As the principle of non-forfeiture has now been adopted by several British Life Offices, and will probably, in the natural course of competition, soon be adopted by many others, it has occurred to me that it may be useful to bring under the notice of the Institute some of the practical points that will have to be considered in the application of the principle.

If the idea of non-forfeiture is accepted to its fullest extent, it follows that no profit, properly so called, should be made by a life office through the forfeiture of policies, in consequence of the inability or neglect of the assured to pay the premiums as they fall due. The surrender-value of a policy is calculated according to certain rules, which should provide for the office receiving an adequate compensation for the loss of the policyholder's contributions to future expenses, as well as for the disturbance in the rate of mortality caused by the withdrawal of a presumably healthy life; and it is in no way necessary for the prosperity of the office, that it should also make a profit, by the forfeiture of the surrender-values that would be paid to the proper parties on application. In fact, if policies are to be strictly non-forfeitable, the calculated surrender-values should in no case be forfeited, but should be applied, in one way or other, for the benefit of the assured or his representatives.

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.”

During the last session of the Institute of Actuaries, I had the honour to submit a paper, the purpose of which was to devise a method of adjustment as even and correct as that of Mr. Woolhouse, and more easy in application. This was to be done by combining two summations of numbers increasing by third differences; the summations being so chosen as to introduce small factors only into the formula, and to admit of its being worked in columnar shape. (Journal, vol. xxiii, page 335.)

Thereupon, Mr. G. F. Hardy showed that Mr. Woolhouse's formula can be used in columnar shape; and Mr. Ackland, improving on Mr. Hardy's arrangement, contributed a table in which an adjustment of the HM decrement was so calculated. (Journal, xxiii, 354.)

This important and unexpected result of the reading of my paper rendered it of little value, except that it supplied a short formula which may be convenient for use where a rough graduation only is required. Any degree of smoothness can be obtained by repeating the process; but this is tedious, and I would now furnish a formula derived in the same manner, and yielding a satisfactory adjustment by a single operation.