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alimentary canal, and a double ventral ganglionated chain, a as the 6th of January 1900, the high commissioner at Cape Town definito vascular system, an excretory system consisting of issued a proclamation giving notice that H. M. government would nephridia, and paired generative organs formed from the coelomic “not recognize as valid or effectual" any conveyance, transfer epithelium. They are divided as follows: (1) Haplodrili (9.0.) or transmission of any property made by the government of the or Archiannelida; (2) Chaetopoda (9.0.); (3) Myzostomida (9.0.), Transvaal republic or Orange Free State subsequently to the noth probably degenerate Polychaeta; (4) Hirudinea (see CHAETOPODA of October 1899, the date of the commencement of the war. A and LEECH); (5) Echiuroidea (q.v.).

(P.C.M.) proclamation forbidding transactions with a state which might ANNET, PETER (1693-1769), English deist, is said to have been still be capable of maintaining its independence could obviously born at Liverpool. A schoolmaster by profession, he became bind only those subject to the authority of the state issuing it. prominent owing to his attacks on orthodox theologians, and his Like paper blockades (see BLOCKADE) and fictitious occupations membership of a semi-theological debating society, the Robin of territory, such premature proclamations are viewed by internaHood Society, which met at the “Robin Hood and Little John” tional jurists as not being jure gentium. The proclamation was in Butcher Row. To him has been attributed a work called A succeeded, on the 9th of March 1900, by another of the high History of the Monafter God's own Heart (1761), intended to show commissioner at Cape Town, reiterating the notice, but confining that George II. was insulted by a current comparison with David. it to "lands, railways, mines or mining rights." And on the ist

The book is said to have inspired Voltaire's Saul. It is also of September 1900 Lord Roberts proclaimed at Pretoria the attributed to one John Noorthouck (Noorthook). In 1763 he was annexation of the territories of the Transvaal republic to the condemned for blasphemous libel in his paper called the Free British dominions. That the war continued for nearly two years Enquirer (nine numbers only). After his release he kept a small after this proclamation shows how fictitious the claim of annexaschool in Lambeth, one of his pupils being James Stephen (1758- tion was. The difficulty which arose out of the transfer of the 1832), who became master in Chancery. Annet died on the 18th South African Railway shares held by the Transvaal government of January 1769. He stands between the earlier philosophic was satisfactorily terminated by the purchase by the British deists and the later propagandists of Paine's school, and “seems government of the total capital of the company from the different to have been the first freethought lecturer" (J. M. Robertson); groups of shareholders (see on this case, Sir Thomas Barclay, Law his essays (A Collection of the Trads of a cerlain Free Enquirer, Quarterly Review, July 1905; and Professor Westlake, in the same 1739-1745) are forcible but lack refinement. He invented a Review, October 1905). system of shorthand (2nd ed., with a copy of verses by Joseph In a judgment of the judicial committee of the privy council in Priestley).

1899 (Coole v. Sprigg, A.C. 572), Lord Chancellor Halsbury made ANNEXATION (Lat. ad, to, and nexus, joining), in interna- an important distinction as regards the obligations of state tional law, the act by which a state adds territory to its dominions; succession. The case in question was a claim of title against the the term is also used generally as a synonym for acquisition. The crown, represented by the government of Cape Colony. It was assumption of a protectorate over another state, or of a sphere of made by persons holding a concession of certain rights in eastern influence, is not strictly annexation, the latter implying the Pondoland from a native chief. Before the grantees had taken up complete displacement in the annexed territory of the government their grant by acts of possession, Pondoland was annexed to Cape or state by which it was previously ruled. Annexation may be Colony. The colonial government refused to recognize the grant the consequence of a voluntary cession from one state to another, on different grounds, the chief of them being that the concession or of conversion from a protectorate or sphere of influence, or of conferred no legal rights before the annexation and therefore mere occupation in uncivilized regions, or of conquest. The could conser none afterwards, a sufficiently good ground in itself. cession of Alsace-Lorraine to Germany by France, although The judicial committee, however, rested its decision chiefly on the brought about by the war of 1870, was for the purposes of interna allegation that the acquisition of the territory was an act of state tional law a voluntary cession. Under the treaty of the 17th of and that “no municipal court had authority to enforce such an December 1885, between the French republic and the queen of obligation " as the duty of the new government to respect existing Madagascar, a French protectorate was established over this titles. “It is no answer,” said Lord Halsbury, “ to say that by island. In 1896 this protectorate was converted by France into the ordinary principles of international law private property is an annexation, and Madagascar then became“ French territory." respected by the sovereign which accepts the cession and assumes The formal annexation of Bosnia-Herzegovina by Austria (Oct.5, the duties and legal obligations of the former sovereign with 1908) was an unauthorized conversion of an “occupation respect to such private property within the ceded territory. AU authorized by the Treaty of Berlin (1878), which had, however, that can be meant by such a proposition is that according to the for years operated as a de facto annexation. A recent case of well-understood rules of international law a change of sovereignty conquest was that cffected by the South African War of 1899- by cession ought not to affect private property, but no municipal 1902, in which the Transvaal republic and the Orange Free tribunal has authority to enforce such an obligation. And if State were extinguished, first de facto by occupation of the whole there is either an express or a well-understood bargain between of their territory, and then de jure by terms of surrender entered the ceding potentate and the government to which the cession is into by the Boer generals acting as a government.

made that private property shall be respected, that is only a By annexation, as between civilized peoples, the annexing state bargain which can be enforced by sovereign against sovereign in takes over the whole succession with the rights and obligations the ordinary course of diplomatic pressure.” In an editorial note attaching to the ceded territory, subject only to any modifying on this case the Low Quarterly Review of Jan. 1900 (p. 1), conditions contained in the treaty of cession. These, however, dissenting from the view of the judicial committee that "no are binding only as between the parties to them. In the case of municipal tribunal has authority to enforce such an obligation," the annexation of the territories of the Transvaal republic and the writer observes that." we can read this only as meant to lay Orange Free State, a rather complicated situation arose out of down that, on the annexation of territory even by peaceable the facts, on the one hand, that the ceding states closed their own cession, there is a total abeyance of justice until the will of the existence and left no recourse to third parties against the previous annexing power is expressly made known; and that, although ruling authority, and, on the other, that, having no means owing the will of that power is commonly to respect existing private to the de facto British occupation, of raising money by taxation, rights, there is no rule or presumption to that effect of which any the dispossessed governments raised money by selling certain court must or indeed can take notice.” So construed the doctrine securities, more especially a large holding of shares in the South is not only contrary to international law, but according to so African Railway Company, to neutral purchasers. The British authoritative an exponent of the common law as Sir F. Pollock, government repudiated these sales as having been made by a there is no warrant for it in English common law. government which the British government had already displaced. An interesting point of American constitutional law has arisen The question of at what point, in a war of conquest, the state out of the cession of the Philippines to the United States, through succession becomes operative is one of great delicacy. As early the fact that the federal constitution does not lend itself to the

exercise by the federal congress of unlimited powers, such as are ANNO, or HANNO, SAINT (C. 1010-1075),archbishop of Cologne, vested in the British parliament. The sole authority for the belonged to a Swabian family, and was educated at Bamberg: powers of the federal congress is a written constitution with He became confessor to the emperor Henry III., who appointed defined powers. Anything done in excess of those powers is null him archbishop of Cologne in 1056. He took a prominent part in and void. The Supreme Court of the United States, on the other thegovernmentor Germany during the minorityof King Henry IV., hand, has declared that, by the constitution, a government is and was the leader of the party which in 1062 seized the person ordained and established " for the United States of America ” of Henry, and deprived his mother, the empress Agnes, of and not for countries outside their limits (Ross's Case, 140 U.S. power. For a short time Anno exercised the chief authority in 453, 464), and that no such power to legislate for annexed the kingdom, but he was soon obliged to share this with Adalbert, territories as that vested in the British crown in council is enjoyed archbishop of Bremen, retaining for himself the supervision of by the president of the United States (Field v. Clark, 143 U.S. 649, Henry's education and the title of magister. The office of 692). Every detail connected with the administration of the chancellor of the kingdom of Italy was at this period regarded as territories acquired from Spain under the treaty of Paris an appanage of the archbishopric of Cologne, and this was probably (December 10, 1898) has given rise to minute discussion. the reason why Anno had a considerable share in setting the

See Carman F. Randolph, Law and Policy of Annexation (New York papal dispute in 1064. He declared Alexander II. to be the and London, 1901); Charles Henry Butler, Treaty-making Power of rightful pope at a synod held at Mantua in May 1064, and took the United States (New York, 1902), vol. i. p. 79 et seq. (T. BA.)

other steps to secure his recognition. Returning to Germany, ANNICERIS, a Greek philosopher of the Cyrenaic school. he found the chief power in the hands of Adalbert, and as he was There is no certain information as to his date, but from the disliked by the young king, he left the court but returned and statement that he was a disciple of Paraebates it seems likely regained some of his former influence when Adalbert fell from that he was a contemporary of Alexander the Great. A follower of power in 1066. He succeeded in putting down a rising against Aristippus, he denied that pleasure is the general end of human his authority in Cologne in 1074, and it was reported he had life. To each separate action there is a particular end, namely allied himself with William the Conqueror, king of England, the pleasure which actually results from it Secondly, pleasure against the emperor. Having cleared himself of this charge, is not merely the negation of pain, inasmuch as death ends all Anno took no further part in public business, and died at Cologne pain and yet cannot be regarded as pleasure. There is, however, on the 4th of December 1075. He was buried in the monastery of an absolute pleasure in certain virtues such as belong to the love Siegburg and was canonized in 1183 by Pope Lucius III. He of country, parents and friends. In these relations a man will was a founder of monasteries and a builder of churches, advocated have pleasure, even though it may result in painful and even clerical celibacy and was a strict disciplinarian. He was a man fatal consequences. Friendship is not merely for the satisfaction of great energy and ability, whose action in recognizing Alexander of our needs, but is in itself a source of pleasure. He maintains II. was of the utmost consequence for Henry IV, and for further, in opposition to most of the Cyrenaic school, that Germany. wisdom or prudence alone is an insufficient guarantee against There is a Vita Annonis, written about 1100, by a monk of Siegerror. The wise man is he who has acquired a habit of wise burg, but this is of slight value. It appears in the Monumenia action; human wisdom is liable to lapses at any moment. Germaniae historica: Scriptores, Bd. xi. (Hanover and Berlin, Diogenes Laertius says that Anniceris ransomed Plato from 1826-1892). There is an "Epistola ad monachos Malmundarienses”

by Anno in' the Neues Archiv der Gesellschaft für ältere deutsche Dionysius, tyrant of Syracuse, for twenty minas. If we are Geschichtskunde, Bd. xiv. (Hanover, 1876 seq.). See also the right in placing Anniceris in the latter half of the 4th century, Annolied, or Incerti poe Teutonici rhythmus de S. Annone, written it is clear that the reference here is to an earlier Anniceris, who, about 1180, and edited by J: Kehrein (Frankfort, 1865); Th. according to Aelian, was a celebrated charioteer.

Lindner, Anno II. der Heilige, Ersbischof von Koln (Leipzig, 1869). ANNING, MARY (1799–1847), English fossil-collector, the ANNOBON, or Anno Bom, an island in the Gulf of Guinea, in daughter of Richard Anning, a cabinet-maker, was born at Lyme 1° 24' S. and 5° 35' E., belonging to Spain. It is 110 m. S.W. of Regis in May 1799. Her father was one of the earliest collectors St Thomas. Its length is about 4 m., its breadth 2, and its and dealers in fossils, obtained chiefly from the Lower Lias in that area 6 sq. m. Rising in some parts nearly 3000 ft. above famous locality. When but a child in 181 she discovered the the sea, it presents a succession of beautiful valleys and first specimen of Ichthyosaurus which was brought into scientific steep mountains, covered with rich woods and luxuriant notice; in 1821 she found remains of a new saurian; the vegetation. The inhabitants, some 3000 in number, are negroes Plesiosaurus,and in 1828 she procured, for the first time in England, and profess belief in the Roman Catholic faith. The remains of a pterodactyl (Dimor phodon). She died on the oth chief town and residence of the governor is called St Antony of March 1847.

(San Antonio de Praia). The roadstead is tolerably safe, and ANNISTON, a city and the county seat of Calhoun county, passing vessels take advantage of it in order to obtain water Alabama, U.S.A., in the north-eastern part of the state, about and fresh provisions, of which Annobon contains an abundant 63 m. E. by N. of Birmingham. Pop. (1890) 9998; (1900), supply. The island was discovered by the Portuguese on the 9695, of whom 3669 were of negro descent: (1910 census) 1st of January 1473, from which circumstance it received its 12,794. Anniston is served by the Southern, the Seaboard name (= New Year). Annobon, together with Fernando Po, was Air Line, and the Louisville & Nashville railways. The city is ceded to Spain by the Portuguese in 1778. The islanders revolted situated on the slope of Blue Mountain, a chain of the Blue against their new masters and a state of anarchy ensued, leading, Ridge, and is a health resort. It is the seat of the Noble Institute it is averred, to an arrangement by which the island was adminis(for girls), established in 1886 by Samuel Noble (1834–1888), a tered by a body of five natives, each of whom held the office of wealthy iron-founder, and of the Alabama Presbyterian College governor during the period that elapsed till ten ships touched at for Men (1905). There are vast quantities of iron ore in the the island. In the latter part of the 19th century the authority vicinity of the city, the Coosa coal-fields being only 25 m. distant. of Spain was re-established. Anniston is an important manufacturing city, the principal ANNONA (from Lat. annus, ycar), in Roman mythology, the industries being the manufacture of iron, steel and cotton. In personification of the produce of the year. She is represented 1905 the city's factory products were valued at $2,525,455. in works of art, often together with Ceres, with a cornucopia An iron furnace was established on the site of Anniston during the (horn of plenty) in her arm, and a ship's prow in the backCivil War, but it was destroyed by the federal troops in 1865; ground, indicating the transport of grain over the sea. She and in 1872 it was rebuilt on a much larger scale. The city was frequently occurs on coins of the empire, standing between a founded in 1872 as a private enterprise, by the Woodstock Iron modius (corn-measure) and the prow of a galley, with ears of corn Company, organized by Samuel Noble and Gen. Daniel Tyler in one hand and a cornucopia in the other; sometimes she holds (1799–1882); but it was not opened for general settlement until a rudder or an anchor, The Latin word itself has various meantwelve years later. It was chartered as a city in 1879. ings: (1) the produce of the year's harvest; (a) all means of

subsistence, especially grain stored in the public granaries for is considered as accruing during each instant of the status for provisioning the city; (3) the market price of commodities, which it is enjoyed, although it is only payable at fixed intervals. especially corn; (4) a direct tax in kind, levied in republican If the enjoyment of an annuity is postponed until after the lapse times in several provinces, chiefly employed in imperial times of a certain number of years, the annuity is said to be deferred. for distribution amongst officials and the support of the soldiery. If an annuity, instead of being payable at the end of each year,

In order to ensure a supply of corn sufficient to enable it to be half-year, &c., is payable in advance, it is called an annuity-due. sold at a very low price, it was procured in large quantities from If an annuity is payable for a term of years independent of Umbria, Etruria and Sicily. Almost down to the times of the any contingency, it is called an annuily certain; if it is to conempire, the care of the corn-supply formed part of the aedile's tinue for ever, it is called a perpetuily; and if in the latter case duties, although in 440 B.C. (if the statement in Livy iv. 12, 13 it is not to commence until after a term of years, it is called a is correct, which is doubtful) the senate appointed a special deferred perpetuity. An annuity depending on the continuance officer, called praefectus annonae, with greatly extended powers. of an assigned life or lives, is sometimes called a life annuity; As a consequence of the second Punic War, Roman agriculture but more commonly the simple term “annuity” is understood was at a standstill; accordingly, recourse was had to Sicily and to mean a life annuity, unless the contrary is stated. A life Sardinia (the first two Roman provinces) in order to keep up the annuity, to cease in any event after a certain term of years, is supply of corn; a tax of one-tenth was imposed on it, and its called a lemporary annuity. The holder of an annuity is called export to any country except Italy forbidden. The price at an annwtant, and the person on whose life the annuity depends which the corn was sold was always moderate; the corn law of is called the nominee. Gracchus (123 B.C.) made it absurdly low, and Clodius (58 B.C.) If not otherwise stated, it is always understood that an annuity bestowed it gratuitously. The number of the recipients of this is payable yearly, and that the annual payment (or rent, as it is free gift grew so enormously, that both Caesar and Augustus were sometimes called) is £1. It is, however, customary to consider obliged to reduce it. From the time of Augustus to the end of the annual payment to be, not £1, but simply 1, the reader the empire the number of those who were entitled to receive a supplying whatever monetary unit he pleases, whether pound, monthly allowance of corn on presenting a ticket was 200,000. dollar, franc, Thaler, &c. In the 3rd century, bread formed the dole. A praefectus annonae The annuity is the totality of the payments to be made (and was appointed by Augustus to superintend the corn-supply; he received), and is so understood by all writers on the subject; was assisted by a large staff in Rome and the provinces, and had but some have also used the word to denote an individual jurisdiction in all matters connected with the corn-market. The payment (or rent), speaking, for instance, of the first or second Office lasted till the latest times of the empire.

year's annuity,-a practice which is calculated to introduce ANNONAY, a town of south-eastern France, in the north of the confusion and should therefore be carefully avoided. department of Ardèche, so m. S. of Lyons by the Paris-Lyons Instances of perpetuities are the dividends upon the public railway. Pop. (1906) 15,403. Annonay is built on the hill stocks in England, France and some other countries. Thus, overlooking the meeting of the deep gorges of the Déome and the although it is usual to speak of £100 consols, the reality is the Cance, the waters of which supply power to the factories of the yearly dividend which the government pays by quarterly instal. town. By means of a dam across the Ternay, an affluent of the ments. The practice of the French in this, as in many other Déôme, to the north-west of the town, a reservoir is provided, matters, is more logical. In speaking of their public funds (rentes) in which an additional supply of water, for both industrial and they do not mention the ideal capital sum, but speak of the domestic purposes, is stored. At Annonay there is an obelisk annuity or annual payment that is received by the public in honour of the brothers Montgolfier, inventors of the balloon, creditor. Other instances of perpetuities are the incomes derived who were natives of the place. A tribunal of commerce, a board from the debenture stocks of railway companies, also the feuof trade-arbitrators, a branch of the Bank of France, and duties commonly payable on house property in Scotland. The chambers of commerce and of arts and manufactures are among number of years' purchase which the perpetual annuities granted the public institutions. Annonay is the principal industrial by a government or a railway company realize in the open centre of its department, the chief manufactures being those of market, forms a very simple test of the credit of the various leather, especially for gloves, paper, silk and silk goods, and governments or railways. flour. Chemical manures, glue, gelatine, brushes, chocolate and Terminable Annuities are employed in the system of British candles are also produced.

public finance as a means of reducing the National Debt (9.0.). ANNOY (like the French ennui, a word traced by etymologists This result is attained by substituting for a perpetual annual to a Lat. phrase, in odio esse, to be “in hatred” or hateful of charge (or one lasting until the capital which it represents can someone), to vex or affect with irritation. In the sense of be paid off en bloc), an annual charge of a larger amount, but

nuisance," the noun annoyance," apart from its obvious lasting for a short term. The latter is so calculated as to pay off, meaning, is found in the English “ Jury of Annoyance" during its existence, the capital which it replaces, with interest appointed by an act of 1754 to report upon obstructions in the at an assumed or agreed rate, and under specified conditions. highways.

The practical effect of the substitution of a terminable annuity ANNUITY (from Lat. annus, a year), a periodical payment, for an obligation of longer currency is to bind the present generamade annually, or at more frequent intervals, either for a fixed tion of citizens to increase its own obligations in the present and term of years, or during the continuance of a given life, or a com near future in order to diminish those of its successors. This bination of lives. In technical language an annuity is said to be end might be attained in other ways; for instance, by setting payable for an assigned stalus, this being a general word chosen aside out of revenue a fixed annual sum for the purchase and in preference to such words as “time," "term" or "period,” cancellation of debt (Pitt's method, in intention), or by fixing because it may include more readily either a term of years the annual debt charge at a figure sufficient to provide a margin certain, or a life or combination of lives. The magnitude of the for reduction of the principal of the debt beyond the amount annuity is the sum to be paid (and received) in the course of each required for interest (Sir Stafford Northcote's method), or by year. Thus, if £100 is to be received each year by a person, he is providing an annual surplus of revenue over expenditure (the said to have“ an annuity of £100." If the payments are made 'Old Sinking Fund "), available for the same purpose. All half-yearly, it is sometimes said that he has “a half-yearly these methods have been tried in the course of British financial annuity of £100"; but to avoid ambiguity, it is more commonly history, and the second and third of them are still employed; said he has an annuity of £100, payable by half-yearly instal. but on the whole the method of terminable annuities bas been ments. The former expression, if clearly understood, is prefer the one preferred by chancellors of the exchequer and by parliaable on account of its brevity. So we may have quarterly, ment. monthly, weekly, daily annuities, when the annuity is payable Terminable annuities, as employed by the British government, by quarterly, monthly, weekly or daily instalments. An annuity fall under two heads :-(o) Those issued to, or held by private

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persons; (b) those held by government departments or by funds papers contributed by Frederick Hendriks to the Assurance under government control. The important difference between Magazine, vol. ii. p. 222, and vol. iii. p. 93. The former of these these two classes is that an annuity under (@), once created, contains a translation of De Witt's report upon the value of life cannot be modified except with the holder's consent, i.e. is annuities, which was prepared in consequence of the resolution practically unalterable without a breach of public faith; whereas passed by the states-general, on the 25th of April 1671, to negoan annuity under (6) can, if necessary, be altered by inter- tiate funds by life annuities, and which was distributed to the departmental arrangement under the authority of parliament. members on the 30th of July 1671. The latter contains the Thus annuities of class (c) fulfil most perfectly the object of the translation of a number of letters addressed by De Witt to system as explained above; while those of class (6) have the Burgomaster Johan Hudde, bearing dates from September 1670 advantage that in times of emergency their operation can be to October 1671. The existence of De Witt's report was well suspended without any inconvenience or breach of faith, with known among his contemporaries, and Hendriks collected a the result that the resources of government can on such occasions number of extracts from various authors referring to it; but the be materially increased, apart from any additional taxation. For this purpose it is only necessary to retain as a charge on the

TABLE OF MORTALITY-HM, HEALTHY Lives—MALE. income of the year a sum equal to the (smaller) perpetual charge Number Living and Dying al each Age, oul of 10,000 which was originally replaced by the (larger) terminable charge,

entering at Age 10. whereupon the difference between the two amounts is temporarily

Age. Living. released, while ultimately the increased charge is extended for

Dying. Age. Living Dying. a period equal to that for which it is suspended. Annuities of

10,000

79
54 6791

129 class (@) were first instituted in 1808, but are at present mainly

9,921

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153 9.921 40

6509 150 regulated by an act of 1829. They may be granted either for

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152 a specified life, or two lives, or for an arbitrary term of years; 14

6207 156 and the consideration for them may take the form either of cash 15

6051 153

16 or of government stock, the latter being cancelled when the

9.784

5898 184 9,784

5714

186 annuity is set up. Annuities (6) held by government departments

9.743

5528 191 date from 1863. They have been created in exchange for per 19 9,684

5337 manent debt surrendered for cancellation, the principal opera

5137 tions having been effected in 1863, 1867, 1870, 1874, 1883. and

4931

215

9,493 1899. Annuities of this class do not affect the public at all,

23
9.434

73 except of course in their effect on the market for government 24 9.361

4276

237 securities. They are merely financial operations between the 25 9,297

4039 246

26 government, in its capacity as the banker of savings banks and

9,249

70
3793

213 9,185

71 other funds, and itself, in the capacity of custodian of the national

28 9,125

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268 finances. Savings bank depositors are not concerned with the

9,054

73 3090 243 manner in which government invests their money, their rights

8,987 74

74 2847 300 being confined to the receipt of interest and the repayment of

31
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75
2547

241 8,848 74

2306 deposits upon specified conditions. The case is, however,

245 33 8,774 73

2061

224 different as regards forty millions of consols (included in the

8,701
76

1837 above figures), belonging to suitors in chancery, which were 35 8,625

79

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36 cancelled and replaced by a terminable annuity in 1883. As the

8,554 75

80

1392 196 37 8,479 81

1196

191 liability to the suitors in that case was for a specified amount of

8,398 87

1005

173 stock, special arrangements were made to ensure the ultimate 39

8.311

88
83

832 172 replacement of the precise amount of stock cancelled.

40
8,223

84
660

119 Annuity Calculations.—The mathematical theory of life

41
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541

117 42 8,057

424 annuities is based upon a knowledge of the rate of mortality 43

7.970

87
332

72 among mankind in general, or among the particular class of 44

7,886
93

74 persons on whose lives the annuities depend. It involves a 45

7.793
97

186

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46 mathematical treatment too complicated to be dealt with fully

7,696 96

90

150
47
7,600

107 in this place, and in practice it has been reduced to the form of

48
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80 tables, which vary in different places, but which are easily 49 7,387 113

93

44 accessible. The history of the subject may, however, be sketched. 50

7,274

15 Abraham Demoivre, in his Annuities on Lives, propounded a very

51
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7,030 simple law of mortality which is to the effect that, out of 86

53 6,910 children born alive, I will die every year until the last dies between the ages of 85 and 86. This law agreed sufficiently well report is not contained in any collection of his works extant, and at the middle ages of life with the mortality deduced from the had been entirely lost for 180 years, until Hendriks discovered it best observations of his time; but, as observations became more among the state archives of Holland in company with the letters exact, the approximation was found to be not sufficiently close to Hudde. It is a document of extreme interest, and (notwithThis was particularly the case when it was desired to obtain the standing some inaccuracies in the reasoning) of very great merit, value of joint life, contingent or other complicated benefits. more especially considering that it was the very first document Therefore Demoivre's law is entirely devoid of practical utility on the subject that was ever written. No simple formula has yet been discovered that will represent It appears that it had long been the practice in Holland for the rate of mortality with sufficient accuracy.

life annuities to be granted to nominees of any age, in the conThe rate of mortality at each age is, therefore, in practice stant proportion of double the rate of interest allowed on stock: usually determined by a series of figures deduced from observa- that is to say, if the towns were borrowing money at 6 %, they tion; and the value of an annuity at any age is found from these would be willing to grant a life annuity at 12%, and so on. numbers by means of a series of arithmetical calculations. The De Witt states that “annuities have been sold, even in the mortality table here given is an example of modern use.

present century, first at six years' purchase, then at seven and The first writer who is known to have attempted to obtain, on eight; and that the majority of all life annuities now current correct mathematical principles, the value of a lise annuity, was at the country's expense were obtained at nine years' purchase "; Jan De Witt, grand pensionary of Holland and West Friesland. but that the price had been increased in the course of a few Our knowledge of his writings on the subject is derived from two l years from eleven years' purchase to twelve, and from twelve to

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16

upwards!

fourteen. He also states that the rate of interest had been mere conjectural estimates. The earliest known reference to successively reduced from 64 to 5 %, and then to 4 %. The any estimate of the value of life annuities rose out of the requireprincipal object of his report is to prove that, taking interest at ments of the Falcidian law, which (40 B.C.) was adopted in the 4%, a life annuity was worth at least sixteen years' purchase; Roman empire, and which declared that a testator should not and, in fact, that an annuitant purchasing an annuity for the give more than three-fourths of his property in legacies, so that life of a young and healthy nominee at sixteen years' purchase, at least one-fourth must go to his legal representatives. It is made an excellent bargain. It may be mentioned that he argues easy to see how it would occasionally become necessary, while that it is more to the advantage, both of the country and of the this law was in force, to value life annuities charged upon a private investor, that the public loans should be raised by way of testator's estate. Aemilius Macer (A.D. 230) states that the grant of life annuities rather than perpetual annuities. It appears method which had been in common use at that time was as conclusively from De Witt's correspondence with Hudde, that follows:- From the earliest age until 30 take 30 years' purchase, the rate of mortality assumed as the basis of his calculations and for each age after 30 deduct 1 year. It is obvious that no was deduced from careful examination of the mortality that had consideration of compound interest can have entered into this actually prevailed among the nominees on whose lives annuities estimate; and it is easy to see that it is equivalent to assuming had been granted in former years. De Witt appears to have that all persons who attain the age of 30 will certainly live to come to the conclusion that the probability of death is the the age of 60, and then certainly die. Compared with this estisame in any half-year from the age of 3 to 53 inclusive; that mate, that which was propounded by the praetorian prefect in the next ten years, from 53 to 63, the probability is greater Ulpian was a great improvement. His table is as follows:in the ratio of 3 to 2; that in the next ten years, from 63 to 73, it is greater in the ratio of 2 to 1; and in the next seven years,

Years'

Years'
Age.
Purchase.

Age.

Purchase. from 73 to 80, it is greater in the ratio of 3 to ; and he places the limit of human life at 80. If a mortality table of the usual

Birth to 20

30
45 to 46

14 form is deduced from these suppositions, out of 212 persons

46 47 alive at the age of 3, 2 will dic every year up to 53, 3 in each of

25 , 30 25

47, 48 30 i 35

48

49 the ten years from 53 to 63, 4 in each of the next ten years from:

35 .. 40

49, 50 63 to 73, and 6 in each of the next seven years from 73 to 80,

40. 41

50 . 55 when all will be dead.

41 , 42

18

55 ,- 60 De Witt calculates the value of an annuity in the following

42, 43

17
60 and

3

43 . 44 way. Assume that annuities on 10,000 lives each ten years of

44. 45

15 age, which satisfy the Hm mortality table, have been purchased. Of these nominees 79 will die before attaining the age of 11, Here also we have no reason to suppose that the element of and no annuity payment will be made in respect of them; none interest was taken into consideration; and the assumption, will die between the ages of 11 and 12, so that annuities will be that between the ages of 40 and 50 each addition of a year to the paid for one year on 9921 lives; 40 attain the age of 12 and nominee's age diminishes the value of the annuity by one year's die before 13, so that two payments will be made with respect purchase, is equivalent to assuming that there is no probability to these lives. Reasoning in this way we see that the annuities of the nominee dying between the ages of 40 and 50. Conon 35 of the nominees will be payable for three years; on 40 sidered, however, simply as a table of the average duration of for four years, and so on. Proceeding thus to the end of the life, the values are fairly accurate. At all events, no more table, 15 nominees attain the age of 95, 5 of whom die before correct estimate appears to have been arrived at until the close the age of 96, so that 85 payments will be paid in respect of of the 17th century. these 5 lives. Of the survivors all die before attaining the age The mathematics of annuities has been very fully treated in of 97, so that the annuities on these lives will be payable for 86 Demoivre's Treatise on Annuities (1725); Simpson's Doctrine of years. Having previously calculated a table of the values of Annuities and Reversions (1742); P. Gray, Tables and formulae; annuities certain for every number of years up to 86, the value compilations of Valuation Tables and Interest Tables, by means of

Baily's Doctrine of Life Annuilics; there are also innumerable of all the annuities on the 10,000 nominees will be found by which the value of an annuity at any age and any rate of interest taking 40 times the value of an annuity for 2 years, 35 times may be found. See also the article INTEREST, and especially that on the value of an annuity for 3 years, and so on-the last term

INSURANCE. being the value of 10 annuities for 86 years—and adding them Commulation lables, aptly so named in 1840 by Augustus together; and the value of an annuity on one of the nominees De Morgan (see his paper “ On the Calculation of Single Life will then be found by dividing by 10,000. Before leaving the Contingencies," Assurance Magasine, xii. 328), show the proporsubject of De Witt, we may mention that we find the corre- tion in which a benefit due at one age ought to be changed, spondence a distinct suggestion of the law of mortality that so as to retain the same value and be due at another age. The bears the name of Demoivre. In De Witt's letter, dated the earliest known specimen of a commutation table is contained 27th of October 1671 (Ass. Mag. vol. iii. p. 107), he speaks of a in William Dale's Introduction to the Study of the Doctrine of “provisional hypothesis " suggested by Hudde, that out of Annuilies, published in 1772. A full account of this work is 80 young lives (who, from the context, may be taken as of the given by F. Hendriks in the second number of the Assurance age 6) about 1 dies annually. In strictness, therefore, the law Magazine, pp. 15-17. William Morgan's Trealise on Assurances, in question might be more correctly termed Hudde's than 1779, also contains a commutation table. Morgan gives the Demoivre's.

table as furnishing a convenient means of checking the correctDe Witt's report being thus of the nature of an unpublished ness of the values of annuities found by the ordinary process. state paper, although it contributed to its author's reputation, it may be assumed that he was aware that the table might be did not contribute to advance the exact knowledge of the used for the direct calculation of annuities; but he appears to subject; and the author to whom the credit must be given of have been ignorant of its other uses. first showing how to calculate the value of an annuity on correct The first author who fully developed the powers of the table principles is Edmund Halley. He gave the first approximately was John Nicholas Tetens, a native of Schleswig, who in 1785, correct mortality table (deduced from the records of the numbers while professor of philosophy and mathematics at Kiel, published of deaths and baptisms in the city of Breslau), and showed how in the German language an Introduction to the Calculation of it might be employed to calculate the value of an annuity on Life Annuities and Assurances. This work appears to have been the life of a nominee of any age (see Phil. Trans. 1693; Ass. quite unknown in England until F. Hendriks gave, in the first Mag. vol. xviii.).

number of the Assurance Magazine, pp. 1-20 (Sept. 1850), an Previously to Halley's time, and apparently for many years account of it, with a translation of the passages describing the subsequently, all dealings with life annuities were based upon I construction and use of the commutation table, and a sketch

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