a recoveree, and a vouchee. The recoverer is the plaintiff or demandant, that brings the writ of entry. The recoveree is the defendant or tenant of the land, against whom the writ is brought. The vouchce, is he whom the defendant or tenant voucheth or calls to warranty of the land in demand, either to descend the right, or to yield him other lands in value, according to a supposed agreement. And this being by consent and permission of the parties, it is therefore said that a recovery is suffered. the globes, is to fit them for performing any problem. curve. RECTIFICATION, in geometry, is the finding a right line, equal in length to a The rectification of curves is a branch of the higher geometry, where the use of the inverse method of fluxions is very conspicuous, of which we shall give an example. Case 1. Let A C G (Plate Miscel. XIII. fig 15.) be any kind of curve, whose ordinates are parallel to themselves, and perpendicular to the axis A Q. Then if the fluxion of the absciss A M be denoted by M m, or by C n, (equal and parallel to M m) and n S, equal and parallel to C r, be the representation of the corresponding fluxion of the ordinate MC; then will the diagonal C S, touching the curve in C, be the line which the generating point would describe, were its motion to become uniform at C; which line, therefore, truly expresses the fluxion of the space A C, gone over. Hence, puting A Mx, CM=y, and A C = 2; we have ( = C S = ✓ Cn2 + Sn2) = A common recovery may be had of such things, for the most part, as pass by a fine. An use may be raised upon a recovery, as well as upon a fine; and the same rules are generally to be observed and followed for the guiding and directing the uses of a recovery, as are observ. ed for the guidance and direction of a fine. That is to say, that when a fine is levied, or a recovery is suffered, a deed is made between the parties really interested, which declares the purposes of the fine or recovery, and this deed is called a deed to lead or to declare the uses, according as it is made before or after the fine or recovery. To enter at full into the learning of fines and recoveries, would be impossible in a general dictionary. It is sufficient to say, that both of them are in the nature of a sham suit, while one of which is compromised, and the other carried on to judgment by and hence x = default between the parties really interested, and the use of them is to enable a married woman to make a good convey. ance, and a tenant in tail to turn his estate into an estate in fee, or, as it is called, to dock or bar the entail. See FINE and ESTATE. In or RECTANGLE, in geometry, the same with a right-angled parallelogram. arithmetic and algebra, a rectangle signifies the same with factum or product. RECTANGULAR, RECTANGLED, RIGHT-ANGLED, appellations given to figures and solids which have one or more right angles: thus a triangle with one right angle, is termed a rectangled triangle; also parallelograms with right angles, squares, cubes, &c are rectangular. Solids, as cones, cylinders, &c. are also said to be rectangular, with respect to their situation, when their axes are perpendicular to the plane of the horizon. The ancient geometricians always called the parabola the rectangular section of a ' +ÿ3; from which, and the equation of the curve, the value of may be determined. Thus, let the curve proposed be a parabola of any kind, the general equation for which is == ( nyn-ly 27-2 a2n-2 an = a2n-2 the fluent of which, universally expressed in an infinite series is y+ 6n-5 + - Case II. Let all the ordinates of the proposed curve A R M (fig. 16) be referred to a centre C: then putting the tangent RP (intercepted by the perpendicular C P) =t, the arch, BN, of a circle, described about the centre C, = x; and the radius C N (or CB) haveży: y (CR): t (RP); and, conży sequently, ż from whence the value of z may be found, if the relation of y and is given. But, in other cases, it will be better to work from the following which is thus derived let the right line : CR be conceived to revolve about the whence, by composition, : : s1 + t2 (y3) : ; therefore, a a1 and consequently+y (= "2) = i. Q. E. D. But the same conclusion may be more easily deduced from the increments of the flowing quantities: for, if Rm, rm, and N n be assumed to represent (, y, x) any very small corresponding increments of AR, CR, and B N; then will CN (a): CR(y) (the arch N n): the similar ух arch Rr= And if the triangle Rr :: a m (which, while the point m is returning back to R, approaches continually nearer and nearer to a similitude with CRB) be considered as rectilinear, we shall also obtain (= Rm2 = R r2+rm2) = RECTUM, in anatomy, the third and last of the large intestines. RECURRING series, is a series consti tuted in such a manner, that, having taken at pleasure any number of its terms, each following term shall be related to the same number of preceding terms, according to a constant law of relation. RECURVIROSTRA, the avoset, in natural history, a genus of birds of the order Gralla. Generic character: the bill long, very thin, and bending considerably upwards; nostrils narrow and pervious; tongue short; feet palmated; hind toe very short and high. There are three species. We shall notice only that which is found in this island. The R. avosetta, or scooping avoset, is as large as a lapwing, and has extremely long legs; its bill is three inches and a half in length. In winter it is often seen in England, particularly at the mouth of the Severn, and on the coasts of Suffolk. In the fens of Cambridgeshire these birds are known to breed, and appear often in vast flocks. Their subsistence is on insects and worms, which they procure from the soft, muddy bottoms with their bills. They often wade into the water to the top of their legs, and are able to swim; but are seldom seen swimming, and never, unless at a very small distance from the shore. In France, on the coasts of Bas Poictou, their nests are plundered annually of several thousands of eggs, which form a + y2 (= "") nourishing and valued food for the pea , as before. See Simpson's "Fluxions." a RECTIFICATION, in chemistry, is nothing but the repetition of a distillation, or sublimation, several times, in order to render the substance purer, finer, and freer from aqueous or earthy parts. RECTIFIER, in navigation, an instrument consisting of two parts, which are two circles, either laid one upon, or let into, the other, and so fastened together into their centres, that they represent two compasses, one fixed, the other moveable; each of them divided into the thirty-two points of the compass, and three hundred and sixty degrees, and numbered both ways, from the north and the south, ending at the east and west in ninety degrees. RECTIFYING the globe. See GLOBE. VOL. X. santry of that district. See Aves, Plate XIII. fig. 4. RECUSANT, a person who refuses to go to church, and worship God after the manner of the church of England, as by law established: to which is annexed the penalty of 201. a month for non-conformity. 23 Elizabeth, c. 1. RED. See COLOUR, DYEING, OPTICS, &c. RED book, of the Exchequer, an ancient record, or MS. volume, in the keeping of the King's remembrancer, containing divers miscellaneous tracts relating to the periods before the conquest. REDDENDUM, a clause in a lease, whereby the rent is reserved to the les sor. See DEED. REDDLE, red-chalk, in mineralogy, a species of the iron genus: its name bespeaks its colour: it soils strongly, and writes; is casily frangible; adheres Gg strongly to the tongue; feels meagre; specific gravity 3.9. Exposed to a red heat, it decrepitates, and becomes black; it may even be melted into a greenish grey spumous enamel. In Silesia it is found in compact limestone: it is principally used for drawing: the coarser kinds are used by the carpenter, the finer by the painter. It is sometimes used in its natural state, and sometimes pulverized, washed, and mixed with gum, and cast into moulds. REDEMPTION, and EQUITY of Redemption, in law. See MORTGAGE. REDOUBT, in fortification, a square work raised without the glacis of the place, about musket-shot from the town; having loop-holes for the small arms to fire through, and surrounded by a ditch. Sometimes they are of earth, having only a defence in front, surrounded by a parapet and ditch. Both the one and the other serve for detached guards to interrupt the enemy's works; and are sometimes made on the angles of the trenches, for covering the workmen against the sallies of the garrison. The length of their sides may be about twenty fathoms their parapets must have two or three banquettes, and be about nine or ten feet thick. They are sometimes (in a siege) called places of arms. : REDUCTION of metals, in chemistry. All metals, even the few that resist the action of heat and air, undergo a similar change when exposed to acids, especially the sulphuric, the nitric, and the muriatic, or a mixture of the two last. All metals, by these means, may be converted into powders, which have no resemblance to the metals from which they were obtained. These powders were for merly called calces; but at present they are better known by the name of oxides. They are of various colours, according to the metal and the treatment, and are frequently manufactured in large quantities, to serve as paints. When these oxides are mixed with charcoal powder, and heated in a crucible, they lose their earthy appearance, and are changed again into the metals from which they were produced. Oil, tallow, bydrogen gas, and other combustible bodies, may be often substituted for charcoal. By this operation, which is called the reduction of the oxides, the combustible is diminished, and indeed undergoes the very same change as when it is burnt. In the language of Stahl, it loses its phlogiston; and this induced him to conclude that metals are composed of earth and phlogiston. Mr. Davy, as we have seen in other parts of this work, inclines to the opinion that there are only two principles in nature, an inflammable and metallic principle. REDUCTION. See ARITHMETIC. REDUCTION of a figure, design, or draught, is the making a copy thereof, either larger or smaller than the original; still preserving the form and proportion. The great use of the proportional compasses is the reduction of figures, &c. whence they are called compasses of reduction. There are various methods of reducing figures; the most easy is by means of the pentagraph, or parallelogram; but this has its defects. See PEN TAGRAPH. REE, REIS, OF REs, a little Fortuguese copper coin. REED, an ancient Jewish measure. See MEASURE. REED, or the Common Reed, in botany, arundo. See ARUNDO. REEF, a term in navigation. When there is a great gale of wind, they commonly roll up part of the sail below, that by this means it may become the narrower, and not draw so much wind: which contracting or taking up the sail they call a reef, or reefing the sail: so also when a top-mast is sprung, as they call it, that is, when it is cracked, or almost broken in the cap, they cut off the lower piece that was nearly broken off, and setting the other part, now much shorter, in the step again, they call it a reefed top-mast. The term "reef" implies also a chain of rocks lying near the surface of the water. There REEL, in the manufactories, a machine serving for the office of reeling. are various kinds of reels, some very simple, others very complex. Of the former kinds those most in use are, 1. A little reel held in the hand, consisting of three pieces of wood, the biggest and longest whereof (which does not exceed a foot and a half in length, and one-fourth of an inch in diameter) is traversed by two other pieces disposed different ways 2. The common reel, or windlass, which turns upon a pivot, and has four flights traversed by long pins or sticks, whereon the skein to be reeled is put, and which are drawn closer, or opened wider, according to the skein. REELING, in the manufactories, the winding of thread, silk, cotton, or the like, into a skein, or upon a bottom, to prevent its entangling. It is also used for the charging or discharging of bobbins, or quills, to use them in the manufacture of different stuffs, as thread, silk, cotton, &c. Reeling is performed different ways, and on different engines. RE-ENTRY, in law, signifies the resuming or retaking a possession in land lately lost. REFERENCE, in law, is where a matter is referred by the Court of Chancery to a master, and by the courts at law to a prothonotary, or secondary, to examine and report to the court. Reference also signifies where a matter in dispute is referred to the decision of an arbitrator. This is done either by parol agreement, or by bond, or upon a suit, in which latter case the party has a rule of court, that the party against whom the award is made shall perform it, and then he may move to have an attachment against him, if he does not perform it. By statute also this may be done, where the parties agree that the award should be made a rule of court, although there is no suit. REFINING. See ASSAYING, REFLECTING circle, an astronomical instrument for measuring angles. It is called reflecting from its property, in common with the Hadley's quadrant (of which it is a modification) of observing one of the objects of the angle to be measured by distinct vision, and the other by reflection of plane mirrors. The first instrument of this kind was invented by Tobias Mayer, in 1770, a celebrated astronomer of Gottingen, who calculated the lunar and solar tables for determining the longitude at sea, for which a reward of 3,000l. was given by the board of longitude In making use of these tables he found that the Hadley's quadrants, though made by the first artists of that time, were not divided with sufficient accuracy for his purpose; he therefore contrived the reflecting and repeating circle; to comprehend which, the reader must turn to our article QUADRANT, by Hadley, from which this instrument differs, principally, in being a whole circle of divisions instead of an octant; and is so contrived, that when an observation has been made, it is repeated upon a fresh portion of the divisions, then a third time, a fourth, and so on as many times as is necessary; the observation is then read off, and the product is divided by the number of observations, made so as to take a mean of the errors there may be in any part of the divisions on the circle. This contrivance, though useful, was found so tedious, in taking so many observations, that it was laid aside in favour of the Hadley's quadrant, to which in point of accuracy it was really superior. For the particular description of this instrument we must refer our readers to a work, entitled "Tabula Motum Solis et Lune," by Tobias Mayer, London, 1770. This instrument received an improvement from the Chevalier de Borda, at Paris, which rendered its operation much more simple; but it was not until the year 1796 that the instrument became much used in the British navy, when it was new modelled by Mr. Edward Troughton, and the objections to the former instruments done away. We have obtained permission from this gentleman to make a drawing of this instrument (see Plate Reflecting Circle) where fig. 1. is a plan of the divided side of the instrument, and fig. 2. a perspective view of its upper side. A A, in both figures is a circle of brass, with a narrow ring of silver let into a circular groove in it, as is seen in fig. 1. on which silver the divisions are made. BBB are three arms carrying verniers at their ends, they are all cast in one piece, and screwed to a truly turned steel axis, fitting into a tube, which is screwed to the centre of the circle (this tube cannot be seen in the plan, but is denoted by a in fig. 2.); the index glass, b, which is a plane silvered mirror, is fastened to the other end of this axis by three screws, in such a posi tion that the centre line of the steel axis it is fixed to, if produced, would exactly coincide with the plane of the silvered surface of the mirror, and consequently that the plane of the mirror produced passes through the centre of the circle A A, perpendicular to its plane. To the upper end of the tube, a (fig. 2.) a crooked plate of brass, d d, is fastened, and connects it with two other tubes, e and f, whose lower ends are fixed to the cross bar frame of the circle; one of these, f, has the mirror, h, called the object glass, placed on it; the other has a telescope, k, fixed to it, directed to the ject glass, h. The instrument is held, when in use, by handles adapted to different occasions, of which there are four; two perpendicular and two parallel to the plane of the circle; of the latter, e, is one on the upper side, supported by a small pillar coming from the interception of two of the bars of the frame, and steadied by entering the tube; a, the other handle is at the divided side of the circle, and is fastened to the circle at the upper side, in the same manner as e, by a crooked hollow tube, G, going round the circle; of the other two handles, one, m, is above the circle, screwed into a cock fixed to it, so that it is perpendicular to the centre of the circle; it comes over the index glass, but does not touch it. The other handle is screwed into the handle of the crooked tube G, so as to be in the same line with the upper handle m; o, are three dark glasses, between the index and horizon glasses, turning on a joint, so as to be put out of the way when necessary, or any one or two of them can be turned in the line of the telescope to darken the light, more or less, in observations of the sun; p, are three other glasses supported by a small pillar behind the horizon glass, which can also be turned back as is necessary. The telescope is screwed into a brass ring, r, this is supported by a square piece of brass, tapped at the corners, so as to form a screw; and by turning s, a nut upon a screw, the telescope can be raised or lowered parallel to itself; there is also an adjustment, to bring the line of collimation of the telescope to be parallel to the plane of the circle. The circle is divided on the silver ring shown in the plan, into 720 parts, each of which answers to a degree; as this instrument measures double the angle shown upon the arc, the same as the Hadley's quadrant, these are subdivided into three, each of which will be twenty minutes. The verniers include fifty-nine of these divisions, and are divided into sixty; the coincidences of these will subdivide each original division of the circle into sixty parts, each equal to twenty seconds. The arm on which the vernier, D, is fixed, has a clamp at its end, to fasten it to the circle; and a fine screw, x, to move it slowly a small quantity after it is clamped. We shall now describe the manner of making an observation, by this instrument, of the angle between two objects, nearly in the same horizontal plane; we suppose all the adjustments of the instrument to be perfect; the observer first holds the instrument in his right hand by the handle screwed to the lower handle of the tube G, he looks through the telescope, k, and unsilvered part of the horizon glass, h, and directs it to one of the objects, which will be in the dotted line, g, he then turns the index, and index glass, b, by its arm D (which must be unclamped) until the other object in the line, y b, is reflected from 6 to h, and from h, by the silvered part of the glass, into the line kg, in which is placed the observer's eye; he then clamps the arm D, and gently turns the screws, x, backwards or forwards, until the reflected image of object in the line y, and the other object k seen through the telescope, both exactly cover one another. The observation is now half made, and the observer reads off and writes down the degrees, minutes and seconds, of each vernier, he then inverts the instrument, holding it by the handle, m, and directs the telescope to the object, in the line, y b, and brings the reflected image of the object, in the line k g, into view, by turning round the index and index glass the same as before; the observation is then read off and registered. To determine the angle measured, a mean of the products of both observations must be taken; this is the angle between the lines, y b and k g. A small microscope, M, in the plan, is used to examine the verniers, and it can be applied to either vernier, as required. The dark glasses, o p, are only wanted in observing the sun or moon. It is evident, that by inverting the instrument, as we have described, the index error is of no consequence, as it will be always more in one observation and less in the other. REFLECTION. As the rays of light are reflected by polished surfaces, so it is found that the rays of caloric have the same property. The Swedish chemist, Scheele, discovered that the angle of reflection of the rays of caloric is equal to the angle of incidence. This has been more fully established by Dr. Herschel. Some very interesting experiments were made by Professor Pictet, of Geneva, which proved the same thing. These experiments were conducted in the following manner. Two concave mirrors of tin, of nine inches focus, were placed at the distance of twelve feet two inches from each other. In the focus of the one was placed the bulb of a thermometer, and in that of the other a ball of iron, two inches in diameter, which was just heated so as not to be visible in the dark. In the space of six minutes the thermometer rose 22°. A similar effect was produced by substituting a lighted candle in the place of the ball of iron. Supposing that both the light and heat acted in the last experiment, he interposed between the two mirrors a plate of glass, with the view of separating the rays of light from those of caloric. The rays of caloric were thus interrupted by the plate of glass, but the rays of light were not perceptibly diminished. In nine minutes the thermometer sunk 14°; and in seven minutes after the glass was removed, it rose about 12°. He therefore justly concluded, that the caloric reflected by the |