We cannot pretend to give a technical list of life assurance and annuity tables : anything we could do in this way, in any space we could give, would be professionally useless, and otherwise worse than uninstructive. We may, however, attempt to point out and to illus trate an epoch of activity which commenced about the year 1840, and which still continues. In the year 1838, the chief of the professional tables were in the well-known works of Price, Morgan, Bally, Milne, Griffith Davies, and Finlaison. The extent of tables, as judged prac ticable, went as far as annuities on two lives, for all ages differing by multiples of five years, at 3, 4, 5, and 6 per cent. Barrett's method, the greatest augmentation of resources which was ever created on this subject by any one person, was not in use for want of sufficient appli cation to acknowledged rates of mortality. Milne'a book best repre sents the laborious character of many computations which are now either reduced to insignificance, or themselves actually tabulated for reference. This valuable work (1815) was published by the author at his own expense, and with a certainty of heavy loss ; and no public acknowledgment of his merit was made, even when it had become apparent that he had changed the basis of life-tables, and introduced an important reformation by the only efficient means—the construction of a body of tables competing in extent with those already in use, and beyond challenge as to accuracy of computation. Barrett's method is nett noticed by Milne in this work ; but it only appeared in Daily's Appendix of ]S13, and Milne could hardly have had time, occupied as lie must have been with his OW11 work, to have thoroughly examined it, much less seriously contemplated the use of it.
The impulse was given by tho Useful Knowledge Society (who how ever had a colleague, as we shall ace), when they brought forward 3Ir. David Jones, and recommended, almost insisted on, a very: considerable extension of his original plan. The only tables in existence for every combination of two lives had been published by Mr. McKean, in 1837, giving on one large sheet the rates 3, 4, 5, 6 per cent., by interpolation from the Carlisle tables. Mr. Jones (whose work was completed in 1843) gave every combination for 3, 31, 4, 41,5, 6 persent., both in the annui ties, and in Barrett's subsidiary tables; that is, twelve tables for all combinations, instead of four tables * for combinations differing by multiples of five years of age : and this far from all. A short account of some of the tables since published will show that the example has been vigorously followed ; both as to the completion of things which bad been but partially done, and as to the origination of new under takings.
In saying that the Useful Knowledge Society first showed the way, in actual print, to the construction of more extensive tables, we should commit great injustice to a most daring and persevering calculator, if we omitted to notice that Mr. Edward Sang could have received no hint from their proceedings. His Assurance and Annuity Tables,' Edinburgh, 1841, large folio, give, for one life and 3 per cent., almost every deduction from the Carlisle tables which an actuary could have supposed possible to be wanted. And Mr. Sang worked with his hands l' as well as with his head. Over and above a table of five decimal logarithms and antilogarithms, every result in the book has its logarithm attached to it. And with this we have the present values of every annuity and assurance, temporary or deferred, which can be made on one life, at any age, and for any duration or deferment : together with a mass of values and premiums for other cases which wo shall not attempt to specify. In 1859, Mr. Sang published a second
volume, containing, also for 3 per cent., a body of results on two lives which meet all the actuaries' cages ; also with logarithms attached. The offices, and many of the actuaries, were at first inclined to look very coldly upon these magnificent efforts; but, so far as we have observed, we think there is now a disposition to acknowledge their utility : their merit was never denied.
Mr. Jones and Mr. Sang, independently of each other, showed that there was no occasion to be frightened at the notion of calculating and printing all the cases of a problem of two lives, or of one life for terms of years : at the time when they began their labours, a routine had been established by the consent of several distinguished writers, which consent caused ordinary calculators to look upon anything beyond the routine as next to impracticable. In 1343, Mr. T. Wigglesworth, in Carlisle Probability-Tables of the Logarithms ....' London, 8vo., gave the logarithm of the chance of surviving every number of years, at every age, from the Carlisle tables. In 1850, Mr. W. Orchard, In ' Single and Annual Assurance Premiums,' London, 8vo., gave tables for converting the value of an annuity into the single or the annual premium for a corresponding assurance ; the necessity for which often arrives in masses of instances together. The rates are 21, 3, 31, 4, 41, 5, 6, and 7 per cent.
In 1850, Mr. H. E. Filipowski, in an appendix to his work on anti logarithms, London, 8vo., gave Carlisle annuities at 3 per cent., for three joint lives, for all combinations of quinquennial ages. This is the first table of three lives : nothing more than specimens had been pre viously published.
In 1851. Messrs. P. Cray, H. A. Smith, and W. Orchard, in Assu rance and Annuity Tables,' London, 8vo., gave, for the Carlisle tables, at 3, per cent., the premium and the annual premium for every case of survivorship assurance ou two lives. In 1850, Mr. W. T. Thomson, of the (Scotch) Standard Life Assurance Company, pub lished, in fifteen:1: sheets, meant to be joined in one, what we may describe as, for the Carlisle tables at 3 per cent., a collection of Barrett's tables, one for each age in the tables : or the number living at every age of life discounted to every lower age. This table might have had its use, if Mr. Thomson himself had not superseded It, in 1853, by his book, entitled ' Actuarial Tables, Carlisle Three per cent.,' Edinburgh, 8vo., giving the ultimate elements of the old form of calculation : that is, the present value and logarithm of every year of annuity, and the logarithm of the risk of death iir each year, from and after every age. These values are put together in successive sums so that the present value of every deferred annuity, and of every deferred and temporary assurance, is gained directly from the table. A complete table of probabilities of living, logarithms and primitives both, is also given ; with some other tables. In 1858, Mr. David Chisholm, in' Commutation* Tables for Joint Annuities and Survivor ship Assurances, based on the Carlisle tables at 3, 4, 5, and 6 per cent.,' London, 2 vols., 8vo., introduced, in addition to Barrett's tables for two joint lives, the form for survivorship assurances, by which such as surances for terms of years, or when deferred, are immediately calculated. There are other efforts with which we are not acquainted : from those which we have cited, the reader may see the very great progress which the actuary's tables have made in the last twenty years.