In a paper which I had the honour of reading before the Institute of Actuaries in December, 1862, an inquiry was made into the rates of mortality and marriage amongst Europeans in India, but was principally confined to the experience amongst military officers, as recorded in the books of the Madras Military Fund, and compared with the records of similar funds in the other Presidencies. The data—which I was favoured with an opportunity of collecting during an elaborate investigation into the position and prospects of the fund—extended over the long period of fifty years, from 1808 to 1857, and related to more than 5,000 officers who had entered the fund in that period, and had either died, or withdrawn, or were living at the close of the observations, on the 1st January, 1858. The subdivision of the facts into two periods, of those who entered from 1808 to 1822, and from 1822 to 1857, showed a very marked diminution at every quinquennial period of age in the rate of mortality up to the age of 50, after which, in the latter period, the numbers were not sufficient fairly to carry on the comparison. On the average of all ages the rate in the former period was 3·92 per cent., and in the latter 2·69 per cent., though allowance must be made for the fact that some of the latter had not attained such advanced ages.

The celebrated interminable fraction 3·14159…, which the mathematician calls π, is the ratio of the circumference to the diameter. But it is thousands of things besides. It is constantly turning up in mathematics: and if arithmetic and algebra had been studied without geometry, π must have come in somehow, though at what stage or under what name must have depended upon the casualties of algebraical invention. As it is, our trigonometry being founded on the circle, π first appears as the ratio stated. If, for instance, a deep study of probable fluctuation from the average had preceded geometry, π might have emerged as a number perfectly indispensable in such problems as—What is the chance of the number of aces lying between a million +x and a million −x, when six million of throws are made with a die? I have not gone into any detail of all those cases in which the paradoxer finds out, by his unassisted acumen, that results of mathematical investigation cannot be: in fact, this discovery is only an accompaniment, though a necessary one, of his paradoxical statement of that which must be. Logicians are beginning to see that the notion of horse is inseparably connected with that of non-horse: that the first without the second would be no notion at all. And it is clear that the positive affirmation of that which contradicts mathematical demonstration cannot but be accompanied by a declaration, mostly overtly made, that demonstration is false. If the mathematicians were interested in punishing this indiscretion, he could make his denier ridiculous by inventing asserted results which would completely take him in.

Demonville.—A Frenchman's Christian name is his own secret, unless there be two of the surname. M. Demonville is a very good instance of the difference between a French and English discoverer. In England there is a public to listen to discoveries in mathematical subjects made without mathematics: a public which will hear, and wonder, and think it possible that the pretensions of the discoverer have some foundation. The unnoticed man may possibly be right: and the old country-town reputation which I once heard of, attaching to a man who “had written a book about the signs of the zodiac which all the philosophers in London could not answer,” is fame as far it goes. Accordingly, we have plenty of discoverers, who, even in astronomy, pronounce the learned in error because of mathematics.

Mr. Baron Maseres, in the preface to his cumbrous work on the Principles of the Doctrine of Life Annuities (1783, quarto), at p. xi., after referring to and commending for its utility the method for finding the value of an annuity on (x) in terms of that of an annuity on (x + 1), has the following:—

“This method was first communicated to me by Dr. Price, but it was published in the year 1779, by Mr. William Morgan, the actuary to the Society for Equitable Assurances, near Blackfriars Bridge, in his Treatise on the Doctrine of Annuities and Assurances on Lives, pp. 56, 57; and it had been published before by Dr Price himself, in his Treatise on Reversionary Payments, Note 0 of the Appendix, and likewise by Mr. Thomas Simpson, in his book on Life Annuities, Prob. 1, Coroll. 7; which last book was published so long ago as the year 1742.