Royal Exchange a splendid desert, compared to what it had been; but the enterprising spirit of our traders, which outstrips all the cold calculations of politicians, may serve to convince the world, that though this spirit may be checked for a short time, it can never be extinguished, nor will all the powers of the earth combined produce the growth of grass between the stones of its pave ment. Mr. The architectural decorations render the exterior and interior fronts of the Royal Exchange an ornament to the vast metropolis of England. The form is square, and the area the same; there are four gates which face the cardinal points, but the principle is in Cornhill. Malcolm informs us that the statutes of George I. and George II. are by Rys. brack; his present Majesty's by Wil ton, which was erected in March, 1764; and that most of the Kings previously to Charles II. were sculptured by Cibber; that of the latter King, which originally stood in the area, is the work of Grinlin Gibbons, the unrivalled carver in wood; those of Charles I. and II. on the principal front, are by Bushnell. The statue of Charles II. in the area, was a few years since replaced by another in a Roman habit, the performance of Mr. Spiller. We shall conclude this slight sketch of the history of the Royal Exchange with a brief description by the author just mentioned. The grand gateway is in the centre intercolumniation of four Corinthian pillars, which are the whole height of the front, and have a complete entab. lature, the great arch reaching to the architrave. In the attic, directly over the gate, are the royal arms, and this forms the base of the steeple, on which there are three gradations, or stories, each bounded by pilasters and pillars, with entablatures and balustrades, and busts in place of vases, the usual ornaments of this sort of magnificent édifices; except the third, which has pediments on each side, with a cupola arising from the centre. On this is a globe and gilt grasshopper. Over each side intercolumniation of the front are circular pediments; above them are attics and balustrades, with the Mercers' crest, and the City supporters. The lesser entrances have divided pediments, and over them Corinthian niches, and pediments containing statues of King Charles the First and Second. The wings of the front are five arches in length, on each side of the gates, three of these form a piazza; the two remaining retire into the main building. The basement in which they are turned is rustic, and the story above them Corinthian, with four pillars, an entablature, and balustrade. The three windows of the projection, and those of the building, are exactly attic in their borders, though placed in Corinthian intercolumniations. The four sides of the quadrangle are magnificent, and richly decorated with the basement arches of the walks, the cornices over them, the niches, statues, pillars, circular windows, entablatures, and balustrade, all in correct proportion and arrangement. ROYENA, in botany, African bladdernut, so named in honour of Adrian Van Royan, a genus of the Decandria Digynia class and order. Natural order of Bicornes. Guaiacanæ, Jussieu. Essential character: calyx pitcher-shaped; corolla one-petalled, with the border revolute; capsule one-celled, four-valved. There are seven species. RUBIA, in botany, madder, a genus of the Tetrandria Monogynia class and order. Natural order of Stellatæ. Rubiaceæ, Jussieu. Essential character: corolla one-petalled, bell-shaped; berries two, one-seeded. There are seven species. See MADDER. RUBRIC, in the canon law, signifies a title or article in certain ancient lawbooks; thus called because written, as the title of the chapters in our ancient Bibles are, in red letters. Rubrics also denote the rules and directions given at the beginning, and in the course of, the liturgy, for the order and manner in which the several parts of the office are to be performed. There are general rubrics and special rubrics, a rubric for the communion, &c. In the Romish missal and breviary are rubrics for matins, for lands, and translations, beatifica. tions, commemorations, &c. RUBUS, in botany, the raspbrery, a genus of the Icosandria Polygynia class and order. Natural order of Senticosa. Rosacea, Jussieu. Essential character: calyx five-cleft; petals five; berry com posed of one-seeded acini. There are thirty-two species; among which is the R. idæus, or common garden raspberry, too well known to need a particular description: it is found wild in many parts of Europe, particularly in rocky mountains, moist situations, woods, and hedges, The varieties of the raspberry are, the red-fruited, the white-fruited, and the twice-bearing. RUBY. See CORUNDUM. RUBY, in heraldry, denotes the red colour wherewith the arms of noblemen are blazoned; being the same which in the arms of others, not noble, is called gules. RUDBECKIA, in botany, so named from Olaus Rudbeck, father and son, professors of botany at Upsal, a genus of the Syngenesia Polygamia Frustranea class and order. Natural order of Compositæ Oppostifolia. Corymbiferæ, Jussieu Essential character: calyx with a double row of scales; crown of the seed a fourtoothed rim; receptacle chaffy, conical. There are seven species. RUDDER, in navigat on, a piece of timber, turning on hinges in the stern of the ship, and which, opposing sometimes one side to the water, and sometimes another, turns or directs the vessel this way or that. The rudder of a ship is a piece of timber hung on the stern posts by four or five iron-hooks, called pintles, serving as it were for the bridle of a ship, to turn her about at the pleasure of the steersman. The rudder being perpendicular, and without-side the ship, another piece of timber is fitted to it at right angles, which comes into the ship, by which the rudder is managed and directed. This latter properly is called the helm or tiller; and sometimes, though improperly, the rudder itself. The power of the rudder is reducible to that of the lever. As to the angle the rudder should make with the keel, it is shown, that in the working of ships, in order to stay or bear up the soonest possible, the tiller of the rudder ought to make an angle of 55° with the keel. A narrow rudder is best for a ship's sailing, provided she can feel it, that is, be guided and turned by it: for a broad rudder will hold much water when the helm is put over to any side; but if a ship have a fat quarter, so that the water cannot come quick and strong to her rudder, she will require a broad rudder. The aft-most part of the rudder is called the rake of the rudder. RUDOLPHINE Tables, a set of astronomical tables that were published by the celebrated Kepler, and so called from the Emperor Rudolph, or Rudolphus. RUELLIA, in botany, named in ho nour of Joannes Ruellius, a genus of the Didynamia Angiospermia class and order. Natural order of Personatæ. Acanthi, Jussieu. Essential character: calyx fiveparted; corolla subcampanulate; stamens approximating by pairs; capsule opening by elastic teeth. There are forty-three species. Swartz observes, that the Ruelliæ are very near allied to the Justicia, in their natural order, flowers, fruit, and habits. RUIZIA, in botany, so named, in honour of Don Hipolito Ruiz, a genus of the Monadelphia Polyandria class and order. Natural order of Columniferæ. Malvarez, Jussieu. Essential character; calyx double, exterior three-leaved: styles ten; capsule ten, one-celled, two-seeded, closely cobering. There are three species, all natives of the Isle of Bourbon. RULE, in arithmetic, denotes an operation performed with figures, in order to discover sums or numbers unknown. The fundamental rules are, addition, subtraction, multiplication and division. But besides these, there are other rules, denominated from their use; as the rule of ALLIGATION, FELLOWSHIP, INTEREST, PRACTICE, REDUCTION, &c. which see in the alphabetical order. RULE of Three, GOLDEN Rule, or RULE of Proportion, is one of the most essential rules of arithmetic; for the foundation of which see the article PROPORTION. It is called the Rule of Three, from having three numbers given to find a fourth; but, more properly, the Rule of Propor tion, because by it we find a fourth number proportional to three given numbers: and because of the necessary and extensive use of it, it is called the Golden Rule. But to give a definition of it, with regard to numbers of particular and determinate things, it is the rule by which we find a number of any kind of things, as money, weight, &c. so proportional to a given number of the same things, as another number of the same or different things is to a third number of the last kind of thing. For the four numbers that are proportional must either be all ap plied to one kind of things; or two of them must be of one kind, and the remaining two of another: because there can be no proportion, and consequently no comparison of quantities of different species: as, for example, of three shil lings and four days; as of six men and four yards. All questions that fall under this rule may be distinguished into two kinds: the first contains those wherein it is simply and directly proposed to find a fourth proportional to three given numbers, taken in a certain order: as if it were proposed to find a sum of money so proportioned to one hundred pounds, as sixty-four pounds ten shillings is to eighteen pounds six shillings and eight-pence, or as forty pounds eight shillings is to six hundred weight. The second kind contains all such questions wherein we are left to discover from the nature and circumstances of the question, that a fourth proportional is sought; and consequent ly, how the state of the proportion, or comparison of the term, is to be made; which depends upon a clear understanding of the nature of the question and proportion. After the given terms are duly ordered, what remains to be done is to find a fourth proportion. But to remove all difficulties as much as possible, the whole solution is reduced to the following general rule, which contains what is necessary for solving such questions, wherein the state of the proportion is given; in order to which it is necessary to premise these observations. 1. In all questions that fall under the following rule there is a supposition and a demand: two of the given numbers contain a supposition, upon the conditions whereof a demand is made, to which the other given term belongs; and it is therefore said to raise the question; because the number sought has such a connection with it as one of these in the supposition has to the other. For example: if three yards of cloth cost 41. 10s. (here is the supposition) what are 7 yards 3 quarters worth? here is the demand or question raised upon 7 yards 3 quarters, and the former supposition. 2. In the question there will sometimes be a superfluous term; that is, a term which, though it makes a circumstance in the question, yet it is not concerned in the proportion, because it is equally so in both the supposition and demand. This superfluous term is always known by being twice mentioned, either directly, or by some word that refers to it Example if three men spend 207 in 10 days, how much, at that rate, will they spend in 25 days? Here the three men is a superfluous term, the proportion being among the other three given terms, with the number sought; so that any number of men may be as well supposed as 3. Rule 1. The superfluous term (if there is one) being cast out, state the other three terms thus: of the two terms in the supposition, one is like the thing sought (that is, of the same kind of thing the same way applied;) set that one in the second or middle place; the other term of the supposition set in the first place, or on the left hand of the middle; and the term that raises the question, or with which the answer is connected, set in the third place, or on the right hand; and thus the extremes are like one another, and the middle term like the thing sought: also the first and second terms contain the supposition, and the third raises the question; so that the third and fourth have the same dependence or connection as the first and second. 2. Make all the three terms simple numbers of the lowest denominations expressed, so that the extremes be of one name. Then, 3. Repeat the questions from the numbers thus stated and reduced (arguing from the supposition to the demand,) and observe whether the number sought ought to be greater or lesser than the middle term, which the nature of the question, rightly conceived, will determine; and accordingly, multiply the middle term by the greater or lesser extreme, and divide the product by the other, the quotient is like the middle term, and is the complete answer, if there is no remainder; but if there is, then, 4 Reduce the remainder to the denomination next below that of the middle term, and divide by the same divisor, the quotient is another part of the answer in this new denomination. And if there is here also a remainder, reduce it to the next denomination, and then divide. Go on thus to the lowest denomination, where, if there is a remainder, it must be applied fraction-wise to the divisor; and thus you will have the complete answer in a simple or mixed number. Note. If any of the dividends is less than the divisor, reduce it to the next denomination, and to the next again, till it be greater than, or equal to, the divisor. EXAMPLES. Qest. 1. If 3 yards of cloth cost 8s. what is the price of 15 yards? Ans. 40s. or 21. Work. yds. s. yds. 3-8-15 15 3)120(40s. Explanation. 3 yards and 8s. contain the supposition, and 8s. is like the thing sought; therefore 8s. is the middle term, and yards on the left: then the demand arises upon 15 yards, and therefore it is on the right. Again, from the nature of the question, it is plain that 15 yards require more than 3 yards, i. e. the answer must be greater than the middle term; wherefore 8s is to be multiplied by 15 yards; the product is 120s. which, divided Explanation. The supposition is in 46. and 28. 9d., this last term being like the thing sought, which is connected with 18b.; wherefore the terms are stated ac. cording to the rule: then the middle term being mixed, it is to be reduced to pence; and then argue thus: 46. cost 33d, 18/b. must cost more; therefore multiply 33d. by 18%. and divide their product by 4: the quotient is 148. and 2 remains, which is to be reduced to farthings, and the product divided by the former quotient, gives 2; so the answer is, 148d. 2 farthings, or 12s. 44d. because 148d. is, by reduction, 128. 4d. Quest. 3. What time will 7 men be boarded for 25% when 3 men paid 251. for 6 months? Answ. 2 months, 16 days, reckoning 28 days to 1 month. Work. men. months. men. 3-6 3 7)18(2 14 Rem. 4 28 7)112(16 days. Explanation. The 251. is a superfluous number; then the supposition is in the 3 men and 6 months, and the demand regards the 7 men: the terms being all simple, you are to argue thus: if 3 men are boarded 6 months for 251. (or any sum), 7 men will be boarded for the same a shorter time: therefore multiply 6 months by 3, and divide the product 18 by 7, whereby the answer is found to be 2 months and 16 days. Note. The first two questions are what is called the rule of three direct, that is, where the third term, being greater or less than the first, requires that the answer also be greater or lesser than the second term. The last, of the rule of three indirect, or reverse; where the third term, being greater or lesser than the first, requires the fourth contrarily lesser or greater than the second. But we have comprehended both in one general rule. And from this observation may be learned what questions are of either kind. RULE, or RULER, an instrument of wood or metal, with several lines delineated on it, of great use in practical mensuration. When a ruler has the lines of chords, tangents, sines, &c. it is called a plane scale. The carpenter's joint rule is an instrument usually of box, &c. twenty-four inches long, and one and a half broad; each inch being subdivided into eight parts. On the same side with these divisions is usually added Gunter's line of numbers. On the other sides are the lines of timber and board measure; the first beginning at 82, and continued to 36, near the other end; the latter is numbered from 7 to 36, 4 inches from the other end. We shall point out some of the uses of this rule. The application of the inches, in measuring lengths, breadths, &c. is obvious. That of the Gunter's line, see under the article GUNTER'S LINE. The use of the other side is that with which we are now concerned. 1. The breadth of any surface, as board, glass, &c. being given, to find how much in length makes a square foot. Find the number of inches the surface is broad, in the line of board measure, and right against it is the number of inches required. Thus, if the surface were eight inches broad, eighteen inches will be found to make a superficial foot. Or more rea dily thus apply the rule to the breadth of the board or glass, that end, marked 36, being equal with the edge, the other edge of the surface will show the inches and quarters of inches, which go to a square foot. 2. Use of the table at the end of the board-measure. If a surface be one inch broad, how many inches long will make a superficial foot? look in the upper row of figures for one inch, and under it in the second row is twelve inches, the answer to the question. 3. Use of the line of timber measure. This resembles the former; for having learned how much the piece is square, look for that number on the line of the timbermeasure; the space thence to the end of the rule is the length, which, at that breadth, makes a foot of timber. Thus, if the piece be nine inches square, the length necessary to make a solid foot of timber is 214 inches. If the timber be small, and under nine inches square, seek the square in the upper rank of the table, and immediately under it is the feet and inches that make a solid foot. If the piece be not exactly square, but broader at one end than the other, the method is to add the two together, and take half the sum for the side of the square. For round timber the method is to girt it round with a string, and to allow the fourth part for the side of the square; but this method is erroneous, for hereby you lose nearly one-fifth of the true solidity; though this is the method at present practised in buying and selling timber. RULE, Coggeshall's sliding, is chiefly used for measuring the superficies and solidity of timber, &c. It consists of two rulers, each a foot long, one of which slides in a groove made along the middle of the other. On the sliding side of the rule are four lines of numbers, three whereof are double; that is, are lines to two radiuses; and one a single broken line of numbers; the three first, marked A, B, C, are figured 1, 2, 3, &c. to 9: and then, 1, 2, 3, &c. to 10. The single line, called the girt-line, and marked D, whose radius is equal to the two radiuses of any of the other lines, is broke for the easier measurement of timber, and figured 4, 5, 6, 7, 8, 9, 10, 20, 30, &c. From 4 to 5 it is divided into ten parts, and each tenth subdivided into 2, and so on, from 5 to 6, &c. On the back side of the rule are, 1. A line of inchmeasure, from 1 to 12; each inch being divided and subdivided. 2. A line of foot-measure, consisting of one foot, divided into 100 equal parts, and figured 10, 20, 30, &c. The back part of the sliding piece is divided into inches, halves, &c. and figured from 12 to 24; so that when drawn wholly out, there may be a measure of two feet. "Use of Coggeshall's Rule for measuring plane superficies." 1. To measure a square; suppose, for instance, each of the sides 5 feet; set 1 on the line B, to 5 on the line A; then against 5 on the line B, is 25 feet, the content of the square on the line A. 2. To measure a long square. Suppose the longest side 18 feet, and the shortest 10: set 1 on the line B, to 10 on the line A; then against 18 feet, on the line B, is 180 feet, the contents on the line A. 3. To measure a rhombus. Suppose the side 12 feet, and the length of a perpendicular let fall from one of the obtuse angles to the opposite side 9 feet; set 1 on the line B, 12, the length of the side on the line A: then against 9, the length of the perpendicular on the line 4. To meaB, is 108 feet, the content. sure a triangle. Suppose the base 7 feet, and the length of the perpendicular let fall from the opposite angle to the base 4 feet: set 1 on the line B, to 7 on the line A; then against half the perpendicular, which is 2 on the line B, is 14 on the line A, for the content of the triangle. 5. To find the content of a circle, its diameter being given. Suppose the diameter 3.5 feet: set 11 on the girt-line D, to 95 on the line C; then against 3.5 feet on D, is 9.6 on C, which is the content of the circle in feet. 6. To find the content of an oval or ellipsis. Suppose the longest diameter 9 feet, and the shortest 4. Find a mean proportional between the two, by setting the greater 9 on the girt-line, to 9 on the line C; then against the less num ber 4 on the line C 6, the mean proportional sought. This done, find the content of a circle, whose diameter is six feet; this, when found by the last article, will be equal to the content of the ellipsis sought. "Use of Coggeshall's Rule in measuring timber." 1°. To measure timber the usual way. Take the length in feet, half feet, and, if required, quarters; then measure half way back again; then girt the tree with a small chord or line, double this line twice very evenly, and measure this fourth part of the girt or perimeter in inches, halves, and quarters. The dimensions thus taken, the timber is to be measured as if square, and the fourth of the girt taken for the side of the square, thus; set 12 an the girt-line D, to the length in feet on the end C: then against the side of the square, on the girt-line D, taken in inches, you have, on the line C, the content of the tree in feet. For an instance suppose the girt of a tree, in the middle, be 60 inches, and at the length 30 feet, to find the content, set 12 on the girt-line D, and 30 feet on the line C then against 13, one-fourth of 60, on the girt-line D, is 46.8 feet, the content on the line C. If the length should be 9 inches, and the quarter of the girt 35 inches; here as the length is beneath a |