On the Law of Mortality

In the following pages I shall have frequent occasion to avail myself of a term which the progress of the analysis of life contingencies has rendered indispensable, but which is not found in any of the standard elementary works in that science. I think, therefore, that I cannot better commence this paper than by an attempt to give an explanation of the expression “force of mortality,” sufficiently ample to obviate any difficulties which might otherwise be experienced on this score.

On the Value of Apportionable Annuities; or of Annuities in which a proportionate part is payable up to the day of death

In former papers, I have investigated the value of an annuity on a single life, when payable half-yearly, quarterly, &c. It still remains to consider the values of annuities on the joint duration of two or more lives, or on the life of the last survivor of several lives, under similar circumstances. It will, however, be more useful to consider first the increase in the value of an annuity on a single life, when a proportionate part of the annuity is payable up to the day of death, instead of the annuity ceasing, as is generally assumed, with the payment that precedes the date of death.

On the Value of Annuities payable Half-yearly, Quarterly, &c. (Part III)

In order to complete the consideration of this question as far as it relates to a single life, I will now give some numerical examples showing the magnitude of the corrections, or the additions to the value of annuities when payable half-yearly, as found from the formulæ of Mr. Baily and Mr. Woolhouse. Those formulæ will also be exhibited under some new aspects.

On the Arrangement of the Data furnished by certain Life Assurance Companies in Scotland, and on the formation of Tables, &c., therefrom; being Contributions towards the ascertainment of the Rate of Mortality of Assured Lives

The mortality statistics of the Scottish Assurance Offices, whose experience it is proposed to develop before combining it with that of the English contributing Offices, have, after passing through various committees, and receiving the benefit of their consideration, eventually passed into my hands for final adjustment and development. Having accordingly considered the subject thus confided to my professional care, I venture to lay before the Institute a brief statement of the views which have occurred to me in regard to the processes which it is proposed to adopt for the arrangement of these data and transforming them into that shape which it is necessary they should assume before becoming the subject of comparison or of calculation.

On the Mortality in the United States of America, as deduced from the last Census, in 1860

There is no country in which, from a combination of circumstances, a census, if accurately taken, is more likely to afford novel and interesting materials than the United States of America. The marvellous progress of the nation, which, in the last 70 years, has increased in numbers from less than 4 millions to nearly 31½ millions in 1860, is alone sufficient to suggest changes in population, in wealth, commerce, cultivation of land, means of transport and circulation, growth of towns, &c., which, if the facts were carefully examined, would throw light upon many obscure questions in social and political economy, and even by the disturbance of their ordinary laws modify and correct the theories which have been mooted.

On the Construction of Tables by the Method of Differences. Section III

We have now to apply the principles laid down in the previous sections to the construction of tables, first of rational, and secondly of irrational, functions. It is only formations of the class last mentioned that are of real importance. A little previous attention to the class first mentioned, however, is desirable, as affording an opportunity of elucidating, under elementary conditions, the arrangement of the work which is found most convenient in practice. The present section will, therefore, be devoted to the formation of successive values of rational functions.

A Budget of Paradoxes (Continued from page 188)

In 1842-43 a Mr. Henson had proposed what he called an aeronaut steam-engine, and a Bill was brought in to incorporate an “Aerial Transit Company.” The present plan is altogether different, the moving power being the explosion of mixed hydrogen and air. Nothing came of it—not even a Bill. What the final destiny of the balloon may be no one knows: it may reasonably be suspected that difficulties will at last be overcome. Darwin, in his Botanic Garden (1781), has the following prophecy:—“Soon shall thy arm, unconquered Steam! afarDrag the slow barge, or drive the rapid car;Or, on wide-waving wings expanded, bearThe flying chariot through the fields of air.”Darwin's contemporaries, no doubt, smiled pity on the poor man. It is worth note that the two true prophecies have been fulfilled in a sense different from that of the predictions. Darwin was thinking of the suggestion of Jonathan Hulls, when he spoke of dragging the slow barge: it is only very recently that the steam-tug has been employed on the canals. The car was to be driven, not drawn, and on the common roads. Perhaps, the flying chariot will be something of a character which we cannot imagine, even with the two prophecies and their fulfilments to help us.