RUBUS, the BRAMBLE and RASPBERRYBUSH, in botany, a genus of the ico. fandria-pentagynia clafs of plants, the corolla whereof confifts of five roundish erecto-patent petals, of the length of the cup, and inserted into it; the fruit is a compound berry; the acini it is compofed of are roundish, and arranged into a clufter, convex at top and concave below, each acinus has only one cell; the feeds are fingle and oblong; the receptacle of the pericarpia is conic; the acini in most of the fpecies grow together fo as to be infeparable without breaking. See plate CCXXXV. fig. 4.

The ufe of this plant in medicine is as a refrigerant and aftringent, and therefore the fruit leaves, &c. are recommended in dyfenteries, vomitings, hæmorrhages of the womb, nofe, &c.

RUBY, rubinus, in natural history, a species of the chroftafima clafs of gems, being a beautiful gem of a red colour with an admixture of purple. See the article GEM.

This in its most perfect and best coloured ftate, is a gem of prodigious beauty and extreme value; it is often found perfectly pure and free from blemishes or foulness, but much more frequently debafed greatly in its value by them, efpecially in the larger fpecimens. It is of very great hardness, equal to that of the fapphire, and fecond only to the diamond. It is various in fize, but lefs fubject to variations in its fhape than most of the other gems. It is ufually found very small, its most common fize being equal to that of the head of the largest fort of pins; but it is found of four, eight, or ten caracts; and fometimes, though very rare, up to twenty, thirty, or forty. It is never found of an angular or cryftalliform fharp, but always of a pebble like figure, often roundish, fometimes oblong and much larger at one end than at the other, and in fome fort refemuling a pear, and is ufually flatted on one fide. It commonly is naturally fo bright and pure on the furface, as to need no polishing; and when its figure will admit of being fet without cutting, it is often worn in its rough ftate, and with no other than its native polish. Our jewellers are very rice, though not perfectly determinate, in their diftinions of this gem, knowVOL. IV.

ing it, in its different degrees of colour under three different names: the first is fimply the ruby, the name given it in its deepest coloured and most perfe&t statë: the fecond is the fpinel ruby; under this name they comprehend those rubies which are of a fomewhat lefs bright colour than the ruby fimply fo called: the third is the balafs ruby; under this name they exprefs a pale yet a very bright ruby, with a lefs admixture of the purple tinge than in the deeper coloured one; this is of lefs value than the deeper one.

We have the true ruby only from the Eaft-Indies; and the principal mines of it are in the kingdom of Pegu and the ifland of Ceylon. We have in Europe crystals tinged to the colour of the ruby, but they have nothing of its luftre or hardness. The ruby feems to owe its colour to gold, it being poffible to feparate a fmall portion of gold from the little native rubies, and alfo to give the true colour of the ruby to fictitious pafte by means of that metal.

The way of preparing a metalline colour from gold and tin, for tinging glass of a ruby colour is, according to Shaw, as follows: Diffolve gold in aqua-regia, and dilute the fine yellow folution with a large proportion of fair water; to the mixture add a fufficient quantity of a faturated folution of tin, made alfo in aqua regia, at feveral times, and a most beautiful red or purple-coloured powder will foon fall to the bottom of the containing glass: decant the liquor and dry the powder, a few grains whereof being melted along with white crystalline glafs will tinge it throughout of an extremely fine purple or ruby colour.

In M. Savary's Dict. de Commerce, we have the following table of the value of rubies, from one carat, or four grains,

arifing from indigeftion, and difcharging itlelf at the mouth with a very difagree.able noife. There are belches owing to repletion, and others to inanition, or emptinefs. Quincy fays hypochondriac and hysteric perfons are particularly liable to this diforder. They are rather to be cured with proper ftomachics than carminatives and hot liquors.

RUDBECKIA, DWARF SUN FLOWER, in botany a genus of the fyngenefiapolygamia clafs of plants, the compound flower of which is radiated; but the hermaphrodite corollulæ of the dife are tubulofe and very numerous: the ftamina are five very fhort capillary filaments; and there is a fmail orbiculated feed after each of the hermaphrodite corollule, and are all contained in the cup, affixed to a paleaceous receptacle.

RUDDER, in navigation, a piece of timber turning on hinges in the ftern of the fhip, and which, opposing fometimes one fide to the water and fometimes another, turns or directs the veffel this way or that. See the article SHIP.

The rudder of a fhip is a piece of timber hung on the ftern pofts by four or five iron-hooks, called pintles, ferving as it were for the bridle of a fhip to turn her about at the pleasure of the fteers-man. The rudder being perpendicular; and without-file the fhip, another piece oftimber is fitted to it at right angles, which comes into the fhip, by which the rudder is managed and directed. This latter properly is called the helm or tiller; and fometimes, though improperly, the rudder itself. The power of the rudder is reducible to that of the lever. See the article LEVER.

As to the angle the rudder fhould make with the keel, it is fhewn, that in the working of fhips, in order to stay or bear up the fooneft poffible, the tiller of the rudder ought to make an angle of 55° with the keel. A narrow rudder is beft for a fhip's failing, provided the 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 fide; but if a fhip have a fat quarter, fo that the water carnot come quick and strong to her rudder, he will require a broad rudder. The aft-moft part of the rudder is called the rake of the rudder. RUDENTURE, in archite¶f.re, the figure of a rope or staff, fometimes plain, tometimes carved, with which the third part

filled up.

There are alfo rudentures in relievo laid on the naked of pilafters not fluted: an inftance of which we have in the church of St. Sapienza at Rome. RUDERATION, in building a term ufed by Vitruvius for the laying of pavment with pebbles.

To perform the ruderation it is neceffary that the ground be well beaten, to make it firm, and to prevent it from cracking; then a ftratum of little ftones are laid, to be afterwards bound together with mortar made of lime and fand. If the fand be new, its proportion may be to the lime as three to one; if dug out of old pavements or wails, as five to two. Ruderation, Daviler obferves, is also used by Vitruvius for the coalfett and most artless kind of malonry, where a wall is as it were cobled up.

RUDIARIUS, in antiquity, a veteran gladiator who had got a discharge from the fervice. See GLADIATOR, RUDIMENTS, rudimenta, the first prin ciples or grounds of any art or science, called alfo the elements thereof. See the article ELEMENT.

RUDIS, a knotty rugged flick, which the

prætor among the Romans gave the gladiators as a mark of their freedom and difmiffion.

RUE, ruta, in botany. See RUTA. RUELLIA, in botany, a genus of the didynamia angiospermia class of plants, the corolla whereof confifts of a fingle petal: the tube is of the length of the cup, with a patulous inclined neck; the limb is quinquifid, patent, and obtufe, with the two upper lacinii more reflex than the reft the fruit is a round capfule, acuminated on both fides, of the length of the cup, femibilocular and bivalve: the feeds being a few in number, are round sh and comprefTed.

RUFF, in ichthyology, a fpecies of the perca, with a cavernous head, and only one fin on the back. See PERCA. The ufual fize to which this fpecies arrives is four or five inches, though fometimes it will grow longer: the head in its general form is compreffed, but flatted a little between the eyes; the beak is fomewhat acute; the breaft.and belly are flatted; the eyes are large, and of a variety of colours; the teeth are small bet numerous, there is a row of them in each jaw, and on the anterior part of the palate there is a number of teeth, fo

RULE OF THREE, GOLDEN RULE, or RULE OF PROPORTION, is one of the moft effential rules of arithmetic; for the foundation of which fee the articles PROPORTION.

minute that they can fcarce be feen; the lateral line is fomewhat crooked; the colour of the fifh is a brownish yellow with a number of black spots; the fin on the back has twenty eight rays, the pectoral-fins eighteen, and the belly-fins each fix.

RUFF, in ornithology, a fpecies of the tringa, with a granulated face, and a red beak and legs: it is about the bignefs of the common jack daw, See the article TRINGA.

The head is round, and covered with a large tuft of feathers, except the anterior part, which is naked, but the skin is elegantly granulated with fmall red tubercles, difpofed regularly and closely over it; the eyes are large, their afpect bright and piercing, and their iris of a bright hazel-colour; the beak is moderately long and obtufe at the end, it is of a bright fine red at the bafe, and fometimes all over; the upper chap is a little longer than the under one; the tongue is extended to the very top of the beak. See plate CCXXXV. fig. 3. RUFTER-HOOD, among falconers, a plain leathern hood, large and open behind, to be worn by an hawk when the is first drawn.

RUGEN, an island of the Baltic-fea, on the coaft of Germany, being part of the dutchy of fwedish Pomerania, separated from the continent by a narrow channel: this ifland is thirty miles long, and near as many broad,

RUINS, a term particularly used for magnificent buildings fallen into decay, by length of time, and whereof there only remains a confufed-heap of materials. RULE, regula, in matters of literature, a maxim, canon, or precept, to be obferved in any art or icience.

The rules of philofophizing, of reafoning, of method, as allo thofe to be obferved in logic, morality, poetry, medicine, rhetoric, &c. have been already delivered under the articles PHILOSOPHY, REASONING, &c.

RULE, in arithmetic, denotes an operation performed with figures, in order to difcover fums or numbers unknown. The fundamental rules are addition, fubtraction, multiplication, and divifion. See the article ADDITION, &c.

But befides thefe, there are other rules denominated from their use; as the rule of alligation, fellowship, intereft, practice, reduction, &c. See the article ApLIGATION, &C.

It is called the Rule of Three from hav ing three numbers given to find a fourth; but more properly, the Rule of Proportion, becaufe by it we find a fourth number proportional to three given numbers and because of the neceffary and extenfive 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. fo proportional to a given number of the fame things, as another number of the fame or different things, is to a third number of the laft kind of thing. For the four numbers that are proportional muft either be all applied to one kind of things; or two of them must be of one kind, and the remaing two of another : because there can be no proportion, and confequently no comparison of quantities of different fpecies: as for example, of three fhillings and four days; or of fix men and four yards.

Ali queftions that fall under this rule may be diftinguifhed into two kinds : the fift contains thefe wherein it is fimply 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 fum of money fo proportioned to one hundred pounds as fixty four pounds ten fhillings is to eighteen pounds fix fillings and eight pence, or as forty pounds eight fhillings is to fix hundred weight. The fecond kind contains all fuch questions wherein we are left to difcover, from the nature and circumstances of the queftion, that a fourth proportional is fought; and confequently, 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 proportional. But to remove all difficulties as much as poffible, the whole folution is reduced to the following general rule, which contains what is neceffory for folving fuch queftons wherein the fate of the proportion is given; in order to which it is neceffary to premife thefe obfervations.

16 1 2

i. Ia

queftion, rightly conceived, will determine; and accordingly, multiply the middle term by the greater or leffer extreme, and divide the product by the other, the quote is like the middle term, and is the complete anfwer, if there is no remainder; but if there is, then,

1. In all questions that fall under the following rule there is a fuppofition and a demand two of the given numbers contain a fuppofition, upon the conditions whereof a demand is made, to which the other given term belongs; and it is therefore faid to raise the question; because the number fought has fuch a connection with it as one of these in the fuppofition has to the other. For example; if 3 yards of cloth coft 41. 10 8. (here is the fuppofition) what are 7 yards 3 quarters worth? here is the demand or question raifed upon 7 yards 3 quarters, and the former fuppofition.

2. In the queftion there will fometimes be a fuperfluous 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 fo in both the fuppofition and demand. This fuperfluous term is always known by being twice mentioned either directly, or by fome word that refers to it. Example, if 3 men fpend 20 l. in 10 days, how much, at that rate, will they spend in 25 days? Here the 3 men is a fuperfluous term, the proportion being among the other three given terms, with the number fought; fo that any number of men may be as well fuppofed as 3.

Rule. First, The fuperfluous term (if there is one) being caft out, state the other three terms thus: of the two terms in the fuppofition, one is like the thing fought (that is, of the fame kind of thing the fame way applied); fet that one in the fecond or middle place; the other term of the fuppofition fet in the first place, or on the left hand of the middle; and the term that raifes the question, or with which the answer is connected, fet in the third place, or on the right hand; and thus the extremes are like one another, and the middle term like the thing fought: alfo the first and fecond terms contain the fuppofifition, and the third raifes the question; fo that the third and fourth have the fame dependance or connection as the first and fecond. This done,

Secondly, Make all the three terms fimple numbers of the lowest denominations expreffed, fo that the extremes be of one name. Then,

Fourthly, reduce the remainder to the denomination next below that of the middle term, and divide by the fame divifor, the quotient is another part of the answer in this new denomination. And if there is here alfo a remainder, reduce it to the next denomination, and then divide. Go on thus to the loweft denomination, where, if there is a remainder, it must be applied fraction-wife to the divifor; and thus you will have the complete anfwer in a fimple or mixed number,

Note, If any of the dividends is lefs than the divifor, reduce it to the next denomination, and to the next again, till it be greater than, or equal to, the divifor. EXAMPLES.

Queft. I. If 3. yards of cloth coft 8 s. what is the price of 15 yards? Answ. 40 s. or 2 1.

Work.

yrds. s. yds. 3-8-15

15

312040 S.

Explanation. 3 yards and 8 s. contain the fuppofition, and 8 s. is like the thing fought; therefore 8 s. is the middle term, and yards on the left: then the demand arifes upon 15 yards, and therefore it is on the right. Again, from the nature of the queftion it is plain, that 15 yards require more than 3 yards, i, e. the answer must be greater than the middle term; wherefore 8 s. is to be multiplied hy 15 yards; the product is 120 s. which divided by 3 yards, quotes 40s, without a remain. der; fo 40s. or 2 1. is the number fought, Queft. II. If 4 lb. of fugar coft 2 s. 9 d. what is the value of 18 lb.? Answer, J2 s. 4 d.

Work. lb. s. d. lb. 4-2:9-18

12

33 d. 18

Expl. The fuppofition is in 4 lb. and 2 s. 9 d. this laft term being like the thing fought,which is connected with 18 lb. wherefore the terms are ftated according to the rule: then the middle term being mixed, it is to be reduced to pence; and then argue thus if 4lb. coft 33 d. 18 lb. 42 farthings. muft coft more; therefore multiply 33 d. by

264 33

2

i

18 lb. and divide their product by 4; the quotient is 148 d. and 2 remains, which is to be reduced to farthings, and the product divided by the former quotient, gives 2; fo the answer is 148 d. 2 farthings, or 12 s. 4 d. because 148 d. is by reduction, 12s. 4 d.

Queft. III. What is the price of 501. of tobacco, when 32 lb. 12 oz. cost 4 l. 10 s.? Answ. 61. 178. 44d.

for 6 months? Answ. 2 months 16 days, reckoning 28 days to 1 month.

Remainder 448

4

Explanation. The fuperfluous number here is IOS. and from the other three terms ftated and reduced, it is argued thus; if 3 Cwt, is carried 160 quarters of a mile for 10 s. then a greater weight will be carried for the fame price 103 qrs. of a mile; therefore multiply 3 by 160, and divide the product 480 by 103, the answer is

103|1848 17,97 lb. 4 Cwt. 2 quarters

103

818 721

97

96

170 lb.

Note. The firft four questions are what is called the rule of three direct, that is, where the third term being greater or Jeffer than the firft, requires that the anfwer alfo be greater or leffer than the fecond term. The two laft questions are of the rule of three indirect, or reverse ; where the third term being greater or

leffer