gled to and fro in an undulatory motion, turning themselves round very quick all the time they moved forwards.

ANIME, a resin obtained from the hymenea courbaril, or locust-tree, which is a native of North America. It resembles copal very much in its appearance, but is readily soluble in alcohol, which copal is not. It is used as a varnish. Alcohol dissolves it *completely; and distilled over, it acquires both the smell and taste of anime.

ANNALS, in matters of literature, a species of history, which relates events in the chronological order wherein they happened. They differ from perfect history in this, that annals are a bare relation of what passes every year, as a journal is of what passes every day; whereas history relates not only the transactions themselves, but also the causes, motives, and springs of actions. Annals require nothing but brevity, history demands ornament. Cicero informs us of the origin of annals: to preserve the memory of events, the pontifex maximus, says he, wrote what passed each year, and exposed it on tablets in his own house, where every one was at liberty to read: this they called annales maximi; and hence. the writers who imitated this simple method of narrating facts were called annalists.

ANNATES, among ecclesiastical writers, a year's income of a spiritual living. These were, in ancient times, given to the pope throughout all christendom, upon the decease of any bishop, abbot, or parish-clerk, and were paid by his successor. In England, the pope claimed them first of such foreigners as he conferred benefices upon, by way of provision; but afterwards they were demanded of all other clerks on their admission to benefices. At the reformation they were taken from the pope, and vested in the king; and finally, queen Anne restored them to the church, by appropriating them to the augmention of poor livings.

ANNEALING, or NEALING, the burning or baking glass, earthen-ware, &c. in an oven or furnace. See GLASS.

ANNOTATION, in matters of literature, a brief commentary, or remark upon a book or writing, in order to clear up some passage, or draw some conclusion from it: thus the critics of the last age have made learned annotations upon all the classics.

ANNOTTO, in commerce, a kind of red dye, brought from the West Indies. This is otherwise denominated arnatto. It is procured from the pulp of the seed-capsules of a shrub called achiotte and urucu; the

bixa orellana of Linnæus, which grows seven or eight feet high, and produces oblong hairy pods, somewhat resembling those of a chesnut. Within each of these are thirty or forty irregularly figured seeds, which are enveloped in a pulp of a bright red colour, and unpleasant smell, somewhat resembling the paint called red lead when mixed up with oil; and it was used as paint by some of the Indians, in the same manner as woad was used by the ancient Britons. The seeds, together with the red tough matter that surrounds them, are softened in a wooden trough with water, until, by a kind of fermentation, which spreads a very nauseous smell, and by diligent stirring and pounding, the kernels are separated from the pulp. This mass is then strained through a seive, and boiled; and upon which a thick reddish scum, which is the pigment, separates. When skimmed off, it is carefully inspissated in another kettle; and after being repeatedly cool, is moulded in roundish lumps, wrapt round with leaves of trees, and packed for sale. It seems to partake of the nature of vegetable albuminous matter. The method of extracting the pulp, and preparing it for market, is simply by boiling the seeds in clear water, til they are perfectly extricated; after which the seeds are taken out, and the water left undisturbed for the pulp to subside. It is then drained off, and the sediment distributed into shallow vessels, and dried generally in the shade. The annotto is now only prepared by the Spaniards. The English had formerly a manufacture at St. Angelo, now ruined. This drug is preferred by the dyers to indigo, and sold one-fourth dearer. The double Gloucester cheese is coloured with this dye, not with marygolds. Some of the Dutch farmers use it to give a rich colour to their butter, and great quantities are said to be applied to the same purpose in the English dairies. The poor people use it instead of saffron; and it is sometimes mixed as an ingredient in chocolate, during the grinding of the cocoa, in the quantity of about two drams to the pound, in order to give it a reddish colour; but the opinion of its being an earth has brought it into disrepute, and this use of it has been discontinued. To water it gives only a pale brownish yellow colour, and is not soluble in that liquid, nor in spirit of wine; but, in order to be fit for dyeing, it requires an alkaline menstruum, to which it gives a bright orange colour; and hence it is useful as an ingredient in varnishes and lacquers, and iu

dyeing wax of a vermillion colour. Wool and silk, boiled in a solution of it by alkaline salts in water, acquire a deep, but not a durable orange dye; for though it is not changed by alum or acids, it is discharged by soaps, and destroyed by exposure to the air. It is said to be an antidote to the poisonous juice of manihot, or cassada. The liquid sold under the name of "Scott's nankeen dye," seems to be nothing but annotto dissolved in alkaline ley.

ANNOYANCE, in law, any injury done to a public place, as a high-way, bridge, or common river; or to a private way, as laying any thing that may breed infection, by encroaching, &c.

ANNUAL plants, generally called annuals, in gardening, signify such plants as are of one year's duration, or which continue for a few months only. Plants that rise from seed sown in the spring, arrive at maturity in the summer or autumn following, producing flowers and ripe seed, and which afterwards perish in their tops and roots, are commonly regarded as annuals. The plants of this tribe are very numerous, as most of those of the herbaceous kinds, consisting of uncultivated plants, weeds, &c. and also a great number of cultivated garden and field plants, both of the esculent and flowery ornamental kinds, are of this description. The last sort are often termed simply annuals. These are divided into the hardy and tender kinds; the former are sown in places where they are designed to remain without transplanting, but the latter are usually sown in hot-beds, in order to be transplanted in the spring, either into pots or borders.

ANNUITIES, any income of a certain yearly amount, payable at particular periods, which may be either yearly, half-yearly, quarterly, monthly, weekly, or at any other intervals. They are usually distinguished into annuities certain, and contingent annuities, or such as are for an uncertain period, being determinable by some future event, such as the failure of a life or lives.

The present value of an annuity is that sum which, if improved at compound interest, would be sufficient to pay the annuity: the present value of an annuity certain, payable yearly, and of which the first payment is to be made at the end of a year, may therefore be calculated in the following

manner.

Suppose a person has 1007. due to him a twelvemonth hence, and he wishes to have the value of the same advanced immediately VOL. I.

the sum which ought to be given as an equivalent thereto, allowing 5 per cent. interest, is 951. 4s. 94d. for this is the sum which, put out to interest at the rate of 5 per cent. will, at the end of the year, amount to 100%. So also, if a person has 1007, due to him at the end of two years, and he wishes to have the value of the same advanced immediately, the sum which ought to be given as an equivalent thereto is 90l. 148. 03d. for this is the sum which, put out at the same rate of interest, will, at the end of two years, amount to 100l. In like manner, if a person has 100%, due to him at the end of three years, and he wishes to have the same advanced immediately, the sum which ought to be given as an equivalent thereto is 861. 78. 8d. for this is the sum which, at the same rate of interest,will at the end of three years amount to 1001. And if these three values are added together, they will make 2721. 68. 6d. being the sum which ought to be paid down for an annuity of 1001. for three years; as this sum improved at the given rate of interest is just sufficient to make the three yearly payments.

As the amount or present worth of 11. for any given term is usually adopted as the foundation of calculations relating to annuities; let r represent the amount of 17. in one year; that is, one pound increased by a year's interest, then r", or r raised to the power whose exponent is any given number of years, will be the amount of 11. in those years; its increase in the same time is r" — 1 ; now the interest for a single year, or the annuity corresponding with the in crease, is r1; therefore, as r-1 is to r"-1, so is u (any given annuity) to a its amount: hence we have

EXAMPLE 1.-What is the present value

of an annuity of 631. to continue for 21 years?

The value in the table against 21 years is 12,821153, which multiplied by 63 gives the answer 807l. 14s. 7d.

EXAMPLE 2.—What present sum is equivalent to a nett rent of 20l. per annum for 69 years?

The value in the table against 69 years is 19,309810, which multiplied by 20 gives the answer 386l. 3s. 11d.

If any of the annuities in the above table, instead of being for an absolute term of years, had been subject to cease if a given life should fail during the term, it is evident that the value would have been lessened in proportion to the probability of the life failing; and, that if instead of being for a certain number of years, the annuity depended wholly on the uncertain continuance of a given life or lives, its value must be ascertained by the probable duration of such life or lives. In order to compute the value of LIFE ANNUITIES, therefore, it is necessary to have recourse to tables that exhibit the number of persons, which, out of a certain number born, are found to be living at the end of every subsequent year of human life, which thus shew what are termed the probabilities of life.

Various tables of this kind have been formed by the different writers on this subject, as Dr. Halley, Mr. Thomas Simpson, M. Kersseboom, M. De Parcieux, Dr. Price, Dr. Haygarth, Mr. Wargențin, M. Susmilch, and others; and the true method of computing the value of life annuities according to the probabilities of any table of mortality is laid down by Mr. William Morgan as follows:

"Was it certain that a person of a given age would live to the end of a year, the value of an annuity of 11. on such a life would be the present sum that would increase in a year to the value of a life one year older, together with the value of the single payment of 11. to be made at the end of a year; that is, it would be 17. together with the value of a life aged one year older than the given life, multiplied by the value of 11. payable at the end of a year. Call the value of a life one year older than the given life N, and the value of 17. payable at the end of a year; then will the value of an annuity on the given life, on the supposi+ XN = 1 × N=

1

tion of a certainty, be

ments, and to be made at the end of every half-year from the time of purchase, the value will be increased about one-fifth of a year's purchase.

The above table is formed from the probabilities of life, as deduced from the register of mortality at Northampton for 46 years, from 1735 to 1780 ; and as it gives the mean values of lives between the highest and lowest, it is better adapted for general use than any other extant. It has of late years been generally adopted for calculating the rates of assurance on lives, and is well suited to this purpose; but it is by no means a proper table for individuals or societies to grant life annuities from, for having been formed

from a register comprehending persons of all ages and conditions, it cannot give a correct representation of the duration and value of such lives as usually form a body of annuitauts, such persons being generally a selection of the best lives from the common mass, the interest of every person who purchases an annuity on any life requiring that he should take care that it is a good life. The best table for regulating the grant of life annuities, is that formed from the table of mortality published by Mr. De Parcieux, from the lists of the French tontines, but even this table gives the values of the advanced ages considerably too low.

cent.