ANO
Moivre's tlieorem in the firft problem of his Annuities on lives; becaufe in the prefent cafe there is one payment more to be made than in the other, yet on the SuppoSition of an equal decrement of life to the extremity of old age, the differ- ence of the rules is but inconfiderable. But if ever we fhouki have tables of obfervation, concerning the mortality of man- kind, intirely to be depended upon, then it would be con- venient to divide the whole interval of life into fuch fmaller in- tervals, as, during which, the decrements of life have been obferved to be uniform, notwithstanding the decrements in fome of thofe intervals mould be quicker, or flower, than others ; for then the theorem here given, would be prefer- able to the other*
PROBLEM II.
To find the value of an Annuity for a limited interval of life, during which the decrements of life may be confldered as equal.
Let a and h reprefent the number of people living in the be- ginning and end of the given interval of years. Let s be that interval ; P, the value of an Annuity certain for that inter- val ; ^.» the value of an Annuity for a life fuppofed to be neceflarily extinct in the time s ; or, which amounts to the iame* the value of an Annuity for a life of which the com- plement 15 St.
Then J^-l X P — if will expreSs the value required. Ex- ample. Let it be required to find the value of an Annuity for an age of 54, to continue 1 6 years, and no longer. Then by Dr. Halley's tables it appears that a — 302, b = 172.
And n ss s =as 16 ; and by the tables of the values of Annuities
certain P= 10.8377; alfo by probl. 1. %j=s ~- L _
6.1 168. Hence by the prefent problem, it follows* that
QA x*?— ^=8.3365; the years purchafe required,
fuppofing intereft at 5 per Cent, per Ann. In the fame manner the value of an Annuity between the age of 42 and 49 is worth 5-3492- y ears purchafe. And from the age of 49 to 54 is worth 4.0374 years purchafe. Now if it were required to determine the value of an Annu- ity or life to continue from 42 to 70, it might be determined from the foregoing partial computations ; but deductions for the chance of the life's failing between 49 and 54, as alfo be- tween 42 and 49, and the difcount of money, during thofe feve- ral intervals, rauft be allowed. Then the value of an An- nuity to continue from 42 to 70 will be found to be 11.0571 years purchafe. In the fame manner of computation the laft 16 years of life, reaching from 70 to 86, when properly dis- counted and alfo diminithed on account of the probability of living from 42 to 70, the value of thofe 16 years will be re- duced to 0.8 ; this being added to 11.0571 before found, the Sum ri.8571 will be the value of an Annuity to continue from 42 to 86 ; and this is the value of a life of 42. Now this value in Mr. De Moivre's tables is but 11.57, on the fuppofition of an uniform decrement of life, from an age given, to the extremity of old age. We fee then how the more accurate obfervations concerning the mortality of man- kind Surnifti corrections to the tables of Annuities in ufe. We mult here obferve, that Mr. De Moivre in this tran- saction has corrected the folutions he had formerly given of two problems, viz. the 23d, and 25th. in the II. edition of his Annuities.
Annuity/^ Lives. See Life.
ANNUNTIATOR, in the Greek church, an officer vvhofe bufinefs is to give notice of the feafts, and holy days to be obferved. Trev. Diet. Univ. T. r. p. 429.
ANOCHUS, an imaginary name of a medicine, concerning which many fruitlefa conjectures have been made. The word occurs only in Gaza's tranflation of the account which Theo- phraftus has left us of the euonymus of thofe times. The author fays, that the goats which eat the leaves and fruit of the euonymus were killed by it, and that they died of a Stop- page of the bowels, which he has exprefled by the word anocho, ™°X U > derived from the verb, «nvp(p» 9 which Signifies a reten- tion of the Stools ; and having added to this error a Second of reading the Greek word xaQttptf&at into x«8a^ E 1ai, he explains it that they muft be cured by anochus, which he mistakes for the name of Some medicine, not understanding it to be the name by which the author expreffed the diSeaSe. It is to be obferved by the way, that the euonymus of the Greeks could not be the fame plant known at this time by that name, Since the cattle eat our euonymus or fufanus when- ever they can get it, and that without any danger ; but the defcriptions of thefe plants in the antient and modern authors fhew alfo that they were very different. See Fus an us
ANOCTORON, in ecclefiaftical antiquity, a name uSed by fome writers for a church. Bingh. Orig. Ecclef. L 8. c. 1 - §.5. AnoRora properly import Roman halls, divers of which were converted into churches.
In which fenfe Anoilora amount to much the fame with baft- lktz % See Basilics.
ANO
ANOCYSTI, in natural hiftofy> the name of a clafs of the 1 echini marini, which have an aperture for the anus at the top of the Shell. r
Some of thefe approach to a hemispheric or Spheroidal figurej others flatter, and in fhape Somewhat refembling a Shield. ANODUS is uSed by Some chemical writers to denote a pu J tritious matter Separated by the kidneys. In this fenfe Anodus ftahds contradiftinguifhed from the Super- fluous part, that is the urine. Paracelf. 1. 1 . de Tartar. Tracd 3. c. 2. Not. ANODYNE {Cycl.) — A ready way of preparing a ufeful, fafe, and efficacious Anodyne is as follows. Take half an ounce of opium, diffolve it in a gentle heat in three ounces of water, ftrain the folution and evaporate it to a dry fubftance. Grind this to powder in a glafs mortar with twice the quantity of loaf-Sugar, and you have an excellent preparation of opium, to be given three or four grains for a dofe. Shaw's Lectures P- 233.
By diiSoIving the opium thus in water, we get rid riot only of its grofs and foul parts, but alfo of it refmous, which are found much more pernicious than the reft ; and by dividing its parts afterwards with Sugar the medicine is rendered more uniform, refoluble, and miScible with animal fluids. But however opium is prepared, it ftill muft be acknowledged that it retains qualities that make it little lefs than apoifonin an over dofe ; whence it were much to be wifhed Something could be found that would be more innocent, and yet Supply it place. And this camphor and nitre will do on many, tho' not on all occafions; Anodykus Mineralis Liquor. See Liquor. ANOINTERS, a religious feet in fome parts of England, So called from the ceremony they ufe of anointing all perfons be- fore they admit them into their church. They found their opinion of anointing upon the fifth of St. James vcrfes 14 and 15. Is there any fick among you (which they account all people to be but themfelvcs) let him call for the elders of the church, and let them pray over hiiii, anointing him with oil in the name of the Lord ; and the prayer of faith fliall Save the fick, and the lord (hall raife him up, and if he" have committted fins, they fliall be forgiven him. The elders 2mong thefe people are fome of the mean tradefmen of the place, and the oil they ufe is that commonly fold in the Thops j with which the profelyte being Smeared over, and fired with zeal, he preSently becomes a new light of this church. Plat's Oxfordshire, p. 208. ANOLE, in zoology, the name of a Species of lizard com- mon in the Weft-Indies, about houfes and plantations. It is of the Size of the common lizard of Europe, but its head is longer, its Skin of a yellowifh colour, and its back variegated with green, blue, and grey lines running from the neck to the tail. They creep into holes for the night, and there make a continual and very difagreeable noife ; in the day time they are always in motion. Rocbefort, Hift. Antiil. ANOLYMPlADES, in antiquity, a name given bytheEleans to thofe Olympic games, which had been celebrated under the direction of the Pifeans and Arcadians. Potter, Ar- chasol. Grasc. I. 2. c, 22.
The Eleans claimed the Sole right of managing the Olympic games, in which they Sometimes met with competitors. The hundred and fourth Olympiad was celebrated by order of the Arcadians, by whom the Eleans were at that time reduced very low ; this as well as thofe managed by the inhabitants of Pifa, they called ayoXvfMrui^as, that is, unlawful Olympiads, and left them out of their annals, wherein the names of the 1 victors and other occurences were rcgiftred. ANOMCEANS, (Cjk/.) in church hiftory, were fometimes called corruptly Anomians, Anomii^ and Anomianii The Anomoeans were a Species of rigid Arians. They con- demned the Semi-arians at the council of Ancyre for holding the to opcitio-tor. Budd. ISag. ad. Theo!. 1. 2. c. 2. p. 458. Prateolus deScribes the Antinomians, under the title of Andmt or Anomasi, Anomceans. Elench. Hasref. 1. 1. n. 40. See alfa Sozom. 1. 4. c. 13. and 284 It. 1. 6- c. 26. Socrat. 1. 2. c. 35. 'tbe.odor, 1. 4. Epiphan, Haeref. 57, or 77. Trev. Diet. Univ. in voc.
The word Anomcean is compounded of «, and voftot, law and more properly belongs to the Sect whom we call Antinomia'nSj than to the Anomceans. See Antinomians* ANOMORHOMBOIDIA, in natural hiftory, the name of 3 genus of Spars; the word is derived from the Greek, a\«f*«7wVy irregular, and ^£01^ a rhomboidal figure. The bodies of this genus are pellucid crystalline Spars of no determinate or regular external form, but always breaking into regularly rhomboidal mafies ; eafily fiflil, and compofed of plates running both horizontally and perpendicularly thro' the manes, but cleaving more readily and evenly in an horizontal than in a perpendicular direction. The plates being ever com- poSed of irregular arrangements of rhomboidal concretions. Of this genus there are five known Species. 1. A white bright and fhattery one ; found in great quantities in the lead-mines of Derbyfhire, Yorkfhufej and Wales. 1* A milk-white ©pake and fhattery one, found in fome parts of France, and very plentifully in Germany, and fometimes in Wales and! Scotland, and in the hills of Yorkfhife, 3. A hard dull and
fnow-
