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either in the whole or half-pay, doing duty in the regiment. REFORMATION, the act of reforming,

or correcting an error or abuse in religion, difcipline, or the like.

The reformation, fo called by way of eminence, is the feparation of the proteftants from the church of Rome, in the beginning and towards the middle of the fixteenth century. See the article LUTHERANS, &c.

REFRACTED, or REFRACTIVE DIAL, one that hews the hour by means of fome refractive transparent fluid. See the article DIAL.

REFRACTION, in general, is the deviation of a moving body from its direct courfe, occafioned by the different denfity of the medium it moves in; or, it is a change of direction, occafioned by a body's falling obliquely out of one medium into another of a different density. The great law of refraction, which holds in all bodies, and all mediums, is, that a body, paffing obliquely out of one mediom into onother wherein it meets with lefs refiftance, is refracted or turned towards the perpendicular; and, on the contrary, in paffing out of one medium into another wherein the refistance is greater, it is refracted or turned from the perpendicular. Hence the rays of light, falling out of air into water, are refracted towards the perpendicular; whereas a ball, thrown into the water, is refracted from it. Now the reason of this difference is, that water, which refists the motion of light lefs than air, refifts that of the ball more; or, to speak more justly,, because water, by its greater attraction, accelerates the motion of the rays of light more than air does.

In order to illuftrate the refraction of light, let A B (plate CCXXI. fig. 1. n° 1.) reprefent a ray moving in air from A to B, and paffing into water at B; and let HK be perpendicular to the furface of the water at the point B. When therefore the ray enters the water, it does not continue its motion ftraight forward in the line B C, but in fome other line, as B D, which is nearer or more inclined to the perpendicular BK: and, on the other hand, if the line DB be fuppofed to be a ray of light moving in water from D to B, and there paffing into air, inftead of continuing its motion ftraight forward in the direction BE, it goes on in Some other direction as BA; which

being lefs inclined to, is more diftant from, the perpendicular BH, as will appear from the following experiment. Let an empty veffel, as BCDE (ibid. n° 2.) have a small object placed at its bottom at A; and let it be fo fituated as that the fight of the object may be intercepted by the fide of the veffel, from an eye placed at Q; then let the vessel be filled with water, and the ray AB, which, before the water was poured in, moved in a right line from A to K, and by fo doing paffed above the eye, will, upon its emerfion out of the water, be bent downward, fo as to ftrike upon the eye at Q and thereby render the object at A visible. This bending of the rays of light, in their paffage out of one medium into another, is owing to the attractive force of the denfer medium acting upon the rays at right angles to the furface.

The fundamental law of the refraction of the rays of light is, that the fine of the angle of incidence is always in a conftant ratio to the fine of the angle of refraction, in all inclinations of the incident ray whatever. See INCIDENCE.

Now that this is the cafe, whatever be the inclination of the incident ray, may be proved experimentally in the following manner: let a brafs quadrant, CFE, (ibid. n° 3.) graduated on both fides, and fixed at its center C, to a perpendicular pillar, CD, have two indices, A and B, one on each fide, moveable on the center C; and let the index A, whereof the ftem G is a continuation, be made to point to the fifteenth degree, and the index B to the fifteenth minute of the twentieth degree: let then the pillar be immei fed in water, till CE, the horizontal edge of the qua. drant, touch the furface of the water; and upon viewing the ftem G, immersed in the water, it will, by reafon of the refraction, appear to have changed its fituation, and to lie in a line with the index B. And the fame thing will like. wife obtain, if the index A be fet at the thirtieth degree, and B at the thirtieth minute of the forty-fecond degree; that is, twenty-five, the fine of the leffer angle of incidence, is to thirty-three, the fine of the correfponding angle of refraction; as fifty, the fine of the greater angle of incidence, is to fixty-fix, the fine of the angle of refraction correfponding thereto. And the fame holds

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Since then the ratio of thefe fines is conftant, it remains that we determine what that ratio is in different mediums; in order to which we fhall firft premise the following lemma, Let GHD, (ibid. n° 4.) be an equilateral triangle, and let the angle D be biffected by the right line DO; let AK, MC, be drawn parallel to the fide GH, and through the point K draw IKN cutting OD in N: then is the angle A KINKB. Allo the triangle is divided into two fimilar and equiangular triangles, NKB and BKD, by the perpendicular KB; and, therefore, the angle NK B is equal to the angle KDB: all which is evident from Euclid's Elements.

Suppofe now that GHD be the section of a prifm of water or glafs, or any pellucid medium; and K M a ray of light paffing through it, parallel to the fide GH; and let it go out of the prifm, and be refracted into the air, on each fide, into the directions K F, ME; and, laftly, upon the point K, defcribe the femi-circle PIQ: then is NKB (= KDB) FK1, the angle of incidence out of the prifm into air, and AKI is the angle of refraction; confequently AR, and FS, are the fines of the angles of incidence and refraction, out of the prifm into air. On the contrary, we may confider FK as the incident ray falling upon the prifm in the point K, and refracted in the direction KM, parallel to the fide G H, which at the point M emerges again into the air in the direction ME, making the angle EML, with the perpendicular ML, equal to the angle FKI. In this cafe the angle FKI is the angle of incidence, and NKB is the angle of refraction in the prifin; which angle of refraction is therefore given, or conftant, as it is always equal to the angle KDB, or half the angle of the prifm.

The angle of incidence, FKI, confifts of two parts, viz. of the given angle AKI(KDB) and the additional angle AKF. Now the angle AKI is known, as being equal to half the angle of the prifm; and the angle FKA is known by placing the prifm by the center of a graduated femi-circle, as ABC, (ibid. fig. 5.) carrying an index, whose two arms, FK and KE, are equally elevated above the horizontal line AC, and correfpond to the incident and

emergent ray F K and ME in the other figure. For here it is evident, if an object be placed on the end of the arm F, it will be feen by an eye looking through the fights at the other end of the index E; and when the object is thus feen, the angle AKF is known by the number of degrees which each arm cuts upon the limb of the femi-circle.

This number of degrees, added to the conftant number thirty degrees, which is equal to half the angle of the prifm, gives the whole angle of incidence FKI; and thus the angle of incidence and refraction being found, the proportion of the fines FS and AR will be discovered, which ratio is always the fame while the matter of the prifm remains the fame, as was before fhewn from the theory, and may by this inftrument be proved by experiment. For example, let the prifm be of water, it will be neceffary to elevate each arm twelve degrees upon the limb, before the image of the object at F can be seen by the eye at E; then 12 +30= 42° FKA+AKI=FKI, the angle of incidence. But the fine FS of 42°, is to the fine AR of 30°, as 4 to 3 very nearly.

Now it is plain, if the ratio of the fines AR and FS were not fixed, fince FS might be in any ratio greater or less than AR, the incident ray FK may make an angle F K I greater or less than fortytwo degrees, and yet the object at F be feen by the eye at E: but this we find by experiment to be impoffible, because there is no elevation of the arms of the index that will exhibit the appearance of the object but the one above-mentioned. If GHD were a prism of glass, as that is a denfer body than water, fo its refractive power will be greater; and, confequently, it will act more ftrongly on the ray KM, at its exit into the air, and cause it to be refracted farther from the perpendicular IK or ML. Therefore the angle of incidence out of air into glafs, viz. FK I, ought to be greater, and fo to require a greater elevation of the legs of the index than before in the prifm of water and this we find, by experiment, is the cafe; for then the elevation, inftead of twelve degrees, muft be about twenty-two or twenty-three degrees.

Hence it is plain, the fine of incidence, FS, must be in a conftant ratio to the fine of refraction, AR; because fince the angle AKL is invariable, being always equal

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to GDO; and in the fame medium, GDH, the angle F K I must always be the fame, because the refractive power is every where fo therefore, the angles being conftant, the fines will be so too, or their ratio to each other always the fame. And as by this inftrument the angles of incidence and refraction, are difcovered, the ratio of their fines will be known of course, for each respective medium thus, in water the fine of forty-two degrees, is to the fine of thirty degrees, nearly as four to three; in glafs, the fine of forty fix degrees is to the fine of thirty degrees, as three to two; or, more nearly as feventeen to eleven: and, to mention no more, it has been found, by fome experiments, that the fine of incidence is to the fine of refraction in diamond, as five to two. But, fince in phyfical matters no authority is comparable to that of Sir Ifaac Newton, we shall give a table from his optics, fhewing the proportion of the fines of incidence and refraction of yellow light, that being nearly a mean between the greatest and least refrangible rays; this is contained in the first column; the fecond column expreffes the denfities of the bodies eftimated by their specific gravities; and the third fhew the refractive power of each body, in respect of its density.

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The refraction of the air in this table is determined by that of the atmosphere, as obferved by aftronomers; for if light pafs through many refracting substances, or mediums, gradually denser and denfer and terminated with parallel furfaces, the fum of all the refractions will be equal to the fingle refraction it would have suffered in paffing immediately out of the first medium into the last.

As to the different refrangibility of the feveral forts of rays of light, it has already been explained under the articles COLOUR and RAINBOW. REFRACTION, in aftronomy. From what has been faid, the refraction of the rays of light, iffuing from a heavenly body, in paffing through the atmosphere of our earth, will be easily understood. Thus, the ray A B (ibid. n° 6.) proceeds from the ftar A in a right line, till it reach the atmosphere of the earth at B; upon entering which, it it will be refracted towards the perpendicular BC, fuppofed to be drawn from B to C, the center of the earth; and as it paffes on through the atmosphere towards it, D, it will be continually refracted the fame way, by reason it all along enters a denfer part of the atmosphere; and hence it will defcribe the curve BD bending downwards, fo as to render the object visible to a spectator at D. But, as all vifion is performed in right lines, the fpectator at D will fee the ftar in the tangent line DE; and, confequently, the apparent place of the ftar will be E; which is higher, or nearer the zenith than its true place A.

From hence, it is, that the fun, moon, and ftars appear above the horizon when just below it; and higher than they ought to do when they are above it. Farther, the refraction of the heavenly bodies is greateft in the horizon, and gradually decreases as their altitudes increase, till near the zenith it becomes fcarcely fenfible, and in the zenith none at all. In taking, therefore, the altitudes of the heavenly bodies, it is abfolutely neceffary to fubtract from the observed altitude their refractions, a table of which we have given under the article QUADRANT, Refraction ferves alfo to account for the oval appearance of the fun and moon near the horizon for the lower these objects are, the greater is the obliquity with which their rays enter the atmosphere, to pals from the nearer to the denfer parts of it; and, therefore, they appear to he 15 Z

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the more elevated by refraction; fo that, when very near the horizon, the lower part of them is thereby more elevated than the upper part: and hence they appear of an oval figure, by reafon their horizontal diameters are no ways altered, while their vertical or upright diameters are shortened by the different refractions of the upper and lower limbs. There is alfo another alteration made by refraction in the apparent diftance of stars: thus, if two fars are in the fame circle of altitude, their apparent diftance is less than the true; but fince refraction makes each of them higher than they really are, it must bring them into parts of the ver ticals, where they come nearer together. REFRACTION of altitude is an arch of a vertical circle, whereby the altitude is increafed by the refraction.

REFRACTION of declination is an arch of a circle of declination, whereby the declination of the object is either increased or diminished by the refraction. REFRACTION of longitude is an arch of the ecliptic, whereby the longitude of the object is increased or diminished by the refraction, REFRACTION of latitude is an arch of a circle of latitude, whereby the latitude of a heavenly object is either increased or diminished by its refraction. REFRACTION in ifland cryftal. There is a double refraction in this fubftance, contrary ways, whereby not only oblique rays are divided into two, and refracted into oppofite parts, but even perpendicular rays, and one half of them refracted. Cauftic by REFRACTION. See the article DIACAUSTIC CURVE. REFRANGIBILITY of light, the difpofition of rays to be refracted. See REFRACTION, LIGHT, and RAY. REFRIGERATIVE, in medicine, a remedy which refreshes the inward parts, by cooling them, as clyfters, ptifans, &c. REFRIGERATORY, in chemistry, a veffel filled with cold water, through which the worm paffes in diftillations; the ufe of which is, to condense the vapours as they pass through the worm. REFUGE, a fanctuary or afylum. See article ASYLUM.

REFUGEES, french proteftants, who by the revocation of the edict of Nantz, have been conftrained to fly from perfecution and take refuge in foreign countries. REGAL, or ROYAL, fomething belonging to a king. See the article ROYAL,

REGALE, a magnificent entertainment or treat given to embassadors, and other perfons of diftinction, to entertain or do them honour.

It is ufual, in Italy, at the arrival of a traveller of eminence, to fend him a regale, that is, a prefent of fweetmeats, fruit, &c. by way of refreshment. REGALE, in the french jurisprudence, is a royal prerogative, which confifts in enjoying the revenues of bishoprics during the vacancy of their fees, of presenting to benefices, and of obliging the new bishop to take an oath of fidelity, and to register it in the chamber of accounts. The enjoyment of the fruits of the fee is called the temporal regale; and that of presenting to the fee, the fpiritual regale.

REGALIA, in law, the rights and prerogatives of a king; which, according to civilians are fix: viz. 1. the power of judicature: 2. the power of life and death: 3. the power of peace and war : 4. a right to fuch goods as have no owner, as waifs, eftrays, &c. 5. affeffments; and 6. the coinage of money.

Regalia is also used for the apparatus of a coronation, as the crown, the fceptre with the cross, that with the dove, St. Edward's ftaff, the globe, and the orb with the cross, four feveral fwords, &c. REGALIA of the church are the rights and privileges which cathedrals, &c. enjoy by the grants of kings; and this term is particularly used for fuch lands and here. ditaments as have been given by kings to the church.

Regalia is alfo fometimes used for the patrimony of the church. REGARD of the foreft, the infpection or

overlight thereof, or the office and province of the regarder. See REGARDER. REGARDANT, in heraldry, fignifies looking behind, and is used for a lion, or other beaft, with his face turned towards his tail.

Villain REGARDANT, or REGARDANT 10 the manor, fignifies a fervant or retainer to the lord, who was thus called from his doing all the base services within the manor, and being charged to fee that it was freed from every thing filthy and loathfome.

REGARDER, an antient officer of the king's foreft, fworn to make the regard of the foreft every year; that is, to take a view of its limits, to enquire into all offences and defaults committed by the

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foresters within the foreft, and to obferve whether all the other officers executed their respective duties. REGEL, or RIGEL, a fixed ftar of the firft magnitude, in orion's left foot, whofe longitude is 72° 10′, and latitude 10° 10. See the article ORION. REGEN, a river of Germany, which rises in the mountains that divide Boltemia from Bavaria, and falls into the Danube at Ratisbon.

REGENERATION, in theology, the act of being born again by a spiritual birth, or the change of heart and life, experienced by a perfon who forfakes a courte of vice, and fincerely embraces a life of virtue and piety.

REGENT, one who governs a kingdom during the minority or abfence of the king.

In France, the queen-mother has the regency of the kingdom during the minority of the king, under the title of queen-regent.

REGENT alfo fignifies a profeffor of arts and fciences in a college, who has a fet of pupils under his care; but here regent is generally reftrained to the lower claffes, as regent of rhetoric, regent of logic, &c. thofe of philofophy are rather called profeffors. The foreign univerfities are generally compofed of doctors, profeffors, and regents.

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REGICIDE, KING KILLER, a word chiefly used with us in fpeaking of the perfons concerned in the trial, condemnation and execution of king Charles I. REGIFUGE, a feast celebrated in antient Rome on the fixth of the calends of March, in memory of the expulfion of their antient kings, and particularly of Tarquin's flying out of Rome on that day. REGIMEN, the regulation of diet, and in a more general fenfe, of all the nonnaturals, with a view to preferve or reftore health.

Dr. Mead obferves, with respect to regimen, that diseases from inanition are generally more dangerous than those which proceed from repletion, because we can more expeditiously diminish than increase the juices of the body. Upon this account, though temperance is beneficial to all men, the antient phyficians advised perfons in good health to indulge a little now and then, by eating and drinking more plentifully than usual: but of the two, intemperance in drinking is fafer than in eating; and if a perfon has committed excefs in the latter, cold

water drank upon a full ftomach will help digeftion; to which it will be of fervice to add lemon juice or elixir of vitriol, if he has eaten high seasoned things, rich fauces, &c. Then let him fit up for fome time, and afterwards fleep. But if a man happens to be obliged to faft, he ought to avoid all laborious work. From fatiety it is not proper to pafs directly to sharp hunger, nor from hunger to fatiety; neither will it be fafe to indulge abfolute reft immediately after exceffive labour, nor fuddenly to fall to hard work after long idlenefs. In a word, all changes in the ways of living fhould be made by degrees. It is allo beneficial to vary the scenes of life, to be fometimes in the country, fometimes in town; to go to fea, to hunt, to be at reft now and then, but more frequently to use exercife, and a moderate fleep. See the articles EXERCISE and SLEEP.

The fofter and milder kinds of aliment are proper for children, and for youths the stronger. Old people ought to leffen the quantity of their food, and increase that of their drink. But yet fome allowance is to be made for custom, especially in the colder climates, like ours; for as in these the appetite is keener, fo the digeftion is better performed.

In the fummer, when the fpirits and fluid parts are apt to evaporate, the aliment fhould be light, moift, fluid, and eafy of digeftion, to repair the lofs with the greater fpeed: and as digeftion depends in part on the due preparation of the aliments, it is neceffary to chew them well, especially if they are hard, that they may be the more intimately mixed with the faliva; for those who eat in a hurry, without much chewing, are very fubject to indigestions. For the qualities of different kinds of food, see DIET, DIGESTION, FLESH, FRUIT,&c. It is well known, that cold flops the pores, and diminishes perfpiration. To fhun this inconvenience, it will be neceffary to put on winter garments pretty early, and to leave them off late, and not to pass too fuddenly from a hot into a cold air, and to avoid drinking any thing cold, when the body is hot, or when a person has been for fome time fpeaking in public.

In fhort, the paffions and affections of the mind produce very fenfible effects. Joy, anger, fear, and forrow, are the principal. In the first, the fpirits are hurried with too great vivacity; in fear or dread, they 15Z 2

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