There are few matters in connection with actuarial science of which it can be said with truth that professional knowledge has gained little during the past two decades—a period which has witnessed a remarkable expansion in both the theoretical and practical branches of the subject of life contingencies. Questions relating to extra risks, and the premiums which should be charged for them, scarcely appear, however, to have occupied the attention of actuaries to a degree at all commensurate with their commercial importance. Within the space of time alluded to above the practical side of the subject has received consideration at the hands of Mr. A. H. Bailey (J.I.A. xv, 77), and Mr. J. Meikle (J.I.A. xix, 268) ; while lines of inquiry and investigation bearing upon points of theory have been pursued by Mr. W. M. Makeham (J.I.A. xiv, 159 and 242), and Mr. J. R. Macfadyen (J.I.A. xvii, 77). Mr. A. G. Mackenzie has also contributed to our available stock of information on the subject in his Note on War Mortality, read before the Actuarial Society of Edinburgh in 1872. I venture to submit, however that there still remains much to be done to bring this branch of the main subject to the same state of enlightenment and completeness that other parts of the science have now attained. The following paper is an attempt to throw light upon a point which has hitherto escaped scientific treatment; and I entertain the hope that, in some cases of official routine, the methods proposed will be found of service.

The combination of circumstances, which for generations past has impelled large numbers of our countrymen to establish homes in distant lands, has wrought vast changes on the surface of the globe. The progress and welfare of Englishmen call, from every continent, for our interest and sympathy; and, while there is, probably, no portion of “Great Britain” which usually attracts more lively interest than Australasia, special attention is just now directed to that important member of the British Empire. The richness of its soil, its varying and salubrious climate, embracing those degrees of temperature most conducive to health, and, above all, its immense possibilities for the future, combine to fascinate the mind, and inspire a wish for further knowledge.

A comparison of the population returns of Australia with those of the United Kingdom, presents a contrast as striking as can be found in any department of social science. The area of the continent,—which is estimated to be somewhat under three million square miles,—contained at the end of the year 1882 about 2,296,000 inhabitants. The average number of persons to the square mile in each colony was as follows:—

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.