gled to and fro in an undulatory motion, bixa orellana of Linnæus, which grows se turning themselves round very quick all the ven or eight feet high, and produces oblong time they moved forwards. hairy pods, somewhat resembling those of a ANIME, a resin obtained from the hy- chesnut. Within each of these are thirty or menea courbaril, or locust-tree, which is a forty irregularly figured seeds, which are native of North America. It resembles co- enveloped in a pulp of a bright red colour, pal very much in its appearance, but is rea- and unpleasant smell, somewhat resembling dily soluble in alcohol, which copal is not. the paint calied red lead when mixed up It is used as a varnish. Alcohol dissolves it with oil ; and it was used as paint by some *completely; and distilled over, it acquires of the Indians, in the same manner as woad both the smell and taste of anime. was used by the ancient Britons. The ANNALS, in matters of literature, a spe- seeds, together with the red tough matter cies of history, which relates events in the that surrounds them, are softened in a chronological order wherein they happened. wooden trough with water, until, by a kind They differ from perfect history in this, that of fermentation, which spreads a very nauannals are a bare relation of what passes seous smell, and by diligent stirring and every year, as a journal is of what passes pounding, the kernels are separated from every day; whereas history relates not only the pulp. This mass is then strained through the transactions themselves, but also the a seive, and boiled; and upon which a thick causes, motives, and springs of actions. An reddish scum, which is the pigment, sepanals require no hing but brevity, history rates. When skimmed off, it is carefully demands ornament. Cicero informs us of inspissated in another kettle; and after bethe origin of annals : to preserve the me- ing repeatedly cool, is moulded in roundish mory of events, the pontifex maximus, says lumps, wrapt round with leaves of trees, he, wrote what passed each year, and ex and packed for sale. It seems to partake posed it on tablets in his own house, where of the nature of vegetable albuminous matevery one was at liberty to read : this they ter. The method of extracting tie pulp, called annales maximi ; and hence. the and preparing it for market, is simply by writers who imitated this simple method of boiling the seeds in clear water, till they narrating facts were called annalists. are perfectly extricated; after which the ANNATES, among ecclesiastical writers, seeds are taken out, and the water left una year's income of a spiritual living. These disturbed for the pulp to subside. It is then were, in ancient times, given to the pope drained off, and the sediment distributed throughout all christendom, upon the de- iuto shallow vessels, and dried generally in cease of any bishop, abbot, or parish-clerk, the shade. The annotto is now only preand were paid by his successor. In Eng- pared by the Spaniards. The English had land, the pope claimed them first of such formerly a manufacture at St. Angelo, now foreigners as he conferred benefices upon, ruined. This drug is preferred by the dyers by way of provision ; but afterwards they to indigo, and sold one-fourth dearer. The were demanded of all other clerks on their double Gloucester cheese is coloured with admission to benefices. At the reformation this dye, not with marygolds. Some of the they were taken from the pope, and vested Dutch farmers use it to give a rich colour in the king; and finally, queen Anne re to their butter, and great quantities are said stored them to the church, by appropriating to be applied to the same purpose in the them to the augmention of poor livings. English dairies. The poor people use it in ANNEALING, or NEALING, the burn- stead of saffron; and it is sometimes mixed ing or baking glass, earthen-ware, &c. in an as an ingredient in chocolate, during the oven or furnace. See GLASS. grinding of the cocoa, in the quantity of ANNOTATION, in matters of litera- about two drams to the pound, in order to ture, a brief commentary, or remark upon give it a reddish colour ; but the opinion of a book or writing, in order to clear up some its being an earth has brought it into disrepassage, or draw some conclusion from it: pute, and this use of it has been discontithus the critics of the last age have made nued. To water it gives only a pale brownlearned annotations upon all the classics. ish yellow colour, and is not soluble in that ANNOTTO, in commerce, a kind of red liquid, nor in spirit of wine ; but, in order dye, brought from the West Indies. This to be fit for dyeing, it requires an alkalive is otherwise denominated arnatto. It is pro- menstruum, to which it gives a bright cured from the pulp of the seed-capsules of orange colour; and hence it is uscful as an a shrub called achiotte and urucu ; the ingredient in varnishes and lacquers, and in chyeing wax of a vermillion colour. Wool the snm which ought to be given as an equiand silk, boiled in a solution of it by alka- valent thereto, allowing 5 per cent. interest, line salts in water, acquire a deep, but notis 951. 48. 9/d. for this is the sum which, a durable orange dye; for though it is not put out to interest at the rate of 5 per cent. changed by alum or acids, it is discharged will, at the end of the year, amount to 1001. by soaps, and destroyed by exposure to the So also, if a person has 1001. due to him at air. It is said to be an antidote to the poi- the end of two years, and he wishes to have sonous juice of manihot, or cassada. The the value of the same advanced immediately, liquid sold under the name of “ Scott's nan the sum which ought to be given as an equikeen dye,” seems to be nothing but annotto valent thereto is 901. 14s. 0 d. for this is the dissolved in alkaline ley, sum which, pat out at the same rate of inANNOYANCE, in law, any injury done terest, will, at the end of two years, amount to a public place, as a high-way, bridge, or to 1001. In like mamer, if a person has common river; or to a private way, as lay- 100!. due to him at the end of three years, ing any thing that may breed infection, by and he wishes to have the same advanced encroaching, &c. immediately, the sum which ought to be ANNUAL plants, generally called an given as an equivalent thereto is 861. 78. 8d. nuals, in gardening, signify such plants as for this is the sum which, at the same rate of are of one year's duration, or which conti- interest,will at the end of three years amount nue for a few months only. Plants that rise to 1001. And if these three values are adfrom seed sown in the spring, arrive at ma ded together, they will make 2721. 68. 6d. turity in the summer or autumn following, being the sum which ought to be paid down producing flowers and ripe seed, and wbich for an annuity of 100l. for three years; asafterwards perish in their tops and roots, are this sum improved at the given rate of incommonly regarded as aunuals. The plants terest is just sufficient to make the three of this tribe are very mumerons, as most of yearly payments. those of the herbaceous kinds, consisting of As the amount or present worth of 11. for uncultivated plants, weeds, &c, and also a any given term is usually adopted as the foungreat number of cultivated garden and field dation of calculations relating to annuities ; plants, both of the esculent and flowery or let r represent the amount of 11. in one namental kinds, are of this description. year; that is, one pound increased by a The last sort are often termed simply an year's interest, then rn, or r raised to the nuals. These are divided into the hardy power whose exponent is any given number and tender kinds; the former are sown in of years, will be the amount of 1l. in those places where they are designed to remain years; its increase in the same time is without transplanting, but the latter are go — 1; now the interest for a single year, or usually sown in hot-beds, in order to be the annuity corresponding with the in: transplanted in the spring, either into pots crease, is -1; therefore, as -- -1 is to or borders. go n-1, so is u (any given annuity) to a its ANNUITIES, any income of a certain amount: hence we have yearly amount, payable at particular periods, u X gore I which may be either yearly, half-yearly, quarterly, monthly, weekly, or at any other EXAMPLE.—To what sum will an annuity intervals. They are usually distinguished of 501. amount in 6 years, at 5 per cent. per into annuities certain, and contingent an annum compound interest? nuities, or such as are for an uncertain period, being determinable by some future 50 X 1.056-1 =3401, 193. Id. event, such as the failure of a life or lives. .05 The present value of an annuity is that In this manner the amount of an annuity sum whic.., if improved at compound in- for any number of years, at any given rate terest, wond be sufficient to pay the an of interest, may be found. But when the puity: the present value of an annuity cer term of years is considerable, it will be tain, payable yearly, and of which the first more convenient to work by logarithms, by payment is to be made at the end of a year, which the labour of all calculations relating may therefore be calculated in the following to compound interest is greatly abridged. manner. There is, however, little occasion in general Suppose a person has 1001, due to him a to calculate the amount or present worth of twelvemonth hence, and he wishes to have annuities, except for particnlar rates of inihe value of the same advanced immediately terest, as the following tables, and others of VOL. I. R a similar nature, for different rates of in- number of years, is found on similar prin. terest which are given in most books on ciples; for as 1l. is the present value of in compound interest, save much time and its amount in n years, and as the prelabour in common practice, and are there sent value of any other amount, and consefore in general use. quently TABLE I. u XIA of must bear the same proporShewing the amount of an annuity of il. in any number of years not exceeding tion to that amount, we have -1 1 - 1 =P 50 Y. Yrs. Amo. Yrs. Amount. Yrs. Amount. EXAMPLE.- What is the present value of 1 1,0000 35 90,3203 69 559,5510 501. per annum for 6 years, at 5 per cent. 2 2,0500 36 95,8363 70 588,5285 33,1525 37 101,6281 71 compound interest? 618,9549 4 4,3101 38 107,7095 72 650,9027 50 5 5,5256 39 114,0950 73 684,4478 1.05 6 6,8019 40 120,7998 74 719,6702 =2531. 158. 8d. .05 7 8,1420 41 127,8398 75 756,6537 8 9,5491 42 135,2317 76 795,4864 But such questions are much more readily 9. 11,0266 43 142,9933 77 836,2607 answered by the following table. 10 12,5779 44 151,1430 78 879,0738 TABLE II. 11 14,2068 45 159,7002 79 924,0274 12 15,9171 46 168,6852 80 971,9288 Shewing the present value of an annuity of 13 17,7130 47 178,1194 81 1020,7903 11. for any number of years not exceeding 14 19,5936 48 188,0254 82 1072,8298 100, at 5 per cent. per annum compound 15 21,5786 49 198,4267 83 1127,4713 interest. 16 23,6575 50 209,3480 84 1184,8448' 17 25,8404 51 220,8154 85 1245,0871. Y. Value. Y. Value. Value, 18 28,1328 52 232,8562 86 1308,3414 19 30,5390 53 215,4990 87 1374,7585 1 ,952381|35|16,374194 69 19,509810 20 33,0659 54 258,7739 88 1444,4964 2 1,859410 36 16,546852 70 19,342677 21 35,7192 55 272,7126 89 1517,7212 3 2,723248 37 16,711287 71 19,373978 22 38,5052 56 287,3-189 90 1594,6073 4 3,545950 38 16,867893 72 19,403788 23 41,4305 57 302,7157 91 1675,3377 5 4,329477 39 17,017041 73 19,432179 24 44,5020 58 318,8514 92 1760,1045 6 5,075692 40 17,159086 74 19,459218 25 47,7271 59 1335,7940 93 1849,1098 7 5,786373 41 17,294368 75,19,484970 26 151,1135 60 353,5837 94 1942,5653 s 6,463213 42 17,423208 76 19,509495 27 54,6691 61 372,2629 95 2040,6935 9/ 7,107822 43 17,545912 77 19,532853 28 58,4026 62 391,8760 96 2143,7282 10 7,7217344 17,662773 78 19,555098 29 62,3227 63 412,4698 97 2251,9146. 1 8,306414 45 17,774070 79 19,576284 SO 66,4388 64 434,0933 98 2365,5103 12 8,863252 4617,380066 80 19,596460 31 70,7608 65 456,7980 99 2484,7859 13 9,393,73 47 17,981016 81 19,615677 32 75,2988 66 480,6379 100 2610,0252 14! 9,898641 48 18,077158 82 19,633978 33 80,0638 67 505,6698 15 10,379658/49 18,168722 83 19,651-107 34 85,0670/ 68 531,9533 16.10,837770150 18,255925 84 19,668007 1711,27 1066 51 18,338977 85 19,683810 EXAMPLE 1.-To what sum will an an 18 11,689587 52 18,418073 86 19,698873 nuity of 105l. amount in 19 years, at 5 per 19/12,085321 53 18,493103 87 19,713212 cent. compound interest? 2012,+62210 54 18,565146 88 19,726869 The number in the table opposite to 19 21 12,821153 55 18,633172 89 19,739875 years is 50,5390, which multiplied by-105 22 13,163003 56 18,698545 90 19,752269 2:3 13,188574 57 18,760519 91 19,764059 gives the answer 32061. 118, 10d. 24 13,798649 58 18,819542 92 19,775294 EXAMPLE 2.-In what time will an an 25 14,093915 59 18,87575493 19,785994 nuity of 25). amount to 3575l. at 5 per cent. 26 14,375185 60 18,929290 94 19,796185 compound interest? 27 14,643034 61 18,980276 95 19,805891 Divide 35751, by 251. the quotient is 143; 28 14,898127 62|19,023834 96 19,815134 the number nearest to this in the table is 29 15,141074'63 19,075080 97 19,823937 142,9933, and the number of years corres 30/15,374451 64 19,119124 98 19,832321 ponding, or 43 years, is the answer. 31 13,592810 65 19,161070 99 19,840306 32 15,802677 66 19,201019 100 19,847910 The present worth of an annuity, or the 33 16,002549 67 19,239066 sum to be given in one present payment as 34 16,193904 68|19,275301 an equivalent for an annuity for any given 1 ur Example 1.-What is the present value · 1 +N. But the fact is, that it is uncertain of an annuity of 631. to continue for en whether the given life will exist to the end years? of the year or not, this last value, therefore, The value in the table against 21 years is must be diminished in the proportion of this 12,821153, which multiplied by 63 gives the uncertainty, that is, it must be multiplied answer 8071, 14s. 7d. by the probability that the given life will EXAMPLE 2.—What present sum is equivalent to a nett rent of 201. per annum for survive one year, or supposing to express 69 years? 6 The valne in the table against 69 years is this probability, it will be X1-." 19,309810, which multiplied by 20 gives the The values of annuities on the joint contianswer 3861. 3s. 11d. nuance of two lives are found by reasoning If any of the annuities in the above table, in a similar manner; and such values, both instead of being for an absolute term of for single and joint lives, are given in the years, had been subject to cease if a given following tables. life should fail during the term, it is evident TABLE III. that the value would have been lessened in proportion to the probability of the life Shewing the value of an annuity of 11. on failing; and, that if instead of being for a a single life, at every age, according to certain number of years, the annuity de the probabilities of the duration of life pended wholly on the uncertain continuance at Northampton, reckoning interest at of a given life or lives, its value must be as 5 per cent, per annum. certained by the probable duration of such life or lives. In order to compute the valne Age. Value. Age. Value. Age. Value. of LIFE ANNUITIES, therefore, it is neces Birth. 8,863 33 sary to have recourse to tables that exhibit 12,740 | 66 7,034 1 year 11,563 34 | 12,623 67 the number of persons, which, out of a cer 6,787 2 | 13,420 35 12,502 68 6,536 tain number born, are found to be living at 3 14,135 36 12,377 69 6,281 the end of every subsequent year of human 4 14,613 37 12,249 70 6,023 life, which thus shew what are termed the 5 14,827 38 12,116 71 5,764 probabilities of life. 6 15,041 39 | 11,979 72 5,504 Various tables of this kind have been 15,166 40 11,837 73 5,245 formed by the different writers on this sub 8 15,226 41 11,695 74 4,990 ject, as Dr. Halley, Mr. Thomas Simpson, 9 15,210 42 | 11,551 || 75 4,744 10 15,139 M. Kersseboom, M. De Parcieux, Dr. 43 11,407 | 76 4,511 15,043 44 | 11,258 77 4,277 Price, Dr. Haygarth, Mr. Wargentin, M. 12 14,937 11,105 78 4,035 Susinilch, and others; and the true method 13 | 14,826 46 10,947 79 3,776 of computing the value of life annuities ac 14 | 14,710 10,784 3,515 cording to the probabilities of any table of 15 14,588 10,616 3,263 mortality is laid down by Mr. William 16 14,460 10,443 82 3,020 Morgan as follows: 17 | 14,334 50 10,269 || 83 2,797 “ Was it certain that a person of a given 18 14,217 51 10,097 84 2,627 52 age would live to the end of a year, the 19 14,108 9,925 85 2,471 20 14,007 53 9,748 86 2,328 value of an annuity of 11. on such a life 21 13,917 9,567 2,193 would be the present sum that would in 22 13,833 55 9,382 2,080 crease in a year to the value of a life one 23 13,746 56 9,193 89 1,924 year older, together with the value of the 24 13,658 57 8,999 90 1,723 single payment of 1l. to be made at the end 25 13,567 58 8,801 91 1,447 of a year; that is, it would be il. together 26 13,473 59 8,599 92 1,153 with the value of a life aged one year older 27 13,377 60 8,392 93 0,816 than the given life, multiplied by the value 28 13,278 61 8,181 0,524 29 13,177 62 of 1l. payable at the end of a year. Call 7,966 0,238 30 13,072 63 7,742 96 0,000 the value of a life one year older than the S1 12,965 64 7,514 given life N, and the value of 1l. payable at S2 | 12,854 65 7,276 1 the end of a year ;; then will the value of The values in this and the following tables, an annuity on the given life, on the supposi- suppose the payments to be made yearly, and to begin at the end of a year; but if all the payments are to be half-yearly pay. 7 11 45 47 48 49 80 87 94 tion of a certainty, be + xN=-* ments, and to be made at the end of every from a register comprehending persons of half-year from the time of purchase, the all ages and conditions, it cannot give a corvalue will be increased about one-fifth of a rect representation of the duration and year's purchase. value of such lives as usually form a body The above table is formed from the pro- of annuitauts, such persons being generally babilities of life, as deduced from the regis- a selection of the best lives from the comter of mortality at Northampton for 46 mon mass, the interest of every person years, from 1735 to 1780; and as it gives the who purchases an annuity on any life requirmean values of lives between the highest and ing that he should take care that it is a good, lowest, it is better adapted for general use life. The best table for regulating the grant than any other extant. It has of late years of life annuities, is that formed from the been generally adopted for calculating the table of mortality published by Mr. De rates of assurance on lives, and is well suited Parcieux, from the lists of the French tonto this purpose; but it is by no means a pro- tines, but even this table gives the values of per table for individuals or societies to grant the advanced ages considerably too low. life annuities from, for having been formed TABLE IV. Shewing the value of an anmity of 1l, on a single life, at every age, according to the probabilities of life, in Mr. De Parcieux’s table of the mortality. Interest at 5 per cent. Age. Value. Age. Value. Age. Value. Age. Value. Age. Value. The calculation of the values of joint lives the inhabitants, taken in the gross, give from any given table of mortality, for every the values of lives much too low for the combination of age, is so laborious a task middling and superior classes of the people that no such table has yet been published. in London itself, and are wholly improper Mr. Simpson, in his select exercises, gave a for general use. A much more comprehentable of the values of two joint lives, agree- sive table of the value of joint lives, has able to the probabilities of life in London; since been calculated by Dr. Price from but the tables founded on the London bills, the Northampton table of mortality, from representing the rate of mortality among which the following table is taken. |