In a note in the introduction to Milne's Treatise on Annuities, the author remarks—“There can, I think, be no doubt but that the mortality is greater among the higher than the middle classes of society. They form too small a proportion of the population to have any sensible effect here; but it would be of importance to the Life Offices to determine the law of mortality among them.” Since the publication of this work, forty-six years ago, some attempts have been made to test the accuracy of this assertion, and to supply the desideratum; but none with which we are acquainted are by any means conclusive.

In the last number of the Assurance Magazine (April, 1861), there appears a letter from Mr. Gompertz, in which reference is made to his and my claims to the discovery of the law, or part of the law, of human mortality. In this letter, Mr. Gompertz declares that my claim cannot interfere with his claim, because I had acknowledged the priority of his discovery. I admit the truth of this declaration, and can add thereto, that I also am able to declare, with equal truth, that his claim, as now described by himself, cannot interfere with any claim hitherto advanced by me. The law of human mortality, now claimed to be discovered by Mr. Gompertz, differs materially from the law which I have declared to exist. The two laws are in accordance with one another only at one period of life (extending, say, from the age of 15 to the age of 55 years), and then only in a partial degree. It is in this partial agreement, at this particular period of life, that the priority of Mr. Gompertz's discovery consists. The description of the law of human mortality, as now believed by Mr. Gompertz to exist, is contained in a paper, referred to in the letter above mentioned, and since published (page 454) in the Appendix to the Report of Proceedings of the Fourth International Statistical Congress, held in London in the year 1860.

There is, probably, no department of an actuary's pursuits where there is such diversity of practice as that of which this paper treats. After the calculation of the premiums and the periodical valuations, the distribution of surplus is infinitely the most important duty that an actuary has to perform. The premium income of the various Life Offices now exceeds £8,000,000 a year, and probably not less than £l,000,000 is annually divided as surplus. Within the last 14 years, one Office alone has divided upwards of £1,200,000; and another, for many years past, has annually distributed as surplus more than £100,000. This will be sufficient to show the magnitude of the interests concerned; and yet, as will be seen in the sequel, these distributions are, in some cases, made in a most arbitrary manner—without reference to principles of justice and equity, and without the basis of accurate reasoning. After what has been written on this subject by Mr. Jellicoe and Professor De Morgan, it is not to be supposed that any actuary would defend the schemes here referred to as equitable; those who do follow them, content themselves with stating their advantages.