is the reduction of figures, &c. whence they are called compaffes of reduction. See the article COMPASS. many of its denomination as is contained in the greater. This is the converfe of the laft, and is termed reduction af "tending. See the articles MULTIPLI CATION and DIVISION. The reduction of the principal monies, coins, weights, measures, &c. antient and modern, foreign and domeftic, may be found under their refpective articles MONEY, COIN, WEIGHT, MEASURE, POUND, FOOT, &c. Thus pounds are reduced into thillings by multiplying with 20; fhillings into pence, by multiplying with 12; and pence into farthings, by multiplying with 4. On the other hand, Chillings are reduced into pounds, by dividing with 20; pence into fillings, by dividing with 12; and farthings into pence, by dividing with 4. Examples. Let it be required to reduce 3571. into fhillings, and thofe fhillings into pence; 357×20=7140 the thilfings in 3571. and 7140X12=85680= the pence in 3571. as was required. Again, let it be required to reduce 85680, into fhillings, and thofe fhillings into pounds; 85680 by 12 = 7140 the fhillings in 3571. and 7140÷ by 20-3571. as was required. If there remain any thing in each divifion, it is refpectively either odd pence, hillings, or farthings; thus 4123788 farthings, being reduced, give 42951. 128. 3 d. But when the numbers propofed, to be reduced are of feveral denominations, and it is required to bring them all to the lowest, you must reduce, as before, the higheft or greatest denomination to the next lefs, adding the numbers that are of that next denomination together; then reduce their fum to the next lower denomination; adding together all the numbers that are of that denomination, and fo proceed gradually on until all is done. There are various methods of reducing figures, &c. the most eafy is by means of the pentagraph, or parallelogram: but this has its defects. See the article PENTAGRAPH. The best and not ufual methods of reduction are as follows: 1. To reduce a figure, as ABCDE (plate CCXXX. fig. 1. n° 1.) into a leis compafs. About the middle of the figure, as z, pitch on a point, and from this point draw lines to its feveral angles A, B, C, &c. then draw. ing the line ab parallel to A B, be parallel to BC, &c. you will have the figure abcde fimilar to ABCDE. If the figure abcde had been required to be inlarged, there needed nothing but to produce the lines from the point beyond the angles, as z D, C, &c. and to draw lines, viz. DC, CB, &c. parallel to the fides dc, cb, &c. 2. To reduce a figure by the angle of proportion, fuppofe the figure ABCDE (ibid. n° 2.) required to be diminished in the proportion of the line AB to ab, (ibid. n° 3.) draw the indefinite line GH (ibid. n° 4.) and from G to H fet off the line AB. On G defcribe the arch HI. Set off the line ab as a chord on HI, and draw GI. Then with the angle IGH, you have all the measures of the figure to be drawn. Thus to lay down the point c, take the interval BC, and upon the point G, defcribe the arch KL. Alfo on the point G defcribe MN; and upon A, with the distance M N, defcribe an arch cutting the preceding one in c, which will determine the fide bc. And after the fame manner are the other fides and angles to be defcribed. The fame procefs will also serve to enlarge the figure. 3. To reduce a figure by a scale. Meafure all the fides of the figure, as ABCDE, (ibid. n° 2.) by a scale, and lay down the fame measures refpectively from a finaller fcale in the proportion required. 4. To reduce a map, defign, or figure by fquares. Divide the original into little fquares, and divide a fresh paper of the dimenfions required into the fame number of fquares, which are to be larger or lefs than the former, as the map is to be enlarged or diminished. This done in every fquare of the fecond figure, draw what you find in its correspondent one in the firit. REQUE REDUCTION to the ecliptic, in aftronomy. The place of any tar reduced to the ecliptic, is that point where the fecondary paffing through the star interfe&ts the ecliptic. See the articles REDUCTION and SECONDARY, REDUCTION, in metallurgy, is the bringing back metalline fubftances which have been changed into fcoriæ or ashes, or otherwife divested of their metallic form, into their natural and original fate of metals again. All metals and femimetals may be reduced by proper management, whatever have been their changes, except only zink, which having been burnt to afhes, admits of no reduction ; but the mixture of gold and filver was never yet radically diffolved by any experiment, whatever fome may have imagined. Even fome earths will turn into metals by the admixture and intimate union of a phlogistion or inflammable principle. REDUCTION into firft matter, is a term which alchemifts ule when they find their fubftances putrify and grow black. Reduction is more particularly used for the converting of a dry matter into a liquid, particularly into water, which by the alchemists is held the principle of all things. RECUCTION, in furgery, denotes an ope ration whereby a diflocated, luxated, or fractured bone is restored to its former ftate or place. See the articles LUXATION and FRACTURE. REDUIT, in military affairs. See the article REDUCT. REDUNDANCY, or REDUNDANCE, a fault in difcourfe, confifting in the use of a fuperfluity of words. Words perfectly fynonymous are redundant, and ought to be retrenched. REDUNDANT HYPERBOLA, is a curve of the higher kind, thus called because it exceeds the conic section of that name, in the number of its hyperbolical legs; being a triple hyperbola with fix hyperbolical legs. See HYPERBOLA, CURVE, and CONIC SECTIONS. REDUPLICATION, in rhetoric, a figure whereby a verle begins with the fame word as the preceding one ends with. See the article ANADIPLOSIS. REDUPLICATION, in logic, a kind of condition expreßled in a propofition indicating or aligning the manner wherein the predicate is attributed to the fubject. Hence reduplicative propofitions, are tuch wherein the fubject is repeated with fome circumftance or condition. Thus, men, as men, are rational: kings, as kings, are fubject to none but God. REE, REIS, or RES, a little portugueze copper coin. See the article COIN. REED, an antient jewish measure. See the article MEASURE. REED, or the Common REED, in botany, arundo. See the article ARUNDO. REEF, a term in navigation. When there is a great gale of wind, they commonly roll up part of the fail below, that by this means it may become the narrower, and not draw fo much wind; which contracting or taking up the fail they call a reef, or reefing the fail: fo alfo when a top-malt is fprung, as they call it, that is, when it is cracked, or almost broken in the cap, they cut off the lower piece that was near broken off, and fetting the other part, now much shorter, in the ftep again, they call it a reefed top-maft. REEL, in the manufactories, a machine ferving for the office of reeling. There are various kinds of reels, fome very fimple, others very complex. Of the former kinds thofe most in use are, 1. A little reel held in the hand, confifting of three pieces of wood, the biggest and longeft whereof (which does not exceed a foot and a half in length, and of an inch in diameter) is traverfed by two other pieces difpofed different ways. 2. The common reel, or windlace, which turns upon a pivot, and has four flights traversed by long pins or fticks, whereon the fkain to be reeled is put, and which are drawn closer or opened wider, according to the skain. A representation of the common reel may be feen in plate CCXXIX. fig. 5. where A is the bench or feat of the reel, B the two uprights, C the arms of the reel. Its arbor turning and hitching, its little lantern of four notches in the teeth of the wheel; D two wheels, the upper one of which moves the lower, by means of a pinion. E a hammer, the handle whereof is lowered by a peg at the bottom of the lower wheel. Fa cord which is rolled round the axle of the lower wheel, and fupports a weight which tops after a certain numbers of turns, to regulate the work-woman. There are other reels used in particular arts, as the reel ufed in milling of filk, &c. and thofe in the reeling and winding of filks. See the article SILK. REELING, in the manufactories, the winding of thread, filk, cotton, or the like, into a fkain, or upon a bottom, to prevent its entangling. It is also used for the charging or difcharging of bobbins or quills, to use them in the manufacture of different ftuffs, as thread, fik, cotton, &c. Reeling is performed different ways, and on different engines. See the article REEL. RE ENTRY, in law, fignifies the refuming or retaking that poffeffion which any one had lately forgone; as where a perfon makes a leafe of lands to another, the leffer thereby quits the poffeffion, and if the leffee covenants that upon non. payment of the rent referved, the leffor may lawfully re-enter, being as much as if it was conditioned for the leffor to take the land again into his hands, and recover the poffeffion again by his own act without the affiftance of the law. Likewife, if a leafe for years be made, with condition that if the leffee affign his terms, the leffor may re-enter, and the leffee in breach of the condition affigns unknown to the leffor, who accepts of rent from the affignee without notice of the affignment, in that cafe it is held the leffor may re-enter, notwithstanding his acceptance of the rent, REEVE of a church, the guardian of it, or the churchwarden. See CHURCH. REEVING, in the fea language, the puting a rope through a block: hence to pull a rope out of a block, is called unreeving. RE-EXCHANGE, in commerce, a fecond payment of the price of exchange, or rather the price of a new exchange due upon a bill of exchange that comes to be protested and to be refunded the bearer by the drawer or indorfer. See the articles EXCHANGE and BILL. RE-EXTENT, in law, a fecond extent upon lands or tenements, complaint being made that the former was partially executed. See the article EXTENT. REFECTION, among ecclefiaftics, a spare meal or repaft juft fufficing for the fupport of life: hence the hall in convents, and other communities, where the monks, nuns, &c. take their refections or meals in common, is called the refectory. REFERENCE, in writing, c. a mark relative to another fimilar one in the margin, or at the bottom of the page, where fomething omitted in the text is added, and which is to be inferted either in read. ing or copying. References are alfo used in books where things being but imperVOL. IV. feally handled, the reader is directed to fome other part or place for a further explanation of them. For the ufe of thefe references in a work of this kind, we res fer the reader to what has been faid upon that fubject in our introduction to this work. REFINING, in general, is the art of purifying a thing; including not only the affaying or refining of metals, but like. wife the clarification of liquors. See ASSAYING and CLARIFICATION. REFINING of gold is performed three ways, viz, either with antimony, fublimate, or aqua fortis; the laft of which is the most utual, and is called depart, or quartation. To refine gold with antimony, they make ufe of a wind-furnace, and a common crucible of a fize answerable to the quantity of gold to be refined; always taking care that the gold and antimony, both together, do not fill the crucible more than half full. After the gold is melted in the crucible, the antimony is thrown in in powder: the proportion of the ana timony to the gold is eight ounces to a pound, if the gold be between fixteen and twenty-two carats fine; if it be under fixteen carats, then they ufe five quarters of a pound to eight ounces of gold; and fill the greater quantity of antimony is required, the coarser the gold is, As foon as they have put the antimony into the crucible, they cover it, and after they have charged the furnace with char coal, they put on the capital, which is let to ftand till fuch time as the crucible is left quite bare; then they take off the capital, and leave the crucible to cool in the furnace of itself, till fuch time as they can take it out by the hand; then they break it, to get out the button or culot, which is a mass of fine gold remaining at the bottom, with the fæces of the antimony, the filver and copper alloy, and fometimes little particles of gold itfelf over it. But notwithtanding the gold thus prepared is very pure, yet the antimony gives it fuch a harsh brittle quality, that it ceafes to be ductile, and must be foft tened by the fire with falt-petre and borax, to bring it to itself. In order to this operation, they prepare what is called a dry coppel, which is a coppel made of crucible earth, that does not imbibe like the coppels made of afhes. When the coppel has been fufficiently heated in the refining furnace, they put the gold into it, and cover it over with charcoal. IS Y As all the afhes and other impurities, that may be floating on the liquid gold, with a pair of bellows. This is repeated again and again, till the impurities of the gold are carried off by the fublimate, appearing of a bright glittering colour; after which being taken out of the crucible, it is caft into an ingot. As foon as the gold is diffolved, which is very foon, by reafon of the remains of the antimony, they blow it with the bellows to drive the mineral entirely away, which now goes off in fmoak; and add to it, as foon as the fumes cease, a little falt-petre and borax in powder, which collect the impurities that remained upon the diffolution, and fix the gold in the coppel in the form of a plate. Then the gold is taken out of the coppel, and melted again in a crucible, with an addition of two ounces of falt-petre and borax in powder, to each eight ounces of gold, as foon as it has ceafed to fume; and then it is caft into an ingot, which upon trial is found to be twenty-three carats, twenty-fix thirty feconds fine. The particles of gold, detained with the alloy in the faces of the antimony, are got out by a dry coppel, with the fame meltings and ingredients, as were used in foftening the former: and when they are certain, by the affay, how much gold the matter contains, they refine it to feparate the copper, and afterwards make the depart or quartation. See the article QUARTATION. As for the gold which may be left stick. ing to the dry coppels, it is got by breaking and pulverizing the crucibles, and by repeated washings of the powder of them. The method of refining gold, by means of fublimate, is this: they begin the process like that with antimony; that is, in the fame furnace, with the fame coal, the fame fire, and the fame crucibles. When the gold is melted in the crucible, they cat in the fublimate, not in powder, but only broken into pieces: the proportion is, if the gold be of twenty-two carats, an ounce or an ounce and a half, or even two ounces of the fublimate to eight ounces of the gold; if of twenty carats, three ounces; and if it be only from eighteen to twelve, five or fix ounces of the fublimate to eight of the gold, in which laft cafe they part the fublimate into two, and put in one half at a time with the gold into a new crucible; which, when the operation is over, leaves the gold of eighteen or twenty carats, according as it was in fineness before. This done, they put the broken fublimate into a crucible with the melted gold, covering it immediately to fmother the mineral; and then fill the furnace with charcoal, having firit put on the capital; after a quarter of an hour they take off the capital, lay the crucible bare, and blow off This method of refining by fublimate, is both cheaper and more complete than that by antimony; but they are both exceeding dangerous, by reafon of the fulphureous and arfenical exhalations; on which account the method by quartation is most practifed. REFINING of filver is performed two ways; one with lead, and the other with faltpetre. In order to refine filver with lead, a cop- As these two metals melt together, the copper before mixt with the filver diffipates into fmoak, or goes away with the fcum; and fo does the lead itfelf, leaving the filver alone in the coppel in its proper degree of fineness. In this method of refining, wherein fix or feven thousand pounds may be refined at once, the metal is drawn out of the coppel two ways; the one by plunging in it, while fill liquid, a thick bar of iron, round which the filver fticks in form of a fhell or cruft, repeating this again and again; the other is by letting the coppel ftand till it is cold; in the bottom of which, the filver fixes in form of a cake. This method of refining filver with lead, is both the best and the cheapest: however, for want of workmen who underftand it, that with falt petre ftill obtains in many places; which is performed in a wind furnace. They firft reduce the filver to be refined into grains, about the fize of a small pea; which is done by firft melting it, then throwing it into a tub of common water, and then heating it over again in a boiler. This being done, they put it into a crucible; putting to every eight ounces of filver two of falt-petre. Then they cover the crucible with an earthen lid (in the form of a dome) exactly luted; which lid, how point of incidence. See MIRROUR. Again, a fine, as CG, drawn from any point, as C, of the reflected ray BC, perpendicular to the fpeculum, is called the cathetus of the reflection, or cathetus of the eye; as a line, A F, drawn from the radiant perpendicular to the fpeculum, is called the cathetus of incidence. ever, must have a little aperture in the middle. The crucible being set into the furnace, and covered with charcoal, which is only to be lighted by degrees, at length they give it the full force of the fire, to put the metal into a perfect fufion. This is repeated three times fucceffively, at an interval of a quarter of an hour. After the third fire they uncover the furnace, and let the crucible cool; and at length break it, to get out the filver, which is found in a button or culot, the bottom of which is very fine filver; and the top mixed with the fæces of the falt-petre, and the alloy of the filver, and even fome particles of fine filver. Then they separate the culot from the impurities, and melt it in a new crucible; and throw charcoal-duft into.the diffolution, and work the whole briskly together. Then they cover the crucible up again, charge the furnace with coal, and give it a fecond fire. Having done this, they blow off the afhes and impurities with bellows, from off the top of the metal, till it appears as clear as a looking glass; and then they throw in an ounce of borax broken to pieces. Then, in the laft place, they cover the crucible up again, and give it the laft fire, and after this caft it into ingots, which are found eleven pennyweight and fixteen grains fine. To recover the filver that may be left in the fæces and scoria, they pound them, and give them repeated lotions in fresh water. REFINING of fugar, fulphur, camphor, nitre, &c. See SUGAR, CAMPHOR, &c. REFLECTING, or REFLECTIVE DIAL. See the article DIAL. REFLECTION, or REFLEXION, in mechanics, the return or regreffive motion of a moving body, occafioned by fome obftacle which hindered it from pursuing its former direction. For the laws of the reflection of moving bodies, fee MOTION, COMMUNICATION of motion, and PERCUSSION. REFLECTION of the rays of light, in catoptrics, is their return, after approaching fo near the furfaces of bodies, as to be thereby repelled, or driven backwards. Thus the ray AB (plate CCXXX. fig. 2. n° 1.) proceeding from the radiant A, and ftriking on the point B of the speculum or plane DE, being returned thence to C; B C reprefents the reflected ray, and B the point of reflection; in refpe&t whereof A B represents the incident ray, or ray of incidence, and B the Of the two angles which the reflected ray BC makes with the mirrour, the fmalleft, CBE, is called the angle of reflection; as, of the two angles the incident ray makes with the fpeculum, the fmaileft, ABD, is called the angle of incidence. If the mirrour be either concave or convex, the fmalleft angles the ray makes with a tangent to the point of reflection and incidence, are the angles of reflection and incidence. The angle CBH, which the reflected ray makes with a perpendicular to the point of reflection, is called the inclination of the reflected ray; as the angle ABH is called the inclination of the incident ray. The great law of reflection is, that the angle of reflection, CBE, is always equal to the angle of incidence, A B D, as has been demonftrated under the article IN CIDENCE. The rays of light are found by experiment to be differently reflexible, in the fame manner, and for the fame reason, that they are differently refrangible; or that thofe rays which were leaft and molt refrangible, were alfo leatt and most reflexible; and, confequently, exhibit the fame colours, and in the fame order. Ste the article COLOUR. Causes of the REFLECTION of light. The opinions of philofophers, relating to the caufe of this difficult phænomenon, b:ing principally four, are thus ftated by Mr. Rowning. 1. It was the opinion of philofophers, before Sir Ifaac Newton difcovered the contrary, that light is reflected by impinging upon the folid parts of bodies. But that this is not the cafe, will appear from the following reafons: and, first, it is not reflected at the first furface of the body, by impinging against; for it is evident, that in order to the due and regular reflection of light, that is, that the reflected rays fhould not be difperfed and scattered one from another, there ought to be no rafures or unevennefs in the reflecting furface large enough to bear a fenfible proportion to the magnitude of a ray of light; because, if the 15 Y 2 furface |