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of the author’s life and writings, to which we refer the reader who desires fuller information. It may be mentioned here that Tetens also gave only a specimen table, apparently not imagining that persons using his work would find it extremely useful to have a series of commutation tables, calculated and printed ready for use.

The use of the commutation table was independently developed in England—apparently between the years 1788 and 1811—by George Barrett, of Petworth, Sussex, who was the son of a yeoman farmer, and was himself a village schoolmaster, and afterwards farm steward or bailiff. It has been usual to consider Barrett as the originator in England of the method of calculating the values of annuities by means of a commutation table, and this method is accordingly sometimes called Barrett’s method. (It is also called the commutation method and the columnar method.) Barrett’s method of calculating annuities was explained by him to Francis Baily in the year 1811, and was first made known to the world in a paper written by the latter and read before the Royal Society in 1812.

By what has been universally considered an unfortunate error of judgment, this paper was not recommended by the council of the Royal Society to be printed, but it was given by Baily as an appendix to the second issue (in 1813) of his work on life annuities and assurances. Barrett had calculated extensive tables, and with Baily’s aid attempted to get them published by subscription, but without success; and the only printed tables calculated according to his manner, besides the specimen tables given by Baily, are the tables contained in Babbage’s Comparative View of the various Institutions for the Assurance of Lives, 1826.

In the year 1825 Griffith Davies published his Tables of Life Contingencies, a work which contains, among others, two tables, which are confessedly derived from Baily’s explanation of Barrett’s tables.

Those who desire to pursue the subject further can refer to the appendix to Baily’s Life Annuities and Assurances, De Morgan’s paper “On the Calculation of Single Life Contingencies,” Assurance Magazine, xii. 348-349; Gray’s Tables and Formulae chap. viii.; the preface to Davies’s Treatise on Annuities; also Hendriks’s papers in the Assurance Magazine, No. 1, p. 1, and No. 2, p. 12; and in particular De Morgan’s “Account of a Correspondence between Mr George Barrett and Mr Francis Baily,” in the Assurance Magazine, vol. iv. p. 185.
The principal commutation tables published in England are contained in the following works:—David Jones, Value of Annuities and Reversionary Payments, issued in parts by the Useful Knowledge Society, completed in 1843; Jenkin Jones, New Rate of Mortality, 1843; G. Davies, Treatise on Annuities, 1825 (issued 1855); David Chisholm, Commutation Tables, 1858; Nelson’s Contributions to Vital Statistics, 1857; Jardine Henry, Government Life Annuity Commutation Tables, 1866 and 1873; Institute of Actuaries Life Tables, 1872; R. P. Hardy, Valuation Tables, 1873; and Dr William Farr’s contributions to the sixth (1844), twelfth (1849), and twentieth (1857) Reports of the Registrar General in England (English Tables, 1. 2), and to the English Life Table, 1864.
The theory of annuities may be further studied in the discussions in the English Journal of the Institute of Actuaries. The institute was founded in the year 1848, the first sessional meeting being held in January 1849. Its establishment has contributed in various ways to promote the study of the theory of life contingencies. Among these may be specified the following:—Before it was formed, students of the subject worked for the most part alone, and without any concert; and when any person had made an improvement in the theory, it had little chance of becoming publicly known unless he wrote a formal treatise on the whole subject. But the formation of the institute led to much greater interchange of opinion among actuaries, and afforded them a ready means of making known to their professional associates any improvements, real or supposed, that they thought they had made. Again, the discussions which follow the reading of papers before the institute have often served, first, to bring out into bold relief differences of opinion that were previously unsuspected, and afterwards to soften down those differences,—to correct extreme opinions in every direction, and to bring about a greater agreement of opinion on many important subjects. In no way, probably, have the objects of the institute been so effectually advanced as by the publication of its Journal. The first number of this work, which was originally called the Assurance Magazine, appeared in September 1850, and it has been continued quarterly down to the present time. It was originated by the public spirit of two well-known actuaries (Mr Charles Jellicoe and Mr Samuel Brown), and was adopted as the organ of the Institute of Actuaries in the year 1852, and called the Assurance Magazine and Journal of the Institute of Actuaries, Mr Jellicoe continuing to be the editor,—a post he held until the year 1867, when he was succeeded by Mr T. B. Sprague (who contributed to the 9th edition of this Encyclopaedia an elaborate article on “Annuities,” on which the above account is based). The name was again changed in 1866, the words “Assurance Magazine” being dropped; but in the following year it was considered desirable to resume these, for the purpose of showing the continuity of the publication, and it is now called the Journal of the Institute of Actuaries and Assurance Magazine. This work contains not only the papers read before the institute (to which have been appended of late years short abstracts of the discussions on them), and many original papers which were unsuitable for reading, together with correspondence, but also reprints of many papers published elsewhere, which from various causes had become difficult of access to the ordinary reader, among which may be specified various papers which originally appeared in the Philosophical Transactions, the Philosophical Magazine, the Mechanics’ Magazine, and the Companion to the Almanac; also translations of various papers from the French, German, and Danish. Among the useful objects which the continuous publication of the Journal of the institute has served, we may specify in particular two:—that any supposed improvement in the theory was effectually submitted to the criticisms of the whole actuarial profession, and its real value speedily discovered; and that any real improvement, whether great or small, being placed on record, successive writers have been able, one after the other, to take it up and develop it, each commencing where the previous one had left off.

ANNULAR, ANNULATE, &c. (Lat. annulus, a ring), ringed. “Annulate” is used in botany and zoology in connexion with certain plants, worms, &c. (see Annelida), either marked with rings or composed of ring-like segments. The word “annulated” is also used in, heraldry and architecture. An annulated cross is one with the points ending in an “annulet” (an heraldic ring, supposed to be taken from a coat of mail), while the annulet in architecture is a small fillet round a column, which encircles the lower part of the Doric capital immediately above the neck or trachelium. The word “annulus” (for “ring”) is itself used technically in geometry, astronomy, &c., and the adjective “annular” corresponds. An annular space is that between an inner and outer ring. The annular finger is the ring finger. An annular eclipse is an eclipse of the sun in which the visible part of the latter completely encircles the dark body of the moon; for this to happen, the centres of the sun and moon, and the point on the earth where the observer is situated, must be collinear. Certain nebulae having the form of a ring are also called “annular.”

ANNUNCIATION, the announcement made by the angel Gabriel to the Virgin Mary of the incarnation of Christ (Luke i, 26-38). The Feast of the Annunciation in the Christian Church is celebrated on the 25th of March. The first authentic allusions to it are in a canon, of the council of Toledo (656), and another of the council of Constantinople “in Trullo” (692), forbidding the celebration of all festivals in Lent, excepting the Lord’s day and the Feast of the Annunciation. An earlier origin has been claimed for it on the ground that it is mentioned in sermons of Athanasius and of Gregory Thaumaturgus, but both of these documents are now admitted to be spurious. A synod held at Worcester, England (1240), forbade all servile work on this feast day. See further Lady Day.

ANNUNZIO, GABRIELE D’ (1863-  ), Italian novelist and poet, of Dalmatian extraction, was born at Pescara (Abruzzi) in 1863. The first years of his youth were spent in the freedom of the open fields; at sixteen he was sent to school in Tuscany. While still at school he published a small volume of verses called Primo Vere (1879), in which, side by side with some almost brutal imitations of Lorenzo Stecchetti, the then fashionable poet of Postuma, were some translations from the Latin, distinguished by such agile grace that Giuseppe Chiarini on reading them brought the unknown youth before the public in an enthusiastic article. The young poet then went to Rome, where he was received as one of their own by the Cronaca Bizantina group (see Carducci). Here he published Canto Nuovo (1882), Terra Vergine (1882), L’ Intermezzo di Rime (1883), Il Libro delle Vergini (1884), and the greater part of the short stories that were afterwards collected under the general title of San Pantaleone (1886). In Canto Nuovo we have admirable poems full of pulsating youth and the promise of power, some descriptive