ANNO

ANNO DOMINI, the Year of our Lord, or the æra DOMINI. of time from the birth of Jesus Christ. This is usually inserted in all public acts and writings of this country, with the addition of the year of the king's reign.

ANNOTATE.

ANNONA CIVILIS, in Antiquity, corn, or provisions of any sort for a year. The tax called by this name, intended to supply the capital and army, was very oppressive in the time of Justinian.

ANNONA MILITARIS, was a name for necessaries stored in the magazines, for the maintenance of an army during a campaign. We read also of annonæ præfectus, or curators, to inspect the sale of corn, annonæ structor, to attend to the provision for the army, annonarius, an officer who had the distribution of the rations to the soldiers, and annonarii, monopolists. ANNONA, in Botany, a genus of plants, belonging to the class Polyandria, and order Polyginia.

ANNONAY, a town of Algiers, 32 miles from Constantina. It is now only remarkable for some ancient ruins, on an elevated spot not far distant from the town.

ANNONDY, a town of France, in Lower Languedoc, 12 leagues from Privas. It is now the head of a canton, in the arrondissement of Tournon, and was formerly the capital of the Upper Vivarois, giving the title of a marquisate to the house of Rohan-Soubise. At present it is chiefly remarkable for its manufacture of paper of a very excellent quality, which was originally conducted by the celebrated aeronaut Montgolfier, who ascended from this place in his balloon, on the 5th of June, 1783.

ANNOT, a town of France, in the department of the Lower Alps, eight leagues from Digne. It is the head of a canton, and contains a population of upwards of 1,000 inhabitants.

ANNOTATE, v. Annoto, from ad, noto, which ANNOTATION, ANNOTATIONIST, AN'NOTATOR. mark we may know it.

Vossius thinks is from the supine Notum: for we note or mark a thing, that from the

To make marks, or remarks or observations. At length hee [M. Tyndall] beethought hym selfe of Cutbert Tunstall then Byshop of London, and especially for the great commendatio of Erasmus, who in his annotations so extolleth him for his learning.

The Whole Workes of Wm. Tyndall, &c. [HENRY SAVILE] carefully collected the best copies of books, written by St. Chrysostome, from various parts of the world, and employed learned men to transcribe, and make annotations on, Wood's Athene Oxonienses.

them.

If it [philology] be only criticism upon ancient authors and languages, he must be a conjuror that can make those moderns, with their comments, and glossaries, and annotations, more learned than the authors themselves in their own languages, as well as the subjects they treat.

Temple, on An. and Mo. Learning.

There are some admirable remarks in the annotations to the se

When the revolution of the anniversary calls on us to perform glorious benefits of Christ's Incarnation, Nativity, Passion, Resurour duty of special meditation, and thankfulness to God for the rection, and Ascension, then we have the offices of Christmas, the Annunciation, Easter, and Ascension.

Taylor's Apo. for Autho, & set Forms of Liturgie. Pref. Those, mighty Jove, mean time, thy glorious care, Who model nations, publish laws, announce Or life or death, and found or change the empire. Prior. Hymn of Callimachus. Her [Queen Elizabeth's] arrival was announced through the coun try by a peal of cannon from the ramparts; and a display of fireworks at night. Gilpin's Tour to the Lakes of Cumberland, &c. ANNUNCIATION DAY, in Ecclesiastical Affairs, a feast of the church, celebrated annually on the 25th of March, in honour of the salutation of the Blessed Virgin, or as some authors hold, of our Saviour himself. Bingham assigns the institution of this festival to the seventh century, about which time the council of Toledo ordered it to be celebrated eight days before Christmas. Several Romish writers bring forward a spurious sermon of St. Athanasius, and another of Gregory Thaumaturgus, to prove its still greater antiquity. The eastern and western churches vary considerably in their season of observing this feast. The Syrian calendar notes it down for the 1st day of December, and distinguishes it by the appellation_of Bascarach, inquiry, or investigation. The Greeks, who are by no means scrupulous in its solemnization, celebrate it even in Lent; while the Armenian churches, in order to prevent it from occurring at that period, hold it on the 5th of January. The pope, at one time, was in the habit of having a certain number of young maidens presented to him on Annunciation

he retained himself in his second edition, except when they were confused by subsequent annotators, or were too minute to merit preservation. Johnson's Pref. to Shakespeare. Give me leave to annotate on the words. Ilive's Orations.

How fitly the Saracens are resembled to locusts, or scorpion tailed locusts, in the Apocal. Mr. Mede has with far more clearness shewn, than the annotationists of the new way.

Worthington's Miscellanies.

those who chose to be married by him, he gave 50 crowns as a portion, those who chose to be devoted as nuns, received 100 crowns. The term Annunciation is also applied to designate that part of the ceremony of the Jewish passover, in which the reason and origin of its celebration are explained, called by the Jews Пn Haggada, or the Annunciation.,

AN

NOUNCE

trouble or molest.

It. Noia, Span. Enojo, Fr.Ennuy. From the Lat. Noxia (Noxia, nos>cia, noia, Menage), from Noceo, to hurt.

To hurt, harm, or injure, to

And be Romaynes bep anyed of here trauail so sore, Of perel on se, & eke on lond, þat heo nul come her no more. R. Gloucester, p. 100. Salomon sayth, that right as mouthes in the shepes fleese anoien to the clothes, and the smale wormes to the tree, right so anoieth sorwe to the herte of man.

Chaucer. The Tale of Melibus, vol. ii. p. 74. But the cheer of the lord is on men that doen yuelis, and who is it that schal anoye you if ye ben sureis and loueris of goodnesse. Wiclif. Peter 1. c. iii. But telleth me your grefe, Paraventure I may in your mischefe Conseile or helpe: and therfore telleth me All your annoy, for it shal ben secree.

Chaucer. The Shipmannes Tale, vol. ii. p. 35. For he was nevere crucyfyed, as thei seyn; but that God made him to stye up to him with outen Dethe, and with outen Anoye. Sir John Maundeville, p. 162.

The lions which against other are of fiercenesse inuicible, they either vanquished, or proued harmles, as though their mouthes being stopped, or els their clawes fast bownden, they had had no power to hurt those whom god would haue preserued withoute any Udall. Paul to the Hebrues, c. xi. For al be it so, that al tarying be anoiful, algates it is not to repreve in yeving of jugement, ne in vengeance taking, whan it is suffisant and resonable.

anoiaunce.

Chaucer. The Tale of Melibæus, vol. ii. p. 77. But certes ye han sodeinly cleped to your conseil a gret multitude of peple, ful chargeant and ful anoyous for to here.

Id. ib. p. 94.

The city of Epidamnus became great and populous; and having for many years together been annoyed with sedition, was, by a war, as is reported, made upon them by the confining Barbarians, brought low, and deprived of the greatest part of their power.

Hobbes' Thucydides. And how he slew with glauncing dart amisse A gentle hynd, the which the lovely boy Did love as life, above all wordly blisse: For griefe whereof the lad n'ould after joy; But pynd away in anguish and selfewild annoy. Spenser's Faerie Queene. Book i. c. vi. K. H. My Lords, at once. The care you have of us To mow down thorns that would annoy our fort. Is worthy praise.

Shakespeare's 2d pt. H. VI, act iii. sc. 1. BART. No. Know the gallant monarch is in arms; And like an eagle o'er his aiery lowers To souse annoyance that comes near his nest.

Id. K. John, act v. sc. 2. Indeed though STIFF-CLAY (commonly called Stukley) be the name but of one or two villages in the midst, yet their nature is extensive all over the country, consisting of a deep clay, giving much annoyance to passengers.

Fuller's Worthies. Huntingdonshire.
Say, what can more our tortured souls annoy,
Than to behold, admire, and lose our joy?

Prior's Pastoral.

The very exercise of industry immediately in itself is delightful, and hath an innate satisfaction, which tempereth all annoyances, and even ingratiateth the pains going with it. Barrow's Sermons.

Preserving his secret unrevealed, and his forces well united, let a hero march and annoy his enemy; for hot iron may form an union with hot iron; so he by equal fierceness, at a time when his foe is fierce, may conclude a firm peace.

Sir Wm. Jones's Hitopadesa. ANNUA PENSIONE, in Ecclesiastical Affairs, an ancient writ for providing the king's unpreferred chaplains with a pension. Where an annual pension was due to the king, from an abbot or prior, by this writ he could nominate any of his chaplains (who were not provided with livings) to receive the same of such parties.

ANʼNUAL, n. ANNUAL, adj. ANʼNUALLY, ANʼNUARY, ANNU'ITANT, ANNUITY,

ANNU'ELLER,

Annuus, from Annus, a year. Yearly, occurring every year. |

For he hathe every zeer of annuelle Rente 300,000 Hors charged with Corn of dyverse Greynes and of Ryzs: and so helede the a fulle noble Lif, and a delycate, aftre the custom of the Contree. Sir John Maundeville, p. 376.

He ordeyned ye annual vse or ceremonie to eate the Paschall Lambe, with whose bloude they sprynkeled the thrasholde and haunse of the dore, with both the postes of the house: and trusting vpon this signe, feared not themselfes in the middles of the slaughter of the Egipcians. Udall. Paul to the Hebrues, cap. xi. There must be Masses dyrges, ther must be anuaries bead me. Bales' Image to both Churches, p. 91. Wherfore first the officers seruauntes, wer put out of the Courte, and many old officers were put to liue in their countreys, but the kyng [Henry the eighth] of his bountie enhaunsed their liuynges, for he that had three pound wages, had sixe pound annuitie, without attendaunce, and he that had-xl.s had foure pound, and so euery man after that rate, and young menne were put in their romes, Hall. Henry VIII. fo. 146.

In London was a preest, an annuellere,
That therin dwelled hadde many a yere,
Which was so plesant and so servisable
Unto the wif, ther as he was at table,
That she wold suffer him no thing to pay
For borde ne clothing, went he never so gay.
Chaucer. The Chanones Yemannes Tale, vol. ii. p. 244.
Get all the town to help, that will be hir'd,
Their pains I'll turn to annual holiday,

If it shall chance, but one bring word of her.
Beau & Fletch. Love's Pilgrimage, act v.

Intelligent of seasons, and set forth

Their aery caravan, high over seas
Flying, and over lands, with mutual wing,
Easing their flight; so steers the prudent crane
Her annual voyage, borne on winds.

Milton's Par. Lost.

Book vii.

My grandfather had seven sonns, of which my father was the youngest to the eldest he gave his whole estate, and to the rest, according to the custome of those times, slight annuities. Memoirs of Col. Hutchinson. Egypt, though there seldom falls any rain there, yet hath abundant recompense made it by the annual overflowing of the river. Ray. On the Creation. The outer and inner bark of trees serve to defend the trunk and boughs from the excesses of heat and cold, and drought, and to convey the sap for the annual augmentation of the tree.

If the consent of the annuitants be requisite for every taxation, they will never be persuaded to contribute sufficiently even to the support of government; as the diminution of their revenue must in that case be very sensible, would not be disguised under the appearance of a branch of excise, or customs, and would not be shared by any other order of the state, who are already supposed to be taxed to the utmost. Hume's Essays.

An annuity is a thing very distinct from a rent-charge, with imposed upon and issuing out of lands, whereas an annuity is a which it is frequently confounded: a rent-charge being a burthen yearly suni chargeable only upon the person of the grantor.

Blackstone's Commentaries.

Different kinds of annuities.

Annuities certain,

their initial letters.

1. The doctrine of annuities has always been considered a subject of considerable importance in all wellregulated states; but in no country is it of so much consequence as in our own; and at no time did it possess such interest, even in England, as at the present; when property, either real or nominal, has attained to a magnitude far beyond what could ever have been contemplated by the most sanguine financier, and the transfer of it from one hand to another is the business of every day, and the concern of almost every person in the higher and middling classes of society.

The term annuity is to be understood here to denote any periodical income arising from money lent, or from houses, lands, salaries, pensions, &c. payable from time to time, either annually, or at any other interval. These may be divided into such as are certain, and such as depend upon some contingency, as the continuance of one or more lives: these latter are called life annuities. Annuities certain may likewise be divided into such as are in possession, and such as are in reversion; the former signifying those that have already commenced, and the latter, those that will not commence till after some particular event, or till some given period of time has elapsed.

With respect to the contingencies on which an annuity may depend, they are to be computed separately, upon the principles of the doctrine of probabilities, which shows the value of any given expectations founded upon the tables of mortality which have been kept at different times and in different places. This subject is consequently attended with greater difficulty than the former, although they both depend ultimately upon the same fundamental principles; we shall, therefore, first solicit the reader's attention to the doctrine of annuities certain; and afterwards pass to those which are contingent.

§ I. Annuities certain.

2. The principal questions relating to the doctrine of these kinds of annuities, may be divided into two parts; viz. those relating to the amount, and those relating to the present value; and these will again evidently differ according as simple or compound interest is used in the calculation. The value of annuities, however, at simple interest, can hardly be considered in the present day in any other light than as a mere matter of speculation; so many ways presenting themselves by which compound interest may be obtained; even the savings of the simple artizan, amounting, perhaps, to not more than a shilling a week, may, by

means of our recent laudable institutions of saving- ANbanks, have all the advantages of compound interest, NUITIES. upon the same terms as the rich fund-holder who appropriates a part of each of his dividends in the purchase of new stock. We might, therefore, without much impropriety, pass over entirely the consideration of annuities at simple interest; but as this article might thus appear incomplete, we shall briefly allude to the subject, and then proceed to examine other cases of more practical utility.

Amount of annuities at simple interest.

3. It may be proper to observe here, once for all, Amount that we shall direct all our investigations, unless the at simple contrary be specified, to those cases where the annuity interest. is 1. and we may then, by a simple proportion, or multiplication, determine the same for any other annuity, as the amounts will evidently have the same ratio as the annuities themselves. This being premised, let

s = the amount of the annuity,
a the annuity,

n = the number of years,

r = the rate of interest per 1. per annum. Now, in the case of the annuity of 11. per annum, it is evident that the amount for 1 year is 1 + r; for 2 years, 1+2r, for 3 years, 1+3r, &c.; and for n years, 1+ nr. And therefore the total amount for n years, will be expressed by the series 1+ (1+r) + (1+2r) + (1+3r),+, &c. 1 + (n−1)r, because it is to be observed, that for the last payment no interest will be obtained; and that when the annuity is for n years, the first sum received will only be at interest for (n-1) year.

This series is obviously an arithmetical progression, whose first term is 1, the common difference, and the number of terms n; moreover, the last term is 1 +

(-1) r; the sum of it will therefore be found by the usual rule, to be

1 + 1+r which sum, being multiplied by any other annuity a, will be the present value of such an annuity. But as the summation of this series is very laborious, and as, after all, it belongs to a case which has little or no practical application, we shall not detain the reader upon this subject, but merely give him Simpson's approximation for the same, which may be safely applied in case such a question should ever occur. Its error is in excess.

Simpson's rule." Divide s, or the amount of the n (n - 1) annuity in the given time, by 1 + nr + 2 for the present value sought."

Amount of annuities at compound interest.

4. The method of calculating the amount of annuities at the end of any given term, improved annually at compound interest, will readily follow from what has been stated above respecting those at simple interest; for we have only to find the amount of each payment put out at compound interest for the remainder of the term, after it becomes due, and to find the sum of all these several amounts.

n =

the number of years;

log. (1+r)

{12 + (n + 1) q} q

r=

the annual interest;

12 + 2 (n + 1) q

in which last formula we substitute, for the sake of

abridging,

9=

(சூன்

1.

an

Note 1. In the above formulæ and investigation we Annuities have supposed the annuity to be payable yearly, and payable balf yearly, consequently n denotes the number of years, and r the quarterly, interest on 17. for one year. But if the annuity &c. be payable half yearly, or quarterly, or every two or three years, we must then consider n to denote the number of payments, and r as the interest payable upon 11. for the time of each payment; that is, for half yearly payments, n must be doubled, and r must be taken half the annual interest; for quarterly payments, the number of them will be 4 n, and the interest r: so also for biennial or triennial payments, the number will be n, orn, and the rate 2 r, or 3r; so that the same formula will apply to any cases of this kind.

pay

Note 2. We here suppose the annuity and the interest upon the annuity to be payable together. It is obvious, that although an annuity may only be able annually, the purchaser may be able to place his several receipts so that they may improve by half yearly or quarterly payments; if this were taken into consideration, the above formulæ would require certain modifications; but it would lead us too far to enter upon this investigation, which, after all, is not of very great importance. The reader, however, will find them treated of in a very luminous manner by Mr. Baily, in his Doctrine of Annuities. To

1 : (1 + r) :: (1.+ r) : (1 + r)2

the amount for two years; and in the same manner (1+r)3 will be the amount for three years, &c.; and, generally, for n years, the amount will be (1 + r)".

Now, as in the case of simple interest, the last payment of the annuity will have no interest attached to it, and the first will only remain at interest for (n-1) years; consequently, the whole amount of such an annuity will be expressed by the series

1 + (1 + r) + (1 + r)2 + (1 + r) 3 +, &c. (1+r)*;

VOL. XVII.

Present

interest.

3. For quarterly payments, n = 80, r01, and Whence a = 25.

10

=2,8971. 6s. 3d.

(1·08) 1o 1 s=200. · 08 Whence it is obvious, that the oftener the payments are made, the greater will be the value of the whole annuity, as is indeed otherwise obvious.

As this formula for s, although simple in its form, is somewhat troublesome to put into numbers, tables of its several values have been computed, answering to the different values of n and r, for annuities of 17. from which that for any other proposed annuity may be obtained by simple multiplication. Such is the following Table I. for any number of years under 50, and for all rates of interest from 2 to 7 per cent. per annum; or from 2 to 7 per cent. per payment.

Let us give an example, by way of illustrating the use of this table.

To what will an annuity of 5007. per annum amount in 40 years, at 4 per cent. per annum, yearly payments?

By the table, the amount of 17. for 40 years, at 4 per cent. is 95.0255

Mult. by

500

Present value of annuities at compound interest.

6. The present value of an annuity is such a sum as, value at put out to interest, will enable us to provide for the compound several payments of the annuity as they become due. In order to ascertain this sum, we must find the present value of these several payments; and the sum of them will be the total present value sought. Hence, then, let p the present worth,

(1 + r) : 1 ::

1 1+r

(1 + r)n−1 (1+r)"

The present worth, therefore, of all the payments, will be

a geometrical progression, of which the ratio is and the sum of it, according to the principles delivered in our treatise on Algebra, is

7. The following examples will illustrate these formulæ.

ann.

1. What is the present value of an annuity of 201. E per ann. for 40 years, at the rate of 6 per cent. per the payments being yearly?

Heren 40, r

whence p 20 ×

2. What ought to be the annual rent or payment for 55 years, for which a premium of 1007. is paid down, allowing interest at 5 per cent. per ann.? Here n = 551⁄2, p = 100, and r = '055; whence a 100 × 055 x (1055)55

(1.055)-1

=51. 16s.

In this case, as in the former, the theorems for p and ainvolve much arithmetical computation, to avoid which, tables of their value are computed to various periods, and for different rates of interest; such are our Tables II. and III.; the other formula, viz. those for n and r, being by no means so frequently required, it would only be a waste of time to reduce them to the tabular form. Note. When the payments are not made annually,