 1881.

It has now been considered desirable to consolidate and amend the law relating to the property of married women, and for this purpose to repeal the Married Women's Property Act, 1870; and the question of Settlement Life Policies therefore came up for reconsideration. The result has been that the new Married Women's Property Act, which came into operation on 1 January last, re-enacts with some material improvements the clause on the subject in the old Act.

Before proceeding to a description of the formulas which form the main subject of this paper, it will be worth while to notice some points in connection with the celebrated “Summation Formula” of Maclaurin, the application of which to life contingencies we owe to Mr. Woolhouse. As Mr. Sutton has shown (J.I.A. xv, p. 307), the formula in question may be very simply established by symbolical methods. Thus, putting D for , we have

If we transpose the quantities ∑Ux and ∫uxdx, we get an expression for the value of the integral in terms of the sum of the function; and inserting the limits of integration, we obtain

Assuming, as in life calculations, that everything vanishes at the upper limit, we have

This important formula, which in practice is very powerful, is usually, at first, rapidly convergent, but ultimately becomes divergent. It has been shown, however, that the convergent portion will always give approximate numerical results. The main reason for reproducing the above demonstration, which will be familiar to most readers, is to show how, by a similar method, we may arrive at another summation formula, slightly more convergent than (1).

Although the Carlisle Table of Mortality, constructed by the late Mr. Milne from certain tabulated facts given by Dr. Heysham, has for many years played an important part in life assurance calculations, I have not been able to find that anyone has taken the trouble to compare the original facts with the Carlisle Table as given to the world by Mr. Milne. This has probably arisen from the somewhat vague manner in which the methods employed are described in Milne's well-known treatise. For many matters, probably, this once-famous mortality table will in the future be supplanted by the Institute's tables published a few years ago; but it is still worthy of some attention, and I therefore make no further apology for bringing this short note before the readers of the Journal.

In Art. 705 (p. 410) of vol. ii of his Treatise, Milne says:— “ Table II ” [being the Carlisle Table, as known to actuaries], “ exhibiting the law of mortality at Carlisle, has been constructed “ from Tables A and C of the last article, by the methods laid “ down from Art. 174 to 183; except that, between the ages of “ 100 and 105 years, the decrements of life are greater than they “ should be, according to the formula of Art. 177. * * * * * “ The population of Carlisle is too small to afford a sufficient “ number of facts for determining the law of mortality with “ accuracy, after the age of 100. * * * * I have therefore “ assumed the annual decrements after the age of 100, as they “ appear in the table, somewhat arbitrarily, so as to fix the limit “ of life at 105 years.”