/a IRK V f £0, .1 ' W Encyclopedia Britannica. Material, TV /jf ATERIAL, denotes fometliing compofed of Material- 1V | matter. In which fenfe the word ftands tfts. oppofed to immaterial. See Matter and Meta- ^ PHYSICS. MATERIALISTS, a fe£l in the ancient church, compofed of perfons who, being prepoffeffed with that maxim in the ancient philofophy, Ex nihilo nihil Jit, “ Out of nothing nothing can arife,” had recourfe to an internal matter, on which they fuppofed God wrought in the creation 5 inflead of, admitting God alone as the l#le caufe of the exiftence of all things. Tertullian vi- goroufly oppofes the doarine of the materialirts in his Material- treatife againft Hermogenes, who was one of their ifts. number. PTaterialifls is alfo a name given to thofe who main¬ tain that the foul of man is material} or that the prin¬ ciple of perception and thought is not a fubdance di- flinft from the body, but the refult of corporeal orga¬ nization : See Metaphysics. There are others, call¬ ed by this name, who have maintained that there is nothing but matter in the univerfe ; and that the Deity himfelf is material. See Spinoza. MATHEMATICS. Definition A /TATH EMATICS is divided into two kinds, pure of mathe- -t-VJL anc) mixed. In pure mathematics magnitude is matics. confidered in the abftradl ; and as they are founded on the fimpleft notions of quantity, the conclufions to which they lead have the fame evidence and certainty as the elementary principles from which thefe conclu¬ fions are deduced. This branch of mathematics com¬ prehends, 1. Arithmetic, which treats of the properties of numbers. 2. Geometry, which treats of extenlion as endowed with three dimennons, length, breadth, and thicknefs, without confidering the phyfical qualities infeparable from bodies in their natural date. 3. Al¬ gebra, fometimes called univerfal arithmetic, wTich compares together all kinds of quantities, whatever be their value. 4. The dircB and inverfe method of Flux- fo/; r,(called on the continent, the differential and integral calculi'), which confider magnitudes as divided into two kinds, condant and variable, the variable magni¬ tudes being generated by motion ; and which deter¬ mines the value of quantities from the velocities of the motions with which they are generated. Mixed Mathe¬ matics is the application of pure mathematics to certain edablidied phyfical principles, and comprehends all the phyfico-mathematical fciences, namely, 1. Mechanics ; 1. Hydrodynamics; 3. Optics; 4. AJlronomy; 5. A- coujlics; 6. EleBricity, and 7. Maghetifm. The hi- dory of thefe various branches of fcience having been given at full length, w7e lhall at prefent dired! the at¬ tention of the reader to the origin and progrefs of pure mathematics. 2. In attempting to difeover the origin of arithmetic VOL. XIII. Part I. and geometry, it would be a fruitlefs talk to conduA the reader into thofe ages of fable which preceded the records of authentic hidory. Our means of informa¬ tion upon this fubjedl are extremely limited and im- perfeft 5 ^ud it w7ould but ill accord with the dignity of a fcience whofe principles and conclufions are alike irrefidible, to found its hidory upon conjedlure and fable. But notwithdanding this obfeurity in which XIie the early hidory of the fciences is enveloped, one thing fciences crl- appears certain that arithmetic and geometry, and fome ginated in of the phyfical fciences, had made confiderable progrefs in Egypt, when the myderies and the theology of that favoured kingdom were tranfplanted into Greece. It is highly probable that much natural and moral know¬ ledge was taught in the Eleufinian and Dionyfian my¬ deries, which the Greeks borrowed from the Egyptians and that feveral of. the Grecian philofophers were in¬ duced by this circumdance to travel into Egypt, in fearch of thofe higher degrees of knowledge, which an acquaintance with the Egyptian myderies had taught them to anticipate. We accordingly find Thales andA c 6l- Pythagoras fuccedively under the tuition of the Egyp-a! C. slo. tian prieds, and returning into Greece loaded with the intellectual treafures of Egypt. By the eftabliOiment of the Ionian fchool at Miletus, Thales indru&ed his E'fcoverics countrymen in the knowledge which he had received ofT1,al®s‘ and gave birth to that fpirit of invedigation and dif- covery with which his followers were °infpired. He taught them the method of afeertaining the height of the pyramids of Memphis by the length of their fhadowsj and there is reafon to believe that he was the A firii 2 MATHEMATICS. who employed the circumfererice of a circle for the menfuration of angles. That he was the author of greater difcoveries, which have been either loft or a- fcribed to others, there can be little doubt ; but thefe are the only fa£ts in the hiftory of Thales which time has fpared. Difcoveries 3- fcience of arithmetic was one of the chief ofPythago-branches of the Pythagorean difcipline. Pythagoras' las- attached feveral myfterious virtues to certain combina¬ tions of numbers. He fwore by four, which he regard¬ ed as the chief of numbers. In the number three he fuppoled many wonderful properties to exift; and he regarded a knowledge'of arithmetic as the chief good. But of all Pythagoras’s difcoveries in arithmetic, none have reached our times but his multiplication table. In geometry, however, the philofopher of Samos feems to have been more fuctefsful. The difcovery of the ce¬ lebrated propofition which forms the 47th of the firft book of Euclid’s Elements, that in every right-angled triangle the fquare of the fide fubtending the right angle is equal to the fum of the fquares of the other two lides, has immortalized his name ; and whether we confider the inherent beauty of the propofition, or the extent of its application in the mathematical fciences, we cannot fail to clafs it among the moft important truths in geometry. From this propofition its author concluded that the diagonal of a fquare is incommen- turate to its fide ; and thus gave occafion to the dif¬ covery of feveral general properties of other incom- menfurate lines and numbers. 4. In the time which elapfed between the birth of Py¬ thagoras and the deftruftion of the Alexandrian fchool, the mathematical fciences were cultivated with great ar¬ dour and fuccefs. Many of the elementary propofitions of geometry were difcovered during this period •, but hi¬ ftory does not enable us to refer each difcovery to its proper author. The method of letting fall a perpendi¬ cular upon a right line from a given point (Euclid, B. 1. prop, xi.) ;—of dividing an angle into two equal parts, (Euclid, B. I. prop. ix.)j and of making an angle equal to a given angle, (Euclid B. I. prop, xxiii.} were in- ofOerioY8 vente^ k)7 Oenopidus of Chios. About the fame time dus and Ze- ^eno(Iorus> fome of whofe writings have been preferved nodorus. by 1 heon in his commentary on Ptolemy, demonftrated, in oppofition to the opinion then entertained, that ifo- perimetrical figures have equal areas. Coeval with this difcovery was the theory of regular bodies, for which we are indebted to the Pythagorean fchool. The cele- 5* About this time the celebrated problem of the du¬ brated pro- plication of the cube began to occupy the attention of Idem of the the Greek geometers. In this problem it was required onheTubeto conftru& a cube whofe folid content fliould be propofed " double that of a given cube; and the afliftance of no and invefti-other inftrument but the rule and compaffes wms to be gated. employed. Ehe origin of this problem has been a- feribed by tradition to a demand of one of the Grecian deities. The Athenians having offered fome affront to Apollo, were affliifted wdth a dreadful peftilence ; and upon conlulting the oracle at Delos, received for an- lwTer, Double the altar of Apollo. The altar alluded to happened to be cubical; and the problem, fuppofed to be of divine origin, was inveftigated with ardour by the Greek geometers,^ though it afterwards baffled all their acutenefs. I he lolution of this difficulty was attempt- A C 450. ed by Hippocrates of Chios. He difcovered, that if two mean proportionals could be found between the fide of the given cube, and the double of that fide, the firft of thefe proportionals would be the fide of the cube fought. In order to effedt this, Plato invented an inftrument compofed of twm rules, one of which moved in grooves cut in two arms at right angles to the other, fo as always to continue parallel with it ; but as this method wras mechanical, and likewife fuppofed the defeription of a curve of the third order, it did not fa- tisfy the ancient geometers. The doctrine of conic Conic fee- fedlions, which wTas at this time introduced into geo-tions difeo- metry by Plato, and which w’as fo widely extended as vered by to receive the name of the higher geometry, was fuccefs- ^a^)' ^ fully employed in the problem of doubling the cube. Menechmus found that the two mean proportionals men¬ tioned by Hippocrates, might be coniidered as the ordi¬ nates of two conic fedfions, wfflich being conftructed ac¬ cording to the conditions of the problem, would interfeff one another in two points proper for the folution of the problem. The queftion having affumed this form, gave rife to the theory of geometrical loci, of which fo many important applications have been made. In doubling the cube, therefore, we have only to employ the inttru- ments which' have been invented for deferibing the conic fedtions by one continued motion. It was after¬ wards found, that inftead of employing two conic fec- tions, the problem could be folved by the interfeclion of the circle of the parabola. Succeeding geometers em¬ ployed other curves for this purpofe, fuch as the con¬ choid of Nicomedes and the ciffoid of Diodes, &c. ^ 2^‘ An ingenious method of finding the two mean proper- • 4 tionals, without the aid of the conic fedfions, was after- A. D. 400. wards given by Pappus in his mathematical colledlions. 6. Another celebrated problem, to trifedl an angle, The trifec- was agitated in the fchool of Plato. It was found that this tion of aa problem depended upon principles analogous to thofe ofan§le* the duplication of the cube, and that it could be con- ftrudted either by the interfedlion of two conic fedlions, or by the interfedlion of a circle with a parabola. Without the aid of the conic fedtions, it was reduced to this fimple propofition :—To draw a line to a femicircle from a given point, which line lhall cut its circumfer¬ ence, and the prolongation of the diameter that forms: its bafe, fo that the part of the line comprehended be¬ tween the two points of interfedlion fliall be equal to the radius. From this propofition feveral eafy conftruc- tions may be derived. Dinoftratus of the Platonic fchool, and the cotemporary of Menechmus, invented a curve by which the preceding problem might be folved. It had the advantage alfo of giving the multiplication of an angle, and the quadrature of the circle, from which it derived the name of quadratrix. 7. While Hippocrates of Chios was paving the way for Hippe- the method of doubling the cube, which was afterwards crates’s given by Pappus, he diftinguiffled himfelf by the qua-nula- drature of the lunulae of the circle ; and had from this A'‘ C' circumftance the honour of being the firft who found a curvilineal area equal tq a fpace bounded by right lines. He was likewife the author of Elements of Geo¬ metry, a work, which, though highly approved of by his cotemporaries, has ftiared the fame fate with fome of the moft valuable produsftions of antiquity. 8. After the conic feilions had been introduced into geometry by Plato, they received many important ad¬ ditions from Eudoxus, Menechmus, and Arifteus. The latter A. C. 380. latter of thefe pRIlofophers wrote five books on conic fac¬ tions, which, unfortunately for fcience, have not reached A. C. 300. our times. Elements of 9* About this time appeared Euclid’s Elements of Geo- Euclid. metry, a work which has been employed for 20C0 years in teaching the principles of mathematics, and which is ftill reckoned the molt complete work upon the fubjeft. Peter Ramus has afcribed to Theon both the propoli- tions and the demonftrations in Euclid. It has been the opinion of others that the propofitions belong to Euclid, and the demonftrations to Theon, while others have given to Euclid the honour of both. It feems moft probable, however, that Euclid merely collected and ar¬ ranged the geometrical knowledge of the ancients, and that he fupplied many new propolitions in order to form that chain of reafoning which runs through his ele¬ ments. This great work of the Greek geometer con- ftfts of fifteen books : the eleven firft books contain the elements of pure geometry, and the reft contain the general theory of ratios, and the leading properties of commenfurate and incommenfurate numbers. Bifcoveries 10. Archimedes, the greateft geometer among the an- ofArchi- cients, flourilhed about half a century after Euclid. /TcTz o '^'e Was t^ie W^° ^oun^ t^ie rati° between the dia- ‘ 2^°' meter of a circle and its circumference ; and, by a me¬ thod of approximation, he determined this ratio to be as 7 to 22. This refult was obtained by taking an arithmeti¬ cal mean between the perimeters of the inferibed and circumfcribed polygon, and is fufficiently accurate for every praftical purpofe. Many attempts have fince been made to affign the precife ratio of the circumfer¬ ence of a circle to its diameter ; but in the prefent ftate of geometry this problem does not feem to admit of a folution. The limits of this article will not permit us to enlarge upon the difeoveries of the philofopher of Syracufe. We can only ftate, that he difeovered the fuperficies of a fphere to be equal to the convex fur face of the circumfcribed cylinder, or to the area of four of its great circles, and that the folidity of the fphere is to that of the cylinder as 3 to 2. He difeovered that the folidity of the paraboloid is one half that of the cir¬ cumfcribed cylinder, and that the area of the parabola is two thirds that of the circumfcribed re&angle ; and he was the firft who pointed out the method of drawing tangents and forming fpirals. Thefe difeoveries are contained in his works on the dimenfion of the circle, on the fphere and cylinder, on conoids and fpheroids, and on fpiral lines. Archimedes was fo fond of his difeovery of the proportion between the folidity of the fphere and that of the cylinder, that he ordered to be placed upon his tomb a fphere inferibed in_ a cylinder, and likewife the numbers which exprefs the ratio of thefe folids. Bifcoveries 1 While geometry was thus advancing with fuch ra- of Apollo- pid fteps, Apollonius Pergaeus, fo called from being nms. born at Perga in Pamphylia, followed in the fteps of A. C zoo. .Archimedes, and w-idely extended the boundaries of the fcience. In addition to leveral mathematical works, which are now loft, Apollonius wrote a treatife on the theory of the conic ledftions, which contains all their properties with relation to their axes, their diameters, and their tangents. He demonftrated the celebrated theorem, that the parallelogram deferibed about the two conjugate diameters of an ellipfe or hyperbola is M A T H E M A T 1 .C S. equal to the rectangle deferibed round the tw’o axes, and that the fum or difference of the fquaves of the two conjugate diameters are equal to the fum or difference of the fquares of the two axes. In his fifth book he de¬ termines the greateft and the leaft lines that can be drarvn to the circumferences of the conic feflions from a given point, whether this point is fituated in or out of the axis. This work, which contains every where the deepeft marks of an inventive genius, procured for its author the appellation of the Great Geometer. 12. There is fome reafon to believe, that the Egyptians Meneluus were a little acquainted with plane trigonometry ; and writes on there can be no doubt that it was known to the Greeks.^ fiei'kal Spherical trigonometry, which is a more difficult part of geometry", does not feem to have made any progrefs till ‘ J the time of Menelaus, an excellent geometrician and aftronomer. In his work on fpherical triangles, he gives the method of conftru&ing them, and of refolving moft of the cafes which were neceffary in the ancient aftro- nomy. An introdudlion to fpherical trigonometry had Theoilo- already been given to the world by Theodofius in his fius’s fphe- Treatife on Spherics, where he examines the relative pro- ncs- perties of different circles formed by cutting a fphere in A" C‘ all diredlions. 13. Though the Greeks had made great progrefs in the pr0grefs 0f fcience of geometry, they do not feem to have hitherto ana.yfis. confidered quantity in its general or abftrafl ftate. In the waitings of Plato wTe can difeover fomething like traces of geometrical analyfis j and in the feventh pro- pofition of Archimedes’s work on the fphere and the cylinder, thefe traces are more diftinftly marked. He reafons about unknown magnitudes as if they were known, and he finally arrives at an analogy, whicl, when put into the language of algebra, gives an equa¬ tion of the third degree, which leads to the folution of the problem. x 4. It was referved, however, for Diophantus to lay the 7-^ anaiy, foundation of the modern analyfis, by his invention offisofiude- the analyfis of indeterminate problems ; for the method 'erminate which he employed in the refolution of thefe problems Pro^lerris has a ftriking analogy to the prefent mode of refolving ^ equations of the lit and 2d degrees. He w^as likewifetiis.an' the author of thirteen books on arithmetic, feveral of A. D. 350. which are now loft. The works of Diophantus were honoured wfith a commentary by the beautiful and learned Hypatia, the daughter of Theon. The fame A -p fanaticifm which led to the murder of this accomplifhed ^I- I5/9- as there is in the Leyden library, an Arabic MS. en- each root in the irreducible cafe, form, when taken toge- titled “ The Algebra of Cubic Equations, or the Solu- ther, a real refult; but the paradox vanilhed when it tion of Solid Problems.” was feen from the demonftration of Bombelli that the Progrefs of 21. The various works of the Greek geometers were imaginary quantities contained in the two numbers of the Arabs tranilated by the xArabs, and it is through the medium the formula neceffarily deftroyed each other by their in geome- 0f an Arabic verfion, that the fifth and fixth books of oppofite figns. About this time M aurolycus, a Sici - Labours of Apollonius have defeended te our times. Mahomet Ben lian mathematician, difeovered the method of fumming Mauroly- Mufa, the author of a work on Plane and Spherical up feveral feriefes of numbers, fuch as the feries 1 2 cu?’ Figures, and Geber Ben Aphla, who wrote a commen- 3, 4, &c. ; 1, 4, 9, 16, &c. and the feries of trlan-^ied i4/ tary on Plato, gave a new form to the plane and fpheri- gular numbers, 1, 3, 6, 10, 15, 21, &c. ^ cal trigonometry of the ancients.. By reducing the 26. The fcience of analyfis is under great obligations Difcoveries theory of triangles to a few propofitions, and by fubfti- to Francis Vieta, a native of France. He introduced of Vieta. tuting, inftead of the chords of double arcs, the fines of the prefent mode of notation, called literal, by employ- Born I540- the arcs themfelves, they fimplified this important branch ing the letters of the alphabet to reprefent * indefinite Died l6°3- of geometry, and contributed greatly to the abridge- given quantities; and we are alfo indebted to him for nient ot aftrunotnical calculation. A treatife on the the method of transforming one equation into another, art of furveying was likewile written by Mahomet of whofe roots are greater or lefs than'thofe of the origi- Bagdad. . na] equation by a given quantity ; for the method of 22. After the deftruction of the Alexandrian fchool multiplying or dividing their roots by any given num- ' ber S' pier, Born 1550 I>ied 1617. M A T H E ber, of depriving equations of the fecond term, and of freeing them from fractional coefficients. The method which he has given for refolvihg equations of the third and fourth degree is alfo new and ingenious, and his mode of obtaining an approximate folution of equations of every order is entitled to hill higher praife. We are alfo indebted to Vieta for the theory of angular feftions, the objedt of wffiich is to find the general ex- preffions of the chords or fines for a ieries of arcs that are multiples of each other. Lop-arithms 27. While analyfis was making fuch progrefs on the invented by continent, Baron Napier of Merchifton in Scotland was Baron Na- bringing to perfeclion his illuftrious difcovery of the lo¬ garithms, a let of artificial numbers, by which the molt tedious operations in multiplication and divifion may be performed merely by addition and fubtra&ion. This difcovery was publiihed at Edinburgh in 1614 in his work entitled Logarithnwrum Cation is Defcriptio, feu ylrithmctica Suppuiationum Mirabilis Slbbreviatio. It is well known that there is fuch a correfpondence be¬ tween every arithmetical and geometrical progreffions, viz. -I0’ I’ *’ o’ r any terms of [«, 2, 4, 8, 16, 32, 64,^ ' : the geometrical progreifion may be multiplied or divided by merely adding or fubtradting the correfponding terms of the arithmetical progreffion, thus the produft of four and eight may be found by taking the lum of the correfponding terms in the arithmetical progreffion, viz. 2 and 3, for their fum 5 points out 32 as the pro- duif of 4 and 8. The numbers o, 1, 2, 3, &c. are therefore the logarithms of 1, 2, 4, 8, &c. The choice of the two progreffions being altogether arbi¬ trary, Baron Napier took the arithmetical progreffion which we have given above, and made the term o cor- refpond with the unit of the geometrical progrefiion, which he regulated in fuch a manner that when its terms are reprefented by the abfcifiae of an equilateral hyperbola in which the firlt abfcifs and the firft ordi¬ nate are each equal to r, the logarithms are reprefent¬ ed by the hyperbolic fpaces. In confequence, however, of the inconvenience of this geometrical progreffion, Baron Napier, after confulting upon the fubjetl with Henry Biiggs of Greffiam College, fubftituted the de¬ cuple progreflion 1, 10, ico, 1000, of which o,- I, 2, 3, 4, &c. are the logarithms. Nothing now remained but to confirucl tables of logarithms, by finding the lo¬ garithms of the intermediate numbers between the terms A. D. 161S. of the decuple progreffion. Napier, however, died be¬ fore he v/as able to calculate thefe tables $ but his lofs was in fome meafure fupplied by Mr Bnggs, who applied himfelf with zeal to this arduous talk, and publilhed in 1618 a table of the logarithms of all numbers from 1 to 1000. In 1624 he publilhed another table containing the logarithms from lOOO to 20,coo, and from 90,000 to 100,000. The defers in Briggs’s tables were filled up by his friends Gellibrand and Hadrian Viacq, who alfo puhlilhed newr tables containing the logarithms of fines, tangents, &c. for 90 degrees. Difcovcrles 28. During the time when Napier and Briggs were of Harriot, doing honour to their country by completing the fy Hem Born 1560. 0f logarithms, algebra w-as making great progrefs in Bied 1631. t]ie }iancjs 0f our countryman Harriot. His Artis ana- Ijticce Praxis, which appeared in 1620, contains along with the difcoveries of its author, a complete view of the Hate of algebra. He fimplified 1^ie nptatiou by M A T I e s. fubftituting finall letters in Head of the capitals introdu¬ ced by Vieta; and he was the firlt who Ihcwed that every equation beyond the firlt degree may be confider- ed as produced by the multiplication of as many fimple equations as there are units in the exponent of the high- elt power ot the unknown quantity, from this he de¬ duced the relation which exilts between the roots of any equation, and the coefficients ol the terms of which it confilts. 29. About the fame time, a foreign author named Fer- Fernei firft nel, phyfician to King Henry II. ot France, had the gives the merit of being the firfi who gave the meafure of themeaiureof Tables of logarithms computed by Mr Briggs. earth. By reckoning the number of turns made by a-1-eaxt . coach wheel from Amiens to Paris, till the altitude of the pole liar was increafed one degree, he ellimated the- length of a degree of the meridian to be 56746 toifes, which is wonderfully near the truth. He alio wrote a work on mathematics, entitled De Proportiontbus.— Menus About this time it was Ihown by Peter Metius, a German ^ mathematician, that if the diameter of a circle be reel num¬ bs circumference will be 355* This refult, fo very near i,ers for the the truth, and expreffed in fo few figures, has preterved diameter the name of its author. _ ference ofa 30. The next author, whofe labours claim our attention, circle~ is the iilultrious Defcartes. We do not allude to thofe wild and ingenious fpeculations by which this philofo-Difcoyeries pher endeavoured to explain the celeltial phenomena but to thefe great difcoveries with which he enriched the kindred fciences of algebra and geometry. He in-Die4 1659.. troduced the prefent method of marking the powers of any quantity by numerical exponents. Pie firfl explain¬ ed the ufe of negative roots in equations, and Ihowed that they are as real and uleful as pofitive roots, the on¬ ly difference between them being founded on the dif¬ ferent manner in which the correi’ponding quantities are confidered. Pie pointed out the method of finding the number of pofitive and negative roots in any equation where the roots are real ; and developed the method of indeierminates which Vieta had obfeurely hint¬ ed at. 31. Though Regiomontanus, Tartalea, and Bombelli, had tefolved feveral geometrical problems by means of algebra, yet the general method of applying geometry to algebra was firft given by Vieta. It is to Defcartes, He exten4s however, that we are indebted for the beautiful and ex- the applica- tenfive ufe which he made of his difcovery. His me-bon of ai- thod of reprefenting the nature of curve lines by equa-Sebra t0 tions, and of arranging them in different orders accord- ing to the equations which diftinguiftied them, opened a vaft field of inquiry to fubfequent mathematicians $ and his methods of conftruffing curves of double cur¬ vature, and of drawing tangents to curve lines, have contributed much to the progrefs of geometry. The inverfe method of tangents, which it was referved for the fluxionary calculus to bring to perfeftion, originated at this time in a problem which Florimundus de Beaune propofed to Defcartes. It was required to conftrucft a I(- curve in which the ratio of the ordinate and fubtangent ftiould be the fame as that of a given line to the por¬ tion of the ordinate included between the curve and a line inclined at a given angle. The curve was con- ftrudled by Defcartes, and feveral of its properties de¬ leted, but he was unable to accompliih the complete A D folution of the problem. Thefe difeoveries of Defcartes were ftudied and improved by his fucocffors, among wh,qni > € whom we may number the celebrated Iludde, who published in Schooten’s commentary on the geometry of J3cfc.artes, an excellent method of determining if an equation of any order contains feveral equal roots, and oi djmovering the roots which it contains. (Difeoveries 3 2.1'he celebrated Pafcal, who was equally diftinguifh- of Faical. ed by hts literary and his fcientific acquirements, extend- Wed 1662. Cd . e boltndarJes of analyfis by the invention of his arith¬ metical triangle. By means of arbitrary numbers pla¬ ced at the vertex of the triangle, he forms all the figur- ate numbers in fucceffion, and determines the ratios be¬ tween the numbers of any two cafes, and the various lunjs reflating from the addition of all the numbers of one. rank taken in any poflible direclion. This in- geni.ous. invention gave rife'to the calculation of proba- Ijilities in the theory of games of chance, and formed the foundation of an excellent treatife of Huygens, en¬ titled D? Ratiocinns in Ludo A/ece, publifhed in i6jy. Rifcoveries _ 33gbeveia^ curious properties of numbers were at the of Fermat. fam<- time difcovered by Fermat at Touloufe. In the tv ra theor>r of P”me numbers, particularly, which had firfl: ed I663, been cqnfidered by Eratofthenes, Fermat made great difeoveries ; and in the dodtrine of indeterminate pro¬ blems, he feems to have been deeply verfed, having re* publifhed the arithmetic of Diophantus, and enriched it with many valuable notes of his own. He invented the.method of difeovering the maxima and minima of variable quantities, which ferves to determine the tan¬ gents of geometrical curves, and paved the way for the invention of the fluxionary calculus. Gavaleri’s 34* Another flep towards the difeovery of fluxions wras method of at this time made by Cavaleri in his geometry of indivi- ^lfibles- hbles. In this work, which was publifhed in 1635, its au- ’A- thor fuppofes every plane furface to confift of an infinite number of planes j and he lays it down as an axiom, that thefe infinite fums of lines and furfaces have the fame ratio when compared with the unit in each cafe as the fuperficies and folids to be meafured. This inge¬ nious method was employed by Cavaleri in the quadrature of the conic fe&ions, and in the curvature of folids ge¬ nerated by their revolution, and in order to prove the accuracy of his. theory, he deduced the fame refults from different principles. The fame 35’' Problems of a fimilar kind had been folved by Fer- fubjeft dif mat anc* Defcartes, and now occupied the attention of cuffed by Roberval. The latter of thefe mathematicians began Roberval. his inveftigation of this fubjetf: about a year before the i634- publication of Cavaleri’s work, and the methods which both of them employed wmre fo far the fame as to be founded on the principles of indivifibles. In the mode, however, which Roberval adopted, planes and folids’ were confidered as compofed of an infinite number of re&.angles, whofe altitudes and the thicknefs of their fe&ions were infinitely fmall.—By means of this method, Roberval determined the area of the cycloid, the cen¬ tre of gravity of this area, and the folids formed by its revolution on its axis and bafe. He alfo invented a general method for tangents, fimilar in metaphyfical principles to that of fluxions, and applicable both to mechanical and geometrical curves. By means of this, he determined the tangents of the cycloid ; but there were, fome curves which refifted its application. Con- fidering every curve to be generated by the motion of a point, Roberval regarded this point as a&ed upon at £very inllant with two velocities afeertained from the M A T H E M A T I C S. nature of the curve. Ele conftrufted a parallelogram having its fides in the fame ratio as the two velocities; and he affumes as a principle, that the dire&ion of the tangent muft fall on the diagonal, the pofition of which being afeertained, gives the pofition of the tangent. 36. In 1644, folutions of the cycloidal problems for-Labours of me.rly refolved by Roberval were publilhed by Toricelli Toricelli. as invented by himfelf. The demonftrations of RoBerval I1U v'm' a given point and the fynchronous curve, fliall be de-1704. fcribed by a heavy body in equal times. He demon- flrated, that of all the cycloids thus interfebied, that which is cut perpendicularly is defcribed in lels time than any other terminating equally at the fynchronous curve. But being unable to give a general folution ol the problem, he applied to Leibnitz, w'ho eafily reiolved it, and at that time invented the method of differencing de curva in curvam. 66. About a month after the death of the marquis de I’Hofpital, John Bernouilli declared himlelf the author of a rule given by the marquis in his Analyfis of Infinites, for finding the value of a frablion, whofe numerator and denominator fliould vanifli at the fame inftant, when the variable quantity that enters into it has a certain given value. The defence made by the marquis’s friends, only induced John Bernouilli to make greater demands, till he claimed as his own the molt important parts of the Analyfis of Infinites : But it does not ap¬ pear, from an examination of the fubjedl, that there is any foundation for his claims. 67. Tow’ards the clofe of 1704, Sir Ifaac Newton pub¬ liflied, at the end of his Optics, his Enumeratio Labours of rum ter tut or din is, and his treatife De ^uadratura Cur- Newton. varum. The firft of thefe papers difplays great abili- 1704.. ty j but is founded only on the common algebra, and the doftrine of feries which Newton had brought to fuch perfedlion. His treatife, De Hhiadratura Curva- rum, contains the refolution of fluxional formula;, with one variable quantity which leads to the qua¬ drature of curves. By means of certain feries he ob¬ tains the refolution of feveral complicated formulae, by referring them to fuch as are more fimple ; and thefe fe¬ ries being interrupted in particular cafes, give the flu¬ ents in finite terms. From this feveral interefting pro- pofitions are deduced, among which is the method of refolving rational fraflions. In 171 r Newton publifh- ed his Method of Fluxions, The objeft of this wrork is1^1 ’ to determine, by fimple algebra, the linear coefficients of an equation that fatisfies as many conditions as there are coe-fricients, and to conftru61 a curve of the parabo¬ lic kind palling through any number of given points. Hence arifes a fimple method of finding the approxi¬ mate quadrature of curves, in which a certain number of ordinates are determinable. It has been the opinion of fome able mathematicians, that this treatife contains the firft principles of the integral calculus with finite differences, afterwards invented by Dr Taylor. A pofthumous work of Newton’s, entitled the Method of1^^' Fluxions, and of Infnite Series, was publiftied by Dr Pemberton about nine years after the death of its au¬ thor 5 but it does not contain any new inveftigations which accelerated the progrefs of the new analyfis. 68. The mathematical fciences were at this time in-Labours of debted to the labours of Manfredi, Parent, and Saurin. Manfredi, The former of thefe geometers publiflred a very able*r‘ work, De ConflruBime Equationum dijjerentialiumprimi, ^0y. ’ gradus. To Parent we are indebted for the problem by which M A T H E M A T I C S. 11 which we obtain the ratio between the velocity of the power, and the weight for finding the maximum effefl of machines ; but his reputation was much injured by the obfcurity of his writings. Saurin was celebrated for his theoretical and practical knowledge of watchmak¬ ing, and was the firft who elucidated the theory of tangents to the multiple points of curves. Account of 69. While the fcience of analyfis was thus advan- the difpute cing with rapidity, the difpute between Newton and between Leibnitz began to be agitated among the mathemati- ^'LLeib- ciails °f Europe. Theie illuftrious rivals feemed to ‘vitZ' have been hitherto contented with (haring the honour of having invented the (luxional calculus. But as foon as the priority of invention was attributed to Newton, the friends of Leibnitz came forward with eagernefs to (upport the claims of their mafter. Faciode 70, a wTork on the curve of fwifteft defcent, Duillier and the folid of lead refidance, publilhed in 1699, Ni- cnmmences cbolas Facio de Duillier, an eminent Genoefe, attributed the^difpiitCfto Newton t]1£ invention of fluxions, and hinted, Newton. t^at Leibnitz, as the fecond inventor, had borrowed from the Englifh philofopher. Exafperated at this im¬ proper infinuation, Leibnitz came forward in his own Leibnitz defence, and appeals to the admiflion of Newton in his defends Princi/jia, that neither had borrowed from the other, lumftlf. He exprefled his convi£lion, that Facio de Duillier was not authorifed by Sir Ifaac, to prefer fuch a charge, and threw himfelf upon the teftimony and candour of the Englifh geometer. -esj-v-,- 1 71. The difcuflion reded in this fituation for feveral makes the }Tears5 till our celebrated countryman. Dr Keill, indi¬ fame charge gated by an attack upon Newton in the Leipfic Jour- againft nal, repeated the fame charge againd Leibnitz. The Leibnitz. German plnlofopher made the fame reply as he did to his former opponent, and treated Dr Keill as a young man incapable of iudging upon the fubjeifL In 1711, i?1:. Dr Keill addreffed a letter to Sir Flans Sloane, fecre- tary to the Royal Society, and accufed Leibnitz of ha¬ ving adopted the differential notation, in order to have it believed, that he did net borrow his caleulus from the waitings of Newton. Leibnitz 72, Eeibnitz was with reafon irritated at this accufation, appeals to and called upon the Royal Society to interfere in his the Royal behalf. A coramjttee of that learned body wras accord- Society. ingly appointed to invedigate the (ubjeiff, and their re- 1712, port was publiflied in 1712, under the title of Commerci- um Epi/lolicum de Analyfipromota. In this report the Who ap- committee maintain that Leibnitz was not the fird point a inventor, and abfolve Dr Keill from all blame in giving committee the priority of invention to Newton. They were cau- to examine tious, however, in dating their opinion upon that part of ana icport. charge in which Leibnitz was accufed of plagiarifm. j 1 ’ 73* atifwer to the arguments advanced in the Com- nouil'i m- tnerciumEpiftolicutn, John Bernouilli, the particular friend plies to °f Leibnitz, publifhed a letter, in which he has the af- their report furance to date, that the method of fluxions did not given in the prece(]e t])e differential calculus, but that it might have ta^en 'ts r'l'e from it. The reafon which he afligns tolicum. for this drange affertion is, that the differential calcu¬ lus was publifhed before Newton had introduced an uniform algorithm into the method of fluxions. But it may as veil be maintained that Newton did not dif- cover the theory of univerfal gravitation, becaufe the attra&ive force of mountains and of fmaller portions of matter was not afeertained till the time of Malkelyne and Cavendidi. The principles of fluxions are allowed to have been difeovered before thofe of the differential cal¬ culus, and yet the former originated from the latter, be¬ caufe the fluxional notation was not given at the fame time ! 74. Notwithdanding the ridiculous affertion of John Remrrksdn Bernouilli, it has been admitted by all the foreign ma-1'16 contro' thematicians, that Newton was the fird inventor of the'^ ^ method of fluxions. The point at iffue therefore is merely this :—did Leibnitz fee any of the writings of Newton that contained the principles of fluxions before he publifhed in 1684 his Nova Methoduspro maximis ct minimis ? The friends of Leibnitz have adduced fome prefumptive proofs, that he had never feen the treatife of Newton, de Analyji, nor the letter to Collins, in both of which the principles of the new calculus were to be found 5 and in order to drengthen their argument, they have not fcrupled to affert, that the writings al¬ ready mentioned contained but a vague and obfeure in¬ dication of the method of duxions, and that Leibnitz might have perufed them without having difeovered it. This fubfidiary argument, however, reds upon the opi¬ nion of individuals j and the only way of repelling it is to give the opinion of an irnpartial judge. M. Mon- tucla, the celebrated hidorian of the mathematics, who being a Frenchman, cannot be fufpeffed of partiality to the Englilh, has admitted that Newton in his trea¬ tife de Analyji “ has difclofed in a very concife and obfeure manner his principles of Huxions,” and “ that the fufpicion of Leibnitz having feen this w'ork is not deditute of probability, for Leibnitz admitted, that in his interview with Collins he had feen a part of the epidolary correfpondence between Newton and that gentleman.” It is evident therefore that Leibnitz had opportunities of being acquainted with the doftrine of fluxions, before he had thought of the differential cal¬ culus 5 and as he was in London where Newton’s trea¬ tife was publilhed, and in company with the very men to whom the new analyfis had been communicated, it is very likely that he then acquired fome knowdedge of the fubjefL In favour of Leibnitz, however, it is but juflice to fay, that the tranlition from the method of tangents by Dr Barrow' to the differential calculus is fo fimple, that Leibnitz might very eafily have perceived it; and that the notation of his analyfis, the numerous applications which he made of it, and the perfection to which he carried the integral calculus, are confiderable proofs that he wras innocent of the charge which the Englifh have attempted to fix upon his memory. 75. In 1708, Remond de Montmort publilhed a cu-Works o« rious work entitled the Analylis of Games of Chance, in the doo which the common algebra was applied to the compu-tr*ne or tatien of probabilities, and the eitimation of chances. Though this work did not contain any great difeovery, 7 yet it gave extent to the theory of feries, and admir¬ ably illuflrated the doCIrine of combinations. The fame fubjeCI was aftenvards difeuffed by M. de Moivre, a French proteftant refiding in England, in a fmall > treatife entitle Menfura Sortis, in which are given the elements of the theory of recurrent feries, and fome very 171 * ingenious applications of it. Another edition was pu¬ blilhed in Englilh in 1738, under the title of the Do&rine of Chances, B a A 1 2 Leibnitz propcfes to Lnglifh the problem of orthogonal trajectories. M A T H E M A T I C S. 1717. 1718. Integration cf rational fractions. *7i9- Labours of Roger Cotes, born 1676. J)r Taylor invents the integral calculus of finite dif- ifrencos. Problem of reciprocal trajectories. 1716. / Refolved by Euler, born 1707, died 17 S3. •V72S- 76. A Ihort thtie before bis death, Leibnitz prcpofed to the Englith geometers the celebrated problem of ortho¬ gonal trajectories, which was to find the curve that cuts a feries of given curves at a Conftant angle, or at an angle varying according to a given law. This pro¬ blem was put into the hands of Sir Ifaac Newton when he returned to dinner greatly fatigued, and he brought it to an equation before he went to reft. Leibnitz being recently dead, John Bernouilli affumed his place, and maintained, that nothing was eafier than to bring the problem to an equation, and that the folution of the problem was not complete till the differential equation of the trajeCtory was refolved. Nicholas Bernouilli, the ion of John refolved the particular cafe in which the interfered curves are hyperbolas with the fame cebtre and the fame vertex. James Hermann and Nicholas .Bernouilli, the nephew of John, treated the fubjeCt by- more general methods, which applied to the cafes in which the interfeCfed curves were geometrical. The moft complete folution, however, was given by Dr Taylor in the Philofophical TranfaClions for 1717, though it was not fufhciently general, and could not apply to fome cafes capable of refolution. This defeCt was fupplied by John Bernouilli, who in the Leipfic TranfaCtions for 1718, publifhed a very fimple folution, embracing all the geotnetrical curves, and a great num¬ ber of the mechanical ones, 77. During thefe difcufiions, feveral difficult problems on the integration of rational fractions were propofed by Dr Taylor, and folved by John Bernouilli. This fub- jeCf, however, had been firft difcuffed by Roger Cotes, profeffor of mathematics at Cambridge, who died in 1710. In his pofthumous work entitled Harmonia Menfuraruni) publifhed in 1716, he gave general and convenient formulae for the integration of rational frac¬ tions ; and we are indebted to this young geometer for his method of eftimating errors in mfxed mathematics, for his remarks on the differential method of Newton, and for his celebrated theorem for refolving certain equa¬ tions. 78. In 1715, Dr Taylor publifhed his learned work entitled Methodus incrementorum direBa et inverfa. In this work the doCtor gives the name of increments or decrements of variable quantities to the differences, whether finite or infinitely fmall, of two confecutive terms-in a feries formed after a given law. When the differences are infinitely fmall, their calculus belongs to fluxions ; but when they are finite, the method of find¬ ing their relation to the quantities by which they are produced forms a new calculus, called the integral cal¬ culus of finite differences. In confequence of this work, Dr Taylor was attacked anonymoufly by John Bernouilli, who laviftved upon the Englifh geometer all that dull abufe, and angry ridicule, which he had formerly heaped upon his brother. 79. The problem of reciprocal traje<5!ories was at this time propofed by the Bernouillis. This problem re¬ quired the curves which, being conftrudfted in two op- pofite direflions in one axis, given in pofition, and then moving parallel to one another with unequal velocities, fliould perpetually interfeft each other at a given angle. It was long difcuffed between John Bernouilli and an anonymous writer, who proved to be Dr Pemberton. It wras by an elegant folution of this problem that the celebrated Euler began to be diftinguiftred among mathematicians. He was the pupil of John Bernouilli, and continued through the whole of his life, the friend and rival of his fon Daniel. The great object of his labours was to extend the boundaries of analylis ; and before he had reached his 21ft year, he publifhed a new and general method of refolving differential equations of the fecond order, fubjetfted to certain conditions. 80. The common algebra had been applied by Leibnitz ^akovn£ and John Bernouilli to determine arcs of the parabola,^1” a&" the difference of which is an algebraic quantity, ima¬ gining that fuch problems in the cafe of the ellipfe and hyperbola refifted the application of the new analyfis. The Count de Fagnani, however, applied the integral calculus to the arcs of the ellipfis and hyperbola, and had the honour of explaining this new branch of geo¬ metry. 81. In the various problems depending on the analyfis Problem of of infinites, the great difficulty is to refolve the differen- ^Amt tial equation to which the problems are reduced. Count James Riccati having been puzzled with a differential 1725. equation of the firft order, with two variable quantities, propofed it to mathematicians in the Leipfic A£!s for 1725. This queftion baffled the fkill of the moft cele¬ brated analyfts, who were merely able to point out a number of cafes in which the indeterminate can be fe- parated, and the equation refolved by the quadrature of curves. 82. Another problem fuggefted by that of Viviani was Problem of propofed in 1718 by Erneft von Offenburg. It W’as re- Orenburg, quired to pierce a hemifpherical vault with any number of elliptical windows, fo that their circumferences fhould be expreffed by algebraic quantities ;—or in other wTords, to determine on the furface of a fphere, curves algebraically re&ifiable. In a paper on the rec¬ tification of fpherical epicycloids, Herman * imagined * that thefe curves were algebraically re&ifiable, andjAA therefore fatisfied the queftion of Offenburg $ but JohntionJs_ Bernouilli (Mem. Acad, Par. 1732.) demonftrated, that 1726. as the rectification of thefe curves depended on the qua¬ drature of the j'yperbola, they were only reCtifiable inpef0ivec[K certain cafes, and gave the general method of determi-jehn Ber- ning the curves that are algebraically reCtifiable on thenouilli. furface of a fphere. 83. The fame fubjeCt was alfo difcuffed by Nicole and Labours of Clairaut, (Mem. Acad. 1734). The latter of thefeClairaut. mathematicians had already acquired fame by his Re- cherches fur les Courbet a double Courbure, publifhed in 1730, before he was 21 years of age 5 but his repu¬ tation was extended by a method of finding curves whofe property confifts in a certain relation between thefe branches expreffed by a given equation. In this refearch, Clairaut pointed out afpecies of paradox in the integral calculus, which led to the celebrated theory of particular integrals which was afterwards fully illuftrat- ed by Euler and other geometers. 84. The celebrated problem of ifochronous curves be-protign, 0f gan at this time to be rcagitated among mathematicians, ifochronous. The obje heavy body defeending along its concavity fhall always reach the loweft point in the fame time, from what¬ ever point of the curve it begins to defeend. Huygens had already fhewn that the cycloid was the ifochronous curve in vacuo. Newton had demonftrated the fame curve to be ifochronous when the defeending body ex¬ periences from the air a refiftahee proportional to its ve¬ locity, 13 M A T H E M A T I C S. * Memoirs locity ; and Euler * and John Bernouillif, had fepa- cf Peters- rately found the ifochronous curve when the refiftance burgh, ^ was as the fquare of the velocity. Thefe three cafes, ^kMein Par anc^ even a fourth in which the reliftance was as the 173®” fquare of the velocity added to the product of the velo¬ city by a conftant coefficient, were all refolved by Fon¬ taine, by means of an ingenious and original method •, Fontaine! ancl lt 1S vei7 remarkable that the ifochronous curve is the fame in the third and fourth cafes.—The method of Fontaine was illuflrated by Euler, who folved a fifth cafe, including all the other four, when the refiftance is compofed of three terms, the fquare of the velocity, the produdl of the velocity by a given coefficient, and a conftant quantity. He found alfo an expreffion of the time which the body employs to defcend through any arc of the curve. Algebra of 85. The application of analytical formulae to the phy- fines and fico-mathematical fciences was much facilitated by the cofines. algebra of fines and cofines with which Frederick Chriftian Mayer, and Euler, enriched geometry. By the combination of arcs, fines, and cofines, formulae are obtained which frequently yield to the method of refo- lution, and enable us to folve a number of problems which the ordinary ufe of arcs, fines, and cofines, wmuld /render tedious and complicated. Improve- 86. About this time a great difcovery in the theory of ment in the differential equations of the firft order was made fepa- ofdiffer°n rat;eV by Euler, Fontaine, and Clairaut. Hitherto tialequa?" geometers had no dire£t method of afcertaining if any tions. differential equation were refolvable in the Hate in which it was prefented, or if it required fome prepara¬ tion prior to its refolution. For every differential equsi- tion a particular method was employed, and their refo¬ lution was often effedled by a kind of tentative procefs, which difplayed the ingenuity of its author, without be¬ ing applicable to other equations. The conditions un¬ der which differential equations of the firft order are. re¬ folvable were difeovered by the three mathematicians whom we have mentioned. Euler made the difcovery in 1736, but did not publifti it till 1740. Fontaine and Clairaut lighted upon it in I7391 Euler after¬ wards extended the difcovery to equations of higher orders. Difcovery g y. The firft traces of the integral calculus w'ith partial of the inte- differences appeared in a paper of Euler’s in the Peteri- fuswith bur§h Tran fa 61 ions for 17345 but d’Alembert,, in his partial dif- work Sur les Vents, has given clearer notions of fcrences. it, and was the firft who employed it in folution of the problem of vibrating cords propofed by Hr iaylor, and inveftigated by F.uler and Eaniel Bernouilli. ^1 he ob¬ ject of this calculus is to find a fun£Hon of feveral vari¬ able quantities, when we have the relation of the coef¬ ficients which affefl the differentials of tshe variable quantities of which this funflion is compofed. Euler exhibited it in various ■points of view7, and fhe'wed its ^ application to a number of phyfical problems 5 and he burX™' afterwards, in his paper entitled Invejigatio FunBionum Tranjac- ex data Differentiahum conditione *, he completely ex- tio/is, 1762. plained the nature, and gave the algorithm of the cal¬ culus. The prin- g8. While the analyfis of infinites was making filch ra- fluxionf progrefs on the continent, it was attacked in England attacked by tbe celebrated Dr Berkeley, bithop of Cloyne, in a by Dr wmrk called the AnnhjJl, ora difconrfe addrejjedto an In- Berkeley, fidel Mathematician, wherein it is examined whether the *734- objeB, principles, and inferences of the modern analyfis, are \more dflinBlij conceived than Religious Myfieries and Points of Faith. In this work the doilor admits the truth of the conclulions, but maintains that the principles of fluxions are not founded upon realbning ftriflly logical and conclufive. This attack called forth Robins and Maclaurin. The former proved that the principles of fluxions wrere confiftent with the ftri6l- eft reafoning, while Maclaurin, in his Treatife of Flux¬ ions, gave a fynthetical demonftration of the principles of the calculus after the manner of the ancient geome¬ tricians, and eftabliffies it with fuch clearnefs and fatis- fa6tion that no intelligent man could refute his affent. The differential calculus had been attacked at an earlier period by Nieuwentiet and Rolle, but the weapons wielded by thefe adverfaries were contemptible when compared with the ingenuity of Dr Berkeley. 89. Notwithflanding this attack upon the principles of Works of the new analyfis, the fcience of geometry made rapid advances in England in the hands of Ihomas Simplon,"5 ^ Landen and Waring. In 1740, Mr Simpfon publifh- ed his Treatife on Fluxions, which, befides many origi-I74c* nal refearches, contains a convenient method of refolv- ing differential equations by approximation, and various means of haftening the convergency of llowly conver¬ ging feries. We are indebted to the fame geometer for feveral general theorems for fumming different feries, whether they are fufceptible of an abfolute or an ap¬ proximate fummation. His Mathematical Dijfertations, publiffied in 1743, his Efiays on feveral SubjeBs in 1 Mathematics, publifhed in 1740, and his SeleB Exer- eifes for Toung Proficients in the Mathematics, publiffi¬ ed in 1752, contain ingenious and original refearches which contributed to the progrefs of geometry. 90. In his Mathe?natical Lucubrations, publiffied in The refidu- 1755, Mr Landen has given feveral ingenious theorems for the fummation of feries 5 and the Philofqphical i ranf- jfy Ljirukjr. affions for 1775 contain his curious difcovery of the reffification of a hyperbolic arc, by means of two arcs 1777. of an ellipfis, which was afterwards more Amply de- m on fixated by Legendre. His invention of a new cal¬ culus, called the refidual analyfis, and in fome re- fpeffs fubfidiary to the method of fluxions, has immor¬ talized his name. It was announced and explained in a fmall pamphlet publiffied in 1715, entitled ix Difcour/e concerning the Rfidual Analyfis. 91. The progrefs of geometry in England was acce-Labours oi' lerated by the labours of Mr Edward Waring, profeffor Waring, of mathematics at Cambridge. His two works entiiledt Phil. Trctnj'- Meditationcs Analytwce, publifhed in 1769, and Medita-17^4> ani^ tiones Algebraicce, and his papers in the PhilofophicaH'??1’ P- TranfaCtlons on the fummation of forces, are filled with I4'J“ original and profound refearches into various branches of the common algebra, and the higher analyfis. 92. It was from the genius of Lagrange, however,Difcoverks * that the higher calculus has received the moft brilliant ^ Ba- improvements. This great man was born in Piedmont. SianSe* He afterwards removed to Berlin, and hence to Paris, where he flill refides. In addition to many improvements upon the integral analyfis, he has enriched geometry with His method a new calculus called the method of variations. The objeft f varia- of this calculus is, when there is given an expreffion ortl0ns* funflion of two or more variable quantities whofe relation is expreffed by a certain law7, to find what this funffion becomes when that law fuffers any variation infinitely {ms'll, H M A T H E fmall, occafloned by the variation of one or more of the terms which exprefs it. This calculus is as much fu- perior to the integral calculus, as the integral calculus is above the common algebra. It is the only means by which vre can refolve an immenfe number of prob¬ lems de maximis et minimis, and is neceiTary for the fo- lution of the moll interelling problems in mechanics. Hii theory His theory of analytical functions is one of the molt brillimit fpecimens of human genius. In the Memoirs tions." of Berlin for 1772 he had touched upon this intereft- ing fubjeft, but the theory was completely developed in 1797 in his work entitled Theorie des fonBions ana- lytiques, contenant les principes da ca/cul dijferentiel, deg a gees de toute confideration dHnfinimcnts petits, on evanoui/fements, ou des /imites, ou des fluxions; et rc- duit a I'anahjfle algebrique des quantilesfluies. In a great number of memoirs which are to be found in the Me¬ moirs of the Academy of Paris, in thofe of the Acade¬ my of Berlin*, and in thofe of the French Academy, La¬ grange has thrown light on every branch both of the common algebra and the new analyfis. Labours of 93, The new geometry has like wile been much indebted a ace" to the celebrated Laplace. His various papers in the Me- * Tom. 6. 7. moires des Spavans Etrangers,* and the Memoirs of the French Academy, have added greatly to the higher calculi, while his application of analyfis to the celellial phenomena, as exhibited in the Mecanique Celefle, and his various difeoveries in phyfical aflronomy, entitle him to a high rank among the promoters of fcience. Works of ^ 94. Among the celebrated French mathematftians of crok^Eof" t^le anc* Pre^ent century, we cannot omit the names of fut, and Coufin, Lacroix, and Boflut *, all of whom have written Legendre, large works on the differential and integral calculi, and illullrated the new analyfis by their difeoveries. The Elemens de Geometric by Legendre is one of the belt and moft original works upon elementary geometry, and his papers in the Memoirs of the Academy con¬ tain feveral improvements upon the new analyfis. Agnefi’s 9$• 1° Italy the mathematical fciences were defiined to analytical be improved and explained by a celebrated female, mftitutions. Donna Maria Gaetana Agnefi was profeflbr of mathe- 11^‘ matics in the univerfity of Bologna, and publifhed a learned work entitled Analytical Inflitutions, con¬ taining the common analyfis, and the differential and in¬ tegral calculi. It has been tranfiated into Englifh by Profeffor Colfon, and was publithed at the expence of ,T . Baron Maferes. A few years ago feveral curious pro- i>n theer°ri Pcrt'es t^ie circle have been difeovered by Mafche- ciiclc. roni, another Italian mathematician, who has publifhed MATICS. them in his interelling work flur le Geometric da Corn- pas. 96. In England the mathematical fciences have been Englifli fuccefsfuliy cultivated by Emerfcn, Baron Maferes, Dr marhemat- M. Young, Dr Hutton, Profeffor Vince, and Profeffor cians' Robertfon of Oxford. The DoBrine of Fluxions by Lmerfon. Emerfon, and his Method of Increments, are good in- troduefions to the higher geometry. The Scriptores Logarithmici of Baron Maferes j his Trails on the Re- ^’aron Ya - flolutmn of Equations ; his Principles of Life Annuities, and his other mathematical papers, do the highelt ho¬ nour to his talents as a mathematician •, while his zeal for the promotion of the mathematical tciences, and his generous attention to thofe r,ho cultivate them, entitle him to the noble appellation of the friend and patron of genius. Dr Mathew Young, bithop of Clonfert, has-Ur M. given a fynthetical demonilration of Newton’s rule for Leung, the quadrature cf fimple curves; and has written on the extraflion of cubic and other roots. Dr Hutton L)r Hutton and Dr Vince have each publifhed feveral elementary and Dr treatifes on mathematics, and have invented inoeni-' lnce‘ ous methods for the fummation of feries. Mr Robert-, T fon of Oxford is the author of an excellent treatife on Robert" conic fedfions. 97. The ancient geometry was affiduoufly cultivated inSeottiflima- Scotland by Dr Robert Simpfcn and Dr Matthew Stew-themati- art. Dr Simpfon’s edition of Euclid and his treatife on c’;ans- conic fedfions have been much admired. The Trails Phjfical and Mathematical of Dr Matthew Stewart, Pr s;®p- and his Propoftiones Gecmetncce more veterum demon- 'on' flrata, contain fine fpecimens of mathematical genius. In the prefent day the names of Profeffor Playfair and Pro-I>)'M' feifor Leflie of the univerfity of Edinburgh, Mr Wal-Stewaif- lace and Mr Ivory now of the Royal Military College at Great Marlow, are well known to mathematicians. Mr Playfair’s Elements of Geometry, and his papers on ^ Piay* the Arithmetic of Impojftble Quantities and on Porifms, are ^ proofs of his great talents as a mathematician and a phllo-, T r. fopher. Mr Leflie, well known for his great difeoveries on * heat, has found a very fimple’ principle, capabRof extenfive application, by which the complicated expreffions in the folution of indeterminate problems may be eafily re- folved. Mr Wallace’s papers on Geometrical For if ms Vr Wal- in the 4th vol. of the Edinburgh Tranfadlions, difplaylace- much genius j and Mr Ivory’s Treatifes in the lafl vol. of Baron Maferes’s Scnptorcs Logarithnnci, and his pa- Mrlvcry. per on A New Series for the Rectification of the Ellitfs, Edin. Tranf. vol. zfth. entitle him to a high rank among modern mathematicians. MAT Mathemati- MATHEMATICAL, any tiling belonging to the cal c fcience of mathematics. Matlock. Matiiematibal Inflruments, fuch infiruments as are w v ufually employed by mathematicians, as compaffes, feales, quadrants, &c. Machine for dividing Mathematical Inflruments. See Ramsden’s Machine. MAI LOCK, a town or village of Derbyfhire, near Wickfworth, fituated on the very edge of the Der- MAT went ; noted for its bath, the water of which is milk- Matlock. warm ; and remarkable* for the huge rocks in its envi-' v rons, particularly thofe called the Torr, on the eait fide of the Derwent, over againft it, which feem to be piled one upon another. It is an extenfive draggling village, built in a very romantic %le, on the fteep’fide of a mountain, riling irregularly from the bottom to nearly the fummit. Near the bath are feveral fmall houfes, whofe fituation is on the little natural horizon¬ tal MAT [ i MatraCs tal parts of the mountain, a few yards above the road, !’ and in fome places the roofs of fome almoft touch the iMatror,. fjoors 0f ot;hers> There are excellent accommodations for company who refort to the bath *, and the poorer inhabitants are fupported by,the fale of petrifadlions, cryftals, &c. and notwithftanding the rockinefs of the foil, the cliffs produce an immenfe number of trees, whofe foliage adds greatly to the beauty of the place. MATRASS, Cucurbit, or Bolthead, among chemifts. See Chemistry, Explanation of Plates. MATRICARIA, Feverfew; a genus of plants, belonging to the fyngenefia clafs ; and in the natural method ranking under the 49th order, CotTipqfitce. See Botany Index. MATRICE, or Matrix. See Matrix. Matrice, or matrix, in Dyeing, is applied to the ffve fimple colours, whence all the reft are derived or corapofed. Thefe are, the black, white, blue, red, and ' yellow or root colour. Matrice, or matrices, ufed by the letter-founders, are thofe little pieces of copper or brafs, at one end whereof are engraven, dentwife, or en crcux, the feve- ral characters ufed in the compofing of books. Each character, virgula, and even each point in a difcourfe, has its feveral matrix ; and of confequence its feveral puncheon to ftrike it. They are the engravers on me¬ tal that cut or grave the matrices. When types are to be caft, the matrice is faftened to the end of a mould, fo difpofed as that when the metal is poured on it, it may fall into the creux or ca¬ vity of the matrice, and take the figure and impreflion thereof. See Letter Foundert. Matrices, ufed in coining, are pieces of fteel in form of dies, whereon are engraven the feveral figures, arms, charafters, legends, See. wherewith the fpecies are to be ftamped. The engraving is performed with feverai puncheons, which being formed in relievo, or prominent, when ftruck on the metal, make an in¬ dented impreffion, which the French call en creux. MATRICULA, a regifter kept of the admiflion of officers and perfons entered into any body or fociety w hereof a lift is made. Hence thofe wrho are admitted into our univerfities are faid to be matriculated. A- mong ecclefiaftical authors, we find mention made of two kinds of matricule ; the one containing a lift of the eccleiiaftics, called matricula clericorum : the other of the poor fubfifted at the expence of the church, called matricula pauperum. MATRICULA was alfo applied to a kind of alms- houfe, where the poor were provided for. It had cer¬ tain revenues appropriated to it, and was ufually built near the church, whence the name was alfo frequently given to the church itfelf. MATRIMONY. See Marriage. MATRIX, in Anatomy, the womb, or that part of the female of any kind, wherein the foetus is conceived and nouriffred till the time of its delivery. See Ana¬ tomy, N° 108. Matrix is alfo applied to places proper for the ge¬ neration of vegetables, minerals, and metals. Thus the earth is the matrix wffierein feeds fprout ; and marcafites are by many confideved as the matrices of metals. The matrix of ores is the earthy and ftony fubftan- 5 ] MAT ces in which thefe metallic matters are enveloped : thefe are various, as lime and heavy fpar, quartz, fluors, &c. MATRON, an elderly married woman. Jury of Matrons. When a widow feigns herfelf with child in order to exclude the next heir, and a fuppofititious birth is fufpesffed to be intended, then, upon the writ de ventre infpiciendo, a jury of women is to be impannelled to try the queftion whether the woman is with child or not. So, if a woman is convifted of a capital offence, and, being condemned to fuffer death, pleads in ftay of execution, that fhe is pregnant, a jury of matrons is impannelled to in¬ quire into the truth of the allegation ; and, if they find it true, the convict is refpited till after her deli¬ very. MATRON A, in Ancient Geography, a river fepa- rating Gallia Celtica from the Belgica (Cefar). Norv the Marne ; which, riling in Champagne near Langres, runs north-weft, and then wreft, and paffing by Meaux falls into the Seine at Charenton, two leagues to the eaft of Paris. MATRONAL I A, a Roman feftival inftituted by Romulus, and celebrated on the kalends of March, in honour of Mars. It was kept by matrons in particu¬ lar, and bachelors w?ere entirely excluded from any lhare in the folemnity. The men during this feall fent prefents to the women, for which a return was made by them at the Saturnalia: And the women gave the fame indulgence to their fervants now which the men gave to theirs at the feaft of Saturn, ferving them at table, and treating them as fuperiors. MATROSSES, are foldiers in the train of artil¬ lery, who are next to the gunners, and aflift them in loading, firing, and fpunging the great guns. They carry firelocks, and march along with the ftore wag¬ gons, both as a guard, and to give their affiftarice in cafe a waggon Ihould break down. MATSYS, Quintin, painter of hiftory and por¬ traits, was born at Antwerp in 1460, and for feveral years followed the trade of a blackfmith or farrier, at leaft till he was in his 20th year. Authors vary in their accounts of the caufe of his quitting his firft occupa¬ tion, and attaching himfelf to the art of painting. Some affirm, that the firft unfolding of his genius was occafioned by the fight of a print which accidentally was fhown to him by a friend who came to pay him a vifit wffiile he was in a declining ftate of health from the labour of his former employment, and that by his copying the print with fome degree of fuccefs, he was animated with a defire to learn the art of painting. Others fay, he fell in love with a young woman of great beauty, the daughter of a painter, and they al¬ lege that love alone wrought the miracle, as he could have no profpeft of obtaining her except by a diftin- guifhed merit in the profeffion of painting : for which reafon he applied himfelf with inceflant labour to ftudy and pradlife the art, till he became fo eminent as to be entitled to demand her in marriage, and he fucceed- ed. Whatever truth may be in either of thele ac¬ counts, it is certain that he appeared to have an un¬ common genius ; his manner was Angular, not refem-* bling the manner of any other mafter ; and his piflures were ftrongly coloured and carefully finiftied, but yet they are fomewhat dry and hard. By many cornpe- Matroa II. Matlys. tsnt. MAT [ 16 ] MAT Matt tent judges it was believed, when they obferved the . T ftrength of expreffion in feme of his compefitions, that ‘ ' if he had ftudied in Italy to acquire fome knowledge of the antiques and the great mailers of the Roman fchool, he would have proved one of the moil eminent painters of the Low Countries. But he only imitated ordinary life ; and feemed more inclined, or at lead more qualified, to imitate the defects than the beauties of nature. Some hiftorical compofitions of this mailer deferve commendation ; particularly a Defcent from the Crofs, which is in the cathedral at Antwerp j and it is jufily admired for the fpirit, {kill, and delicacy of the whole. But the mod remarkable and bed known pic¬ ture of Matfys, is that of the Two Mifers in the galle¬ ry at Windfor. He died in 1529. MATT, in a (hip, is a name given to rope-yarn, junk, &c. beat flat and interwoven \ ufed in order to preferve the yards fx-om galling or rubbing, in hoiding jor lowering them. MATTER, in common language, is a word of the fame import with body, and denotes that which is tan¬ gible, vifible, and extended •, but among philofophers it fignifies that fubdance of which all bodies are com- pofed ; and in this fenfe it is fynonymous with the word Element. It is only by the fenfes that we have any communi- -cation with the external world ; but the immediate ob- je£ls of fenfe, philofophers have in general agreed to term qualities, w'hich they conceive as inhering in fomething which is called their fubjeB or fubjlratum. It is this fubflratum of fenfible qualities which, in the language of philofophy, is denominated matter; fo that matter is not that which we immediately fee or handle, but the concealed fubjeB or fupport of vifible and tangible qualities. What the moderns term quali¬ ties, was by Ariftotle and his followers called form ; but fo far as the two do&rines are intelligible, there ap¬ pears to be no eflential difference between them. From the moderns we learn, that body confids of matter and qualities ; and the Peripatetics taught the fame thing, when they faid that body is compofed of matter and form. How philofophers WTre led to analyze body into matter and form, or, to ufe modern language, into matter and qualities; what kind of exiffence they at¬ tribute to each ; and whether matter muff be conceived as felf-exiilent or created—are queftions which (hall be confidered afterwards (See Metaphysics). It is fuf- ficient here to have defined the term. MAI I HEW, or Gofpel of St Matthew, a cano¬ nical book of the New Teftament. St Matthew wrote his gofpel in Judea, at the re- queft of thofe he had converted ; and it is thought he began in the year 41, eight years after Chrift’s refurreiflion. It was written, according to the tefti- mony of all the ancients, in the Hebrew or Syriac language ; but the Greek verfion, which now pafles for the original, is as old as the apoftolical times. St. Matthew the Evangelifts Day, a feftival of the Chriftian church, obferved on September 21 ft. St Matthew, the fon of Alpheus, -was alfo called Levi. He was ef Jewifti original, as both his names difeover, and probably a Galilean. Before his call to the apoftolate, he was a publican or toll-gatherer to the Romans j an office of bad repute among the Jews, on account of the covetoufnefs and exaflion of Matthew, thofe who managed it $ St Matthew’s office parti- v~ ’ r cularly confiding in gathering the cuftoms of all merchandife that came by the fea of Galilee, and the tribute that paffengers were to pay wdio went by water. And here it was that Matthew fat at the re¬ ceipt of cuftoms, when our Saviour called him to be a difciple. It is probable, that, living at Capernaum, the place of Chrift’s ufual relidence, he might have fome knowledge of him before he was called. Mat¬ thew immediately expreffed his fatisfadlion in being called to this high dignity, by entertaining our Sa¬ viour and his difciples at a great dinner at his own houfe, whither he invited all his friends, efpecially thofe ot his own profeflxon, hoping, probably, that they might be influenced by the company and converfation of Chrift. St Matthew continued with the reft of the apoftles till after our Lord’s afeenfion. For the firft eight years afterwards, he preached in Judea. Then he betook himfelf to propagating the gofpel among the Gentiles, and chofe Ethiopia as the feene of his apofto¬ lical miniftry j where it is faid he fuffered martyr¬ dom, but by what kind of death is altogether uncer¬ tain. It is pretended, but without any foundation, that Hyrtacus, king of Ethiopia, defiring to marry Iphigenia, the daughter of his brother and predeceflbr vEglippus, and the apoftle having reprefented to him that he could not lawfully do it, the enraged prince ordered his head immediately to be cut off. Baronius tells us, the body of St Matthew was tranfported from Ethiopia to Bithynia, and from thence was carried to Salernum in the kingdom of Naples in the year 954, where it was found in 1080, and where Duke Robert built a church beaxing his name. St Matthew, a town of Spain, in the kingdom of Arragon, feated in a pleafant plain, and in a very fer¬ tile country watered with many fprings. W. Long, o. 15. N. Lat. 40. 22. Matthew of Paris. See Paris. Matthew of Wefminfer, a Benedidline monk and accompliftied fcholar, who wrote a hiftory from the beginning of the world to the end of the reign of Ed¬ ward I. under the title of Flores Hiforiarum ; which was afterwards continued by other hands. He died in 1380. St MATTHIAS, an apoftle, tvas chofen inftead of Judas. He preached in Judaea and part of Ethi¬ opia, and fuffered martyrdom. See the ABs of the Apofles, chap. i. There was a gofpel publilhed un¬ der Matthias’s name, but rejected as fpurious; as likewife fome traditions, wThich met with the fame fate. St Matthias's Day, a feftival of the Chriftian church, obferved on the 24th of February. St Mat¬ thias was an apoftle of Jefus Chrift, but not of the number of the twelve chofen by Chrift himfelf. He obtained this high honour upon a vacancy made in the college of the apoftles by the treafon and death of Judas Ifcariot. The choice fell on Matthias by lot ; his competitor being Jofeph called Barfabas, and furnamed Jufus. Matthias was qualified for the apoftleftiip, by having been a conftant attendant upon our Saviour all the time of his miniftry. - He was, probably, one of the 70 difciples. After our Lord’s refurredtion, he preached the gofpel firft in Judaea. Afterwards MAT [ i? ] M A U Mnttiacx Afterwards it is probable he travelled eaihvards, his Aqtxa; relidence being principally near the irruption of the river Apfarus and the haven Hyffus. The barbarous ■ , people treated him with great rudenefs and inhumani¬ ty •, and, after many labours and fufferings in convert- ing great numbers to Chriftianity, he obtained the crown of martyrdom ^ but by what kind of death, is uncertain.—They pretend to {how the relics of St Mat¬ thias at Rome ■, and the famous abbey of St Mat¬ thias near Treves boafts of the fame advantage : but doubtlefs both without any foundation. There was a gofpel afcribed to St Matthias ; but it was univerfally rejedled as fpurious. MATTIACiE AqujE, or Mattiaci Fontes, in Ancient Geography, now Wilhaden, oppofite to Mentz, in Weteravia. E. Long. 8. N. Lat. 50. 6. MATT1ACUM, or Mattium, in Ancient Geogra¬ phy, a town of the Mattiaci, a branch of the Catti in Germany. Now Marpurg in Heffe. E. Long. 8. 40. N. Lat, 50. 40. MATTINS, the firft canonical hour, or the firft part of the daily fervice, in the Romifh church. MATTHIOLUS, Peter Andrew, an eminent phylician in the i6th century, born at Sienna, was well {killed in the Greek and Latin tongues. He wrote learned commentaries on Diofcorides, and other wrorks which are efteemed ; and died in 1577. MAT GRANTS, in Pharmacy, medicines which promote the fuppuration of tumors. MATY, Matthew, M. D. an eminent phyfician and polite writer, wras born in Holland in the year 1718. He was the fon of a clergyman, and w’as ori¬ ginally intended for the church ; but in confequence of feme mortifications his father met with from the fynod, on account of the peculiar fentiments he en¬ tertained about the dodlrine of the Trinity, turned his thoughts to phyfic. He took his degree of M. D. at Leyden j and in 1740 came to fettle in England, his father having determined to quit Holland for ever. In order to make himfelf knowm, he began in 1749 *0 publifh in French an account of the produftions of the Englitb prefs, printed at the Hague under the name of the "journal Britannique. This journal, which conti¬ nues to hold its rank amongft the bed of thofe which have appeared fince the time of Eayle, anfwered the chief end he intended by it, and introduced him to the acquaintance of fome of the moft refpedlable lite¬ rary characters of the country he had made his own. It was to their aCtive and uninterrupted friendfhip he owTed the places he afterwards poffelTed. In 1758 he was chofen fellow, and in 1765, on the refignation of Hr Birch, wdib died a fewr months after, and had made him his executor, fecretary to the Royal Society. He had been appointed one of the under librarians of tlm Britifh muieum at its firft inftitution in 1753, an<^ ^e" came principal librarian at the death of Hr Knight in 1772. Ufeful in all thefe fituations, he promifed to be eminently fo in the laft, when he was feized with a languifhing dilbrder, which in 1776 put an end to a life which had been uniformly devoted to the purfuit of fcience and the offices of humanity. He was an early and adive advocate for inoculation \ and when there was a doubt entertained that one might have the fmallpox this w'ay a fecond time, tried it upon him- lelf unknown to his family. He was a member of VOL. XIII. Part 1. the medical club (with the Drs Parfons, Templeman, ^ waty, Fothergill, Watfon and others), which met every fortnight in St Paul’s Churchyard. He was twice married, viz. the firft time to Mrs Elizabeth Boifra- gon } and the fecond to Mrs Mary Deners. He left a fon and three daughters. He had nearly finifhed the Memoirs of the earl of Chefterfield ; which were completed by his fon-in-law Mr Juftamond, and pre¬ fixed to that nobleman’s Mifcellaneous Works, 1777, 2 vols. 4to. Maty, Paul Henry, M. A. F. R. S. fon of the former, was educated at Weftminfter and Trinity col¬ lege Cambridge, and had their travelling fellowffiip for three years. He was afterwards chaplain to Lord Stormont at Paris in 17—, and foon after vacated his next fellowfhip by marrying one of the three daughters of Jofeph Clerk, Efq. filler of the late Captain Charles Clerk (who fucceeded to the command on the death of Captain Cook). On his father’s death in 1776, he was appointed to the office of one of the under libra¬ rians of the Britifh mufeum, and was afterwards prefer¬ red to a fuperior department, having the care of the antiquities, for which he was eminently qualified. In 1776 he alfo fucceeded his father in the office of fecretary to the Royal Society. On the difputes re- fpe£Hng,the reinftatement of Dr Hutton in the depart¬ ment of fecretary for foreign correfpondence in 1784, Mr Maty took a warm and diftinguilhed part, and re- figned the office of fecretary j after which he under¬ took to affift gentlemen or ladies in perfebling their knowledge of the Greek, Latin, French, and Italian claffics. Mr Maty was a thinking confcientious man j and having conceived fome doubts about the articles he had fubferibed in early life, he never could be pre¬ vailed upon to place himlelf in the way of ecclefiaftical preferment, though his connexions were amongft thofe who could have ferved him eflentially in this point ; and foon after his father’s death he withdrew himfelf from miniftering in the eftabliftied church, his reafons for which he publilhed in the 47th volume of the Gent. Magazine, p, 466. His whole life was thenceforwards taken up in literary purfuits. He received look from the duke of Marlborough, with a copy of that beauti¬ ful work, xhe. Gemmcc Mar/bunenfes, of which only 100 copies were worked off for prefents ; and of which Mr Maty wrote the French account, as Mr Bryant did the Latin. In January 1782 he fet on foot a Review of publications, principally foreign^ which he carried on, with great credit to himfelf and fatisfadlion to the public, for near five years, when he was obliged to difeontinue it from ill health. He had long laboured under an afthmatic complaint, which at times made great ravages in his cosftitution, and at laft put a pe¬ riod to his life in Jan. 1787, at the age of 42 ; leaving behind him one fon.—Mr Maty was eminently ac¬ quainted with ancient and modern literature, and parti¬ cularly converfant in critical refearches. The purity and probity of his nature wrere unqueftionable 5 and hi* humanity was as exquifite as it wmuld have been exten-* five, had it been feconded by his fortune. MAUBEUGE, a town of the Netherlands, in Hai- nault, with an illuftrious abbey of canoneffes, who muft be noble both by the father and mother’s fide. This place w7as ceded to France in 1678 5 and fortified after the manner of Vauban. In September 1793, the C Auftrians M A U [ i Mauraueo Audriafts formed the blockade of this place, but were j! ^ . driven from their pofition in the following month. It ..i-Hj-.ertms. feate(j 0n t}lg river Sambre, in E. Long. 5. o. N. Eat. 50. 15. MAUCAUCO, Macaco, or Maki, a genus of quadrupeds belonging to the order Primates. See Mam¬ malia Index. MAVIS, a fpecies of turdus. See ORNITHOLOGY Index. MAUNCH, in Heraldry, the figure of an ancient coat fleeve, born in many gentlemen’s efcutcheons. MAUNDY THURSDAY, is the Thurfday in pafi- fison week ; which was called Maunday or Mandate Thur/datf, from the command which our Saviour gave Ids apoftles to commemorate him in the Lord’s lupper, which he this day inflituted ; or from the new com¬ mandment which he gave them to love one another, after he had wafned their feet as a token of his love to them. MAUPERTUIS, Peter Louis Morceau de, a Celebrated French academician, was born at St Malo in 16985 and was there privately educated till he arriv¬ ed at his 16th year, when he was placed under the ce¬ lebrated profePfior of philofophy M. le Blond, in the college of La Marche, at Paris. He foon difcovered a paffion for mathematical fludics, and particularly for geometry. He likewife pra£lifed inftrumental mufic in his early years with great fuccefs 5 but fixed on no profeffion till he was 20, when he entered into the ar¬ my. He firft ferved in the Grey Mufqueteers 5 but in the year 1720, his father purchafed for him a company of cavalry in the regiment of La Rocheguyon. He re¬ mained but five years in the army, during which time he purfued his mathematical lludies with great vigour 5 and it was foon remarked by M. Freret and other aca¬ demicians, that nothing but geometry could fatisfy his adiive foul and unbounded thirft for knowledge. In the year 1723, lie was received into the Royal Academy of Sciences, and read his firft performance, which was a memoir upon the conftruclion and form of mufical inftruments, November 15. 1724. During the firft years of his admiflion, he did not wholly con¬ fine his attention to mathematics ; he dipt into natu¬ ral philofophy, and difcovered great knowledge and dexterity in obfervations and experiments upon animals. If the cuftom of travelling into remote climates, like the fages of antiquity, in order to be initiated into the learned myfteries of thofe times, had full fubfifted, no one would have conformed to it with greater eager- nefs than M. de Maupertuis. His firft gratification of this paffion was to vifit the country which had given birth to Newton 5 and during his refidence at London he became as zealous an admirer and fol¬ lower of that philofopher as any one of his own countrymen. His next excurfion was to B'afil in Switzerland, where he formed a friendllnp with the fa¬ mous John Bemouilli and his family, which continued to his death. At his return to Paris, he applied him- felf to his favourite ffidies with greater zeal than ever : ' —And how well he fulfilled the duties of an academi¬ cian, may be gathered by running over the memoirs of the academy from the year 1724 to 1736 5 where it ap¬ pears that he was neither idle nor occupied by objefts of finall importance. The moft fublime queftions in geometry and the relative fciences received from his s ] M A U hands that elegance, clearnefs, and precifion, fo re- Mauprrtita. markable in all his writings. In the year I73^> he "y was fent by the king of France to the polar circle, to meafure a degree, in order to afeertain the figure of the earth, accompanied by Meffrs Clairault, Camus, Le Monnier, 1’Abbe Outhier, and Celfius the cele¬ brated profeflbr of aftronomy at Upfal. This diftinc- tion rendered him fo famous, that at his return he was admitted a member of almoft every academy in Eu¬ rope. In the year 1740 Maupertuis had an invitation from the king of* Pruffia to go to Berlin 5 which was too flattering to be refufed. His rank among men of let¬ ters had not wholly effaced his love for his firft pro- feflion, namely, that of arms. He followed his Prut- fian majefty into the field, and was a witnefs of the difpofitions and operations that preceded the battle of Molwitz 5 but was deprived of the glory of being pre- fent, when victory declared in favour of his royal pa¬ tron, by a Angular kind of adventure. His horfe, dur¬ ing the heat qf the aftion, running away with him he fell into the hands of the enemy 5 and was at firft but roughly treated by the Auftrian foldiers, to whom he could not make himfelf known for want of lan¬ guage 5 but being carried prifoner to Vienna-, he re¬ ceived fuch honours from their Imperial majefties as were never effaced from his memory. From Vienna he returned to Berlin 5 but as the reform of the aca¬ demy which the king of Pruffia then meditated was not yet mature, he went again to Paris, where his af¬ fairs called him, and was chofen in 1742 dire&or of the Academy of Sciences. In 1743 he was received in¬ to the French academy ; which was the firft inftance of the fame perfon being a member of both the aca¬ demies at Paris at the fame time. M. de Maupertuis again affumed the foldier at the fiege of Fribourg, and was pitched upon by Marfhal Cogny and the Count d’Argenfon to carry the news to the French king of the furrender of that citadel. He returned to Berlin in the year 1744, when a marriage was negotiated and brought about by the good offices of the queen-mother, between our author and Mademoifelle de Borck, a lady of great beauty and merit, and nearly related to PvT. de Borck at that time minifter of ftate. This determined him to fettle at Berlin, as he was extremely attached to his new fpoufe, and regarded this alliance as the moft fortunate cir- cumftance of his lire. In the year 1746, PvL de Maupertuis was declared by Ins Pruffian majefty prefident of the Royal Academy of Sciences at Berlin, and foon after by the fame prince was honoured with the order of Merit: However, all thefe accumulated honours and advantages, fo far from leffening his ardour for the fciences, feemed to furniffi new allurements to labour and application. Not a day paffed but he produced fome new projeft or effay for the advancement of knowledge. Nor did he confine himfelf to mathematical ftudies only : metaphyfics, chemiftry, botany, polite literature, all {hared his at- - tention, and contributed to his fame. At the fame time, he had, it feems, a ftrange inquietude of fpi- rit, with a morofe temper, which rendered him miferable amidft honours and pleafures.—Such a temperament did not promife a very pacific life 5 and be was engaged in feveral quarrels. He had a,. M A U [ Manpertuis. a quarrel with Koenig the profeffor of philofophy at Franeker, and another more terrible with Voltaire. Maupertuis had inferted into the volume of Memoirs of the Academy of Berlin for 1746, a difcourfe upon the laws of motion j which Koenig was not content with attacking, but attributed to Leibnitz. Mauper¬ tuis, flung with the imputation of plagiarifm, engaged the academy of Berlin to call upon him for his proof j which Koenig failing to produce, he was llruck out of the academy, of which he was a member. Several pamphlets were the confequence of this ; and Voltaire,' for feme reafon or other, engaged againtt Maupertuis. We fay, for fome reafon or other ; becaufe Mauper¬ tuis and Voltaire were apparently upon the moll ami¬ cable terms j and the latter refpedled the former as his mailer in the mathematics. Voltaire, however, ex¬ erted all his wit and fatire againll him *, and on the whole was fo much tranfported beyond what was thought right, that he found it expedient in 1753 to quit the court of Pruffia. Our philofopher’s conftitution had long been con- fiderably impaired by the great fatigues of various kinds in which his adlive mind had involved him ; though from the amazing hardlhips he had undergone in his northern expedition, molt of his future bodily fuffer- ings may be traced. The intenfe lharpnefs of the air could only be fupported by means of itrong liquors, which ferved to increafe his diforder, and bring on a fpitting of blood, which began at lead 1 2 years before he died. Yet flill his mind feemed to enjoy the greateft vigour ; for the belt of his writings were pro¬ duced, and moll fublime ideas developed, during the time of his confinement by ficknefs, when he was un¬ able to occupy his prefidial chair at the academy. He took feveral journeys to St Male, during the laft years of his life, for the recovery of his health : And though he always received benefit by breathing his native air, yet Hill, upon his return to Berlin, his diforder like- wife returned with greater violence.—His lall journey into France was undertaken in the year 1757 ; when lie was obliged, foon after his arrival there, to quit his favourite retreat at St Malo, on account of the danger and confufion which that town w’as thrown in¬ to by the arrival of the Englilh in its neighbourhood. From thence he went to Bourdeaux, hoping there to meet with a neutral fhip to carry him to Hamburgh, in his way back to Berlin; but being difappointed in that hope, he went to Thouloufe, where he remained feven months. He had then thoughts of going to Italy, in hopes a milder climate would rellore him to health : but finding himlelf grow worfe, he rather inclined to¬ wards Germany, and went to Neufchatel, where for three months he enjoyed the converfation of Lord Marifchal, with whom he had formerly been much connedled. At length he arrived at Bafil, October 16. 1758, where he was received by his friend Ber- nouilli and his family with the utmolt tendernefs and affedtion. He at firlt found himfelf much better here than he had been at Neufchatel : but this amendment was of Ihort duration 5 for as the winter approached, his dilorder returned, accompanied by new7 and more alarming fymptoms. Fie languithed here many months, during which be was attended by M. de la Condamine 5 and died in 1759. He wrote in French, 1, The figure of the earth de- ip ] M A U termined. 2. The meafure of a degree of the meridian. Maul 3. A difcourfe on the parallax of the moon. 4. A J|. f difcourfe on the figure of the liars. 5. The elements : of geography. 6. Nautical aftronomy. 7. Elements of aftronomy. 8. A phyfical differtation on a white inhabitant of Africa. 9. An eifay on cofmography. 10. Refledlions on the origin of languages. 11. An eflay on moral philofophy. I 2. A letter on the pro- grefs of the fciences. 13. An effay on the formation of bodies. 14. An eulogium on M. de Montefquieu. 15. Letters, and other works. MAUR, St, was a celebrated difciple of St Bene- di£l. If we can believe a life of St Maur aferibed to Fauflus his companion, he was fent by Benedict on a milhon to France. But this life is confidered as apo¬ cryphal. In rejedling it, however, as well as the cir- cumftances of the midion, we mull beware of denying the million itfelf. It is certain that it was believed in France as early as the 9th century ; and notwithlland- ing the filence of Bede, Gregory of Tours, and others, there are leveral documents which prove this, or at lead render it extremely probable. A celebrated fo- ciety of Benedidtines, took the name of St Maur in the beginning of the lall century, and received the fandlion of Pope Gregory XV. in 1621. This fo- ciety was early dillinguilhed by the virtue and the knowledge of its members, and it Hill fupperts the charadler. There are perhaps fewer eminent men in it than formerly ; but this mull be aferibed to the le¬ vity of the age, and partly to the little encouragement for the refearches of learned men. The chief perfons of ingenuity which this fociety has produced are, the Fathers Menard, d’Acheri, Mabillon, Ruinart, Ger¬ main, Larin, Montfaucon, Martin, Vaiflfette, le Nourri, Martianay, Martenne, Maffuet, &c. &c. See L'Hi- /foire Litteraire de la Congregation de St Maur, pub- lilhed at Paris under the title of BruJJels, in a.to, 1770, by Dom. Tallin. M A URIC E A U, Francis, a French furgeon, who applied himfelf with great fuccefs and reputation to the theory and pradlice of his art for fi veral years at Paris. Afterwards he confined himfelf to the difor- ders of pregnant and lying-in-women, and was at the head of all the operators in this way. His Obfervn- tions fur la grojjejfe and fur Caccouchement des femmes, fur leurs maladies, et celles des enfans nouveaux, 1694, in 4to, is reckoned an excellent work, and has been tranfiated into feveral languages, German, Flemifh, Ita¬ lian, Englifh : and the author himfelf tranflated it into Latin. It is illullrated with cuts. Fie publilhed ano¬ ther piece or two, by way of fupplement, on the fame fubjedl ; and died at Paris in 1709. MAURICE, St, commander of the Theban le¬ gion, was a Chriftian, together with the officers and fold iers of that legion, amounting to 6600 men This legion received its name from the city Thebes in Egypt, where it was raifed. It was fent by Dio¬ cletian to check the Bagaudac, who had excited fome difturbances in Gaul. Maurice having carried his troops over the Alps, the emperor Maximinian com¬ manded him to employ his utmoll exertions to extir¬ pate Chrillianity. This propofal was received with horror both by the commander and by the foldiers. The emperor, enraged at their oppolition, command¬ ed the legion to be decimated 5 and when they ftill C 2 declared M ’ A U L 20 ] M A U Maurice, declared that they would fooner die than da any thing prejudicial to the Chritlian faith, every tenth man of thofe who remained was put to death. Their perfe- verance excited the emperor to ftill greater cruelty *, for when he favv that nothing could make them relinqu’dh their religion, he commanded his troops to furround them, and cut them to pieces. Mau¬ rice, the commander of theft' Chriftian heroes, and Exuperus and Candidus, officers of the legion, who had chiefly mitigated the foldiers to this noble re¬ finance, fignalized themfelves by their patience and their attachment to the doctrines of the Chriilian re¬ ligion. They were maffacred, it is believed, at A- gaune, in Chablais, the 22d of September 286.— Notwithftanding many proofs which fupport this tranf- aclion, Dubordier, Hottinger, Moyle, Barnet, and Moiheim, are difpofed to deny the fa£t. It is de¬ fended, on the other hand, by Hickes an English writer, and by Dom Jofeph de Liile a Benedictine monk cJe la congregation de Saint Vannes, in a work of his, entitled Defence de la Verite du Martyre de la Le¬ gion Thebcnne, 1737. In defence of the fame fad, the reader may confult Hijioria di S. Mauritie, by P. Rof- fignole a Jefuit, and the Acda SanBorum for the month of September. The martyrdom of this legion, written by St Encherius biffiop of Lyons, was tranfinitted to poiterity in a very imperfed manner by Surius. P. Chif- fiet a Jefuit, difcovered, and gave to the public, an ex- ad copy of this wmrk. Don Ruinart maintains, that it lias every mark of authenticity. St Maurice is the pa¬ tron of a celebrated order in the king of Sardinia’s do¬ minions, created by Emanuel Philibert duke of Savoy, to reward military merit, and approved by Grego¬ ry XIII. in 1572. The commander of the Theban le¬ gion muft not be confounded with another St Maurice, mentioned by Theodoret, who fuffered martyrdom at Apamea in Syria. Maurice, (Mauritius Tiberiusf was born at Ara- biffus in Cappadocia, A. D. 539. He was defcend- ed from an ancient and honourable Roman family.— After he had filled leveral offices in the court of Tibe¬ rius Conllantine, he obtained the command of his ar¬ mies againil the Perfians. His gallantry was fo con- ipicuous that the emperor gave him his daughter Conftantina in marriage, and inverted him with the purple the 13th Augurt 582. The Perfians ftill continued to make inroads on the Roman territo¬ ries, and Maurice fent Philippicus, his brother-in-law, agr.inft them. This general conduced the war with various fuccefs. At firft he gained feveral fplendid vihtories, but he did not continue to have a decided fuperiority. As there was a great ufe for foldiers in thefe unfortunate times, the emperor iffued a man¬ date in 592, forbidding any foldier to become a monk till he had accomplifhed the term of his military fer- vice. Maurice acquired much glory in rertoring Chof- roes II. king of Perfia, to the throne, after he had been depofed by his lubjedts. The empire was in his reign haraffed by the frequent inroads of the Arabian tribes. He purchafed peace from them, by granting them a penfion nearly equal to 100,000 crowns j but thefe barbarians took frequent opportunities to renew the war. In different engagements the Romans de- ftroyed 50,000, and took 17,000 prifoners. Thefe were deftroyed, on condition that the king of the 4-hari ftiould return ail the Roman captives in his dominic»s. Maurice. Regardlefs of his promife, he demanded a ranfom of 10,000 crowns. Maurice, full of indignation, refiTed the firm : and the barbarian, equally enraged, put the captives to the fword. While the emperor, to revenge this cruelty, was making preparations againft the A- bari, Phocas, who from the rank of centurion had attained the higheft military preferment, affumed the purple, and was declared emperor. He purfued Mau¬ rice to Chalcedon, took him prifoner, and condemned him to die. The five fons of this unfortunate prince were maffacred before his eyes, and Maurice, humbling himfelf under the hand of God, was beard to ex¬ claim, Thou art jujf, 0 Lord, and thy judgements are 'without partiality. He was beheaded on the 26th No¬ vember 602, in the 63d year of his age and 20th of his reign. Many writers have eftimated the charac¬ ter of this prince by his misfortunes inftead of his actions. They believed him guilty without evidence, and condemned him without reafon. It cannot be de¬ nied, however, that he allowed Italy to be haraffed } but he was father to the reft of the empire. He re- ftored the military difcipline, humbled the pride of his enemies, fupported the Chrittian religion by his laws, and piety by his example. He loved the fciences, and was the patron of learned men. Maurice, eleeior of Saxony, fon of Henry la Pieux, was born A, D. 1521. He was early remark¬ able for his courage, and during his whole life he was engaged in warlike purfints. He ferved under the emperor Charles V. in the campaign of 1544 againtt France ; and in the year following againft the league of Smalkalde ; with which, although a Proteftant, he would have no manner of connexion. The emperor, as a reward for his fervices, in the year 1547, made him eleftor of Saxony, having deprived his coufin John Frederick of that eledtorate. Ambition had led him to fecond the views of Charles, in the hope of being eledlor, and ambition again detached him from that prince. In 1551 he entered into a league againft the emperor, together with the eledlor of Branden- burgb, the Count Palatine, ,the duke of Wirtem- burg, and many other princes. This league, encou¬ raged by the young and enterprifing Henry II. of France, was more dangerous than that of Smalkalde. The pretext for the affbciation was the deliverance of the landgrave of Heffe, whom the emperor kept pri¬ foner. Maurice and the confederates marched, in 1552, to the defiles of Tyrol, and put to flight the Imperial troops who guarded them. The emperor and his brother Ferdinand narrowly efcaped, and fled from the conquerors in great diforder. Charles hav¬ ing retired into Paffau, where he had colle&ed an army, brought the princes of the league to terms of accommodation. By the famous peace of Paffau, which was finally ratified the 12th of Auguft 1552, the emperor granted an amnefly without exception to all thole who had carried arms againft him from the year 1546. The Proteftants not only obtained the free exercife of their religion, but they tvere admit¬ ted into the imperial chamber, from which they had been excluded fince the vidlory of Mulberg.—Mau¬ rice foon after united himfelf with the emperor againft: the margrave of Brandenburg, who laid wafte the German provinces. He engaged him in 1553, gain¬ ed M 'A ' U [2 Maurka. ed ti e battle of Siverfhaufen, and died of the wounds he had received in the engagement two days af¬ ter. He was one of the greatelt proteftors of the Lu¬ therans in Germany, and a prince equally brave and politic. After he had profited by the Ipoils of John Frederick, the chief of the Proteilants, he became himfelf the leader of the party, and by thefe means maintained the balance of power againil the emperor in Germany. Maurice de Naffau, prince of Orange, fucceeded to the government of the Low Countries after the death of his father William, who was killed in 1584 by the fanatic Gerard. The young prince was then only eighteen years of age, but his courage and abi¬ lities were above his years. He was appointed cap¬ tain general of the United Provinces, and he reared that edifice of liberty of which his father had laid the foundation. Breda fubmitted to him in 15905 Zut- phen, Deventer, Hull!, Nlmeguen, in 1591. He gained feveral important advantages in 1 592, and in the year following he made himfelf mailer of Gertru- denburg. When he had performed thefe fplendid fervices, he returned to the Low Countries by the way of Zealand. His fleet was attacked by a dreadful tempeft, in which he loft forty vefiels, and he him- ieix had very nearly pcriftied. His death would have been confidered by the Hollanders as a much greater calamity than the lofs of their vefiels. They wratched over his fafety with exceeding care. In 1594, one of his guards was accufed of an intention to take away his life ; and it was generally believed that he was bribed t-3 this iervice by the enemies of the republic. He fell a facrifice at Bruges, either to his own fanaticifm or to the jealous anxiety of the friends of Maurice. The prince of Orange, increafing in reputation, de¬ feated the troeps of the archduke Albert in 1597, anc^ drove the Spaniards entirely out of Holland. In 1600 he was obliged to raife the fiege of Dunkirk ; but he took ample vengeance on Albert, whom he again de¬ feated in a pitched battle near Nieuport. Before the aftion, this great general fent back the ftiips which had brought his troops into Flanders: My brethren (laid he to his army), we mujb conquer the enemy or drink up the waters of the fea. Determine for yourfehes ; / have determined I /hall either conquer by your bravery, or I [hall never furvive the difgrace of being conquered by men in every ref peel our inferiors. This fpeech elevated the foldiers to the higheft pitch of enthufiafm, and the vidlory was complete. Rbinberg. Grave, and Eclufe, cities in Flanders, fubmitted to the conqueror the fol¬ lowing year. Maurice, howTever, not only laboured for the commonwealth, but alfo for himfelf. He co¬ veted the lovereignty of Holland, and was onpofed in the profecution of his defign by the penfioner Barne- veldt. The zeal and adlivity of this wife republican eoft him his life. He wTas an Arminian 5 and at this time Maurice defended Gomar againft Arminius.— Taking advantage of the general odium under which the Arminians lay. he found means to get Barneveldt condemned in 1619. His death, wholly owing to the cruel ambition of the prince of Orange, made a deep impreffion on the minds of the Hollanders. The truce with Spain being expired, Spinola laid fiege to Breda in 1624, and in fix months, by the proper di- recLon of his great talents, though with great flangh- i ] M A U ter of his troopc, he took the place. The prince of Maurt:-?, Orange, unfuccefsful in every attempt to raife the Mauritania. fiege, died of vexation in 1625, aged 55 years, with the reputation of the greateft warrior of his time.— “ The life of this ftadtholder (fays the abbe Ray- .nal) was almoft an uninterrupted feries «f battle?, of fieges, and of victories. Of moderate abilities in every thing elfe, he fhone confpicuous in his military capacity. His camp was the ichool oi Europe ; and thofe who received their military education in his ar¬ mies augmented, perhaps, the glory of their mafter.— Like Montecuculi, he difeovered inimitable fidll in his marches and encampments 5 like Vauban, he pof- feffed the talent of fortifying places, and of rendering them impregnable 5 like Eugene, the addrefs of find¬ ing fubfiftence for great armies in countries barren by¬ nature, or ravaged by war ; like Vendome, the happy.' talent of calling forth, in the moment they became neceflary, greater exertions from ins foldiers than could reafonably be expedted 5 like Conde, that infallible quicknefs of eye which decides the fortune of battles g like Charles XU. the art of rendering his troops al¬ moft invincible to cold, hunger, and fatigue j like Turenne, the fecret of making war with the leaft pof- fible expence of human blood.1’ The Chevalier Folard maintains, that Maurice was the greateft commander of infantry iince the time of the Romans. He ftudied the military art of the ancients, and applied their rules with great exadlnefs in the various occurrences of war. He not only took advantage of the inventions of o- thers, but he enriched the fcience of war with feveral improvements. Telefcopes were firft ufed by him for a military purpofe 5 and, befides a kind of gallery in. condudling a fiege, and the plan of blockading a ftrong place, which were of his invention, he greatly improved the whole art by his method oi: puftnng an attack with great vigour, and of defending, for the greateft length of time, and in the beft manner, a place befkged. In ihort, the many ufeful things which he pradlifed or invented, placed him in the higheft rank among men of a military charadle: . On one occafion, a lady of quality alked him, Who was the frjl general of the age ? Spinola (replied he ) is the fecond. It was his conftant pradlice, during fleep, to have twm guards placed by his bedfide, not only to de¬ fend him in cafe of danger, but to aw'ake him if there iho-uld be the leaft occafion. The w’ar betwixt Spain and Holland was never carried on with greater keen- nefs and animofity than during his adminiftration.— The Grand Signior, hearing of the vaft torrents of blood {bed in this conteft, thought that a great em¬ pire muft depend on the decifion. The objedt of fo many battles was pointed out to him on a map, and he faid coldly, If it were my hnfn- fs, I would fend my pioneers, and order them to cajl this little corner of earth into the fea. Maurice, like many great men, was im¬ patient under contradiction, and too much devoted to women. He was fucceeded by Frederick Henry his brother. MAURITANIA, an ancient kingdom of Africa, bounded on the weft by the Atlantic ocean, on the fouth by Getulia or Libya Interior, and on the north by the Mediterranean 5 comprehending the greater part of the kingdoms of Fez and Morocco—Its an¬ cient limits are not exaCtly mentioned by any hiftorian; neither^ N M A U [ 22 ] M A U ZMauritanfo. neither can they now be afcertained by any modern ob- Hefperides, and made himfelf mafter of all the gold-Mauritania. v—~~l fervations, thefe kingdoms being but little known to en fruit there. Bochart thinks that the fable alluded y'”—^ Europeans. chiefly to naval engagements, wherein Hercules, for This country was originally inhabited by a people the molt part, was vi&orious j though Antonis from called concerning the etymology of which name time to time received fuccours by fea. But at laft authors are not agreed. It is probable, however, that Hercules, coming up with one of his fquadrons which this country, or at leaf! a great part of it, was firfl had a llrong reinforcement on board, made himfelf called Phut, fince it appears from Pliny, Ptolemy, and matter of it, and thus rendered Antaeus incapable for St Jerome, that a river and territory not fir from Mount the future of making head againft him. The fame Atlas went by that name. From the Jerufalem Tar- author likewife infinuates, that the notion of Antmus’s gum it likewife appears, that part of the Mauri may gigantic ftature prevailing for fo many centuries a- be deemed the offspring of Lud the fon of Mifraim, mongff the Tingitanians, pointed out the lize of the fince his defendants, mentioned Geneffs x. are there veffels of which his fleets and fquadrons were corn- called 'KuViio, Mauri, or Mauritani. It is certain, pofed. As for the golden apples fo frequently men- that this region, as well as the others to the eaftward tioned by the old mythologifts, they were the trea- ot it, had many colonies planted in it by the Phoeni- fures that fell into Hercules’s hands upon the defeat clans. Procopius tells us, that in his time two pillars of Antaeus; the Greeks giving the oriental word ol white Hone were to be feen there, with the follow- Sxn, riches, the flunification affixed to their own term ing iufcription in the Phoenician language and charac¬ ter upon them : “ We are the Canaanites, that tied from JoJhua the fon of Nun, that notorious robber.” Ibnu Rachic, or Ibnu Raquig, an African writer cited by Leo, together with Evagrius and Nicephorus Cal- lillus, afiert the fame thing. The Mauritanians, according to Ptolemy, were di¬ vided into ieveral cantons or tribes. The Metagonitce were feated near the flraits of Hercules, now thole of Gibraltar. The Saccojii, or Cocojii, occupied the coaft of the Iberian fea. Under thefe two petty na¬ tions the Majices, Verues, and Verbiccc or Vervica', were fettled. The Salifce cr Sahnfcc, were fituated lower, towards the ocean ; and, flill more to the fouth, the Volubiiiani. The Maurenjii and Herpiditari poffiefled the eaftern part of this country, which was \ terminated by the Mulucha. The Angaucani, or j7/ngacaucani, NeBiberes, Zagrenjh, Banurber, and Va- cutitce, extended themfelves from the fouthcrn foot of Ptolemy’s Atlas Minor to his Atlas Major. Pliny mentions the Baniurce, whom Father Hardouin takes to be Ptolemy’s Baniubse ; and Mela the Atlantes, whom he reprefents as poffefled of the weftern parts of this diftriiff. The earliefl prince of Mauritania mentioned in hiftory is Neptune ; and next to him were Atlas and Antaeus his two Ions, both famous in the Grecian fables on account of their wars with Hercules. An- tceus, in his contention with that hero, feems to have behaved with great bravery and refolution. Having received large reinforcements of Libyan troops, he cut off great numbers of Hercules’s men. But that celebrated commander, having at laft intercepted a flrong body of Libyans fent to the relief of Antmus, gave him a total overthrow, wherein both he and the beft part of his forces were put to the fword. This decifive action put Hercules in poffeffion of Libya and Mauritania, and confequently of the riches of all thefe kingdoms. Hence came the fable, that Her¬ cules, finding Antaeus, a giant of an enormous fize with whom he was engaged in Angle combat, to re¬ ceive freffi ftrength as often as he touched his mother earth when thrown upon her, at laft lifted him up in tne air and iqueezed him to death. Flence likewife may be deduced the fable intimating that Hercules rook the globe from Atlas upon his own fhoulders, overcame the dragon that guarded the »rchards of the 3 apples. With regard to the age in which Atlas and An¬ taeus lived, the moft probable luppofition feems to be that of Sir Ifaac Newton. According to that iliuf- trious author, Ammon the father of Sefac was the firft king of Libya, or that vaft trad! extending from the borders of Egypt to the Atlantic ocean ; the con- queft of which country was effedled by Sefac in his father’s lifetime. Neptune afterwards excited the Libyans to a rebellion againft Sefac, and flew him ; and then invaded Egypt under the command of Atlas or Antaeus, the fon of Neptune, Sefac’s brother and ad¬ miral. Not long after, Hercules, the general of The- bais and Ethiopia for the gods or great men of Egypt, reduced a fecoi'd time the whole continent of Libya, having overthrown and flain Antaeus near a town in Thebais, from that event called Ant as a or Antteopolis: this, we fay, is the notion advanced by Sir Ifaac New¬ ton, who endeavours to prove, that the firft redudlion of Libya, by Sefac, happened a little above a thou- fand years before the birth of Chrift, as the lall, by Hercules, did fome few years after. Now, though we do not pretend to adopt every particular cxrcum- ftance of Sir Ifaac Newton’s fyftem, yet we cannot forbear .obferving, that it appears undeniably plain from Scripture, that neither the weftern extremity of Libya, nor even the other parts of that region, could poffibly have been fo well peopled before the time of David or Solomon, as to have fent a numerous army to invade Egypt. For Egypt and Pho?nicia, from whence the greateft part of the anceftors of the Li¬ byans came, and which were much nearer the place from whence the firft difperfion of mankind was made, could not themfelves have been greatly overftocked with inhabitants any confiderable time before the reign of Saul. And that fuch an invafion happened in the reign of Neptune, or at leait of his fon Antaeus, has been moft fully evinced by this moft excellent chrono- loger. From the defeat of Antaeus, nothing remarkable occurs in the hiftory of Mauritania till the times of the Romans, who at laft brought the w’hole kingdom under their jurifdiftion j tor wffiich fee the article Rome. i. With regard to the cuftoms, &c. of this people, it would feem from what Hyginus infinuates, that they fought only with clubs, till one Bel us, the fon. of Neptune, as that author calls him, taught them M A U [ 23 1 M A U Mauritania.them the ufe of the fword. Sir Ifaac Newton makes k“^ v ' this Belas to have been the fame perfon with Seloftris king of Egypt, who overran a great part of the then known world. 2. All perfons of diftin£lion in Mau¬ ritania went richly attired, wearing much gold and fdver in their clothes. They took great pains in cleanf- ing their teeth, and curled their hair in a curious and elegant manner. They combed their beards, which were very long, and always had their nails pared ex¬ tremely clofe. When they walked out in any num¬ bers, they never touched one another, for fear of dif- concerting the curls into which their hair had been formed. 3. The Mauritanian infantry, in time of ac¬ tion, ufed fhields made of elephants fkins, being clad in thofe of lions, leopards, and bears, which they kept on both mght and day. 4. The cavalry of this nation was armed with bread fhort lances, and carried targets or bucklers, made Kkewife of the fkins of wild beads. .They ufed no faddles. Their horfes were fmall and fwift, had wooden collars about their necks, and were fo much under the command of their riders, that they would follow them like dogs. The habit of thefe ho rfemen was not much different from that of the foot above mentioned, they condantly wearing a large tunic of the fkins of wil’d beads. The Phutaei, of whom the Mauritanians were a branch, were emi¬ nent for their fhields, and the excellent ufe they made of them, as w*e leam from Homer, Xenophon, Hero¬ dotus, and Scripture. Nay, Herodotus feems to in¬ timate, that the fhield and helmet came from them to the Greeks. 5. Notwithdanding the fertility of their foil, the poorer fort of the Mauritanians never took care to manure the ground, being drangers to the art of hufhandry } but roved about the country in a wild favage manner, like the ancient Scythians or Arabes Scenitm. J hey had tents, or mapalia, fo extremely fmall, that they could fcarce breathe in them. Their food was corn, herbage, &c. which they frequently did eat green, without any manner of preparation, being deditute of wine, oil, and ail the elegancies as well as many necelfaries of life. Their habit was the fame both in fummer and winter, confiding chiefly of an old tattered, though thick garment, and over it a coarfe rough tunic ; which nnfwered probably to that of their neighbours the Numidians. Mod of them lav every night upon the bare ground j though fome of them drewed their garments thereon, not unlike the prefent African Kabyles and Arabs, who, according to Dr Shaw, ufe their hykes for a bed and covering in the night. 6. If the mod approved reading of Ho¬ race may be admitted, the Mauritanians diot poifoned arrows; which clearly intimates, that they had force Ikill in the art of preparing poifons, and were excellent dartmen. J his lad obfervation is countenanced by Hercd'an and Atlian, who entirely come into it, affirm¬ ing them to have been in fuch continual danger of be¬ ing devoured by wild beads, that they durd not dir out of their tents or mapalia without their darts. Such perpetual exercife mud render them exceedingly fkil- ful in hurling that weapon. 7. The Mauritanians fa- crificed human vrehras ta their deities, as the Phoe¬ nicians, Carthaginians, &c. did. i he country people were extremely rude and bar¬ barous ; but thofe inhabiting cities mud undoubtedly have had at lead fome fmaitering in the literature of the feveral nations they deduced their origin from. That Mauritla, the Mauritanians had feme knowledge in naval affairs, ^a"rit:US', « feems probable, not only from the intercourfe they had with the Phoenicians and Carthaginians, as well as the lifuation of their country-; but likewife from Orpheus, or Onomacritus, who aflerts them to have made a fettlcment at the entrance into Colchis, to which place they came by fea. Magic, forcery, divination, &c. they appear to have applied themfelves to in very early times. Cicero and Pliny fay, that Atlas v;as the inventor of adrology, and the dodlrine of the fphere, i. e. lie fird introduced them into Mauritania. This, according to Diodorus Siculus, gave rile to the fable of Atlas’s bearing the heavens upon his dioulders. The fame author relates, that Atlas indrucled Hercules in the dotlrine of the fphere and adrology, or rather adronomy, who afterwards brought thofe fciences into Greece. MAURITIA, the GlNKGOf or Maidenhair tree: A genus of plants belonging to the natural order of palmre. See Botany Index. MAURITIUS, or Maurice, an ifland of Africa,, about 400 miles ead of Madagafcar, lying in the la¬ titude of 20 and 21 degrees fouth. It is about 150 miles in circumference. In the beginning of the 16th century it was difeovered by the Portuguefe, who- knowing that Pliny and other ancient writers had mentioned the ifland of Cerne in thefe Teas, took it for granted that this mud be it ; and accordingly we find it fiyled Cerne or Sirne, in their maps : but, not- wilh'landing this, they did not think fit to fettle it; and indeed their force was fo fmall, in companion of the vafl dominions they grafped, that it was very ex- cufable. However, according to their laudable cu- flom, they put fome hogs, goats, and other cattle, up¬ on it, that in cafe any of their drips either going to the Indies or returning to Portugal diould be obliged to touch there, they might meet with refrefliments. The Dutch, in the fecond voyage they made to the ' Ead Indies under their admiral James Cornelius Van- neck, came together with five fliips on the 15th of September 1568; anchored in a commodious port, to which they gave the name of Warwick Haven; and gave a very good account of the place in their jour nals. Captain Samuel Cadleton, in the Pearl, an Englilh Ead India fliip, arrived there- on the 27th of March 1612 ; and taking it to be an ifland undiicover- ed before, bedowed upon it the name of England's Fa¬ red, though others of his crew called it Pearl Ijland ■: and in the account of their voyage, written by John J atton the mader of the diip, celebrated it as a place very convenient for (hipping, either outward or home¬ ward bound, to refredi at. This they fometimes ac¬ cordingly did, and brought fome cargoes of ebony, and rich wood from thence, but without fixing any fettlsment. At length, in 1638, the Dutch feated themfelves here: and it is highly remarkable, that at the very, time they were employed in making their fird fettle- rr.ent, the French lent a vefiel to take potTedion of it, who found the Dutch beforehand with them, and re¬ plied the affiflance of an Englilh Indiaman, wooding and watering in another port of the ifland, who very frankly offered it, to drive the Dutch from their half- fettled pods. They continued for fome time in quiet. polTellion.. % M A U [ 24 ] M A U Mauritius, pofleffion of the. places they fortified m this ifiand, to which they gave the name of Mauritius, in honour of Prince Maurice their ftadtholder. But having en¬ gaged the French, who were fettled on Madagafcar, to deal 50 of the natives, and fell them for (laves, for the improvement of the Dutch fettlements here, this proved the ruin of both colonies j for the negroes ftirprifed and roafiacred the French in Madagafcar-, and the (laves in Mauritius (led into the centre ot the ifiand •, from whence they fo much and fo inceffantly molefled thofe who had been formerly their mafters, that they chofe to quit a country where they could no longer remain in. any tolerable degree of fafety. The Eaft India Company, however, from motives of con- veniency, and a very imperfeff notion of its value, dil- approved this meafure, and therefore ordered it to be refettled ; which was accordingly done, and three forts erefted at the principal havens. Things now went on fomewhat better than they did before ; but they were (hill very much difturbed by the revolted negroes in the heart of the ifle, whom they could never fubdue. One principal ufe that the company made of this place, was to fend thither (late prifoners, who, as they were not men of the bed morals, quickly cor¬ rupted the reft of the inhabitants, and rendered them fuch a race of outrageous fmugglers, the fimation of the place concurring with their bad difpofition, that, after various ineffedlual attempts made to reform them, orders wrere at length given to abandon Mauritius a fecond time, which, after fome delays, wrere put in execution in the year 1710. Twro years after this, the French took poffeflion of it, and named it the ijle de France. This name has obtained among themfelves, but the Europeans in ge¬ neral continue to call it Mauritius. It lies in S. Lat. 20. 15. E, Long. ,6. 15. The inconveniences arifing from the w'ant of a port at the ifiand of Bour¬ bon, induced the French to take poffeflion of Mauri¬ tius, it having two very good harbours, to fortify which no expence has been fpared. That on the north-weft is called Port Louis, that on the fouth-eaft fide of the ifland is called Port Bourbon. The trade-wind from the fouth-eaft in thefe latitudes blow's all the year round, excepting for a few days at the fummer fol- ftice, when it is interrupted by hard gales and hurri¬ canes from the north. The eafe with which this wind enables (liips to enter the port of Bourbon, caufed the French, wdien they firft took poffeflion of this fpot, to efteem it the bed port in the ifland j but experience pointing out to them, that the fame wind often ren¬ dered the paffage out of the harbour fo difficult, that a Ihip was fometimes obliged to wrait a confiderable time before the weather admitted of her putting to fea, this harbour is in a great meafure abandoned, and the prin¬ cipal town and feat of government is now fixed at Port Louis, which is nearly in the middle of the north fide of the ifland, and its entrance is through a channel formed by twro flioals, wdfich advance about two miles into the: fea. When a (hip arrives oppofite to this channel, the fouth-eaft wind hinders her from entering the port under fail, and (he muft either warp in with cables or be towed in with boats. The neceffity of this operation, joined to the extreme narrownefs of the channel, which does not admit of two drips abreaft of .each other catering at the fame time, is one of the bed 2 defences the harbour has againft an attack by fea •, for, Mauritius, from thefe obftacles, an enemy would find it a matter ——y——' of the greateft difficulty to force the port; and in ad¬ dition to this natural ftrength, they have built two forts and as many batteries, which are mounted with heavy cannon, and entirely command the approach to the harbour, (liould drips prefume to force an entry under fail. This port is capable of containing 100 fail of (Lips, and is wrell provided with every requifite for repairing and even building of (hips. This port has proved of the greateft advantage to France in the fe- veral wars which have been carried on between Great Britain qnd her ; and has proved of great utility to the French Eaft India Company’s commerce 5 for here their (hips and crews w-ere fure to meet with all necef- fary refrefhment after a long voya'ge. The port of Bourbon is alfo for ified •, and an army landed here would find it an extremely difficult ta(k to pafs the mountains to the different parts of the iiland. There are feveral places between the north-eaft extremity and Port Louis where boats may land, but all thefe are de¬ fended by batteries ; and the country behind them is a continued thicket : The reft of the coaft is inaccefti- ble. In the north-eaftern quarter is a plain extending about 10 miles from eaft to w!eft, and in fome places five miles inland from the northern coaft. All the reft of the ifland is full of high and Keep mountains, lying fo near to one another, and the intervals between them fo narrow, that, inftead of valleys, they rather referable the beds of torrents; and thefe are choked with huge fragments of rocks which have fallen from the deep fides of the impending mountains. On the (ummits of the mountains ice is frequently to be found, and they are covered with forefts of ebony and other large trees. The ground they (hade produces herbage, fhrubs, and plants of various forts, from the common grafs to the ftrongeft thorn, and that in fuch profufion, that they form a thicket fo clo(e!y interwoven, that no progrefs can be made but by means of a hatchet. Notwnthftanding thefe difficulties, plantations have been formed on thefe mountains, and very confiderable pro¬ grefs has been made in the plains •, but the produdfions, although moftly of the fame kind, arc not only in lefs quantity, but of an inferior quality to thofe produced at Bourbon ifland. In a courfe of years, however, the fbttlement coft fo much, and was confidered in every light worth fo little, that it had been more than once under deli¬ beration, whether, after the example, of the Dutch, they ftiould not leave it again to its old negro in¬ habitants ; which fooner or later in all likelihood would have been its fate, if, in 1735, t^e fHrno-’s M. de la Bourdonnais had not been fent thither with the title of governor general of the French i[lands. He found this ifle in the wmrft (late poflible, thinly inhabited by a fet of lazy people, who equally hated induftry and peace, and who wTere continually flatter¬ ing this man to his face, and belying him wherever and as far as they durft. He gave himfelf no trouble about this, having once found the means to make him¬ felf obeyed he faw the vaft importance of the ifland j he conceived that it might be fettled to great advan¬ tage ; and, ’without fo much as expecting the thanks of thofe for whom he laboured, he began to execute this great defign. Kis firft ftep was to bring over black M A U [ 'Mauritius, black boys from Madagafcar, whom be carefully u—Y~— trained up in good principles, and in continual exer- cife ; by which he rendered them fo good (oldiers, that he very quickly obliged the Merones, or wild negroes, either to lubmit or to quit the iiland : he taught the planters to cultivate their lands to advantage ; he, by an aqueduct, brought freih w^ater to the fea lide ; and whereas they had not fo much as a boat at his coming thither, he made a very fine dock, where he not only built fioops and large veffels, but even a Hup of the burden of 500 tons. However incredible it may feem, yet it is certainly fa£t, that in the {pace of five years he converted this country into a paradile, that had been a mere wildernefs for 5000 ; and this in fpite of the inhabitants, and of the company, who being ori¬ ginally prejudiced by them, behaved ill to him at his return. He foon made the cardinal de Fleury, how¬ ever, fenfible of the true (late of things •, and compel¬ led the company to acknowledge, though they did not •reward, his fervices. He afterwards returned into the Indies, and perfe&ed the work he had begun, and to him it is owing that the ifie of France was rendered <>ne of the fineft and moft important fpots upon the globe. Here no coffee is raifed 5 but by the indefa¬ tigable induifry of M. de Bourdonnais, fugar, indigo, pepper, and cotton (which are not at Bourbon), came to be cultivated with fuccefs. Since the departure of that moft excellent governor, the plantations have been neglected, and are fallen off; but if a proper fpirit of a&ivity was raifed among the inhabitants, they might foon be made to refume their fiouriftung appearance. Mines of iron have been difeovered in the mountains near the great plain, in the north-eaft part of the ifiand ; and thefe mountains affording in great abun¬ dance the neceffary fuel, forges have been erefted : but the iron produced is of a very in'erior quality, it being brittle, and only fit for making cannon-balls and bomb-fhells. Black cattle, fheep, and goats, are pre- ferved with difficulty j the firft generally die before they have been a year in the ifland, and this occafions frequent importations of them from Madagafcar and other parts. Common domeftic poultry breed in great plenty ; and, with fiffi and turtle, fuinifh a great part of the food of the European inhabitants. The approach to the ifland is extremely dangerous, it being furreunded with ledges of rocks, and many of them covered by the fea. The fhore abounds with coral and (hells. This ifiand is faid to contain 60 ri¬ vers : fome are confiderabie ftreams, and moft of them have their fources from lakes, of which there are\ feve- lal in the middle part of the ifiand. The rivers affjrd plenty of various kinds of fiih, particularly eels. Thefe are of an enormous fize, fome having been found that were fix feet long, and fix inches in circumference, and fo extremely voracious, that it is dangerous to bathe in thofe parts of the river where they lie, as they will feize a man without fear, and have ftrength fufficient to keep him under water till he is drowned. Here is a great variety of birds, and bats as large as a young kitten : the inhabitants efieem them a deli¬ cate morfel. The air is both hot and moift, but not unwholefome. The place abounds with infedts, which are very troubleforne •, but there are no ferpents. It has been difeovered, that off Port Louis the fouth- eaft wind generally blows with leaft ftrength about Vol. XIII. Parti. 5 ] M A X f’unrife ; and it alfo happens, on four or five days, at Manma intervals, in the courfe of a month, that early in the c morning the wind ceafes in the northern part of the 1 '“■.‘'.V' ifiand for an hour or two, when a breeze rifes, al¬ though but faintly, from the north-weft ; during which, a fiu’p (lationed at the entrance of the channel to avail herfelf of this breeze, may enter the harbour and attack the forts. This ifiand, during the period of the French revo¬ lution, did not entirely efcape from the ftorm which then agitated the parent country. In the year 1799, a confpiracy was formed, and broke out, for the pur- pofe of refitting the government which had been efta- bliihed under the authority of the republic. It was, however, foon fuppreflbd oy the activity of the munici¬ pality and governor-general, fupported by the major! y of the inhabitants, and order and tranquillity were again reftored. The population of this ifland in 1799 amounted to bj.oo'o, viz. 55,000 (laves, and 10,000 whites and mulattocs. The following is a ftate of the produce of this iiland in 1800. Coffee, 6000 bales, of too lbs. French. Indigo, 300,000 lbs. from 2s. to 8s. per lb. Cotton, 2coo bales, of 250 lbs. Raw fugar, 20.000,000 lbs. Cloves, 20,000 lbs. MAURUA, one of the Society ifiands in the South fea. It is a fmall ifiaud, entirely lurrounded with a ridge of rocks, and without any harbour for (hipping. It is inhabited , and its produftions are the fame with thofe of the neighbouring ifiands. A high round hill riles in the middle of it, which may be leen at .he diftance of 10 or 12 leagues. W Long. 152 32. S. Lat. 16. 25. MAUSOLEUM, a magnificent tomb or fepulchral monument. The word is derived from Maulolus king of Caria, to whom Artemiiia his widow ere&eu a moil ftately monument, eftesnted one of the wonders of the world, and called it, from his own name, Mau- foleum. St ■ AWES, a town of Cornwall, in England, feated on the eaft fide of Falmouth haven, in W. Long. 4 56 N. Lat. 50. 6. Though but a hamlet of the pariiii of St Juft, two miles off, without a minifter, or either church, chapel, or meeting-houfe, it has lent members to parliament ever fince 1562 who are re¬ turned by its mayor or portreve. It confifts but of one ftreet, under a hill, and fronting the fea, and its inhabitants fubfift purely by filhing. K. Henry VIII. built a caftle here, oppoiite to Pendennis, for the bet¬ ter fecurity of Falmouth haven. It has a governor, a deputy, and two gunners, with a platform of guns. Here is a fair the Friday after St Luke’s day. MAXENITUS, Marcus Aurelius Valerius, a . fon of the emperor Maximianus Hercules, was, by the voluntary abdication of Dioclefian, and of his father, raifed to the empire A. D. 306. He afterwards in¬ cited his father to reaffume his imperial authority ; and in a perfidious manner deftroyed Severtis, who had delivered himfelf into his hands, and relied upon his honour for the fafety of his lile. His vicfoiies and fucceffes were impeded bv Galerius Maximianus, who oppofed him with a powerful torce. The defeat I) and Maxilla li Maximus. M AX [ 26 ] M A Y and voluntary death of Galerius foon relfored peace to Italy j and Maxentius paffed into Africa, where , he rendered himfelf odious by his cruelty and oppref- fion. He foon after returned to Rome, and was in¬ formed that Conftantine wTas come to dethrone him. He gave his adverfary battle near Rome, and, after he had loft the vidtory, he fled back to the city. The bridge over which he croffed the Tiber w’as in a de¬ cayed fituation, and he fell into the river, and was drowned, A. D. 312. The cowardice and luxuries of Maxentius were as confpicuous as his cruelties. He opprefted his fubjedls with heavy taxes, to gratify the cravings of his pleafures, or the avarice of his fa¬ vourites. He was debauched in his manners, and nei¬ ther virtue nor innocence were fafe whenever he was inclined to voluptuous purfuits. His body was de¬ formed and unwieldy. I'o vifit a pleafure ground, or to exercife himfelf under a marble portico, or walk on a ftrady terrace, was to him a Herculean labour, which required the greateft exertions of ftrength and refolution. MAXILLA, the Jaw. See Anatomy, X° 20— 26. MAXIM, an eftablifhed propofttion or principle 5 in which fenfe it denotes much the fame with axiom. MAXIMILIAN I. emperor of Germany, ligna- lized himfelf againft the French while he was king of the Romans, and after he was emperor entered into the army of Henry VIII. of England as a volunteer againft that nation t he was a protestor of learned men, and abolifhed an iniquitous tribunal, ftyled Ju¬ dicium occultum Wejlphalice ; he compofed fome poems, and the memoirs of his own life. He died in 1519, aged 60. MAXIMUM, in Mathematics, denotes the greateft quantity attainable in any given cafe. If a quantity conceived to be generated by motion increafes or decreafes till it arrives at a certain magni¬ tude or pofition, and then, on the contrary, grows greater or leffer, and it be required to determine the faid magnitude or pofition, the queftion is called a pro¬ blem de maximis et minimis. MAXIMUS, a celebrated Cynic philofopher, and magician, of Ephefus. He inftrufled the emperor Julian in magic j and, according to the opinion of fome hiftorians, it was in the converfation and com¬ pany of Maximus that the apoftafy of Julian originat¬ ed. The emperor not only vifited the philofopher, but he even fubmitted his waitings to his infpeftion and cenfure. Maximus refufed to live in the court of Julian •, and the emperor,, not diflatisfied with the re- fufal, appointed him high pontiff in the province of Lydia, an office which he difeharged with the great¬ eft moderation and juftice. When Julian went into the eaft, the philofopher promifed him fuccefs, and even faid that his conquefts would be more numerous and extemive than thofe of the fon of Philip. He perfuaded his imperial pupil, that, according to the doftrine of metempfyehofis, his body was animated by the foul which once animated the hero whofe greatnefs and vic¬ tories he w7as going to eclipfe. After the death of Julian, Maximus was almoft facrificed to the fury of the foldiers; but the interpofition of his friends faved his life, and he retired to Conftantinople. He wras foon after accrued of magical practices, before the em¬ peror Valens, and beheaded at Ephefus, A. D. 366. Maximus He wrote fome philofophical and rhetorical treatifes, II fome of which were dedicated to Julian. They are all now loft. v—— Maximus of Tijre, a Platonic philofopher, went to Rome in 146, and acquired fuch reputation there, that the emperor Marcus Aurelius became his fcholar, and gave him frequent proofs of his efteem. This phi¬ lofopher is thought to have lived till the reign of the emperor Commodus. There are ftill extant 41 of his differtations •, a good edition of which wms printed by Daniel Heinfius, in 1624, in Greek and Latin, with notes. Maximus Marius. See Marius. MAY, the fifth month in the year, reckoning from our firft, or January ; and the third, counting the year to begin with March, as the Romans anciently did. It was called Maius by Romulus, in relpecl to the fenators and nobles of his city, who were named majores ; as the following month was called Junius, in honour of the youth of Rome, in honorem jumorum, who ferved him in the war; though fome will have it to have been thus called from Maia, the mother of Mer¬ cury, to whom they offered facrifice on the firft day of it ; and Papius derives it from Madius, eo quod tunc ter¬ ra madeat. In this month the fun enters Gemini, and the plants of the earth in general begin to flower.— The month of May has ever been efteemed favour¬ able to love and yet the ancients, as xvell as many of the moderns, look on it as an unhappy month for marriage. The original reason may perhaps be referred to the feaft of the Lemures, which was held in it. Ovid alludes to this in the fifth of his Fafti, when he fays, Nec mdiuc tccdis eachm, ncc virginis apta Tempora ; quae nupft, non diuturna fuit ; Hac quoque de caufa,Ji te proverbia tanguni, Menfe malum Maio nubere vu/gus ait. MAr-dew. See Dew. Max-duke, a fpecies of cherry, See Prunes, Bota¬ ny Index* May, IJle of, a fmall iftand at the mouth of the frith of Forth, in Scotland, about a mile and a half in circumference, and feven miles from the coaft of Fife, almoft oppofite to the rock called the Bafs. It formerly belonged to the priory of Pittenvveem j and was dedicated to St Adrian, fuppofed to have been martyred in this place by the Danes ; and hither, in times of Popifh fuperftition, barren women ufed to come and worfhip at his (brine, in hopes of being cured of their fterility. Flere is a tower and light- houfe built by Mr Cunningham of Barns, to whom King Charles I. granted the iiland in fee, with power to exaft twopence per ton from every (hip that paffes, for the maintenance of a lighthoufe. In the middle of it there is a frefti-water fpring, and a fmall lake.-— The foil produces pafturage for 100 (beep and 20 black cattle. On the weft fide the fteep rocks render it inacceffible 5 but to the eaft there are four landing places and good riding. It was here that the French fquadron, having the chevalier de St George on board, anchored in the year 1708, when the vigilance of Sir George Byng obliged him to relinquilh his de- fign, and bear away for Dunkirk. The (bores all round MAY [ 2 May round the iiland abound with fifh, and the cliffs with 11 water fowl. Mayprne.^ ]yjAy? Thomas, an eminent Engliflr poet and hifto- rian in the i yth century, was bom of an ancient but decayed family in Suffex, educated at Cambridge, and afterwards removed to London, where he contra&ed a friendfhip with leveral eminent perfons, and particu¬ larly with Endymion Porter, Efq. one of the gentle¬ men of the bedchamber to King Charles I. While he refided at court, he wrote the five plays now extant under his name. In 1622, he published a tranllation of Virgil’s Georgies, with annotations j and in 1635 a poem on King Edward III. and a tranllation of Lu¬ can’s Pharfalia ; which poem he continued down to the death of Julius Coefar, both in Latin and Englilh verfe. Upon the breaking out of the civil wars he adhered to the parliament ; and in 1647, he publiih- ed, “ The hiftory of the parliament of England, which began November the third, MECXL. With a fliort and accefiary view of fome precedent years.” In 1640, he publilhed, Hijloriae Parliamenti An¬ glia ftreviarium, in three parts •, which he after¬ wards tranfiated into Englifh. He wrote the Hi- llory of Henry II. in Englilli verfe. He died in 1642. He went well to reft over night, after a cheer¬ ful bottle as ufual, and died in his fleep before morn¬ ing : upon which his death was imputed to his tying his nightcap too clofe under his fat cheeks and chin, which caufed his fuffocation but the facetious An¬ drew Marvel has written a poem of 100 lines, to make him a martyr of Bacchus, and die by the force of good wine. He -was interred near Camden in Weftminfter Abbey ; which caufed Ur Fuller to fay, that “ if he were a biaffed and partial writer, yet he lieth buried near a good and, true hiftorian indeed.” Soon after the reftoration, his body, with tbofe of feveral others, was dug up, and buried in a pit in St Margaret’s churchyard j and his monument, which was erefted by the appointment of parliament, was taken down and thrown afide. MAYER, Tobias, one of the greateft aftronomers and mechanics the 18th century produced, was born at Mafpach, in the duchy of Wirtemberg 1723. He taught himfelf mathematics, and at the age of four¬ teen defigned machines and inftruments with the great- eft dexterity and juftnefs. Thefe purfuits did not hin¬ der him from cultivating the belles lettres. He ac¬ quired the Latin tongue, and wrote it wdth elegance. In 1750, the univerfity of Gottingen chofe him for their mathematical profeffor 5 and every year of his ftiort life was thenceforward marked with fome confi- derable difeoveries in geometry and aftronomy. He publilhed feveral works in this way, W'hich are all rec¬ koned excellent ; and fome are inferted in the fecond volume of the “ Memoirs of the univerfity of Got¬ tingen.” His labours feem to have exhaufted him j for he died w’orn out in 1762. MAYERNE, Sir Theodore de, baron of Aul- bone, was the fon of Lewis de Mayerne, the celebrated author of the General Hiftory of Spain, and of the Monarchic anjlo-democratique, dedicated to the ftates- general. He was born in 1573, and had for his god¬ father Theodore Beza. He ftudied phyfic at Mont¬ pelier, and was made phyfician in ordinary to Hen- 7 ] MAY ry IV. who promifed to do great things for him, pro- Maytem, vided he would change his religion. James I. of Eng-, 1 a^‘!e' land invited him over, and made him firft phyfi¬ cian to himfelf and his queen, in which office he feiv- ed the whole royal family to the time of his death in 1655. His works were printed at Ltmdon in 1700, and make a large folio, divided into two books j the firft containing his Conjiha, Fpi/lolcv, et Obfervationes ; the fecond his Pharmacopoeia variaque mcdicamentorum formulae. MAYHEM. See Maim. _ MAYNE, Jasper, an eminent Engliih poet and divine in the 17th century, who was bred at Oxford, and entered into holy orders. While his majefty re¬ fided at Oxford, he was one of the divines appointed preach before him. He publilhed in 1647 to piece entitled oxaomaxia, or The people's war ex¬ amined according to the principles of reafon andferipture, by Jafper Mayne. In 1648 he was deprived of his ftudentlhip at Chrift church, and two livings he had ; but was reftored with the king, who made him his chaplain and archdeacon of Chichefter ; all which he held till he died. Ur Mayne was held in very high efteem both for his natural parts and his acquired accompliffiments. He was an orthodox preacher, and a man of fevere virtue and exemplary behaviour *, yet of a ready and facetious wit, and a very Angular turn of humour. From fome ftories that are related of him, he feems to have borne fome degree of re- femblance in his manner to the celebrated Ur Swift ; but if he did not poffefs thofe very brilliant parts that diftinguilhed the Uean, he probably was lefs fubjedf to that capricious and thofe unaccountable whimfies which at times fo greatly eclipfed the abi¬ lities of the latter. Yet there is one anecdote re¬ lated of him, which, although it refledls no great ho¬ nour on his memory, as it feems to carry fome degree of cruelty with it, yet is it a ftrong mark of his re- femblance to the Uean, and a proof that his propen- fity for drollery and joke did not quit him even in his lateft moments. The ftory is this: The Uoffor had an old fervant, wTho had lived with him fome years, to whom he had bequeathed an old trunk, in which he told him he would find fomething that would mahe him drink after his death. The fervant, full of ex¬ pectation that his mailer, under this familiar expref- fion, had left him fomewhat that would be a reward for the affiduity of his paft fervices, as foon as decency would permit, flew to the trunk \ when, behold, to his great difappointment, the boafted legacy proved to be a red herring. The doClor, however, bequeathed many legacies by will to pious ufes •, particularly 50 pounds towards the rebuilding of St Paul’s cathedral, and 200 pounds to be diftributed to the poor of the parilhes of Caffington and Pyrton, near Wattington, of both which places he had been vicar. In his younger years he had an attachment to poetry 5 and wrote two plays, the latter of which may be feen in the tenth volume of Uodfley’s Colleclion, viz. 1. Amorous war, a tragi¬ comedy. 2. The city-match, a comedy. He publilh¬ ed a poem upon the naval viftory by the duke of York over the Dutch, printed in 1665. He alio tranfiated into Engliffi from the Greek part of. Lucian’s Dia¬ logues. D 2 MAYNOOTH, MAY [ 23 ] MAY MAYNOOTH, ot Manooth, a poft town in the county of Kildare, and province of Leinfter, in Ireland, near 12 miles from Dublin. Though not very large, it is regularly laid out, and conlifts of good houfes. Here is n charter fchool, which was opened 27th July 1 759. MAYNWARING, Arthur, an eminent political writer in the beginning of the 18th century, llaid fe- veral years at Oxford, and then went to Chefliire, where he lived fome time with his uncle Mr Francis Cholmondeley, a very hoaeft gentleman, but extremely averfe to the government of King William III. to whom he refufed the oaths. Here he profecuted his fludies in polite literature with great vigour 5 and com¬ ing up to London, applied to the fludy of the law. He was hitherto very zealous in antirevolutional principles, and wrote feveral pieces in favour of King James II. ; but upon being introduced to the duke of Somerfet and the earls of Dorfet and Burlington, be¬ gan to entertain very different notions in politics. His father left him an eftate of near 800I. a year, but fo encumbered, that the intereft money amounted to al- moft as much as the revenue. Upon the conclulion of the peace he went to Paris, where he became ac¬ quainted with Mr Boileau. After his return he was made one of the eommiffioncrs of the cuftoms, in which poll he diifinguhhed himfelf by his fkiJl and in- dudry. He wras a member of the Kit cat club, and was looked upon as one of the chief fupports of it by his pleafantry and wit. In the beginning of Qpeen Anne’s reign, the lord treafurer Godolphin engaged Mr Donne to quit the office of auditor of the irripreits, and made Maynwaring a prefent of a patent for that office worth about 2000I. a-year in a time of bufinefs. He had a confiderable ffiare in the Medley, and was author of feveral other pieces. The Examiner, his an- tagonift in politics, allowed that he wTrote with toler¬ able fpirit, and in a malferly (lyle. Sir Richard Steele dedicated the firft volume of the Tatler to him. MAYO, one of the Cape de Verd iilands, lying in the Atlantic ocean, near 300 miles from Cape Verd in Africa, about 17 miles in circumference. The foil in general is very barren, and water fcarce ; however, they have fome corn, yams, potatoes, and plantains, with plenty of beeves, goats* and affes. What trees there are, grotv on the fides of the hills, and they have fome figs and w-ater melons. The fea round about the bland abounds wuth fiffi. The chief com¬ modity is fait, wuth wffiich many Engliffi (hips are loaded in the fummer time. The principal towm is Pimfa, inhabited by negroes, who fpeak the Portu- guefe language, and are itout, lufty, and fleffiy. They are not above 200 in number, and many of them go quite naked. W. Long. 23. 5. N. Lat. 15. 10. P.Iayo, a county of Ireland, in the province of Con¬ naught, having Sligo and the fea on the north, Rof- cornmon on the f>uth, Leitrim and Rofcommon on the eaft, and the Atlantic ocean on the w'eft. It contains 724,640 Iriffi plantation acres, 75 pariibes, nine baronies, and one borough. It gives title of earl to the family of Bourke. This county takes its name from an ancient city, built in 664; the ruins of the ca¬ thedral, and f;rae traces of the ftone walls which en- compaffed the city, yet remain on the plains of Mayo. It was a univerfity, founded for the education of fuch of the Saxon youths as wmre converted to the Chriftian Mayor; faith : it was fituated a little to the fouth of Lough Conn and is to this day frequently called Mayo of the Saxons, being celebrated for giving education to Alfred the Great kincr of England. As this town has gone to decay, Balinroke is reckoned the chief town. The county by the fea is mountainous 5 but inland has good padures, lakes, and rivers. It is about 62 miles long, and 52 broad. Caftlebar is the affizestowm. —Mayo was formerly a biffiop’s fee, which is now united to TuAM. MAYOR, the chief magifirate of a city or town;, chofen annually out of the aldermen. The wrord, an¬ ciently -wrote ineyr, comes from the Britiffi miret, i. e, cujlodirc, or from the old Engliffi maier, viz. pot eft as, and not from the Latin major. King Richard I. hi¬ ll 89, changed the bailiff of London into a mayor, and from that example King John made the bailiff of! King’s Lynn a mayor anno 1204 : Though the fa¬ mous city of Norwuch obtained not this title for its chief magiftrate till the feventh year of King Hen-, ry V. anno 1419 ; fince wffiich there are few towns of note but have had a mayor appointed for govern¬ ment. Mayors of corporations are juffices of peace pro tempore, and they are mentioned in feveral ftatutes ; but no perfon ffiail bear any office of magiftracy con¬ cerning the government of any town, corporation, &c. who hath not received the facrament according to the* church of England within one year before his elec¬ tion, and who ffiall not take the oaths of fupremacy, See. If any perfon intrudes into the office of mayor, a quo warranto lies againft him, upon which he {hall not only be cuffed, but fined. And no mayor, or perfon holding an annual office in a corporation for one year, is to be elefted into the fame office for the next} in this cafe, perfons obffru&ing the choice of a fucceffor are fubjeft to idol, penalty. Where the mayor of a corporation is not chofen on the day ap-. pointed by charter, the next officer in place {hall the day after hold a court and ele6I one 5 and if there be a de¬ fault or omiffion that w-ay, the eleftors may be com¬ pelled to choofe a mayor, by a writ of mandamus out of the king’s bench. Mayors, cr other magiftrates of a corporation, who ffiall voluntarily abfent them- felves on the day of election, are liable to be imprifon- ed, and disqualified from holding any office in. the cor¬ poration. Mayor's Courts. To the lord mayor and city of London belong feveral courts of judicature. The higheft and moft ancient is that called the hujhngs, de- ffined to fecure the law's, rights, franchifes, and cuffoms of the city. The fecond is a court of requejl, or of confcience ; of w hich before. The third is the court of the lord mayor and aldermen, where alfo the ffieriffs fit 5 to which may be added two courts of flieriffs, and the court of the city orphans, whereof the lord may¬ or and aldermen have the cuftody. Alfo the court of common council, which is a court or affembly, wherein are made all by-laws which bind the citizens of London. It confifts, like the parliament, of two houfes : an upper, confiffing of the lord mayor and aldermen ; and a lower, of a number of common council men, chofe by the feveral wards as reprefen- tatives M A Z [ 29 ] M E A IWaza tatives of the body of the citizens. In the court of II . common council are made laws for the advancement of Mazarine. tracje^ anj committees yearly appointed, &c. But acts made by them are to have the ailent of the lord mayor and aldermen, by flat, n Geo. I. Alfo the chamberlain’s court, where every thing relating to the rents and re¬ venues of the city, as alfo the affairs of fervants, &c. are tranfafted. Laftly, To the lord mayor belong the courts of coroner and of efcheator; another court for the confervation of the river Thames; another of gaol- delivery, held ufually eight times a-year, at the Old Bailey, for the trial of criminals, whereof the lord mayor is himfelf the chief judge. There are other courts called wardmotes or meetings of the wards; and courts of halymote or affemblies of the feveral guilds and fraternities. MAZA, among the Athenians, was a fort of cake made of flour boiled with wrater and oil, and fet, as the common fare, before fuch as w^ere entertained at the public expence in the common hall or Prytnneum. MAZAGAN, a llrong place of Africa in the king¬ dom of Morocco, and on the frontiers of the province of Duguela. It was fortified by the Portuguefe, and befieged by the king of Morocco with 200,000 men in 1562, but to no purpofe. It is fituated near the fea. W. Long. 8. 15. N. Lat. 33. 12. MAZARA, an ancient town of Sicily, and capi¬ tal of a confiderable valley of the fame name, which is very fertile, and watered with feveral rivers. The town is a bilhop’s fee, and has a good harbour; is feated on the fea coaft, in E. Long. 1 2. 30. N. Lat. 37- 53- MAZARINE, Julius, a famous cardinal and prime minifler of France, was born at Pifcina in the province of Abruzzo, in Naples, in 1602. After having finifhed his fludies in Italy and Spain, he en¬ tered into the fervice of Cardinal Sachetts,.and became well fkilled in politics, and in the interelts of the princes at war in Italy •, by wdiich means he was enabled to bring affairs to an accommodation, and the peace of Oueiras was fliortly concluded. Cardinal Richlieu being taken with his conduft, did from thenceforward highly efteem him j as did alfo Cardinal Antonio, and Louis XIII. who procured him a car¬ dinal’s hat in 1641. Richlieu made him one of the executors of his will ; and during the minority of Louis XIV. he had the charge of affairs. At laft he became the envy of the nobility, which occafioned a civi w7ar 5 whereupon Mazarine w’as formed to re- t're, a price was fet on his head, and his library fold. Notwithftanding, he afterwards returned to the court in more glory than ever; concluded a peace with Spain, and a marriage treaty betwixt the king and the in¬ fanta. This treaty of peace paffes for the mafter- piece of Cardinal de Mazarine’s politics, and procured him the French king’s moil intimate confidence : but at lafl his continual application to bufinefs threw him into a dffeafe, of which he died at Virvciennes in 1661.—Cardinal Mazarine was of a mild and affable temper. One of his greatefl talents was his knowing mankind, and his being able to adapt himfelf, and to ailume a charadler conformable to the circumftances of affairs. Fie poffeffed at one and the fame time the bifhopric of Metz, and the abbeys of St Arnauld, St Clement, and St Vincent, in the fame city ; that of St Dennis, Clugny, and Vitffor, of Marfeilles ; of St MazzeoM, Michel at Soiffons, and a great number of others. at' He founded Mazarine college at Paris ; which is alio called the college of the four nations. '1 here has been publilhed a colleClion of his letters, the moft copi¬ ous edition of which is that of 1745> *n 2 vols. duo¬ decimo. MAZZUOLI. See Parmigiano. MEAD, a wholefome, agreeable liquor, prepared with honey and water- One of the beft methods of preparing mead is as fol¬ lows : Into twelve gallons of water put the whites ot fix eggs ; mixing thefe wTell together, and to the mix¬ ture adding twenty- pounds of honey. Let the liquor boil an hour, and when boiled, add cinnamon, ginger, cloves, mace, and rofemary. As foon as it is cold, put a fpoonful of yeft to it, and turn it up, keep¬ ing the veffel filled as it works; when it has done working, flop it up clofe ; and, wken fine, bottle it oft for me. Thorley fays, that mead not inferior to the beft of foreign wines may be made in the following manner : Put three pounds of the fineft honey to one gallon of wTater, and two lemon peels to each gallon; boil it half an hour, w’e-ll feummed ; then put in, while boiling, lemon peel : work it with yeft ; then put it in your veffel with the peel, to ftand five or fix months, and bot¬ tle it off for ufe. If it is to be kept for feveral years, put four pounds to a gallon of water. The author of the Dictionary of Chemiftry direfls to choofe the whiteft, pureft, and beft tafted honey, and to put it into a kettle with more than its weight of water : a part of this liquor muft be evaporated by boiling, and the liquor feummed, till its confidence is fuch, that a frefh egg (ball be fupported on its forface without finking more than half its thicknefs into the liquor; then the liquor is to be drained, and poured through a funnel into a barrel; this barrel, which ought to be nearly full, snuft be expofed to a heat as equable as poffible, from 20 to 27 or 28 degrees of Mr Reaumur’s thermometer, taking care that the bung- hole be (lightly covered, but not doled. The pheno¬ mena of the fpirituous fermentation will appear in this liquor, and will fubfift during two or three months, according to the degree of heat; aftei^ which they will diminifti and ceafe. During this fermentation, the barrel muft be filled up occafionally with more of the fame kind of liquor of honey, fome of which ought to be kept apart, on purpofe to replace the liquor which flows out of the barrel in froth. When the fermenta¬ tion ceafes, and the liquor has become very vnious, the barrel is then to be put into a cellar, and w-ell clofed ; a year afterwards the mead will be fit to be put into bottles. Mead is a liquor of very ancient ufe in Britain. See Feast. Mead, Dr Richard, a celebrated Englifti phyfi- cian, was born at Stepney near London, where his father, the Reverend Mr Matthew M ad, had been one of the two miniilers of that pariih ; ' but in 1662 wras ejeCfed for nonconformity, but continued to preach at Stepney till his death. As Mr Mead had a handfome fortune, he bellowed a liberal education upon 13 children, of whom Richard W’as the eleventh; and for that .purpofe kept a private tutor in his houfe, who. M E A [ 30 ] M E A Mead. who taught him the Latin tongue. At 16 years of age Richard was fent to Utrecht, where he ftudied three years under the famous Graevius; and then choofing the profefiion of phyfic, he went to Leyden, where he attended the leftures of the famous Pitcairn on the theory and practice of medicine, and Her¬ man’s botanical courfes. Having alio fpent three years in thefe ftudies, he went’ with his brother and two other gentlemen to vifit Italy, and at Padua took his degree of dodtor of philofophy and phyfic in 5695. Afterwards he fpent fome time at Naples and at Rome j and returning home the next year, fettled at Stepney, where he married, and pradlifed phyfic, with a fuccefs that laid the foundation of his future greatnefs. In 1703, Dr Mead having communicated to the Royal Society an analyfis of Dr Bonomo’s difcoveries relating to the cutaneous worms that generate the itch, which they inferted in the Philofophical Tranf- adlions j this, with his account of poifons, procured him a place in the Royal Society, of which Sir Ifaac Newton was then prefident. The fame year he was eledled phyfician of St Thomas’s hofpital, and was al- fo employed by the furgeons to read anatomical lec¬ tures in their hall, which obliged him to remove into the city. In 1707 his Paduan diploma for dodtor of phyfic was confirmed by the univerfity of Oxford 5 and being patronized by Dr RadclifFe, on the death of that famous phyfician he fucceeded him in his houfe at Bloomfbury-fquare, and in the greateft part of his bufinefs. In 1727 he was made phyfician to King George II. whom he had alfo ferved in that capacity while he w7as prince of Wales; and he had afterwards the pleafure of feeing his twm fons-in-law, Dr Nichols and Dr Wilmot, his coadjutors in that eminent fta- tion. Dr Mead was not more to be admired for the qua¬ lities of the head than he was to be loved for thofe of his heart. Though he wras himfelf a hearty whig, yet, uninfluenced by party principles, he was a friend to all men of merit, by whatever denomination they might happen to be diftinguifhed. Thus he was intimate with Garth, with Arbuthnot, and writh Freind 5 and long kept up a confiant correfpondence with the great Boerhaave, who had been his fellow ftudent at Ley¬ den : they communicated to each other their obferva- tions and projefts, and never loved each ether the lefs for being of different fentiments. In the mean time, intent as Dr Mead was on the duties of his profeflion, he had a greatnefs of mind that extended itlelf to all kinds of literature, which he fpared neither pains nor money to promote. He caufed' the beautiful and fplen- did edition of Thuanus’s hiftory to be publifhed in 1713, in feven volumes folio : and by his interpofition and affiduity, Mr Sutton’s invention of drawing foul air from fhips and other clofe places was carried into execution, and all the fhips in his majefly’s navy pro¬ vided with this ufeful machine. Nothing pleafed him more than to call hidden talents into light; to give encouragement to the ’greateft projefls, and to fee them executed under his own eye. During almoft half a century he was at the head of his bufinefs, which brought him one year above feven thoufand pounds, and for feveral years between five and fix thoufand } yet clergymen, and in general all men of learning, ♦ 2 were welcome to his advice. His library confified Meadow, of 10,000 volumes, of which his Latin, Greek, and Meal, oriental manuferipts, made no inconfiderable part. v " He had a gallery for his pictures and antiquities, yrhich coft him great fums. His reputation, not only as a phyfician, but as a fcholar, was fo univerTally efla- blifhed, that he correfponded with all the principal li¬ terati in Europe : even the king of Naples fent to de¬ fire a complete colletlion of his works ; and in return made him a prefent of the two firft volumes of Signior Bajardi, which may be confidered as an introdudion to the collection of the antiquities of Herculaneum, At the fame time that prince invited him to his pa¬ lace, that he might have an opportunity of fhowing him thofe valuable monuments of antiquity ; and no¬ thing but his great age prevented his undertaking a journey fo fuited to his tafie. No foreigner of learn¬ ing ever came to London without being introduced to Dr Mead ; and on thefe occafions his table was always open, and the magnificence of princes was united with the pleafures of philofophers. It was principally to him that the feveral counties of England and our co¬ lonies abroad applied for the choice of their pbyfi- cians, and he was likevvife confulted by foreign phy- ficians from Ruffia, Pruflia, Denmark, &c. He wrote, befides the above works, 1. A Treatife on the Scurvy, 2. De variolis et morbillis differtatio. 3. Medico facra: five de Morbis infignioribus, qm in Bibhis niemoratitur, Commentarius. 4. Manila et Pracepta medico. 5. A Difcourfe concerning petlilential cofttagion, and the methods to be ufed to prevent it. The works he wrote and publifhed in Latin were tranflated into Englifh, under the Dodor’s infpedion, by Thomas Stack, M. D. and F. R. S. 'Ibis great phyfician, naturalift”, and antiquarian, died on the 16th of Fe¬ bruary 1794. MEADOW, in its general fignification, means pafture or grafs lands, annually mown for hay : but it is more particularly applied to lands that are fo low as to be too moitt for cattle to graze upon them in winter without fpoiling the fward. For the manage¬ ment and watering of meadows, fee Agriculture, P- 435- MEAL, the flour of grain. The meal or flour of Britain is the fineft and whiteft in the world. The French is ufually browner, and the German browner than that. Our flour keeps well with us : but in carry¬ ing abroad it often contrads damp, and becomes bad. All flour is fubjed to breed worms j thefe are white in the white flour, and brown in that which is brown j they are therefore not alwaysdiflinguifhable to the eye: but when the flour fetls damn, and fmells rank and mufty, it may be conjedured that they are there in great abundance. The colour and the weight are the two things which denote the value of meal or flour 5 the whiter and the heavier it is, others things being alike, the better it always is. Pliny mentions thefe two cha- raders as the marks of good flour; and tells us, that Italy in his time produced the finefl: in the worlds This country indeed was famous before his time for this produce ; and the Greeks have celebrated it 5 and Sophocles in particular fays, that no flour is fo white or fo good as that of Italy. The corn of this coun¬ try has, however, loft much of its reputation fince that time } M E A [ .si ] M E A Mead, time ) and the reafon of this Teems to be, that the —v _ whole country being full of fulphur, alum, vitriol, marcafites, and bitumens, the air may have in time af¬ fected them fo far as to make them diffufe themfelves through the earth, and render it lefs fit for vegetation j and the taking fire of feme of thefe inflammable mi¬ nerals, as has fometimes happened, is alone fufficient to alter the nature of all the land about the places where they are. The flour of Britain, though it pleafes by its white- nefs, yet wants fome of the other qualities valuable in flour; the bread that is made of it is brittle and does not hold together, but after keeping a few days becomes hard and dry as if made of chalk, and is full of cracks in all parts ; and this mull: be a great difad- vantage in it when intended for the fervice of an army, or the like occafions, where there is no baking every day, but the bread of one making mull neceffarily be kept a long time. The flour of Picardy is very like that of Britain ; and after it has been kept fome time, is found improper for making into pafle or dough. The French are forced either to ufe it immediately on the grinding, or elfe to mix it with an equal quantity of the flour of Brittany, which is coarfer but more unftuous and fatty •, but neither of thefe kinds of flour keep well. The flour of almoft any country will do for the home confumption of the place, as it may be always frelh ground ; but the great care to be uled in feledl- ing it, is in order to the fending it abroad, or furnilhing flrips for their own ufe. The faline humidity of the fea air rails metals, and fouls every thing on board, if great care be not taken in the preferving them,. This alfo makes the flour damp and mouldy, and is often the occafion of its breeding infedls, and being wholly fpoiled- The flour of fome places is conflantly found to keep better at fea than that of others •, and when that is once found out, the whole caution needs only be to carry the flour of thofe places. Thus the French find that the flour of Poitou, Normandy, and Guienne, all bear the fea carriage extremely well ; and they make a confiderable advantage by carrying them to their A- merican colonies. 1 he choice of flour for exportation being thus made, the next care is to preferve it in the flrips : the keep¬ ing it dry is the grand confideration in regard to this; the barrels in which it is put up ought to be made of dry and well feafened oak, and not to be larger than to hold two hundred weight at the moft. If the wood of the barrels have any fap remaining in it, it wall moi- llen and fpoil the flour ; and no wood is fo proper as oak for this purpofe, or for making the bins and other vefiels for keeping flour in at home, fince wdren once well dried and fcafoned it will not contradf hu¬ midity afterwards. The beech wood, of which fome make their bins for flour, is never thoroughly dry, but always retains fome fap. The fir will give the flour a tafte of turpentine *, and the aflx is always fubject to be eaten by worms. The oak is preferable, becaufe of its being free from thefe faults j and w hen the feveral kinds of wood have been examined in a proper manner, there may be others found as fit, or poflibly more fo, than this for the purpofe. The great tefl is their havr ing more or lefs fap. See Flour and Wood. MEAN, in general, denotes the middle between two extremes : thus wre fay the mean distance., mean proportion, &c. Mean, Arithmetical, is half the fum of the two ex¬ tremes, as 4 is the arithmetical mean between 2 and 6; for L+-=+, Mean, Geometrical, is the fquare root of the rect¬ angle, or product of the two extremes : thus, X9 — V9—3 To find two mean proportionals between two ex¬ tremes : multiply each extreme by the fquare of the other, then extraft the cube root out of each product, and the two roots will be the mean proportionals re¬ quired. Required two proportionals betrveen 2 and l6, 2 X 2 X 16:^164, and ^■y/64 — 4. Again, 3 v/2 X i6*—3^512 = 8. 4 and 8 therefore are th# tw'O proportionals fought. MEARNSSHIRE, a county of Scotland. See Kin¬ cardineshire. MEASLES, a cutaneous difeafe attended with a fever, in which there is an appearance of eruptions that do not tend to a flippuration. See Medicine Index. MEASURE of an angle, is an arch deferibed from the vertex in any place between its legs. Hence angles are dillinguilhed by the ratio of the arches, de¬ feribed from the vertex between the legs to the peri¬ pheries. Angles then are diftinguiihed by thofe arches j. and the arches are diflinguiflied by their ratio to the periphery. Thus an angle is faid to be fo many degrees as there are in the faid arch. Measure of a folid, is a cube whofe fide is an inch, a foot, or a yard, or any other determinate length. In geometry it is a cubic perch, divided into cubic feet, digits, &c. Measure of velocity, in Mechanics, is the fpace paff- ed over by a moving body in a given time. To mea- fure a velocity, therefore, the fpace mufi: be divided into as many equal parts as the time is conceived to be divided into ; the quantity of fpace anfwering to fuch a part of time is the meafure of the velocity. Measure, in Geometry, denotes any quantity affumed as one, or unity, to which the ratio of the other homoge¬ neous or fimilar quantities is expreffed. Measure, in a legal and commercial fenfe, denotes a certain quantity or proportion of any thing bought, fold, valued, or the like. It is neceflary, for the convenience of commerce, that an uniformity Ihould be obferved in weights and meafures, and regulated by proper ftandards. A foot- rule may be ufed as a flandard for meafures of length, a bufliel for meafures of capacity, and a pound for weights. There Ihould be only one authentic ftan- dard of each kind, formed of the molt durable ma¬ terials, and kept with all poflible care. A fufficient number of copies, exadtly correfponding to the prin¬ cipal fhmdard, may be diflributed for adjufling the weights and meafures that are made for common ufe. There arc feveral ftaudards-of this kind both in England. 'M E A L 32 ] M E A •Meafure. England and Scotland. See the article Weights and “ v Mrafurcs. If any one of'the flandards abo're mentioned be juflly pr ferved, it will ferve as a foundation for the others, by which they may be correfted if inaccurate, or restored if entirely loft. For inftance, if we have a ftandard foot, nve can ealily obtain an inch, and can make a box which fhall contain a cubical inch, and may ferve as a ftandard for mcaiures of capacity. If it be known that a pint contains 100 cubical inches, we may make a veflel five inches fquare, and four inches deep, which will contain a pint. If the llan- d«vd oe required in any other form, we may fill this vellel xvith water, and regulate another to contain an equal quantity. Standards for weights may be obtain¬ ed from the fame foundation ; for if we know how many inches of water it takes to weigh a pound, we have on'y to meafure that quantity, and the weight which balances it may be aiTumed as the ftandard of a pound. Again, If the flandard of a pound be given, the meafure of an inch may be obtained from it •, for we may weigh a cubical inch of water, and pour it into a regular veiTel -, and having noticed how far it is filled, we may make another veffel of like capacity in the form -of a cube. The fide of this vefftl may be ai- fiirned as the ftandard for an inch ; and ftandards for a foot, a pint, or a buftiel, may be obtained from it. Water is the molt proper fubftance for regulating ftandards ; for all other bodies differ in weight from others of the fame kind •, whereas it is found by expe¬ rience that fpring and river water, rain, and melted fnow, and all other kinds, have the fame weight ; and this uniformly holds in all countries when the water is pure, alike warm, and free from fait and minerals. t hus, any one ftandard is fufficient for reftoring all the reft. It may further be defired to hit on feme ex¬ pedient, if poffible, for reftoring the ftandards, in cafe that all of them Ihould ever fall into diforder, or (hould be forgotten, through the length of time, and the vi- ciffitudes of human affairs. This feems difficult, as no words can convey a precife idea of a foot-rule, or a pound weight. Meafures, affumed from the dimen- lions of the human body, as a foot, a hand-breadth, or a pace, muft nearly be the fame in all ages, unlefs the fize of the human race undergo fome change ; and therefore, if we know how many fquare feet a Roman acre contained, we may form fome judgement of the nature of the law which reft rifted the property of a Roman citizen to feven acres •, and this is lufficient to render hiftory intelligible •, but it is too inaccurate to regulate meafirres for commercial purpofes. The fame may be faid of ftandards, deduced from the meafure of a barley-corn, or the weight of a grain of wheat. If the diftance of two mountains be accurately meafured and recorded, the nature of the meafure ufed will be preferved in a more permanent manner than by any ftandard •, for if ever that meafure fall into di'uie, and another be fubftituted in its place, the diftance may be meafured again, and the proportion of the tlandards may be afeertained by comparing the new and ancient didances. But the moft accurate and unchangeable manner of cflablififing ftandards is, by comparing them with the length of pendulums. The longer a pendulum is, it 1 vibrates the flower ) and it muft have one precife length Meafure. in order to vibrate in a fecond. The ilighteft differ- --"v-**— ence in length will occafion a difference in the time ; which will become abundantly fenfible after a number of vibrations, and wall be eafily obferved if the pendu¬ lum be applied to regulate the motion of a clock. The length of a pendulum which vibrates feconds in Lon¬ don is about 39-g- inches, is conftantly the fame at the fame place, but it varies a little with the latitude of the place, being ihorter as the latitude is lefs. There¬ fore, though all ftandards of weights and meafures rvere loft, the length of a fecond pendulum might be found by repeated trials : and if the pendulum be pro¬ perly divided, the juft meafure ,of an inch will be ob¬ tained ; and from this all other ftandar is may be re- ftored. See WJiitehurJl on Invariable Measures. Meafures are various, according to the various kinds and dimenfions of the things meafured.—Hence arife lineal or longitudinal meafures, for lines or lengths j fquare meafufes, for areas or fuperfices ; and folia or cubic meafures, for bodies and their capacities ; all which again are very different in different countries and in different ages, and even many of them for different commodities. Whence arife other divifions of ancient and modern meafures, domeftic and foreign ones, dry meafures, liquid meafures, &c. 1. Long Meafures, or Meafures of Application. i.J The Englifh and Scotch Standards. The Englilh lineal ftandard is the yard, containing 3 Englifn feet •, equal to 3 Paris feet 1 inch and TJT of an inch, or ^ of a Paris ell. The ufe of this mea¬ fure was eftablidied by Henry I. of England, and the ftandard taken from the length of his own arm. It is divided into 36 inches, and each inch is fuppofed equal to 3 barleycorns. When ufed for meafuring cloth, it is divided into four quarters, and each quar¬ ter fubdivided into 4 nails. The Engliffi ell is equal to a yard and a quarter, or 45 inches, and is ufisd in meafuring linens imported from Germany and the Low Countries. The Scots elwand was eftabliffied by King David I. and divided into 37 inches. The ftandard is kept in the council chamber of Edinburgh, and being compar¬ ed with the Engliffi yard, is found to meafure 373- inches •, and therefore the Scots inch and foot are lar¬ ger than the Engliffi, in the proportion of 1 80 to 185 5 but this difference being fo inconfiderable, is feldom attended to in practice. The Scots ell, though for¬ bidden by law, is ftill ufed for meafuring fome coarfe commodities, and is the foundation of the land meafure of Scotland. • Itinerary meafure is'the fame both in England and Scotland. The length of the chain is 4 poles, or 22 yards; 8o chains make a mile. The old Scots com¬ puted miles were generally about a mile and a half each. The reel for yarn is 2\ yards, or 10 quarters, in circuit ; 1 20 threads make a cut, 12 cuts make a hafp or hank, and 4 hanks make a ipindle. 2. ] The French ftandard was formerly the aune or ell, containing 3 Paris feet 7 inches 8 lines, or 1 yard \ Englilh ; the Paris foot royal exceeding the Engliffi by tIIo parts, as in one of the following tables. This ell Meafure- M E A t .33 ] M E A ell is divided two ways: viz. into halves, thirds, fixths, Xhe French, however, have alfo formed an entirely Meature. and twelfths j and into quarters, half-quarters, and new fyftem of weights and meafures, according to the ' fixteenths. following table. Proportions of the meafures of each fpe- cies to its principal meafure or unity. 10,000 1,000 IOO 10 o 0.1 0.01 O.OOX Firil part of the name which indicates the proportion to the principal meafure or unity. Myria Kilo Hedto Deca Deci Centi Mini Proportion of the principal meafures f between themfelves and the length of the meridian. Value of the principal meafures in the! ancient French meafures. \ Value in Englifh meafures. Length. Metre. 1 0,000,cooth part of the di- ilance from the pole to the e- quator. 3 feet 11 lines and nearly 1^116839.383. Capacity. Litre. A decimetre cube. i pint and TV or i litron and T nearly. 6i .083 inches, which is more than the wine, and lefs than the beer quart. Weight. Agrarian. For firewood, Gramme. Are. Stere. Weight of a centimetre cube of di¬ ddled water. l 8 grains and 841,000 parts. 100 fquare metres. Two fquare perches des eaux et foie;. 22,966 grains. 11.968 fquare yards, One cubic metre. demi-voie, or -J. of a cord des eaux et foret. The Englifh avoirdupois pound weighs troy grain? 7004; whence the avoirdupois ounce, whereof 16 make a pound, is found equal to 437.75 troy grains. —And it follows that the troy pound is to the avoir¬ dupois pound as 88 to 107 nearly; for as 88 to 10 fo is 5760 to 7003.636 : that the troy ounce is to the avoirdupois ounce, as 80 to 73 nearly ; for as 80 to 73,_fo is 480 to 438. And, laftly, That the avoirdupois pound and ounce is to the Paris two marc weight and ounce, as 63 to 68 nearly ; for as 63 to 68, fo is 7004 to 7559.873. See Weight. The Paris foot exprefled in decimals, is equal to I.o654of the Englifh foot, or contains 12.785 Englifh inches. See Foot. 3.] The ftandard in Holland, Flanders, Sweden, a good part of Germany, many of what were formerly called the Hans Jowns, as Dant%ich and Hamburgh, and at Geneva, Franchfort, &c. is likewife the ell : but the ell, in all thefe places, differs from the Paris ell. In .Holland, it contains one Paris foot eleven lines, or four- fevenths of the Paris ell. The Flanders ell contains two feet one inch five lines and half a line ; or feven- twelfths of the Paris ell. The ell of Germany, Bra¬ bant, &c. is equal to that of Flanders. 4.3 The Italian meafure is the branchio, brace, or fathom. I his obtains in the ftates of Modena, Ve¬ nice, florence, Lucca, Milan, Mantua, Bologna, Vol. XIII. Part I. 6 &.c. but is of different lengths. At Venice, it con¬ tains one Paris foot eleven inches three lines, or eight fifteenths of the Paris ell. At Bologna, Modena, and Mantua, the brace is the fame as at Venice. At Lucca it contains one Paris foot nine inches ten lines or half a Paris ell. At Florence, it contains one foot nine inches four lines, or forty-nine hundredths of a Paris ell. At Milan, the brace for meafuring of filks is one Paris foot feven inches four lines, or four-ninths of a Paris ell : that for woollen cloths is the fame with the ell of Holland. Laftly, at Bergama, the brace is one foot feven inches fix lines, or five-ninths of a Paris ell. The ufual meafure at Naples, however is the canna, containing fix feet ten inches and two lines, or one Paris ell and fifteen feventeenths. 5. ] The Spanijh meafure is the vara or yard, in fome places called the barra ; containing feventeen twenty-fourths of the Paris ell. But the meafure in Caftile and Valencia is the pan, fpan, or palm ; which is ufed, together with the canna, at Genoa. In Ar- ragon, the vara is equal to a Paris ell and a half, or five feet five inches fix lines. 6. ] The Portugucfe meafure is the cavedos, contain¬ ing two feet eleven lines, or four-fevenths of a Paris ell; and the vara, an hundred and fix whereof make an hundred Paris ells. 7. J The Fkdmontefe meafure is the ras, containing one _M E A [ 34 ] Meafure. one Paris foot nine inches ten lines, or half a Paris eli. gueze ' v l'’1"11 in Sicily, their meafure is the canna, the fame with that of Naples. 8. ] The Mufcovy meafures are the cubit, equal to one Paris foot four inches two lines j and the arcin, two whereof are equal to three cubits. 9. ] The Turhijh and Levant meafures are the picq, containing two feet two inches and twm lines, or three- fifths of the Paris ell. The Chinefe meafure, the cobre ; ten whereof are equal to three Paris ells. In Perfia, and fome parts of the Indies, the gueze, where¬ of there are two kinds ; the royal gueze, called alfo the gue%e monkelfer, containing two Paris feet ten inches eleven lines, or four fifths of the Paris ell j and the ftiorter M E A , called fimply only two thirds of the for- At Goa and Ormuz, the meafure is the vara, the fame with that of the Portuguefe, having been intro¬ duced by them. In Pegu, and fome other parts of the Indies, the cando or candi, equal to the ell of Venice. At Goa, and other parts, they ufe a larger cando, equal to feventeen Dutch ells j exceeding that of Babel and Balfora by ^ per cent, and the vera by In Siam, they ufe the ken, fliort of three Paris feet by one inch. The ken contains two foks, the fok two keubs, the keub twTelve nious or inches, the niou to be equal to eight grains of rice, i. e. to about nine lines. At Camboia, they ufe the halier ; in Japan, the tatam ; and the fpan on fome of the coafts of Guinea. Meafure, Tables of Long Meafurc. 1. English. Barley-corn Inch 9 27 36 54 12 18 108 36 Palm 3|Span qj i-fFoot 6! 2 4 12 18o| 60 216 72 594j 198 23760'; 7920 20 (0 24j 8 66i 22 26401 880 I9008063360 21 l 2O.704O Cubit 2 lYard 6 16 660 5280 ll\ 4 j 2 11 | 54 440 j 220 3520 Pace 1760 3tu 132 Fathom 2! Pole no 40 1056 j88o 320 Furlong Mile. 2. Scripture Meafures reduced into Englijh. Digit Palm 1 2 96 144 192 1920 Span Cubit 24 361 12 48, 16 Fathom Ezekiel’s reed Arabian pole 480 160 80 j 20 i4 i3y 10 Schcenus, or meafuring line ?f Dec. feet. p- o 0.912 o 3-648 o 10.944 1 9.888 7 3’SS2 10 11-328 14 7.104 145 11.04 3. m Mcafure. M E A [ 35 3 3. The Scripture Itinerary Meafures. M E A Cubit 400 2000 4000 I 2000 96JOO Stadium 5 Sabbatb day’s journey io 2 jEaftern mile 3° 240 ', 48 24 Parafan A day’s journey Da&ylus, digit Doron, dochme 4. Grecian. 1 2 16 18 20 24 96 9600 76800 ^il-Lichas 24 2400 19200 i^-jOrtbodoron 1 T1 A 1 c Iti Spitbame Foot i4 14 960 7680 2-rri 14 1 8 Syarri 800 i 600 Cubit 14 I T 5t ?33t Pygon 4 480 6981^6400 6800 4266-7-I3840 Eng. Miles. Paces. Feet. o o 1.824 o 145 4.6 o 729 3.000 I 403 1.000 4 I53 S-00^ 33 172 4.00® ubit larger Pace Furlong 400 3200 100 800 Mile Paces. Feet. o o o o o o o o o o o o - o o o 100 4 805 5 Dec. 0,7554t£ 3.0218 | 7-5546 i 8.3101.^ 9.0656 | 0.0875 i-5984 1 3- I09 1 6.13125 o525 4- 5 o Meafure. Digitus i4 16 20 24 40 80 10000 80000 tranfverfus Uncia Palmus minor Pes 5. Roman. 1 2 I5 18 40 60 75oo 60000 10 20 24 2500 625 Palmipes Cubitus lyjGradus 3t| 2Taffus 500 20000 5000 4000 4164 33331 25°: I25 2000:1000 Stadium Milliare E 2 Paces. Feet. Dec. o o 0.7254 o o 0.967 o o 2.901 o o 11.604 O I 2.505 o I 5.406 0 2 5.01 o 4 10.02 120 4 4-5 967 O o. 6. Proportion M E A Meafure. [ 36 ] M E A 6. Proportion of feveral Long Meafures to each other, brj M. Picard. The Rhinland or Leyden foot (12 whereof make the Rhinland perch) fuppoled The Englifh foot The Paris foot The Amfterdam foot, from that of Leyden, by Snellius - - - The Danifli foot (two whereof make the Da- nifh ell) - - * The Swedifh foot The Bruffels foot The Dantzick foot, from Hevelius’s Selenogra- phia - T’ae Lyons foot, by M. Auzout The Bologna foot, by the fame The braccio of Florence, by the fame, and Fa¬ ther Marfenne The palm of the archite&s at Rome, accord¬ ing to the obfervations of Meffrs Picard and Auzout - The Roman foot in the Capitol, examined by Mefffs Picard and Auzout - 653 or 6 $34- 696 67 54 720 629 6584 609 f 636 757r 843 1290 4944 The fame from the Greek foot From the vineyard Mattei From the palm - From the pavement of the Pantheon, fuppofed to contain 10 Roman feet From a flip of marble in the fame pavement, fuppofed to contain three Roman feet From the pyramid of Ceftius, fuppofed to con¬ tain 9 ^ Roman feet From the diameters of the columns in the arch of Septimius Severus. From a flip of porphyry in the pavement of the Pantheon - - See on this fubjedl Phil. Tranf. vol. iy. art P- 774- 652 6574 6584 653 650 6534 653t 653t . 69. 7. Proportions of the Long Meafures of federal nations to the Englijh foot, taken fror?i Meffrs Greaves, Au^out, Picard, and Eifcncbmid. See Foot. The Englifh ftandard foot being divided into 1000 equal parts, the other meafures will have the proportions to it, which follow. Englifh foot • Paris foot Venetian foot Rhinland foot Strafburgh foot Norim berg foot Eantzick foot Danifh foot Swedifh foot Derahor cubit of Cairo Perfian arifh Greater Turkifh pike Feet. IOOO 1068 1161 1033 952 1000 944 1042 9774 1824 2200 Inches. I 2 I 2.8l6 I3-944 12.396 14.424 12 11.328 12.504 II 733 12.888 38.364 26.4 Leffer Turkifh pike Braccio at Florence Braccio for woollen at Sienna Braccio for linen at Sienna Canna at Naples Vera at Almaria and Gibraltar Palmo di Archtetti at Rome Canna di Archtetti Palmo di braccio di mercantia Genoa palm Bolognian foot Antwerp ell Amflerdam ell Leyden ell Paris draper’s ell Paris mercer’s ell Feet, 213 I I9f 3 1242 J974 6880 2760 732 73 20 6954 815 1250 2283 2268 2260 3929 3937 Inches. 25-572 22.956 14.904 23.688 82.56 SS-12 87.84 87.84 83.46 9.78 15 27.396 27.216 27.12 47-h8 47.244 Meafure, 8. Different Itinerary Meafures. A French league is about A German mile A Dutch mile An Italian mile A Spanilh league A Ruffian verfl Englifh miles ditto ditto ditto 34 ditto 1- ditto. 24 4 34 x 1 TT II. Square, Superficial, or Land Meafure. 1. Englifh fquare meafures are raifed from the yard of 36 inches multiplied into itfelf, and thus produ¬ cing 1296 fquare inches in the fquare yard; the divi- vifions of this are fquare feet and inches ; and the mul¬ tiples, poles, roods, and acres. Becaufe the length of a pole is 5! yards, the fquare of the fame contains 3°4 fqtiare yards. A fquare mile contains 640 fquare acres. In meafuring fens and woodlands, 18 feet are generally allowed to the pole, and 21 feet in forefl lands. A hide of land, frequently mentioned in the earlier part of the Englifh hiftory, contained about 100 arable acres ; and 5 hides were efteemed a knight’s fee. At the time of the Norman conquefl, there were 243,600 hides in England. 2. Scotch fquare or land meafure is regulated by the Scotch ell: 36 fquare ells — 1 fall, 40 falls = 1 rood, 4 roods — 1 acre.—The proportion between the Scotch and Englifh acre, fuppofing the feet in both meafures alike, is as 1369 to 1089, or nearly as 5 to 4. If the difference of the feet be regarded, the proportion is as 10,000 to 7869. The length of the chain for meafuring land in Scotland is 24 ells, or 74 feet —A hufhand-land contains 6 acres of fock and fcythe land, that is, of land that may be tilled with a plough or mown with a fcythe ; 13 acres of arable land make one ox-gang, and four ox-gangs make a pound- land of old extent. 3. French fquare meafures are regulated by 12 fquare lines in the inch fquare ; 12 inches in the foot, 22 feet in the perch, and 100 perches in the arpent or acre. TdlLi$ Meafure. M E A [ Tables of Square Meafure. i. English. 2. Grecian (quare meafures were the plethron or acre, by fome faid to contain 1444, by others 10,000 fquare feet j and aroura, the half of the plethron. Tl»e aroura of the Egyptians was the fquare 100 cubits. 3. Roman fquare meafure reduced to Engliih. The integer was the jugerum or acre, which the Romans divided like the libra or as: thus the jugerum con¬ tained / As Deunx Dextans Dodrans Bes Septunx Semis Quincunx Triens Quadrans Sextans Uncia Square feet. 19200 16800 14400 12000 9600 7200 4800 2400 28800 288 26400 j 264 24000 240 21600 216 192 168 5 44 1 20 96 72 48 24 2 3 8 w as 18 10 2 34 25 *7 9 1 32 24 16 8 Square feet. 250.05 183-85 117-64 51-42 257.46 191.25 1 25.02 58.82 264.85 198 64 13 2-43 66.21 Note, Adhis major was 14,400 fquare feet, equal to a femis j clima, 3600 fquare feet, equal to fefcuncia j and a£lus minimus equal to a fextans. III. Cubical Meafures, or Meafures of Capacity, for Liquids. I. The Eng’lifh meafures were originally raifed from troy weight: it being enafted by feveral ilatutes, that eight pounds troy of wheat, gathered from the middle of the ear, and well dried, fhould weigh a gallon of wine meafure, the divifions and multiples whereof were to form the other meafures at the fame time it was alfo ordered, that there Ihould be but one liquid mea¬ fure in the kingdom : yet cuflom has prevailed ; and there having been introduced a new weight, viz. the avoirdupois, we have now a fecond itandard gallon ad- 3*7 ] M E A juded thereto, and therefore exceeding the former in the proportion of the avoirdupois weight to troy weight. From this latter ftandard are raifed two fe¬ veral meafures, the one for ale, the other for beer. The fealed gallon at Guildhall, which is the ftandard for wines, fpirits, oils, &c. is fuppofed to contain 231 cubic inches ; and on this fuppofition the other mea¬ fures raifed therefrom will contain as in the table un¬ derneath : yet, by adhual experiment, made in 1688, before the lord mayor and the commiffioners of excife, this gallon was found to contain only 224 cubic inches: it was, however, agreed to continue the common ftip- pofed contents of 231 cubic inches : fo that all com¬ putations (land on their old footing. Hence, as 12 is to 231, fo is 1444 to 2814 the cubic inches in the ale gallon : but in effeOf the ale quart contains 704 cubic inches, on which principle the ale and beer gallon will be 282 cubic inches. The feveral diviftons and mul¬ tiples of thefe meafures, and their proportions, are ex¬ hibited in the tables underneath. The barrel for ale in London is 32 gallons, and the barrel for beer 36 gallons. In all other places of England, the barrel, both for ale and beer, is 34 gallons. 2. Scotch liquid meafure is founded on the pint. The Scotch pint was formerly regulated by a ftandard jug of cart metal, the cuftody of which was committed to the borough of Stirling. This jug was fuppofed to contain 105 cubic inches-, and though, after feveral careful trials, it has been found to contain only about 1034 inches-, yet, in compliance with eftablithed cu- ftom, founded on that opinion, the pint foups are ftill regulated to contain 105 inches, and the cuftomary ale meafures are about T? above that ftandard. It was enadled by James I. of Scotland, that the pint ftiould contain 41 ounces trone weight of the clear w’ater of Tay, and by James VI. that it ihould contain 55 Scots troy ounces of the clear water of Leith. This affords another method of regulating the pint, and alfo afcer- tains the ancient ftandard of the trone weight. As the water of Tay and Leith are alike, the trone weight muft have been to the Scots troy weight as 55 to 41 5 and therefore the pound trone muft; have contained about 21| ounces Scots troy. 4 gills = 1 mutchkin. 2 mutchkins = 1 chopin. 2 chopins ~ 1 pint. 2 pints — I quart. 4 quarts — I gallon. The Scotch quart contains 210 inches j and is, there¬ fore, about -A- lefs than the Engliih wine gallon, and about 4 lefs than the ale gallon. 3. As to the liquid raeafures of foreign nations, it is to be obferved, that their feveral veffels for wine, vi¬ negar, &c. have alfo various denominations accord¬ ing to their different fizes and the places wherein they are ufed. The woeders of Germany, for hold¬ ing Rhenifh and Mofelle wines, are different in their gauges 5 feme containing 14 aumes of Amfterdam meafure, and others more or lefs. The aume is reckon¬ ed at Amflerdam for 8 fteckans, or 20 verges, or for 4 of a tun of 2 pipes, or 4 barrels, of French or Bour- deaux, which 4 at this latter place is called tierforr, becaufe Meafure. 1 M E A Mgaiurc. hecaufe 3 of tliera make a pipe or 2 barrels, and 6 the '""~v ihid tun. The fteckan is fixteen mingles, or 32 pints; and the verge is, in refpeft of the faid Rhenith and Mofelle, and fome other forts of wine, 6 mingles; but, in meafuring brandy it confifts of 6^ mingles. The aume is divided into 4 anckers, and the ancker into 2 fteckans, or 32 mingles. The ancker is taken fometimes for ^ of a tun, or 4 barrels ; on which footing the Bourdeaux barrel ought to contain at Amflerdam (when the calk is made according to the juft gauge) 12^ fteckans, or 200 mingles, wine and Ices; or 12 fteckans, or 192 mingles, racked wine; lo that the Bourdeaux tun of wine contains ;o fteckans, or 800 mingles, wine and lees; and 48 fteckans, or 768 mingles, of pure wine. The barrels or poingons of Nantes and other places on the river .Loire, con¬ tain only 1 2 fteckans, Amfterdam mealure. The wine tun of Rochelle, Cogniac, Charente, and the ille of Rhe, differs very little from the tun of Bourdeaux, and confequently from, the barrels and pipes. A tun of wine of Chaloffe, Bayonne, and the neighbouring places, is reckoned 60 fteckans, and the barrel 15, Amfterdam me a fire. The muid of Pans contains 150 quarts or 300 pints, wine and lees ; or 280 pints clear wane ; of which muids 3 make a tun, and the fradlions are, M E A At Rochelle, Cogniac, the ifle of Rhe, and the country of Aunis, - 27 Veertels At Nantes, and feveral places of Bre¬ tagne and Anjou - - 29 Veertels At Bourdeaux, and different parts of Guienne - - 32 Verges At Amfterdam, and other cities of Holland - - 30 Veertels At Hamburgh and Lubeck - 30 Verges At Emfeden - - 27 Verges In Provence and Languedoc, brandy is fold by the quintal, the calks included ; and at Bruges in Flan¬ ders, the verges are called fejlers of 16 flops each, and the fpirits is fold at fo much per flop. Olive oil is alfo (hipped in calks of various ffzes, according to the cuftom of the places where it is em¬ barked, and the conveniency of ftowage. In England it is fold by the tun of 236 gallons ; and at Amfter¬ dam by the tun of 717 mingles, or 1434 pints. In Provence it is fold by milleroles of 66 Paris pints; from Spain and Portugal it is brought in pipes or butts, of different gauges; at the firlt place it is fold by roves, where 40 go to the butt ; and at the latter place by almoudas, whereof 26 make a pipe. Train oil is fold in England by the tun, at Amfterdam by the barrel. [ 38 ] Meafure. a. The muid The fetier , The quart The pint The chopin The demi-fetier The muid is aifo compofed of pipes or pompons, quarteaux, queves, and demiqueves; thofe poin^ons of Paris and Orleans contain about 15 fteckans Am¬ fterdam meafure, and ought to weigh with the calk 665'b. a little more or lefs. In Provence they reckon by milleroles, and the millerole of Toulon contains 66 Paris pints, or too pints of Amfterdam nearly, and the Paris pint is nearly equal to the Englilh wine quart (a). The butts or pipes from Cadiz, Malaga, Alicant, Benecarlo, S loe, and Mataro, and from the Canaries, from L'lbon, Oporto, and Fayal, are very different in their gauges, though in affreightments they are all reckoned two to the tun. Vinegar is meafured in the fame manner as wine ; but the meafures for brandies are different : thefe fpirits from France, Spain, Portugal, &c. are gene¬ rally (hipped in large calks called pipes, butts, and pieces, according to the places from whence they are , imported, &c. In France, brandy is (hipped in calks called pieces at Bourdeaux, and pipes at Rochelle, Cogniac, the hie of Rhe, and other neighbouring places, which contain fome more and fome lefs, even from 60 to 90 Amfterdam verges or veertels, accord¬ ing to the capacity of the veffels, and the places they come from, which, being reduced into barrels, will ftand as follows, viz. Tables of Lifyuw Meafure. 1. English. Solid inches be >■§ <| c I (36 letiers j 4 quarts 2 pints 2 chopins 2 demi-fetiers 2 poiffons (a) Ihefe are the old meafures of France, the account of which, for the fake of companion, is here retained. — 3 ffl'eafure. M E A [ 39 ] 2. Jewish reduced to Englifti Wine Meafure. Caph Log 5t 16 32 96 960 4 Cab 1 2 24 72 18 720. 180 Hln 2 Seah Batb, or Epha Cor on, or Chomer 6030 10 3. Attic reduced to Englilh Wine Meafure. Cochliarion 2 Cheme 2t 10 7^ 60 3° 120 60 720 : 360 My drone 2 Conche Cyathos 14 Oxybaphon 24; 12 48 288 8640 4320 3456 144 12 72 6 j 4Cotyle 8| zJXeftes 6iChous 12 1728^64 576 J4472 1 2 Metretes 4. Roman reduced to Englidi Wine Meafure. Ligula 4 Cyathus I 2 24 48 288 II52 2304 li Acetabulum 2,Q^uartarius 6 4I 2Hemina 12 8! 2 Sextarius 72 48 24 12 288 192! 96' 48; 24 384 192 96' 48 vongius ! 4 Urna 46080 11520 7680I3840 I92oj96oji6o 2 Amphora Culeus 40^0 M E A r- 11 S Solid Grail. 3 . 1 £ inches. o o| 0.177 o o£ 0.211 0 St °-844 1 2 2-533 2 4 5.067 7 4 iJ-2 75 5 7-625 Gal. Pints, g* Dec. n s- 0 TTro- 0.0356-/-JJ re- 0.0712 4 0.089 tre I I '4? 0.17844 o A 0.35644 t °-535 4 o 4 2.141 4 O I 4-283 o 6 25.698 10 2 19.629 Gal. Pints. g-Dec. 0 o-pV 0.117-rV o o o o o o 3 7 I43 oA 0.469 4 o 4 0.704 -4 04 1.40 o 4 2.818 1 5.636 7 4-942 4 4 5-33 1 10.66 Meafure. II.095 IV. Meafurs?^ M E A r 40 ] M E A ‘Meafure. v " IV. Meafures of Capacity for things Dry. 1. ] Eng/ifh dry or corn meafure. The ftandard for meafuring corn, fait, coals, and other dry goods, in England, is the Winchefter gallon, which contains cubic inches. The bufhel contains 8 gallons, or 2178 inches. A cylindrical vcffel, x81-inches diame¬ ter, and 8 inches deep, is appointed to be ufed as a bufhel in levying the malt tax. A velfel of thefe di- menfions is rather lefs than the Winchefter bulhel of 8 gallons, for it contains only 2150 inches; though probably there was no difference intended. The deno¬ minations of dry meafure commonly ufed, are given in the firft: of the fubjoined tables. Four quarters corn make a chaldron, 5 quarters make a xvey or load, and 10 quarters make a ton. In meafuring feacoal, 5 pecks make a bufhel, 9 bufhels made a quarter or vatt, 4 quarters make a chaldron, and 21 chaldrons make a fcore. 40 feet hewn timber make a load. 50 feet unhewn timber make a load. 32 gallons make a herring barrel. 42 gallons make a falmon barrel, i cwt. gunpowder makes a barrel. 2;6 lbs. foap make a barrel. 10 dozen candles make a barrel. 1 2 barrels make a laft. 2. ] Scotch dry meafure. There was formerly only «ne meafure of capacity in Scotland ; and fome com¬ modities were heaped, others fraihed, or meafured ex- a£lly to the capacity of the ftandard. The method of heaping was afterwards forbidden as unequal, and a larger meafure appointed for fuch commodities as that cuftom had been extended to. The wheat firlot, ufed alfo for rye, peafe, beans, fait, and grafs feeds, contains 21 pints 1 mutchkin, meafured by the Stirling jug. The barley firlot, ufed alfo for oats, fruit, and potatoes, contains 31 pints. A difter- ent method of regulating the firlot was appointed from the dimenfions of a cylindrical veffel. The diameter for both meafures was fixed at 19^ inches, the depth 7-f inches for the wheat firlot, and io£ for the barley firlot. A ftandard conftrufled by thefe meafures is rather lefs than when regulated by the pint ; and as it is difficult to make veffels exaftly cylindrical, the regu¬ lation by the pint has prevailed, and the other method gone into difufe. If the Stirling jug contains 103!- inches, the wheat firlot will contain 2109 inches ; which is more than 2 per cent, larger than the legal malt bufhel of England, and about 1 per cent, larger than the Winchefter buthel: and the barley firlot will contain 3208 inches. The barley boll is nearly equal to fix legal malt bufhels. In Stirlingfhire, 17 pecks are reckoned to the boll : in Invernefsfhire, 18 pecks : in Ayr (hire, the boll is the fame as the Englifh quarter. And the firlots, in many places, are larger than the Linlithgow ftandard. 3. ] Trench dry, are, the lition, bufhel, minot, mine, feptier, muid, and tun. The litrou is divided into two demilitrons, and four quarter litrons, and contains 36 , cubic inches of Paris. By ordonnance, the litron is to be three inches and a half high, and three inches Ip lines broad. The litron for fait is larger, and is divided into two halves, four quarters, eight demi- Meafure. quarters, and 16 mefurettes. The French bufhel is different in different jurifdicb'ons. At Paris it is di¬ vided into demibufhels ; each demihufhel into two quarts ; the quart into two half quarts ; and the half quart into two litrons : fo that the bufhel contains 16 litrons. By ordonnance the Paris bulhel is to be eight inches twro lines and a half high, and ten inches broad, or in diameter within-fide. The minot con- fifts of three bufhels, the mine of two minots or fix bufhels, the feptier of two mines or 12 bufhels, and ' the muid of 12 feptiers or 144 bufhels. The bu¬ fhel of oats is eftimated double that of any other grain ; fo that there go 24 bufhels to make the feptier, and 288 to make the muid. It is divided into four pico- tins, tbre picotin containing two quarts, or four litrons. The bufhel forfait is divided into two half bufhels, four quarters, eight half quarters, and 16 litrons ; four bu¬ fhels make a minot, 16 a feptier, and 192 a muid. The bufhel for wrood is divided into halves, quarters, and half quarters. Eight bufhels make the minot, 16 a mine; 20 mines or 320 bufhels, the muid. For plafter, 12 bulhels make a fack, and 36 lacks a muid. For lime, three bufhels make a minot, and 48 minots a muid. The minot is by ordonnance to be 11 inches 9 lines high, and 14 inches 8 lines in diameter. The minot is compofed of three bufhels, or 16 litrons i four minots make a feptier, and 48 a muid. The French mine is no real veffel, but an eftimation of fe- veral others. At Paris the mine contains fix bufhels, and 24 make the muid ; at Rouen the mine is four bu¬ fhels; and at Dieppe 18 mines make a Paris muid. The feptier differs in different places: at Paris it con¬ tains two mines, or eight bufhels, and 12 feptiers the muid. At Rouen the feptier contains two mines or 1 2 bulhels. Twelve feptiers make a muid at Rouen as well as at Paris ; but 12 of the latter are equal to 14 of the former. At Toulon the feptier contains a mine and a half; three of which mines make the feptier of Pa ris. The muid or muy of Paris confifts of 1 2 feptiers; and is divided into mines, minots, bufhels, &c. That for oats is double that for other grain, i. e. contains twice the number of bulhels. At Orleans the muid is divided into mines, but thofe mines only contain two Paris feptiers and a half. In fome places they ufe the tun in lieu of the muid ; particularly at Nantes, where it contains 10 feptiers of 16 bulhels each, and weighs between 2200 and 2250 pounds. Three of thefe tuns make 28 Paris feptiers. At Rochelle, &c. the tun con¬ tains 42 bufhels, and weighs two per cent, lefs than that of Nantes. At Breft it contains 20 bufhels, is equal to 10 Paris feptiers, and weighs about 2240 pounds. See Tun. 4.3 Dutch, Swedifj, Po/i/7j, Pruffian, and Mufcovite. In thefe places, they eftimate their dry things on the foot of the la/l, lefl, leth, or /edit; fo called according to the various pronunciations of the people who ufe it. In Holland, the laft is equal to 19 Paris feptiers, or 38 Bourdeaux bufhels, and weighs about 4560 pounds ; the laft: they divide into 27 mudes, and the mude into four fcheples. In Poland, the laft is 40 Bourdeaux bufhels, and weighs about 4800 Paris pounds. In Pruffia, the laft is 133 Paris feptiers. In Sweden and Mufcovy they meafure by the great and little laft ; the firft con¬ taining 12 barrels, and the fecond half as many. See Last. -MEA [41] ME ^u'"c?v^1 t)le)r likewife ufe the cliefford, fevcnths, or I y I tomoli and three Yvhicn is different in various places : that of Archangel A fevenths, make the Me a fare. is equal to three Rouen bufhels. 5.] Italian. At Venice, Leghorn, and Lucca, they eflimate their dry things on the foot of the ftaro or ifaio 5 the ftaro of Leghorn weighs 54 pounds: 112 ftaros and feven-eighths are equal to the Amfterdam laft. At Lucca, 119 ftaros make the laft of Amfterdam. The Venetian ftaro weighs 1 28 Paris pounds: the ftaro is divided into four quarters. T hirty-five ftaros and one-fifth, or 140 quarters and four-fifths, make the laft of Amfterdam. At Naples and other parts, they ufe the tomolo or tomalo, equal to one-third of the Paris fep- tier. Thirty-fix tomoli and a half make the carro, and a carro and a half, or 54 tomoli, make the laft of Am¬ fterdam. At Palermo, 16 tomoli make the falma, and four mondili the tomolo* Ten falmas and three- laft of Amfterdam. _ 6.] Flemijh. At Antwerp, &c. they meafure by the viertel; 3 2 and one-half whereof make 19 Paris fep- tiers. At Hamburgh, the fchepel j 90 whereof make 19 Paris feptiers. 7.] Spanifh and Portuguefe. At Cadiz, Bilboa, and St Sebaftian, they ufe the fanega; 23 whereof make the Nantes or Rochelle tun, or nine Paris feptiers and a half: though the Bilboa fanega is fomewhat larger, infomuch that 21 fanegas make a Nantes tun. At Se¬ ville, &c. they ufe the anagoras, containing a little more than the Paris mine j 36 anagoras make J9 Paris fep¬ tiers. At Bayonne, &c. the concha j 30 whereof are equal to nine Paris feptiers and a half. At Lifbon, the alquiver, p very fmall meafure, 240 whereof make 19 Paris fepliers, 60 the Lifbon muid. Tables of Dry Meafure. 1. English. 2. Scripture Dry, reduced to Englifh. fT O o o O ►d ^ 5* 0 024 0 5 tV I O I 303 16 o o 32 o I « 0.031 0.073 1.211 4.O36 12.107 26.5OO 28.969 Vol. XIII. Parti. F 3. Attic Meafure. M E A [ 42 ] M E A 3. Attic Meafures of Capacity for Things dry, reduced to EnglKh Corn Meafure. Cochliarion xoCyathos 60 120 180 i Oxybaphon 12 4|Cotyle 21Xeft.es 8 18 12 8640 864! 576 i4 144 72 Choenix Medimnos 48 4. Roman Meafures of Capacity for Things dry, reduced to Englifh Corn meafure. Ligula Cyathus " 1-ij Acetabulum - " * Hemina 24 48 384 768 96 192 64 128 16 32 Sextarius Semimodius 2 Modius 16 n o f’T' O o o o o o ^ EL p g5 O ^ o £L 3* r- r ( : o o o^- o o 0TXT O O O -g- O 08-!- OOI OIO IOO 0.276x3- 2.763 i 4.144 { 16-579 I5-7°5 i 3-Soi C/3 •£'0 . o D O O * pr O.OI O.04 O.06 O.24 O.48 3-84 7.68 Meafure. Measure of Wood for Firing, is ufually the cord four feet high, and as many broad, and eight long this is divided into two half cords, called ways, and by the French membrures, from the pieces ftuck up¬ right to bound them ; or mijes, as being fuppofed half a waggon load. Measure for Horfes, is the hand, which by ftatute contains four inches. Measure, among Botanifs. In defcribing the parts of plants, Tournefort introduced a geometrical fcale, which many of his followers have retained. They mea- fured every part of the plant 5 and the effence of the defcription conftfted in an accurate menfuration of the whole. T As the parts of plants, however, are liable to va¬ riation in no circumftance fo much as that of dimen- fion, Linnaeus very rarely admits any other raenfura- tion than that arihng from the refpeftive length and breadth of the parts compared together. In cafes that require adlual menfuration, the fame author re¬ commends, in lieu of Tournefort’s artificial fcale, the following natural fcale of the human body, which he thinks is much more convenient, and equally ac¬ curate. The fcale in queftion confifts of 11 degrees, which are as follow : 1. A hair’s breadth, or the diameter of a hair, [capi/lus'). 2. A line, {lined), the breadth ©f the crelcent or white appearance at the root of the. finger (not thumb), meafured from the fkin towards' the body of the nail 5 a line is equal to 12 hair¬ breadths, and is the I2th part of a Parifian inch. 3. A nail {unguis), the length of a finger nail j equal to fix lines, or half a Parifian inch. 4. A thumb {pol- lex), the length of the firft or outermoft joint of the thumb equal to a Parifian inch. 5. A palm (pal- snus), the breadth of the palm exclufive of the thumb equal to three Parifian inches. 6. A fpan (fpithama) the diftance between the extremity of the thumb and that of the firft finger when extended equal to feven Parifian inches. 7. A great fpan (dodrans), the di¬ ftance between the extremity of the thumb and that of the little finger, when extended j equal to nine inches. 8. A foot (pel), meafuring from the elbow to the bafis of the thumb j equal to i 2 Parifian inches. 9. A cubit (cubitus), from the elbow to the extre¬ mity of the middle finger j equal to 17 inches. 10. An arm length (brachium), from the armpit to the extre¬ mity of the middle finger 5 equal to 24 Parifian inches, or two feet. 11. A fathom (orgya), the meafure of the human ftature ; the diftance between the extremities of the two middle fingers, wdten the arms arc extended j equal, where greateft, to fix feet. Measure is alfo ufed to fignify the cadence and time obferved in poetry, dancing, and mufic, to render them regular and agreeable. The different meafures or metres in poetry, are the different M E A [ 43 ] M E A Meafm-e. different manners of ordering and combining tlie quan- —-v tides, or the long and ffiort fyllables. Thus, hexame¬ ter, pentameter, iambic, fapphic verfes, &c. conhft of different meafures. In Englith verfes, the meafures' are extremely vari¬ ous and arbitrary, every poet being at liberty to intro¬ duce any new form that he pleafes. The moft ufual are the heroic, generally confifting of five long and five fhort fyllables *, and verfes of four feet j and of three feet and a caefura, or fingle fyllable. The ancients, by varioufly combining and tranfpof- ing their quantities, made a vaft variety of different meafures. Of words, or rather feet of two fyllables, they formed a fpondee, confifting of two long fyllables j a pyrrhic, of two fhort fyllables •, a trochee, of a long and a ftiort fyllable ; and an iambic, of a fhort and a long fyllable. Of their feet of three fyHables they formed a mo- loffus, confifting of three long fyllables ; a tribrach, of three fhort fyllables •, a dadtyl, of one long and two fhort fyllables *, and an anepEeft, of two ftiort and one long fyllable. The Greek poets contrived 124 dif¬ ferent combinations or meafures, under as many dif¬ ferent names, from feet of two fyllables to thofe of fix. Measure, in Mujtc, the interval or fpace of time which the perfon who beats time takes between the rifing and falling of his hand or foot, in order to con- dudt the movement, fometimes quicker, and fometimes flower, according to the kind of mufic, or the fubjedl that is fung or played. The meafure is that which regulates the time we are to dwell on each note. See Time. The ordinary or common meafure is one fecond, or 60th part of a minute, which is nearly the fpace be¬ tween the beats of the pulfe or heart; the fyftole, or contraction of the heart, anfwering to the elevation of the hand 5 and its diaftole, or dilatation, to the letting it fall. The meafure ufually takes up the fpace that a pendulum of two feet and a half long employs in making a fwing or vibration. The meafure is regu¬ lated according to the different quality or value of the notes in the piece by which the time that each note is to take up is expreffed. The femibreve, for inftance, holds one rife and one fall; and this is called the meafure or ’whole mca/ure, fometimes the meafure note, or time note; the minim, one rife, or one fall \ and the crotchet, half a rife, or half a fall, there being four crotchets in a full meafure. Measure Binary, or Double, is that wherein the rife and fall of the hand are equal. Measure Ternary, or Triple, is that wherein the fall is double to the rife j or where two minims are played during a fall, and but one in the rife. To this pur- pofe, the number 3 is placed at the beginning of the lines, when the meafure is intended to be triple 5 and a C, when the meafure is to be common or double. This rifing and falling of the hands was called by the Greeks and 9-e«f. St Auguftine calls it plaufus, and the Spaniards compos. See Arsis and Thesis. Powder Measures in Artillery, are made of copper, and contain from an ounce to 12 pounds : thefe are very convenient in a fiege, when guns or mortars are loaded with loofe powder, efpecially in ricochet firing, Meafunng, &c. , Meat- , MEASURING, or Mensuration, is the ufing ~v'~’ a certain known meafure, and determining thereby the precife extent, quantity, or capacity of any thing. Measuring, in general, includes the praCHcal part / of geometry. From the various fubjeCts on which it is employed, it acquires various names, and conftitutes various arts. See Geometry, Levelling, Mensu¬ ration, Trigonometry, &c. MEAT. See Food, Diet, Drink, &c. Amongft the Jews, feveral kinds of animals wrere forbidden to be ufed as food. The flcfti with the blood, and the blood without the, flefh, were prohibit¬ ed ; the fat alfo of facrificed animals was not to be eaten. Roaft meat, boiled meat, and ragouts, were in ufe among the Hebrews, but w^e meet wfith no kind of feafoning except fait, bitter herbs, and honey.— They never mingled milk in any ragout or hafh, and never ate at the fame meal both meat and milk, butter, or cheefe. The daily provifion for Solomon’s table wTas 30 meafuies of fine wheat flour, 60 of common flour, 10 fat oxen, 20 pafture oxen, 100 ftieep, be- fides venifon and wildfowd. See Luxury. The principal and moft neceffary food among the ancient Greeks, was bread, which they called and produced in a wicker bafket called r.anov. Their loaves w7ere fometimes baked under the allies, and fometimes in an oven. They alfo u!ed a fort of bread called ma%a. Barley meal w'as ufed amongft the Greeks, which they called xytpflov. They had a fre¬ quent difti called fJ^uv, wffich was a compofition of rice, cheefe, eggs, and honey, wrapped in fig-leaves. The MvrrdJoy was made of cheefe, garlic, and eggs, beaten and mixed together. Their bread, and other fubftitutes for bread, were baked in the form of hol¬ low plates, into w'hich they poured a fauce. Garlic, onions, and figs, feem to have been a very common food amongft the poorer Athenians. The Greeks, cfpecially in the heroical times, ate flefli roafted ; boil¬ ed meat feldom wyas ufed. Fifti feems not to have been ufed for food in the early ages of Greece. The young people only, amongft the Lacedemonians, ate animal food j the men and the old men were fupport- ed by a black foup called ftsyx which to people of other nations was always a difagreeable mefs. Grafs- hoppers and the extremities or tender fhoots of trees w^ere frequently eaten by the poor among the Greeks. Eels dreffed with beet root were efteemed a delicate dilh, and they were fond of the jowd and belly of falt- fifh. Neither were they without their fweet-meats j the deffert confifted frequently of fruits, almonds, nuts, figs, peaches, &c. In every kind of food we find fait to have been ufed. The diet of the firft Romans confifted wholly of milk, herbs, and roots, which they cultivated and. dreffed with their own hands j they alfo had a kind of gruel, or coarfe grofs pap, compofed of meal and boiling water ; this ferved for bread : And when they began to ufe bread, they had none for a great while but of unmixed rye. Barley-meal was eaten by them, w'hich they called Polenta. When they began to eat animal food, it was efteemed a piece of luxury, and an indulgence not to be juftified but by fome particu- F 2 Jar M E A [ 44 ] ‘ M E A lar occafion. After animal food had grown into com¬ mon ufe, the meat which they moft frequently produced upon their tables was pork. Method of Prefsrvitig F/eJh-MEAT without fpices, ttnd with venj little fait. Jones, in his Mifcellanea __ Cunofa, gives us the following defcription of the Moorilh Elcholle, which is made of beef, mutton, or camel’s flelh, but chiefly beef, which is cut in long flices, and laid for 24 hours in a pickle. They then remove it out of thofe jars or tubs into others with water; and when it has lain a night, they take it out, and put it on ropes in the fun and air to dry. When it is thoroughly dried and hard, they cut it into pieces of two or three inches long, and throw it into a pan or caldron, which is ready with boiling oil and fuet fufficient to hold it, where it boils till it be very clear and red wdien cut. After this they take it out, and fet it to drain $ and when all is thus done it Hands to cool, and jars are prepared to put it up in, pouring upon it the liquor in which it was fried 5 and as foon as it is thoroughly cold, they Hop it up clofe. It will keep two years ; will be hard, and the hardeft they look upon to be the befl: done. This they dilh up cold, fometimes fried with eggs and garlic, fometimes Hewed, and lemon fqueezed on it. It is very good any way, cither hot or cold. MEATH, commonly fo^ called, or otherwife Eajl Meath, to diftinguifli it from the county called Wejl Meath : A county of Ireland, in the province of Leinfler, bounded by the counties of Cavan and Louth on the north, the Irifh channel on the eafl, Kildare and Dublin on the fouth, and WeH Meath and Long¬ ford on the wefl. It is a fine champaign country, abounding with corn, and well inhabited. It returns 14 members to parliament 5 and gives title of earl to the family of Brabazan. It contains 326,480 Irifii plantation acres, 139 pariflies, 12 baronies, and fix boroughs ; chief town, Trim. This diflria being the moH ancient fettlement of the Belgians in Ireland, the inhabitants were efieemed the eldefi and moH honour¬ able tribe : from which feniority their chieftans were eledled monarchs of all the Belgse ; a dignity that was continued in the Hy-n-Faillian without intermiflion. until the arrival of the Caledonian colonies, under the name of Tuath de Danan, when Conor-Mor, chief- tan of thefe people, obtained, or rather ufurpecl, the monarchial throne, obliged Eochy Failloch, with fe- veral of his. people, to crofs the Shannon, and eflablifli themfelves in the prefent county of Rofcommon, where Crothar founded the palace of Atha or Croghan, a circumHance which brought on a long and bloody war between the Belgian and Caledonian races, which was not finally terminated until the clofe of the 4th cen¬ tury, w'hen the Belgian line was rcHored in the perfon of O’Nial the Great, and continued until Briam Bo- romh ufurped the monarchial dignity, by depofing Malachy O’Malachlin, about the year 1001. Tuathal Tet&homar, by a decree of the Tarah affembly, fepa- rated certain large trails of land fr om each of the four provinces, where the borders joined together 5 whence under the notion of adopting this fpot for demefne lands to fupport the royal houfehold, he formed the county or kingdom of Meath, which afterwards be¬ came the peculiar inheritance of the monarchs of Ire¬ land. In each of the portions thus feparated from the four provinces, Tuathal caufed palaces to be ereff- Meath, ed, which might adorn them, and commemorate the v~~ name in which they had been added to the royal do¬ main. In the traft taken out of Munfier, he built the palace called Fkchtaga, where the facred fire, fo cabed, w’as kindled, and w here all the priefls and druids annually met on the lafi day of October j on the evening of which day it was enaded, that no other fire flrould be ufed throughout the kingdom, in order that all the fires might be derived from this, which being lighted up as a fire of facrifice, their fuperflition led them to believe would render all the reit propitious and holy j and for this privilege every family wTas to pay three¬ pence, by way of acknowledgment to the king of MunHer. The fecond royal palace was ereded in the proportion taken out of Connaught, and was built for the affembly called the convocation of Vifneach, at w'hich all the inhabitants were fummoned to appear on the iH day of May, to offer facrifice to Beal, or Bel, the god of fire, in whore honour two large fires being kindled, the natives ufed to drive their cattle between them, which w’as fuppofed to be a prefervative for them againfi accidents and diflempers, and this was called Beal-Tinne, or Bel-Tine, or the feffival of the god of fire. The king of Connaught at this meeting claimed a horfe and arms from every lord of a manor or chieftan, as an acknowledgement for the lands ta¬ ken from that province, to add to the territory of Meath. *1 he third was that which 1 ailtean ereded in the part taken from Ulfler, where the fair of that name was held, w’hich w’as remarkable for this parti¬ cular circumHance, that the inhabitants brought their children thither, males and females, and contraded them in marriage, where the parents having agreed upon articles, the young people were joined according¬ ly 5 every couple contraded at this meeting paid the king of Ulfler an ounce of filver by way of acknow'- ledgement. The royal manfion of Tarah, formerly deflroyed. by fire, being rebuilt by Tuathal, on the lands originally belonging to the king of Leinfler, was reckoned as the fourth of thefe palaces ; but as a fa¬ bric of that name had flood there before, we do not find that any acknowledgement was made for it to the king of Leinfter. Meath, with Clonmacnois, is a bi(hop’s fee, valued in the king’s books at 3731. 7s. o^d. fterling, by an ex¬ tent returned anno 28th Elizabeth ; but," by a former extent taken anno 30th Henry VIII. the valuation a- mounts to 373I. 12s. which being the largeft and moft profitable for the king, is the meafure of the firft fruits at tnis day. This lee is reputed to be worth annually 3400!. 1 here w^ere formerly many Epif- copal fees in Meath, as Clonard, Duleek, Kells, Trim, Ardbraccan, Donlhaghlin, Slaine, and Foure, befides other* of lefs note 5 all thefe, except Duleek and Kells, were confolidated, and their common fee was fixed at Clonard, before the year 1152 ; at which time the divifions of the bilhoprics in Ireland were made by John Paparo, cardinal prieft, entitled Cardinal of St Lawrence in Damafo, then legate from Pope Eu¬ gene III. to the Irith. This divifion was made in a lynod held on the 6th of March in the abbey of Mel- lifont, or, as fome fay, at Kells : and the two fees of Duleek and Kells afterwards fubmitted to the fame fate. The conftitution of this diocefe is Angular, hav- tng M E C [ 45 ] MEG Meath ing no dean nor chapter, cathedral, or economy.— H Under the bifliop, the archdeacon is the head officer, to ,Meca;nas. ^ w],orn> anej to tJie dergy in general, the conge d"1 ehre iffued while biffiops were elective. The affairs of the diocefe are tranfafled by a fynod, in the nature of a chapter, who have a common feal, which is annually lodged in the hands of one of the body, by the ap¬ pointment and vote of the majority. The diocefe is divided into twelve rural deaneries. Of Clonmacnojs, now annexed to Meath : There is no valuation of this fee in the king’s books j but it is fuppofed to be included in the extent of the fee of Meath, taken anno 30th Henry VIII. The chapter of this fee conliffed anciently of dean, chanter, chan¬ cellor, treafurer, archdeacon, and twelve prebendaries, but tnoft of their poffeffions have fallen into lay hands. At prefent the deanery is the only part of the chapter which fublifts, to which the prebend of Cloghran is annexed, and he hath a feal of office, which appears to have been the ancient epifcopal feal of this fee. This fee was founded by St Kiaran, or Ciaran, the younger, in 548 or 549 5 and Dermod, the fon of Ceronill, king of Ireland, granted the lite on which the church was built. Wef Meath. See Westmeith. MEATUS auditorius. See Anatomy, N° 144. MEAUX, an ancient town of France, in the de¬ partment of the Seine and Marne, with a biffiop’s fee, feated in a place abounding in corn and cattle, on the river Marne, which divides it into two parts j and its trade confifts in com, wtoo1, and cheefe. It fuftained a liege of three months againft the Engliffi in 1421. E. Long. 2. 58. N. Lat. 48. 58. MECAiNAS, or Mecoenas, C Cilnius, a cele¬ brated Roman knight, defcended from the kings of Etruria. He has rendered himfelf immortal by his liberal patronage of learned men and of letters ; and to his prudence and advice Auguftus acknowledged him¬ felf indebted for the fecurity he enjoyed. His fond- nefs for pleafure removed him from the reach of ambi¬ tion $ and he preferred dying, as he was born, a Ro¬ man knight, to all the honours and dignities which either the friendthip of Auguflus or his own popularity could heap upon him. To the interference of Mecaenas, Virgil owed the retribution of his lands ■, and Horace was proud to boall that his learned friend had obtain¬ ed his forgivenefs from the emperor, for joining the caufe of Brutus at the battle of Philippi. Mecaenas was himfelf fond of literature : and, according to the mod received opinion, he wmote a hiftory of animals, a journal of the life of Auguitus, a treatile on the different natures and kinds of precious ftones, belides the tw'o tragedies of Oftavia and Prometheus, and other things, all now loft. He died eight years be¬ fore Chrift •, and on his deathbed he particularly re¬ commended his poetical friend Horace to the care and confidence of Auguftus. Seneca, who has liberally commended the genius and abilities of Mecaenas, has not withheld his cenfure from his diffipation, indolence, and effeminate luxury. From the patronage and en¬ couragement which the princes of heroic and lyric poetry among the Latins received from the favourite of Auguftus, all patrons of literature have ever fince been called Mecccnates. Virgil dedicated to him his Geor¬ gies, and Horace his Odes. MECCA, an ancient and very famous town of Afia, Mecca., in Arabia Felix j feated on a barren fpot, in a valley furrounded with little hills, about a day’s jour¬ ney from the Red fea. It is a place of no ftrength, having neither walls nor gates *, and the buildings are very mean. That which lupports it is the refort of a great many thoufand pilgrims annually, for the ffiops are fcarcely open all the year befides. The inhabitants are poor, very thin, lean, and fwarthy. The hills about the town are very numerous; and confift of a blackiih rock, feme of them half a mile in circumfe¬ rence. On the top of one of them is a cave, where they pretend Mahomet ulually retired to perform his devotions, and hither they affirm the greateft part of the Alcoran was brought him by the angel Gabriel. The town has plenty of water, and yet little garden- fluff ; but there are feveral forts of good fruits to be had, fuch as grapes, melons, w ater melons, and cucum¬ bers. There are alfo plenty of ftreep brought thither to the fold to the pilgrims. It ftands in a very hot cli¬ mate ; and the inhabitants ufually fleep on the tops of their houfes for the fake of coolneis. In order to pro¬ tect themlelves from the heat through the day, they carefully ftmt the windows, and water the ftreets to re- frelh the air. There have been inftanees of perfons fuf- focated in the middle of the town by the burning wind called Simoom. As a great number of the people of diftindlion in the province of Hedsjas flay in the city, it is better built than any other in Arabia. Arnongft the beauti¬ ful edifices it contains, the moft remarkable is the fa¬ mous Kaba or Caaba, “ The houfe of God,” which was held in great veneration by the Arabs even before Mahomet’s time. No Chriflian dare go to Mecca ; not that the ap¬ proach to it is prohibited by any exprefs lawr, or that the fenfible part of the Mahometans have any thing to objeifl: to it ; but on account of the prejudices of the people, who regarding this ground as facred, think Chriflians unworthy of fetting their foot on it; it would be profaned, in the opinion ©f the fuperftiti- ous, if it wTas trod upon by infidels. The people even believe, that Chriftians are prevented from approach- ing by fome fupernatural power; and they tell tire ftory of an infidel, who having got fo far as the hills that furround Mecca, all the dogs of the city came out, and fell upon him ; and who, being flruck with this miracle, and the auguft appearance of the Kaba, immediately became a muffulman. It is therefore to be prefumed that all the Europeans who deferibe Mecca as eye-witneffes, have been renegadoes efcaped from Turkey. A recent example confirms this fuppo- fiticn. On the promife of being allowed to preferve his religion, a French furgeon was prevailed on to ac¬ company the Emir Hadsji to Mecca, in quality of phy- fician ; but at the very firft ftation, he was forced to fubmit to circumcifion, and then he was permitted to continue his journey. . Although the Mahometans do not allovr Europeans to go to Mecca, they do not refufe to give them de- feriptions-of the Kaba, and information with regard to that building •, and there are perfons who gain their bread by making defigns and little piftures of the Kaba, and felling them to pilgrims. See Caaba. The Mahometans have fo high an opinion of the fanftity y M EC [ 46 1 M E C 'Mecca, fan&ity of Mecca, that they extend it to the places v * in the neighbourhood. The territory of that city is held facred to certain diftances, which are indicated by particular marks. Every caravan finds in its road a fimilar mark, which gives notice to the pilgrims when they are to put on the modeft garb in which they mult appear in thole facred regions. Every muflulman is • obliged to go once in his life, at lealt, to Mecca, to perform his devotions there. If that law was rigour- oufiy enforced, the concourfe of pilgrims wTould be prodigious, and the city would never be able to con¬ tain the multitudes from all the countries where the Mahometan religion prevails. We mull therefore, fuppofe, that devotees alone perform this duty, and that the others can eafily difpenfe with it. Thofe whofe circumftances do not permit a long abfence, have the liberty of going to Mecca by a fubftitute.— A hired pilgrim, however, cannot go for more than one perfon at a time ; and he muft, to prevent frauds, bring an atteftation in proper form, from an Imam of Mecca, that he has performed the requifite devotions on behalf of fuch a perfon, either alive or dead 5 for, after the deceafe of a perfon who has not obeyed the law7 during his life, he is Hill obliged to perform the journey by proxy. The caravans, which are not numerous, when we -confider the immenfe multitude of the faithful, are compofed of many people who do not make the jour¬ ney from purpofes of devotion. Thefe are merchants, w?ho think they can tranfport their merchandifes with more fafety, and difpofe of them more eafily; and contratlors of every kind, w7ho furnilh the pilgrims and the foldiers w'ho efcort the caravans, with necefla- ries. Thus it happens, that many people have gone often to Mecca, folely from views of intereft. The ■noil confiderable of thofe caravans is that of Syria, commanded by the pacha of Damafcus. It joins at fome diftance the fecond from Egypt, which is con¬ duced by a bey, who takes the title of Emir Hadsji. One comes from Yemen, and another, lefs numerous, from the country of Lachfa. Some fcattered pilgrims arrived by the Red fea from the Indies, and from the Arabian eftablilhments on the coaits of Africa. The Perfians come in that which departs from Bagdad 5 the place of conduCor to this lalt is bellowed by the pacha, and is very lucrative, for he receives the ranfoms of the heretical Perfians. It is of confequence to a pilgrim to arrive early at the holy places. Without having been prefent from the beginning at all the ceremonies, and without hav¬ ing performed every particular aC of devotion, a man cannot acquire the title of Hadsji : this is an honour very much coveted by the Turks, for it confers real advantages, and makes thofe who attain it to be much refpeCed. Its infrequency, however, in the Maho¬ metan dominions, (hows how much the obfervation of the law commanding pilgrimages is negleCed. A fi¬ milar cuftom prevails among the Oriental Chriftians, who are alfo exceedingly emulous ot the title of Hadsji, or Mokdafi, which is given to pilgrims of their com¬ munion. In order to acquire this title, it is not fuffi- cient that the perfon has made the journey to Jerufa- lem *, he mult alfo have kept the paffover in that city, and have alfilted at all the ceremonies of the holy wTeeks. After all the eflential ceremonies are over, the pil- Mecliani- grims next morning move to a place where they fay cal- Abraham went to olier up his fon Ifaac, which is " about tw7o or three miles from Mecca : here they pitch their tents, and then throw feven fmall Hones againft a little fquare Hone building. This, as they affirm, is performed in defiance of the devil. Every one then purchafes a Iheep, which is brought for that purpofe, eating fome of it themfelves, and giving the reit to the poor people who attend upon that occafion. Indeed thefe are miferable objefts, and iuch ftarved creatures, that they feem ready to devour each other. After all, one would imagine that this was a very fandlified place j and yet a renegado who w7ent in pilgrimage thither, affirms there is as much debauchery pradtifed here as in any part of the Turkilh dominions. It is 25 miles from Jodda, the lea port town of Mecca, and 220 fouth-eaft of Medina. E. Long. 40. 55. N. Lat. 21. 45. MECHANICAL, an epithet applied to whatever relates to mechanics : Thus we fay, mechanical powers, caufes, &c. See the articles Power, Cause, &c. The mechanical philofophy is the fame with what is otherwife called corpufcular philofophy^ which explains the phenomena of nature, and the operations of corpo¬ real things, on the principles of mechanics, viz.; the motion, gravity, arrangement, difpofition, greatnefs or fmallneis, of the parts which compofe natural bodies. See Corpuscular. This manner of reafoning is much ufed in medicine ; and, according to Dr Quincy, is the refult of a tho¬ rough acquaintance with the ftructure of animal bo¬ dies : for confidering an animal body as a compofition out of the fame matter from which all other bodies are formed, and to have all thofe properties which concern a phyfician’s regard, only by virtue of its peculiar con- ftrudion ; it naturally leads a perfon to confider the feveral parts, according to their figures, contexture, and ufe, either as wheels, pulleys, w7edges, levers, fcrew'S, cords, canals, llrainers &c. For which pur¬ pofe, continues he, it is frequently found helpful to defign in diagrams, wffiatfoever of that kind is under conlideration, as is cuftomary in geometrical demonftra- tions. For the application of this dodrine to the human body, fee the article Medicine. Mechanical, in mathematics, denotes a conftruc- tion of fome problem, by the affilfance of indruments, as the duplicature of the cube and quadrature of the cir¬ cle, in contfadiftindion to that which is done in an ac¬ curate and geometrical manner. Mechanical Curve, is a curve, according to Defcartes, which cannot be defined by any algebraic equation \ and fo Hands contradiHinguiHied from algebraic or geo¬ metrical curves. ‘ Leibnitz and others call thefe mechanical curves tranfcendental, and diffent from Defcartes, in excluding them out of geometry. Leibnitz found a new kind of tranfcendental equations, whereby thefe curves are de¬ fined : but they do not continue conHantly the fame in all points of the curve, as algebraic ones do. See the article Transcendental. Mechanical Solution of a problem is either when the thing is done by repeated trials, or when lines ufed in V. MEC [47] MEC Meeliant- in the folution are not truly geometrical, or by organ!- which are tiled for raifmg greater Weights, or over- Meeham. cal- cal conftru£tion. coming greater refiftances, than could be elxeaed by, ^ ' , 1 ^ ' Mechanical Powers, are certain Ample machines, the natural ftrength without them. See Mechanics. MECHANICS. Definition, i. TV TECHANICS is the fcience which enquires into 1-Vx t]le iaws 0f the equilibrium and motion of folid bodies j into the forces by which bodies, whether ani¬ mate or inanimate, may be made to a£l upon one ano¬ ther ; and into the means by which thefe may be in- creafed fo as to overcome fuch as are more powerful.— The term mechanics was originally applied to. the doc¬ trine of equilibrium. It has by feme late writers been extended to the motion and equilibrium of all bodies, whether, folid, fluid, or aeriform ; and has been employ¬ ed to comprehend the fciences of hydrodynamics and pneumatics. EIISTORY. Proorefsof 2* -^s t^e k^ence mec^anics *s intimately con- praftical netted with the arts of life, and particularly with thofe mechanics which exift even in the rudeft ages of fociety, the con- among the ftruction 0f machines mull have arrived at conliderable ancients. perfe&ion before the theory of equilibrium, or the limpled properties of the mechanical powers, had en¬ gaged the attention of philofophers. We accordingly find that the lever, the pulley, the crane, the capftan, and other Ample machines, w'ere employed by the an¬ cient architects in elevating the materials of their buildings, long before the dawn of mechanical fcience ; and the military engines of the Greeks and Romans, fuch as the catapultce and baliftce, exhibit an extenfive acquaintance with the conftruftion of compound ma¬ chinery. In the fplendid remains of Egyptian architec¬ ture, which in every age have excited the admiration of the world, we perceive the moft furpriAng marks of mechanical genius. The elevation of immenfe maffes of ftone to the tops of their ftupendous fabrics mult have required an accumulation of mechanical power which is not in the pofteffion of modern architefts. Ariftotle 3* The earlieft traces of any thing like the theory of the firft mechanics are to be found in the waitings of Ariftotle. who at- ln fome 0f fiis works we difeover a few erroneous and the^tlf1 r r °bfcure opinions, refpe&ing the doclrine of motion, and ofmecha- tf16 nature of equilibrium *, and in his 7.8th mechanical nics. queftion he has given fome vague obfervations on the JB. C. 32c. force of impulfe, tending to point out the difference be¬ tween impulfe and preflure. Ele maintained that there cannot be two circular meftions oppolite to one another •, that heavy bodies defeended to the centre of the uni- verfe, and that the velocities of their defeent were pro¬ portional to their weights. 4. The notions of Ariftotle, however, were fo con- hr-s tl™6 eSfu^ed and erroneous, that the honour of laying the foun- foundation dation of theoretical mechanics is excluftvely due to the of theoreti- celebrated Archimedes, w'ho, in addition to his inven- cal media- t;ons jn geometry, difeovered the general principles of "1CS‘ 2,q hydroftaties. In his two books, De Equiponcierantibus, J he has demonftrated that when a balance with unequal arms, is in equilibrio, by means of two weights in- its oppofite feales, thefe weights muft be reciprocally pro¬ portional to the arms of the balance. From this gene¬ ral principle, all the other properties of the lever, and of machines referable to the lever, might have been deduced as corollaries •, but Archimedes did not follow the difeovery through all its confequerices. In de- f monftrating the leading property of the lever, he lays it down as an axiom, that if the two arms of the ba¬ lance are equal, the two weights muft alfo be equal when an equilibrium takes place j and then (hows that if one of the arms be increafed, and the equilibrium ftill continue, the weight appended to that arm muft be proportionally diminilhed. This important difeovery condudled the Syracufan philofopher to another equally ufeful in mechanics. Reflefting on the conftruftion of his balance, which moved upon a fulcrum, he perceived that the two weights exerted the fame preffure on the fulcrum as if they had both refted upon it. He then conftdered the fum of thefe two weights as combined with a third, and the fum of thefe three as combined with a fourth 5 and faw that in every fuch combination the fulcrum muft fupport their united weight, and there¬ fore that there is in every combination of bodies, and in every Angle body which may be conceived as made up of a number of leffer bodies, a centre of prejfure or gravity. This difeovery Archimedes applied to par¬ ticular cafes, and pointed out the method of Anding the centre of gravity of plane furfaces, whether bounded by a parallelogram, a triangle, a trapezium or a parabola. The theory of the inclined plane, the pulley, the axis in peritrochio, the ferew, and the wedge, which was Arft publilhed in the eighth book of Pappus’s mathematical colledtions, is generally attributed to Archimedes. It appears alfo from Plutarch and other ancient authors, that a greater number of machines which have not reached our times was invented by this philofopher. The military engines which he employed in the Aege of Syracufe againft: tbofe of the Roman engineer Ap- pius, are faid to have difplayed the greateft mechanical genius, and to have retarded the capture of his native city. 5. Among the various inventions which we have re-invent;ofi ceived from antiquity, that of water mills is entitled to of water the higheft place, whether we conAder the ingenuitynu'-1 HtKj which they difplay, or the ufeful purpofes to which w‘rcl they are fubfervient. In the infancy of the Roman re¬ public the corn was ground by hand-mills conAftlng of two millrtones, one of which was moveable, and the other at reft. The upper millftone was made to revolve either by the hand applied direftly to a winch, or by means of a rope winding round a capftan. The precife time when the irnpulfe or the weight of water 'was fub- ftituted in'the place of animal labour, is not exaflly known. From an epigram in the Anihologia Grceca there is reafon to believe that water mills were invented during the reign of Auguftus-j but it is ftrange that in the- 45 Hifiorv. PtevimiS d fcovers the paral- leiogram of forces. Died in ^3S- tl>e description given of them by Vitruvius, who lived under that emperor, they are not mentioned as of re¬ cent origin. The invention of wind mills is of a later date. According to fome authors, they were firll ufed in trance in the lixth century j while others maintain that they were brought to Europe in the time of the crufades, and that they had long been employed in the eaft, where the icarcity of water precluded the applica¬ tion of that agent to machinery. 6. ihe fcience of mechanics feems to have been fta- tionary till the end of the i6th century. In 1577 a ■treatile on mechanics was publifhed by Guidus Ubal- ,dus, but it contained merely the difeoveries of Archi¬ medes. Simon Stevinus, however, a Dutch mathe¬ matician, contributed greatly to the progrefs of the fcience. Ele difeovered the parallelogram of forces ; and has demonilrated in his Statics, publilhed in 1386, that ir a body is urged by two forces in the direction of the fides of a parallelogram, and proportional to thefe fides, the combined a£!ion of thefe two forces is equi¬ valent to a third force afling in the dire&ion of the diagonal of the parallelogram, and having its intenlity proportional to that diagonal. This important dif- ccvery, which has been of fuch fervice in the different departments of phyfics, fhould have conferred upon its author a greater degree of celebrity than he has actual¬ ly enjoyed. His name has fcarcely been enrolled in the temple of fame, but jutlice may yet be done to the memory of fuch an ingenious man. He bad likewife the merit of illuflrating other parts of ftatics; and he appears to have been the firff who, without the aid of the properties of the lever, difeovered the laws of equi¬ librium in bodies placed on an inclined plane. His works were reprinted in the Dutch language in 1605. They were tranflated into Latin in 1608, and into trench in 1634 ; and in thefe editions of his works his Statics w'ere enlarged by an appendix, in which he treats of the rope machine, and on pulleys adfing ob- Lucas Va- I’Tiely. 'lerimwrites 7* doctrine of tire centre of gravity, wdiich had on the cen-been applied by Archimedes only to plane furfaces, treot gra- was' now extended by Lucas Valerius to folid bodies. In his work entitled De Centro Graviton's Solidorum Liber, publifhed at Bologna in 1661, he has difeufled this fubjeCI with fuch ability, as to receive from Gali¬ leo the honourable appellation of the Novus nojlrce Difeoveries <£tat^s Archimedes. of Galileo. 8. In the hands of Galileo the fcience of mechanics Born 15154. affumed a new form. In 1572 he wrote a fmall treatife Died xCiqa. on which he reduced to this principle, that it requires an equal power to raife two different bodies to altitudes in the inverfe ratio of their weights, or that the fame power is requifite to raife 10 pounds to the height of 100 feet, and 20 pounds to the height of 50 feet. This fertile principle was not purfued by Galileo to its different confequences. It wTas left to Defcartes to apply it to the determination of the'equilibrium of machines, which he did in his explanation of machines and engines, without acknowledging his obligations to the Tufcan philofopher. In addition to this new prin¬ ciple, Galileo enriched mechanics with his theory of lo¬ cal motion. E his great difeovery has immortalized its author j and w'hether we confider its intrinfic value, or the change which it produced on the pbyfical fciences, we are led to regard it as nearly of equally importance 3 M E C H A N 1 C S. Hi ft of v< vity of fo- lids. J66x. with the theory of univeral gravitation, to which it paved the way, The firii hints of this new theory were given in his SYSTEMA CoSMICUM, Dialogus II. The fubjeft was afterwards fully difeuffed in another, entitled Difcurfus ct Dcmonjlraticnes Mathematicce cir- i638" ca duas novas Scientias pertinences ad Mechanicam et Motum Localcm, and publifhed in 1638. This work is divided into four dialogues 5 the firft of which treats of the refiilance of folid bodies before they are broken : The fecond points out the caufe of the cohefxon of folids. In the third he difeuffes his theory of local motions, comprehending thofe which are equable, and thofe which are uniformly accelerated. In the fourth he treats of violent motion, or the motion of proje£liles ; and in an appendix to the work he demonftrates feveral propolitions relative to the centre of gravity of folid bodies. In the firtt of thefe dialogues he has founded his reafoning on principles which are far from being correbf, but he has been more fuccefsful in the other three. In the third dialogue, which contains his celebrated theory, he difeuffes the doftrine of equable motions in fix theorems, containing the different relations between the velocity of the moving body, the Ipace which it deferibes, and the time employed in its defeription. In the fecond part of the dialogue, which treats of ac¬ celerated motion, he confiders all bodies as heavy, and compofed of a number of parts which are alfo heavy. » , Hence he concludes that the total weight of the body is proportional to the number of the material particles of which it is compofed, and then reafons in the follow- ing manner. As the weight of a body is a power al¬ ways the fame in quantity, and as it conftantly afts without interruption, the body muff be continually re¬ ceiving from it equal impulfes in equal and fuccellive inftants of time. When the body is prevented from falling by being placed on a table, its weight is in- ceffantly impelling it downwards, but thefe impulfes are inceffantly deltroyed by the refiitance of the table which prevents it from yielding to them. But where the body falls freely, the impulfes which it perpetually receives are perpetually accumulating, and remain in the body unchanged in every refped excepting the di¬ minution which they experience from the refiftance of air. It therefore follows, that a body falling freely is uniformly accelerated, or receives equal increments of velocity in equal times. Having eftablifhed this as a definition, he then demonftrates, that the time in which any fpace is deferibed by a motion uniformly accelerat¬ ed from reft, is equal to the time in which the fame fpace would be deicribed by an uniform equable motion ' with half the final velocity of the accelerated motion j and that in every motion uniformly accelerated from reft, the fpaces deferibed are in the duplicate ratio of the times of defeription. After having proved thefe theorems, he applies the doeftrine with great fuccefs to the afeent and defeent of bodies on inclined planes. 9. The theory of Galileo wras embraced by his pu- Labours of pil Toricelli, who illuftrated and extended it in his ^°ncelIi* excellent work entitled De motu gravium naturaliter 1 44‘ accelerato, publifhed in 1644. In his treatife De motu projedlorum, publifhed in the Florentine edition of his wmrks, in 1664, he has added feveral new and import¬ ant propofitions to thofe wdiich were given by his mafter on the motion of projeftiles. I t' f 10. It was sft>out this time that fteam began to be the^fteam employed engine. M E C H Hiftory. employed as the firft mover of machinery. This great v difcoverv has been afcribed by the Englilh to the mar¬ quis of Worcefter, and to Papin by the French 5 but it is almol! certain, that about 34 years before the date of the marquis’s invention, and about 61 years before the conrtru£lion of Papin’s digefter, fleam was employ¬ ed as the impelling power of a ftamping engine by one Brancas an Italian, who publifhed an account of his invention in 1629. It is extremely probable, however, that the marquis of Worcefter had never feen the w7ork of Brancas, and that the fire-engine w7hich he mentions in his Century of Inventions wTas the refult of his own ingenuity. The advantages of fleam as an impel¬ ling power being thus knowm, the ingenious Captain Savary invented an engine which raifed w'ater by the expanfion and condenfation of fleam. Several engines of this conftruftion were a£lually ere£led in England and France, but they wrere incapable of railing water from depths which exceeded 35 feet. The fleam-engine re¬ ceived great improvements from our countrymen New¬ comen, Brighton, and Blakey j but it was brought to its prefent ftate of perfeflion by Mr Watt of Birming¬ ham, one of the moft accomplifhed engineers of the prefent age. Hitherto it had been employed merely as a hydraulic machine for draining mines or railing wa¬ ter, but in confequence of Mr Watt’s improvements it has long been ufed as the impelling pow7er of almoft every fpecies of machinery. It is a curious circum- flance, that the fleam-engine was not only invented, but has received all its improvements, in our own country. D'fc ver'es II* ^ucce^s Galileo in inveftigating the doc- of Huygens. tr^ne rectilineal motion, induced the illuftrious Huy- 167$. gens to turn his attention to curvilineal motion. In his celebrated work De Horologia Ofcillatorio, publilh- ed in 1673, he has Ihown that the velocity of a heavy body defeending along any curve, is the fame at every inftant in the direction of the tangent, as it would have been if it had fallen through a height equal to the cor- refponding vertical abfeifs; and from the application of this principle to the reverfed cycloid with its axis verti¬ cal, he difeovered the ifochronifm of the cycloid, or that a heavy body, from whatever part of the cycloid it begins to fall, always arrives at the lowrer point of the curve in the fame fpace of time. By thefe difeuf- fions, Huygens was gradually led to his beautiful theo¬ ry of central forces in the circle. This theory may be applied to the motion of a body in any curve, by con- fidering all curves as compofed of an infinite number of fmall arcs of circles of different radii, which Huygens had already done in his theory of evolutes. The theo¬ rems of Huygens concerning the centrifugal force and circular motions, were publiihed without demonftrations. They were firft demonftrated by Dr Keill at the end of his Introdu&ion to Natural Philofophy. The demon- ftrations of Huygens, however, which w7ere more prolix than thofe of the Englilh philofopher, were afterwards given in his polthumous works. 12. About this time the true laws of collifion or per- cuflion w7ere feparately difeovered by Wallis, Huygens, and Sir Chriftopher Wren in 1661, without having the leaft communication with each other. They were tranfmitted to the Royal Society of London in 1668, and appeared in the 43d and 46th numbers of their Tranfaftions. The rules given by Wallis and Vol. XIII. Part I. 1700. The laws of collifion fi! [covered by Wallis, Huygens, and Wren. 1661. A N I C S. Wren are publilhed in N° 43, pp. 864 and S67, and thofe of Huygens in N° 46, p. 927. The founda¬ tion of all their folutions is, that in the mutual collifion of bodies, the abfolute quantity of motion of the centre of gravity is the fame after impaft as before it, and that when the bodies are elaftic, the refpeftive velocity is the fame after as before the Ihock.—We are indebted like- *wife to Sir Chriftopher Wren for an ingenious method of demonftrating the laws of impulfion by experiment. He fufpended the impinging bodies by threads of equal length, fo that they might touch each other when at reft. When the two bodies were feparated from one another, and then allowed to approach by their own gravity, they impinged againft each other when they arrived at the pofitions w7hich they had when at reft, and their velocities w7ere proportional to the chords of the arches through which they had fallen. Their ve¬ locities after impact were alfo meafured by the chords of the arches through which the ftroke Vad forced them to afeend, and the refults of the experiments coin¬ cided exactly w ith the deduftions of theory. The laws of percuflion w7ere afterwards more fully inveftigated by Huygens, in his pofthumous work De Motu Corporum ex Percufjione, and by Wallis in his Mechanica, pub- liflied in 1670. 13. The attention of philofophers was at this time di-Mechanical refled to the tw7o mechanical problems propofed by problems Merfennus in 1635* The firft of thefe problems w7as Propcfeil by to determine the centre of ofcillation in a compound ^er!ennus* pendulum, and the fecond to find the centre of percuf- fion of a fingle body, or a fyftem of bodies turning round a fixed axis. The centre of ofcillation is that point in a compound pendulum, or a fyftem of bodies moving round a centre, ,in which, if a fmall body were placed and made to move round the fame centre, it would perform its ofcillations in the fame time as the fyftem of bodies. The centre of percuflion, which is fituated in the fame point of the fyftem as the centre of ofcillation, is that point of a body revolving or vibrat¬ ing about an axis, w7hfch being ftruck by an immove¬ able obftacle, the whole of its motion is deitroyed. Thefe two problems were at firft difeuffed by Defcartes ip;yg.cns and Roberval, but the methods which they employed f0.ves the w7ere far from being correft. The firft folution of the problem of problem on the centre of ofcillation was given by Huy-tfie tre gens. He affumed as a principle, that if feveral weights °fo“lcllla" attached to a pendulum ddeended by the force of gra¬ vity, and if at any inftant the bodies w7ere detached from one another, and each afeended with the velocitv it had acquired by its fall, they would rife to fuch a height that the centre of gravity of the fyftem in that ftate would defeend to the fame height as that from which the centre of gravity of the pendulum had de- feended. The folution founded on this principle, which was not derived from the fundamental laws of mecha¬ nics, did not at firft meet with the approbation of phi- lolophers j but it was afterwards demonftrated in the cleareft manner, and now forms the principle of the confervation of aftive forces.—The problem of the centre of percuflion was not attended with fuch difficul¬ ties. Several incomplete folutions of it w7ere given by different geometers ; but it w7as at laft refolved in an accurate and general manner by James Bernouilli by the principle of the lever. Works of 14. In 1666, a treatife De Vi PercuJRonis, was pub-Bt ell!- G lifted MECHANICS. 1-6 S 6. Labours of ’Varignou. Parent on the maxi¬ mum effedt cfmachines. * Mem. de VAcad^ *7°4' De la Hire writes on the teeth of wheels. lidied by J. Alpbonfo Borelli, and in 1686, another work, De Motionibus Naturalibus a Gravitate Pendentibus; but he added nothing to the fcience of mechanics. His in¬ genious work, De Motu Animalium, however, is en¬ titled to great praife, for the beautiful application which it contains of the laws of Katies to explain the various motions of living agents. 15. The application of Katies to the equilibrium of machines, was firK made by Varignon in his Project of a new SyKem of Mechanics, publilhed in 1687. The fubjedt was afterwards completely difeufled in his Nou- velle Mecanique, a pcKhumous work publilhed in 1725- In this work are given the firK notions of the celebrated principle of virtual velocities, from a letter of John Bernouilli’s to Varignon in 1717. The virtual velo¬ city of a body is the infinitely fmall fpace, through which the body excited to move has a tendency to deferibe in one inKant of time. This principle has been fuccirsfully applied by Varignon to the equilibri¬ um of all the fimple machines. The refiKance of folids, which was firK treated by Galileo, was difeufled more corre£Hy by Leibnitz in the Adla Eruditorum for 1687. In the Memoirs of the Academy for 1702, Varignon has taken up the fubjedt, and rendered the theory much more univerfal. 16. An important flep in the conflrudtion of machin¬ ery was about this time made by Parent. He remark¬ ed in general that if the parts of a machine, are fo arran¬ ged, that the velocity of the impelling pow7er becomes greater or lefs according as the weight put in motion becomes greater or lefs, there is a certain propor¬ tion between the velocity of the impelling power, and that of the weight to be moved, which renders the ef- fedl of the machine a maximum or a minimum *. He then applies this principle to underlhot wheels, and Ihorvs that a maximum effedf wdll be produced when the velocity of the Kream is equal to thrice the velocity of the wheel. In obtaining this conelufion, Parent fup- pofed that the force of the current upon the wheel is in the duplicate ratio of the relative velocity, which is true only when a Angle floatboard is impelled by the W’ater. But when more floatboards than one are added upon at the fame time, it is obvious that the momentum of the water is diredlly as the relative velocity ; and by making this fubKitution in Parent’s demonflration, it will be found that a maximum effedf is produced wdien the velocity of the current is double that of the wheel. This refult was firK obtained by the Chevalier Borda, and has been amply confirmed by the experiments of Smeaton. (See Hydrodynamics, $. 279, 280, 281) The principle of Parent was alfo applied by him to the conKrudtion of windmills. It had been generally fup- pofed that the moK efficacious angle of wreather was 45°j but it was demonKrated by the French philofo- pher that a maximum efledf is produced when the fails are inclined 54-y degrees to the axis of rotation, or, when the angle of wreather is 35degrees. This con- clufion, however, is fubjedl to modifications which will be pointed out in a fubfequent part of this article. 17. The Trade de Mecanique of De la Hire, publifh- ed feparately in 1695, and in the 9th volume of the Memoirs of the French Academy from 1666 to 1699, contains the general properties of the mechanical powers, and the defeription of feveral ingenious and ufeful ma¬ chines. But it is chiefly remarkable for the Trade dcs Epicycloides, which is added to the edition publiffi- Hiflory. ed in the Memoirs ol the Academy. In his intereKing treatife, De la Hire confiders the genefis and properties of exterior and interior epicycloids, and demonKrates, that when one wheel is employed to drive another, the one will move fometimes w'ith greater and fometimes with lefs force, and the other wdll move fometimes with greater and fometimes with lefs velocity, unleis the teeth of one or both of the wheels be parts of a curve gener¬ ated like an epicycloid. The fame truth is applicable to the formation of the teeth of rackwork, the arms of levers, the wipers of Hampers, and the lifting cogs of forge hammers; and as the epicycloidal teeth when pro¬ perly formed roll upon one another without much fric¬ tion, the motion of the machine will be uniform and pleafant, its communicating parts will be prevented from wearing, and there will be no unneceflary wade of the impelling power. Although De la Hire wTas the firft who publiffied this important difeovery, yet the honour ^i!c0T • • ■ ^ j • j yery op cDi1® of it is certainly due to Olaus Roemer, the celebrated Danifh aKronomer, who difeovered the fucceffive pro- teeth firft pagation of light. It is exprefsly Kated by Leibnitz *,made by in his letters to John Bernouilli, that Roemer commu-K‘oemer‘ nicated to him the difeovery 20 years before the pub- * Mfcel- lication of De la Hire’s work ; but Kill we have no ground for believing that De la Hire was guilty of pla-p. ^15 ^IC* giarifm. Roemer’s refearches were not publiihed ; and from the complete difeuffion which the fubjeCt has re¬ ceived from the French philofopher, it is not unlikely that he had the merit of being the lecond inventor. Even Camus f, who about 40 years afterwards gave z^Cot/rs~dc complete and accurate theory of the teeth of wheels, Mathema- was unacquainted with the pretenfions of Roemer, and tiyue, Liv. aferibes the difeovery to De la Hire. x- et X1, 18. The publication of Newton’s Principia contri-DKcovenes buted greatly to the progrefs of mechanics. His dif-0^ ^,ewt011* coveries concerning the curvilineal motion of bodies, combined with the theory of univerfal gravitation, ena¬ bled philofophers to apply the icience ot mechanics to the phenomena of the heavens, to afeertain the law of the force by which the planets are held in their orbits, and to compute the various irregularities in the folar fyHem, which arife from the mutual a6tion of the bo¬ dies which compofe it. The Mecanique Celejle of Ea Place will be a Handing monument of the extenfion which mechanics has received front, the theory of gravity. The important mechanical principle of the confervation of the motion of the centre of gravity is alio due to Newton. He has demonftrated in his Principia, that the Kate of the centre of gravity of feveral bodies, whe¬ ther in a Kate of reK or motion, is not affedfed by the reciprocal a6tion of thefe bodies, whatever it may be, fo that the centre of gravity of the bodies which a6t upon one another, either by the intervention of levers, or by the laws of attraction, will either remain at reK, or move uniformly in a right line. 19. We have already feen that the principle of theprjnc;p|e 0f confervation of aCtive forces was difeovered by Huygens the confer- when he folved the problem of the centre of ofcillation. vat|on The principle alluded to, confiKs in this that in all the adtions of bodies upon each other, whether that aCtion covered by- con frits in the percuffion of elaKic bodies, or is commu- Huygens, nicated from one body to another by threads or inflexi¬ ble rods, the fums of the mafles multiplied by the fquares of the abfolute velocities remain always the fame. This MECHANICS. 51 * Mem. de A' Acad. Berlin, 1748. Hlftoiy. This important law is eafily deducible from two limpler jaws admitted in mechanics. 1. That in the collifion of elaftic bodies, their refpedlive velocities remain the fame after impa£t as they were before it; and 2. That the quantity of a61ion, or the produff of the mafles of the impinging bodies, multiplied by the velocity of their centre of gravity, is the fame after as before impaff. The principle of the confervation of aflive forces, was regarded by its inventor only as a limple mechanical Rendered theorem. John Bernouilli, however, confiidered it as a general by general law of nature, and applied it to the folution of Daniel Ber-j’gygj-ft’ problems which could not be refolved by direfl nouilli. roethods ; but his fon Daniel deduced from it the laws of the motion of fluids from veflels, a fubjeft which had been formerly treated in a very vague manner. He afterwards rendered the principle more general *, and {bowed how it could be applied to the motion of bodies influenced by their mutual attraffions, or folicited to¬ wards fixed centres by forces proportional to any func¬ tion of the diftance. Daniel Ber- 2o. After the parallelogram of forces had been in- other philo tr°duced into ftatics by Stevinus, it was generally ad- fophers de- fitted upon the fame demonftration which was given for monftrate the compofition of motion. The firfi: complete demon- the paral- ftration was given by Daniel Bernouilli in the Commen- ^°^am taries of Peterlhurgh for 1726, independent of the con- fideration of compound motion. This demonftration, W'hich was both long and abftrufe, was greatly fimpli- fied by D’Alembert in the Memoirs of the Academy for 1769. Fonfeneix and Riccati have given a very in¬ genious one in the Memoirs of the Academy of Turin for 1761. This was alfo improved by D’Alembert, who gave another in the fame Memoirs, and a third in his Traite de Dynamique, publifhed in 1743. Dr Ro- bifon * has combined the demonftrations of Bernouilli and D’Alembert with one by Frifi, and produced one that is more expeditious and Ample. La Place has likewife given a demonftration of the parallelogram of forces in his Mecanique Selejle. Difpute 21. About the beginning of the 18th century, the nieafure'of ce^e^rate<^ difpute about the meafure of active forces active was keenly agitated among philofophers. The firft forces. fpark of this war, which for 40 years England main¬ tained fingle-handed againft all the genius of the conti¬ nent, was excited by Leibnitz. In the Leipfic a<5ts for 1686, he aflerted that Defcartes was miftaken in making the force of bodies proportional to their Ample velocity, and maintained that it followed the ratio of the fquare of the velocity. He fhewed, that a body, with a velocity of two feet, acquires the power of rai- fing itfelf to a height four times as great as that to which a body could rife with a velocity of only one foot ; and hence he concludes, that the force of that body is as the fquare of its velocity. The abbe de Co- tilon, a zealous Cartefian, allowed the premifes of Leibnitz, but denied his conclufion. The body, faid he, which moves with a velocity of two feet, will cer¬ tainly rife to quadruple the height of another body that has only the velocity of one foot j but it will take twice the time to rife to that height, and a quadruple effeft, in a double time, is not a quadruple force, but only a double one. The theory of Leibnitz was fup- ported by John Bernouilli, Herman, Gravefende, Muf- c.henbroeck, Poleni, Wolff, and Bulfingerj and the opi¬ nion of Defcartes by Maclaurin, Stirling, Clarke, De- * Si/p.En tycl. § ’namics. faguliers, and other Englifti philofophers. The quef- Hiftory. tion was at laft involved in metapbyfical reafoning; and if the difpute did terminate in favour of either party, the Englilh philofophers were certainly viilorious. It appears, in the cleared: manner, that the force of a moving body, indicated by the fpace which it defcribes, is as the Ample velocity, if we conAder the fpace as de- fcribed in a determinate time j but it is as the fquare of the velocity, if we do not eonfider the time in which the fpace is defcribed. The queftion, therefore, comes to be this : In eftimating the forces of bodies in motion, ought we to take time into confideration ? If, with the followers of Leibnitz, we rejedt this element, then we may maintain that the force of a child is equal to that of a man carrying a load, becaule the child is alfo ca¬ pable of carrying the fame load, though in fmall parts and in a greater length of time. 22. In 1743, D’Alembert publifhed his Traite' deQ'Alem- Dynamique, founded upon a new principle in mecha-bsrt’s prin- nics. This principle was firft employed by James Ber-cipk of ^7- nouilli in his folution of the problem of the centre of <1 ofcillation 5 but D’Alembert had the honour of genera- lifing it, and giving it all that fimplicity and fertility of which it was fufceptible. He fhowed, that in what¬ ever manner the bodies of one fyftem adl upon another, their motions may always be decompofed into two others at every inftant, thofe of the one being deftroy- ed the inftant following, and thofe of the other retain¬ ed, and that the motions retained are neceffarily known from the conditions of equilibrium between thofe which are deftroyed. This principle is evidently a confe- quence of the laws of motion and equilibrium, and has the advantage of reducing all the problems of dynamics to pure geometry and the principles of ftatics. By means of it D’Alembert has refolved a number of beau¬ tiful problems which had efcaped his predeceffors, and particularly that of the preceflion of the equinoxes, which had occupied the attention of Newton. In his Traite de Dynamique, D’Alembert has likewife reduced the whole of mechanics to three principles, the force of inertia, compound motion, and equilibrium 5 and has il- luftrated his views on this fubject by that profound and luminous reafoning which charadlerifes all his writ- ingS* 23. Another general principle in dynamics was Euler, about this time difcovered feparately by Euler, Daniel Bernouilli, and the chevalier D’Arcy, and received the ™ArCy &di{- name of the confervation of the momentum of rotatory cover the motion. According to the two firft philofophers, the conferva- principle may be thus defined : In the motion of feve-tlon 0* ft16 ral bodies round a fixed centre, the fum of the products of the mafs of each body multiplied by the velocity of motion. * its motion round the centre, and by its diftance from that centre, is always independent of the mutual adlion 174(7. which the bodies may exert upon each other, and al¬ ways preferves itfelf the fame, provided the bodies are not influenced by any external caule. This principle was given by Daniel Bernouilli in the Memoirs of the Academy of Berlin for 1746 5 and in the fame year by Euler in the firft: volume of his works. They were both led to the difcovery, while inveftigating the mo¬ tion of feveral bodies in a tube of a given form, and which can only turn round a fixed point. The princi¬ ple difcovered by the chevalier D’Arcy was given in a memoir dated 1746, and publiftied in the Memoirs of G 2 tbf 5 2 M E C H A N I C S, Hiftory. The prin- ciple of lea ft a Euler extended the principle of leaft adlion, and ftiewed, “ that in the trajedlories defcribed by means of central forces, the integral of the velocity multiplied by the element of the curve, is either a maximum or a minimum.'1' This remarkable property, which Euler recognifed only in the cafe of infulated bodies, was generalifed by Lagrange into this new principle, “ that the fum of the produdhs of the maffes by the integrals of the velocities, multiplied by the ele¬ ments of the fpaces defcribed, is always a maximum or a minimum.” In the memoirs of Turin, Lagrange has employed this principle to refolve feveral difficult pro¬ blems in dynamics ; and he has ffiewn f, that when it is combined with the conlervation of adtive forces, and developed according to the rules of his method of varia¬ tions, it furnifties diredlly all the equations neceffary for the folution of each problem, and gives rife to a fimple and general method of treating the various problems concerning the motion of bodies. 26. An important difcovery in rotatory motion, w7as at this time made by Profeffor Segner. In a paper, entitled Specimen '1 neorice Turiinum, he demonHrated, Hiftory. that if a body of any form or magnitude, after it has received rotatory motions in all diredtions, be left en¬ tirely to itfelf, it will always have three principal axes of of rotation j or, in other words, all the rotatory motions with which it is aftedied, may be reduced "to three, which are performed round three axes, perpendicular to each, palling through the centre of gravity of the re¬ volving body, and preFerving the fame polition in abfo- lute fpace, while the centre of gravity is either at reft or moving uniformly in a flraigbt line. 27. The force of torfion began at this time to be in-r , veftigated by Coulomb, who publilhed tw'o ingenious papers on the fubjedf, in the Memoirs of the French into the Academy. He has fuccefsfully employed this principle f°rce in feveral phyfical refearches, but particularly in deter-torfion' mining the law of magnetic adHon, and in finding the laws of the refiftance of fluids when the motions are ex¬ tremely flow *. It was by means of an elegant experi- ^ ment on the principle of torfion that Mr Cavendiffi dl, determined the mutual attraction of two maffes of lead, Nat. and thence deduced the mean denfity of the earth.— tom. iii.p. We are alfo indebted to Coulomb for a complete fet of experiments oh the nature and effedls of fridtion. By employing large bodies and ponderous weights, andAnc,.‘nto conducting his experiments on a large fcale, he has^ corredted errors wffiich neceffarily arofe from the limit-0 n 1 ^ ed experiments of preceding writers; he has brought to light many new and interefting fadts, and confirmed others which had hitherto been partially eftablifhed. The moft curious refult of thefe experiments Ts the ef- fedt of time in increafing the fridtion between twro fur- faces. In fome cafes the fridtion reaches its maximum after the rubbing furfaces have remained in contadt for one minute $ and in other cafes five or fix days wTere neceffary before this effedt was produced. The in- creafc of fridtion, which is generated by prolonging the time of contadt, is fo great, that a body, weighing 1650 pounds, was moved with a force of 64 pounds when firft laid upon the correfponding furface. After remaining in contadt: for the fpace of three feconds, 100 pounds were neceffary to put it in motion ; and when the time was prolonged to fix days, it could fcarcely be moved with a power of 622 pounds f. p^Nenteis^ 28. One of the moft important treaties on the fei- ence of motion is the Mechanics of the celebrated Eu¬ ler, publilhed in 1736. It contains the whole theory Works on of redtilineal and curvilineal motion in an infulated mechanics, body, affedted by any accelerating forces, either in va¬ cuo or in a refilling medium. He uniformly ufes the analytical method, and has employed the principle of the vis inertice, and that of compdund motion, for putting his problems into equations. By the vis iner- tice, motion is at every moment of time redlilineal and Euler’s me- uniformj and by the principle of compound motion, achanics' body, expofed to the adtion of any number of forces, tending to alter the quantity and the diredlion of its motion, will move in fuch a diredtion as to reach the very point at which it would have arrived, had it obeyed fucceffively each of the forces which adt upon it.— In the Mecanique Anahjtique of Lagrange, pub-Lagrange’s lilhed in 1788, all the mechanical problems are redu-Meca' ced to general formulae, which, being developed, fur-fytigue.^" niffi us with the equations that are neceffary for the fo- " lution of each problem j and the different principles which ^ Theory. Prony’s Architec¬ ture Hy- draultque and Meca nique Phi lojopkique which have been difcoveved for facilitating the folutions of mechanical quedions, are brought under one point of view, and their conneaion and dependence clearly pointed out. The Architeciure Hy dr antique, by M. Prony, publUhed in 1790, and t\iz Mecanique l/nto- fophique, of the fame author, publUhed in 1799) c^n' tains all the late improvements in mechanics, and a complete view both of the theory and application of that fcience. The firft: of thefe works is intended chiefly for the ufe of the engineer, though an exten- ' five acquaintance with the higher geometry is nece.- fary for perufing it with advantage. _ His Mecamque Philofophique is a profound work, in which, without the aid of a fingle diagram, he gives all the formulae, and the various theorems and problems which belong to the fcknces of mechanics and hydrodynamics. Every al- mechanics. . . . , -, ternate page contains a methodical table of tne relults obtained in the preceding page, the defcription of the fymbols, and the theorems, problems, and formulae which may have been obtained.— 1 he Iraite de Me- canique Elcmentaire, by M. Franceur, publiflied in 1802 in one volume octavo, is an excellent abridge- ment of the works of Prony, and is intended as an in¬ troduction to the Mecanique Philofaphique of that au¬ thor, to the Mecanique Analytique of Lagrange, and to the Mecanique Celejie of Laplace. None ot thele works have been tranilated into Englilh *, but their place is well fupplied by a Treatife on Mechanics Theoretical, Pra&ical, and Defcriptive, by Ountnus Gregory, A. M. publiflied in 1806, and containing a complete view of the latell improvements, both in the theory and practice of mechanics. PART I. THEORY OF MECHANICS. _ , r 20. the theory of mechanics properly compre- theorftkal. hends, 1. Dynamics. 2. The motion of projeftiles. mechanics. 1. The theory of ample machines, or the mechanical powers. 4. The theory of compound machines, and their maximum effbas. 5. The doctrine of the centre of gravity. 6. The centre of ofeiliation, gyration, etc. 7. 'The collifion of bodies. 8. The theory of rotation. 9. The theory of torfion. 10. The ftrength of materi¬ als j and, xi. The equilibrium of arche-, domes.— 1 he fubjeds of Dynamics, Projectiles, Rotation, and Strength of Materials having been already a > y treated by Dr Robifon, under their refpeftive heads, we {hall now dired the attention of the reader to the other branches of theoretical mechanics. Chap. I. On Simple Machines, or the Mechanical Powers. Divifion of machines into Ample and com¬ pound. ao. The fimple machines have been generally rec¬ koned fix in number. 1. The lever ; 2. The wheel and axle, or axis in peritrocluo ; 3. The puney 5 4. The inclined plane •, 5. The wedge j and, 6. i he ferew : to which fome writers on mechanics have added the balance, and others the rope-machine. It is evi¬ dent, however, that all thefe machines may be reduced to three, the lever, the inclined plane, and the rope- machine. The pulley, and the wheel and axle, are ob- vioufly compofed of an affemblage of levers ; the ba¬ lance is a lever with equal arms ; the wedge, is compo¬ fed of two inclined planes, with their bafes in contact j and the [crew is either a wedge or an inclined plane, wrapped round a cylinder.—Under the head of fimple machines, therefore, we cannot, in Itridt propriety, in¬ clude any of the mechanical powers, excepting the le¬ ver, the inclined plane, and the rope-machine. \ Definitions. 31. Def. I. When two forces aa againfi each other Definitions, by the intervention of a machine, the one force is call¬ ed the power, and the other the weight. The weight is the refiltance to be overcome, or the effea to be pro¬ duced. The power is the force, whether animate or inanimate, which is employed to overcome that refift- ance, or to produce the required effea. 3 2. Def. 2. The power and weight are faid to ba¬ lance each Other, or to be in equilibrio, when the ef¬ fort of the one to produce motion in one direaion, is equal to the effort of the other to produce motion in the oppofite direaion ;—or when the. weight oppoies that degree of refiflance which is precifely required to deftroy the aaion of the power. Sect. I. On the Lever. 22. Definition. A lever is an inflexible bar or Levers di rod moving freely round a point called its fulcrum, °r vided into ^ centre of motion. ... . , , • 1 Levers have been generally divided into three kinds. In levers of the firft kind the fulcrum is fituated be¬ tween the power and the weight, as in fteelyards, foit- fars, pincers, &c. Levers of the fecond kind have the weight between the power and the fulcrum, as^n cuttino- knives faftened at the point of the blade, and in the oars of a boat where the water is regarded as the fulcrum. In levers of the third kind, the power is be¬ tween the weight and the fulcrum, as in tongs, fneers for fheep, &c. The bones of animals are generally confidered as levers of the third kind, for the. muLies, by the contra&ion of which the power or moving force is generated, are fixed much nearer to the joints or cen¬ tred of motion than the centre of gravity of the weight to be raffed. On this fubjeft, fee Paiey’s Natural Theology, chap. 7, 8. and Borelli de Motu Amma- lium. Axioms. 24. Axiom i. Equal weights aSling at the eptremi- .. ties of equal arms of a freight lever, and having the lines of the direBion in which they a® at equal angles to thefe arms, will exert the fame effort to turn the lever round its fulcrum. This axiom has been generally re- ftrifled to the particular cafe when the weights aft per¬ pendicularly to the arms of the lever •, but no reafon can be affigned for fuch a limitation. The truth m the axiom is 35°felt-evident when the angles formed by the arms of the lever and the dinf&ion of the forces are 80% as when they are 90°, for in each ca!e the two weights * exert t M E C H cxeit their imluence upon the lever in precifely the fame circumftances. 35. Axiom 2. If two equal weights are placed at the extrem'ties of a lever fupported by two fulcra ; and if thefe fulcra are at equal di/lances from the weights, or the extrernities of the lever ; the preffure upon the fulcra will be equal to the fum of the weights, and the preffure upon each Julcrnm will be equal to one of the weights. I he lever being fuppofed devoid of weight, it is ob¬ vious, that as each fulcrum is fimilarly fituated with re- fpedt to both the weights, the preflure upon each mull be equal $ and as the fulcra fupport both the equal weights, the preffure upon each mull be equal to one of the weights. Proposition I. 35. If two weights or forces a&ing at equal angles upon a ftraight lever, devoid of weight, are in equilibrio, they are reciprocally proportional to their diftances from the fulcrum. 37- Case i. When the weights act on contrary fides of the fulcrum. Let AB be a lever devoid of weight, and let it be Plate fupported upon the two fulcra f F, fituated in fuch a CCCXVI. manner that A/=/F=FB. Then if two equal Jig. 1. weights C, D of one pound each are fufpended at the extremities A, B, fo as to ad in the direftions AC, ED, making the angles CAB, DBA equal, thefe rveights will be in equilibrio, for fmce A/=rFB (Axiom 1.) the effort^of the weight D to turn the lever round the fulcrum F, will be equal to the effort of the weight C to turn it round the fulcrum/i Now (Axiom 2.) the preffure upon the fulcrum f is equal to one pound, therefore if that fulcrum be removed, and a weight E of one pound be made to aft upward at the point F, the weights C and D will continue in equilibrio. Then it is obvious that fmce FB=Ff the weight E of one pound afting upwards at the point f fo that the angle D/FrrDBA, will have the fame effeft as an equal weight afting downwards at B. By removing the weight E, therefore, and fufpending its equal C at the extremity B, the equilibrium will flill be preferved. But the weights D, C, fufpended at B, are equal to two pounds, and the weight C is only one pound j and as FA is double of FB, it follows that a weight of two pounds, placed at the end of one arm of a lever, will be .in equilibrio with a weight of one pound placed at twice the diftance of the former from the fulcrum. But 2 : 1=2 FB or AF ; FB, that is, when the di¬ ftances are as 2 to 1, an equilibrium takes place if the weights are reciprocally proportional to thefe di¬ ftances. 38. Case 2. When the weights aft on the fame fide of the fulcrum. Fig. a. Let AB be a lever in equilibrio upon the ful¬ crum F, and let FA be equal to FB, confequently (cafe 1.) we muft have CnDrzri pound. Now as the fulcrum F fupports a weight equal to C-f-D=2 pounds, the equilibrium will continue if a weight £ of two* pounds is made to aft upwards at the point F, for in this cafe it fupplies the place of the fulcrum. It is ob- xious alfo that a fulcrum placed at A or B will fupply Jfie place of the weights at thefe parts without aftefting 4 A N I C S. the equilibrium. Let, therefore, the weight D be rfi- Theory, moved, and let the extremity B reft upon a fulcrum ; ' "" v “ then fince the lever is in equilibrio, we have a weight ErrC-}-D—2 pounds afting at F, and balancing a weight C of one pound afting at A. But 2 : iznAB : FB, confequently when there is an equilibrium between two weights C, D afting at the diftances 2 and 1 from the fulcrum, and on the fame fide of the fulcrum, the weights are.reciprocally proportional to thefe diftances. 39. Again, let AB be the fame lever fupported by Fiv 1 the fulcra/ F, and let A/=FB and/F—2FB. Then * if two weights C, D of one pound each be fufpended at the extremities A, B, they will be in equilibrio as be¬ fore. But fince the fulcrum / fupports a preffure of one pound (Axiom 2.), the equilibrium will ftill con¬ tinue when that fulcrum is removed and a weight of one pound made to aft in a contrary direftion fP at the point f fo that the angle P/F may be equal to DBA. Now, (Axiom 1.) a weight E of one pound afting upward at/.will be in equilibrio with a weight E' of one pound afting downwards at/'; F/being equal t0 L/', and therefore by removing E from the point/ and fubftituting E at the point /', an equilibrium will ftdl obtain. But fin.ce F/—2FB a weight of one pound fufpended from/will have the fame influence in turn¬ ing the lever round F as a weight of two pounds fuf¬ pended at B (Cafe 2.). Let us remove, therefore, the weight E' from/', and fubftitute a weight Gr=2E', fo as to aft at B. Then fince the equilibrium is not deftroy- ed, we have a weight C of one pound afting at the di¬ ftance FA, and the weights D-f-G~3 pounds afting at the diftance FB. But FAz=3FB and D + G=r3C confequently C : D-J-G~f B : FA : That is, when the diftances from the fulcrum are as 3 to 1, and when an equilibrium exifts, the weights are reciprocally propor¬ tional to thefe diftances. 40. By making FA in fig. 2. equal to 2FB it may Fig- V be fhewn, as in Cafe 2. that the weights are reciprocally proportional to their diftances from the fulcrum, when they aft on the fame fide of the fulcrum, and when the diftances are as 3 to 1. 41. In the fame w'ay the demonftration maybe ex-Fig. 3. tended to any commenfurable proportion of the arms b7 making EA to FB in that proportion, and keeping /A always equal to FB. Hence we may conclude in general, that when twm weights afting at equal angles upon a ftraight lever devoid of weight, are in equilibrio, they are reciprocally proportional to their diftances from the centre of motion. £. £. D. 42. Cor. 1. If two weights afting at equal angles Corollarfe* upon the arms or a ftraight lever devoid of weight are reciprocally proportional to their diftances from the ful¬ crum, they will be in equilibrio. For if an equilibrium does not take place, the pro¬ portion of the weights muft be altered to procure an equilibrium, and then, contrary to the propofition, the weights would balance each other when they were not reciprocally proportional to their diftances from the fulcrum. 43. Cor. 2. If a weight W be fupported by a hori¬ zontal.lever refting on the fulcra A, B, the preffure up-Fi? d on A is to the preffure upon B in the inverfe ratio of * their diftances from the point where the weight is fuf¬ pended, that is, as BF to FA. For if we fuppofe B to be the fulcrum, and if removing the Theory. Fig- 5- Fig. tf. M E C H the fulcrum A, we fupport the extremity A of the lever by a weight E equivalent to the weight fuftained by the fulcrum A, and afting upwards over the pulley P, then the weight E or that fuftained by A : WrrBF : BA (Prop, i.) 5 and if we conceive A to be the ful¬ crum, and fupport the extremity B by a weight F e- qual to that which was fupported by the fulcrum B, we ihall have the weight F or the weight fuftained by B : W=AF : AB. Hence ex ccquo the w-eight fuf¬ tained by A is to the weight fuftained by B as BF is to FA. 44. Cor. 3. We may now call the two weights P and W, the power and the weight, as in fig. 5, and fince P : W—FB : FA, we have (Geometry, Seft. iv. Theor. 8.) PxFA=WxEB, when an equilibrium takes place, W x FB „T P X FA confequently P: FA FA- W= W x FB FB FB= P P X F A W 45. Cor. 4. We have already feen (Axiom 2.) that when the power and the weight are on contrary fides of the fulcrum, the preffure upon_ the fulcrum is equal to P-f-W or the fum of the weights ; but it is obvious that when they a<5t on the fame fide of the ful¬ crum, the preffure which it lupports will be P W", or the difference of their weights. 46. Cor. 5. If a weight P be ftrifted along the arm of a lever AD, the weight W, which it is capable of balancing at A, will be proportional EA. When the weights are in equilibrio (Cor. 3.) W : P=FA : FB, or by alternation W : FArrP : FB, and if w be another value of W and^'n another value of FA, we (hall alfo have tu : V—fa : FB or w -.fa— P : FB, confequently (Euclid, Book v. Prop. xi. and xvi.) W’ : iu=FA :/tf, that is, W varies as FA. Cor. 6. It is obvious that the truths in the preced¬ ing propofition and corollaries, alfo hold when the lever has the form reprefented in figure 6. only the ftraight lines AF, FB are in that cafe the length of the arm. Defcription a*]. Cor. 7. Since by the laft corollary b A .fa—. of the fteel-\y'. Wf it follows that in the Roman fat era or fee In ard, yard or fta- js mereiy a lever with a long and (hort arm, hav¬ ing a weight moveable upon the long one, the diltances at which the conftant weight rruft be hung are as the weights fufpendcd from the ftiorter arm. The fteelyard is reprerented in fig. 7. where AB is the lever with un¬ equal arms AF, FB, and F the centre of motion. The body W, whofe w-eight is to be found, is fufpended at the extremity B of the lever, and the conftant weight P is moved along the divided arm FB till an equili¬ brium takes place. As foon as this happens, the num¬ ber placed at the point of fufpenfion D, indicates the weight of the body. If the lever is devoid of weight, it is obvious that the fcale EB wall be a fcale of equal parts of which EB is the unit, and that the weight of the body W will be always equal to the conftant weight P multiplied by the number of divifions between. P and F. Thus if the equilibrium takes place when P is pull¬ ed out to the 1 2 divifion, we ftiall have =12 P, and if P“1 pound, W=i 2 pounds. But when the gravity Fi£- 7- A N I C S. 55 of the lever is confidercd, which muft be done in the Tieory. ^ real fteelyard, its arms are generally of unequal weight, J "v and therefore the divifions of the fcale muft be afeer- tained by experiment. In order to do this, remove the weight P, and find the point C, at which a weight P7 equal to P being ftffpended, will keep the unequal arms in equilibrio, C will then be the point at which the equal divifions muft commence. For when W and P are placed upon the fteelyard and are in equilibrio, W balances P along with a weight which, placed at D, would funport P placed at C: iherefore Wx BF=r PxDF+PxCF; but PxDF+PxCF=Px DC, confequently Wx BF=P X DC,and (Geometry, Sed. iv. Theor. 8.) W : DCzrzP : BF. By taking different values of the variable quantities W and DC as w and dc, we Ihall have w : dc~V : BF, confequently (Euclid, B. V. Prop. xi. and xvi.) W : m^:DC : dc, that is, the weight of W varies as DC, and there¬ fore the diviftons muft commence at C. If the arm BF had been heavier than FA, which, however, can fcarce- ly happen in pradlice, the point C would have been on the other fide of F. In conftru&ing fteelyards, it might be advifable to make the unequal arms balance each other by placing a weight M at the extremity of the lighter arm, in which cafe the fcale will begin at F. In the Danifh and Swedish Danifti and fteelyard the body to be weighed and the conftant Su-dlfh weight are fixed at the extremities of the fteelyard, butftee'Jar, confidered as without weight, fo that a cz=.cf—fd—db. Then if/ be the centre of motion or point of fufpenfion, the cy¬ linder AB will be in equilibrio ; for the weight AB may be regarded as compofed of a number of pairs of equal weights, equally diftant from the centre of mo¬ tion. For the fame reafon, if we conceive the cylinder to be cut through at F the equilibrium will continue, c, d being now the points at which the weights AF, FB ad, and their diftances c/, d/from the centre of motion being equal. Confequently the arms AF, FB have the fame energy in turning the lever round/as if weights equal to AF, FB were iufpended at the diftance of their middle points c, d from the fulcrum. Let P therefore, in fig. 5. be the power, W.the^. weight, m the weight of the arm AF, and ff the weight lg‘ - of FB. Then when there is an equilibrium we ftiall have (Prop. I. Cor. 3.) PX AF-fX |AF=WX FB + « X J-FB anci fince the weight m ading at half the diftance AF is the fame as half the weight m, ading at Theory, the whole diflance AF, we may fubftitutew x AF — jnftead of m X 4 AF, and the equation becomes iM-1 m'x AF—W:X FB. Hence W+4« X FB P"" AF ' W: P4-i« X AF , - ~Z 71 FB MECHANICS: Hence AE x F/« = BK X F/i, and AE: BK or P : W Theory. ~F«: Ffw. E. D. . 53. Cor. 1. The forces P and W are reciprocally proportional to the fines of the angles which their di-FlS- 1- & 2- redlions make with the arms of the lever, for 1 m is evidently the line of the angle FA wz, and F n the fine of the angle FB«, FA, FB being made the radii ;— therefore P : W — Sm. FB n : Sm. FA or I : W , m W + i» X 'iFB m=: — 2P AF x ?AF _2tvV FB AF= W+4« XFB FB: Sin. FA»z ’ Sin. FB« Sin. FA77?, we have Ymzz: Since F A : F /» zz Rad. FA X Sin. FA777 Rati. and lince FB X Sin.FErz’ Rad. P-j-4"z P-f l/TZ X ^F W 50. Cor. If the arms of the lever are not of uniform deniity and thicknefs, inftead of the diftar.ee of their middle points, we muft take the diftance of their centre of gravity from the fulcrum. Prop. III. r j, If two forces a£Ung in any dire&ion, and in the fame plane, upon a lever of any form, are in equilibrio, they will be reciprocally propor¬ tional to the perpendiculars let fall from the fulcrum upon the dire£tions in which they aft. 52. Let AFB be a lever of any form, F its fulcrum, Plate ^ points to which the forces, or the power P and CCGXVIL w ’ t are and AE, BK the direftions in *‘S' which thefe forces aa. Make AE to BK as P is to W, and they will therefore reprefent the forces applied at A and B. Draw AC perpendicular to AF and EC parallel to it, and complete the parallelogram ADEC. In the fame way form the parallelogram BGKH. Produce EA and KB towards m and n if neceffary, and let fall F m, F n perpendicular to AE, BK produced. Then P (hall be to W as En is to Fm. By the refolution of forces (Dynamics, 140.) the force AE is equivalent to forces reprefented by AD and AC, and afting in thefe dire&ions. But as AD afts in the dire&ion of the arm AF, it can have no influ¬ ence in turning the lever round F, and therefore AC reprefents the portion of the force AD which contri¬ butes to produce an angular motion round F. In the fame way it may be fhewn that EG is the part of the force BK which tends to move the lever round E. Now fuppofe AF produced to B, FB, being made equal to FB and B'G'zziBG. Then by Prop. I. AC : B'G' zzFB' : FA i but by Axiom 1. the effort of BG to turn the lever round F is equal to the effort of the equal force B' G' to turn the lever round F 5 therefore AC : BGzzFB : FA and AC X FAzzBG X FB. Now the triangles ACE, AE 777 are fimilar, becaufe the angles at F and M are both right, and on account of the parallels DF, AC, MACzr ADF; theretore AC : A.EzzF777: FA, and AC X FA=z AE X F777. For the fame reafon in the fimilar triangles BGK, Bb 77 we have BG : BK=Fn : FB, and BK xF« zz BG xFB. FB: F77zzRad. : Sin. FB;/, tve have F777: but in the cafe of an equilibrium P : W=F/2 : Ftt/, con , , ^ FB X Sin. FB v FA x Sin.FA777 fequently P : W rz Rad. ' Rad. and fince magnitudes have the fame ratio as their equi¬ multiples, P : WzzEB X Sin, EB« : FA X Sin. FA777. ^4. Cor. 2. The energies of the forces P, W to turn the lever round the fulcrum F is the fame at what¬ ever point in the ditecHons 777 E, 77 K they are applied, for the perpendiculars to which thefe energies are pro¬ portional remain the fame.—The truth of this corollary has been affumed as an axiom by fome writers on me¬ chanics, who have very readily deduced from it the preceding propofition. But it is very obvious that the truth affuraed as felf-evident is nearly equivalent to the truth which it is employed to prove. Thofe who have adopted this mode of demonftration illuftrate their axiom by the cafe of a folid body that is either puftied in one dire&ion with a ftraight rod, or drawn by a cord ; in both of which cafes it is manifeft that the effeft of the force employed is the fame, at whatever part of the rod or firing it is applied : But thefe cafes are completely different from that of a body moving round a fixed centre. 55. Cor. 3. If AE and BK the dire£lions in which •the forces P, W are exerted be produced till they meet at L ; and if from the fulcrum Ethe line FS be drawn parallel to the direction AL of one force till it meets B L, the direftion of the other } then LS, SF will reprefent the two forces. For as the fides of any triangle are as the fines of the oppofite angles LS : SFzz fin. Li'S : fin. FLS \ but on account of the parallels FS, AL the angle LFSzzFLA, and FL being radius Ym is the fine of FLA or LFS, and F77 the fine of FLS, there¬ fore by fubftitution LS : SY=Ym : F//, that is as the force W : P. 56. Cor. 4. If feveral forces aft upon a lever, and keep it in equilibrio, the fum of the produfts -of-the forces and the perpendiculars from the fulcrum to the direftion of the different forces on one fide is equal to the fum of the produfts on the other. For fince the energy of each force to turn the lever is equal to the produft of the force and the perpendicular from the fulcrum on the line of its direftion ; and fince in the cafe of an equilibrium, the energy of all the forces on one fide of the fulcrum muft be equal to the energy of all the forces on the other fide, the produfts proportion¬ al to their energies muft alfo be equal. 57. Cor. 5. If two forces aft in a parallel direftiotv upon an angular lever whofe fulcrum is its angular point, # MECHANIC Theory. Fig- 3* Fig. 4- Fig- 5- Fig. 5. Fig 7. point, tliefe forces will be in equllibiio when a line drawn from the fulcrum upon the line which joins the two points where the forces are applied, and parallel to the di- re&ion of the forces, cuts it in fuch a manna that the two parts are reciprocally proportional to the forces applied. Let AFB be the angular lever, whole fulcrum is F, and let the forces P, W be applied at A and B in the parallel directions P w, W n •, then if the line l D, pa¬ rallel to P fTi or W w, cut AB in fuch a manner that DB : DA=rP : W, the forces will be in equilibrio. Draw F m perpendicular to P m, and produce it to « j then fmce Aw, B« are parallel, mn vn\\ alfo be perpendicular to B «, and by the propolition (Art. J1-) F w : F w = P : W. Now, if through F, there be drawn m' n' parallel to AB, the triangles F m F n n' will be fimilar, and we (hall have F« : F m~Yn' : b m', but on account of the parallels AB, m' n'; F n' : Y m' rrDB : DA, therefore DB : DAr=P : W. 58. Cor. 6. Let CB be a body moveable round its centre of gravity F, and let two forces P, W aft upon it at the points A, B in the plane AbB, in the directions AP, BW j then fince this body may be re¬ garded as a lever whofe fulcrum is F, the forces will be in equilibrio w’hen P : W —F n : F m the perpendicu¬ lars on the direftions in which the forces aft. 59. Cor. 7. If AB be an inflexible rod moveable round F as a fulcrum, and aCted upon by two forces P, W in the directions A m, A n, thefe forces will be in equilibrio when they are to one another as the per¬ pendiculars F F w.—For by cor. 2. the forces may be confidered as applied at 111 and », and w b may be regarded as the lever j but by the propofition (Art. 51.) p ; W=F«:Fw,- Fw, Y n being perpendiculars upon Aw, Aff. , , 1 xfr' 60. Cor. 8. Let DE be a heavy wheel, and btr an obftacle over which it is to be moved, by a lorce P, aCting in the direction AH. Join Ab and draw F w, F n perpendicular to CA and' AH. 1 he weight of the wheel is evidently the weight to be raifed, and may be reprefented by W aCting at the point A in the vertical direction AC. We may now confider AF as a lever whofe fulcrum is F, and by cor. 7* there wid be aa equilibrium when P : WrrF n \Y ru. Since b ni re- prefents the mechanical energy of the power P to turn the wheel round F, it is obvious that when FG is equal to the radius of the wheel, the weight P, however great, has no power to move it over the ooltacle ; .or when FG—AC, Ym =0, and Fw> be drawn perpendicular from the point P' to FC, Y f> will be the lever with which the man in the fcale tends to turn the lever ^ round the fulcrum •, and as Fp is greater than F A, tne man .Wt Vol. XIII. Part I. s. 57 preponderate. In the fame way it may be fliovvn, that Theory, if the man in the fcale AP prefles upwards againft x point C, more remote from the fulcrum than A, he will diminifti his relative weight, and the fcale W will preponderate, for in this cafe the fcale affumes the pofition AP", and Yp/ becomes the lever by which it ads. 62. Cor. xo. If a weight W be fupported by an Tig. S. inclined lever "refting on the fulcra A, B, the pref- fure upon A is to that upon B inverfely, as A f is to f b, the fe&ions of a horizontal line by the vertical di¬ rection of the w-eight W. Remove the fulcrum A, and fupport the extremity A by a weight P, equal to the preflure upon A 5 then B being the centre of motion, and m n being drawn through F perpendicular to the directions of the forces A wz, Ey, and confequently parallel to A b, we have (Art. 51.) P : W=F n : Y m-=z fb : f A. that is, the preffure upon A is to the preffure upon B inverfely as A f is tofb. - Scholium. 63. Various attempts have been made by different wai¬ ters on mechanics to give a complete and fatisfaClory demonftration of the fundamental property of the lever. The firft of thefe attempts wTas made by Archimedes, wTho affumes as an axiom, that if twro equal bodies be placed upon a lever, they will have the fame influence in giving it a rotatory motion as if they were both placed in the middle part between them. This truth, how7ever, is far from being felf-evident, and on this account Mr Vince * has completed the demonflration by making this axiom a preliminary propofition. The p 3. demonftration of Galileo f is both fiiiiple and elegant, , y and does not feem to have attraCled much notice, 'et E)em'(m, though in principle it is exaftly the fame as that ofjirationes Archimedes completed by Mr Vince. Galileo fufpends a folid cylinder or prifm from a lever by feveral ^al; threads. When the lever is hung by its centre, the1’'5 * whole is in equilibrio. Fie then fuppofes^the cylinder to be cut into two unequal parts, which from their mode of fufpenfion ftill retain their pofition, and then imagines each part of the cylinder to be fufpended by its centre from the lever. Here then we have two unequal weights hanging at unequal diftances from the centre of fufpenfion, and it follows from the conftruc- tion, that thefe weights are in the reciprocal ratio of their diftances from that centre. Mr Vince, on the other hand, employs a cylinder balanced on a fulcrum; He fuppofes this cylinder divided into unequal parts, and thus concludes from his preliminary propofition, that thefe unequal parts have the fame effesft in turning the lever as if the weight of thefe parts was placed in their centres ; which is done by Galileo by fufpending them from their centres. From this the fundamen¬ tal property of the lever is eafily deduced.— T he next demonftration was given by Huygens, who affumes as an axiom, that if any weight placed upon a lever is removed to a greater diftance from the fulcrum, its ef¬ fort to turn the lever will be increafed. This axiom he might have demenftrated thus, and his demonftra¬ tion would have been completely fatisfadlory, though it applies only to cafes where the arms of the lever pjate are commenfurable. Let AB. be a lever .with equal CCCXVI. weights C, D, (imported on the fulcra /, F, fo that kg. 1. e H A/= MECHANICS. '*• Account of New- toiis Dif- t emeries Plate Theory. A /rrFB ; then, as was fliown in Prop. I. the weights ■ '"'V— ' will be in equilibrio, and each fulcrum will fupport a weight equal to C or D. By removing the fulcrum f, the weight C muft defeend, as the equilibrium is de- "ftroyed by a weight equal to C a&ing at f; therefore the weight C, at the diltance AF, has a greater eftea in turning the lever than an equal weight D placed at a lefs diftance FB.—In Sir Ifaac Newton’s demonflra- tion, it is fuppofed that if a given weight aft in any dire&ion, and if feveral radii be drawn from the ful¬ crum to the line of diredlion, the effort of that weight to turn the lever will be the fame to whatever of thefe radii it is applied. It appears, however, from Art. 54. that this principle is far from being leif-evident, and therefore the demonftration which is founded upon it cannot be admitted as fatisfaclory. The demondration given by Maclaurin * is fimple and convincing, and has been highly approved of by Dr F.Young, and other ■writers on mechanics, though it extends only to any commenfurable proportion of the arms. Fie luppoles the lever AB with equal arms to be in equilibrio upon CCX X VII. j.}le fuicrum Fj by means of the equal forces P, W, in which cafe the fulcrum F will evidently be preffed dowm with a weight equal to 2 P~P-J-AY Fie then fubditutes, indead of the weight P, a fixed obdacle O, which will not dedroy the equilibrium, and conjiders the fulcrum as fill loaded with a weight equal to P-f- vV. The preffure on F being therefore equal to 2 P or P_l_W, a weight E equal to 2 P, and a&ing upwards, is lubdituted in the room of that preffure, fo that the equilibrium will dill continue. He: e then we have a lever AB of the fecond kind, influenced by two forces E and W a fling at different didances from the fulcrum A; and fince E=2P=2W, and ABrrlAF, we have E : WrzAB : AF, wdrich expreffes the funda¬ mental property of the lever. Without objefling to the circumdance that this demondration applies only to the lever of the fecond kind, we may be allowed to obferve, that it involves an axiom which cannot be called felf evident. It is certainly manifed that when P and W are in equilibrio, the preffure upon the ful¬ crum is — 2 P=rP-j~W; but it by no means follows that this preffure remains the fame when the fixed obdacle O is fubdituted in the room of P. On the contrary, the axiom affirmed is a refult of the propofition which it is employed to prove, or rather it is the propofition itfelf. For if, when the extremity A bears againd the ob¬ dacle O, the preffure upon F is equal to 2 W, the force W obvioufly produces a preffure rr 2W at half the didance AB, which is the property to be demondrated. -—The demondrations given by Mr Landen and Dr Hamilton, the former in his Memoirs, and the latter f See alfo in his Effays f, though in a great meafure fatisfaflory, Mil. Tianf.^xt long and tedious. In the demondration of Dr Ha- vol. xciii. nulton, he employs the following propofition 3 that when a body is at red, and afted upon by three forces, they will be to one another as the three fides of a tri¬ angle parallel to the direflion in which the forces aft. When the three Forces aft on one point of a body, the propofition is true, but it is not applicable to the cafe jj>f a lever where the forces are applied to three different points, and at all events the demondration does not hold when any two of the forces aft in parallel direc- Theory, tions. The demondration which we have given in ~ v f Prop. I. is new, and different from any that have been noticed. The truths on which it is founded are per- feftly axiomatic ; and the only objeftion to which it feems liable is, that the demondration extends only to a commenfurate proportion of the arms of the lever.— An analytical demondration of the fundamental pro¬ perty of the lever was given by Fonceneix in the Mif- cellan. Jour. tom. ii. p. 321. which was afterwards im¬ proved by D’Alembert in the Mem. de I’Acad. 1769. p. 283. Prop. IV. 64. When feveral levers AB, a a fly whofe fulcra Plate are F,^ /:«/ N : W—/3 (p :a

Prop. V. 65. To explain the new property of the lever dis¬ covered by M. iEpuius, and extended by Van Swinden. Let AFB be any lever whofe fulcrum is F, and to ^ whofe extremities A, B are applied the forces P, W in the direftions AY, BO. Join AB, and produce it on both fides towards E and I. Produce alfo the lines YA,VB till they met in H, and from H, through the fulcrum F, draw HFf dividing AB into two parts Af B f Let UM be a line given in pofition, and let «, p reprefent the angles which the direftion of the forces YA, VB make with that line. Let YA and AB like- wife reprefent the intenfity of the forces P, AA, and let VA be refolved into AE and YF 3 and the force VB into BI and VI.—Then the lever cannot be in equili¬ brium till I. EAx/A-flBx/B is a maximum. II. Or pitting

b for tlie arms AF, BF, and n for the angles EAB, EBA, there cannot be an , If^orv- t ——V—' equilibrium unlefs i'-’g- 3- Tang. W. b (Sin. (I X Cof. n—Sin. n X Cof. /3)— P. a (Sm. * X Coi. m—Sin, w x Co(».') P. a (Col. as x Col. to-(-Sin. » X Sin. to) -}-W. b (Cof. p X Cof. w-j-Sin. p x Sin. «.) As the demonftrations of thefe different cafes are far from being elementary, we lhall only refer the reader to the memoir upon this fubjeft given by iEpinus in the Nov. Comment. Fetropol. tom. viii. p. 271. Scholium. 66. This property of the lever was only confidered by iEpinus in the cafe of a re£H!ineal lever with equal arms •, but was extended by J. H. Van Swinden. When the lever is redlilineal and with equal arms, we have AF=FB=Ayi=B /^ and alfo m~n~o, fo that, if the laft formula is fuited to thefe conditions, we lhall have the formula of iEpinus* Prop. VI. 67. If a power and weight a£Hng upon the arms of any lever be in equilibrio, and if the whole be put in motion, the velocity of the power is to the velocity of the weight as the weight is to the power. Let AFB be any lever whofe fulcrum is F, and let the power P and weight W be applied to its extremi¬ ties A, B, fo as to be in equilibrio. Draw F to, F« perpendicular to AD, BE the direftion of the forces P, W. Then hippofe an uniform angular motion to be given to the lever, fo as to make it defcribe the fmall angle AFA', the pofition of the lever will now be A'FB', and the dire&ions of the forces P, W will be A'D', B'E' parallel to AD, BE refpedtively, fince the angle AEF is exceedingly fmall. Join AA', BB', and from A' and B' draw A'x, B'z perpendicular to AD and BE. Now it is obvious, that though the point A has moved through the fpace AA7 in the fame time that the point B has defcribed the fpace .BB', yet A x is the fpace defcribed by A in the diredlion AD, and B 2; the fpace defcribed by B in the direftion BE. For if we fuppofe a plane paffing through A at right angles to AD, and another through P parallel to the former plane, it is manifeft that A x meafures the ap¬ proach of the point A to the plane paffing through P $ and for the fame reafon B 55 meafures the approach of the point B to a plane paffing through W at right angles to WB. Therefore Ax, B« reprefent the (paces uniformly and fimultaneoufly defcribed by the points A, B, and may therefore be taken to denote the velocities of thefe points (Dynamics, § 14.); confe- quently the velocity of A : the velocity of B=A*: B ss. Isiow, in the triangles A x A', F to A, the exterior an¬ gle x AF= A to F+w F, A (Euclid. B. I. Prop. 32.) and A'AF=AtoF, becaufe AFA' is fo exceedingly fmall that A'A is fenfibly perpendicular to AF-, confe- quently x AA'rr AE to : and as the angles at w and to are right, the triangles A x A', A to F are fimilar (Geometry, Theor. XX. Se£L IV.). Therefore, Ax: AA'—Fto : FA, and in the fimilar tri¬ angles AFA', BFB' A A': BB'rrFA : FB, and in the fimilar triangles BB'iZ, BF w, BB' : B 25=rFB : F therefore by compofition we have A x : B ;s=F to ; Fn. But by Propofition II. P : WrzF « : F to, confequent- lj A x : B 2=W : P, that is, the velocity of the power is to the velocity of the weight as the weight is to the power. £L E. D. 68. Cor. Since Ax : B 3=W : P we have AarxP rrBzxW, that is, the momenta of the power and weight are equal. Sect. II. On the Inclined Plane. 69. Definition. An inclined plane is a plane fur- Cf cxvilt face AB, fupported at any angle ABC formed with Fig. 4- the horizontal plane BC. The inclination of the plane is the angle which one line in the plane AB forms with another in the horizontal plane BC, both thefe lines being at right angles to the common interfeflion of the^ two planes.—The line BA is called the length of the plane, AC its height, and BC the length of its bafe. 70. In order to underhand how the inclined plane a£fs as a mechanical power, let us fuppofe it neceffary to elevate the weight D from C to A. If this weight is lifted by the arms of a man to the point A, he muff fupport the whole of the load j but when it is rolled up the inclined plane, a confiderable part of its weight is fupported upon the plane, and therefore a much fmaller force is capable of raifing it to A. Prop. I. 71^ When any weight W is kept in equilibrio up-Fig. 5. on an inclined plane by a power P, the power is to the weight as the fine of the plane’s inclina¬ tion is to the fine of the angle which the direc¬ tion of the power makes with a line at right angles to the plane. Let MN be the inclined plane, NO a horizontal line, and MNO the inclination of the plane, and let the weight W be fuftained upon MN by means of the power P afling in the diredlion AE. From the point A, the centre of gravity of the weighs draw AB per¬ pendicular to the horizontal plane ND, and AF per¬ pendicular to MN 5 produce EA till it meets the plane in C, and from the point F where the body touches the plane draw F to at right angles to AC, and F « at right angles to AB. Then, fince the whole body may be confidered as colle&ed in the centre of gravity A, AB will be the dire&ion in which it tends to fall, or the di- redlion of the weight, and EA is the dire&ion of the power •, but AF is a lever whofe fulcrum is F, and fince it is a died upon by two forces which are in equilibrio, we lhall have (Art. 59.) P : W=F n :¥ m, that is,, as the perpendiculars drawn from the fulcrum to the direction in which the forces aft. Now FA being radius, F n is the fine of the angle FAB, and F to is the fine of the angle FAC ; but FAB is equal to MNO the angle of the plane’s inclination, on account of the right angles at F and B and the vertical angles at D; and FAC is the angle which the diredlion of the power makes with v a line perpendicular to the plane j therefore P; W H 2 as 6o MECHANICS. • Theory, as the fine of the plane’s inclination, is to the fine of the angle formed by the direction of the power with a line at right angles to the plane. 72. Cor. 1. When the power a&s parallel to the plane in the direction AE', P is to W as EA to E «, that is, as radius is to the fine of the plane’s inclination, or, on account of the fimilar triangles FA n, MNO, as the length of the plane is to its height. In this cafe the power acts to the greateft advantage. 73. Cor. 2. When the power a£ls in a vertical line A t, F w becomes equal to or coincides with F «, and W’e have P : W—F « : F that is, the power in this cafe fuftains the whole weight, 74. Cor. 3. When the power a&s parallel to the bafe of the plane in the direction Ac, PiW^FwiFy* ~F n \ A n. 7 5. Cor. 4. When the power adls in the direftion AF e' perpendicular to the plane, it has no power to refill the gravity of the weight j for the perpendicular from the fulcrum F, to which its energy is proportional, vanifiies. fpherical body which they fupport. The whole of its matter being fuppofed to be colledled in its centre of gravity F, its tendency downwards will be in the ver¬ tical line FO. The readtion of the planes upon F is evidently in the diredtion MF, NF perpendicular to the iurface of thefe planes, and therefore wTe may con- fider the body F as influenced by three forces adling in the diredlions FC, FM, FN j but thefe forces are re- prefented by the fides of the triangle ABC perpendicu¬ lar to their diredtions, (£> YNAMICS, §. 144.), confe- quently the abfolute weight of the body F, the preflure,. upon the plane AC, and the preflhre upon the plane EC, are refpedtively as AB, AC, and EC, that is, a* the fines of the angles ACD, ABC, BAG, for in every triangle the fides are as the lines of the oppofite angles, or, to exprefs it in fymbols, W being the abfolute weight of the body, vj the preffure on AC, and w' the prefl'ure on BC, Theory. W : 10 : wr=AB : AC : BC, or W : w : "u/r^fin. ACB : fin. ABC : fin. BAG'. 76. Cor. 5. Since the body W adts upon the plane in a direction AF perpendicular to the plane’s furface, (for its force dowmwards may be refolved into two, one parallel to the plane, and the other perpendicular to it), and fince the readtion of the plane mult alfo be perpen¬ dicular to its furface (Dynamics, § 149.), that is, in the diredtion FA, then, when the diredtion of the power is A c parallel to the horizon, the power, the wreight, and the preffure upon the plane, will be refpedtively as the height, the bafe, and the length of the plane. The weight W is adted upon by three forces •, by its oivn gravity in the diredtion A n, by the readtion of the plane in the diredtion AF, and by the power P in the diredtion AF. Therefore, fince thefe forces are in equilibrio, and fince A jf is parallel to « F, and Fy to A«, the three fides AF, Ay Yf, will reprefent the three forces (Dynamics, §. 144.)* Eut the triangle AFy is fimilar to A « F, that is, to MNO, for it wras already Pnewn that the angle n AF is equal to MNO, therefore, fince in the triangle AFy AF reprefents the prefibre on the plane, A f the weight of the body, and F f the energy of the power, thefe magnitudes will alfo be reprefented in the fimilar triangle MNO by the fides MN, MO, NO. 77. CoR.. 6. If a power P and weight W are in equilibrio upon two inclined planes AB, AC; P : W~ Fig 6. AB : AC. Let p be the power, which adling on the weight W in a diredlion parallel to the plane w’ould keep it in equilibrio, then we have p \ Wz=AD : AC ; but fince the firing is equally firetched at every point, the fame powerp wall alfo fufiain the power P, con- fequently P :/>—AB : AD, and by compofition P : W = AB : AC. Prop. II. 78 If a fpherical body is fupported upon two in¬ clined planes, the preflures upon thefe planes will be inverfely as the fines of their inclination, while the abfolute weight of the body is repre¬ fented by the fine of the angle formed by the two planes. Let AC, BC be the two inclined plane-, and F the But on account of the parallels AB, DF, the angle ABC~BCF, and BACizrACD, therefore the pref- fures upon the planes are inverfely as the fines of their inclination^ the abfolute weight of the body being re¬ prefented by the fine of the angle formed by the fur- faces of the two planes. 79. Cor. I. Since the two fides of a triangle are Corollaries, greater than the third, the fum of the relative weights lupported by the two planes is greater than the abfolute weight of the body.. 80. Cor. 2. If the inclination of each plane is 6o°, then ACB mull alfo be 6o°, and the triangle ABC equilateral, confequently the prefl'ure upon each plane is equal to the abfolute weight of the body. 81. Cor. 3. When the inclination of each plane increafes, the prefl'ure which each fuftains is alfo in- creafed ; and when their inclination diminifhes till it almoft vanifties, the piefiure upon each plane is one half of the abfolute weight of the body F, Prop. III. 82. If a body is raifed with an uniform motion along an inclined plane, the velocity of the power is to the velocity of the weight as the weight is to the power. Let the weight W be drawn uniformly up the in- Fig. 8. dined plane AB, from B to D, by a power whofe di¬ rection is parallel to DH. Upon DB defcribe the circle BFEDN, cutting BC in E, and having pro¬ duced HD to F, join FP, FB, FE, and draw DC per¬ pendicular to BD. Now the angles BED, BED are right (Geometry, Seft. II. Theor. 17.), and there¬ fore, though the power moves through a fpace equal to BD, yet its velocity in the direction DH is meafured by the fpace ED uniformly delcribed ; and lor the fame reafon, though the weight W defcribes the fpace BD, yet its velocity in the direClion in which it aCts, that is, in a vertical direction, is evidently meafured by the fpace DE uniformly defcribed. Then becaufe |the triangle DEE is equal to DFE, (Geometry, SeCt. II. Theor. 15.) and DBErrDCH, (Geometry, SeCt. iV. Theor. 23.) and FDE—DHC, (Geometry, SeCt. I. Theor. 21.) Fig. 7. M E C H A N Theory. 2i.) tKe triangles DFE, DHC are fimilar, and (Geo- —y metry. Sea IV. Theor. 20.) DF : DErrDH :HC. But DH : HC=(in. DCH : fin. HDC, that is, (art, 71.) DF : DE, or the velocity of the power to the ve¬ locity of the weight, as W : P. $)• E. D. Scholium. 82. The inclined plane, when combined with ether machinery, is often of great ufe in the elevation of weights. It has been the opinion of fome writers, that the^huge maffes of done which are found at great alti¬ tudes in the fplendid remains of Egyptian architeaure, were raifed upon inclined planes of earth, with the aid ®f other mechanical powers. This fuppofition, how¬ ever, is not probable, as the immenfe blocks of granite which compofe the pyramids of Egypt-could not pof- fibly have been raifed into their prefent fituation by any combination of the mechanical powers with which we are acquainted.—dhe inclined plane has. been very advantageoufly employed in the duke of Bridgewater s canal. After this canal has extended 40 miles on the fame level, it is joined to a fubterraneous. navigation about 12 miles long by means of an inclined plane, and this fubterraneous portion is again connefted by an inclined plane with another fubterraneous portion aoout 106 feet above if. This inclined plane is a ftratum of done which (lopes one foot in four, and is about 453 feet long. The boats are conveyed from one portion of the canal to another by means of a w'indlafs, fo that a loaded boat defending along the plane turns the. axis of the windlafs, and raifes an empty boat—A pair of flairs, and a road that is not level, may be regarded as inclined planes-, and hence it is a matter of great importance in carrying a road to the top of a hill, to choofe fuch a line that the declivity may be the leatt poffible. The additional length, which, in order to effea this purpofe muft fometimes be given to tne.lineot road is a trifling inconvenience, wdien compared with the advantages of a gentle declivity. Fig. 9. I c s. DE : BE= fin. DBF : fin. BDE, and on account of the parallels DE, AB, the angle BDE= ABD, con- fequently P : />=fin. DBE : fin. BDE. 86 Cor. 1. When the line joining the pulleys is horizontal, as AC, then P ■ : f°r FA are evidently the lines of the angles DBE, BDE. 87. Cor. 2. Any of the powers is to the weight, as the fine of the angle which the other makes with the direftion of the weight, is to the fine of the angles which the power makes with one another, for hnce DB reprefents the weight, and BE the power P, we. have BE: BD=fm. BDE. :fin. BED j but on account of the parallels DE, AB, the angle DEB—ABC, the angle made by the diredlion of the powers, confequent- ly BE : BD, that is, fi : W=fin. ABF : fin. ABC. In the fame way it may be ihown that P : W —mn CBF : fin. ABC. Hence we have I : W — fin. CBFfl-fin• ABF7fin. ABC, that is, the fum, of the powers is to the weight, as the fum of the. fines of the angles which the powers make with the Sect. III. On the R^e Machine. 84. Definition. When a body fufpended by two or more ropes, is fuftained by powers which ad. by the afliftance of thefe ropes, this affemblage of ropes is called a rope machine. Prop. I. 8 c If a weight is in equilibrium with two powers acting on a rope machine, thefe powers are verfely as the fines of the angles which the ropes form with the dire£tion of the weig it. Let the weight W be fufpended. from the point B, where the ropes AB, BC are joined,, and let the powers P, p afting at the other extremities of the ropes which pais over the pulleys A, C, k«P‘his.we1^'J1 equilibrio, we (hall have P :/=fin. CBD : fin. ABD. Produce WB to F, and let BD reprefent the force exerted by W then by drawing DE parallel to AB, the fides of the triangle BDE will reprefent the three forces by which the point B is foliated (Dynamics, 144 ), for AB. CB are the directions of the forces P and p. We have therefore P :/>erDE:BE; but lines Ui tut - r , 1 • V diretion of the weight is to the (me of the angle which, the powers make with one another. 88. Cor. 3. The two powers P, />, are alio diretly proportional to the cofecants of the angles formed oy the diretion of the powers with the di ret ion of the weight. For fince P :/>=fin. DBE : fin. BDE, and by the principles of trigonometry, (in. DBE : fin. DBE — cofec. BD E : cofec. DBE, we have P :/> — coiec. ABF ■ cofec. CBF. It is alfo obvious that P :/> as the fecants of the angles which thele powers form with, the horizon, fince the angles which they make with the horizon are the complements of . the angles which. they form with the diretion of the weight, and the coie- cant of any angle is juft the fecant of its complement, therefore P : />=rfec. BAF : iec. LCF. Chap. II. On Compound Machines. 80 Definition. Compound machines are thole which are compofed of two or more Ample machines, either of the fame or of different, kinds. I be numoer of compound machines is unlimited, but thofe which properly belong to this chapter, are, 1. I he wheel and axle; 2. The pulley; 3. The wedge; 4. I he ferew ; and 5. The balance. Sect. I. On the Wheel and Axle. 00. The wheel and axle, or the axis in peritrochio, Fig. i« is reprefented in fig. 9. and confifts of a wheel AB, and cylinder CD having the fame axis, and moving upon pivots E, F placed at the extremity of the cylinder. The power P is moft commonly applied to the circum¬ ference of the wheel, and aa* in the direaion o* the tangent, while the weight W is elevated by a rope- which coils round the cylinder CD in a p ane perpen¬ dicular to its axis—In this machine a mnch or handle - EH is fometimes fubftituted mflead of the wheel, and fometimes the power is applied to the levers S S hxec in the periphery of the wheel ; but in all thefe forms the principle of the machine remains unaltered--- That the wheel and axle is an affemblage o. levers vnil be obvious, by confidering that the very lame efleft would be produced.if a number of levers v.ere to ra*:- cUjuti. 6*2 MECHANICS. Theory, diate from the centre C, and if a rope carrying the v power P were to pafs over their extremities, and extri¬ cate itfelf from the defcending levers when they come into a horizontal pofition. 91. Axiom. The effeft of the power to turn the cylinder round its axis, is the fame at whatever point in the axle it is fixed. Prop. I. 92. In the wheel and axle the power and weight will be in equilibrium, when they are to one another reciprocally as the radii of the circles to which they are applied, or when the power is to the weight as the radius of the axle is to the radius of the wheel. Tig. 11. Let AD be a fedlion of the wheel, and BE a fec- tion of the axle or cylinder, and let the power P and weight W aft in the direftions AP, WP, tangents to the circumferences of the axle and wheel in the points A, B, by means of ropes winding round thefe circum¬ ferences. As the effeft is the fame according to the axiom, let the power and weight aft in the fame plane as they appear to do in the figure, then it is obvious that the effort of the power P and weight W wall be the fame as if they were fufpended at the points A, B ; confequently the machine may be regarded as a lever AFB, whole centre of motion is F. But fince the di¬ reftions of the power and weight make equal angles with the arms of the lever, we have (Art. 36.) P : W = FB : FA, that is, the power is to the weight as the radius of the axle is to the radius of the wheel. Corollaries. 93* Cor. 1. If the power and weight aft obliquely to the arms of the lever in the direftions A/>, B iu, draw Ym Yn perpendicular to A /» and B w, and as in the cafe of the lever (Art. 51.) there will be an equili¬ brium when P : W—F« : Ym. Hence the tangential direftion is the moll advantageous one in which the power can be applied, for FA is always greater than Ym, and the lead advantageous direftion in which the weight can be applied, for it then oppofes the greateft refinance to the power. 94. Cor. 2. If the plane of the wheel is inclined to the axle at any angle x, there will be an equilibrium when P : Wr= femidiameter of the axle : fin. x. 95. Cor. 3. When the thicknefs of the rope is of a fenfible magnitude, there will be an equilibrium when the power is to the weight as the fum of the radius of the axle, and half the thicknefs of its rope, is to the fum of the radius of the wheel and half the thick¬ nefs of its rope ; that is, if T be the thicknefs of the rope of the wheel, and t the thicknefs of the rope of the axle, there will be an equilibrium when P:W—FB-fTl ; FA-j-TT. 96. Cor. 4. If a number of wheels and axles are fo combined that the periphery of the firff axle may aft on the periphery of the fecond wheel, either by means of a firing or by teeth fixed in the peripheries of each, and the periphery of the fecond axle on the periphery of the third wheel, there will be an equilibrium when the power is to the weight as the produft of the radii of all the axles is to the produft of the radii of all the the wheels. This corollary may be demonftrated by k 2 . the fame reafoning which is ufed in Art. 63. for the Tftrory. combination of Levers. 97. Cor. 5. In a combination of wheels, where the motion is communicated by means of teeth, the axle is called the pinion. Since the teeth therefore muft be nearly of the fame fize, both in the wheel and pinion, the number of teeth in each will be as their circum¬ ferences, or as their radii 5 and confequently in the com¬ bination mentioned in the preceding corollary, the power will be to the weight, in the cafe of an equili¬ brium, as the produft of the number of tew'd in all the pinions is to the produft of the number of teeth in all the wheels. Prop. II. * 98. In the wheel and axle the velocity of the weight is to the velocity of the powei’ as the power is to the weight. If the power is made to rife through a fpace equal to the circumference of the wheel, the weight will evidently deferibe a fpace equal to the circumference of the axle. Hence, calling V the velocity of the power, v that of the weight, C the circumference of the wheel, and c that of the axle, we have V: v~Q, : c. But by the propofition P: Wzrc: G, therefore P : W : V. Scholium. 99. The conftruftion of the main-fpring box of the Onthefufee fufee of a watch round which the chain is coiled, is a of a watcli. beautiful illuftration of the principle of the wheel and axle. The fpring-box may be confidered as the wheel, and the fufee the axle or pinion to which the chain communicates the motion of the box. The power re- fides in the fpring wound round an axis in the centre of the box, and the weight is applied to the lower cir¬ cumference of the fufee. As the force of the fpring is greateft when it is newly wound up, and gradually de- creafes as it unwinds itfelf, it is neceffary that the fufee fhould have different radii, fo that the chain may aft upon the fmalleft part of the fufee when its force k greatefi, and upon the largeft part of the fufee when its force is leaft, for the equable motion of the watch requires that the inequality in the aftion of the fpring fhould be counterafted fo as to produce an uniform ef¬ feft. In order to faccomplifii this, the general outline of the furface of the fufee mufi be an Apollonian hyper¬ bola in which the ordinates are inverfely as their re- fpeftive abfeiffae. For further information on this fub- jeft, fee Rec/ierc/tes des Mat hem at. par M. Parent. tom. ii. p. 678. ; Traite d'Hor/ogerie, par, M. Berthoud, tom. i. chap. 26. $ and Traite de Mecanique, par M. de la Hire, prop. 72. Sect. II. On the Pulley. 100. Definition.—The pulley is a machine cora-Qnt[:)<. pofed of a wheel with a groove in its circumference, pUiiey. and a rope which paffes round this groove. The wheel moves on an axis whofe extremities are fupported on a kind of frame called the block, to which is generally fufpended the weight to be raifed. A fyfiem of pulleys is called a muffle, which is either fixed or moveable ac¬ cording as the block which contains the pulleys is fixed or moveable. Prop* MECHANICS. Theory. Prop. I. ioi. In a Tingle pulley, or fyftem of pulleys where the different portions of the rope are parallel to each other, and where one extremity ol it is fixed, there is an equilibrium when the power is to the weight as unity is to the number of the portions of the rope which fupport the weight. 'igv 12. 10 2. Case i. In the fingle faxed pulley A A let the power P and weight W be equal, and a£t againft each other by means of the rope PBAW, palling over the pulley AA ; then it is obvious that whatever force is exerted by P in the dire£fion PBA, the fame force mull be exerted in the oppofite direftion WBA, con- fequently thefe equal and oppofite forces mull be in equilibria •, and as the weight is fupperted only by one rope, the propofition is demonftrated, for P:W=ri : I. Pig, I3. 103. Case. 2. In the fingle moveable pulley, where 0 the rope, fafiened at H, goes beneath the moveable pulley D and over the fixed pulley C, the weight to be raifed is fufpended from the centre of the pulley D by the block />, and the power is applied at P in the direftion PE. Now it is evident that the portions CF/>, HGD of the rope fuftain the weight W, and as they are equally firetched in every point, each muft fuftain one half of W •, but (Cafe I.) in the fingle pulley C the rope CEP fuftains a weight equal to what the rope CF/> fuftains 5 that is, it fuftains one-half of W. Con- fequently P=^W, or W= 2P, when there is an equi¬ librium ; and fince the weight W is fupported by two firings, we have P : W =1:2. TV. 14- 15. 104- Case 3* When the fame rope paffes round a 10? ^ number of pulleys, the ropes which fupport the weight W are evidently equally ftretched in every part, and therefore each of them fuflains the fame weight. Confequently if there be ten ropes fupporting the weight, each fuftains -.yh part of the weight, and therefore P=1^W, or W=.io P, which gives us P : W=i t 10.—The pulley in fig. 15. is the patent pulley invented by Mr White, in wdiich the lateral fri&ion and ihaking motion is con- fiderably removed. Prop. II. 105. In a fyftem of ti moveable pulleys fufpended by feparate and parallel ropes, there is an equi¬ librium when P :W=i: 2W; that is, if there are 4 pulleys «—4, and P : W= 1 : 2 x 2 X 2 X 2, or P :W=i : 16. ‘ w This fyftem is reprefented in fig. 17. where the rope ,7’ which carries the power P paffes over the fixed pulley M, and beneath the moveable pulley A, to the hook E where it is fixed. Another rope fixed at A prffes over B and is fixed at F, and fo on with the reft. Then by Art. 103. P : the weight at A—J : 2 The weight at A : the weight at Bzrri : 2 The weight at B : the weight at C= 1 : 2 The weight at C : the wreight at D or W = 1 : 2 j and therefore by compofition P: W—1 : 2 X 2 X 2 X 2 or P; W=i : 16. O. E. D. 63 Prop. III. Tiieoiy. io<5. In a fyftem of moveable pulleys whofe num¬ ber is «, fufpended by feparate and parallel ropes, whofe extremities are fixed to the weight W, there is an equilibrium when P : W : 1 : 2" Fig. 18. —1. In this fyftem of pulleys, the rope which fuftains the power P paffes over the pulley C, and is fixed to the weight at D. Another rope attached to the pulley C paffes over the pulley B and is fixed to the weight at E, and a third rope faftened to B paffes over A and is fixed at F. Then it is manifeft that the rope CD fuftains a weight equal to P and fince the pulley C is pulled downward wdth a weight equal to 2 P, the rope BC muft fupport a weight equal to 2 P, and the rope B the fame weight) confequently the rope AB fuftains 4 P. The whole weight therefore is P4-2P-I-4P, and hence P : W=P : P-f 2P+4P, or P;W=i:t _}_2-F4 &c. to « terms, fo that P : W^i : 27<—1. Prop. IV. 107. In the fyftem of pulleys reprefented in pig. fig. 19. and called a Spaniih barton, in which two pulleys are fupported by one rope, there is. an equilibrium when P : W = 1 '.4. In this combination of pulleys, the rope AB which fupports the power P paffes over the moveable pulley- A, and beneath C towards H, where it is fixed. Ano¬ ther rope, attached to the pulley A, paffes over the fixed pulley B, and is faftened at E to the pulley C, which ‘ fupports the weight W. Then, fince the rope AP fup- perts 1 pound, the rope AC alfo fupports I pound, and therefore the pulley A, or the rope BA, is pulled? down with a force of 2 pounds. But the rope BDE is equally ftretched with BA, confequently the pulley C to which DE is attached, is pulled upwards with a force of 2 pounds. Now the rope AC fupporting 1 pound, the rope GH muft likewife fupport 1 pound, confeauently, fince DE fuftains 2 pounds, AC 1 pound, and HG 1 pound, they will together fuftain Wr^ pounds, and therefore P : W=ri : 4. Prop. V. 108. In the fyftem of pulleys reprefented in fig. Flg> 20_ 20. called a Spaniih barton, where two pulleys are fupported by one rope, there is an equili¬ brium when P : W= 1 ‘.5. In this fyftem the rope PB paffes over B round C, and is fixed at E. Another rope attached to B paffes round AF and is fixed at I to the pulley CD, which carries the weight W. Now the rope BP being ftretched with a force of I pound, the ropes BGC, CDE art alfo ftretched with a force of 1 pound each, and the pulley CD is pulled upwards with a force of 2 pounds. But fince the three ropes BP, ED, and GC, are each ftretched with a force of 1 pound, the pulley B and the rope BA, upon which they all aft in one direction, muft be pulled down with a force of 3 pounds. Now the rope FI is equally ftretched with BA, confequentiy it will draw the pulley CD upwards with a force of 3 pounds^, Theory. r 64 M K G H Theory. pounc!«, nnd fince it Is drawn upwards by the ropes -v CG. DF with a force of two pounds, the whole force will fudain W—5 pounds ; but this force of 5 pounds is by the hypothefis in equilibrio with P or 1 pound, confequently P : AV— 1 : 5. Plate Prof. VI. Fig. r. 109. V/hen the ropes are not parallel, and when two powers are in equilibrio with a weight by- means of a puiley, and have their directions at equal angles to the direction of the weight, each of thefe powers is to the weight as the radius of the pulley is to the chord of that por¬ tion of the pulley’s circumference with wdiich the rope is in contact. Let the weight W fufpended from C be fuftained in equilibrio by two powers P, />, which a£i by a rope PCF.E/ pafling over the pulley CHEF, and touching the arch CFE of its circumference. Then lince the angles PWD, /> WF) are equal, and the powers P,in equilibrio, P muft be equal to p; and making WA =WB, and drawing AI parallel to PW, and BI pa¬ rallel to/>W j WB, BI, WI will refpedtively repre- fent the forces P, /», W or P : : WrFWB : BI: WI, Dynamics Art. 144. Now the triangles WBI, CDE having their refpedlive fides at right angles to each other/are fimilar; confequently WB : BI : WJ =:CD : DE : EC, that is, P : />: W = CD : DE : EC ; but CD, DE are equal to radius, and EC is obvioully the chord of the arch CFE, therefore P : W or p : W as radius is to the chord of the arch with which the rope is in contaff. 110. Cor. 1. Any of the powers is alfo to the weight as radius is to twice the cofine of the angle wdn'ch either rope makes wdth the direclion of the weight. For fince CG is the cofine of DCG, and fince CE is double of CG, CE is equal to 2 cofine DCG — 2 Cos PWD ; but P : W=CD : CE, hence we have by fubftituting the preceding value of CE, P : W~CD or radius : z Cof. PWD. Scholium. hi. By means of this propofition and corollary, the proportion between the powers and the weight in the various fyftems of pulleys, repfefented in fig. 12, 13, 14, 15, 16. 17, 18, 19, 20. when the ropes are not parallel, may be eafily found. Prop. VII. 112. In a fyftem of moveable pulleys, where each has a feparate rope, and where the ropes are not parallel, there is an equilibrium when the power is to the weight as radius is to the cofmes of half the angles made by the rope of each pulley, multiplied into that power of 2 whofe exponent is the number of pulleys. Let the power P fuflain the weight W by means of the pulleys A, B, C j let P, />, 55- be the different powers which fupport the pulleys A, B, C, and let MAP, NBA, RGB be the angles formed by the ropes. Then, by the laft propcfition, A N I C S. P : /Srrrad. ; 2 cof. MAP p : : 2 cof. NB A 7r:Wrrrad. : 2 cof. RGB, confequemly P :W—rad. : 2 cof. M A P x 2 cof. NBA x 2 coi. RGB, or, which is the fame thing, P : W—rad. : 2x2x2 X cof. MAP X cof. NBAx cof. RGB. Prop. VIII. 113. In a fmgle pulley, or in a combination of pulleys, the velocity of the power is to the ve¬ locity of the weight as the weight is to the power. 114. Case i. In the fingle fixed pulley, it is ob-Fig. 1: vious, that if the weight W is raifed uniformly one inch, the power D will alio defcribe one inch, confe¬ quently velocity of P : velocity of WrzW : P. 115. Case 2. In the fingle moveable pulley, wFenpio-. ij, the weight W is raifed one inch, the ropes become one inch ihorter •, and lince the rope has alw’ays the fame weight, the powrer mult defcribe twTo inches, therefore velocity P : velocity W“ W : P. 116. Case 3. In the combination of pulleys, in Figs. 14,15, figs. 14, 13, 16, when the weight rifes one inch, each II5* of the four firings becomes an inch Ihorter, fo that P muff delcribe four inches, as the length of the rope is invariable j confequently velocity P : velocity W =: W : P. 11 7. Case 4. In the fyftem exhibited in fig. 17. it Fig. r?. is evident, that wrhen the weight W rifes one inch, the rope DC is lengthened twm inches, the rope CB four inches, the rope BA eight inches, and the rope AFP, to which the pow'er is fufpended, 16 inches 5 fo that fince the powder of this pulley is as 16 to 1, we have velocity P: velocity W—W : P. 118. Case 5. In the combination of pulleys, repre-Fig. iS, fented in fig. 1 8. when the weight W rifes one inch, all the three ropes CD, BE, AF are each Ihortened one inch. But while CD ihortens one inch, CP be¬ comes one inch longer ; while BE ftiortens one inch, BC becomes one inch longer, and CP two inches longer (art. 110.) ; and while AF ftiortens one inch, AB be¬ comes one inch longer, BC two inches longer, and QV four inches longer 5 therefore CP is lengthened al¬ together feven inches, and as the power of the pulley is as 7 to 1, we have, as before, velocity P velocity WrrW : P. 119. Case 5. In the fyfiem of pulleys, called the Fig. 1^. Spanilh barton, fig. 19. when the weight W rifes one inch, the three ropes AC, DE, FIG are each fhorten- ed one inch. By the fhortening of HG, CA one inch each, the rope AP is lengthened two inches ; and by the fhortening of DE one inch, BA is lengthened one inch, and AP two inches (art. 115.) ; confequently, fince AP is lengthened in all four inches, and fince the power of the pulleys is four, we have velocity P : velo¬ city W—W : P. 120. Case 6. In the other Spanifh barton, in fig. 20. Fig. 2». when the weight is elevated one inch, the three ropes DE, IF, CG are each one inch fhorter. While ED, and CG fhorten one inch each, BP is lengthened two inches, J M E C H Theory. inches, and while IF becomes one inch fhorter, AB be- —v—comes one inch longer \ but when AB is lengthened one inch, BP becomes one inch longer, and ED, CG one inch {hotter each, and by this ihortening of ED, CG, the rope B is lengthened two inches, therefore, fince the rope BP is lengthened altogether five inches, and fince the pulleys have a power of five, we have, as formerly, velocity P : velocity W— Yv : P. Sect. III. On the Wedge. j2i. Definition. A.wedge is a machine compofed of two inclined planes with their bafes in contact 5 or, more properly, it is a triangular prifm, generated by the motion of a triangle, parallel to itfelf, along a ft might lice pafting through the vertex of one of its angles. The wedge is called ifofcelcs, reel angular, Plate or fealene, according as the triangle ABC by which CCXIX. the wedge is generated, is an ifofceles, a re&angular ' fig. 3. or a fealene triangle. The part AB is called the head or back of the wedge, DC its altitude, and AC, BC its faces.—The wedge is generally employed for cleaving wood, or for quarrying llones; but all cutting inftruments, fuch as knives, fwords, chifels, teeth, S^c. properly belong to this mechanical power, when they aft in a direftion at right angles to the cutting fiirface ; for when they aft obliquely, in which cafe their power is increafed, their operation refembles mojre the aftion of a faw. Fig. 3- Prop. I. 122. If each of the faces of an ifofceles wedge, which are perfe&ly fmooth, meet with' an equal reft fiance from forces a£ling at equal angles of inclination to their faces, and if a power aft; perpendicularly upon the back, thefe forces will be in equilibrio, when the power upon the back is to the fum of the refiftances upon the fules, as the fine of half the angle of the wedge, multiplied by the fine of the angle at which the refilling forces aft; upon its faces, is to the fquare of radius. Let ABC be the wedge, AC, BC its aft mg faces, and MD, ND the direftions in which the refilling forces aft upon thde faces, forming with them the equal angles DMA, DNB. Draw CD, DF, DE at right angles to three fides of the wedge, and join F, E meeting CD in G, On account of the equal triangles CAD, CDB f Euclid, Book i. Prop. 26.) AD DB ; and in the equal triangles ADM, BDN, MD = ND. In the fame way DFrrDE and AF—BE, therefore CF=CE. But in the triangles CFG, CFG there are two fides IT , CG equal to EC, CG, and the angle FCG = ECG, con- fequently FG-GE, and FGC, ABC are both right an- aks, therefore FE is parallel to AB.—Now the force MD fs refolvable into DF, FM, of which FM has no effeft upon the wedge. But, as the effeftive force FD is not m direft oppofition to the perpendicular force exerted on the back of the wedge, we may refolve it into the two forces EG, GD, of which GD afts in direft oppofition to the power, while I G afts in a direftion parallel to the back of the wedge. In the fame way it may be {hewn that EG, GD are the only effeftive forces which refult VOL. XIII. Part I. A N I C S. G from the force ND. But the forces FG, EG being ^ j equal and oppofite, deftroy each other j coniequentiy 2 GD is the force which oppofes that which is exerted upon the back of the wedge, and the wedge will be kept at reft if the force upon the back is equal to 2 GD, that is, when the force upon the back is to the fum of the refiftances upon the faces as 2GD is to MD + ND, 01 as 2 GD : 2 DM, or as GD is to DM. Now DG : DF — fin. DFG : radius, or as (Euclid, vt. 8. j fin. DCF : radius, and DF : MD~fin. DMF : radius-, therefore by compofi- fition, DG : MD = fin. DCF X fin. DMF : rad. X rad. or radTjk But, DG : MD as the force upon the back is to the fum of the refiftances, therefore the force up¬ on the back is to the fum of the refiftances as fin. DCL X fin. DMF is to the fquare of the radius. 123. Cor. I. If the direftion of the refilling forces Corollaries, is perpendicular to the faces of the wedge, DMF be¬ comes a right angle, and therefore its fine is equal to radius. Confequently we have, in this cafe, the force upon the back to the lum of the refiftances, as fin, DCl X rad. is to radms|\ that is, as fin. DCF is to radius, of as AD half the back of the wedge is to AC the length of the wedge. 1 24. Cor. 2. In the particular cafe in the propoft- tion, it is obvious that the forces MF, NF are not op- pofed by any other forces, and therefore the force upon the back will not fuftain the refilling forces; but in the cafe in cor'. 2. the forces MF, NE vanilh, and there¬ fore the other forces will fuftafti each other. 125. Cor. 3. If the refilling forces aft in a direc¬ tion perpendicular to AB, the angle DMI1 becomes equal to ACD, and therefore the force upon the back to the fum of the refiftances as iiu. ACD|J is to radiusj*, that is, as the fquare of AD half the back of the wedge is to the fquave of AC the length of the wedge. 126. Cor. 4. When the direftion of the refiftances is parallel to the back of the wedge, the angle of in¬ clination DMC becomes the complement of the feml- angle of the wedge, and therefore the force upon the back is to the fum of the refiftances as the fin. ACD X cof. ACD is to the fquare of the radius, that is, as DA X DC is to AC2. But in the fimilar triangles DAF, DAC, we have DF : DA—DC : AC, and Db X AC—DA X DC, confequently the force upon the back of the wedge is to the lum of the refiftances as DF X AC is to AC*, that is, as DF : AC. Prop. II. 127. If, on account of the friaion of the wedge, or any other caufe, the refiftances are wholly effeclive, that is, if the refilling furfaces adhere to the places to which they are applied without Hiding, there will be an equilibrium, when the force upon the hack is to the fum of the refin¬ ances, as the fine of the acute angle which the dire£lion of the refilling forces makes with the back of the wedge is to radius. Join MN, which will cut DC perpendicularly at the p point Fig. 66 MECHANIC S. Theory. point H. Then, fince the forces MD, ND are refolvable 1" v into MH, HD and into-NH, HD, and fince MH, HN deftroy each other, the force upon the back is futlained by 2 HD. Confequently, the force upon the back is to the fum of the refirtances as 2 HD is to 2 MD, or as HD is to MD. Bat the angle ADM, which the direc¬ tion of the forces makes with the back of the wedge, is equal to DMN, and HD is the fine of that angle, MD being radius, therefore the force upon the back is to the fum of the refiflances as fin. ADM : radius. Q. E. D. Corollaries. i 28. Cor. I. Since the angle AMD—MDC -{-MCD, the angle MDC is the difference between MCD the fe- miangle of the wedge, and AMD the angle which the direciion of the refilling forces makeswTith the face ofthe wedge, and fince HD is the cofine of that angle, MD being radius, we have the force upon the back to the fum of the refinances, as the cofine of the difference be¬ tween the femiangle of the wedge and the angle which the direction of the refilling forces makes with the Hoe of the wedge, is to radius. Prop. III. 129. When there is an equilibrium between three forces adling perpendicularly upon the Tides of a wedge of any form, the forces are to one an¬ other as the Tides of the wedge.^ This is obvious from Dynamics, §. 144. Cor. 2. where it is ffiewn that when three forces are in equilibrio, they are proportional to the fides of a triangle, wdiich are refpedlively perpendicular to their directions. Prop. IV. 130. When the power adting upon the back of a wedge is in equilibrio with the refiftances op- pofed to it, the velocity of the power is to the velocity of the refiftance as the refiftance is' to ^ the powder. Fjg. 3. Produce DM to K, and draw CK perpendicular to DK. Then, by Art. 1 22. the power is to the refin¬ ance as MD : DH. Let the wedge be moved uni¬ formly from D to C, and DK is the fpace uniformly defcrihed by the refilling force in the direction in which it aCts j therefore, the velocity of the power is to the ve¬ locity of the refillance as DC : DK ; that is, on ac¬ count of the equiangular triangles DHM, DKC, as MD : DH $ that is, as the refinance is to the power. Sect. IV. On the Screw. 131. Definition. A fcrewHs a cylinder with an inclined plane w rapped round it, in fuch a manner, that the furface of the plane is oblique to the axis of the cy¬ linder, and forms the fame angle with it in every part of the cylindrical furface. When the inclined plane winds round the exterior furface of a folid cylinder, it is called a male fcrew 5 but when it is fixed on the in¬ terior circumference of a cylindrical tube, it is called a female fcrew. In the female fcrew, the fpiral grooves formed by the inclined plane on the furface of the cy¬ lindrical tube, muff be equal in breadth to the inclined plane in the male fcrew, in order that the one may Theory, move freely in the other. By attending to the mode v~*~ in which the fpiral threads are formed by the circum¬ volution of the inclined plane, it will appear, that if one complete revolution of the inclined plane is deve¬ loped, its altitude will be to its bafe as the diftance be¬ tween the threads is to the circumference of the fcrew. Thus, ItX. a b c (fig. 4.) be the inclined plane, whofe 4 bafe is # c and altitude b c, and let it be wrapped round the cylinder MN (fig. 5.) of fuch a fize that the points a, c may coincide. The furface ab oi the plane (fig. 4.) will evidently form the fpiral thread 0 c £ (fig. 5.), and a b the difiance between the threads will be equal to b c (fig. 4.) the altitude of the plane, and the circumfer¬ ence ofthe fcrew MN will be equal to aciYit bafe of the plane. If any body, therefore, is made to rife' along the plane a de b in fig. 5. or along the fpiral thread of the fcrew, by a force adting in a direftion parallel to a dc b, there will be the fame proportion between the power and the refiftance as if the body afeended the plane a b c (fig. 4.). 132. A male fcrew with triangular threads is repre-pjT 5 ^ fented by AB (fig. 6.), and its correfponding female fcrew by AB (fig. ’y.'). A male fcrew with quadrangu¬ lar threads is exhibited in fig. 8. and the female fcrew pj0. 8 in which it works in fig. 9. The friclion is confidera- ° bly lefs in quadrangular than in triangular threads, though, when the fcrew is made of wood, the triangular threads fhotdd be preferred. When the ferews are me¬ tallic and large, the threads ftiould be quadrangular; but the triangular form is preferable in fmall ferews. When the fcrew is employed in pra£lice, the power is always applied to the extremity of a lever fixed in its head. This is fhewn in fig. 10. where AB is the lever a£ling Fig- IO< upon the fcrew1 BC, which works in a female fcrew7 in the block F, and exerts its force in bending the fpring CD. Prop. I. 133. If the fcrew is employed to overcome any refiftance, there will be an equilibrium when the power is to the refiftance as the diftance be¬ tween two adjacent threads is to the circum¬ ference deferibed by the power. Let FAKbe a feddion of the fcrew reprefented in fig. pig. u. 8.perpendicular to its axis; CD a portion ofthe inclined plane which forms the fpiral thread, and P the power, which, when applied at C in the plane ACF, will be in equilibrium with a weight upon the inclined plane CD. Then, in the inclined plane, when the direction of the power is parallel to the bafe, we have (Art. 72.) P: W, as the altitude of the plane is to the bafe, or (Art. 131.) as the diftance between two threads is to the whole circumference FKCF. If we fuppofe another power P' to afl at the end of the lever AB, and deferibe the arch HBG, and that this power produces the fame effeft at B as the power P did at C, then (Art. 36.), we have P;: P—CA : BA, that is, as FKCF is to the circumfe¬ rence HBG ; but it was fhewn before, that P : W— as the diftance between two contiguous threads is to FKCF; therefore, by compofition, P' : W as the diftance between two threads is to HBG or the circumference of a circle wftiofe radius is AB. E. D. 134. Cor.. I. It is evident from the propofition that the mechanics. 67 Theory. Fig. 12. the power does not In the leaft depend upon the fize of ' the cylinder FCK, but that it increafes with the di- ftance of that point from the centre A, to which the power is applied, and alfo with the Ihortnefs of the di- ftance between the threads. Therefore, if P,/> be the powers applied to two different fcrews, D,« the di- ftances of thefe powers from the axis, and. 1, t the di- llances between the threads 5 their energy in overcom¬ ing a given refinance will be direftly as their diftances from the axis, and inverfely as the diftances of their threads, that is, P : p—~r^ • -T"* 01‘ ^ vanes as . Prop. II. 135. In the endlefs fcrew, there will be an equi¬ librium when the power is to the weight, as the diftance of the threads multiplied by the radius of the axle, is to the diftance of the power from the axis of the fcrew multiplied by the radius of the wheel. The endlefs fcrew, which is reprefented in fig. 12. confifts of a fcrew EF, fo combined with the wheel and axle ABC, that the threads of the fcrew may work in teeth fixed in the periphery of the wheel, and thus com¬ municate the power exerted at the handles or winches P,/>. Let W reprefent the power produced by the fcrew at the circumference of the wheel $ then, by the laft propofition, P : W/ as the diflance between the threads is to the diflance of P from the axis of the fcrew\ but (Art. 92.) in the wheel and axle W': W as the radius of the axle is to the radius of the wheel ; therefore, by compofition, P : W as the diftances of the threads multiplied by the radius of the axle C, is to the diftance of the power P from the axis multiplied by the radius of the wheel AB. Prop. III. 136. When there is an equilibrium in the fcrew, the velocity of the weight is to the velocity of the power, as the power is to the weight. It is obvious from fig. 11. that while the power de- fcribes the circumference of the circle HBG uniformly, the weight uniformly riles through a fpace equal to the diftance°between two adjacent threads j therefore, the velocity of the power is to the velocity of the weight as the diftance between the threads is to the arch dejciibe.d by the power, that is, (by Art. 133.), as the weight is to the power. Prop. IV. 137. To explain the conftru&ion and advantages * See ?bii. of Mr Hunter’s double fcrew *. Tranf vol. . f 1 t> a Ixxi. p. 58. Let the fcrew CD work m the plate of metal J5 A, 13. and have n threads in an inch : the cylinder CD, ot which this fcrew is formed, is a hollow tube, which is alfo formed into a fcrew, having «-j-i threads in an inch, and into this female fcrew is introduced a male fcrew DE, having, of courfe, n-J-1 threads in an inch. The fcrew DE is prevented from moving round with CD by the frame ABGF and the crofs bar aby but is Fig. ir. permitted to afcend and defcend without a motion of, -theory rotation. Then, by a revolution of the fcrew CD, the other fcrew DE will rife through a fpace equal to -, and if the circumference defcribed by the « + i X« lever CK be tn inches, we fhall have P:W== : ra-MX* m; or P : W=ri winy^n-\-\. 138. This reafoning will be more perfpicuouS by fup- pofing /?, or the number of threads in CD, to be 1 2, and, »-|-l or the number of threads in DE will confe- quently be x3. Let us fuppofe that the handle CK is turned round 12 times, the fcrew CD will evidently afcend through the fpace of an inch, and if the fcrew DE is permitted to have a motion of rotation along with CD, it will alfo advance an inch. Let the fcrew DE be now moved backwards by 12 revolutions, it will evidently defcribe a fpace of 4't °f inch, and the confequence of both thefe motions will be that the point £ is advanced xy of an inch. But, fince DE is prevented from moving round with CD, the fame effect will be produced as if it "had moved 12 times round with CD, and had been turned 12 times backwards j that is, it will in both cafes have advanced Ty an inch. Since, therefore, it has advanced Ty of an inch in X 2 turns, it will defcribe only t*t °f tt> or yhs °f an inch uniformly at one turn \ but if the length of the lever CK is 8 inches, its extremity K will defcribe, in the fame time, a fpace equal to i6X3'J^}^= S°-2^5^ Inches, the circumference of the circle defcribed by K } •thertiore the velocity of the weight is to the velocity of the power, as T-fyr of an inch is to 50.2656 inches, or as 1 is to 7841.433^’ that is, (Art. : — 1 : 7841.4336. Hence the force of this double fcrew is much greater than that of the common fcrew, for a common one with a lever 8 inches long mull have 156 threads in an inch to give the fame power, which would render it too weak to overcome any confiderable refiftance. . 139. Mr Hunter propofes * to conned with his * double fcrews, a wheel and a lantern, which are .put Jn Aw*/v5L motion by a winch or handle. The power of this com- P pound machine is fo great, that a man, by exerting a force of 32 pounds at the winch, will produce an effect of 1 72 100 pounds 5 and if we fuppofe this effect to be deftroyed by fridion, there will remain an efftd of 57600 pounds.—In fome fcrews it would be advan¬ tageous, infte«d of perforating the male fcrew CD, to have two cylindrical fcrews of different kinds at d.iT- rent parts of the fame axis. Scholium. 140. The fcrew is of extenfive ufe as a mechanical power, when a very great preflure is required, and is very fuccefsfully employed in the printing prefs. In the prefs which is ufed for coining money, the power ox the fcrew is advantageoufly combined with an impuhive force, which is conveyed to the fcrew by the intervention of a lever. The fcrew is alfo employed for raifing water, in which form it is called the fcrew of Archimedes; (Hydrodynamics, $. 328) j and it has been lately employed in the fiour mills in America for pufhing the flour which comes from the millftones, to the end of a long trough, from which it is conveyed to other parts t 63 M ECU Theory. of tlic machinery, in order to undergo the remaining ' proceffes. In this cafe, the fpiral threads are very large in proportion to the cylinder on which they are fixed. 141. As the Icvdr attached to the extremity of the fcrew moves through a very great fpace when compared with the velocity of its other extremity, or of any body which it puts in motion •, the fcrew is of immenfe ufc in fubdividing any fpace into a great number of minute parts. Hence it is employed in the engines for dividing mathematical inftruments, and in tho/e which have been recently ufed in the art of engraving. It is likewife of great ufe in the common wire micrometer, and in the divided objedl-glafs micrometer, hiftruments to which the fcience of adronomy has been under great obliga¬ tions. See Micrometer. Sect. V. the Balance. Kate 142. DEFINITION. The balance, in a mathematical -.CCXX. fenfe, is a lever of equal arms, for determining the 'r' weights of bodies.—-The phyfical balance is represented in fig. 1. where FA, FB are the equal arms of the ba¬ lance, F its centre of motion fituated a little above the centre of gravity of the arms, FD the handle which al¬ ways retains a vertical pofition, P, W the feales fuf- pended from the points A, B, and CF the tongue or index of the balance, -which is exaflly perpendicular to the beam A3, and is continued below the centre of motion, fo that the momentum of the part below F is equal and oppofite to the momentum of that part which is above it. Since the handle FD, fufpended by the hook, H, mud hang in ;? vertical line, the tongue CF will alfo be vertical when its pofition coincides v^ith that of ' FD, and confequently the beam AB, which is perpen- A N I C S. dicular to Cb, mud be horizontal. When this happens, Theory, the weights in the fcale are evidently equal. ' v— Prop. I. 143. fo determine the conditions of equilibrium in Fig. 2. a phyfical balance. I.et AOB be the beam, whofe weight is S, and let P, Q be equal weights expreffed by the letter /«, and placed in the feales, whole weights are L and /. Let O he the centre of motion, and g the centre of gravity of the whole beam, when unloaded, we dnll have in the cafe of an equilibrium, ^ I- /’-fl-X AC~/>-f/xBC-j-Sx Cc; for fince S is the weight of the beam and ^ its centre of gravity, its mechanical energy in aiding againd the weights is zzryxCe, the didance of its centre of gravity fiotn the vertical line palling through the centre of mo¬ tion O. f < II- fince AC~ EC ; AC—/> x BC = o. Then, after tranfpofition, take this from the equation in N° I. and we (hall have, HI. /xBC-Lx AC +SxCc; or L— Let us now fuppofe that a fmall weight w is placed in the fcale L, the line AB which joins the points of fufpenfion will be no longer horizontal, but will afiume an inclined pofition. Let BA Arrp be the angle which the beam makes with the direftion of gra¬ vity. Then by refolving the weight of the beam which OGr Ct t a£ts in the direction O the parts —— and will be . Vg in eqmlibno, and we (hall have, IV. />-}-L X AO X sin. a VO-f S x OG X Sin. /.+/+iu X BO X Sin. ABO-f S x C ex Cof. -[-L-\-lX OC x Sin. X OG x Sin 5.5* ^e" pends upon ./Epinus’s property of the lever, winch we GCCXVHl.^ve explained in Art. 65* The angular lever Ah B, l,g' ^ in which AFrzFB, is moveable roundwhich is equi- difiant from A and B. The weight P is fufpended by a thread from A, and the body W, wb ch is to oe weighed, is fufpended by a thread from B. Hence it is obvious, that with different bodies the lever AT B will have different degrees of inclination, and tne index ■ or tongue LF/, which is perpendicular to AB, wall form different angles ZFL, b\ f with the line of direc¬ tion ZF b. Now, by Art. 57. and by fubftituting for b B, b A the fines of the angles F b B, Yb A, to which they are proportional, and alio by taking inftead .of Y b B the difference of the angles^i B,jfF b, and in¬ ftead of AF by the fum of thefe angles, we fhall have Ludlam’s balance. Plate Tang./F b~ P—W X Tang. AFB Fig. 4. ■p+W whence, by tranfpofition, and by Geomeirv, iheor. YIII. Sea. IV. P_|-W : P—W- fang. —4— : Tang./F^. Hence, when the angle formed by the arms of the ba¬ lance, and the angle of aberration/F £ or ZFL, are known, the weights may be found, and vice verfa. Chap. IV. On the Centre oj Inertia, or Gravity. ! 54. Definition.—The centre ofinertia, or the centre of gravity, of any body or fyftem of bodies, is that point upon which the body or fyftem of bodies,. when.influ¬ enced only by the force of gravity, will.be in equilibrio in every pofttion. The centre of inertia of plane, fur- faces bounded by right lines, and alfo of fome folids may be eaftly determined by the common geometry. The application of the method of fluxions, however, to this branch of mechanics is fo fimple and beautiful, that we fhall alfo avail ourfelves of its affiftancc. The cents"? of gravity has been called, by fome writers, the centre of poftlion, and by others, the centre of mean diftances. Prop. I. 155. To find the centre of inertia of any number of bodies, whatever be their pofition. Let AFfCD be any number of bodies influenced by the force of gravity. Suppofe the bodies A, B conne&ed by the inflexible line AB confidered as devoid of weight, then find a point F, fo that the weight of A : the weight of ErrBF : FA. The bodies A, B will therefore be in equjUbrio about the point F in every pofition (Art. 36.), and the preffure upon F will be e- qual to Aff-B. Join FC, and find the point/, lo that A-j-B : C~C f: fY ; the bodies A, B, C will confe- quently be in equilibrio, upon the point//which will fuftain a preffure equal to A-rE«j- C. Join D/ and take the point p, fo that A+B-f-C : D~y> i) : £>/} the bodies A, B, C, D wall therefore be in equilibria about the point 4>, which will be their common centre of inertia, and which fupports a weight equal to A-j-B -j-C-f-D. In the fame manner we may find the centre of inertia of any fyftem o? bodies, by merely connecting the laft fulcrum with the next body by an inflexible right line, and finding a new fulcrum from the magni¬ tude of the oppofite weights which it is to fuftain. 156. Cor. 1. If the weights of the bodies A, B, C, D be increafed or diminished in a given ratio, the centre of inertia of the fyftem will not be changed, for the pofi- tions of the points F,/ are determined by the rela¬ tive and not by the abfolute weights of the bodies. 157. Cop.. 2. A motion of rotation cannot be commu¬ nicated to a body by means of a force adding upon its centre of inertia j for the refiftances which the inertia of each particle oppofes to the communication of motion adt in parallel diredlions, and as they are proportional to the weights of the particles, they will be in equili- brio about the centre of gravity. Prop. II. 158. To find the centre of inertia of any number of bodies placed in a ftraight line. Let A, B, C, D, L be any number of bodies whofe Fig. 5. common centre of gravity is ;p. In the ftraight line AE take any point X. Then fince all the bodies are in equili¬ brio about their common centre of gravity —Yf, therefore, by multiplying and tranfpofing, we have A-j-B xF/rrAx Atf-)-B X B £. Inthevery fame way, by drawing wG % parallel to the plane, it may be ftiewn that A-f-B-j-C X G.f—A. x A tf-j-B X B Z'-j-C x C c. Q- E- D. 116. Cor. By dividing by A-j-B-f-C we have „ Ax A^ + BxBT-f-CxC c ” A+B+C Prop. IV. 163. To find the centre of inertia of a ftraight line, compofed of material particles. If we confider the ftraight line as compofed of a number of material particles of the fame fize and den- fity, it is evident that its centre of inertia will be a point in the line equidiftant from its extremities. For if we regard the line as a lever fupported upon its mid¬ dle point as a fulcrum, it will evidently be in equilibrio in every pofition, as the number of particles or weights on each fide of the fulcrum is equal. Prop. V. 164. To find the centre of inertia of a parallelo- gram. Let A BCD be a parallelogram of uniform denfity, b;fe tnat n is the centre of gravity of the fiction b c d. It fol¬ low's, therefore, that A/ will pafs through the centre of gravity of the pyramid. In the fame wray it may be fhewn, by confidering ABD as the bafe, and D the vertex, and making F G will be a circular fe&ion. / M E C H Theory. fe£l!on, whole diameter is 2DErr2y, and fince the v " srea of a circle is equal to its circumference multiplied by its diameter, we have (making tt—j.i 416) 2 fry'1 x, “the circular fection whofe diameter is DGj and fince a.-X 2 7ry*x, or 2 frxy'x, will reprefentthe momentum ^ n n i -r-n duentof ot the weight, we mail have FB— ^—r-, fluent of 2 7T ifx fluent of yxx ana dividing by 2 x y, we have i1 B=r —^—1-. fluent of yx 1 75. In finding the centre of inertia of the furfaces of folids, the elements or fmall weights are the circum¬ ferences of circles, whofe radii are the ordinates of the curve by whofe revolution the folid is-generated. Now, the furface of the folid may be conceived to be gene¬ rated by the circumference of a circle increafing gra¬ dually from B towards A and C ; making % therefore equal to BD, its fluxion s multiplied into the peri- phery of the circle whofe diameter is DG, that is, 2 tt y 2; will exprefs the elementary furface or fmall weight whofe diameter is DG. Then, fince x X 2 wy 2, or ifcxy^ will be the momentum of the elementary weight, we fliall have FB—■—U--rit^ and di¬ fluent of 2fr y % .. „„ fluent of xy % t iding by 2 tt we obtain 1 B~ d__. fluent of y 2; 176. If the body, w’hofe centre of inertia is to be found, be a curve line, as GBD, then it is manifeft that the fmall weights will be expreffed by the fluxion of GBD, that is, by 22;, fince GBD=:2 BD—22;; con- fequently their momenta will be 2x%, and we fliall fluent 2 x z fluent x % fluent x 2; Fig. 12, A N I C S. vinculum) its ralue R- (R—x) x( 2 R x—x1) Fig. 11. have FB—- fluent 2 z fluent % Prop. IX. 177. To find the centre of inertia of a circular fegment. Let AE—v, FC—y, and AD the radius of the cir¬ cle = R, confequently ME— 2 R—EA. Then, fince by th$ property of the circle (Geometry, Theor. 28. Sedt. IV.") MExEA—BE% we have, by fubftitution, BE2 = 2 R X EA— EA x EA, or y2 =: 2 R x — x2 j hence y—\/,2 R at—x2. Now, by Art. 174. we have the diliance of the centre of gravity from A, that is, . „ fluent x y x • AG— 1—7“ } but the fluent or y x or the fum of fluent y x all the weights, is equal to the area of half the feg¬ ment ABEC ; therefore AG=^AAfA Then, by JLX D JL-J fubftituting inftead of y, in this equation, the value of it deduced from the property of the circle, wre have fluent of xx V lRx AG—- or, in order to find ABEC GD the diflance of the centre of gravity from the cen¬ tre, we muft fubilitute inftead of x (without ^he -x, and we have GD—'fluent . , , . Now, in omier to find the 4-ABLE fluxion of the numerator of the preceding fraction, af- fume z— 2 R x—x2, and "z^f— 2 R x—xs, and by tak¬ ing the fluxion, we have 2;—2 R x—2xxz=. 2 R—2X Xx j but this quantity is double of the firft term of the nu¬ values in the fradlional formula, we obtain GD vAr x- 55 4 • z} 2 3 j but fince y=r2Rx- we have, by raifing both fides to the third power, p3~ _ A X 8 y* 2 Rx- 14 ; therefore G D; 4 V* 4 ABEC 4ABEC T_(2 y)* ' — ~ a ^S» t1ae diftance of the centre of gra- AbiiL vity of a circular fegment from the centre of the circle, is equal to the twelfth part of the cube oPtwice the or¬ dinate, (or the chord of the fegment) divided by the area of the fegment. 178. Cor. When the fegment becomes a femicircle we have 2y“2r*, and therefore = GD—‘ ^ ; (2r)3 8 x^3 r3 ABEC “ 12 ABEC 12 ABEC lyAtiEC* t,Wt “• ,he ^ tance of the centre of gravity of a femicircle from the centre of the femicircle, is equal to the cube of the ra¬ dius, divided by one and a half times the area oi the fegment. Prop. X. 179. To find the centre of inertia of the feflcr of a circle. Let ABDCbe the fe£lor of the circle. By Art. 157. find m the centre of inertia of the triangle BCD, and by the laft propofition find G the centre of inertia of the fegment *, then take a point ?i fo fituated bettveen G and m, that ABEC : BCRzzm/i : G//, then the point n will be the centre of gravity of the fedlor.— By proceeding in this way, it will be found that D /?, or the diftance of the centre of gravity of the fedfor from the centre of the circle, is a fourth proportional to the femiarc, to the femichord, and to two-thirds of the radius. Prop. XL 180. To find the centre of inertia of a plane fur¬ face bounded by a parabola whofe equation is y—<7 x”. Since y—axn, multiply both terms by xx, and x fe- parately, and we have y x x — a x +2x, and y x—axnx. But, by Art. 174. we have FBrz fluent of x !/: ,tht fluent yx fore, by fubftituting the preceding values of xy yx in the formula, we obtain FBnr; and fluent of a xwTtx fluent of a xnx and 'i heory. merator, therefore — z=R—x X x. By fubflituUng thefe fluent 2 MECHANICS. Theory. and by taking the fluents it becomes a w “f-1 .,R .r .v Fig. 13. in this formula, we obtain FB —^Uent f for fluent of R .v FB: «-{-2 a xtl+'1 11 -{- X Xv. If//, therefore, be equal to then y—ax\, and, fquaring both fides, if—cfx, which is the equation of the common or Apollonian parabola. Hence, FB=r that is, the diftance of the centre of gravity from the vertex is 3-ths of the axis. When n is equal to I, then y=ra,v, and the para¬ bola degenerates into a triangle, in which cafe FB —jX, as in Art. 165. Prop. XII. 181. To find the centre of inertia of a folid, ge¬ nerated by the revolution of the preceding curve round its axis. Smce ijzza xn, fquare both Tides, and we have y*=: a%x>n; then multiply both fides by.rw, and at feparate- ly, we obtain y1xx=a2xln+'x, and y*x=a2xtnx. But, , _ fluent of ifxx , by Art. 174. we have FBrr —— J therefore, fluent of y*x by fubftituting the preceding values of y*x x, and . fluent of a2x*n+Tx xn that formula, wTe obtain FBr= ——> and fluent of a2x2nx by taking the fluents we (hall have a2x* ” 2/?+ 1 FBzz 2 //+2 2//-P1 2 n -f- 2 y R y x x % R ^2; R y v 2; (and dividing by yis): Rv/c R x By y taking the fluents we obtain FB=r j R x2 Rv x, a fluent 2//-|-i When n—^i the folid becomes a common parabo¬ loid, and we obtain FBrrr-hv. When n— 1, the folid becomes a cone, and FB as in Art. 171. Prop. XIII. 182. To find the centre of gravity of a fpherical furface or zone, comprehended between two parallel planes, or of the fpherical furface of any fpherical fegment. Let BMNC be a feflion pf the fpherical furface comprehended between the planes BC, MN, and let EP=a?, ECzzy, DCzrR, and 2= the arc CN. Sup- pofe the abfeifla EP to increafe by the fmall quantity E 0, draw 0 r parallel to EC, C s parallel to E 0, and C r perpendicular to DC ; then it is evident, that in the fimilar triangles CDE, C s r, EC : DC = C J1 : C r, that is, y : R= C r : C r j but C r is the flux¬ ion of the arc NC, and C s the fluxion of the abfeif- fa PE •, therefore y : R ~ a? : 2;, and szymR x, and z R v , , „„ fluent of x 1/ z ~ . Now, by Art. 175. FB— ;——, y fluent of x y z therefore, by fubftituting the preceding value of z VOL. XIII. Part I. which requires no corredlion, as the other quantities vanith at the fame time with x. 183. When DP is equal to DC, the folid becomes a fpherical fegment, and EA becomes the altitude of the fegment, fo that univerfally the centre of gra¬ vity of the fpherical furface of a fpherical fegment is in the middle of the line which is the altitude of the fegment, or in the middle of the line which joins the centres of the two circles that bound the fpherical fegment. 184. When the fpherical fegment is a hemifpheroid, the centre of gravity of its hemifpherical furface is ob- vioufly at the diftance of one-half the radius from its centre. Prop. XIV. 185. To find the centre of gravity of a circular arc. Let BAG be the circular arc, it is required toy^ find its centre of inertia, or the diftance of the cen¬ tre of inertia of the half arc AC from the diameter HG } for it is evident, that the line which joins the centres of gravity of each of the femiarcs AB, AC mull be parallel to PIG, and therefore the diftance of their common centre of gravity, which muft be in that line, from the line HG, will be equal to the diftance of the centre of gravity of the femiarc from the fame line. Make PCrzDE—v; EC—y; DC—DA —R, and AC = 2;, then it may be Ihewn, as in the laft propofition, that y : R—a? : 2; ; hence zyzzfLx. But, by Art. 176. . fluent of y x . . . , . r we have FB— —, y being in this cale equal to x in the formula in Art. 176. and fubftituting the , r • . , fluent of R a; preceding value or y z, it becomes fU— , R x and, taking the fluent, we have FB—, which re¬ quires no eorreftion, as the fluent of y 2; vaniihes at the fame time with x. Calling //, therefore, the diftance of the centre of inertia of the arc BAG from the cen¬ tre D, we have cl———, and //z = R a; : hence 2; : x x zrR : //, or 2 Z : 2 v—R : d, that is, the diftance of the centre of inertia of a circular arc from the centre of the circle is a fourth proportional to the arc, the chord of the arc, and radius. 186. When the arc BAG becomes a femicircle, PC or X is equal, to DG or radius, fo that we have 2 2; : 2 R =z R : yi(h to profecute the fubjefl. 9. In the fedlor of a circle, the centre of inertia is TU diilant from the centre of the circle, by a quantity which is a fourth proportional to the femiarc, the femi- chord, and two-thirds of the radius. 10. In a fpherical furface or zone, comprehended between two planes, the centre of inertia is in the mid¬ dle of the line which joins the centres of the two circu- lai planes by which it is bounded. When one of the circular planes vanilhes, the Ipherical zone becomes the fpherical furface of a fpherical fegme.nt j there¬ fore, 11. In a fpherical furface of a fpherical fegment, the centre of inertia is in the middle of its altitude or ver- fed fine 1 confequent-ly, 1 2. The centre of inertia of the fuvface of a com¬ plete fphere coincides with the centre of the fphere. 13. In a fpherical fegment, the centre of inertia is diilant from the vertex by a quantity equal to tX x, where a is the diameter of the fphere, 6 ci—4.V and x the altitude or verfed line of the fegment. Hence, 14. The centre of inertia of a hemifphere is dillant from its vertex by a quantity equal to five-eighths of the radius, or it is three-eighths of the radius diilant from the hemifphere ; and, 15. The centre of inertia of a complete fphere coin¬ cides with the centre of the fphere. 16. In a circular arc the centre of inertia is diftant • 1^. X from its centre by a quantity equal to , where R is Scholium II. Pofitianof jgp, it is frequently of great ufe to know the po- tp" centre f]tjon tp,e of inertia in bodies of all forms, we feoTes^of infha!l collsdl all the leading refults which might have various been obtained, by the method given in the preceding forms. propolitions. 1. The centre of inertia of a flraight line is in its middle point. 2. The centre of inertia of a parallelogram is in the interfe&ion of its diagonals. 3. The centre of inertia of a triangle is diilant from its vertex two-thirds of a line drawn from the vertex to the middle of the oppofite fide, 4. The centre of inertia of a circle, and of a regular polygon, coincides with the centres of thefe figures. 5. The centre of inertia of a parallelepiped is in the interfedlion of the diagonals joining its oppofite angles. 6 The centre of inertia of a pyramid is dillant from its vertex three-fourths of the axis. 7. The centre of inertia of a right cone is in a point 'in its axis vvhofe diitance from the vertex is three-fourths of the axis. 8. In the fegment of a circle, the centre of inertia is diilant from the centre of the circle a twelfth pa;t of the cube of the chord of the fegment divided by the area of the fegment, or dz L C3 :1T’ where d — the dif- tance of the centre of inertia from the centre of the circle, C = the chord of the fegment, and A its axis. the radius, x the femichord, and z the femiarc. Hence, 17. In a femicircular arc the centre of inertia is dif¬ tant from its centre .63662 R, and, 1 8. The centre of inertia of the circumference of a circle coincides with the centre of the circle. 19. In a circular iedlor the centre of inertia is dif- 2 ^ R # T tant from the centre of the circle , where R i§ the radius, a the arc, and c its chord. 20. In a fpherical ledlor, compofed of a cone and a fpherical fegment, the centre ol inertia is diilant from the vertex of the fegment by a quantity equal to 2 R -}- 3 ^ 8 ■, where R is radius, and x the altitude or verfed fine of the fegment. 21. In an ellipfis the centre of inertia coincides with the centre of the figure. 22. The centre of inertia of an oblate and prolate fpheroid, folids generated by the revolution of an el- lipfe round its leffer and its greater axis refpectivtiy, coincides with the centres of the figures. 23. In the fegnient of an oblate fpheroid the centre of inertia is diilapt from its vertex by a quantity equal to ^ f?] - 'lx • • • — x x, where m is the leffer axis, cr axis of rota- 6 ru—4 A.’ tion, and x the altitude of the fegment. Hence, 24. In a hemifpheroid the centre of inertia is dillant from its vertex five-eighths of the radius. 23. The centre of inertia of the fegment of a prolate fpheroid M E CH Tncwy. fplieroid is diftant from its vertex by a quantity equal to 4 n 3 where n is the greater axis, or axis of rc- 6 m—4 x tation. . 26. In the common or Apollonian parabola, the di- flance of the centre of inertia from its vertex is three- fifths of the axis. 27. In the cubical parabola the didance of the cen¬ tre of inertia from its vertex is four-fevenths of the axis, in the biquadratic parabola five ninths of the axis, and in the furfolid parabola fix-elevenths of the axis. 28. In the common femiparabola, the dlftance of its centre of gravity from the centre of gravity of the whole parabola, in the diredion of the ordinate paffing through that centre, is -g- of the greateffc ordinate. 29. In the common paraboloid, the difiance of the centre of inertia from its axis, is equal to 4 of the axis. 30. In the common hyperboloid, the diffance @r the X*) 4<7-|-3* centre of inertia from the vertex is equal ^ x where a is the tranfverfe axis of the generating hyper¬ bola, and a; the altitude of the folid. _ 31. In the fruflura of a paraboloid, the didance of the centre of inertia from the centre of die finalled: circular end is aR’-H h X b, where h is the didance Ra+r* • 4 between the centres of the circles which contain the paraboloidal fruftum, R the radius of the greater circle, and r the radius of the leffer circle. ?2. In a conic fruftum or truncated cone, the cu- ftance of the centre of inertia from the centre of the . 3Rz-f-2R r-l-?'51 h , • , . fmalleft circular end is _|_pq rX 4 W liC" ie‘ prefents the diftance between the centres oi tne circles which contain the friiftum, and R, r tne rauii of the circles. 33. The fame formula is applicable to ary regular pyramid, R and r reprefenting the Ikies of the two •polygons by which it is contained. Prop. XIV. 190. If a quantity of motion be communicated to a fyftem of bodies, the centre of gravity of the fyftem will move in the fame direction, and with the fame velocity, as if all the bodies were collected in that centre, and received the fame quantity of motion in the fame direction. fK 14. Let A, B, C be the bodies which compofe the fvftem, and let F be the centre of gravity of the bodies B C, * and / the centre of gravity of the whole fyftem, as determined by Art. 155. 1 ben if tne oody A re¬ ceives fuch a momentum as to make it move to a m a fecend, join Fa, and take a point !p lo that F b in a fe- cond ; and having drawn ^>G parallel to h b, tah£ 2- point G, fo that

c=rC : B, the fpaces B/3, C * will reprefent the mutual a£licn of the bodies 13, C, that is B /3 will reprelent the action of C upon B, or the motion which is the refult of that action, and Cx the aclion of B upon C, or the motion which rcfuits from it. Then, fince F is the common centre of gra¬ vity, of B and C, we have (Art. 155") • CrrfC : FB, but B : C=C» : B/3, therefore FC : FB—Cx : P & ; but C * is a magnitude taken from FC, and B /3 is a magnitude taken from FB, confequently (Playfair’s Euclid, Book V. Prop. 19.) the remainder x¥ : /2 F — FC : F B, that is, xF : ft F=B : C, that is (Art. 155.) ft.re point F continues to be the centre of gra¬ vity notwithlfanding the adtion of the bodies B, C. If the fyftem is compoftd ©f leveral bodies, tne fame thing may be proved of every two of the bodies, and confe- quently of the whole fyftem. See INN!embert ,r I)yna~ nnque, A.rt. 7^* a''‘4 Newton's Pvincipia, I. oe£t. III. Cor. 4. Prop. XV. 193. If a body is placed upon a horizontal plane, or fufpended by two threads, it cannot be in K 3 equilibno M E C H equilibrio unlefs a perpendicular drawn from the centre of gravity to the horizontal plane, or to a horizontal line palling through the two threads, fall within the bafe of the body, or upon that part of the horizontal line which lies between the threads. 194. 1. Let ABCD be a body placed in the horizon¬ tal plane CD, G its centre of gravity, and GE a per¬ pendicular drawn to the horizontal line DE. Then the whole matter of the body ABCD may be conceived as united in its centre of gravity G, and as its tendency downwards is in the vertical line GE, it can defcend only by turning round the point C as a centre. Here then we have a body G placed at the end of a lever GC whofe fulcrum is C, and its power to turn round C is reprefented by the quantity of matter in G multi¬ plied by the perpendicular CE, let fall from the ful¬ crum upon its line of direblion 5 and as there is no force to counterbalance this, the body G, and confe- quently the body ABCD, will fall by turning round C. When the vertical line GE coincides with GC, EC vanishes, and the weight of the body concentrated at G has no power to turn the lever round C, but is fup- ported upon the fulcrum C. When the vertical line GE, (by fome writers called the line of direSlion), falls within the bafe CD, it is obvious that the weight at G has no influence in producing a motion round C or D, 1 mt is employed in preffing the body upon the ho¬ rizontal plane ED. Fig. 16. ipy. 2. Let the body AGED be fufpended at the points /, by the threads h f h' Q, and let G be the cen¬ tre of gravity of the body. Join G (p, Gf draw/ip paral¬ lel to the horizon, and through G draw no parallel to f (p. Continue h f h'(p to 0 and «, and draw G i perpen¬ dicular to /', tt, &c. be the particles of the furface ABCD; D, r/, ^ their dittance from the centre of rotation P, and A, a, the arches which they deferibe, whde GP is the dittance of the centre of gravity of the furface ABCD from the centre P, and Gg the arch defenbed by it. Then by Art. 161. P X D -\-f> X r/-f 7T X P -f-/1+7r X GP, but D: d\ 'h :G P=: A.:a:x\ G^-, therefore P X A-[-/> X 7rX«= P-f-/,+7r X G^-. But P X A-]-/ X a + X &c. make up the whole folid n D, and P-j-/,-|~^', &c. make up the whole furface ABCD ; therefore the fo¬ lid a D is equal to the generating furface ABCD mul¬ tiplied by the path of its centre of gravity. O. E. D. 207. Cor. 1. Let us fuppofe the circle BACO to be I;V generated by the revolution of the line DA round the point D ; then fince the centre of gravity of the line DA is in its middle point G, the path of this centre will be a circumference whofe radius is DG, or a line equal to half the circumference BONAB, therefore, by the theorem, the area of the circle BONB will be equal to the radius DA multiplied by the femicircumfe- rence, which coincides with the refult obtained from the principles of geometry. See Playfair’s Geometry, Supp. B. I. Prop. 5. In the fame way, by means of the preceding theorem, we may readily determine the- area of any furface, or the content of any folid that is generated by motion. Scholium. 208. The centro-baryc method, which is one of the fineft inventions of geometry, was firft noticed by Pap¬ pus in the preface to the feventh book of his matnema- tical colleftiops, but it is to Father Guldinus that we are indebted for a more complete difeufhon of the fuo- ]e£L He publilhed an account of his difeovery partly in 1631;, and partly in 1640, in his work entitled De Centro Gravitatis, lib. ii. cap. 8. prop. 3. and gave an in- direttt demonttration of the theorem, by (bowing the con¬ formity of its refults with thofe which were obtained by other means. Leibnitz demonftrated the theorem in the cafe of fuperficies generated by the revolution of curves, but concealed his demonltration (Aft. Leipf. 1693, p. 493- MECHANICS. Theory. ,493., The theorem of Leibnitz, however, as well as that rof Guklinus, was demonflrated by Varignon in the Me¬ moirs of the Academy for 1714, p. 7 3. Leibnitz ob- lerves that the method will Hill hold, even if the centre round which the revolution is performed be continually changed during the generating motion. For further information on this fubjedl, the reader is referred to Dr Wall is’s work, De Calculo Centri Gravitatis, Hut¬ ton’s Mensuration, Prony’s Architedlure Hydraulique, vol. i. p. 83, and Gregory’s Mechanics, vol. i. p. 64. Prop. XVIII. 209. To Ihow the ufe of the doctrine of the centre of gravity in the explanation of fome mechanical phenomena. On the mo- t^e equilibrium and motion of animals, we per- tion of ani- ceive many phenomena deducible from the properties of nrals. the centre of gravity. When we endeavour to rife from a chair, we naturally draw our feet inwards, and reil upon their extremities, in order to bring the centre of gravity dire&ly below our feet, and we put the body into that polition in which its equilibrium is tottering, a po- lition which renders the fmalleit force capable of pro¬ ducing motion, or of overturning the body. In this fiiuation, in order to prevent ourfelyes from falling backwards, we thruft forward the upper part of the body for the purpofe of throwing the centre of gravity beyond our feet ; and when the equilibrium is thus de- flroyed, we throw out one of our feet, and gradually raife the centre of gravity till the poiition of the body is eredf.—When we walk, the body is thrown into the polition of tottering equilibrium by reding it on one foot; this equilibrium is dedroyed by puihing for¬ ward the centre or gravity, and the body again affumes the pontion of tottering equilibrium by reding it on the ■other foot. During this alternate proccfs of creating and dpdroying a tottering equilibrium, the one foot is placed upon the ground, and the other is railed from it 5 but in running, which is performed in exactly the fame way, both the feet are never on the ground at the fame time : At every ftep there is a thort interval, during which the runner does not touch the ground at all. 210. W'hen we afeend an inclined plane the body is thrown farther forward than when we walk on a hori¬ zontal one, in order that the line of dirediion may fall without our feet 5 and in defeending an inclined plane, ♦ the body is thrdwn backward, in order to prevent the line of diredfion from falling too fuddenly without the bafe. In carrying a burden, the centre of gravity is brought nearer to the burden, fo that the line of direc¬ tion would fall without our feet if we did not naturally lean towards the fids op polite to the burden, in order to keep the line of 'direction within our feet. When the burden is therefore/ carried on the back, we lean for¬ ward ; when it is carried in the right arm, we lean to¬ wards the left ; when it is carried in the left arm, wre lean towards the right ; and when it is carried before the body, we throw the head backwards. 211. When a horfe walks, he firft lets cut one of his fore feet and one of his hind feet, fuppofe the right foot; then at the fame inffant he throws out bis left fore foot and his left hind foot, fo as to be fupported only by the two right feet. His trvo right feet are then Theory, brought up at the fame inflant, and he is fupported on- v ly by his two left feet.—When a horfe pulls at a load which he can fcarcely overcome, he raifes both his fore feet, his hind feet become the fulcrum of a lever, and the weight of the horfe colledled in his centre of gravi¬ ty aids as a weight upon this lever, and enables him to furmount the obfiacle. (See Appendix to Fergufon’s Leflures, vol. ii.) 212. When a rope-dancer balances bimfelf upon the Method in fore part of one foot, he preferves his equilibrium in two w^‘ch a ways, either by throwing one of his arms or his elevated foot, or his balancing pole, to the fide oppofite to that to- equili- wards which he is beginning to fall, or by (hifting thebrium. point of his foot, on which he rells, to the fame fide to¬ wards which he is apt to fall ; for it amounts to the fame thing whether he brings the centre of gravity diredlly above the point of fupport, or brings the point of fupport direclly below the centre of gravity. For this purpofe the convex form of the foot is of great ufe, for if it had been perfectly llat, the point of fup¬ port could not have admitted of fmall variations in its petition *. * See Dr 213. We have already feen (Art. 197.) that any body Young’s is more eafily overturned in proportion to the height o£^'at.u>?1 its centre of gravity. Hence it is a matter of great V0JZ; p/’ importance that the centre of gravity of all carriages fhould be placed as low as pcffible. This may often be effedled by a judicious difpofition of the load, of which the heaviest materials fhould always have the lowed: place. The prefect conflrmSHcn of our mail The con. and poft coaches is therefore adverfe to every principle ftrudlion of of fcience, and the caufe of many of thofe accidents in which the lives of individuals have been loft. The elevated pofition of the guard, the driver, and the out fide paffengers, and the two boots which contain the baggage, raifes the centre of gravity of the load¬ ed vehicle to a very great height, and renders it much more eafi’y overturned than it would other-wife have been. When any accident of this kind is likely to hap¬ pen, the paiTengers ftiould bend as low as poffible, and endeavour to throw themfelves to the elevated fide of the carriage.— In two wheeled carriages where the horfe bears part of the load upon its back, the elevation of the centre of gravity renders the draught more difficulty by throwijig a greater proportion of the load upon the horfe’s back when he is going down hill, and when he has the legit occafion for it ; and taking the load from the back of the horfe when he Is going up hill, and requires to be preffed to the ground. 214. A knowledge of the laws of the centre of gra-Fig. 24- vity enables us to explain the experiment reprefented in fig. 24. where the veflel of water CG is fufpended on a rod AB, pafling below its handle, and refting on the end E of the beam DE. The extremity B of the rod AB is fupported by another rod BF, which bears a- gainft the bottom of the veflel ; fo that the veftel and the two rods become, as it were, one body, which, by Art. 199. will be in equilibrio when their common centre of gravity C is in the fame vertical line with the A loaded point of funport E. cylinder 215. The cylinder G may be made to afeend the in-may be dined plane ABC by putting a piece of lead or any heavy fubftance on one fide of its axis, fo that the cen-dined plane ti e of gravity may be moved from G towards g. Hence by its owa it mail coach¬ es errone¬ ous. MECHANIC S. 7# A double cone may be made to afcend an inclined plane by its own weight. Fig. ad. Theory, it is obvious, that the centre of gravity £ will defcend, and ——v-~~ by its defcent the body will rife towards A. The inclina¬ tion of the plane, however, muft be fuch, that before the motion commences, the angles formed by a vertical line drawn from g with a line drawn from G perpenui- cularly to AB, mult be kfs than the angle of inclina¬ tion ABC, or, which is the fame thing, when the ver¬ tical line drawn from g does not cut the line which lies between the point of contact and the centre oi the cy¬ linder. When the vertical line, let fall from g, meets the perpendicular line drawn from G to the plane in tne point of contaft, the cylinder will be in equilibrio on the inclined plane. 216. Upon the fame principle, a double fcalene cone may be made to afcend an inclined plane without being loaded with a weight. In fig. 26. let ABc- be the feSion of a double inclined plane, AB, BC being Ac¬ tions of its furfaces perpendicular to tne line in which the double fcalene cone ALiEFC moves. Fnen, once the centre of gravity of a cone is in the line joining, the vertex and the centre of its bafe, and fince the axis of a fcalene cone is not perpendicular to its bale, the line which joins the centres of both tne cones, when m the pofition reprefented in the figure, vviil he above the line which joins the centres of their bafes. If the cncie, Fig. 27. therefore, in fig. 2 7 reprefents the bafe of one of Te cones, and C its centre, the line which joins the cen¬ tres of gravity of the two cones w'ill terminate in fome point G at a difiance from the centre, and therefore the double cone will afcend the plane upon the fame prin¬ ciples, and under the lame conditions, as thoie men¬ tioned in the latl paragraph. Chap. V. On the Motion of Bodies along inclined Planes and Curves, on the Curve of fwftejl defcent, and on the Ofctllations of Pendulums. Prop. L 217. When a body moves along an inclined plane, the force which accelerates or retards its motion, is to the whole force of gravity as the height of the plane is to its length, or as the fine of its inclination is to radius. Let ABC be the inclined plane, A the place of the body, and let AB reprefent the whole force of gravi¬ ty t The force AB is equivalent to the lwo ton.es AD, DB or AE, AD, of which AD is the force nhat accelerates the motion cf the body down the plane, while AE is deftroyed by the refifiance or.re¬ action of the plane. i he part of the force of .gravity, therefore, which makes the body arrive at C is repie- fented by AD, while the whole force of gravity is re¬ prefented by AB * hut the triangle ABD is equiangu¬ lar to ABC, and AD : A B~AB : AC, that is the accelerating force which makes the body de.fcend the inclined plane, is to the whole force of gravity as r e height of the plane is touts length, or as the fine of the plane’s inclination is to radius for when AC is ramus, AB becomes the fine of the angle ACB. . 2t 8. Cor. I. Since the force of gravity, which is uniform, has a given ratio to the accelerating force, the accelerating force is al!o uniform *, confeqm ntly the law’s of accelerated and retarded motions, as exhibited in the article Dtt NAMICS, are alfo Hue when the bodies move along inclined planes. If H, therefore, repre- Theory. fent the height AB ot the plane, L its length AC, g * the force of gravity, and A the accelerating force, we (hall have, by the propofition, L : H~y : A, hence El Plate eccxxi. ■ %• 1. A—o-X—-j or> fince ^ : A~radius: fin. ACB, and A E — g x fin. ACB. Now, from the principles of Dynamics, s — \ gd,v ■.gt—\/2gS, and t — g Jwhere s is the fpace deferibed, g the force of g gravity, or 32^ feet, v the velocity, and t tne time. Making in the preceding equation, we avail have /r=fin. c? X v'—g fin.^/rr V 2g s'irn.tp, and t= g. 1m.

— 2 g s', and dividing by 2g ; s fin. -n r i r : : AB. But-r-^rr iin. : therefore, hn. (p fin.

: «/3, But, on account of the fimilar triangles ABc, ab (i, we have, AB : Aczza b : a fi. Hence (Euclid, Book v. Prop. 11. 16.) Time along AB : Time along cZ'—Time along Ac : Time along ct$. (a) See Wood’s Principles of Mechanics, p. 58. note; and alfo Gregory’s Mechanics, vol. i. p. 112. where ibis corollary is demonftrated by the method of fluxions. 3 MECHANICS. Theory. In the fame way it may be (hewn, that Time along EC : Time along b c=z:Time along c G ! Time along /3 «, Time along CD : Time along c be an infinitely fmall arc, the perpendicu¬ lar to the curve drawn from the points P/> will meet at M, and Pp may be regarded as a circular arc, wdiofe radius is MP. An infinitely fmall cycloidal arc at F may likewife be confidered as a circular arc whofe ra¬ dius is BF. As thefe properties of the cycloid are demon- ftrated in almofl every treatife on mechanics, arid as their demonflrations more properly belong to geometry than to mechanics, they are purpofely omitted to make room for more important matter. 233. Definition.—If a body defeend from any point of a curve, and afeend in the fame curve till its velocity is deftroyed, the body is faid to ofcillate in that curve, and the time in wTich this defeent and af- cent are performed is called the time of an ofcillation or vibration. 234. Definition.—A cycloidal pendulum is a pen¬ dulum which ofcillates or vibrates in the arch of a cy¬ cloid. 235. Definition.—Ofcillations which are perform¬ ed in equal times are faid to be ifochronous. Prop. V. Fig. 4. 236. The velocity of a cycloidal pendulum BP at the point F, varies as the arch which it de- feribes. The velocity of the pendulum at F is that which it would have acquired by falling through EF (Prop. 2. and Cor 3. Prop. 2.), and the velocity of a falling bo¬ dy is as the fquare root of the fpace which it deferibes A N I C S. (D ynamics, §. 37.), therefore the velocity of the pen- Theory, dulum P, when it reaches F, varies as V EF. But v (Geometry*, Se£t. IV. Theor. 23. and 8.) FE varies as FN2 and flnee IC is a con Rant quantity, FE will vary sts FN2 varies, or, to adopt the notation ufed in the article Dynamics, FErAFN2, or vTEriiFN, but the ve¬ locity acquired by falling through EF varies as V^FE, therefore the velocity ol the pendulum at F varies as FN, that is, as FP, for (Art. 232. N° 5.) FN is equal to half FP. £. E. D. Prop. VI. 237. If the pendulum begins its ofcillation from the point P, the velocity of the pendulum at any point R varies as the fine of a circular arc whofe radius is FP, and whofe verfed fine is PR. Through F draw /> F y parallel to AD, and with a Fig. 4. radius equal to the cycloidal arc FP, deferibe the femi- circle /> 0 y. Make p r equal to the arc PR of the cy¬ cloid, and through r draw r m perpendicular to p F. Through the points P, R draw' PE, RT parallel to AD, and cutting the generating circle CNF in the points N, S.—By Prop. 4. the velocity at R varies as VET, that is, as VEF—TF, or fince CF is conftant, as VCFxEF—CFxTF, that is, as VeN2—FS% (For, Playfair’s Euclid, Book. I. Prop. 47, Book II. Prop. 7. and Book. III. Prop. 35; FN2=;CFxEF, and F3—CFxTF), that is, as V4FN2—4FS2, that is (Art. 232. N° 5.) as VFP2—FR\ But F/> or F m was made equal to FP, and,/> r being made equal to PR, the remainder F r mull be equal to FR, therefore, the velocity at R varies as m1—Fr2, but (Euclid 47. 1.) r m—^Fm*—Fr2, and rm is by con- flru£lion equal to the fine of a circular arc, whofe ra¬ dius is FP, and verfed fine PR, confequently, the ve¬ locity at R varies as the fine of that arc. Q. E. D. 238. Corollary. The velocity of the pendulum at F is to the velocity of the pendulum at R, as F m :r m, for the verfed fine is in this cafe equal to radius, and therefore the correfponding arc mull be a quadrant whofe fine is alfo equal to radius or F m. Prop. VII. 239. The time in which the pendulum performs ^ one complete ofcillation from P to O, is equal to the time in which a body would deferibe the femicircle po q, uniformly with the velo¬ city which the pendulum acquires at the point F. Take any infinitely fmall arc RV, and making r v equal to it, draw vo parallel to r w, and mn to r v. Now, by the laft propofition, and by Dynamics, Art. 28. } the velocity with which RV is deferibed is to the velocity with which mo is deferibed as rm is to Fm, that MECHANICS. 83 llieovy. R V m 0 m n >n 9 that is as— : or as: '-i for mn—rv—TLV. rm Y m r m Y m But in the fimilar triangles Y mr, m n 0, Y m :r mtz.m 0 : m «, confequently , therefore the velocity r m r tn M-ith which RV is defcribed is equal to the velocity with which w 0 is defcribed, and the times in which thefe equal fpaces are defcribed muft likewnfe be equal. The fame thing may be demonftrated of all the other correfponding arcs of the cycloid and circle, and there¬ fore it follows that the time in which the pendulum performs one complete ofcillation is equal to the time in which the feaiicircle po q\% uniformly defcribed with the velocity acquired at F. Prop. VIII. 240. The time in which a cycloidal pendulum performs a complete ofcillation is to the time in which a body would fall freely through the axis of the cycloid, as the circumference of a circle is to its diameter. Tig. 4. Since FP=2FN, and fince the velocity acquired by falling down NF is equal to the velocity acquired by falling down PF, the body, if it continued to move uniformly with this velocity, would defcribe a fpace equal to 2PF (Dynamics, § 37* N® 6.) in the fame time that it would defeend NF or CF (Art. 219). Calling T therefore the time of an ofcillation, and t the time of defeent along the axis, we have, by the preced¬ ing propofition, Tzrrtime along p 0 q, with the velocity at F, and by the preceding paragraph, /urtime along F/>, with the fame velocity j therefore T: Amtime alongp oq with velocity at V : time along Fp with the fame velocity; that is, T : t—p 0 q :Yp — 2/> oq \ 2 F/irrthe circumference of a circle : its di¬ ameter. 241. Cor. 1. The ofcillations in a cycloid are ifochronous, that is, they are performed in equal times whatever be the lize of the arc which the pendulum deferibes. For the time of an ofcillation has a conftant ratio to the time of defeent along the axis, and is there¬ fore an invariable quantity. 242. Cor. 2. The ofcillations in a fmall circular arc whole radius is BF, and in an equal arc of the cycloid, being ifochronous (Art. 232. N° 8.), the time of an ofcil¬ lation in a fmall circular arc wall alfo be to the time of defeent along the axis, as the circumference of a circle is to its diameter. 243. Cor 3. Since the length BF of the pendulum k double of the axis CF, the time of an ofcillation in a cycloid or fmall circular arc varies as the time of de- feending along CF, half the length of the pendulum, the force of gravity being conftant. But the time of defeent along CF varies as \/CY, therefore the time of an ofcillation in a fmall circular or cycloidal arc varies as the fquare root of half the length of the pen¬ dulum, or as the fquare root of its whole length. If T, t therefore be the times of ofcillations of two pendulums, T = and L and L, / their refpedftive lengths, wre have by this co¬ rollary T : \/ L : vV, and T X \/I—t X -v/h. ; hence Tx \// /'X\/L y7 5 v^L ’ v —T ’ —- fr°m which we may find the time in wThich a pendulum of any length will vibrate ; a pen¬ dulum of 39.2 inches vibrating in one fecond. 244. Cor. 4. When the force of gravity variec, which it does in going from the poles to the equator, the time of an ofcillation is diredlly as the fquare root of the length of the pendulum, and inverfely as the fquare root of the force of gravity. The time of an ofcillation varies as the time of defeent along half the length of the pendulum, and the time of defeent through any fpace varies as where r is the fpace de¬ fcribed and g the force of gravity ; but in the prefent cafe x = — ; therefore, by fubftitution, the time of defeent along half the length of the pendulum, or the • c r mi • • vTL \/h« time of an oiculation, vanes as —-—, oras—r—„ x'g Vg Hence T : J -^-7- '■ -^7-, from which it is eafy to de- Yg Vg duce equations fimilar to thofe given in the preceding corollary. 245. Cor. 5. Since T ^xTrii V/L ; and if the time of ofcillation is 1 fecond, we have \/§'— VT, or gtizh, that is, the force of gravity in different lati¬ tudes varies as the length of a pendulum that vibrates feconds. 246. Cor. 6. The number of ofcillations which a pendulum makes in a given time, and in a given la¬ titude, are in the inverfe fubduplicate ratio of its length. The number of ofcillations n made in a given time are evidently in the inverfe ratio of t, the time of each Theory. ofcillation j that is rrzp. — \ but by Corollary 3. yV, therefore n ~ -77-, and /: from which it is egfy to find the length of a pendulum which will vi¬ brate any number of times in a given time, or the number of vibrations which a pendulum of a give» length will perform in a given time. Prop. IX. 2.47. To find the fpace through which a heavy body will fall in one fecond by the force of gravity. Since by Propofition 8. the time of an ofcillation : time along half the length of the pendulum as 3.14159 is to i, and fince the fpaces are as the fquares of the times, the fpaces defcribed by a heavy body in the time of an ofcillation will be to half the length of the pendulum as 3.141 59I* is to 1. Now it appears from the experiments of Mr Whitehurft, that the length of a pendulum which vibrates feconds at London at 113 feet above the level of the fea, in a temperature of • ' * ’ L 2 ' j6o° M E C H A N I C S! 6o° of Fahrtnlieit, and when the barometer is 30 inches, have 2V, or B' 39.1196 inches 5 hence iz : 3.14159I - -^9.1196, 2B'=V : 2V ; but 2V is the velocity of B', and V is the velocity of 2B', therefore when one body is double of the other, they r . j will remain at reft vrhen the maffes of the bodies are in- i9:5598 X 3.«4i59f=^;o87 feet the fpace required. ^ ^ velocities> I he methods of determining the centre of olcillation, In (he farae wa the prOp0riti0n tnay be demonftrated gyration, and percuffion, properly belong to this chap- tlje bodieg are tQ one another In COmmen- ter, but they have been already given in the article furabI tion. Rotation, to which we muft wifties to profecute the fubjebl. refer the reader who Prop. II. Theory. Chap. VI. On the Collifion or Impuljion of Bodies. 248. Def. 1. When a body moving with a cer¬ tain velocity ftrikes another body, either at reft or in motion, the one is faid to impinge againft, or to im- pell the other. This effect has been diftinguiftied by the names colliiion, impulfion or impulfe, percuflion, and impaft. 249. Def. 2. The collifion or impulfion of two bodies is faid to be direB when the bodies move in the fame ftraight line, or when the point in which they ilrike each other is in the ftraight line which joins their centres of gravity. When this is not the cafe, the im¬ pulfe is faid to be oblique. 250. Def. 3. A hard body is one which rs not fuf- ceptible of compreffion by any finite force. An elafic body is one fufceptible of compreftion, which recovers its figure with a force equal to that which comprefles it. A foft body is one which does not recover its form after compreffion. There does not exift in nature any body which is either perfedlly hard, perfedftly elaftic or perfeblly foft. Every body with which we are ac¬ quainted poffeffes elafticity in fome degree or other. Diamond, cryftal, agate, &c. though among the bard- eft bodies, are highly elaftic \ and even clay itfelf will in fome degree recover its figure after compreffion. It is necefiary, however, t© confider bodies as hard, foft, or elaftic, in order to obtain the limits between which the required refults muft be contained. 251. Def. 4. The mafs of a body is the fum of the material particles of which it is compofedj-,* and the momentum, or moving force, or quantity of motion of any body is the product arifing from multiplying its mafs by its velocity. Prop. I. 252. Two hard bodies B, Br with velocities VjV' ftriking each other perpendicularly, will be at reft: after impulfe, if their velocities are inverfe- ly as their maffes. 1. When the two bodies are equal, their velocities muff be equal in the cafe of an equilibrium after im¬ pulfe, ana therefore B : B'=:V' : V, or BV — B'V' j for if they are not at reft after impulfe, the one muft carry the other along with it : But as their mafles and velocities are equal, there can be no reafon why the one ffiould carry the other along with it. 2. If the one body is double of the other, or B~2B', we Ihould have V'zrlV7. Now infteadof B we may fub- ftimte two bodies equal to B', and inilead of V' we may fubftitute two velocities equal to V, with which the bodies B' may be conceived to move 5 confequently we 253. To find the common velocity v of two hard bodies B, B' whole velocities are V, V', after ftriking each other perpendicularly. If the bodies have not equal quantities of motion they cannot be in equilibrio after impulfe. The one will carry the other along with it, and in confequence of their hardnefs, they will remain in contact, and move with a common velocity v. 1. In order to find this, let us firrt fuppofe B' to be at reft and to be ftruck by B in motion. The quantity of motion which exifts in B before impulfe is BV, and as this is divided between the two bodies after impulfe, it muft be equal to the quantity of motion after impulfe. But Z'XB-I-B' is the quantity of motion after impulfe, ' BV therefore v X B + B'nBV, and •y—,. 2. Let us now fuppofe that both the bodies are in motion in the fame direflion that B follows B’. In order that B may impel B', we muft have V greater than V'. Now we may conceive both the bodies pla¬ ced upon a plane moving with the velocity V'. The body B', therefore, whole velocity is V' equal to that of the plane, will be at reft upon the plane, while the velocity of B with regard to B', or the plane, will be V—V'} confequently, the bodies are in the fame cir- cumftances as if Br u'ere at reft, and B moving with the velocity V—V'. Therefore, by the lail cafe, we have the common velocity of the bodies in the move- Bv BV' able plane - - > ancl by adding to this V', the velocity of the plane, we lhall have v, or the abfolute BV-f-B'V' velocity of the bodies after impulfe, v—— Hence the quantity of motion, after impadf, is equal to the fum of the quantities of motion before impaft. 3. If the impinging bodies mutually approach each other, we may conceive, as before, that the body B' is at reft upon a plane which moves with a velocity V' in an oppofite direftion to V, and that B moves on this plane with the velocity V +V'. Then, by Cafe I. will be the common velocity upon the plane after impulfe j and adding to this V', or the velocity of the plane, we (hall have v, or the abfolute velocity , • ^ BV—B'V' TT of the bodies after impact, v~——• Hence the quantity of motion after impadt is equal to the differ¬ ence of the quantities of motion before impaft. It is obvious that v is pofitive or negative, according as BV is greater or lefs than B'V', fo that when BV is great¬ er than B'V', the bodies will move in the diredtion of B’s Thecy. ■urzV ; for in this cafe there can be no M E B’s motion •, and when BV is lefs than B \ dies will m< ve in the direftion of A’s motion. 2''4 AH the three formulae which we have given, may be comprehended in the following general formu¬ la • for when B' is at reft, V'-O, and la, v — B-j-A' the formula affutnes the form which it has in Cafe x. 2^r. Cor. I. If B=rB', and the bodies mutually approach each other, the equation in Cafe 3. becomes ^ V—-V—V'=the velocity gamed by B in conte- quence of compreflion.—But, when the bodies llr.ve to recover their form by the force of reftitution, the oody B will move backwards in confequer.ee of this torce, while B' will move onward in its former diredion with an acce¬ lerated velocity. Hence, from the force of reftitution, h will again lofe the velocity V—v, and B will, a lecond time, gain the velocity ^-V' 5 confequently, the whole velocity loft by B is 2 V—and the whole velocity- gained by B'is 2ti—2 V'. Now, fubtrading this jols from the original velocity of B, we have J —2 V 2 vi for the velocity of B after impad, and adding the ve¬ locity gained by B to its original velocity, we have y/+2 2'V7 for the velocity of B' after impad; Now the hence we have ■ 2 v —. 2 v—V —V—2 V- ■y" = V'+ 2 v—2 V'rr 2V—V. Now, fubftituting in thefe equations, the value ot v ar found in Cafe 2. Prop. 2. we obtain BV—B'V+2 B'V' v - B+B' BV'—B'V' + 2BV *'"= B+B'” * 261 2 When the bodies move in oppofite diredions' or mutually approach each other, the body B is in pre- cifely the fame circumftances as in the preceding . ^ Theory. but the body B' lofes a part of Its velocity equal to _2 u-f- 2 V'—V'. Hence wejiave, by the fame reafon- mg that was employed in the preceding cafe, vr ~2v V' ‘1>"=2V+V, and by fubftituting inftead of v its value, as determined m Cafe 3. Prop. 2. or by merely changing the fign of V' in the two laft equations in the preceding corollary, we obtain the two following equations, which will an- Iwer for both cafes, by ufing the upper fign when the bodies move in the fame direftion, and the under fign b'hen they move in oppofite direftiotis. ~ s. and V_V'> both the bodies will recoil or move back¬ wards after impart with the fame velocities which they had before impart. For in the formula in Cafe 2. with the inferior figns, when B—B' and V—V', we have 270. Cor. 9. If the bodies move in oppofite direc- B—3 B' tions, and Vr: V', wTe have v'—V x ,3 B—B' and v" =vx B-f-B' B-}-B' Hence it is obvious, that if Brrj B', ‘V BV—TFV—*—? B'V' B'-j-B' /,_.±:BV,=frB/V'-f 2 BV B+B' From the preceding equation the following corol¬ laries may be deduced. „ 26z. Cor. t. The velocity gained by the body that is ft ruck, and the velocity loft by the impinging body, are twice as great in elaftic as they are in hard bodies; for in hard bodies the velocities gained and loft were V', and V—v 5 whereas in elaftic bodies the velo¬ cities gained and loft were 2v—2 V', and 2 V 2 v. . 26 3- Cor. If one of the bodies, fuppofe B', is at ref, its velocity V'rzo, and the preceding equation be¬ comes VB—VB' B + B' 2 VB :B+B' 264. Cor. 3. If one of the bodies B' is at reft, and their maffes equal, we have BrrB', and V'=o, by fubftituting which in the preceding formulae, we’ ob¬ tain v'~o, and v'f—'V j that is, the impinging body -B remains at reft after impart, and the body B' that is ftruck when at reft moves on with the velocity of the body B that ftruck it, fo that there is a complete transfer of B’s velocity to B'. 265. Cor. 4. If B' is at reft and B greater than B', both the bodies will move forward in the dirertion of B s motion j for it is obvious from the equations in Cor. 2. that when B is greater than B', v1 and v" are both pofitive. 266. Cor. 5. If B' is at reft, and B lefs than B', the impinging body B will return backwards, and the body B' which is ftruck will move forward in the direc¬ tion in which B moved before the ftroke. For it is evi¬ dent that when B is lefs than B', v’ is negative, and v" pofitive. 267. Cor. 6. If both the bodies move in the fame di- re&ion, the body B' that is ftruck will after impart move with greater velocity than it had before it. This is obvious from the formula in Cafe 1. of this propofi- tion. 268. Cor. 7. If the bodies move in the fame direc¬ tion, and if B~B', there will at the moment of im¬ part be a mutual transfer of velocities, that is, B will move on with B'’s velocity, and B' will move on with B’s velocity, For in the formulae in Cale 1. when B=: B, we have v'—V and v"~V. 269. Cor. 8, r hen the bodies move in oppofte di- reBions, or mutually approach other, and when B=B' 4 or if one of the impinging bodies is thrice as great as the other the greateft will be flopped, and the fmalleft will recoil with a velochy double of that which it had before impart For fince 6 = 3 B', by fubftituting this value of B m the preceding equations, we obtain v —0, and v"~ 2 V. 271. Cor. 10. If the impinging bodies move in oppofite dirertions, and if B—B', they will both recoil alter a mutual exchange of velocities. For when B__B', we have v’~—V', and t/'zttV. 272. Cor. 11. When the bodies move in oppofite dirertmns the_ body which is ftruck, and the body which ftnkes it, will flop, continue their motion or return backwards according as BV—B'V is enual to or greater or lefs than 2 B'V'. 1 ^ * 273. Cor. \ 2. The relative velocity of the bodies alter impart, is equal to their relative velocity before impart, or, which is the fame thing, at equal inftants be- - lore and after impart, the diftance of the bodies from each other is the fame. For in the different cafes we have t/-2 V j v"~2 i;=pV'. But the relative ve¬ locity before impart is in the different cafes V—-V'y ancl the relative velocity after impart is v'—71.'—V—yq 274. Cor. 13. By reafoning fimilar to that which was employed in Prop; 2. Cor. 3. it may be {hewn : 2 B as their relative velocity before im- part is to the velocity gained by B' in the dirertion of B s motion 5 and B-f-B' : 2 B' as their relative ve¬ locity before impart is to the velocity loft by B in the dirertion of A’s motion. I4‘ Tta vis viva, or the fum of the pro- durts of each body multiplied by the fquare of its ve¬ locity, is the fame before and after impart, that is. B vn + B' v"*=BV* + B'V', From the formula at the end of Cafe 2. we obtain P^g~BTxBW+B'V'»^ B+B'f* ,2_+BB'x"BV*+B'V'* , , . B : , hence their fumB7/',xB'‘y''1 B + B'|* __B—B'I’x BV» + B'V'2+4 BB'xBV^+’B'V'* B + B'|2 ^ BV’+B'V'* X B—B'J + 4 B B' — _— =BVJ-L B'V'*. B+B'* ^ 276. Cor. 14. If feveral equal elaftic bodies B, B'', B'"? B"", &c. are in contart, and placed in the fame ftraight line, and if another elaftic body of the fame magnitude impinges againft B, they'will remain at reft, except the laft body B"", which will move on with the velocity of /3. By Art. 264. B will transfer tp M E C H A N I C S. 87 nieory to B'7 all its velocity, and therefore B will be at reft, in the fame way B" will transfer to B'" all its velocity, and B" will remain at'reft, and fo on with the reft ; bat when the laft body B"" is fet in motion, there is no other body to which its velocity can be transferred, and therefore it will move on with the velocity which it received from B'", that is, with the veloci¬ ty of /3. 277. Cor, 1 If the bodies decreafe in fize from B to B"", they will all move in the dire&bn of the impinping body /3, and the velocity communicated to each body will be greater than that which is communi¬ cated to the preceding body. 278. Cor, 16. If the bodies increafe in magnitude, they will all recoil, or move in a diredlion oppoiite to that of &, excepting the laft, and the velocity com¬ municated to each body wall be lefs than that which is communicated to the preceding body. Prop. IV. 279. To determine the velocities of two imperfectly elaflic bodies after impulfe, the force of com- preflion being in a given ratio to the force of reftitution or elafticity. Let B, B' be the two bodies, V, V their velocities before compaft, 7/, ’v" their velocities after impadt, and I : « as the force of compreftion is to that of reftitu¬ tion. It is evident from Cafe I. Prop. 8. that in con- fequence of the force of compreffion alone we have, V—v—velocity loft by B 7 froin compreflion. velocity gamed by B 3 But the velocity which B lofes and B' gains by the force of compreflion will be to the velocity which B lofes and B' gains by the force or reftitution or elaftici¬ ty as 1 :» j hence ! : n—\ v :nV—«XI, the velocity loft by B^ from ela- 1: ti—V—V': n v-n V' the velocity gained by^B 3 fticity. therefore by adding together the two portions of ve¬ locity loft by B, and alfo thofe gained by B', we ob¬ tain I4.«V—the whole velocity loft by B, X _|_« ^__i V', the whole velocity gained by B Hence by fubtra&ing the velocity loft by B in confe- quence of collifion from its velocity before impaa, we ftiall have v' or the velocity of B after impad, and by adding the velocity gained by B' after collifton to its velocity before impad, we (hall find v" or the velocity of B' after impad, thus v>—\ x i-f-« v the velocity of B after impad. 7/'—V'+ 1 —1 -j-/zV/the velocity of B' after impad. Now by fubftituting in the place of y its value as de¬ termined in Cafe 2. Prop. 2. we obtain r+^BV-BV'. E + E' . ^ - v T b+B' 280. Cor, I. Hence by converting the preceding e- quation into analogies, B-}-B. ; i-j-i/xB as the relative velocity of the bodies before impad is to the velocity gained by B' in the divedion of B’s motion 5 and B-f B' : i-j-z/xB' as the relative velocity of the bodies before impad is to the velocity loft by B. 281. Cor. 2. The relative velocity before impad is to the relative velocity after impsd as the force of com¬ preflion is to the force of reftitution, or as I : The relative velocity after impad is v'—or tak¬ ing the preceding values of thefe quantities v''—v'~\7' Theory. i+nx BV— BV'l v_i-j-ftXB'V—B'V' B + B' B + B' :V'. y | 1 T” X dividing by B + B' we have +_t/-V'—V+V—V'+« x Y—V'rr«XV-Tv; the relative velocity after irapad. But the relative velocity before impad is V—V', and V—V' : «X V V'— i : n. Q. E. D. The quantity V' has evident¬ ly the negative lign when the bodies move in oppofite diredions. 282. Cor. 3. Hence from the velocities before and after impad we may determine the force of reftitution or elafticity. Prop. V. 283. To find the velocity of a body, and the di- re£Hon in which it moves after impinging upon a hard and immoveable plane. 284. Case i. JV/ien the impinging body is perfectly When the hard. Let AB be the hard and immoveable plane, body is per- and let the impinging body move towards AB in the fedtly hard, diredion CD, and with a velocity reprefented by CD. Flg- 6- Then the velocity CD may be refolved into the two velocities CM, MD, or MD, FD j CM Dt being a parallelogram. But the part of the velocity FD, which carries the body in a line perpendicular to the plane, is completely deftroyed by impad, while the o- ther part of the velocity MD, which carries the body in a line parallel to the plane, will not be affeded by, the collifion, therefore the body will, after impad, move along the plane with the velocity MD. Now, CD : MDirradius : cof.^CDM, therefore fince MD* = CF the,, fine of the angle of incidence CDF, the velocity before impaB is to the velocity after impaB, as radius is to the fine of the angle of incidence j and fince AM=CD—MD, the velocity before impaB is to the- velocity lojl by impaB, as radius is to the verfed fne of the complement off the angle of incidence. 285. Case 2. When the impinging body is pcrfcBly- when the elajlic. Let the body move in the diredion CD with body is per- a velocity reprefented by CD, which, as formerly, may el:+ be refolved to MD, FD. The part of the velocityt,c- MD remains after impad, and tends to carry the body parallel to the plane. The other part of the velocity FD is deftroyed by compreflion 5 but the force of refti¬ tution or elafticity will generate a velocity equal to FD, but in the oppofite diredion DF. Confequently the impinging body after irnpad is lolicited by two ve¬ locities, one of which would carry it uniformly from D to F in the fame time that the other would carry it uni- fermly from M to D, or from D to N j the body will^ therefore^ 88 MECHANICS. Theory. When the body is im- perfectly elaftic. rig- 7- tlierefore, move along DE, tlie diagonal of the paral¬ lelogram DFEN, which is equal to the parallelogram DFCM. Hence the angle CDF is equal to the angle EDF, therefore, when an clnjlic body impinges oblique¬ ly againjl an immoveable plane, it will be rejleRed from the plane, fo that the angle of reflexion is equal to the angle of incidence. Since CD, DE are equal (paces deibiibed in equal times, the velocity of the body after impadl will be equal to its velocity before impaft. 2 86 Case 3. When the impinging body is imperfeRly elaflis* In DF take a point m, fo that DF is to D m as the force of compreflion is to the force of reftitution or elafticity, and having drawn m e parallel to DB, and meeting NE in e, join D e j then, if the impinging bo¬ dy approach the plane in the direction CD, with a ve¬ locity repretented by CD, D e will be the direction in which it will move after impaft. Immediately after compreflion, the velocity DF is deflroyed as in the lafl cafe, while the velocity MD tends to carry the body parallel to the plane. But, by the force of reftitution, the body would be carried uniformly along D m, per¬ pendicular to the plane, while, by the velocity MDrr DNzrtfz ei it would be carried in the fame time along m e, confequently, by means of thefe two velocities, the body will deferibe D e, the diagonal of the parallelo¬ gram D e N. The velocity, therefore, before impaft is to the velocity after impaft as DC : D e, or as DE : D e, or as fin. D cE, fin. DE e, or as fin. Dem: fin. DE e, or as fin. FD e : fin. FDE. Nowq by pro¬ ducing D £ fo as to meet the line CE produced in G, we have, on account of the parallels FE, m e, D in: DF —m e : FG j but, FD being radius, FE is the tangent of FDE, or FDG the angle of incidence, and FDG is the tangent of the angle of reflexion FDG : Therefore D m : DF=tang.^CDF : tang. -^LFDG. Confe¬ quently, when an imperfeRly elaflic body impinges a- gainfl a plane, it will be refledfed in fuch a manner that the tangent of the angle of reflexion is to the tangent of the angle of incidence, as the force of compreflion is to the force of reflitution or elaflwity ; and the velocity be¬ fore incidence will be to the velocity after reflexion, as the fine of the angle of reflexion is to the fine of the angle of incidence. Scholium. 287. When the furface againft which the body im¬ pinges is curved, wje muft conceive a plane touching the furface at the place of incidence, and then apply the rules in the preceding propofition. The doftrine of the oblique collifion of bodies is of great ufe both in acouftics and optics, where the material _ particles which fuffer reflexion, are regarded as perfeftly elaf¬ tic bodies. Trop. VI. 258. To find the point of an immoveable plane which an elaftic body moving from a given place muft ftrike, in order that it may, after re¬ flexion, either from one or two planes, im¬ pinge againft another body whofe pofition is given. 289. Case i. When there is only one reflexion. Let C be the place from which the impinging body is to Theorv. move, and let E be the body which is to be firuck af¬ ter reflexion from the plane AB. From C let fall y CH perpendicular to AB, continue it towards C till HG=rCH, and join G, E by the line GDE; the point D where this line cuts the plane, is the place againft which the body at C muff impinge in order that, after reflexion, it may ftrike the body at E. ft he triangles CDH,HDG aie equiangular, becaufe two fides and one angle of each are relpectively equal, therefore the angles DCH, DGH are equal. But on account of the parallels FD, CG the angle EDF=rDGC~DCH, and DCH~ FDC, therefore the angle of incidence FDCrrFDE tjie angle of reflexion ; confequently by Prop. 4. a body moving from C and impinging on the plane at D will, after reflexion, move in the line DE, and ftrike the body at E. 290. Case 2. When there are two reflexions. Let Fig. 8. AB, BL be the two immoveable planes, C the place from which the impinging body is to move, and F the body which it is to ftrike after reflexion from the two planes, it is required to find the point of impaci D. Draw CHG perpendicular to AB, fo that HG=CH. Through G draw GMN parallel to AB, cutting LB . produced in M, and make GMrrMN. Join N, F, and from the point E, where NF cuts the plane BL, draw EG, joining the points EG : the point D will be the point of the plane, againft which the body at C muft impinge, in order to ftrike the body at I. By reafoning as in the preceding cafe, it may be (hewn, that the angle CDHmEDB, therefore DE will be the path of the body after the firft reflexion. Now, the triangles GEM, EMN are equiangular, beaaufe GM =MN, and the angles at M right, therefore DEB = FEL, that is, the body after reflexion at E will ftrike the body placed at F. Prop. VII. 291. To determine the motions of two fpherical bodies which impinge obliquely upon each other, when their motion, quantities of matter, and radii, are given. Let A, B be the two bodies, and let CA, DB 'reFig.5. the directions in which they move before impaft, and let thefe lines reprefent their refpeCtive velocities. Join A, B the centres of the bodies, and produce it both ways to K and I. Draw LM perpendicular to IK, and it will touch the bodies at the point of impa£t. Now, the velocity CA may be refolved into the two velocities Cl, I A, and the velocity DB into the velo¬ cities DK, KB, but CA and DB are given, and alfo the angles GAI, DBK, confequently Cl and IA, and DK and KB may be found. The velocities Cl, DK, which are parallel to the plane, will not be altered by collifion, therefore 1A, KB are the velocities with which the bodies direftly impinge upon each other, confequently their effefts or the velocities after impaft may be found from Prop. 3. j let thefe velocities be re- prefented by AN, BP. Take AFrrCI and BH—DM, and having completed the parallelograms AFON, BPQH, draw the diagonals AO,BQj Then, fince the body A is carried parallel to the line LM with a velocity CI=:AF, and bom the line LM by the velo¬ city AN, it will defer foe AO, the diagonal of the pa¬ rallelogram M E C H A N I C S. So r Theory, rallelogvam NFj and for tlie fame reafon the body v—B will ddcribe the diagonal B£) of the parallelo¬ gram Pii. 292. Corollary. If A=B, and if the body which is ft ruck moves in a given direction and with a given velocity after impad, the dire&ion of the impinging body, and the velocity of its motion, may be eafily F- IC< found. Let the body D impinge againft the equal body C, and let CB be the dire&ion in which C moves after impadf, it is required to find the dire&ion in which D will move. Draw D c, touching the ball C at c, the place where the ball D impinges •, produce BC to E, and through c draw A c F perpendicular to EB, and complete the reclangle FE. The force D c may be refolved into the forces E c, c F, of which E c is employed to move the ball C in the diredlion CB and with the velocity E c ; but the force c F has no fhare in tire impulfe, and is wholly employed in making the body D move in the direftton CA, and with the velocity CF. Scholium. The pheno- 293. In the preceding propofition, we have endea- mena of vours'd to give a fhort and perfpicuous view 01 the com- impulficn mon tlieory of impulfion. The limits of this article owing to| win not peiTnit us to enter upon thofe interefting fpecu- fwces1 C lations to which this fubjed has given rife j but thofe which pre- who are anxious to purfue them v/ill find ample aflift- vent bodies ance jn the article IMPULSION, in the Supplement to from com- ^ laq edition of this work, where Dr Robifon has mathemati- treated the fubjeft with his ufual ability. It may be cal contact, proper however to remark, that all the pnenomena ot impulfe as well as preflure, are owing to the exiftence cf forces which prevent the particles of matter from coming into mathematical contail. I he body which is ft ruck, in the cafe of collifion, is put in motion by the mutual repulfion of the material particles at the point of impaft, while the velocity of the impinging body is diminiftied by the fame caufe. Hence we fee the abfurdity of referring all motion to impulfe, or_ of attempting to account for the phenomena of gravita¬ tion, ele.aricity, and magnetifm by the intervention of any invifible fluid. Even if the fuppofition that fuch a medium exifls w-ere not gratuitous, it would be _ impof- ftble to ftiew that its particles, by means of whidi the impulfe is conveyed, are in contaa with the particles of the body to which that impulfe is communicated. Bon Geor- 294. A phyfico-mathematical theory of percuflion, in ges Juan’s which the impinging bodies are confidered as imper- phyfico ma-fedly elaftic, has been lately given by Don Georges thematical in his Examen Maritimo, a Spanifti work which rercuffion has been tranflated with additions by M. L’Eveque, un¬ der the title of Examcn maritime, theonque et pratique, on Traite de mecanique, applique a la conjlruchon, et a la manceuvre des vaijjeaux et autres batwiens. dhis theory has been embraced by many eminent French philofophers, and may be feen in Prony’s ArchiteBure Hijdrauhque, vol. i. p. 208, and in Gregory s Mechanics, vol. 5. p. 291. We {hall endeavour, under the artic*e Percussion, to give a fhort account of this interefting theory, which has been found to accord with the moft accurate experiments. 295. In fome cafes of collifion the refults of experi¬ ments are rather at variance with thofe of theory,, in confequence of the communication of motion not being Vol. XIII. Part I. exa&ly inftantaneous. “ If an ivory ball (fays Mr Theory^ Lellie) ftrikes againft another of equal weight, there ““ v fliould, according to the common theory, be an exact transfer of motion. But if the velocity of the impin¬ ging ball be very confiderable, fo far from flopping iud* denly, it will recoil back again with the fame force, while the ball udiich is ftruck will remain at reft ; the reafon is, that the fhock is fo momentary, as not to per¬ mit the communication of impulfe to the whole mafs of the fecond ball ; a fmall fpot only is affedled, and the confequence is therefore the fame as if the ball had impinged againft an immoveable wall. On a perfect acquaintance with fuch fads depends, in a great mea- fure, the fkill of the billiard player. It is on a fimilar principle that a bullet fired againft a door which hangs freely on its hinges will perforate without agitating it in the leaft. Nay, a pellet of clay, a bit of tallow, or even a fmall bag of water, difeharged from a piftol will produce the fame efteft. In all thefe inftances the impreflion of the ftroke is confined to a fingle fpot, and no fufficient time is allowed for diffufing its aF=24 feet. But in addition to the refiftance arifing from the work to be performed, the two men have to overcome the re¬ fiftance arifing from the fri£tion of the pifton in the bar¬ rels, which we may fuppofe equivalent \.of, of the lever is equal to 1594 pounds aiding at the dif- tance of 2.5 feet from F. The mechanical energy, there¬ fore, of the fum of all the refiftances will be =2.5 X 1594=398.75, while the energy of the moving force, or the fum of all the moving powers, is equal to 500. 300. Def. 2.—The impelled point of a machine is that point to which the moving power is applied, if there is only one power, or that point to which ail the moving powers are reduced, or at which the moving force is fup- pofed to aft. The working point of a machine is that point at which the refiftance afts if it is fingle, or that point to which all the refiftances are reduced, and at which they are fuppofed to aft when combined. Thus in fig. I. G is the impelled point of the machine, and Fig. t. D the working point. Had a fingle force tt been ap¬ plied at the point B to raife a fingle weight a, aiding M E C H Theory, at the point A, then E would have been the impelled point, and A the working point of the machine. In the ■wheel and axle, the point of the wheel at which the rope touches its circumference is the impelled point, while the working point is that point in the circumfe¬ rence of the axle where the rope which carries the weight is in contaft with it. 201. Def. 3.—The velocity of the moving power, and the velocity of the refiftance, are refpe&ively the fame as the velocity of the impelled point, and the velocity of the working point. 002. Def. 4.—The eJeSi of a machine, or the work performed, is equal to the refiftance multiplied by the velo¬ city of the working point 5 for when any machine raftes a mafs of matter to a given height in a certain time, the effeft produced is meafured by the produtl of the mals, and the height through which it rifes, that is, by the produa of the mafs by the velocity with which it moves. 20 2 Def c.—The momentum of impulfs is equal to the moving force multiplied by the velocity of the impelled point. 204. In any machine that has a motion of rotation, let SxphHa- ^ ^ tlie veiocjty 0f the impelled point, and y the velocity of the working point. When the machine is a lever, x,y will exprefs the perpendiculars Jet fall from the centre of motion upon the line of diredion in which the forces aa 5 and if the machine is a whee and axle, x,y will reprefent the diameters of the wheel and the axle relpeftively. In compound machines which may be regarded as compofed of levers, (Art. 90 ) * will reprefent the fum of all the levers by which the power afts, and y the fum of all the levers by which the refiftance afts. .. , , 20 c. Let P be the real preffure which the moving power exerts at the impelled point of the machine, and R the aftual preffure which the mere refiftance of the work to be performed exerts at the working point, or which it direftly oppofes to the exertion of the power. Let n be the inertia of the power P, or the mafs of matter which the power P muft move with the ve¬ rity of the impelled point, in order that P may exert its preffure at the impelled point j and let b be t e in¬ ertia of the refiftance R, or the mafs of matter which muft be moved with the velocity of the working point m qo^^inc^the'refiftance arhing from the friftion of the communicating parts is an uniformly retarding force it may be meafured by a weight afting at the working point of the machine, which wall oppofe the fame refiftance to the moving power as the fnftion of ^^o^Let m be the inertia of tlm machine or rather tha3t quantity of matter, which afting at the working point of the machine will require the fame part of the moving force to give it an angular motion, then fmce y reprefents the arm of the lever by which the refiftance afts or the diftance of the working point from the centre of motion; and finee the momentum of inertia or the momentum with which any mafs revo ving rou centre refifts being put in motion is e that is, vzkF/, or is = ^ / F 5 but F, the accelerating force, which generates the velocity of the impelled point, is r 11 1 r 1 P Y*—R x y—

Rya a xz ~{-b tf-\-mif ’ which reprefents the work performed, is equal to the fluxion of the numerator, becaufe the denominator is conflant, that is, V xy R—2RR y*—

wbich being little oreater than 1, will not alter the refult, the refiftance ftiould be one half of the force which would keep the impelling power in equilibrio. 31 Case 2. When b varies at the fame time with R, it will in moft cafes vary in the lame proportions, and therefore may be reprefented by any multiple of R, as , of uniform denfity, be fufpended from the points A, B, fo that it forms a catenary whofe altitude is D k, the required height of the 'arch. Divide AB into any number of equal parts, fuppofe eight, and let the vertical lines I m, 2 n, 30, drawn from thefe points, interfeft the catenary in the points a, b, c. From the points a, b, c k, r, s, t, fufpend pieces of chain of uni¬ form denfity, and form them of fuch a length, that when the whole is in equilibrio, the extremities of the chains may lie in the line T'U'V'$ then the form which the catenary A £ B now affumes, will be the form of an equilibrated arch, which, when inverted like AKB, will fupport the roadway TUV, fimilar to T'U'V'. This Theory- MECHANIC S. This is obvious from tlie latl paragraph, for the pieces is parallel to it. of chain a m, bn,co,k\J, &c. are forces afting upon the points <7, b, c, k of the catenary, and are proportional to a m, b n, c o, &c. the dillances of the points a, by c, k, &c. from the roadway. 322. An arch of this conftruftion will evidently an- fwer for a bridge, in which the weight of the materials between the roadway and the arch Hones is to. the weight of the arch Hones, as the weight of all the. pieces of chain fufpended from a, b, c, &c. is to the weight of the chain A k B. As the ratio, however, of the weight of the arch Hones to the weight of the fuperincumbent materials is not known, we may aflume a convenient thicknefs for the arch Hones, and if from this ailumed thicknefs their weight be computed, and be. found to have the required ratio to the w7eight of the incumbent mafs, the curve already found will be a proper form for the arch. But if the ratio is different from that of the wTeight of the whole chain to the wreight of the ful- pended chains •, it may be eafrly computed how much muff be added to or fubtraded from the pieces of chain, in order to make the ratios equal, fhe new curve which the catenary then affumes, in confequence of the change upon the length of the fufpended chains, will be the form of an equilibrated arch, the weight of whofe arch Hones is equal to that which was affumed. r _ Let us now fuppofe that the lines CD, D.E, EB, &c. can move round the angular points D, E, B, F, &c. the extremities A, C being immoveabley and that forces proportional to D^, Ee, B£, &c. are ex¬ erted upon the points D, E, B, F, &c. and in the direftion Dt/, Ee, &c. Now, by the refolution of forces, the force Dd, may be refolved into the forces Dc, T>p, the force E e into the forces E y, E r, and the force B b into the forces B j, B /, and fo on with the red. The force D c produces no other effea. than to prefs the point A on the plane on which it reds, and is therefore deHroyed by the refiflance of that plane y but the remaining force D /> tends to bring the point D to¬ wards E, and to enlarge the angle ADE y this force, however, is deHroyed by the equal and oppofite force E y, and in the fame w7ay the forces E r, B 7, Fa; are deHroyed by the equal and oppofite forces, Br, F£, Gu, while the remaining force G to is deHroyed by the re¬ finance of the plane which fupports the point C. When the lines AD, DE, &c. therefore are adled upon by vertical forces proportional to D or E ^=fln. c dT) or- d~Dp : fin. AE) d, that is, by taking the reciprocals Scholium. D c:E q— fin. AD d ' fin. t/D />’ Fig. S. 323. In moH cafes the catenarian curve thus deter¬ mined w7ill approach very near to a circular arc equal to 120 degrees, wdfich fprings from the piers fo as.to form an angle of 60 degrees w7ith the horizon. 1 he form of the arch, however, as determined in the pre¬ ceding propofition, is fuited only to thofe cafes in which the fuperincumbent materials exert a vertical preffure. A quantity of loofe earth and gravel exerts a pieffuie in almofl every dire&ion, and therefore tends to defiroy the equilibrium of a catenarian arch. T his tendency, however, may be removed by giving the arch a greater curvature towards the piers. This will make it approach to the form of an ellipfis, and make it fpring more ver¬ tically from the piers or abutments. 324. We fhall now proceed to deduce the form of an arch and its roadway, by eflablifliing an equilibrium a- mong the weights of all the materials between the arch and the roadway. T his method w7as given by Emerfon in his Fluxions, publilhed in I742> an^ afterwards by Dr Hutton in his excellent work on bridges. Prop. II. 325. To determine the form of the roadway or extrados, when the form of the arch or intrados is given. Let the lines AD, DE, EB, BF, FG, GH lie in the fame plane, and let them be placed perpendicular to the horizon. From the points D, E, B, &c. draw the vertical lines D */, E f, B Z>, &c. and taking D/> of any length, make E r equal to D/>, &c. and complete the parallelogramsp c, q r. Again, make B and com¬ plete the parallelogram ts; in like manner make Ek=sb, and complete the parallelogram Fy'j and fo on with all the other lines, making the fide of each parallelogram «qual to that fide of the preceding parallelogram which and for. the fame reafon E q :.B j: Hence ’fin. E e q ' fin. £ B r I fin. E e q Slow, fince E y : E crzfin. Eeq\ fin. E q cr. we have E ^ ' ^ q C] that is, fince DE/wrrE q e, and fin. E e q ^ E <7 xfin. DE m „ . 1 ? EB=E eq\E e— — • But Eqz=:{ hi c . .. 11 fin. e EB therefore, by fubflitution, we obtain fin. DE m E e~ "fin. Eeq fin. E tw cE m ’ fin> e E wf” But 1 MECHANIC S. Fig-9. Fig. IC. But the angle of contaft D.E m varies with the curvature at the point E, and the curvature varies as the-reciprocal of the radius of curvature, therefore the angle of contact varies as the reciprocal of the radius of curvature ; hence by fubfutution, E e±i : radius of curvature xe -- '»* In order to get rid of the confufion in fig. 8. where the arch is a polygon, let us fuppoie ABC, fig. 9. to be the curve, m n a tangent to any point E, and E c a vertical line ; then the prejjure at any point of the arch is reci¬ procally as the radius of curvature at that point, and the fquare of the fine of the angle which the tangent to that point of the curve forms with a vertical line. 327. Corollary Let us now fupjtofe that the arch ABC fupports a mafs of homogeneous materials lying be¬ tween the roadway TUV and the arch AEBCj and the whole being fuppofed in equilibrio, let us determine the weight which preffes on the point E. The weight of the fuperincumbent column Y. c h dvaries as ILcytgd, hut. g d—Y dY.im. d Y g,Y d being radius, undid Yg — E n B, on account of the parallels Yc, UB, there¬ fore the weight of the column Yc b d varies as E cX E^xhri. E«B, that is, as E c X fin* E/z B, becaufe E is a conftant quantity ; but the preffure at E was proved to vary as : there- radius curvature X fin* e E nd fore the weight of the column YcbdnxYcy. fin. E« B varies alfo as this quantity, that is, E c X fin* E n B~ 7 7: radius curvature x fin. e Y nd But as the angle E « B is equal to the angle e E m, we ftiall have, by fubftitution and divifion, Ecrr- -, that is, of the arch, or R, therefore, E c=: 1 rJ £3 Se£L IV. and Divifion, we have by the notation R : BF : DF R3__|BF3 b* Tlieory. =iBF3 DF3, hence • R x fin* GE e fubftitution, E cf=-~r-, that is, fince R is conftant, E crz--1-* But when the point E coincides with B, • b 3 the cofine b becomes equal to radius j therefore, in that cafe E c~-~, and E c becomes BU =: m, hence : Yc, and by Geometry, Theor, 8. fide by m therefore have DF3 772 R3 772 BF3 and multiplying each £3 ~ DF3 7 the vertical diftance of tR but 772 R3 -E c. b* furface of the radius curvature xfin* e E m\l When an arch fupports a roadway, the preffure ex¬ erted upon any point of it, is reciprocally as the radius of curvature, and the cube of the fine of the angle which the tangent to that point forms with a vertical line. 328. Flaving thus obtained an expreflion for Ec, we fhall proceed to fhew the application of the formula to the cafe when the arch is a portion of a circle. Let EB be the arch of a circle whofe centre is F. Let the radius — R, BD = verfed fine, BE=.v, DF=cof. BErr/?, BUrz://;. Draw the tangent GE, and through E the vertical line ce, which will be parallel to BE. Then fince GEF is a right angle, and eEF—EFB, the angle GEe is the complement of EFB, therefore, fin. GE crrcof. EFBnrFD. But, in the prefent cafe, the radius of curvature is the radius 1 » or by f ^ T7 wish3 BUxBF3 roadway from the point r, or E -——,y rr-——^—. When the point E coincides with B, BF—DF, and E e=:BU. When E coincides with A, the cofine DF vanifties, and therefore E c, or the diftance of the point A from the extrados or roadway, is infinite. The curve VUcT, therefore, will run up to an infinite height, approaching continually to a vertical line, drawn from A, which will be its afymptote. Such a form of the extrados, however, is inadmiftible in prac¬ tice j and therefore a femicircular arch is not an arch of equilibration. When the arch is lefs than a femi- circle, as PBR, the curve terminates in the point p ; and as it does not rife very much above a horizontal line, palling through U when the arch is fmall, we might produce a perfed! equilibrium, by making the roadway horizontal as £ U “u, and making the denfity of the fuperincumbent columns P 72, Yo, which prefs upon the points P, E refpedlively, in the ratio of P/>, E c, the diftances of thefe points from the curvili-’ neal roadway. 329. The inconvenience, however, arifing from the inflexion of the extrados, may be conliderably removed by throwing the point of contrary flexure to a greater diftance, which may be done by diminiftiing BU, the thicknefs of the incumbent mafs above the keyftone. Thus, if BU is diminifhed to Yd, and if points a, b are taken in the lines P/>, Yc, fo that P27 : Pp—Y b : Yc—Yd : BU, and fo on with all the points in the arcli 5 and if a new roadway v d b a t be, drawn through thefe points, the equilibrium of the arch will ftill continue, for the various preffures which it fuftained, though they are diminilhed, preferve the fame proportion. 330. Let us fuppofe it neceffary to have the extrados a horizontal line, and let it be required to find YU~m when there is an equilibrium. In this cafe the point H coincides with U •, or rather, when the curve U c T cuts the horizontal line t U v, the point H coincides with U. By fubftituting BF—BD inftead of DF in the value of E c, formerly determined, and by putting BDrry, 772 R3 we have E c=~—r~~l,* But when H coincides with U, . R—fI c coincides writh 0, and therefore E 0—E c~ BD B U 772 R3 =:y-}-m, confequently, and multiplying byJR.—y^, we have 7«R3=r?/ X R—yY -T ^ X R—y\*, or 772 R3-J-/72X R—yl3= y X R—yY, and, dividing by the coefficients of 7/2, we have -}-•> that is, 7/xR- tnzz- — R3_R_3,|3 The thichnefs of the roadway above the hey stone, when the extrados is a fraight line, is equal to the quotient arifing MECHANICS. 97 Theory. ariRm from multiplying the verfaifme of half the arch may, therefore, conclude, that when the arch is to be *—v—- by the cube of its cojine, and dividing this product by the circular with a horizontal roadway, an arch ojild de- difference between the cube of the radius, and the cube of grees approaches nearejl to an arch of equilibration, r r ... _1 nr,r.r.c th^ tlirlnplt nf 332. When the arch is elliptical, it will be ti the cofine; or, to change the exprelTions, the thicknefs of the roadway above the keystone, when the roadway is a freight line, is equal to the quotient arifng from multi¬ plying the height of the arch, by the cube of the differ¬ ence between the radius of the arch and its height, and dividing this produB by the difference between the cube of the radius, and the cube of the difference between the radius and the height of the arch. 331. When the arch is a femicircle R—y vanilhes, and m becomes equal o, fo that the femicircular arch is evidently inadmiflible. But when the arch is lefs than a femicircle, the value of m will be finite. Thus, if the arches are refpeftively Arch. 6o°, we have m—\ the fpan, 90°, we have in—\ of the fpan, or 1 io°, we have of the fpan nearly. The two fir ft arches of 60® and 90°, manifeftly give too great a thicknefs to the part BU or m. In the third arch of no0, the thicknefs of BD is nearly what is given to it by good architeas, and is therefore the beft in pradice •, for if the arch were made greater than iio°, the thicknefs of BU or m would be too fmall. It is obvious, however, that an arch of no is not an arch of perfeB equilibration, for this can be the cafe only when the roadway has the form U z r. \\ hen the roadway, therefore, is horizontal, as U r, there is 1U/ uni, ILVyi ^ J 1 _n> . - When the arch is elliptical, it will be found, ^pncal as in the circle, that m _ y x R—yj3 ■R3_.R=73- An elliptical PeriVr0 v circular •c . arches arch, however, has the advantage of a cncular one, wjien t{jeir when the tranfverfe axis is horizontal ; for as it is tranfverfe _ much flatter, the point of contrary flexure in the extra- ^1S dos is thrown at a greater diftance, and therefore it will, with lefs inconvenience, admit of a horizontal roadway. Elliptical arches have alfo the advantage of being more elegant, and likewife require lefs labour and materials. 333. The cycloidal arch is likewife fuperior to a circu¬ lar one, but inferior to thofe which are elliptical. Para¬ bolic, hyperbolic, and catenarian arches, may be em¬ ployed when the bridge has only one arch, and is to rife high 5 but in other cafes they are inadmiflible. The method of determining the roadway for all thefe forms of arches, will be found in Dr Hutton s excellent work on the Principles of Bridges, p. 3 - _ See aifo E- merfon’s Mifcellanies, p. 156* j and his work on Fluxions, publiftied in 1742, 1534. When the form of the roadway is given, theOntheme- fhape of the intrados for an arch of equilibration may chanical be determined. x\s the mveftigation is very difficult, equiilbra_ unlefs when the roadway is a horizontal line, we lhall tjon> merely give the formula, which will enable any per- fon to conftrua the curve. In all the other curves the producefTb^the'weight'of^h^materials in ^^iSylhe^fonovving formas antrefof"pe" by rials Mowg Z left e^Ubm.ion and has been called ,/« mMccl lighter than thofe below U ; but the unbalanced pref- curve of equilibration. fare is fo trifling, that it may be fafely negkaed. We EDrrAFx , , , BU-f-BD+x/lBUxBD-fBD1 Hyperbol. log ^ g-g Hyperbol. log. BU +BF+x/2 BU x BF -f BFa BU for any other arch whofe fpan and thicknefs are as the numbers 100, 40, 6 •, only the values of c U and c E muft be increafed or diminiftied in the fame ratio as thefe numbers. From this formula, which correfpsnds with figure 11. Dr Hutton has computed the following table, contain¬ ing the values of f U and f E, for an arch whofe fpan AC is 100, whofe height BF is 40, and whofe th'ck‘ nefs at the crown or BU is 6. The table will anfwer Tml* for couJlruOing,he Cun,'of Equilibration, when the fpan height, and thicUefs at the crown, are as the numbers 100, 4°» anc* Value of c U. Value of cE. o 2 4 6 8 10 12 13 6.000 6- 035 6.144 6.324 6.580 6.914 7- 330 7 S71 7-834 Value of cU. Value of cE. 15 16 J7 18 J9 20 21 22 23 8.120 8.430 8.766 9 168 ig-sn 9-934 10.381 10.858 11.368 Value of cU. Value of c E. 24 25 26 27 28 29 3° 31 32 Value of cV. 11.911 12.489 13.106 13.761 14-4 5 7 15.196 1 c.980 16.811 i7-693 VaMie of cE. 33 34 35 S6 37 38 39 40 41 Value of cU. 1 8.627 19.617 20.665 21.774 22.948 24.190 25-5°5 26.894 28.364 Value : cE. 42 43 44 45 46 47 48 49 5° 29.919 3**56 33.29 35-I3 37 °75 39-i?p 41.29- 43-^ 46,0: b Vol. XIII. Part I. N MECHANICS. Theery. 335* The conftrucl!o$l of arches has alfo been dedu- v ccd from confidering the arch-ftones as fruftums of po- lifhed wedges without fridion, which endeavour to force their way through the arch. This principle has been adopted by Belidor, Parent, Boffut, Prony, and other French philofophers, and likewife by our ingeni¬ ous countryman, the late Mr Atwood. This theory, however, is more plaufible than ufeful. So far from the arch-llones having liberty to Hide between thofe which are contiguous to them, without fridlion, they are bound together by the ftro'ngeft cement, and fometimes connected by iron pins or wedges. The theory like- M'ife requires, that the weight of the arch muft regular¬ ly increafe as the portion of the vertical tangent cut off by lines drawn from a given point in a direction paral¬ lel to that of the joints, and therefore either the den- iity or the magnitude of the arch-ftones muft be very gre*at at the fpring of the arch, where the portion of the vertical tangent is a maximum. Thofe who with to be acquainted with the mode of inveftigation, by which the equilibrium of arches is eftabliihed in this theory, may ccnfult Prony’s Archkcclure Hijdrauhque, tom. i. p. 152. On the ConJIruBion of Piers and Abutments. 336. In the conftru&ion of piers and abutments, there are two circumftances which claim our attention. 1. The ftrength that muft be given to them, in order to refift the lateral thruft which they fuftain from the adjacent femiarches, and which tend either to overfet them, or make them Hide upon their bafe. 2. The form which muft be given to their extremities, fo that the force of the current may be a minimum.—The ad- hefion of the pier to the place on which it refts is al¬ ways much greater than one-third of the preflure *, and .as the lateral thruft of the arch which this adhefion re¬ fills, is oblique to the horizon, and may be refolved in¬ to two forces, one of which is horizontal, and the other vertical, we have the vertical portion of the la¬ teral thruft, the weight of the pier, and the fridlion on its bafe, combined in refifting the horizontal portion of the lateral thruft, which tends to make the pier Aide upon its bafe, fo that there is no danger of the pier yielding to fuch a preflfure.—We do not here confider, that the lateral thruft which tends to give a horizontal motion to the pier, is completely counteradled by the lateral thruft of the oppofite femiarch, becaufe it is ne- ceflary that the pier ihould have fuffieient liability to refill the lateral thruft of one femiarch, in cafe of the failure of the oppofite one. Let us therefore conlider the ftrength of the pier which will prevent it from be¬ ing overfet. 337. For this purpofe, let ABC be an arch, MHTO the pier, and BUHA the loaded femiarch, whofe pref- fure tends to overturn the pier. Let G be the centre «f gravity of the mafs BUHA : Join GA, and from G draw GK perpendicular to AC. Then, lince the whole prefture of the arch is exerted at its fpring A j and fince this preffure is the fame as if the whole weight of the ajch were collefled into the point G, GA will be the direflion in which the weight of the arch and the fuperincumbent mafs a£ls upon the point A. Now, by DyyAiyics, the force GA may be re¬ folved into the two forces GK, KA, one of which KA Theory, endeavours to give the pier a motion of rotation about w—y—— the point O, while the other GK denotes the weight of the loaded arch in the dire6iion GK. Putting W, therefore, for the weight or area of the fuperincumbent Wy KA mafs, we have GK : KArrW : ——^—, the prelfure Giv upon A. Now, as this force tends to turn the pier round O by means of the lever OA, and as ON=: AM is the perpendicular from the centre of motion upon WyKA the line of dire£lion, we have AM X —---•— for the GK force which tends to overturn the pier. Now, the force which is oppofed to this is the weight of the pier MHTO collefted in its centre of gravity g, which ads by the vertical lever O »z=GOM, becaufe g is in the centre of the redangle TM (Art. 164.). But the weight or area of the pier may be reprefented by OM X MH ; therefore, the force which refills the lateral thruft of the loaded arch is OMyMHx^OM, or 4MHxOM. Now, in the cafe of an equilibrium be- WxKA tween thefe oppofing forces, we have AMy——1 =rTMHxOM% which, by redudion, becomes OM AMxWxKA MH x GK This formula gives us the breadth of the pier wdiich is capable of balancing the lateral thruft j and therefore OM muft be taken a lit¬ tle greater than the preceding value. In pradice, OM is generally between one-fifth and one-feventh of AC, the fpan of the arch. The method of finding the cen¬ tre of gravity G of the loaded arch, whether the arch is in perfed equilibrium or not, may be feen in Dr Hutton’s work, already quoted, p. 49. A very fimple method of doing this is to form the part BVHA of a piece of card, and to find its centre of gravity G by the rules given in Articles 201, 202, 203. This in¬ deed fuppofes all the materials to be homogeneous j but if they are of various kinds, we can load the arch made of card in a fimilar manner, and determine its centre of gravity as before. 338. The limits of this article will not permit us to ap¬ ply the method of fluxions to the determination of the form which ftiould be given to the ends of the pier, in order that the impulfe of the current may be the leaft poflible. The theory of the refiftance of fluids, indeed,, differs fo widely from experiment, that fuch an invefti¬ gation would, in this place, be of little pradical utility. It may be fufficient merely to remark, that the pier fhould have an angular form, and that the impulfe of the current will be diminifhed as the angle is more acute. When the ends arefemicircular, the impulfe of the ftream is reduced to one half j and though a triangular termination of the piers reduces the impulfe ftill more, yet femieircular ends are more pleafing to the eye, and are particularly advantageous when fmall veffels have occafion to pafs the arch. When thofe veffels happen to impinge againft the piers, the femicircular ends are more able to bear the fliock, and do lefs injury to the veffel, while the additional quantity of uiafonry will give greater liability to the pier,. '•Qm Theory. MECHANICS. : " ' v 'J ijn the ConJlruBion of Domes, 339. Definition. A dome, cupola, or vault, is an arched roof, either of a fpherical, conoidal, or fphe- roidal form. The following propofition, taken from Dr Robifon’s article upon this fubjeft, in the Supplement to the laft edition of the Encyclopaedia Britannica, contains a ve¬ ry brief view of the theory of domes. Proposition. 340. f( To determine the thicknefs of a dome vault¬ ing when the curve is given, or the curve when, the thicknefs is given. p;ate “ Let B £ A, figure 1. be the curve which pro CCCXXIIl. duces the dome by revolving round the vertical Fig-1. axis AD. We {hall fuppofe this curve to be drawn through the middle of all the arch-ftones, and that the courfing or horizontal joints are every where perpen¬ dicular to the curve. We (hall fuppofe (as is always the cafe) that the thicknefs KL, HI, &c. of the arch- ftones is very fmall, in comparifon with the dimenfions of the arch. If we confider any portion HA h of the dome, it is plain that it preffes on the courfe, of which HL is an arch-ftone, in a direftion b C perpen¬ dicular to the joint HI, or in the direction of the next fuperior element /3 of the curve. As we proceed downwards, courfe after courfe, we fee plainly that this direction muft change, becaufe the weight of each courfe is fuperadded to that of the portion above it, to complete the preffure on the courfe below. Through B draw the vertical line BCG, meeting 0 b, produced in C. We may take b c X.o exprefs the preffure of all that is above it, propagated in this diredlion to the joint KL. We may alfo fuppofe the wreight of the courfe HL united in b, and adling on the vertical. Let it be reprefented by £ F. If we form the paral¬ lelogram b FGC, the diagonal b G will reprefent the direftion and intenfity of the whole preffure on the ioint KL. Thus it appears that this preffure is conti¬ nually changing its direflion, and that the line, which will always coincide with it, muft be a curve concave downward. If this be precifely the curve of the dome, it will be an equilibrated vaulting ; but fo far from being the ftrongeft form, it is the weakeft, and it is the li¬ mit to an infinity of others, which are all ftronger than it. This will appear evident, if we fuppofe that b G does not coincide with the curve A ^ B, but paffes without it. As we fuppofe the arch-ftones to be ex¬ ceedingly thin from infide to outfide, it is plain that this dome cannot ftand, and that the weight of the upper part will prefs it down, and fpring the vaulting outwards at the joint KL. But let us fuppofe, on the other hand, that £G falls within the curvilineal ele¬ ment b B. This evidently tends to pu(h the arch-ftone inward, tow’ard the axis, and would caufe it to Hide in, fince the joints are fuppofed perfectly fmooth and flip¬ ping. But fince this takes place equally in every ftone of this courfe, they muft all abut on each other in the 'vertical joints, fqueezing them firmly together. There¬ fore, refolving the thruft b G into two, one of which is perpendicular to the joint KL, and the other parallel Fheo to it, we fee that this laft thruft is withftood by the v vertical joints all around, and there remains only the thruft in the dire6tion of the curve. Such a dome muft therefore be firmer than an equilibrated dome, and can¬ not be fo eafily broken by overloading the upper part. When the curve is concave upwards, as in the lower part of the figure, the line b C always falls below b B, and the point C below B. When the curve is con¬ cave downwards, as in the upper part of the figure, 'b C; paffes above, or without b B. The curvature may be fo abrupt, that even b' G' {hall pafs without rb B', and the point G' is above B'. It is alfo evident that the force which thus binds the ftones of a horizon¬ tal courfe together, by pufhing them towards the axis, will be greater in flat domes than in thofe that are more convex •, that it will be ftill greater in a cone j and greater ftill in a curve whofe convexity is turned inwards : for in this laft cafe the line b G will deviate moft remarkably from the curve. Such a dome will ftand (having polilhed joints) if the curve fprings from the bafe with any elevation, however fmall j nay, fince the fridlion of two pieces of ftone is not lefs than half of their mutual preifure, fuch a dome will ftand, although the tangent to the curve at the bottom ftrould be horizontal, provided that the horizontal thruft be double the weight of the doma, which may eafily be the cafe if it do not rife high. “ Thus we fee that the {lability of a dome depends on very different principles from that of a common arch, and is in general much greater. It differs alfo in another very important circumftance, viz. that it may be open in the middle : for the uppermoft courfe, by tending equally in every part to Aide in toward the axis, preffes all together in the vertical joints, and a£is on the next courfe like the key-ftone of a common arch. Therefore an arch of equilibration, which is the wTeakeft of all, may be open in the middle, and carry at top another building, fuch as a lantern, if its weight do not exceed that of the circular fegment of the dome that is omitted. A greater load than this w'ould indeed break the dome, by caufing it to fpring # up in fome of the lower courfes 5 but this load may be increafed if the curve is flatter than the curve of equi¬ libration : and any load whatever, which will not crufb the ftones to powder, may be fet on a truncate cone, or on a dome formed by a curve that is convex toward the axis; provided always that the foundation be effec¬ tually prevented from flying out* either by a hoop or by a fufficient mafs of folid pier on which it is fet.” “ We have feen that if b G, the thruft compounded of the thruft b C, exerted by all the courfes above HILK, and if the force b F, or the weight of that courfe, be everywhere coincident with b B, the ele¬ ment of the curve, we {hall have an equilibrated domej if it falls wdthin it, we have a dome which will bear a greater load ; and if it falls without it, the dome will break at the joint. We muft endeavour to get analytical expreflions of thefe conditions. Therefore draw the ordi¬ nates b $ b", BDB", C d C". Let the tangents at b and &"meet the axis in M, and make MO, MP, each equal to/'c, and complete the parallelogram MONP, and draw 0£) perpendicular to the axis, and produce b F, cutting the ordinates in E and e. It is plain that MN N 2 is •-< VO JOO M E C H Theory. Is to MO as the weight of the arch HAh to the ‘ thruft b c which it exerts on the joint KL (this thruft being propagated through the courfe of HiLK) j and that MO, or its equal be^ox^d, may reprel'ent the weight oi the half AH. “ Let AD be called x, and DB be called y. Then b e—x, and e C=y (becaufe £ c is in the direftion of the element /3 £). It is alfo plain, that if we make y conftant, BC is the fecond fluxion of or BC=z and b e and BE may be confidered as equal, and taken indifcriminately for x. We have alfo bCzz ^^-{-y1. Let d be the depth or thicknefs HI of the arch-ftones. Then d^x'+y* will reprefent the tra¬ pezium HL * and flnce the circumference of each courfe increafes in the proportion of the radius ^x1 will exprefs the w'hole courfe. If^/^he taken to reprefent the fum or aggregate of the quantities an¬ nexed to it, the formula will be analogous to the fluent of a fluxion, and+y2 will reprefent the whole mafs, and alfo the weight of the vaulting, down to the joint HI. Therefore we have this proportion, Jdy : dy*Jx*-Yy* zzb e : £ F, —b e : CG, ~ ^ d : dyx^x^y* CG,=:x : CG. Therefore CG=r- /- — • Jdys/x'+y' “ If the curvatiu-e of the dome be precifely fuch as puts it in equilibrium, but without any mutual preflure in the vertical joints, this value of OG mull be equal to CB, or to x, the point G coinciding with B. This condi- d y x sjxz -j-//2 A N I C S. dy x V x* +y greater than J dysf we learn that the upper part of the dome mud not be made very heavy. This, by dimini thing the proportion of £ F to b C, diminifties the angle cbG, and may fet the point G above B, which will infallibly fpring the dome in that place. We fee here alfo, that the algebraic, ana- lyfis exprefles that peculiarity of dome-vaulting, that the weight of the upper part may even be fupprefl'ed. “ The fluent of the equation dy^x' + rf r n r J dy^ xz -\-if t +7 tion will be expreffed by the equation fd y J ^-i-j/2 d y \/ ar-f y* But or, more conveniently, by — , Jdys/x'+y* x this form gives only a tottering equilibrium, indepen¬ dent of the friftion of the joints and the cohefion of the cement. An equilibrium, accompanied by fome firm ft ability, produced by the mutual preflure of the vertical joints, may be expreffed by the formula orby ^£±£=*1+1 jJyJx'+f * j‘l,J£>■'+>/ x ‘ w^here t is fome variable pofitive quantity, which in¬ creafes when x increafes. This laft equation will alfo exprefs. the equilibrated dome, if / be a conftant quan- fdys/ a?2 +y , . , t> a xr x This will give d = tity, becaufe in this cale — is —o. « Since a firm liability requires that dyx s/xz +y' 'ITieorv. is moft eafily found. Itis’L.Jdy^x'-^if—'L x-^ht, where L is the hyperbolic logarithm of the quantity an¬ nexed to it. If wTe confider y as conftant, and correct the fluent fo as to make it nothing at the vertex, it may be expreffed thus, LJdy^x* -j-y2—L a~ L .v—Ly-j- L/. This gives us L —X and there. fore J a y « This laft equation will eafily give us the depth of vaulting, or thicknefs d of the arch, when the curve is „ . . dii*s/x*y* tx-\-tx , / given. For its fluxion is ——-j i » and d __at x-\. at x—^ js an expreffed in known quan- y y*J x' -j-y1* tities j for we may put in place of t any power or funaion of * or of y, and thus convert the expreflion into another, which will ftill be applicable to all forts of curves. « Inftead of the fecond member —-f-~ we might ^ x 1 employ ^, where /> is fome number greater than uni- x ty. This will evidently give a dome having liability j „ , dvx\/x1-\-yz becaufe the original formula —' vvill then be greater than a w»ix . t, yij V ^2-f y* Each of thefe forms has its advantages when applied to -f lhall be greater than #, and CG mull be greater than CB : Hence we learn, that figures of too great curva¬ ture, whofe fides defcend too rapidly, are impro¬ per. Alfo, fince liability requires that we have U X particular cafes. Each of them alfo gives d— :: . _ — Y yy*J x'+y* vj/hen the curvature is fuch as is in precife equilibrium. And, lallly, if ^ be conftant, that is, if the vaulting be of uniform thicknefs, we obtain the form of the curve} becaufe then the relation of ^ to « and to y is given. « The chief ufe of this analyfis is to difcover what curves are improper for domes, or what portions of given curves may be employed with fafety. Domes mechanics. Theorv. are generally built for ornament; and we fee that there •—y— is great room for indulging our fancy in the choice. All curves which are concave outwards will give domes of great firmnefs : they are alfo beautiful. Ihe Gothic dome, whofe outline is an undulated curve, may be made abundantly firm, efpecially if the upper part be convex and the lower concave outwards. “ The chief difficulty in the cafe of this analyfis arifes from the neceffity of expreffing the weight of the the incumbent part, or Jdysjx7,-\-y'. This requires the meafurement of the conoidal furface, which, m moft cafes, can be had only by approximation by means of infinite feriefes. _ . . “ The furface of any circular portion of a iphere is very eafily had, being equal to the circle defcribed with a radius equal to the chord of half the arch. This radius is evidently rrxA^-f-V*. # “ In order to difcover what portion of a hemilphere may be employed (for it is evident we cannot employ the whole) when the thicknefs of the vaulting is uni- form, we may recur to the equation or formula d 1/ X X* — y\ — j'dyj AT’-fy1. Let a be the ra- x ayy dins of the hemifphere. We have x _ —-^-====p and x — - a'y* a‘—yl\i AD DB 0.4 3-4 11.4 a6.6 52*4 91.4 146.8 223.4 326.6 475-4 100 200 3°o 400 500 600 700 800 900 1000 AD 610.4 744 904 1100 J336 15 22 i738 1984 2270 2602 DB AD D B 1080 1140 1200 1260 13:0 1360 1400 1440 1480 T520 2990 3442 3972 443 2 495 2 5336 5756 6214 6714 7260 1560 1600 1640 1670 1700 1720 1740 1760 1780 1800 Subftituting thefe values in the /— ^r a' yy formula, we obtain the equation We eafily obtain the fluent of the fecond member —A*—(fjcf—y1, and y — asj—y^er®f'01re if the radius of the fphere be 1, the half breadth of the dome mult not exceed \/—4 X or 0.786, and the height will be .618. The arch from the vertex is about 510 49'. Much more of the hemifphere can¬ not Hand, even though aided by the cement, and by the friflion of the courfing joints. This laft circum- llance, by giving connexion to the upper parts, es the whole to prefs more vertically on the courfe be¬ low, and thus diminilhes the outwrard thruft y but it at the fame time diminiffies the mutual abutment .of the vertical joints, which is a great caufe of firmnefs m the vaulting. A Gothic dome, of which the upper part is a portion of a fphere not exceeding 450 from the ver¬ tex, and the lower part is concave outwards, will be very ftrong, and not ungraceful. _ , “ 341. Perfuaded that what has been faid on the lub- jeft convinces the reader that a vaulting perfedly equi¬ librated throughout is by no means the belt form, pro¬ vided that the bafe is fecured from feparatmg, we think it unneceffary to give the inveffigation ot that form, which has a confiderable intricacy,. and mail merely give its dimenfions. The thicknefs is fuppo e uniform. The numbers in the firll column of the taole exprefs the portion of the axis counted from the vertex, and thofe of the fecond column are the length of the ordinates, “ The curve formed according to thefe dimenfions will not appear very graceful, becaufe there is an a- brupt change in its curvature at a fmall diftance front its vertex j if, however, the middle be occupied by a lantern of equal or of fmaller wreight than the part whofe place it fupplies, the whole will be elegant, and free from this defeat. “ The connexion of the parts arifing from cement and from friaion has a great effed on dome-vaulting. . In the fame w-ay as in common arches and cylindrical vaulting, it enables an overload on one place to break the dome in a diftant place. But the reliftance to this effect is much greater in dome-vaulting, becaufe.it ope¬ rates all round the overloaded part. Hence it hap¬ pens that domes are much lefs {battered by partial violence, fuch as the falling of a bomb, or the like. Large holes may be broken in them without much affedting the rell j but, on the other hand, it greatly diminiffies the ilrength which fliould.be derived.from the mutual preffure in the vertical joints. Fndlion prevents the Aiding in of the arch-ftones which pro¬ duces this mutual preffure in the vertical joints, ex¬ cept in the very higheft courles, and even there it greatly diminiffies it. Thefe caufes make a great change in the form, which gives the greateff flrength ; and as their laws of adion are but very imperfeaiy underftood as yet, it is perhaps impoffible, in the pre- fent ftate of our knowledge, to determine this form with tolerable precifion. We fee plainly, however, that it allows a. greater deviation from the beft form than the other kind of vaulting ; and domes may be made to rife perpendicular to the horizon at the bafe, although of no great thicknefs 5 a thing which muff not be attempted in a plane arch. . The immenfe ad¬ dition of ftrength which may be derived from hooping largely compenfates for all defeds ; and there is hard- ly any bounds to the extent to which a very thin dome- vaulting may be carried, when it is hooped or framed in the direction of the horizontal courfes. The root of the Halle du Bled at Paris is but a foot thick, and its diameter is more than 200, yet it appears to have abundant ftrength.” Scholium. 342 The fe£tion of the dome of St Paul’s cathedral is part of an ellipfe yvhofe conjugate diameter is parallel to the horizon. It is built ot wood, and confined by ftrong iron chains j and is fupported by carpentry refting oa a cone of brick w-ork. £ GHAF. >102 Theory. ' MECHANICS. Chap. IX. On the "Force of Torfon, Taking the fquare root of both Tides of the equation, Theory, we have •Fig. 2. 343- Definition. Let^rz be a metallic wire firm¬ ly fixed in the pincers^ by means of the fcrew s; let the cylindrical weight P, furnifhed with an index e o, be fulpended at the lower extremity of the wire ; and let the axis of the cylinder, or the wire^a produced, terminate in the centre of the divided circle MNO. Then, if the cylinder P is made to move round its axis fo that the index e o may defcribe the arch ON, the wire g a will be twitted. If the cylinder be now left to itfelf, the wire will, in confequence of its elafticity, endeavour to recover its form ; the index e o will there¬ fore move backwards from N, and ofcillate round the axis of the cylinder. The force which produces thefe ofcillations is called the force of torfion, and the angle meafured by the arch ON is called the angle of torfon. Prop. I. 344. To deduce formulae for the ofcillatory mo¬ tion of the cylinder, on the fuppofition that the rea£tion of the force of torlioil is proportional to the angle of torfion, or nearly proportion¬ al to it. Fig. 3. Let P£) be a fedlion of the cylinder P in fig. 2. and let all the elements of the cylinder be projeded upon this circular fedion in r J n X 180°. 345. In order to compare the force of torfion with the force of gravity in a pendulum, we have for the time of a complete ofcillation of a pendulum whofe length is /, g being the force of gravity, T T= T8o°. Therefore, fince the time in which the cylinder ofcil- lates mutt be equal to the time in wdiich the pendulum ofcillates, we have rPf J n l X 180®. Hence dividing by 180°, and fquaring both fides, we obtain - ^ f±r J n We mutt therefore find for a cylinder the value of J'p r*, or the fum of all the particles multiplied by the fquares of their diftances from the axis. Now, if we make 5r~6.283l8 the ratio of the circumference of a circle to its radius, tf=radius of the cylinder, Arrits length, becomes mutiplying by 180 it becomes 7” n A2 u*=- 2 m Av+t 7+7“ X i8o°=— 2 n T=— m ^XtSo0* Therefore p r2 i r p r * x i8o> an^ fmceJ—— == Let us now confider the other part of the motion fronv A to B', and fuppofe the angle AC M7, w7e fhall- find, by calling tT the velocity of the point A, — 1—^ and by redu£lion But ^ ^ is the mg 2 / weight W of the cylinder, therefore, by fubftituting W ° IP cP inflead of g y., we obtain a very Ample formu¬ la for determining the value of n from experiments.. If it were required to find a weight Q, which,, afting at the extremity of a lever L, would have a mo¬ mentum equal to the momentum of the force of torfion when the angle. of torfion is A—M, we muft make Q.xB=«xA—M. 346. In the preceding inveftigation we have fuppofed* what is conformable to experiment, that the force of torfion is proportional to the angle of torfion, which gives us « X A—M for the momentum of that force. Let us now fuppofe that this momentum is altered by any quantity S, then the momentum of the force of torfion will become n X A—M—S', and the general equation will affume this form * X A=M—S x y • . a M , and by multiplying in place of t its value —-—, and taking the fluent, we have n x 2AM—M2—ij' Now, in order to find the value of T or a complete ofcillation, we muft divide the ofcillation into two parts, the firft from B to A, where the force of torfion accelerates the velocity «, while the retarding force, arifing from the refiftance of the air and the imper- fedlion of elafticity, diminifhes the velocity u j and the n M'2 m M/Vh1 U2—a2 pp r* —+-Ah-=:—-x/—• Then, by fubftituting inftead of U its value as lately found, and taking the fluents, we fhall have, when the velocity vanifhes, or when the ofcillation is finifhed, »X)' + 2 Av+I+M,v+* A+M' * and if the retarding forces are fuch, that at each ofcil¬ lation, the amplitude is a little diminifhed, we fhalh have for the approximate value of A—M' A—IVT; 2 A y «Xv+l’ and if the angle A—M' is fo fmall that it may Be treated as a common fluxional quantity,, we fhall then have for any number N of ofcillations NX 2 m «Xv + x I v, 1 1 y 1 X Ml-3~ IT3’ where M reprefents the angle to which A becomes equal after any number of ofcillations N. Hence we^ obtain M- 1 ( Nx 2 w X »—1 «Xv+i which determines the value of M after any number of ofcillations N. 348. Ex. 2. If S—m x A—MI’+zw' X A—M and v1 being different values of m and y, we fhall obtain by following the mode of inveftigation in the laft ex=»- ample, 2 m A’+‘+M’+- , ^ A',+1+M,,+* ^ ”XA-M=—X - a+m"+7+Ix a+m • and if the retarding force is much lefs than the force of torfWn, M tave for j# apirosimat. vsiue oP aXA—M, ■f lOA i Theory. Torfion balance. Fig. a. MECHANICS. « X A—M *2 m Av '7+T" + 2 m Ky* /-fi * 349. Ex. 3. In general, if X A—M[>'-(- tn' X A=Ml/+^ X A—X A—M|/^, &c. we (hall always have for an ofcillation when S is fmaller than the force of tor lion, 2 m Av 2m'Av' »XA-M=—+7^r- 2m"A'1" _ 2m",AV"' ■7q~r+ /"+T- &c. 350. Having thus given after Coulomb, the mode of deducing formulae for the ofcillatory motion of the cy¬ linder, we Hi all proceed to give an account of the refults of his experiments. In thefe experiments M. Coulomb employed the torfion balance reprefented in fig. 2. in which he fufpended cylinders of different weights from iron and brafs wires of different lengths and tbickneffes } and by obferving carefully the duration of a certain number of ofcillations, he was enabled to determine, by means of the preceding formulae, the laws of the force of torfion relative to the length, the thicknefs, and the nature of the wires em¬ ployed. If the elafticity of the metallic wires had been perfeft, and if the air oppofed no refiftance to the of- cillating cylinder, it would continue to ofcillate till its motion was flopped. The diminution of the ampli¬ tudes of the ofcillations, therefore, being produced fole- ly by the imperfe&ion of elafticity, and by the refift¬ ance of the air, M. Coulomb was enabled, by obferving the fucceflive diminution of the amplitude of the ofcil¬ lation, and by fubftrading the part of the change which was due to the refiftance of the air, to afcertain, with the afliftance of the preceding formula:, according to what laws this elaftic force of torfidn was changed. 351. From a great number of experiments it appeared, that when the angle of torfion was not very great, the ofcillations were fenfibly ifochronous •, and therefore it may be regarded as a fundamental law, T/iat for all metallic wires, when the angles of torfion are not very great, the force of torfion is fenfibly proportional to the angle of torfion. Hence, as the preceding formulae are founded on this fuppofition, they may be fafely applied to the experiments. 352. In all the experiments, a cylinder of two pounds weight ofcillated in twice the time employed by a cy¬ linder which weighed only half a pound j and there¬ fore the duration of the ofcillations is as the fquare root of the weights of the ofcillating cylinders. . Confequently the teniion of the wires has no lenfible influence upon the force of torfion. If the tenfions however be very great relative to the ftrength of the metal, the force of torfion does fuffer a change ; for when the weight of the cylinder, and confequently the tenfion of the wire, is increafed, the wire is lengthened, and as this diminilhes the diameter of the wire, the duration of the ©fcillation muft evidently be affected. 353- When the lengths of the wires are varied without changing their diameters or the weights of the cylin¬ ders, the times of the fame number of ofcillations are as the fquare roots of the lengths of the wires, a refult alfo deducible from theory. 354. When the diameters of the wires are varied without changing their lengths, or the weight of the cylinders, the momentum of the force of torfion varied as the fourth power of the diameters of the wires. Now this refult is perfectly conformable to theory j for if we fuppofe two wires of the fame fubftance, and of the fame length, but having their diameters as one to tw’o, it is obvious that in the wore whofe diameter is double of the other, there are four times as many parts extended by torfion, as in the fmaller ware, and that the mean extenfion of all thefe parts will be proportional to the diameter of a wire, the fame as th£ mean arm of a lever is, relative to the axis of rotation. Hence it ap¬ pears that, according to theory, the force of torfion of two wnres of the fame nature and of the fame length, but of different diameters, is proportional to the fourth pow7er of their diameter. 355. From this it follows in general, that in metallic wfires the momentum of torfion is direftly in the com¬ pound ratio of the angle of torfion and the fourth power of their diameter, and inverfely as the length of the wires. If a therefore be the angle of torfion, A the length of the thread, £ its diameter, and F the force of torfion, we (hall have Theory, where m is a conftant coefficient for wires of the fame metal, depending on the tenacity of the metal, and deducible from experiment. 356. When the angle of torfion is not great, relative to the length of the wire, the index of the cylinder re¬ turns to the pofition which it had before the torfion took place, or, in other w7ords, the wire untwifts itfelt by the fame quantity by which it had been twifted. But when the angle of torfion is very great, the wire does not completely tmtwift itfelf, and therefore the centre of torfion will have advanced by a quantity equal to that which it has not untwfifted.—When the angle of torfion was below 450, the decrements of the ampli¬ tudes of the ofcillations were nearly proportional to the amplitudes of the angle of torfion j but when the angle exceeded 450, the decrements increafed in a much greater ratio.—The centre of torfion did not begin to advance or be difplaced till the angle of torfion was nearly a femicircle : its difplacement was very irregular till the angle was one circle and 10 degrees, but be¬ yond this angle the torfion remained nearly the fame for all angles. 357. The theory of torfion is particularly ufeful in delicate refearches, where fmall forces are to be afeer- tained with a precifion which cannot be obtained by ordinary means. It has been fuccefsfully employed by Coulomb in difeovering the laws of the forces of electricity and magnetifm, and in determining the refiftance of fluids when the velocities are very fmall. PART MECHANIC S. i=5 Practical Ivlechanics- Practical Mechanics. V PART II. ON THE CONSTRUCTION OF MACHINERY. chines where one heavy body is employed to rai»e another merely by its weight, the inertia ot the power and the reiiltance, viz. a, b, are proportional to P, R, the powers and refinances themfelves, and confequenti v P, R may be fubftituted in the formula in the place ot —Tlie engineer therefore muft conlider, befoie ne conilruft his machine, what elements ihould enter into the formula, and what fhould be omitted, in order that he'-may adapt it to the circumftances of the cafe, and ob¬ tain from his machine the greateft poflible effect. 360. When the inertia of the power and that of the re-T^fand the fiftance are proportional to the power andreuitance thena-tween felves 5 and when the inertia and iri6tion of the machine veiocities of /p I the impel- may be omitted, the formula becomes y—d Ttr-i-11—1 led fncl J -tv working from which the following table is computed, which points of contains the values of y for diflerent values of P$ R be-a mac InP* ing fuppofed —10, and m~\. Table containing the beji Proportions between the Ve¬ locities of the Impelled and Working I oints of a Ma¬ chine, or between the Levers by which the Power and Reji/lance a£l. Proportional value of the impelling power, or P Value of the ve¬ locities of the working point or y; or of the lever by which the re- fiftance afts, that of x being 1. 1 2 3 4 5 6 7 8 9 10 11 12 r3 14 15 16 17 18 W 0.048809 0.095445 0.140175 0.183216 0.224745 0.264911 0.303841 0.341641 0.378405 0.414214 0.449138 0.483240 o.5i6575 0-549'93 0.581139 0.612451 0.643168 o 673320 0.702938 Proportional value of the impelling power, or P. Value of the velo¬ cities of the work¬ ing point, or y; or ef the lever by which the refift- ance a<£ls, that of x being 1. 20 2 I 22 23 24 25 26 27 28 29 3° 40 5° 60 70 80 90 100 0.732051 0.760682 0.788854 0.816590 0.843900 0.870800 0.897300 0.923500 0.949400 0.974800 1.000000 1.236200 x.449500 1,645700 1.828400 2.000000 2.16230® 2.316600 358. WE have already feen, when confidenng the maximum effects of machines, the various caufes which aifeft their performance. It appeared from that invef- tigation, that there mult be a certain relation between the velocities of the impelled and working points of a machine, or between the power and the reliftance to be overcome, before it can produce a maximum effeft, and therefore it muft be the firft object of the engineer to afeertain that velocity, and to employ it in the con- firu&ion of this machine. The performance of the ma¬ chine is alio influenced by the friftion and inertia of its various parts 5 and as both thefe act as refiftances, and therefore deftroy a confiderable portion of the impel¬ ling power, it becomes an object of great importance to attend to the Amplification of the machinery, and to af¬ eertain the nature of friction fo as to diminifh its ef¬ fect, either by the application of unguents or by mecha¬ nical contrivances. Since the impelled and working points of a machine are generally conne£ted by means of toothed wheels, the teeth muft be formed in fuch a manner, that the wheels may always a£t upon each other with the fame force, otherwife the velocity of the machine will be variable, and its ftru£ture foon injured by the irregularity of its motion. 1 he irregular mo¬ tion of machines fometimes arifes from the nature of the machinery, from an inequality in the refiftance to be overcome, and from the nature of the impelling power. In large machines, the momenta of their parts are generally fufficient to equalize thefe irregula¬ rities j but in machines of a fmall fize, and in thofe where the irregularities are confiderable, we muft em¬ ploy fly-wheels for regulating and rendering uniform their variable movements. Ihefe various fubje£!s, and others intimately connected with them, we lhall now proceed to dilcufs in their order. Chap. I. On the Proportion between the Velocity oj the Impelled and Working points of Machines) and between the Power and Refifancc, in order that they may perform the greatejl work. 359. In the chapter on the maximum effeft of ma¬ chines we have deduced formulae containing x and y, the velocities of the impelled and working points of the ma¬ chines, and including every circumftance which can affeft their mbtion. The formula which exhibits the value of y, or the velocity of the working point, affumes various forms, according as we negleft one or more of the ele¬ ments of which it is compofed.—When the work to be performed refifts only by its inertia, which is the cafe in urging round a millftone or heavy fly, the quantity R may be negledled, and the fecond formula, (Page 92. col. 2.) ftiould be employed. In fmall machines, and par¬ ticularly in- thofe where the motion is conveyed by wheels with epicycloidal teeth, the. friftion is very trifling, and the element

-lec hai.ics. tjie ta{jie t^at w]len P—jo, y or the diameter of the axle is i, upon the fuppoiition that the diameter x of the wheel is 1 ; but as x mufl be — 6, we (hall have y~6. 361. Inftead ofufingthe preceding table, we might find the beft proportion between x and y by a kind of tenta- R.7/—7/2 tive procefs, from the formula —fi » . p > > which x X “4- Xv y A N I C S, expreffes the work performed. This method is indeed Praftica! tedious and we mention it only for the fake of Ihowing Mecnari'('s', the conformity of the refults, and of proving that there 'r"~~v is a certain proportion between x and y which gives a maximum effect. Let x—6, as in the preceding para¬ graph, and let us fuppofe y to be fuccedively 5, 6, and 7, in order to fee which of thefe values is the belt. Since Prr:3, R=i, and x=6, we have When y~5 When y=6 When y=y P .r R y—R* y* _ 3 X 6 X t X S"1 X 3 X 5 _ AL_0 488 P a?2-|-R y% 3 X 6 x 6-|- iXjX5* 133 ' P vR ij—R1 y*_ 3 x6x J X6—1 X 6x^__72 __ P jcs-fRyr"'~" 3x6x64-1x6x6 i44~0‘^00 p a; R y y* _ 3X6XI X ? —1 X7X7 ___ 7 7 _ Pa;J4-R/ — 3 X6X64-X X7 X? ~~ iyy—0'^0^ It appears therefore that when y~5, 6, 7, the wmrk per¬ formed is 0.488 ; 0.5000 ; 0.49045 ; lo that the effefl is a maximum when y~6, a retult fimilar to what was obtained from the table. To find the 362. When the machine is already conffrudied, x heft proper-aT1cj y cannot be varied fo as to obtain a maximum ef- tween the '^e ^ame °bje£l however will be gained by pro¬ power and perly adjufting the power to the work when the work the refill- cannot be altered, or the work to the power when the anee. power is determinate. The formulas in Prop. 2. Chap. 7. exhibit the values ol R under many circumftances, and it depends on £he judgement of the engineer to feledf fuch of them as are adapted to all the conditions of the cafe. 363. The following table is founded on the formula which anfwers to the cafe where the inertia of the impelling power is the fame with its pref- fure, and where the inertia and the fridlion of the ma¬ chine may be fafely negle&ed. The fecond column contains the different values of R correfponding to the values of y in the firft column. The numbers in the third column fhew the ratio of y to R, or they have the fame proportion to 1, which R has to the refiftance which will balance P. In the table it is fuppofed that P~ 1 and x— 1. Table containing the bejl proportions between the Power and the Refiftance, the inertia of the impelling power be¬ ing the fame with its prejjure, and the JriElion and inertia of the Machine being omitted. Values of y, or the velo¬ city of the working point; a-being equal to 1, Values of R, or the refift¬ ance to be overcome, P being ~ 1. I.8885 I.3928 O.8986 O.4142 O.183O 0.II1I .O.O772 O.O580 O.O457 Ratio of R to the refill, nee which would balance P. O.4724 O.4639 0.4493 O.4142 0.3660 °-3333 0.3088 0.2900 0.2742 to I Values of y, or the velo¬ city »f the working point; xbeing equal to 1. 7 8 9 10 11 12 13 x4 Values of R, or the refift¬ ance to be overcome, P being — 1. O.03731 O.03125 0.02669 O.02317 O.02037 0.01809 O.Ol622 O.OI466 Ratio of R to the refinance which would balance P. 0.261I7 to I 0.25000 0.24021 • 0.23170 • O.22407 • 0.21708 ■ 0.21086 ■ 0.205 24' 0.19995 364. To exemplify the ufe of the preceding table, let us fuppofe that we are to raife -water by means of a fimple pulley and bucket, with a power — 10, and that it is required to find the refiftance R, or the quan¬ tity of water which muft be put into the bucket, in or¬ der that the work performed may be a maximum. In the fimple pulley, x, y, the arms of the vertical le¬ vers or the velocities of the impelled and working points are equal ; and fince x is fuppofed in the table to be ~ 1, we have y=i, which correfponds in the table with 0.4142, the value of R, P being — 1 in the ta¬ ble : But in the prefent cafe Pzrio. Therefore, 10 : 1=0.4142 : 4.142, the value of R when P=io. 365. The fame refult might be obtained in a more P# R y—— R2 ^ * circuitous method by means of the formula v, ;-rw— J Pad-J-Ry* which expreffes the performance of the machine. Thus, let »=i ; y=i j P=io, and let us fuppofe R fuccef- fively equal to 3 ; 4 -, 4.142 j 5*, fo that we may de¬ termine which of thefe values gives the greateft per¬ formance. WJieu MECHANICS. Practical Mechanics. 107 Practical Mechanics. When R = 3, tlie preceding formula becomes j—^—I*^IS4* When R=4, the formula becomes 10x4—4X4_24_ io+4 14 1-7143- .... _ , , IOX4-I42—4-I42j,_24.26384_T „t When R=4.I42, the formula becomes -"7^142 10X5—5X5_2?_ When R= the formula becomes —-7——~ J io-f-5 15 1.6666. Hence it appears, that when R=3 5 4 5 4-M2 i 5 5 wor,k pe^ed is refpeaively = 1.6154 5 I-7M3 5 I-7I57 5 1-6666 ; fo that the work performed is a maximum wdien R 18—4.142, tne lame remit which was 00- tained from the table. Chap. II. On the Simplification of Machinery. ^66. As the inertia of every machine adds greatly to the refiftance to be overcome, and as the fridiion of the communicating parts is proportional to the preflure, it becomes a matter of great practical importance,^ that the different parts of a machine fhould be proportioned to the drains to which they are expofed. If the beam of a fleam-engine, for example, is larger than what is necelfary, an immenfe portion of the impelling power mull be defiroyed at every ftroke of the piflon, by drag¬ ging the fuperfluous mafs from a ftate of reft into mo¬ tion ; the preflure upon the gudgeons will alfo be in- creafed, and their fritlion in their fockets proportional¬ ly enlarged. The engineer, therefore, Ihould be w^ell acquainted with the ftrength of the materials oi which the machine is to be conftrudfed, and Ihould frame its dif¬ ferent parts in fuch a manner that they may not be .heavier than what is neceffary for refilling_the forces with which they are urged.—When the motions oi tire machine are necelfarily irregular, and when the ma¬ chine may be expofed to accidental ftrains, the. parts nmft be made confiderably ftronger than what is ne- ceflary for refilling its ordinary ftrains ; but it is not often that fuch a precaution Ihould be obferved. Ihe gudgeons of w^ater-wdieels, and of the beams of fleam- engines, ought to be made as ihort and final 1 as pofh- ble, as the fridlion increafes with the rubbing furfaces. This is very feldom attended to in the conftruflion of water-wheels. The diameter of the gudgeons^, is fre¬ quently thrice as large as what is necelfary for fupport- ing the weight of the wheel. 367. In the conftru£fion of machinery we mull not only attend to the fimplification of the parts, but alfo to the number of thefe parts, and the mode of con- netling them. From the nature and quantity of the work to be performed, it is eafy to atcertain the velo¬ city of the working point wrhich is moft proper for per¬ forming it. Now- this velocity may be procured, in a variety of ways, either by a perplexing multiplicity of wheels, or by more Ample combinations. Ihe choice of thefe combinations mull be left folely to the judge¬ ment of the engineer, as no general rules can be laid down to diredl him. It may be ufeful, however, to rema rk, that the power Ihould always be applied, as near as poffible to the working point of the machine, and that when one wheel drives another, the diameter pf the one ftiould never be great, when the diameter of the other is very fmall. The fize of wheels is oiten determined from the ftrains to which they are expofed. If, for example, we are obliged to give a certain velo¬ city to an axle by means of a wheel with 120 teeth, and if the force with which this wheel is urged, re¬ quires the teeth to be at leaft one inch thick in order to prevent them from breaking, w'e {hall be obliged to make its diameter at leaft feven feet 5 for fuppofing the fpaces between the teeth to be equal to the thicknefs of the teeth, the circumference of the wheel mull at leaft be equal-to 120 + 120—240 inches, the fum of the teeth and their intervals, which gives a diameter of fix feet eight inches. There are fome cafes where our choice of combination muft be diredled by the nature of the machinery. If the work to be performed is a load railed with a certain velocity by means of a rope wind¬ ing round a hollow drum, and if the fimpleft combina¬ tion of mechanical powers for producing this velocity fhould give a fmall diameter to the drum, then this com¬ bination muft give way to another which correfponds with a larger fize of the drum, for, on account of the inflexibility of the ropes, a great portion of the impel- ling power would be wafted in winding them about tne circumference of a fmall drum. 368, The advantages of Amplifying machinery areDefcnptioa well exemplified in the following capftane, which unites ^ P°wer- great ftrength and fimplicity. It is reprefented in fig. 4. ftane/ ‘ where AD is a compound barrel compofed of two cy- finders of different radii. The rope DEC is fixed atcccXXIII, the extremity of the cylinder D ; and after palling over^,.^ the pulley E, which is attached to the load by means'^ 4' of the hook F, it is coiled round the other cylinder D, and fixed at its upper end. The capftane bar AB urges the compound barrel CD about its axis, fo that W’hile the rope coils round the cylinder D it unwinds it- felf from the cylinder C. Let us fuppofe that the am¬ meter of the part D of the barrel is 21 inches, while the diameter of the part C is only 20 inches, and let the pulley E be 20 inches in diameter. When the barrel AD, therefore, has performed one complete revo¬ lution by the preffure exerted at B, 63 inches of rope, equal to the circumference of the cylinder, will be ga¬ thered upon the cylinder D, and 60 inches will be un¬ winded from the cylinder C. The quantity of wound rope, therefore, exceeds the quantity that is unwound by 6; 60—3 inches, the difference of their refpe&ive pe¬ rimeters ; and the half of this quantity, or 14 inches, will be the fpace through which the load or pulley E moves by one turn of the bar. If a fimple capftane of the fame dimenfions had been employed, the length of rope coiled round the barrel would have been 60 O 2 inches: io3 MECHANICS. PracHcal inches j and the fpace defcribed by the pulley, or load Mechanics. cvercorae, would have been 30 inches. Now, as t|ie pOWer ;s t0 the weight as the velocity of the weight is to the velocity of the power, and as the velocity of the power is the fame in both capibanes, the weights which they will raiie will be as i|- to. 30. If it is wifli- ed to double the power of the machine, we have only to cover the cvlinder C with lathes a quarter of an inch thick, fo’that the difference between the radii of each cylinder may be half as little as before } for it is obvious that the power of the capilane increafes as the difference between the radii of the cylinders is dimini (li¬ ed. As we increaie the power, therefore, we increafe the ftrength of our machine, while all other engines are proportion ably enfeebled by an augmentation of power. Were vee for example to increafe the power of the common capftane, we muft diminifh the barrel in the fame proportion, fuppofing the bar AB not to ad¬ mit of being lengthened, which will not only diminifh its ftrength, but deftroy much of its power by the ad¬ ditional flexure of the rope,—This capftane may be ea- fily converted into a crane by giving the compound barrel a horizontal pofltion, and fubftituting a winch inftead of the bar AB. The fuperiority of fuch a crane above the common ones does not require to be pointed out *, but it has this additional advantage, that it allows the weight to flop at any part of its progrefs, without the aid of a ratchet wheel and catch, becaufe the two parts of the rope pull on the contrary fides of the barrel. The rope indeed which coils round the larger part of the barrel a£ts with a larger lever, and confequently with greater force than the other j but as this excefs of force is not fufficient to bvercome tne fridlion of the machine, the weight will remain fta- tionary in any part of its path. {Appendix to Fergu- fotPs LeBnres, vol. ii.). Compound principle on which the preceding capftane chine'on a" conftru&ed, might be applied with great advantage the'fame when two feparate axles AC, BD are driven by .means principle, of the winch H and the wlieels B and A. It is evi¬ dent that when the winch is turned round in one di- r lg 5* region, the rope R is umvinded from the axle BD ; the wheel B drives the wheel A, fo that the axle AC moves in a direftion oppofite to that of BD, and the rope is coiled round the axle AC. If the wheels A, B are of the fame diameter and the fame number of teeth, the weight W will be ftationary, as the rope winded ■about one axle will be always equal to what is unwind¬ ed from the other. If the wheels have different diame¬ ters, or different numbers of teeth, the quantity of rope wound round the one axle wall exceed what is un¬ wound from, the other, and the weight will be raifed. Chap. III. On thr Nature of Fritiion and the Me¬ thod of diminijhing its effects in Machinery; and on the rigidity of Ropes. 370. The fri&ion generated in the communicating parts of machinery, oppofes fuch a reftftance to the impel¬ ling power, and is fo injurious to the machine itfelf, that an acquaintance with the nature and effedls of this re¬ tarding force, and with the method of diminiftnng its effe£Is on machinery, is of infinite importance to the . pra£tical mechanic. 371. The fubjeft of fiiclion has been examined at PraAical great length by Amontons, Bulfinger, Parent, Euler, Mechanic?. and Boffut, and has, lately occupied the attention of our ingenious countryman Mr Vince of Cambridge. He found that the friftion of hard bodies in mo-RefuIts of tion is an uniformly retarding force, and that the vince’s ex¬ quantity of friclion confidered as equivalent to a weightl>erunen1;3' , _ M _l_\V >< S drawing the body backwards is equal to M where M is the moving force exprefled by its weight, W the weight of the body upon the horizontal plane, S the fpace through which the moving force or weight defeended in the time /, and 16.087 feet, the force of gravity. Mr Vince alfo found that the quantity of fridlion increafes in a lefs ratio than the quantity of matter or weight of the body, and that the friftion of a body does not continue the fame when it has dif¬ ferent furfaces applied to the plane on w’hich it moves, but that the fmalleft furfaces wfill have the leaft fridlion. 372. Notwithftanding the attempts of preceding philofopbers to unfold the nature of friclion, it was referved for the celebrated Coulomb to furmount theExperi- difficulties which are infeparable from fuch an in-merits or veftigation, and to give an accurate and fatisfadloryCoulonii>' view of this difficult branch of mechanical philofo- phy. By employing large bodies and conducing his experiments on a large (bale, he has correfted feveral errors which arofe from the limited experiments of others; he has brought to light many new and link¬ ing phenomena, and confirmed others which were hi¬ therto but partially eftabliflied. As it wxnild be foreign to the nature of this work to follow this ingenious phi- lofopher through his numerous and varied experiments^ we (hall only prefent the reader with the interefting re- fults to which they led. 1. The fridlion of homogeneous bodies, or bodies of the'fame kind, moving upon one another, is generally fuppofed to be greater than that of heterogeneous bo¬ dies ; but Coulomb has (hewn that there are exceptions to this rule. Ele found, for example, that the fri&ion of oak upon oak was equal to ^ of the force of pref- fion } the fridlion of pine againft pine and that of oak againft; pine 15 1.78 The fri&ion of oak againft; copper was —, and that of oak againft iron nearly the fame. 2. It was generally fuppofed, that in . the cafe of wood, the fri&ion is greateft when the bodies are drag¬ ged contrary to the courfe of their fibres $ but Coulomb has (hewn that the fridlion is in this cafe fometimes the fmalleft. When the bodies moved in the direftion of their fibres, the fri&ion was —— of the force with ’ 2-34 which they were preffed together •, but when the mo¬ tion was contrary to the courfes of the fibres, the fric¬ tion was only —7. 3-76 . . 3. The longer the rubbing furfaces remain in contact, the greater is their fridlion,-r-Wfi.en wood vvas moved upon Practical upon wood, according to the direaion of the fibres, the Mechanics, friftion was increafed by keeping the furtaces in con- tad for a few ieconds *, and when the time was prolong¬ ed to a minute, the fridion feemed to have reached its fartheft limit. M E C H A NIGS. lc5> faces were very fmall hr ccfpea'to tire force with which JglM ' ike fviBion was ditmnijhea by aug- t , .1 f* ? 4.1^^ yx' Q C tart next umu. But when the motion was contrary to the courfe of the fibres, a greater time was neceffary be¬ fore the fridion arrived at its maximum. When wood was moved upon metal, the fridion did not attain its maximum till the furfaces continued in contad tor five cr fix days ; and it is very remarkable, that when wooden furfaces wrere anointed with tallow, the time requilite for producing the greatelt quantity ot fridion is increafed. The increafe of fridioa which is gene¬ rated by prolonging the time of contad is fo great, that a body weighing 1650 pounds was moved with a force of 64 pounds when firft laid upon its correipond- ing furface. After having remained in contad for the fpace of three feconds, it required 160 pounds to put it in motion ; and, when the time was prolonged to fix days, it could fcarcely be moved with a force ot 622 wounds. When the furfaces of metallic bodies were moved upon one another, the time of producing a maxi¬ mum of fridion was not changed by the interpofition of olive oil; it was increafed, however, by employing fwine’s greafe as an unguent, and was prolonged to five or fix days by befmearing the furfaces with tallow. 4. Friciion is in general proportional to the force with which the rubbing furfaces are prejfed together; and is, for the mojl part, equal to between 4- and ^ of that Jorce. —In order to prove the firft part of this propofition. Coulomb employed a large piece of wood, whole lur- face contained three fquare feet, and loaded it fuccel- fively with 74 ponnds, S74 pounds, and 2474 pounds. In thefe cafes the fridion was fucceflively 1 0f the force of preftion j and when a lefs furface and 2.2X they were prencu, iuc j> j— j ^ menting the rapidity : the fridion, on the contrary, was increafed when the furfaces were very large when com¬ pared with the force of preffion. When the wood was moved contrary to the diredion of its fibres, the “po¬ tion in every cafe remained the fame. . If wood be moved upon metals, the fridion is greatly increafed by an increafe of velocity •, and when metals ^o^c upon wood befmeared with tallow, the fridion is ftill aug¬ mented by adding to the velocity. When metals move upon metals, the fridion is always a conftant quantity ■, but when heterogeneous fubftances are employed which are not bedaubed with tallow, the fridion is fo increa¬ fed with the velocity, as to form an arithmetical pro- greflion when the velocities form a geometrical one. 7. ThefriBion of loaded cylinders rolling upon a ho¬ rizontal plane, is in the direB ratio of their weights, and the inverfe ratio of their diameters. In Coulomb s ex¬ periments, the fridion of cylinders of guaiacum wood which were two inches in diameter, and v. ere oa e with 1 coo pounds, was 18 pounds or f $ of the force o preftion. In cylinders of elm, the fridion was greater by T, and was fcarcely diminiftied by the interpofition of tallow. 472. From a variety of experiments on the mdion of die axes of pulleys, Coulomb obtained the following refults.—When an iron axle moved m a brals bulti the ffidion was £ of the preflion 5 but when the bufh was befmeared with very clean talloiy, the fridion was only A •, when fwine’s greafe was mterpoied, the fric¬ tion amounted to other weights were ufed, the fridion was ^ 1 Similar refults were obtained in all Coulomb’s experiments, even, when metallic furfaces were employ¬ ed. The fecond part of the propofition has alfo been eftabliftied by Coulomb. He found that dm greateft fridion is engendered when oak moves upon pine, and that it amounts to of the force of preflion 5 on the contrary, when iron moves upon brafs, the leaft fridion is produced, and it amounts to 4 of the force o ^FriBion is in general not increafed by augmenting th?rubbing furfaces.-Whcn a fuperficies of three feet fquare was employed, the fndion, with different weights, was at a medium j but when a fmall furface was ufed’the fridion inftead of being greater, as might have been expeded, was only Friction di- 6. FriBion for the mojl part is not augmented by an increare 0f velocity. In fome cales, it is dmmijhed by increafing ^ augmentation of celerity.—U. Coulomb found, that the veloci- whe/wood moved upon wood in the diredion of the fibres, the fridion was a conftant quantity, however much the.velocity was varied j but that when the lur- and when olive oil was employ¬ ed as an unguent, the fridion was never lefs than f or J: . When the axis was of green oak, and the bufli of guaiacum wood, the fridion was when tallow was interpofed •, but when the tallow was removed, fo that a fmall quantity only covered the furface, the fric¬ tion was increafed to When the bufti was made of elm, the fridion was in fimilar circumftances T1- and * which is the leaft of all. If the axis be made of box, and the buth of guaiacum wood, the fridion wiL be Ar and TV, circumftances being the fame as before. If the axle be of boxwood, and the bufh of elm, the fridion will be ^ ^ > and if.11tb;e “V™11 and the bufh of elm, the fridion will be ^ of tne x0rce °f 2X4'Having thus confidered the nature and effeds of Method of fridion, we (hall now attend to the method of leffening the refiftance which it oppofes to the motion of ma-th^ffe^ chines The moft efficacious mode of accomphuimg this is'to convert that fpecies of fridion widen anies from one body being dragged over another, into taat which is occafioned by one body rolling upon another. As this will always diminifh the refiftance, it may be eafily effeded by applying wheels or rollers to the foc- kets or bufhes which fuftain the gudgeons of large wheels, and the axles of wheel carnages. Ca.atus feems to have been the firft who recommended this ap- naratus It was afterwards mentioned by Sturmius and Fnfiion Wolflu’s; but was not ufed in. pradice till Sully applied wheels., it to clocks in the year 1716, and Mondran to cranes in 172 c. Notwithllanding thefe fohtary attempts to introduce fridion wheels, they feem to have attrad- ed little notice till the celebrated Euler examined 1 10 MECHANICS. Practical Mechanics, Friclion maybe di- minifhed bj a judicious application of the im¬ pelling power. Plate CGCXXIII. Fig. 6. and explained, with his ufual accuracy, their nature and advantages. The diameter of the gudgeons and pivots fhould be made as fmall as the weight of the wheel and the impelling force will permit. The gudgeons fhould l*elt upon wheels as large as circumftances will allow, having their axes as near each other as poflible, but no thicker than what is abfolutely neceffary to fuflain the luperincumbent weight. When ^hefe precautions are properly attended to, the refdlance which arifes from the fridlion of the gudgeon, &c. will be extremely trifling. 3 75. The eft efts of friftion may likewife in Come mea- fure be removed by a judicious application of the impell¬ ing power, and by proportioning the ftze of the friftion wheels to the preflure which they feverally fuftain. If we fuppofe, for example, that the weight of a wheel, whofe iron gudgeons move in bullies of brafs, is 100 pounds; then the friftion ariftng from both its gud¬ geons will be equivalent to 25 pounds. If we fup¬ pofe alfo that a force equal to 40 pounds is employed to impel the wheel, and afts in the direftion of gravi¬ ty, as in the cafes of overlhot wheels, the preffure of the gudgeons upon their fugports will then be 140 pounds and the friftion 35 pounds. But if the force of 40 pounds could be applied in fuch a manner as to aft in dueft oppofition to the wheel’s weight, the pref¬ fure of the gudgeons upon their fupports would be 100—40, or 60 pounds, and the friftion only 15 pounds. It is impofTible indeed to make the moving force aft; in direft oppofition to the gravity of the wheel, in the cafe of water-mills j and it is often im- prafticable for the engineer to apply the impelling power but in a given way : but there are many cafes in which the moving force may be lo exerted, as at leaf! not to increafe the friftion which arifes from the wheel’s weight. 376. When the moving force is not exerted in a per¬ pendicular direftion, but obliquely as in underfhot wheels, the gudgeon will prefs with greater force on one part of the locket than on any other part. This point will evi¬ dently be on the fide of the biifh oppofite to that where the power is applied ; and its diftance from the lowelt point of the focket, which is fuppofed circular and con¬ centric with the gudgeon, being called x, we fhall have H Tang, x — —, that is, the tangent of the arch con¬ tained between the point of greateft preflure and the loweft point of the bulb, is equal to the fum of all the horizontal forces, divided by the fum of all the vertical forces and the weight of the wheel, FI reprefenting the former, and V the latter quantities. The point of g-reateft preflure being thus determined, the gudgeon muft be fupported at that part by the largeft friftion wheel, in order to equalize the fiiftion upon their axles. The application of thefe general principles to par¬ ticular cafes is fo Ample as not to require any illuf- tration. To aid the conceptions, however, of the praftical mechanic, we may mention two cafes in which friftion wheels have been fuccefsfully employed. 377. Mr Gottlieb, the conftruftor of a new crane, has received a patent for what he calls an anti-attrition ’ axle-tree, the beneficial eifefts of which he has alcer- tained by a variety of trials. It confifts of a fteel roller R about four or fix inches long, which turns within a groove cut in the inferior part of the axle-tree C which runs in the nave AB of the wheel. When the wheel- carriages are at reft, Mr Gottlieb has given the friftion Praftical wheel its proper pofition j but it is evident that the Mechanics, point of greateft preflure vs ill change when they are 1" ”"v put in motion, and will be nearer the front of the car¬ riage. This point, however, will vary with the weight of the load *, but it is fufliciently obvious that the fric¬ tion roller flrould be at a little diftance from the loweft point of the axle-tree. 378. Mr Garnett of Briftolhas applied friftion rollers in a d’fierent manner, which does not, like the preced¬ ing method, weaken the axle-tree. Inftead of fixing them in the iron part of the axle, he leaves a fpace be¬ tween the nave and the axis to be filled with equal roll¬ ers almoft touching each other. A feftion of this Fig. 7. apparatus is reprefented in fig. 7. where ABCD is the metallic ring inferted in the nave of the wheel. The axle-tree is reprefoted at E, placed between the friftion rollers I, I, I, made of metal, and having their axes inferted into a circle of brafs which pafles through their centres. The circles are rivetted together by means of bolts palling between the rollers, in order to keep them feparate and parallel. 379. As it appears from the experiments of Coulomb, that the leaf! friftion is generated when poliihed iron moves upon brafs, the gudgeons and pivots of wheels, and the axles of friftion rollers, ftiould all be made of poliihed iron; and the bulhes in which thefe gudgeons move, and the friftion wheels, Ihould be formed of po- lilhed brafs. 380. When every mechanical contrivance has been Friftion di- adopted for diminifhing the cbftruftion which arifes rn'n^ecl by from the attrition of the communicating parts, it may un2uent'’ be Hill farther removed by the judicious application of unguents. The moft proper for this purpofe are fwine’s greafe and tallow when the furfaces are made of wood, and oil when they are of metal. When the force with which the furfaces are prefled together is very great, tallow will diminiih the friftion more than fwine’s greafe. When the wooden furfaces are very finall, unguents will leffen their fiiftion a little, but it will be greatly diminilhed il wood moves upon metal greafed with tallow. If the velocities, however, are increafed, or the unguent not often enough renewed, in both thefe cafes, but particularly in the laft, the unguent will be more injurious than ufeful. The beft mode of applying 'it, is to cover the rubbing furfaces with as thin a ftra- tum tis poflible, for the friftion will then be a conftant quantity, and will not be increafed by an augmentatjon of Velocity. 381. In ftnall works of wood, the interpofition of the powder of black lead has been found very ufeful in re¬ lieving the motion.- The ropes of pulleys fhould be rubbed with tallow, and whenever the ferew is ufed, the fquare threads ihould be preferred.” slppendix to Fergufon's LeEiures, vol. ii. 382. When ropes pafs over cylinders or pulleys, aOn theri- confiderable force is neceflary to bend them into theS'dityof form of the circumference round which they are coiled. roiJes‘ The force which is neceflary to overcome this refiflance is called the Jliffnefs or rigidity of the ropes. This im¬ portant fubjeft wTas firft.examined by Amontons, * w\io*tMem’ contrived an ingenious apparatus for afeertaining the^^'1^9' rigidity of ropes. Flis experiments were repeated and' confirmed in part by fubfequent philofophers, but par¬ ticularly by M. Coulomb, who has inveftigated the fub- jeft MECHANICS. Practical jeft with more care and fuccefs than any of his prede- Mechanics. ceflbrs. His experiments were made both with the ap- ' paratus of Amontons, and with one of his own inven¬ tion j and as there was no great difcrepancy in the re- fuits, he was authorifed to place more contidence in his experiments. The limits of this article will not per¬ mit us to give ai> account of the manner in which the experiments were conduced, or even to give a detailed view of the various conclufions which were obtained. We can only prefent the reader with fome of thofe leading refults which may be ufeful in the conftrudlion of ma¬ chinery. 1. The rigidity of ropes increafes, the more that the fibres of which they are compofed are twilled. 2. The rigidity of ropes increafes in the duplicate ratio of their diameters. According to Amontons and Defaguliers, the rigidity increafes in the fimple ratio of the diameters of the ropes; but this probably arofe from the flexibility of the ropes which they employed : for Defaguliers remarks, thatw’henhe ufed a rope whole diameter was half an inch, its rigidity was increafed in a greater proportion ; fo that it is probable that if they had employed ropes from two to four inches in diame¬ ter, like thofe ufed by Coulomb, they w’ould have ob¬ tained fimilar refults. (See N° 9.) 3. The rigidity of ropes is in the fimple and direct ratio of their tenfion. 4. The rigidity of ropes is in the inverfe ratio of the diameters of the cylinders round which they are coiled. 5. In general, the rigidity of ropes is dire&ly as their tenlions and the fquares of their diameters, and in- verfely as the diameters of the cylinders round which they are wound. 6. The rigidity of ropes increafes fo little with the velocity of the machine, that it need not be taken into the account when computing the effedls of machines. 7. The rigidity of fmall ropes is diminiflied when pe¬ netrated with moifture ; but w’hen the ropes are thick, their rigidity is increafed. 8. The rigidity of ropes is increafed and their ftrength diminilhed when they are covered with pitch ; but when ropes of this kind are alternately immerfed in the fea and expofed to the air, they lalt longer than when they are not pitched.—This increafe of rigidity, however, is not fo perceptible in fmall ropes as in thole which are pretty thick. ' v 9. The rigidity of ropes covered with pitch is a fixth part greater during froit than in the middle of fummer, but this increafe of rigidity does not follow the ratio of their tenfions. 10. The refiftance to be overcome in bending a rope over a pulley or cylinder may be reprefented by a for_ oD® . mula compofed of tw'O terms. The firft term ——— is a conftant quantity independent of the tenfion, a being a conftant quantity determined by experiment, Dn a power of the diameter D of the rope, and r the radius of the pulley or cylinder round wfliich the rope is coil- b ed. The fecond term of the formula is T X , r where T is the tenfion of the rope, b a conftant quanti¬ ty, and D« and r the fame as before. Hence the com- I I 1 J)n t Practical X at-TZ'. Tne Mechanics. 1 r t « D" , w h plete formula is ——-f- i X V V r exponent n of the quantity D diminiflies with the flexi¬ bility of the rope, but is generally equal to 1.7 or 1.8; or, as in N° 2. the rigidity is nearly in the duplicate ratio of the diameter of the rope. When the cord is much ufed, its flexibility is increafed, and n becomes equal to 1.5 or 1.4. Chap. IV. On the Nature and Advantages of Fh Wheels. 383. A fly, in mechanics, is a heavy wheel or cylinder which moves rapidly upon its axis, and is applied to machines for the purpofe of rendering uniform a deiul- tory or reciprocating motion, arifing either from the nature of the machinery, from an inequality in the refiftance to be overcome, or from an irregular applica¬ tion of the impelling power. When the firft: mover is inanimate, as wind, water, and fleam,an inequality of force obvioufiy arifes from a variation in the velocity of the wind, from an increafe or decreafe of water occafioned by fudden rains, or from an augmentation or diminution of the fleam in the boiler, produced by a variation in the heat of the furnace ; and accordingly various methods have been adopted for regulating the adlion of thefe variable powers. The fame inequality of force obtains when machines are moved by horfes or men. Every animal exerts its greateft flrength when firft fet to Work. After pulling for fome time, its flrength will be impair¬ ed ; and when the refiftance is great, it will take fre¬ quent though fhort relaxations, and then commence its labour with renovated vigour. Thefe intervals of reft and vigorous exertion muft always produce a varia¬ tion in the velocity of the machine, which ought parti¬ cularly to be avoided, as being detrimental to the com¬ municating parts as well as the performance of the ma- ‘ chine,, and injurious to the animal which is employed to draw it. But if a fly, confifting either of crofs bars, or a mafly circular rim, be conneffed with the machinery, all thefe inconveniences will be removed. As every fly wheel muft revolve with great rapidity, the momen¬ tum of its circumference muft be very confiderable, and will confequently relift every attempt either to accelerate or retard its motion. When the machine therefore has been put in motion, the fly wheel will be whirling with an uniform celerity, and with a force capable of con¬ tinuing that celerity when there is any relaxation in the impelling power. After a ftiort reft the animal renews his efforts ; but the machine is now moving with its for¬ mer velocity, and thefe frelh efforts will have a tendency to increafe that velocity. The fly, however, now afls as a refilling power, receives the greateft part of the fuperfluous motion, and caufes the machinery to preferve its original celerity. In this way the fly fecures to the engine an uniform motion, whether the animal takes occafional relaxations or exerts his force with redoubled ardour. 384. We have already obferved that a defultory ©r va¬ riable motion frequently arifes from the inequality of the refiftance, or work to be performed. This is particu¬ larly manifeft in thralhing mills, on a fmall fcale, which are driven by water. When the corn is laid unequally 12 M E 'C H A N I C S. Pradlical on die feeding board, fo tliat too mucli Is taken in by -Mechanics, rol]ers, this ir.creafe of refinance inftantly affedts the machinery, and communicates a defultory or irregular motion even to the water wheel or firrt mover. This variation in the velocity of the impelling power may be diftindtly perceived by the ear in a calm even¬ ing when the machine is at work. The beft method of corredHtig thefe irregularities is to employ a fiy wheel, which will regulate the motion of the machine when the refinance is either augmented or diminilhed. In machines built upon a large fcale there is no neceffity for the interpofition of a fly, as the inertia of the ma¬ chinery fupplies its place, and reflfls every change of mo¬ tion that may be generated by an un’equal admiffion of the corn. 385. A variation in the velocity of engines arifes alfo from the nature of the machinery. Let us fuppofe that a weight of looo pounds is to be taifed from the bottom of a well 50 feet, by means of a bucket attached to an iron chain which winds round a barrel or cylinder, and that every foot length of this chain w-eighs two pounds, It is evident that the reflflance to be overcorile in the flrfl; moment is ico® pounds added to 50 pounds the weight of this chain, and that this refiftance diminifhes gradually as the chain coils round the cylinder, till it is only 1000 pounds when the chain is completely wound up. The refiftance therefore decreafes from 1050 to 1000 pounds j and if the impelling power is inanimate, the velocity of the bucket will gradually increafe •, but if an animal is employed, it will generally proportion its aclion to the refilling load, and muft therefore pull with a greater or lefs force according as the bucket is near the bottom or top of the well. In this cafe, howrever, the afliftance of a fly may be difpenfed wdth, becaufe the refiftance diminilhes uniformly, and may be render¬ ed conftant by making the barrel conical, fo that the chain may wind upon the part neareft the vertex at the commencement of the motion, the diameter of the bar¬ rel gradually increafing as the weight diminilhes. In this way the variable refiftance will be equalized much better than by the application of a fly W'heel, for the ily having no motion of its own muft neceffarily wafte the impelling power. 386. Having thus pointed out the chief caufes of a variation in the velocity of machines, and the method of rendering it uniform by the intervention of fly wheels, the utility, and in fome inftances the necelfi- ty, of this piece of mechanifm, may be more obvioufty illuftrated by Ihewing the propriety of their application in particular cafes. See 387. In the defcription of Vaulone’s pile engine *, Part III. rea(ler w;n obferve a ftriking inftance of the Plate utility of fly wheels. The ram (,) is raifed between CCCXXIX. the guides bb by means of horfes adling againft the Fig. 1. levers S, S ; but as foon as the ram is elevated to the top of the guides, and difcharged from the fol¬ lower G, the refiftance againft which the horfes^ have ■been exerting their force is fuddenly removed, and they would inftantaneoully tumble down, were it not for the fly O. This fly is connedted with the drum B by means of the trundle X, and as it is moving with a very great force, it oppofes a fufficient refiftance to Prafficjl the action of the horfes, till the ram is again taken up Mec^anics‘ by the follower. 3SB. When machinery is driven by a fingle-ftroke fteam engine, there is fuch an inequality in the impel¬ ling power, that for two or three feconds it does not a£I at all. During this interval of inadlivity the ma¬ chinery' would necefiarily flop, were it not impelled by a mafly fly wheel of a great diameter, revolving with rapidity, till the moving power again refumes its energy. 389. If the moving power is a man adting with a handle or winch, it is fubjedt to great inequalities. The greateft force is exerted when the man pulls the handle upwards from the height of his knee, and he adts with the lead force when the handle being in a vertical po- fition is thruft from him in a horizontal diredlion. I he force is again increafed when the handle is puftied downwards by the man’s weight, and it is diminiftied when the handle being at its loweft point is pulled to¬ wards him horizontally. But when a fly is properly connedfed with the machinery, thefe irregular exer¬ tions are equalized, the velocity becomes uniform, and the load is railed with an equable and fteady mo¬ tion. 390. In many cafes, where the impelling force is al¬ ternately augmented and diminiftied, the petformance of the machine may be increafed by rendering the refi¬ ftance unequal, and accommodating it to the inequali¬ ties of the moving power. Dr Robifon obferves that “ there are fome beaujiful fpecimens of this kind of adjuftment in the mechanifm of animal bodies.” Befides the utility of fly wheels as regulators of machinery, they have been employed for accumulating or colledting power. If motion is communicated to a fly wheel by means of a fmall force, and if this force is continued till the wheel has acquired a great velocity, fuch a quantity of motion will be accumulated in its circumference, as to overcome refiftances and produce effedts which could never have been accomplifhed by the original force. So great is this accumulation of powTer j that a force equivalent to 20 pounds applied for the fpace of 37 feconds to the circumference of a cylinder 20 feet diameter, which weighs 4713 pounds, would, at the diftance of one foot from the centre, give an impulfe to a mufket ball equal to what it receives from a full charge of gunpowder. In the fpace of fix minutes and 10 feconds, the fame effedf would be produced if the cylinder was driven by a man who conftantly exerted a force of 20 pounds at a winch one footlong (^d). 391. This accumulation of power is finely exem¬ plified in the fling. When the thong which contains the ftone is fwung round the head of the flinger, the force of the hand is continually accumulating in the re¬ volving ftone, till it is difcharged with a degree of rapi¬ dity which it could never have received from the force of the hand alone. When a ftone is projected from the hand itfelf, there is even then a certain degree of force accumulated, though the ftone only moves through the arch of a circle. If we fix the ftone in an opening at the '(d) This has been demonftrated by Mr Atwood. See his Treatife on Reftilineal and Rotatory Motion. M E C H i ^raflica! extfernity of a piece of wood two feet long, and dif- iMechanics. charge it in the ufual way, ther& will be more force ac- 1J ~v cumulated than with the hand alone* for the done defcribe's a larger arch in the fame time, and muft therefore be projected with greater force. 392. When coins or medals are ftruck, a very coniiderable accumulation of power is neceffary, and this is effe£ted by means of a fly. rl he force is firft accumulated in weights fixed in the end of the fly. This force is communicated to two levers, by which it is far¬ ther condenfed : and from thefe levers it is tranfmitted to a fcrew, by which it fuffers a fecond condenfation. The ft amp is then impreffed on the coin or medal by itieans of this force, which was firft accumulated by the fly, and afterwards augmented by the intervention of two mechanical powers. 393. Notwithftanding the great advantage of fly wheels, both as regulators of machines and colleaors of power, their utility wholly depends upon the pofition which is afligned them relative to the impelled and working points of the engine. For this purpofe no particular rules can be laid down, as their pofitions depend altogether on the nature of the machinery. \\ e may obferve however, in general, that when fly wheels are employed to regulate machinery, they fhould be near the impelling powei j and when ufed to accumulate force in the working point they fhould not be far diftant from it. In hand mills for grinding corn, the fly is for the moft part very injudicxoufly fixed on the axis to which the winch is attached whereas it fhould always be fattened to the upper millftone fo as to revolve with the fame rapidity. In the firft'pofition indeed it muft equalize the varying efforts of the power which moves the winch} but when it is attached to the turning millftone* it not only does this, but contributes very efteilually to the grind¬ ing of the corn. Description 394* new kind of fly, called a conical pendulum, of the co- has been ingenioutly employed by Mr Watt for procin- nical pen- jng a determinate velocity at the working point of Ins dul“m* fteam-engine. It is reprefented in fig. 8. where AB 1®' ' Js a vertical axis moving upon pivots, and driven by means of a rope palling trom the axis of the large fly over the fheave EF. The large balls M, N are fixed to the rods NG, MH, which have an angular motion round P, and are conne&ed by joints at G and H, with the rods G E,vH K attached to the extremity ofthe lever K L whofe centre of motion is L, and whofe other extremity is connefted with the cock whicn admits the fleam into the cylinder. The frames CD and QR prevent the balls from receding too far from the axis, or from ap¬ proaching too near it. Now when this conical pendu¬ lum is put in motion, the centrifugal force of the balls M N makes them rec«de from the axis AB. In con- fequence of this recefs, the points, C, H, _K are deprefs- ed and the other extremity of the lever is raided j and the cock admits a certain quantity of fleam into tne cy¬ linder. When the velocity of the fly is by any means Increafed, the balls recede ftill farther from the axis, the extremity of the lever is railed higher, and the cock clofes a little and diminifhes Ihe fupply of fleam. From this diminution in the impelling power, the velocity of the fly and the conical pendulum decreafes, and the balls re- fume their former pefition. In this wTay, vvhen there is any increafe or diminution in the velocity of the fly, Vol. XIII. Part I. .NIGS. . US the correfponding increafe or diminution in the centrifu- gal force of the balls raifes or depreffes the arm of the lever,, Lv;1Jtu1' admits a greater or a lefs quantity of fteam into the cylin¬ der, and reftores to the engine its former velocity. Chap. V. On the- ’Teeth of Wheels, and the Wipers of Stampers. 395. In the conftrufUon of machines, we muft not only attend to the form and number of their parts, but aifo to the mode by which they are to be conneded. ft would' be eafy to Ihew, did the limits of this article permit it, that, when one wheel impels another, the impelling power will fometimes aft with greater and fometimes with lefs force, unlefs the teeth of one or both of the wheels be parts of a curve generated after the manner of an epicycloid by the revolution of one circle along the convex or concave fide of another. It may be fufficient to Ihew, that, when one wheel impels another by the ac¬ tion of epicycloidal teeth, their motion will be unitorm. Let the w heel CD drive the wheel AB by means of the epicycloidal teeth mp, « ory acting upon the infinitely Fig- fmall pins or fpindles a, b% c ; and let the epicycloids m p, n q, &c. be generated by the circumference of the wheel AB, rolling upon the convex circumference of the wheel CD. From the formation of tne epicycloid it is obvious that the arch a b is equal to tn n, and the arch a c \.o m 0/ for during the formation of the part n b of the epicycloid n q, every point of the arch a b \s ap¬ plied to every point of the arch tn n, and the fame hap¬ pens during the formation of the part c 0 of the epicy¬ cloid 0 r. Let us now fuppofe that the tooth tjip be¬ gins to aft on the pin a, and that b, c are fucceffive pofitions of the pin a after a certain time ; then, « q, 0 r will be the petitions of the tooth tttp aitei the fame time but a b'zz.tn n and a C—tn 0, thereiore the wheels AB, CD, when the arch is driven by epicychfidal teeth, move through equal ipaces in equal times, that is, the force of the wheel CD, and the velocity of the wheel AB, are always uniform. 396. In illuftrating the application of this property of the epicycloid, which w’as difeovered by Chaus Roemer the celebrated Danilh aftronomer, we {hall call the fmall wheel the pinion, and its teeth the leaves of the pinion. The line which joins the centre of the wheel and pinion is called the line of centres. Fhere are tnree different ways in which the- teeth of one wheel may drive another, and each of thefe modes of action ic- quires a different form for the teeth. 1. When the aflion is begun and completed after the teeth have paffed the line of centres. 2. When the aftion is begun and completed before they reach the line of centres. 2* When the adlion is carried on, on both hdes or the line of centres. . „ 007.I. The firft of thefe modes of aftion is reprefented Firlt mode in fig. I. where B is the centre af the wheel (d), A that0 of the pinion, and AB tne line of centres. It is evident cccXXI\ » from the figure, that the part b of the tooth af oi the Fig. 1. wheel, does not aft on the leaf tn of the pinion till they arrive at the line of centred AB j and that ail the aftion is carried on after they have palled this Him, and is completed when the leaf m comes into the fituation n. When this mode of aftion is adopted, the aftmg faces p of (D) In figs. I, 2, 3, 4, the letter B is fuppofed to be placed at the centre of the wheels. M E *C H A N 1 C S. Prafticr.l of the leaves of the pinion Should be parts of an interior Mechanics. epiCyCIoid, generated by a circle of any diameter rolling upon the concave fuperficies of the pinion, or within the circle a dh \ and the faces ab of. the teeth of the wheel fliould be portions of an exterior epicycloid formed by the fame generating circle rolling upon the convex fu¬ perficies o dp oi the wheel. 398. But when one circle rolls within another whofe diameter is double that of the rolling circle, the line ge¬ nerated by any point of the latter is a firelight line, tend¬ ing to the centre of the larger circle. Therefore, if the generating circle above mentioned firould be taken wdth its diameter equal to the radius of the' pinion, and be made to roll upon the concave fuperficies a d h of the pinion, it will generate a ftraight line tending to the pinion’s centre, which wall be the form of the faces of its leaves ; and the teefh of the wheel will be exterior epicycloids, formed by a generating circle, whofe dia¬ meter is equal to the radius of the pinion, rolling upon the convex fuperficies odp of the wheel. This refitili- Fig. 2. neal form of the teeth is exhibited in fig. 2. and is per¬ haps the mofi advantageous, as it requires lefs trouble, and may be executed with greater accuracy, than if the epicycloidal form had been employed, though the teeth are evidently weaker than thofe in fig. 1. ; it is recom¬ mended both by De la Hire and Camus as particularly advantageous in clock and watch work. Fig. 1. 399. The attentive reader will perceive from fig. t. that in order to prevent the teeth of the wheel from aft- ing upon the leaves of the pinion before they reach the line of centres AB 5 and that one tooth of the wheel may not quit the leaf of the pinion till the fucceeding tooth begins to aft upon the fucceeding leaf, there muff be a certain proportion between the number of leaves in the pinion and the number of teeth in the wheel, or between the radius of the pinion and the radius of the wheel, when the difxance of the leaves AB is given. But in machinery the number of leaves and teeth is always known from the velocity which is re¬ quired at the working point of the machine : It be¬ comes a matter therefore of great importance to de¬ termine with accuracy the relative radii of the w'heel and pinion. Relative 400. For this purpofe, let A, fig. 2. be the pinion hav- hze of the Jng t]ie afting faces of its leaves ftraight lines tending to )h:op a A' the centre, and B the centre of the wheel, AB will be the diftance of their centres. Then as the tooth C is fup- pofed not to aft upon the leaf Km till it arrives at the line AB, it ought not to quit Km till the following tooth F has reached the line AB. But fince the tooth always afts in the direftion of a line drawn perpendicu¬ lar to the face of the leaf Km from the point of contaft, ihe line CH, drawn at right angles to the face of the leaf km, will determine the extremity of the tooth CD, or the laid part of it which flrould aft upon the leaf Km, and will alfo mark out CD for the depth of the tooth. Now, in order to find AH, HB, and CD, put a for the number of teeth in the wheel, b for the num- b^- of leaves in the pinion, c for the diftance of the pi- ; gvots A and B, and let x be the radius of the wheel, and 7/ that of the pinion. 'Then, fince the circumference of the wheel is to the circumference of the pinion, as the number of teeth in the one to the number of leaves in the other, and as the circumferences of circles are pro¬ portional to their radii, we {hall have a : b—x : y, then by compofition (Fuel. v. 18.) a-^-b ; b—c :y (c being equal to-v-f-.y), and confequently the radius of the pinion, Practical c li Mechanics, viz. y—-—^-j; then by inverting the firft analogy, we -—v have b : o.—y : x, and confequemly the radius of the wheel, viz. •, y being now a known number. Now, in the triangle AHC, right-angled at C, the fide AH is known, and likewife all the angles (HAC being equal to the fide AC, therefore, may be found by plain trigonometry. Then, in the triangle ACB, the ^iCAB, equal to HAC, is known, and alfo the fides AB, AC, which contain it ; the third fide, therefore, viz CB, n ay be determined ; from which DB, equal to HB, already found, being fub- ftrafted, there will remain CD for the depth of the teeth. When the aftion is carried on after the line of centres, it often happens that the teeth will not work in the hollows of the leaves. In order to pre¬ vent this, the CBH muft always be greater than half the KBP. The HBP is equal to 360 degrees, divided by the numoer of teeth in the wheel, and CBH is eafily found by plain trigonometry. 401. If the teeth of wheels and the leaves of pinions be formed according to the direftions already given, they will aft upon each other, not only with uniform force, but nearly without friftion. The one tooth rolls upon the other, and neither Aides nor rubs to fuch a degree as to retard the wheels, or wear their teeth. But as it is impoffible in praftice to give that perfeft curvature to the faces of the teeth which theory requires, a quan¬ tity of friftion wdll remain after every precaution has been taken in the formation of the communicating parts. 402. 2. The fecond mode of aftion is not fo advantage- geccm[-] cus as that which we have been confidering, and fliould, mode of if poflible, always be avoided. It is reprefented in aftion. fig. 3. where A is the centre of the pinion, B that ofpjg, ^ the wheel, and AB the line of centres. It is evident from the figure that the tooth C of the wheel afts upon the leaf D of the pinion before they arrive at the line BA; that it quits the leaf when they reach this line, and have aflumed the pofition of E and F; and that the tooth c works deeper and deeper between the leaves of the pinion, the nearer it comes to the line of centres. From this laid circumflance a confiderable quantity of friftion arifes, becaufe the tooth C does not, as before, roll upon the leaf D, but Aides upon it ; and from the fame caufe the pinion foon becomes foul, as the duft which lies upon the afting faces of the leaves is puAied into the interjacent hollows. One advantage, how¬ ever, attends this mode of aftion : It allows us to make the teeth of the large wheel reftilineal, and thus renders the labour of the mechanic lefs, and the ac¬ curacy of his work greater, than if they had been of a curvilineal form. If the teeth C, E, therefore of the wheel BC are made reftilineal, having their furfaces direfted to the wheel’s centre, the afting faces of the leaves D, F, &c. muft be epicycloids formed by a ge¬ nerating circle, whofe diameter is equal to the radius Bo of the circle op, rolling upon the circumfeience m n of the pinion A. But if the teeth of the wheel and the leaves of the pinion are* made curvilineal as in the figure, the faces of the teeth of the wheel muft be portions of an interior epicycloid formed by any gefte- ■ ' ’ -' ' rating m e c H A N I C S. •pracVical rating clrcl« rolling within the concave fuperficies of I I Mechanics. Now, In the triangle APB, AB Is known, and alfo Pra&ical the ctrcleT^ and the f^ces of the pinion’s leaves muft PB, which is the cofine of the angle ABD, be portions of an exterior epicycloid produced by roll- being perpendicular to DB ; AP or the radius of j- nnnn the convex circum- the pinion therefore may be found by plane tngo- Thinl mode of aftion. Fig. 4- Relative diameters of the wheel arid pinion. ing the fame generating circle upon the convex circum¬ ference tn ti of the pinion. 403. 3. The third mode of aftion, which is reprefented in fig. 4'. is a combination of the two firlt modes, and confequently partakes of the advantages and difadvan- tages of each. It is evident from tne figuie that the portion e b oi the tooth afts upon the part b c oi the leaf till they reach the line of centres AB, and that the part ed of the tooth afts upon the portion b a o'i the leaf after they have palled this line. Hence the afting parts e h and b c muft be formed according to the direftions given for the firft mode of aftion, and the remaining parts ed, b a, muft have that curvature which the fecond mode of aftion requites j confequent- \y eh ftiould be part of an interior epicycloid formed by any generating circle rolling on the concave cir¬ cumference tn n of the wheel, and the correfponding part £ c of the leaf Ibould (be part of an exterior epi¬ cycloid formed by the fame generating circle rolling upon b EO, the convex circumference of the pinion : the remaining part c d oi the tooth Ihould be a poition of an exterior epicycloid, engendered by any genera¬ ting circle rolling upon e L, the concave fuperficies of the wheel: and the correfponding part b a of the leaf Ihould be part of an interior epicycloid defcribed by the fame generating circle, rolling along the concave fide b EO of the pinion. As it would be extremely troublefome, however, to give this double curvature to the afting faces of the teeth, it will be proper to ufe a generating circle, whofe diameter is equal to the radius of the wheel BC, for defcribing the interior epicycloid e h and the exterior one b c, and a generating circle, whofe diameter is equal to AC, the radius of tne pi¬ nion, for defcribing the interior epicycloid b a, and the exterior one e d. In this ca!e the two interior epi¬ cycloids e h, b a, will be ftraight lines tending to the centres B and A, and the labour of the mechanic will by this means be greatly abridged. 404. In order to find the relative diameters of the wheel and pinion, when the number of teeth in the one and the number of leaves in the other are given, and when the diftance of their centres is alfo given, and the ratio of ES to CS, let a be the number of teeth in the wheel, b the number of leaves in the pinion, c the diftance of the pivots A, B, and let m be to n as ES to CS, then the arch ES, or ^ SAE, will be equal 36o° and LD, or LED, will be equal to But ES : CS= tfz : n; confequently LD : : /?, therefore (Eucl. vi. 16.) LCx — BE 1 360 but LD is equal to , the pinion therelore may be found by plane trigo¬ nometry. The reader will obferve, that the point P marks out the parts of the tooth D and the leai SP where they commence their aftion ; and the point I marks out the parts where their mutual aftion ceafes (e) ; AP therefore is the proper radius of the pinion, and BI the proper radius of the wheel, the parts of the tooth L without the point I, and of th« leaf SP without the point P, being fuperlluous. Now, to find BI, wre have ES : CS—wz: n, and CS: LDX « X and JL'w“ therefore by fubftitution LC 360 X » m but ES was ihewn to be ~ 360 therefore, by fubfti¬ tution, CS— 3^,° "E-. Now the arch ES, or^lEAS, being equal to 360 X« b m 360 and CS, or ^ CAS, being equal to b m their difference EC, or the angle EAC, 360 360 X n q 360° X m—n bm b m The will be equal to ^ EAC being thus found, the triangle EAB, or IAB, which js almoft equal to it, is known, becaufe AB is given, and likewife AI, which is equal to the cofine of the angle IAB, AC being radius, and AIC being a right angle, confequently IB the radius of the wheel may be found by trigonometry. It was former¬ ly Ihewn that AC, the radius of what is called the pri- c b mitive pinion, was equal to - and that BC the AC X a „ radius of the primitive wheel was equal to ^ . It then we fubftraft AC or AS from AP, we ftiall have the quantity SP which muft be added to the radius of the primitive pinion, and if we take the difference of BC (or BE) and DE, the quantity LE will be found, which muft be added to the radius of the primitive wheel. We have all along fuppofed that the wheel drives the pinion, and have given the proper form of the teeth upon this fuppofition. But when the pinion drives the wheel, the form which -was given to the teeth of the whefel in the firft cafe, muft in this.be given to the leaves of the pinion ; and the ftiape which was formerly given to the leaves of the pinion muft now be transferred to the teeth of the wheel. 401?. Another form for the teeth of wheels, differ-Form of ent from any which we have mentioned, has been re- the tee.th commended by Dr Robifon. He (hews that a perfeft tQ uniformity of aftion may be fecured, by making the bjfon. afting faces of the teeth involutes of the wheel’s circum¬ ference, which are nothing more than epicycloids, the centres of whofe generating circles are infinitely diftant. Thus, in fig. 1. let AB be a portion of the wheel on (e) The letter L marks the of the arch b O wkh the upper and P with I. interfeftion of the line BE with the arch e m, and the letter E the interfeftion furface of the kar m. The letters D and S-correfpond with L and E refpeftively, M E C HA NIGS. Practical which the tooth is to he fixed, and let Ap a be a thread Mechanics. }appeci round its circumference, having a loop hole at jv.r f™*'' its extremity a. In this loop hole fix the pin a, and with it defcribe the curve or involute a b c de h, by unlapping the thread gradually from the circumference Ap m. This curve will be the proper fhape for the teeth of a wheel whole diameter is AB. Dr Robifon ob- ferves, that as this form admits of feveral teeth to be acting at the fame time (twice the number that can be admitted in M. de la Hire’s method), the preffure is divided among feveral teeth, and the quantity upon any one of them is fo diminifhed, that thofe dents and im- prelTions which they unavoidably make upon each other are partly prevented. He candidly allows, however that the teeth thus formed are not completely free from Aiding and friftion, though this Aide is only -^-th of an inch, when a tooth three inches long fixed on a wheel ten feet in diameter drivesanother wheel whole diameter is two feet. Append, to YerguforPs LeElures. 406. On the Formation of Exterior and Interior Y.pi cycloids, and on the Difpojition of the Teeth on the Wheels Circiwijerence. Nothing can be of greater importance to the prac- Me'hanicaltm^d mechanic, than to have a method of drawing epi- method cf cycloids with facility and accuracy ; the following, we forming truft, is the mod Ample mechanical method that can epicycloids. employed.—Take a piece of plain wood GH, fig. 6. and fix upon it another piece of wood E, having its 3?ig. 6. circumference mb of the fame curvature as the circular bafe upon which the generating circle AB is to roll. When the generating circle is large, the feg- ment B will be fufficient: in any part of the circum¬ ference of this fcgment, fix a fharp pointed nail a, floping in fuch a manner that the didance of its point from the centre of the circle may be exaftly equal to its radius} and fallen to the board GH a piece of thin brafs, or copper, or tinplate, a b, didinguifhed by the dotted lines. Place the fegment B in fuch a pofiuon that the point of the nail a may be upon the point b, and roll the fegment towards G, fo that the nail a may rife gradually, and the point of contact between the two circular fegments rnay advance towards m; the curve a b deferibed upon the brafs plate will be an ac¬ curate exterior epicycloid. In order to prevent the ferments from Aiding, their peripheries Aaould be rub¬ bed with rolin or chalk, or a number of fmall iron points may be fixed on the circumference of the generating fegment. Remove, with a file, the part of the brafs on the left hand of the epicycloid, and the remaining concave arch or gage a b will be a pattern tooth, by means of which all the red may be eafily farmed. When an interior epicycloid is wanted, the concave lide of its circular bafe mult be ufed. fhe method of de- feribing it is reprefented in fig. 7. where CD is the ge- p. nerating circle, F the concave circular bafe, MN the ^ piece of wood on which this bale is fixed, and cd the interior epicycloid formed upon the plate of brals, by rolling the generating circle C, or the generating feg- ment D, towards the right hand. The cycloid, which is ufeful in forming the teeth of rack work, is generated precifely in the fame manner, with this difference only, that the bafe on which the generating circle rolls mud be .a draight line. In order that the teeth may not embarrafs one ano- Practical ther before their aftion commences, and that one tooth -Mechanics, may begin to afl; upon its correfponding leaf of the pi- cifpofnioa nion, before the preceding tooth has ceafed to a£t upon0fthe the preceding leaf, the height, breadth, and didance of teeth, the teeth mud be properly proportioned. For this pur- pofe the pitch-line or circumference of the wheel, w’hich is reprefented in fig. 2. and 3. by the dotted arches, mud be divided into as many equal fpaces as the num¬ ber of teeth which the wdieel is to carry. Divide each of thefe fpaces'into 16 equal parts; allow 7 of theie for the greatef. breadth of the teeth, and 9 for the dif- tance between each •, or the didance of the teeth may be made equal to their breadth. If the w’heel drive a trundle, each fpace fhould be divided into 7 equal parts, and 3 of tbefe allotted for the thicknefs of the tooth, and 3^ for the diameter of the cylindrical dave of the trundle. If each of the fpaces already mentioned, or if the didance between the centres of each tooth, be divided into three equal parts, the height of the teeth mud be equal to two of thefe. Thefe didances and heights, however, vary according to the mode of aflion which is employed. The teeth diould be rounded oft at the extremities, and the radius of the wheel made a little larger than that which is deduced from the rules in Art. 400, 404. But when the pinion drives the wheel, a fmall addition Ihould be made to the radius of the pinion. On the Nature of Bevelled Wheels, and the method of giving an epicycloidalform to their Teeth. 407. The principle of bevelled wheels was pointed out Bevelled by De la Hire, fo long ago as the end of the i 7th centu- wbceis' ry. It confids in one fluted or toothed cone afting upon another, as is reprefented in fig. 8. where the cone OD Fig- ^ drives the cone,OC, conveying its motion in the direc¬ tion OC. If thefe cones be cut parallel to their bafes as at A and B, and if the two fmall cones between AB and O be removed, the remaining parts AC and BD may be confidered as two bevelled wheels, and ED will a£t upon AC in the very fame manner, and with the fame eftedl, that the whole cone OD added upon the whole cone OC. If the fedfion be made nearer the bafes of the cones, the fame eft'edf will he produced : this is the cafe in fig. 9. where CD and Fig. §• DE are but very fmall portions of the imaginary cones ACD and ADE. 408. In order to convey motion in any given diredfion, and determine the relative fize and fituation of the wheels for this purpofe, let AB, fig. 10. be the axis Fig. ip. of a wheel, and CD the given direction in which it is required to convey the motion by means of a wheel fixed upon the axis AB, and adting upon another wheel fixed on the axis CD, and let us fuppofe that the axis CD muft have four times the velocity of AB, or muff perform four revolutions while AB performs one. Then the number of teeth in the wheel fixed upon AB muft be four times greater than the number of teeth in the wheel fixed upon CD, and their radii muft have the fame proportion. Draw c d parallel to CD at any convenient diftance, and draw a b parallel to AB at four times that diftance, then the lines im and in drawn perpendicular to AB and CD refpedtively, will mark the fituation and hie of the wheels required. Ip Practical Mechanics. On the for¬ mation of their teeth. M E C H this cafe the cones are O n i and O m t\ and srn i r/> m i, are the portions of them that are employed A N I C S. . . 117 the vertex C of the cone_MCG approaches to N till it Fig. S. @n crown wheels. Fig. 11. The formation of the teeth of bevelled wheels is more difficult than one would at firft imagine, The teeth of fuch wheels, indeed, muft be formed by the fame rules which been have given for other wheels \ but fince dif¬ ferent parts of the fame tooth are at different diltances from the axis, thefe parts muft have the curvature of their ailing furfaces proportioned to that diftance. Xhus, in fig. 10. the part of the tooth at r muft be more incurya- ted than the part at i, as is evident from the infpeaion of fig. 9. *, and the epicycloid for the part i muft be formed by means of circles whofe diameters are im and F/, while the epicycloid for the part r muft be gene¬ rated by circles whofe diameters are C n and D d. 409. Let us fuppofe a plane to pafs through the points O, A, D ; the lines AB, AO, will evidently be in this plane, which may be called the jb/ane of centres. Now, when the teeth of the wheel DE, which is fuppofed to drive CD the fmalleft of the two, commence their a£lion on the teeth of CD, when they arrive at the plane of centres, and continue their a£lion after they have paffed this plane, the curve given to the teeth of CD at C, ffiould be a portion of an interior epicycloid formed by any generating circle rolling on the concave fuper- ficies of a circle whofe diameter is twice C n perpendi¬ cular to CA, and the curvature of the teeth at t ihould be part of a fimilar epicycloid, formed upon a circle, whofe diameter is twice im. The curvature of the teeth of the wheel DE at D, ftiould be part of an ex¬ terior epicycloid formed by the fame generating circle roiling upon the concave circumference of a circle whole diameter is twice D d perpendicular to DA \ and the epicycloid for the teeth at F is formed in the fame way, only inftead of twnce D d, the diameter of the circle muft be twice Ff When any other mode of a6!ion is adopted, the teeth are to be formed in the fame manner that we have pointed out for common wheels, with this difference only, that different epicycloids, are neceflary for the parts F and D. It may be fufficient, however, to find the form of the teeth at F, as the re¬ maining part of the tooth may be ftiaped by direfting a ftraight rule from dilterent points of the epicycloid at F to the centre A, and filing the tooth till every part of its afling furface coincide with the fide of the ruler. The reafon of this operation will be obvious by attending to the lhape of the tooth in fig. 8. Vt hen the fmall wheel CD impels the large one DE, the epicycloids which were formerly given to CD muft be given to DE, and thofe which were given to DE muft be transferred to CD. _ .... 410. The wheel reprefented in fig. 11. is fometimes called a crown wheel, though it is evident from the figure that it belongs to that fpecies of wheels which we have juft been conftdering \ for the afting fun aces of the teeth both of the wheel MB and of the pinion EDG are dire&ed to C the common vertex of the two cones CMB, CEG. In this cale the rules for bevelled W’heels muft be adopted, in which AS is to oe confider- ed as the radius of the wheel for the profile of the tooth at A, and MN as its radius for the profile of the tooth at M \ and the epicycloids thus formed will be the fec- tions or rrofiles of the teeth in the direbfion Mi , at ripht angles to iViC the furfac.es of the cone. W- hen tne vertex 01 uic cuuc r Mechanics. be in the fame plane with the points M, G, lome ox , x — 1 the curves will be cycloids and others involutes, as in the cafe of rack work, for then the cone CEG will revolve upon a plane furface. Appendix to Fergufon's Lec¬ tures. Sect. II. On the Wipers of Stampers, isfc. the Teeth of Rackwork, (b’c. fa'c. 411. In fig. 12. let AB be the wheel which is employ-Dg. 1*. ed to elevate the rack C, and let their mutual aflion not commence till the afting teeth have reached the line of centres AC. In this cafe C becomes as it ;we.e the pinion or wheel driven, and the afting faces of its teeth muft be interior epicycloids formed by any gene¬ rating circle rolling wfithin the circumference/*^ ; but asp q is a ftraight line, thefe interior epicycloids will be cycloids, or curves generated by a point in.the circum¬ ference of a circle, rolling upon a ftraight line or plane furface. The afting face op, therefore, will be part of a cycloid formed by any generating circle, and m ny the afhng face of the teeth of the wheel, muft be. an exterior epicycloid produced by the fame generating circle rolling on to r the convex furface of the wheel. If it is reejuired to make 0p a ftraight line, as in the figure, then to n muft be an involute of the circle to 1 formed in the manner reprefented in fig. 5. 412. Fig. t 2. likewife reprefents a wheel depreffing the rack c when the third mode of aftion is uted. In this cafe alfo c becomes the pinion, and DE the wheel; e h therefore muft be part of an interior epicycloid formed by any generating circle rolling on the concave fide f .r of the wheel, and b c muft be an exterior epicy¬ cloid produced by the fame generating circle rolling upon the circumference of the rack. Fhe remaining part cd oi the teeth of the wheel, muft be an exterior epicycloid deferibed by any generating circle moving upon the convex fide ex, and ba muft be an interioi epicycloid engendered by the fame generating circle rolling within the circumference of the rack. But as the circumference of the rack is in this cafe a ftraight line, the exterior epicycloid be and the interior one ba will be cycloids formed by the fame generating circles which are employed in defcribing the other epicy¬ cloids. Since it would be difficult, however, as has already been remarked, to give tbis compound curva- x ture to the teeth of the wheel and rack, we may ufe a - generating circle wffiofe diameter is equal to D A? the radius of the wheel, for defcribing the interior epicy¬ cloid e h, and the exterior one b c ; and a generating circle whofe diameter is equal to the radius ot the rack, for defcribing the interior epicycloid a b, and the ex¬ terior one de > a b and e h, therefore, will be ftraight lines and b c wull be a cycloid, and de an involute of the circle c x, the radius of the rack being infinitely great. 413. In the fame manner may the form of the teeth of rack-work be determined, when the fecond mode of aftion is employed, and when the teeth of the wheel or rack are circular or re&ilineal. But if the rack be - part of a circle, it muft have the fame form for its teeth as that of a wheel of the fame diameter with the circle of which it is a part, Ih.* 11 3 M E C H A N I C S, Fvacfrical Mechanics. Proper form of wipers. In inacliinery, where large weights ore to be railed, fuch as Hiliiug.mills, mills for pounding ore, &c. or w'here large piftons are to be elevated by the arms or levers, it is of the greatefl confequence that the power fhould raife the weight with an uniform force and velo¬ city ; and this can be effecled only by giving a proper form to the wiper. Now there are twro cafes in which this unifor¬ mity of motion may be required, and each of thefe de- ** mands a different form for the communicating parts. I. When the weight is to.be raifed vertically, as the piilon - of a pump, &c. 2. When the weight to be railed or depreffed moves upon a centre, and rises or falls in the arch of a circle, fuch as the fledge hammer in a forge, &c. Fig 13. 414. 1. Let AH be a wheel moved by any power which is fufKcient to raife the weight MN by its extre¬ mity O, from O to e, in the fame time that the wheel moves round ©ne-fourth of its circumference, it is re¬ quired to fix upon its rim a wing OBCDEH which fhail produce this effec! with an uniform effort. Di¬ vide the quadrant OH into any number of equal parts O m n, &c. the more the better, and 0 e into the fame number 0 b, b c, c d, &c. and through the points H draw the indefinite lines AB, AC, AD, AE, and make AB equal to A AC to Ac, AD to A and AE to Acj then through the points O,B, C, D, E, draw the curve OBCDE, which is a portion of the fpiral of Archimedes, and wull be the proper form for the wiper or wdng OHE. It is evident that when the point m has arrived at O, the extremity of the wreight will have arrived at b ; becaufe AB is equal to A b, and for the fame reafon, when the points n,p, H have fucceffively arrived at O, the extremity of the weight will have arrived at the correfponding points c, dl e. The motion therefore will be uniform, becaufe the fpace defcribed by the weight is proportional -to the fpace defcribed by the moving power, O b being to O c as O w to O If it be required to raife the weight MN with an accelerated or retarded motion, we have only to divide the line O e according to the lawT of acceleration or retardation, and divide the curve OBCDE as before. When the 415. 2. When the lever moves upon a centre, the weight riles wejght will rife in the arch of a circle, and confequent- ofacircfi, ly a new form muff be given to the wipers or wings. Fig. 14. Let AB, fig. 14. be a lever lying horizontally, which it is required to raife uniformly through the arch BC into the pofition AC, by means of the wffieel BFH furnilhed wdth the wing BNOP, which acts upon the extremity C of the lever 5 and let it be required to raife it through BC in the fame time that the wheel BFH moves through one-half of its circumference; .that is, while the point M moves to B in the direftion MFB. Divide the chord CB into any number of equal parts, the more the better, in the points 1, 2, 3, and draw the lines \ a 'lb 3c parallel to AB, or a horizontal line palling through the point B, and meet¬ ing the arch CB in the points D, c D, and BD cutting the c’icle BFH in the points ?n, a, o^p. Having drawn the diameter BM, divide the fe- micircle BFM into as many equal parts as the chord CB, in tne points q, s, u. Take B and let it from q to r : Take B n and fet it from ,r to t : Take B 0 and fet it from u to v, and laffly let Up from M to E. Through the points E, draw the indefinite lines DN, DO, DP DQ^, and make DN equal to D c; DO equal to D £ ; DP equal to Da ; and DC^ equal to DC. Then through the points (^, P, O, N, B, draw the fpiral B, N, O, P, O, which v ill be the proper form for the wing of the wheel when it moves in the clix-edlion EMB, That the fpiral BNO will raife the lever AC,' with an uniform motion, by atffing upon its extremity c, will appear from the flighteft attention to the conftruc- tion of the figure. It is evident, that when the point q arrives at B, the point r will be in becaule B m is equal to q r, and the point N will be at c, becaufe DN is equal to Dc; the extremity of the lever, there¬ fore, will be found in the point c, having moved through B c. In like manner, when the point s has arrived at B, the point t will be at n, and the point O, in b, where the extremity of the lever will now be found ; and fo on with the reft, till the point M has ar¬ rived at B. The point E will then be in p, and the point Q. in Cq fo that the lever will now have the po¬ fition AC, having moved through the equal heights B c, c b, b a, a c, (f) in the fame time that the power has moved through the equal fpaces q B, s q, a s, M u. The lever, therefore, has been raifed uniformly, the ra¬ tio between the velocity of the power, and that of the weight, remaining always the fame. 416. If thewdieelD turn in a contrary diredHon, ac* cording to the letters MHB, we muft divide the femi- circle BH EM, into as. many equal parts as the chord c B, viz. in the points e,gi h. Then, having fet the arch B m from e to d, the arch B n from g lo f, and the reft in a fimilar manner, draw through the points d,f h, E, the indefinite lines Dll, DS. DT, D£): make DR equal to Dc ; DS equal to Db ; DT equal to Do, and D£) equal to DC ; and though the points B, R, S, T, Q, defcribe the fpiral BRSTQq which will be the proper form for the wing, wdren the wheel turns in the dire&ion MEB. For, when the point c arrives at B, the point d will be in m, and R in c, where the extre¬ mity of the lever will now be found, having moved through B c in the fame time that the power, or wheel, has moved through the divifion e B. In the lame man¬ ner it may be {hewn, that the lever will rife through the equal heights c b,b a^a C, in the fame time that the powTer moves through the correfponding fpaces eg,gi, z M. The motion of the lever, therefore, and alfo that of the power, are always uniform. Of all the pofitions that can be given to the point B, the moft difadvanta- geous are thofe which are neareft the points F, H ; and the moft advantageous pofition is when the chord B e is vertical, and paffes, when prolonged, through D, the centre (f) The arches Be, c£, &c.' are not equal : but the perpendiculars let fall from the points e, a,b, &c. upon the horizontal lines, palling through a b, &c. are equal, being proportional to the equal lines e 1, 1., 2. Fuel. VI. 2. • 1 / M E C H A Praaicrl centre of tlie circle (g). In this particular cafe the Wech'tnxs j-wo curves have equal bafes, though they differ a litUe U—in poii t of curvature. The farther that the centre A is diftait, the nearer do thefe curves referable each other ; and if it were infinitely diilant, they would be exaftly fimilar, and would be the ipirals of Archimedes, as the extremity c would in this cafe rife perpendicularly. It will be eafily perceived that 4, 6, or 8 wings mav be placed upon the circumference of the circle, and may be formed by dividing into the fame number of equal parts as the chord BC, or of the cir¬ cumference, inftead of the femicircle BFM. That the wing BNO may not a& upon any part of the lever between A and C, the arm AC (hould be bent 3 and that the fribtion may be diminifhed as much as poffible, a roller (hould be fixed upon its extremity C. When a roller is ufed, however, a curve muff al¬ ways be drawn parallel to the fpiral defcribed accord¬ ing" to the preceding method, the diftance between it and the fpiral being everywhere equal to the radius of the roller. If it (hould be required to raife the lever with an accelerated or retarded motion, we have only to di¬ vide the chord BC, according to the degree of retarda¬ tion or acceleration required, and the cucle into the fame number of equal parts as before. , 417. As it is frequently more convenient to raife or deprefs weights by the extremity of a cohftant radius, furnifhed with a roller, inftead of wings fixed upon the periphery of a wheel 3 we (hall now proceed to deter¬ mine the curve which muft be given to the arm of the lever, which is to be raifed or deprefled, in order that this elevation or deprellion may be effected with an uni¬ form motion. Let AB be a lever, which it is required to rafte uniformly through the arch BC, into the pofition AC, by means of the arm or conftant radius DE, mov¬ ing upon D as a centre, in the fame time that the ex¬ tremity E deferibes the arch EeY. Froin the point C draw CH at right angles to AB, and divide it into any number of equal parts,"fuppofe three, in the points I 2 3 and through the points 1, 2, draw 102b, paral¬ lel to the horizontal line AB, cutting the arch CB in the points a, b, through which draw a A, b A. Upon D as a centre, with the diftance DE, deicribe the arch NIGS. . 1 119 Ez’eF, and upon A as a centre, with the diftance PraCfcal AD, deferibe the arch e OD, cutting the arch Eh e F ' in the point e. Divide the arches E ie, and Y s e, each into the fame number of equal parts as the perpendicu¬ lar <*H, in the points and through thefe points, about the centre A, deferibe the arches k », ig, q r, m 11. Take S3 a? and fet it from k to /, and take g f, and fet it from 1 to h. Fake r q alio, and let it from s to t, and fet n m from 0 to />, and from e to O. Then through the points E,/. //, O, and 0,/,/>, F draw the two curves E///O, and , which will be the proper form that muft be given to the arm or the lever. ' If the handle DE moves from E tow-ards F, the curve EO muft be ufed, but if in the contrary diredfion, we muft: employ the curve Oh. It is evident, that when the extremity E of the handle DE, has run through the arch E h, or rather E /, the point / will be in .£, and the point z in #, becaufe x s is equal to /£/, and the lever will have the pofition A For the fame reafon, when the extremity E of the handle has arrived at z, the point h wall be in z, and the point g in f and the lever will be raifed to the po¬ fition A a. Thus it appears, that the motion of the pow’er and the weight are ahvays proportional. When a roller is fixed at E, a curve parallel to EO, or OF, muft be drawn as, formerly. See Appendix to Feign- Jon's Letiures, Chap. VI. On the Firji Movers of Machinery. 418. The powders which are generally employed as the firft movers of machines are water, wind, fleam, and animal exertion^ The mode of employing water as an impelling power has already been given at great length in the article Hydrodynamics. The application of wind to turn machinery wdll be. difeufled in the chapter on Windmills 3 and what regards fleam will be more properly introduced into the article Steam-Engine. At prefent, therefore, wre (hall only make a few general remarks on the ftrength of men and horles 3 and con¬ clude with a general view' of the relative powers of the firft movers of machinery. The following table con¬ tains the weight which a man is able to raife through a certain height in a certain time, according to diffe» _ rent.authors. Table of the Strength of Men, according to different authors. Number of pound' rai fed. }1 ’J £ IOOO 60 " 25 17°. IOOO iooe 3° or 30 Height to which j lime in which it the weight is railed ' is raifed 180 1 220 I 33° 225 2.45 feet j P-i 60 minutes 1 fecond 145 feconds 1 fecond 60 mirjutes 60 minutes I fecond i fecond Duration of the Work. 8 hours half an hour 10 hours Names of the au¬ thors. Euler Bernouilli Amontons Coulomb Defaguliers Smeaton Emerfon Schulze. (g) In the figure we have taken the point B in a difadvantageous pofition, becaufe the mterfeaions are m this •safe more diftincL . I 20 M E C H A N I C S. PrafticaT Mechanic^ Force of men ac¬ cording to A men tons. According to Befa- .guliers. Refults of Coulomb’s experi¬ ments. 419. According to Amontons, a man weighing 133 pounds French, afeended 62 feet French by Iteps in 34 i'econds, but was completely exhaufted. The lame au¬ thor informs us that a fawyer made 200 llrokes of 18 inches French each, with a force of 25 pounds, in 145 feconds $ but that he could not have continued the ex¬ ertion above three minutes. 420. It appears from the obfervations of Defaguliers, that an ordinary man can, for the fpace of ten hours, turn a winch with a force of 30 pounds, and with a ve¬ locity of two feet and a half per lecond $ and that two men working at a windlafs with handles at right angles to each other cen raife 70 pounds more eafily than one man can raife 30. The reafon of this is, that when there is only one man, he exerts variable efforts at dif¬ ferent politions of the handle, and therefore the motion of the windlafs is irregular •, whereas in the cafe of two men, w’ith handles at right angles, the effefl; of the one man is greateh when the effeft of the other is leaft, and therefore the motion of the machine is more uniform, and will perform more work. Defagu¬ liers alfo found, that a man may exert a force of 80 pounds with a fly when the motion is pretty quick, and that by means of a good common pump, he may raife a boglhead of water 10 feet high in a minute, and con¬ tinue the exertion during a whole day. 421. A variety of interefting experiments upon the force of men were made by the learned M. Coulomb. He found that the quantity ©f action of a man who af- cended flairs wnth nothing bi t his own weight, was double that of a man loaded with 223 pounds avoirdu¬ pois, both of them continuing the exertion for a day. In this cafe the total or abfolute effect of the unloaded man is the greateft poffible ; but the ufeful effett which he produces is nothing. In the fame way, if he were load¬ ed to fuch a degree that he was almoft incapable of moving, the ufeful effeft would be nothing. Hence there is a certain load with wdiich the man will produce the greateft ufeful effeft. This load M. Coulomb found to be 173.8 pounds avoirdupois, upon the fuppo- -fition that the man is to afeend flairs, and continue the exertion during a whole day. When thus loaded, the quantity of adlion exerted by the labourer is equivalent -to 183.66 pounds avoirdupoisraifed through 3282 feet. This method of working is however attended with alofs of three fourths of the total aftion of the workman.—It appears alfo from Coulomb’s experiments, that a man go¬ ing up flairs for a day raifes 205 chiliogrammes (a chilio- gramme is equal to three ounces five drams avoirdu¬ pois) to the height of a chiliometre (a chiliometre is equal to 39571 Englilh inches) •,—that a man carrying wosd up flairs raifes, together with his own weight, 109 chiliogrammes to one cniliometre ;—that a man weigh¬ ing 150 pounds French, can afeend by flairs three feet French in a fecond, for the fpace of I 5 or 20 feconds •, —that a man cultivating the ground performs Iff as much labour as a man afeending flairs, and that his quantity of aftion is equal to 328 pounds avoirdupois raifed through the fpace of 3282 feet-,—that a man with a winch does f as much as by afeending flairs — and that in a pile engine, a man by means of a rope drawn horizontally, raifed for the fpace of five hours 55t pounds French through one foot French in a fe- £ond.—-When men v/alk on a horizontal road, Cou.- lomb found that the quantity of aclion was a maximum Practical when they were loaded, and that this maximum quan- ^ehanics, tity of aftion is to that which is exerted by a man loaded with 190.25 pounds avoirdupois as 7 to 4.—The weight which a man ought to carry in order that the vfeful ef- feB may be a maximum, is 165.3 pounds avoirdupois. When the workman, however, returns unloaded for a new' burden, he muft carry 200.7 pounds avoirdu¬ pois. 422. According to Dr Robifon a feeble old man raifed feven cubic feet of water =0:437.5 pounds avoir¬ dupois, n4 feet high, in one minute, for eight or ten hours a day, by w’alking backwards and forwards on a lever j—and a young man weighing 135 pounds, and carrying 30 pounds, raifed 9I cubic feet of water =578.1 pounds avoirdupois, ni feet high, for 10 hours a clay, without being fatigued. 423. From the experiments of Mr Buchanan, it ap¬ pears that the forces exerted by a man pumping, ail¬ ing at a winch, ringing and rowing, are as the numbers 1742, 2856, 3883, 4095. 424. According to Defaguliers and Smeaton, the On the power of one horfe is equal to the power of five men. Several French authors fuppofe a horfe equal, to 101 es‘ feven men, while M. Schulze confiders one horfe as equivalent to 14 men.—Two horfes, according to the experiment of Amontons, exerted a force of 150 pounds French, when yoked in a plough. Accord¬ ing to Defaguliers, a horfe is capable of draw-ing, with a force of 200 pounds, two miles and a half an hour, and of continuing this ailion eight hours- in the day. When the force is 240 pounds he can work on¬ ly fix hours. It appears from Smeaton’s reports, that by means of pumps a horfe can raife 250 hog (heads of water, 10 feet high, in an hour.—The moft difadvan- tageous way of employing the power of a horfe is to make him carry a load up an inclined plane, for it was obferved by De la Hire, that three men, with 100 pounds each, will go fafter up the inclined plane than a horfe with 300 pounds. When the horfe walks on a good road, and is loaded with about two hundred weight, he may eafily travel 25 miles in the fpace of feven or eight hours. 425. When a horfe is employed in raifing coals by means of a wheel and axle, and moves at the rate of about two miles an hour, Mr Fenwick found that he could continue at work 12 hours each day, two and a half of which were (pent in (hort intervals of reft, when he raifed a load of 1000 pounds avoirdupois, with a velocity of 13 feet per minute 5—and that he will exert a force of 75 pounds for nine hours and a half, when moving with the fame velocity. Mr Fenwick alfo found that 230 ale gallons of water delivered every minute on an overfhot water wheel, 10 feet in diameter that a common fleam engine, with a cylinder eight inches in diameter, and an improved engine with a cylinder 6.1 2 inches in diameter, will do the work of one horfe, that is, will raife a weight of 1000 pounds avoirdupois, through the height of 13 feet in a minute. It appears from Mr Smeaton’s experiments, that Dutch fails in the4r com¬ mon pofition with a radius of nine feet and a half,—that Dutch fails in their beft pofition with a radius of eight feet, and that his enlarged fails with a radius of feven feet, perform the fame work as one man ; or perform one- 3 Practical Mechanics. MECHANICS. 121 one-fifth part of the work of a horfe. Upon thefe fafts columns of which are taken from TMr Fenwick s y 1^ec'rianjc5> we have conftru£ted the following table, the four fiift on Practical Mechanics. Table Kwing the relativeJlrength of Overjhot Wheels, Steam Engines, Horfes, Men, and Wind-mills of J different kinds. Number of ale gallons delivered on an overfhot wheel, 10 feet in dia meter, every minute. Diameter of the cylinder in the com¬ mon fteam- engine, in inches. Diameter of the cylinder of the im¬ proved fteam-engine, in inches. Number of horfes work¬ ing 12 hours per day, and moving at the rate of two miles per hour. 250 39° 528 660 79O 970 1170 I445 1 ^84 1740 1900 2100 2300 2500 2686 2870 3°55 3240 3420 375° 4000 4460 4850 525° 8. 9*5 10.5 ii-5 12.5 14. 15-4 16.8 17-3 18.5 19.4 20.2 21. 22. 23.1 23-9 24.7 25-5 26.25 27. 28.5 29.8 31- 1 32- 4 33- 6 6.12 7.8 8.2 8.8 9-35 io-55 n-75 12.8 13.6 14.2 14.8 15.2 16.2 I7- 17.8 18.3 19. 19.6 20.1 20.7 22.2 23- 23*9 24.7 25-5 Number of men work¬ ing 12 hours a-day. Radius of Dutch fails in their com¬ mon politico, in feet. Radius of Dutch fails in their belt polition, in feet. 1 2 3 4 5 6 7 8 9 10 11 12 *3 M !5 16 *7 18 *9 20 22 24 26 28 3° 5 1 10 15 20 25 3° 35 40 45 5° 55 60 65 70 75 80 85 9° - 95 100 no 120 130 140 I5° 21.24 30.04 36.80 42.48 47-5° 52-03 56.90 60.09 63-73 67.17 70.46 73-59 76-59 79-49 82.27 84.97 87.07 90.13 92.60 95.00 99.64 104.06 108.32 112.20 116.35 Radius of Mr Smea- ton’s en¬ larged fails, in feet. 17.89 25-3° 30.98 35-78 40.00 43.82 47-33 50.60 53-66 56-57 59-33 61.97 64.5 66.94 69.28 7I-55 73-32 75-90 77.98 80.00 83.90 87.63 91.22 94.66 97.98 15-65 22.13 27.11 35-oo 38 34 4I-4I 44.27 46.96 49-50 5I-9I 1 54-22 56-43 58.57 60.62 62.61 64.16 67.41 68.23 70.00 73-42 76.68 79-81 82.82 85.73 Height lo which thefe different powers will raife ioog pounds avoir¬ dupois n a minute. 13 26 39 52 65 78 90 104 117 130 M3 156 169 182 i95 208 221 234 247 260 286 3^ 338 364 39° 426. Dutch feils are always conftru their power was greateft of all, though the furface act¬ ed upon by the wind remained the fame. It the tails be farther enlarged, the effieft is not increafed in pro¬ portion to the furface *, and befid^s, when the quantity of cloth is great, the machine is much expofed to in¬ jury by hidden fqualls of wind. In Mr Smeaton s ex¬ periments, the angle of weather varied with the di- ftance from the axis *, and it appeared from feveral trials, that the moft efficacious angles were thole in the fallowing table. Parts of the radius EA, which is di vided into dpart- Angle with the axis. Angle of weather 72 71 72 74 77t 83 18 J9 . 18 middle 16 124 7 If the radius ED of the fail be 30 feet, then the fail will commence at 4 ED, or 5 feet from the axis, where the angle of inclination will be 72 . At ^ , or 1 o feet from the axis, the angle will be 71 , and fo on. On the EffeEi of Wind-mill Sails. 433. The following maxims deduced by Mr Smeafon from his experiments, contain the tnoft accurate infor¬ mation upon this fubjeft. A NI C S. . „ *23 Maxim 1. Tilt: velocity of wind-mill fills, ^ unloaded or loaded, fo as to produce a maximum etteCt, , is nearlv as the velocity of the wind, their ffiape an £^pe(q.s 0f pofition being the fame. . wind-mill Maxim 2. The '.load at the maximum is nearly, fail*, ac- but fomewhat lefs than, as the fquare of the velocity cordmg to of the wind, the ffiape and pofition of the fails being ^ the fame. „ . Maxim 3. The effeds of the fame fails at a maxi¬ mum, are nearly, but fomewhat lefs than, as the cubes the velocity of the wdnd. , Maxim 4. The load of the fame fails at the maximum Js nearly as the fquares, and their effects as the cubes of their number of turns in a given time. , Maxim 5. When fails are loaded, fo as to produce a maximum at a given velocity, and the velocity of the wind increafes, the load continuing the fame: I ft, The increafe of effe£f, when tne inoeaie of the velocity of the wund is fmall, will be nearly as the fquares of thofe velocities: 2dly, When the velo^ city of the wind is double, the effefts will be near¬ ly as 10 : 274: But, 3dly, When the velocities compared are more than double of that where the given load produces a maximum, the eliecE mcreae nearly in the Ample ratio of the velocity of the wind. „ . Maxim 6. In fails where the figure and pofitidns are fimilar, and the velocity of the wind the fame, the number of turns in a given time will be reciprocally as the radius or length of the fail. Maxim 7. The load at a maximum that iails of a fimilar figure and pofition will overcome at a g.v^-.i diftance from the centre of motion, will be as the cube of the radius. „ „ . Maxim 8. The effeds of fails of fimilar figure and pofition are as the fquare of the radius. _ _ Maxim 9. The velocity of the extremities of Dutch fails, as well as of the enlarged fails, in all taeir ufual pofitions when unloaded, or even loaded to a mum, are confiderably quicker than the velocity ot the " 434. A new mode of conftruding the fails of wind-mills has been recently given by Mr Sutton, and fully de- feribed by Mr Hefleden of Barton, in a work excluhve- ly devoted to the fubjed. The limits of this article will not permit us to enter into any difeuffion refpeding the principles upon which Mr Sutton’s gravitated fails are conilruded •, but the fubied (hall be refumed under the article Windmill. If may be proper however to remark that Mr Sutton gives his fails the form reprefented in fig. 4. and makes pjg. 3; the angle of weather at the point M, eqmdiflant from A and B, equal to 22* 30'. The inclination of the fail at any other point N of the fail, is an angle whole fine is the diftance of that point from the centre of mo¬ tion A, the radius being the breadth of the ial1 tliat point. Fig. 3. ffiews the angles at the different points of the fail-, and the apparent and absolute breadths of the fail at thefe points. Mr Sutton s mode of regulating the velocity of the fails, and ot bringing them to a ftate of reft is particularly in¬ genious. & On MECHANICS. i 24 Fr flical Mechanics. Qn Horizontal Wind-mills. Horizontal 43.?* Various opinions have been entertained refpeft- ■yv'iiiG-miils. jng t]le relative advantages of horizontal and vertical wind mills. Pv'ir Smeaton, with great juflice, gives a decided preference to the latter ; but when he afferts that horizontal wind-mills have only or Tg of the power of vertical ones, he certainly forms too low ati eftimate of their power. Mr Beatfon, on the contra¬ ry, who has received a patent for the conftru<3ion of a new horizontal wind-mill, feems to be prejudiced in their favour, and greatly exaggerates their comparative value. From an impartial invedigation, it will proba¬ bly appear, that the truth lies between thefe tw’o oppo- fite opinions } but before entering on this difcuflion, we muft firft confider the nature and form of horizontal wind-mills. f'Z- 4’ 436. In fig. 4. CK is the windfliaft, which moves up¬ on pivots. Four crofs bars, CA, CD, IB, FG, are fix¬ ed to this arbor, which carry the frames APIB, DEFG. The fails AI, EG, are ftretched upon thefe frames, and are carried round the axis CK, by the perpendicu¬ lar impulfe of the wind. Upon the axis CK, a toothed wheel is fixed, which gives motion to the particular machinery that is employed. In the figure, only two fails are reprefented j but there are always other two 'Common placed at right angles to thefe. Now, let the fails be method of expoled to the wind, and it will be evident that no mo- baclfthe ti0n en^Ue ’ *"0r tlle ^°rCe t^le W‘n£* UPon t^e ^ fails .--gainft counterafled by an equal and oppofite force up- the wind. on fail EG. In order then, that the wund may communicate motion to the machine, the force upon the returning fail EG mult either he removed by fcreening it from the wind, or diminiihed by making it prefent a lefs furface when returning againft the wind. The firft of thefe methods is adopted in Tartary, and in fome provinces of Spain j but is objefled to by Mr Bcatfon, from the inconvenience and cxpence of the machinery and attendance requifite for turning the fcreens into their proper pofitions. Notwithftanding this^objeftion, hoivever, I am difpofed to think that this is the beft method of diminifhing the adh’on of the wind upon the returning fails, for the moveable fereen may eafily be made to follow the diretftion of the wind, and affume its proper pofition, by means of a large wooden weathercock, without the aid either of men or machinery. It is true, indeed, that the refiftance of the air in the returning fails is not completely remo¬ ved j but it is at leal! as much diminiftied as it can be by any method hitherto propofed. Befides, when this plan is reforted to, there is no occafion for any move- able flaps and hinges, which muft add greatly to the expence of every other method. Beatfon’s 437. The mode of bringing the fails back againft aaethod. t}ie wind, which Mr Beatfon invented, is, perhaps, the fimpleft and beft of the kind. He makes each fail AI to confift of fix ®r eight flaps or vanes, AP b 1, b 1 c 2 &c. moving upon hinges reprefented by the dark lines’ AP, b 1, c 2y See. fo that the lower fide b 1, of the firft flap overlaps the hinge or higher fide of the fecond flap, and fo on. When the wind, therefore, a£ls upon the fail AI, each flap will prefs upon the hinge of the one immediately below it, and the whole furface of the fail tvill be expofed to its aftion. But when the fail AI returns againft the wind, the flaps will revolve round upon their hinges, and prefent only their edges to the Piiufticai wind, as is reprefented at EG, fo that the refiftance Mechanics., occafioned by the return of the fail muft be greatly di- ~\r—^ miniftied, and the motion will be continued by the great fuperiority of force exerted upon the fails in the pofition AI. In computing the force of the wind upon the fail AI, and the refiftance oppofed to it by the edges of the flaps in EG, Mr Beatfon finds, that when the preffure upon the former is 1872 pounds, the re¬ fiftance oppofed by the latter is only about 36 pounds, °.r tt Part of the whole force ; but he neglects the ac - tion of the wind upon the arms CA, &c. and the frames which carry the fails, becaufe they expofe the fame ftirface in the pofition AI, as in the pofition EG. This omiflion, however, has a tendency to mif- lead us in the prefent cafe, as we ftiall now fee, for we ought to compare the whole force exerted upon the arms, as well as the fail, with the whole refiftance which thefe arms and the edges of the flaps oppofe to the motion of the windmill. By infpe&ing fig. 4. it will appear, that if the force upon the edges of the flaps, Which Mr Beatfon fuppofed to be 12 in number, amounts to 36 pounds, the force fpent upon the bars CD, DG, GF, FE, &c. cannot be lefs than 60 pounds. Now, fince thefe bars are a&ed upon with an equal force, when the fails have the pofition AI, 1872-}-6o ~I932 he the force exerted upon the fail AI, and its appendages, while the oppofite force upon the bars and edges of the flaps when returning againft the wind will be. 36-f 60=96 pounds, which is nearly 0f *932i inftead of as computed by Mr Beatfon. Hence wx may fee the probable advantages of a fereen over moveable flaps, as it will preferve not only the fails, but the arms and the frame which fupport it from the aftion of the wind. ’ 438.. We fliall now conclude this chapter with aCompari- comparifon of the power of horizontal and vertical f°ns be- wind-mills. It was already ftated, that Mr Smeaton ra- twefn ver' ther underrated the former, while he maintained that Kortonll they have only ^ or Vg- the power of the latter. He wind-mills, oblerves, that when the vanes of a horizontal and a ver¬ tical mill are of the fame dimenfions, the power of the latter is four times that of the former, becaufe, in the firft cafe, only one fail is a£led upon at once, while, in the fecond cafe, all the four receive the impulfe of’the wind. This, however, is not ftri&ly true, fince the vertical fails are all oblique to the direction of the wind. Let us fuppofe that the area of each fail is 100 fquare feet j then the power of the horizontarfail will be 100, and the power of a vertical fail may be called 100 X fine 700* (70° being the common angle of inclination) r= 88 nearly j but fince there are four vertical fails, the power of them all will be 4x88= 352; fo that the powrer of the horizontal fail is to that of the four vertical ones as 1 to 3.52, and not as 1 to 4, according to Mr Smeaton. 'But Mr Smenton alfo obferves, that if we confider the farther difadvan- tage which arifes from the difficulty of getting the fails back .againft the wind, we need not wonder if horizon¬ tal wind-mills have only about | or ^ the power of the common fort. We have already feen, that the re¬ fiftance occafioned by the return of the fails, amounts to of the whole force which they receive j by fub- tradling —, therefore, from we fliall find that the MECHANIC S. 12; Mechanics, tlie power of horizontal wind-mills is only or lit- l'‘' v tie more than ^ that of vertical ones. This cal¬ culation proceeds upon a fuppofition, that the whole force exerted upon vertical fails is employed in turning them round the axis of motion *, whereas a confiderable part of this force is loft in preffing the pivot of the axis or windlhaft againft its gudgeon. Mr Smeaton has overlooked this circumftance, othervvife he could never have maintained that the power oi four vertical fails was quadruple the power of one horizontal fail, the di- menfions of each being the fame. 1 aking this circum¬ ftance into the account, we cannot be far wrong in fay¬ ing, that in theory at leaft, if not in praftice, the power of a horizontal wind-mill is about or ^ ot the power of a vertical one, when the quantity of iurface and the form of the fails is the fame, and when every part of the horizontal fails has the fame diftance from the axis of motion as the correfponding parts of the ver¬ tical fails. But if the horizontal fails have the pofitjon AI, EG, in fig. 4. inftead of the pofition CA dm, CD 0 their power will be greatly increafed, though the quantity of furface is the fame, becauie the part CP 3 rw being transferred to Bl3*/, has much more power to turn the fails. Chap. VIII. On the Conjiruclion of Wheel Car¬ riages. On the fizc 439- It is evident from Art. 60, that when a wheel of carnage furmounts an obftacle, it aifts as a lever of the firft kind, wheels. ancj that its power to overcome fuch refiftances in- crrxxV creaks w*th its diameter. The power of the force P, j,-- 6. for example, to raife the wheel NB over the eminence C, is proportional to the vertical lever FC, which increafes with the diameter of the wheel, while the lever of refiftance FA, by which the weight of the wheel atts, remains unchanged ; hence we fee the advantages of large wheels for overcoming fuch obftacles as generally refift the motion of wheel-car¬ riages. There are fome circumftances, however, wdiich, independent of the additional weight and expence of large wheels, prefcribe limits to their iize. If the ra¬ dius AC of the wheel exceeds the height of that part of the horfe to which the traces are attached, the line oftraftion DA will be oblique to the horizon, and part of the power P will be employed in prefting the wheel upon the ground. A wheel exceeding four and a half feet radius, which is the general diftance from the ground of that part of the horfe to which the traces are attached, has ftill the advantage of a fmaller wheel j hut when we confider that the traces or poles of the cart will, in this cafe, rub againft the tlanks of the horfes, fo that the power of the wheel is diminifhed by the increafe of its weight, we {hall be convinced that no power is gained by making the radius of the wheels greater than four and a half feet. Even this fize is too great, as (hall be afterwards ftiown, when we treat of the line of traftion, fo that we may fafely af- fert, that the diameter of wheels fhould never be great¬ er than fix feet. The fore wheels of our carriages are ftill unaccountably fmall, and it is not uncommon to fee carts moving upon wheels fcarcely 14 inches in dia¬ meter. The convenience of turning is urged as the rea- fbn for dimipiftiing the fore wheels of carriages, and the facility of loading the cart is confidered as a fufti- Practical cient reafon for ufing wheels fo fmall as 14 inches. Mec'hJlnlcs‘, The firft of thefe advantages, however, may be obtain¬ ed by going to the end of a ftreet, or to a proper place for turning the carriage j and a few additional turns of a vvindlafs will be fuffi-.ient to convey the heavieft loads into carts mounted on high wheels. 440. The next thing to be determined is the fnape of the wheels. Now it is certainly a matter of furprife how the unnatural (hape which is at prefent given to them could ever have been brought into ufe. A cy¬ lindrical wheel, with the fpokes perpendicular to the naves, is undoubtedly the form which every mechanic would give to his wheels, before he had heard of the pretended advantages of concave or diihing wheels, or thofe which have inclined fpokes and conical rims. It has been alleged, indeed, that the form reprefented in fig. 5. when A r, B j is the conical rim, and 0 A, /> B the inclined fpokes, renders the wheel ftronger than it would otherwiie be ; that by extending the bale of the carriage it prevents it from being overturned *, that it ^ hinders the fellies from rubbing againft the load or the fides of the cart j and that when one wheel falls into a rut, and therefore fupports more than one half of the load, the fpakes are brought into a vertical pofition, which renders them more capable of fuftaining the ad¬ ditional weight. Now it is evident that the fecond of thefe advantages is very trifling, and may be obtained, when required, by interpofing a piece of board between the wheel and the load. 441. The other two advantages exift only in very bad roads; and if they are neceffary, which we much queftion, in a country like this, where the roads are fo excellently made and fo regularly repaired, they can eafily be procured, by making the axle-tree a few inches longer, and increafing the ftrength of the fpokes. But it is allowed on all hands that perpendicular fpokes are preferable on level ground. I he inclination of the fpokes therefore, which renders concave wheels advan¬ tageous in rugged and unequal roads, renders them dif- advantageous ■when the roads are in good order j and where the good roads are more numerous than the bad ones, as they certainly are in this country, the difad- vantages of concave wheels mutt overbalance their advantages. It is true indeed that in concave wheels,, the fpokes are in their ftrongeft pofition, when they are expoied to the fevereft {trains, that is, when one wheel is in a deep rut, and fuftains more than one half of the load : but it is equally true that on level ground, wher? the fpokes are in their weakeft pofition, a lets feverc {train, by continuing for a much longer time, may be equally if not more detrimental to the wheel. Upon thefe obfervations, we might reft the opi¬ nion which we have been maintaining, and appeal for its truth to the judgement of every intelligent and unbiaf- fed mind j but we fliall go a ftep farther, and endeavour to (how that concave diihing wheels are more ex pen- five, more injurious to the roads, more liable to be broken by accidents, and lefs durable in general, than thofe wheels in which the fpokes are perpendicular to the naves. By Impeding fig. 5. it will appear that the whole of the preffure which the wheel AB fuftains is exerted along the inclined fpoke fis, and therefore a&s obliquely upon the level ground «D, whether the rims are conical or cylindrical. This oblique a£tion muft neceffarilyy J 25 M E e H A N I C S. Pra^slcs.s neceflarlly injure the roads, by loofening the ftones more V j. between B end I) than between B and ?/, and if the load were fufficiently great, the ftones would ftart up between s and D. The texture of the roads, indeed, is fufficiently firm to prevent this from taking place ; but in consequence of the oblique preffure, the ftones between r and I) will at lead be loofened, and by ad¬ mitting the rain the whole sf the road will be materially damaged. But when the fpokes are perpendicular to the nave as fin, and when the rims mA, are cylindrical, or parallel to the ground, the weight fuftained by the wheel will aft perpendicularly upon the road; and how¬ ever much that weight is increafed, its action can have no tendency to derange the materials of which it is compofed, but is rather calculated to confolidate them, and render the road more firm and durable. 442. It vvas obferved that concave wheels are more expenfive than plane ones. This additional expence arifes from the greater quantity of wood and workman- ihip which the former require; for in order that difhing wheels may be of the fame perpendicular height as plane ones, the fpokes of the former muft exceed in length thofe of the latter, as much as the hypothenufe s'A of the triangle oAn exceeds the fide and there¬ fore the weight and the refiftance of fuch wheels rauft be proportionably great. The inclined fpokes, too, cannot be formed nor inferted with fuch facility as per¬ pendicular ones. The extremity of the fpoke which is fixed jnto^ the nave is inferted at right angles to it, in the direftion ofi, and if the rims are cylindrical, the other fpoke fliould be inferted in a fimilar manner; while the intermediate portion has an inclined pofition. There are therefore two flexures or bendings in the fpokes of concave wheels, which requires them to be formed out of a larger piece of wood, than if they had no fuch flexures, and render them liable to be broken by any fudden ftrain at the points of flexure. 443* fhall now dilmifs the fubjeft of concave wheels with one obfervation more, and we beg the reader’s attention t6 it, becaufe it appears to be decifive of the queftlon. 1 he obftacles which carriages have to encounter, are almoft never fpherical protuberances that permit the elevated wheel to refume by degrees its hori¬ zontal pofition. I hey are generally of fuch a nature, that the wheel is inftantaneoufly precipitated from their top to the level ground. Now the momentum with which the wheel ftrikes the ground is very great, arifing frOt.i a fucceflive accumulation of force. The velocitv Oi .lie elevated wheel is confiderable when it reaches the top of the eminence, and while it is tumbling into the level ground, it is receiving gradually that propoition of the load which was transferred to the other wheel, till having recovered the whole, it impin¬ ges againft the ground with great velocity and force. But in concave wheels the fpoke which then ftrikes the ground, is in its weakeft pofition, and therefore much more liable to be broken by the impetus of the fall, than the fpok.es of the lovveft wheel by the mere tranf- ference of additional weight. Whereas, if the fpokes be perpendicular to the nave, they receive this fudden ftiock in their flrongeft pollution, and are in no danger of giving way to the firain. 444. In the preceding obferrations we have fuppo- led the rims of the wheels to be cylindrical. In con¬ cave wheels, however, the rims are uniformly made of Practical a conical form, as Ar, B r, fig. 5. which not only in- Mechanics, creafes the difadvantages which we have aferibed to ""’“’■v'—**- them, but adds many more to the number. Mr Gum¬ ming, in a late Treat!ie on Wheel Carriages, foiely devoted to the confideration of this fingle point, has ftiewn with great ability the difadvantages of conical rims, and the propriety of making theni cylindrical ; but we are of opinion that he has aferibed to conical rims feveral difadvantages which arife chiefly from an inclina¬ tion of the fpokes. He inlifts much upon the injury done to the roads by the ule of conical rirns; yet though we are convinced that they are more injurious to pave¬ ments and highways than cylindrical rims, we are equally convinced, that this injury is occafiored chiefly by the oblique preffure of the inclined fpokes. The defects of conical rims are fo numerous and palpable, that it is wonderful how they lliould have been fo long overlooked. Every cone that is put in motion upon a plane Surface will revolve round its vertex, and if force is employed to confine it to a ftraight line, the fmaller parts of the cone will be dragged along the ground and the friftion greatly increafed. Now when a carriage moves upon conical wheels, one part of the cone rolls while the other is dragged along, and though confined to a reftilineal direftion by external force, their natural tendency to revolve round their vertex occafions a great and continued friftion upon the linch pin, the ftioulder of the axle-tree, and the fides of deep ruts. 445. The ftiape of the wheels being thus determined, we muft now attend to fome particular parts of their conftruftion. The iron plates of which the rims are compofed ftiould never be lefs than three inches in breadth, as narrow rims fink deep into the ground, and therefore injure the roads and fatigue the horfes. Mr Walker, indeed, attempts to throw ridicule upon the aft of parliament which enjoined the ufe of broad wheels; but he does not afiign any fufficient reafon for his opi¬ nion, and ought to have known that feveral excellent and well devifed experiments were lately inftituted by Boulard and Margueron, which evince in the moft fatif- faftory manner the great utility of broad wheels. Upon this fubjeft an obfervation occurs to us, which has not been generally attended to, and which appears to remove all the objeftions which can be urged againft broad rims. When any load is fupported upon two points, each point fupports one half of the weight; if the points are increaled to four, each will fuftain one fourth of the load, and fo on ; the preffure upon each point of fupport diminiffiing as the number of points increafes. If a weight therefore is fupported by a broad furfoce, the points of fupport are infinite in num¬ ber, and each of them will bear an infinitely fmall por¬ tion of the load ; and, in the fame way, every finite portion of this furface will fuftain a part of the weight inverfely proportional to the number of fimilar portions which the furface contaius. Let us now fuppofe that a cart carrying a load of fixteen hundred weight is fup¬ ported upon wheels whofe rims ars four inches in breadth, and that one of the wheels paffes over four ftones, each of them an inch broad and equally high, and capable of being pulverized only by a preffure of four hundred pounds weight. Then as each wheelTuftains one half of the load, and as the wheel which paffes over 3 MECHANICS. - "Wl over the ftones has four points of fupport, each ftone M- . ; . ■ will bear a weight of two hundred weight, and there- ' fore will not be broken. But if the fame cart, with rims only two inches in breadth, Pnould pafs the lame way, it will cover only two of the Hones; and the wheel having now only twro points of lupport, each ftone will be prelTed with a weight of four hundred weight, and will therefore be reduced to powder. Hence we may infer that narrow wheels are in another " point of view injurious to the roads, by pulverizing the materials of which they are compofed. 446. As the rims of wheels wear fooneft at their edges, they Ihould be made thinner in the middle, and ought to be faftened to the fellies with nails of fuch a kind that their heads may not rife above the furface of the rims. In fome military waggons w7e have (een^ the heads of thefe nails rifing an inch above the rims, which not only deftroys the pavements of ftreets, but oppofes a continual refiftance to the motion of the wheel. It thefe nails were eight in number, the wheel would ex¬ perience the fame refiftance, as if it had to furmount eight obftacles, one inch high, during every revolution. The fellies on which the rims are fixed Ihould in carria¬ ges be three inches and a fourth deep, and in waggons four inches. The naves thould be thickeft at the place where the fpokes are inferted ; and the holes in which the fpokes are placed fhould not be bored quite through, as the greafe upon the axle-tree would infinuate itlelf between the fpoke and the naves, and prevent that clofe adhefion which is neceffary to the ftrength of the wheel. On the Pqfition of the Wheels. 447. It muft naturally occur to every perfon refleft- ing upon this fubjedt, that the axle-trees Ihould ^ be ftraight and the wheels perfedlly parallel, fo that they may not be wider at their higheft than at their loweft point, whether they are of a conical or a cylindiical form. In this country, however, the wheels are always made concave, and the ends of the axle-trees are uni- verfally bent downwards, in order to make them Ipread at the top and approach nearer below. In fome car¬ riages which we have examined, where the wheels were only four feet fix inches in diameter, the difiance of the wheels at top was fully fix feet, and their diftance below only four feet eight inches. By this foolilh pradtice the very advantages which may be derived ±rom the concavity of the wheels are completely taken away, while many of the difadvantages remain ; more room is taken np in the coach-houfe, and the carriage is more liable to be overturned by the contraction or its bafe. 448. With fome mechanics it is a pradice to bend the ends of the axle-trees forwards, and thus maKe the wheels wider behind than before. This blunder has been ftrenuoufly defended by ?vlr Henry Leighton, who maintains that wheels in this pofition are more favourable for turning, fince, when the wheels aie paral¬ lel, the outermoft when turning would prefs againft the linch pin,'and the innermoft would reft againft the Ihoulder of the axle-tree. In redlilineal motions, how¬ ever, thefe converging wheels engender a great deal of fridtion both on the axle and the ground, and muft therefore be more difadvantageous than parallel ones. On the Line of Ttnclion, end the Method by which Mechanics. Horfes exert their frength. ■—' ' 449. M. Camus attempted to (hew that the line of trac¬ tion ihould always be parallel to the ground on which the carriage is moving, both becauie the horfs can exert his greateft ftrength in this ciredtion, and becauie the line of draught being perpendicular to the vertical fpoke of the wheel, afts with the largeft poffible lever. M. Couplet, however, confidering that the roads are never perfedlly level, and that the wneels are conitant- ly furmounting fmall eminences even in the beft of roads, recommends the line of traflion to be oblique to the horizon. By this means the line of draught HA, (which is by far too much inclined in the figure) Fig. placing the centre of gra¬ vity at m. We have ftill, however, to determine the proper length oi b a and b m, the diftance of the cen- * tre of gravity from the axle, and from the horizontal line DA ; but as thefe depend upon the nature and inclination of the roads, upon the length o* the {halt DA, which depends on the fize of the horfe, on the magnitude of the load, and on other variable circum- ilances, it would be impoflible to fix their value. If the load, along with the cart, weighs 400 pounds ; if the diftance DA be eight feet, and if the horie fhould bear 50 pounds of the weight, then b A fliould be one foot, which, being one-eighth of DA, will make the preffure upon D exa&ly 50 pounds. If the road flopes four inches in a foot, bm muft be four inches, or the angle b Am ftrould be equal to the inclination of the road ; for then the point m will rife to « when amend¬ ing fuch a road, and will prefs with its greateft force on the back of the horfe. 454* When carts are not made in this manner, we may, in fome degree, obtain the fame end by judi- dioufly difpofing the load. Let us fuppofe that—t ie centre of gravity ic at O when the cart is. loaded wit a homogeneous materials, fuch as fand, lime, c-c. tien if the load is to confift of heterogeneous fubftances,_ or bodies of different weights, we ftiould place the heavltft at the bottom and neareft the front, which will not on- • Vol. XIII. Part I. ly lower the point 0, but will bring it forward, and Praaical nearer the proper pofition m. Part of the load, too, . might be fufpended below the fore part of the carriage in dry weather, and the centre of gravity would ap¬ proach ftill nearer the point m. When the point m is thus depreffed, the weight on the horfe is not only ju- dicioufly regulated, but the cart would be prevented from overturning j and in rugged roads the weight lul- tained by each wheel would be in a great degree equs- lifed. Defeription of different Carriages. 455. In figure 8. is reprefented a carriage invented by Carriages Mr Richard, a phyfician in Rochelle, which moves th.a^ve without horfes, merely by the exertion of the paffengers. The machinery by which this is effe&ed is placed in a plg. g. box behind the carriage, and is fhewn in figure 9. where A A is a fmall axis fixed into the box, and B a pulley over which a rope paffes whofe two extremities are tied to the ends of the levers ortreddles C, D : the other ends of the levers are fixed by joints to the crofs ‘S' 9' • beam MN. The cranks FF are fixed to the axle K.L, and move upon it as a centre. Each of them has a detent tooth at F which catches in the teeth of the wheels H, H, fo that they can move from F to H without moving the wheel, but the detent tooth catches in the teeth of the wheels when the cranks are brought backward, and therefore bring the wheel along with them. WFen the foot of the paffenger, therefore, is placed upon the treddle D, it brings down the crank F and along with it the wheel H, fo that the large wheels fixed on the fame axis perform part of a revolution ; but when D is depreffed, the rope DA defcer.d'., the extremity C ot the other treddle rifes, and the crank F riling along with it, takes into the teeth of the wheel H, to that when the elevated treddle C is depreffed, the wheels H, H, and confequently the wheels I, I perform another part of a revolution. In this way, by continuing to work at the treddles, the machine advances with a regular pace. 436. A carriage of this kind, wheie tb- meet; mu fin :s much more fimple and beautilul than that which we have deferibed, has been lately invented and conftrud- ed by Mr Na'myth of Edinburgh, a gentleman whofe mechanical genius is fcarcely inferior to his talents as a painter. The pulley B and axle A A, are rendered un- neceffary ; leather itraps are fubftituted in place of the cranks F, F, and the whole mechanifm is contained in two final) cyclindrical boxes about fix inches in dia¬ meter, and one and a hall broad. _ _ . 437. A carriage driven by the adion of the wind is Fig* ie. exhibited in fig. 10 It is fixed on four wheels, and mo-’ ved by the impulfe of the wind upon the fails C, D, being guided by the rudder E. Carriages of this kind will aniwer very well in a level country where the roads are good and the wind fair \ and are laid to be much ufed in China. In Holland they fometimes ufe fimilar vehicles for travelling upon the ice ; but they have a {ledge inftead of wheels, fo that if the ice ftiould happen to break, there will be no danger of finking. Stephirius, a Dutchman is faid to have conftruded one of thefe carriages wuth wheels, wThich travelled at the rate of 21 miles-an hour with a very ftreng wind.^ 458. The carriage reprefented in fig. II. is made Fig. n, fo as to fail againft the wind by means of the fpiral fails i I 30 otiou E, F, G, H, one of which F is expanded by the wind. Machines ^ *le *mPu^£ t^e wind upon the fails gives a rotatory 1 ^motion to the axle M, furndhed with a cog-wheel K, w'hofe trundles ad; upon teeth placed oa the infrde of the fore-wheels. Fi®'. ra. 459- A carriage which cannot be overturned is repre- fented in figure 1 2. where AB is the body of the carriage, confining of a hollow globe, made of leather or wood, the bottom of which is placed an immoveable weight M E C H A N I C S. proportioned to. the load which the carriage is to Defuiptwn bear. Two horizontal circles of iron D, E connected with bars HI, and two vertical circles F, G, furround iVIach^es. the globe 5 and the wheels are fattened by a handle K to the perpendicular bars HI. Then fince the body ^ I3‘ of the carriage moves freely in every cjiredion within the iron circles, the centre of gravity will always be near C, and the carriage will preferve an upright po- fidon even if the wheels and frame were overturned. PART III. DESCRIPTION OF MACHINES. Atwood’s oiachine, Plate ccexxvr. Fur. i. ?. 3 See. Chip. I. Machines which illujirate the doctrines of Mechanics^ or are connected with them. I. Atwood's Machine. 4f)0. THE ingenious machine invented by Mr Atwood for illultrating the dodrines of accelerated and retarded motion, is reprefented in figs. 1, 2, 3, 4, 5, 6, and en¬ ables us to difeover, 1. The quantity of matter mo- veT 2..The moving force. 3. The fpa.ee defer!bed. 4. The time of defeription j and 5. The velocity ac¬ quired at the end of that time. 461. 1. Of the quantity of matter moved.—In order to obferve the effeds of the moving force, which is the ob- jed of any experiment, the interference of all other forces fhould be prevented : the quantity of matter moved, therefore, confidering it before any impellin j force has been applied, fliould be without weight ; for though it be impoinble to abftrad weight from anv Tig. r. fubltance whatever, yet it may be fo counteraded as to produce no feniible effed. Thus in the machine fig. 1. A, B reprefent two equal weights affixed to the extremities of a very fine filk thread : this thread is ftretched over a wheel or fixed pulley abed, move¬ able round a horizontal axis: the two weights A,B being equal and ading againft each other, remain in equilibrio 5 and when the leaft weight is fuperadded to either (fetting afide the effeds of fridion), it will preponderate. When A, B are fet in motion by the adion of any weight m, the fum A-fB-fw, would coufhtute the whole mats moved, but for the inertia of the materials, which muff neceffarily be ufed in the communication of motion. Thefe materials confifl of, 2. 'i he wheel abed, over which the thread fudaining A and B paffes. 2. I he four tridion wheels on which the axle of the wheel abed reffs. 3. The thread by which the bodies A and B are conneded, fo as when fet in motion to move with equal velocities. The weight and inertia of the thread are too frnall to have any fenfible effed on the exoeriments ; but the inertia of the other materials conftitute a confiderable propor¬ tion of the mafs moved, and mull therefore he taken into account. Since when A and B are put in mo¬ tion, they muff move with a velocity equal.to that of the circumference of the wheel abed to which the thread is applied j it follows, that if the whole mafs of the wheels were accumulated in this circumference, its in¬ ertia would be truly eftimated by the quantity of mat¬ ter moved ; but fince the parts of the wheels move vyith different velocities, their effeds in refilling the communication of motion to A and B by their inertia will be different ; thofe parts which are* furthell from the axis refilling more than thole which revolve nearer in a duplicate proportion of thofe diilances, (fee Rota¬ tion). If the figures of the wheels were regular, the didances of their centres of gyration from their axes of motion would be given, and confequently an equivalent w-eigNht, which being accumulated uniformly in the circumference abed, would exert an inertia equal to that of the wheels in their conllruded form, would alfo be given. But as the figures are irregular, recourfe mult be had to experiment, to affign that quantity of matter, which being accumulated uniformly hr the cir¬ cumference of the wheel abed, would refill the com¬ munication of motion to A in the fame manner as th© wheels. In order to afeertain the inertia of the wheel abed, with .that of the fridion wheels, the weights AB being removed, the following experiment was made : . A wight of 30 grains was affixed to a filk thread of mconliderable weight 5 this thread being wound round the wheel abed, the weight 30 grains by defeend- ing from red communicated motion to the wheel and by many trials was obferved to deferibe a fpace of about 38-j inches in 3 feconds. From thefe data the equivalent mafs or inertia of the wheels will be known from this rule. Let n weight P, fig. 2. be applied to communicate motion to a fyftem of bodies by means of a very flenderFi£- and flexible thread going round the wheel SLDiM tnrough the centre of which the axis paffes (G beincr’ the common centre of gravity, R the centre of gravity or tne matter contained in this line, and O the centre of olcillation). Let this weight delcend from red through any convenient fpace r inches, and let the ob- ferved time of its defeent be t feconds 5 then if / be the [pace through which bodies defeend. freely by gravity in one fecond, the equivalent weight fought = WxSRxSO P X /V SD1 “ ^ “P* Here we have />—30 grains, r-3 feconds, l~ 193 P X — P— 30X9X193 inches, r—38.5 inches j and 385 30—1323 grams, or 2| ounces. This is the inertia equivalent to that of the wheel aoed, and the friclion wheels together: for the rule extends to. the edimation of the inertia of the mafs contained in all the wheels. The refida.nce to motion therefore arifing from the wheel’s inertia, will be the fame as if they were cblo--• fplutely \ \ MECHANICS. r3* Defcrtpuon lately reitioved, and a mafs of 2|- ounces uniform- c'f. ly accumulated in the circumference of the wheel ‘Machines. a c 'J'his being premifed, let the boxes A and B be replaced, being fufpended by the filk thread over the wheel or pulley abed, and balancing each other : fuppofe that any weight m be added to A fo that it fhall defeend, the exaft quantity of matter moved, dur¬ ing the defeent of the weight A, will be afeertained, for the whole mafs will be A-f-B-f-t*-}-2oz. In order to avoid trouhlelbme computations in ad- jufting the quantities of matter moved and the moving forces, feme determinate weight of convenient magni¬ tude may be affumed as a standard, to which all the ethers are referred. This ftandard weight in the fub- fequent experiments is ^ of an ounce, and is reprefent- ed by the letter m. The inertia of the wheels being therefore ounces, will be denoted by 11 A and B are two boxes conftrudted fo as to contain differ¬ ent quantities of matter, according as the experiment may require them to be varied : the weight of each box, including the hook to which it is fufpended, mi oz. or according to the preceding eftimation, the weight of each box will be denoted by 6 m ; thefe ^ boxes contain fuch weights as are reprefented by fig. 3. each of which weighs an ounce, fo as to be equiva¬ lent to 4 w-, other weights of \~m, and aliquot parts of my fuch as may be a!fo in¬ cluded in the boxes, according to the conditions of the different experiments hereafter deferibed. If 4^ oz. or 19 m, be included in either box, this with the weight of the box itfelf will be 2577* •, fo that when the weights A and B, each being 25 m, are ba¬ lanced in the manner above repvefented, their whole mafs will be 30 m, which being added to the inertia of the wheels 11 m, the fum will be 61 m. Moreover, three circular weights, fuch as that which is repre¬ fented at fig. 4. are conflrufted ; each of which oz. of vi : if one of thefe be added to A and one to B, the wrhole mafs will now become 63 m, perfectly in equili- brio, and moveable by the leaf! weight added to either (fetting afide the effeiffs of friftion), in the fame manner precifely as if the fame weight or force were applied to communicate motion to the mafs 63 m, exifling in free fpace and without gravity. 462. 2. The moving force. Since the wTeight of any fubftance is conftant, and the exafl quantity of it cafily eflimated, it will be convenient here to apply a weight to the mafs A as a moving force : thus, when the fyf- tem confifls of a mafs according to the preced¬ ing defeription, the w’hole being perfectly balanced, let %• 5* a weight ^ oz. or m, fuch as is reprefented in fig. 5. be applied on the mafs A 5 this wall communicate motion to the whole fyflem ; by adding a quantity of matter tn to the former mafs 63 m, the w'hole quantity of mat¬ ter moved will now' become 64/775 and the moving force being ~m, this will give the force which accel¬ erates the defeent of K—-—-—, or ~ part of the acce- 64772 ^64 lerating force of gravity. By the preceding conftruflion, the moving force may be altered without altering the mafs moved ; for fuppofe the three weights m, twro of which are placed on and one on B, to be removed, then will A ba¬ lance B. If the weights 3 m be all placed on A, the moving force will become 3 77/, and the mafs moved Defcriptiofa 64772 as before, and the force which accelerates the dc- jVTalj1;re3 3 m _ 3 parts of the force by which gra- feent of A- ^ 64 772 64 vity accelerates falling bodies. Suppofe it were required to make the moving force 2 772, the mafs moved continuing the fame. Let the three weights, each of which = 7/2, be removed 5 A and B wall balance each other 5 and the whole mafs will be 6 x 772: let \tn, fig. 5. be added to A, and •jTTzFig. 5. to B, the equilibrium will be preferved, and the mafs moved will be 62 m 5 now let 2 772 be added to A, the moving force will be 2/77, and the mafs moved 64772 as before ; wherefore the force of acceleration Part of the acceleration of gravity. Thefe alterations in the moving force may be eafily made in the more elemen¬ tary experiments, there being no necefiity for alter¬ ing the contents of the boxes A and B : but the pro¬ portion and abfolute quantities of the moving force and mafs moved, may be of any affigned magnitude, ac¬ cording to the conditions of the propofition to be illuf- trated. 463. 3. Of the [pace deferibed. The body A, fig. 1. pjg. It defeends in a vertical line 5 and a fcale about 64 inches in length divided into inches and tenths of an inch is adjufted vertical, and fo placed that the defeending weight A may fall in the middle of a fquare ilage, fixed to receive it at the end of the defeent : the beginning of the defeent is eftimated from o on the fcale, when the bottom of the box A is on a level with o. The de¬ feent of A is terminated when the bottom of the box ftrikes the dage, which may be fixed at different diftan- ces from the point o 5 fo that by altering the pofition of the fidge, the fpace deferibed from reft may be of any given magnitude lefs than 64 inches. 464. 4. The tune of defeription is obferved by a pendu¬ lum, vibrating feconds 5 and the experiments intended to iliuftrate the elementary propofitions, may eafily be fo conftruffed that the time of motion (hall be a whole number of feconds. The eftimation of the time, there¬ fore, admits of confiderable exactnefs, provided the ob- ferver takes care to let the bottom of the box A begin its defeent precifely at any beat of the pendulum 5 then the coincidence of the itroke of the box againft the ftage, and the beat of the pendulum at the end of the time of motion, wall (how how nearly the experiment and the theory agree. There might be various devices for letting the weight A begin its defeent at the infianp of a beat of the pendulum W 5 for inftance, let the bottom of the box A, when at o on the fcale, reft on a flat rod, held in the hand horizontally ; its extremity being coincident with o, by attending to the beats of the pendulum 5 and with a little practice, the rod which fupports the hex A may be removed at the moment the pendulum beats, fo that the defeent of A fliall commence at the fame inftant. 46 5. Of the velocity acquired. It remains only to dr- feribe in w’hat manner the velocity acquired by the de¬ feending weight A, at any given point of its path is made evident to the fenfes. The velocity of A’s de¬ feent being continually accelerated will be the fame in two points of the ipace defciabed. This is occafioned by the conftant adlion of the moving force 5 and fince the velocity of A at any iuftant is xneafured by the fpace R 2 wThieh of Machines. Fig 6. ,32 M E C H Defcription which would be deicribed by it moving uniformly for a given time with the velocity it had acquired at that in- ftant, this mealure cannot be experimentally obtained, except by removing the force by which the defcending body’s acceleration was caufed. In order to (how in what manner this is effefted par¬ ticularly, let us again fuppofe the boxes A and B~25m each, fo'as together to be =50 m; this with the wheel’s inertia 11 m will make 61 m; now let m be added to A, and an equal weight m to B, thefe bodies will ba¬ lance each other, and the whole mafs will be 63 tn. If a weight tn be added to A, motion will be commu¬ nicated, the moving force being m, and the mafs mov¬ ed 64 m. In eftimating the moving force, the circular weight —m w'as made ufe of as a moving force : but for the prefent purpofe of {bowing the velocity acquir¬ ed, it will be convenient to ufe a flat rod, the weight of which is alfo ~m. Let the bottom of the box A be placed on a level with o on the fcale, the whole mafs being as defcribed above =63 m, perfectly balanced. Now let the rod, the weight of wdiich —m, be placed on the upper furface of A; this body will delcend along the fcale in the fame manner as when the moving force w7as applied in the form of a circular weight. Suppofe the mafs A, fig. 6. to have defcended by conftant accel¬ eration of the force of m, for any given time, or through a given fpace : let a circular frame be fo afRxed to the fcale, contiguous to which the weight defcends, that A may pafs centrally through it, and that this circular- frame may intercept the rod m by which the body A has been accelerated from reft. After the moving force m has been intercepted at the end of the given fpace or time, there wall be no force operating on any part of the fyftem which can accelerate or retard its motion : this being the cafe, the weight A, the inftant after m has been removed, muft proceed uniformly w-ith the velocity wdiich it had acquired that inftant : in the fubfequent part of its defcent, the velocity being uni¬ form will be meafured by fpace defcribed in any conve¬ nient number of feconds, 466. Mr Atwood’s machine is alfo ufeful for eftima¬ ting experimentally the velocities comn unicated by the impadl of bodies elaftic and nonelaftic •, the quantity of reliftance oppofed by fluids, as well as for various other purpofes. Thefe ufes we {hall not infill on ; but the properties of retarded motion being a part of the pre¬ fent fubjehl, it may be neceffary to {how in what man¬ ner the motion of bodies refilled by conftant forces are reduced to experiment by means of the inftrument above defcribed, w'ith as great eafe and precifion as the pro¬ perties of bodies uniformly accelerated. A fingle in- llance will be fufficient: Thus, fuppofe the mafs con¬ tained in the weights A and B, fig. 6. and the wTeels to be 61 nr, when perfedlly in equilibrio let a circular weight m be applied to B, and let twm long weights or rods, each —m, be applied to A, then will A defcend by the aclibn of the moving force m, the mafs moved ,, bSing 64 m : fuppofe that when it has defcribed any gi¬ ven fpace by contlant acceleration, the twTo rods m are intercepted by the circular frame above defcribed, while A is defcending through it, the velocity acquired by that defcent is known ; and when the two rods are in¬ tercepted, the weight A will begin to move on with the velocity acquired, being now retarded by the con¬ ftant force m; and iince the mafs moved is 62 tn, the A N I C 3. force of retardation will be ^ part of that force'where- Defcrfptio* by gravity retards bodies thrown perpendicularly up- °f wards. The weight A will therefore proceed along ^ a chines^ the graduated fcale in its defcent, with an uniformly retarded motion, and the fpaces defcribed, times of mo¬ tion, and velocities deftroyed by the refilling force, will be fubjedl to the fame meafures as in the examples of accelerated motion already defcribed. In the preceding defer!ptions, two fuppofitions have been aflumed, neither of which is mathematically true : but it might be eafily ftrown that they are fo in a phyfical fenfe 5 the errors occafioned by them being infcnfible in prablice. 2 Machine for illuf rating the Theory of the Wedge. 467. This machine is reprefented in fig. 7. where Plate KiLM and LMNO are two flat pieces of wood joined-CCCXXVI* together by a hirfge at LM ; P is a graduated arch on*1^?” which thefe pieces of wmod can be moved fo as to fub- tend any angle not greater than 6o°, and a, b tw’o ferews for fixing them at the required angle. The back of the wedge will therefore be reprelented by IKNO, its {harp edge by LM, and its two fides by KILM, LMNO. The weight p fufpended to the v\edge by the hook M, and the weight of the w'edge itfelf, may be confidered as the force employed to drive the w'edge. The wooden cylinders AB, CD, have their extremities made like two flat circular plates to prevent the wedge from flipping off at one fide. To the pivots of thele cy¬ linders, two of which are reprefented at e andy^ are fatt¬ ened the cords Wjy'U, CV, AX, which palling over, the pulleys U, V, X, W are faftened to the two bars uv, x w, on which any equal weights Y, Z may be hung at pleafure. The tendency of thefe weights is evidently to draw the cylinders towards each other, and they may therefore be regarded as the refiitance of the wood adting againft the fides of the wedge. The cylinders themfelves are fufpended by their pivots to the threads E, F, G, H, which may be fixed to the ceiling of the room, or to the horizontal beam of a frame made on purpofe.—By placing various equal weights at Y and Z, it may be eafy to determine the proportion be- tw'een the power and the refiftance when the wedge is in equilibrio.—In this machine the impelling power is the preffure of the weight p, whereas, in the real wedge, the impelling pow'er is always an impulfive force w'hich is infinitely more powerful. 3. Machine for illuf rating the effeBs of the centrifugal force in flattening the poles of the Earth. 468. Fig. 8. reprefents this machine, which confifts of two flexible circular hoops, AB and CD, crofting pne another at right angles, and fixed to the vertical axis EF at its lower extremity, but left looie at the pole or iwterfedlion e. If this axis be made to revolve rapidly by means of the winch tn, and the wheel and pinion n, 0, the middle parts A, B, C, D will, by their cen¬ trifugal force, fwell out and tlrike againft the frame at F and G if the pole e, when finking, is not flopped by means of a pin E fixed in the vertical axis. The hoops, therefore, will have a fpheroidal form ; the equatoreal being larger than the polar diameter. Machine 4. Machine for trying the Strength of Materials. [jetoengtli 469. The piece of wood, whofe ftrength is to beofmRte' tried,nals* MECHANICS.. 133 Drfcriptatmd, is represented by EF, and the force is applied to of it by means of the winch A, which winds up the rope ^Machines paffing over the pulley w, and below the pulley w, y~~7Cr' and’attached to the point D of the beam EF. The cccxxvn. pulleys Hide on two parallel bars fixed m a frame, held i'ig. i. down by a projeding point, at G, of the lever GR, which is graduated like a fteelyard, and meafiires the force employed. The beam EF is held by a double vice IK with four ferews, two of which are mvmble. When a tvire is to be torn it is fixed to the crofs bar LM i and when any body is to be cruflied, it mutt be placed beneath the lever NO, the rope BC being fix¬ ed to the hook N, and the end O being held down by the click which a£ts on the double ratchet OP. The lever is double from O to Q., and ads on the body by a loop fixed to it by a pin. See Young's Nat. Philof. vol. i. p. 768. from which this drawing and defeription are taken. 5. Machine in which all the Mechanical powers are combined. Combina- 470. The lever AB, whofe centre of motion is C, is tioo of all fixed to the endlefs ferew DE, which drives the wheel the mecha- ancj axle FHG. Round the axle G is coiled a rope meal pow- which paffes round the four pulleys K, L, m, n, and is’ fixed to a hook at m on the lower block, which carries the wTeight W. When equal weights are fu- fpended on the lever at equal diilances from the ful¬ crum C, the lever becomes a balance, and the wedge and inclined plane are evidently included in the endlefs ferew DE. If the wheel F has 30 teeth, if the le¬ ver AB is equal to twice the diameter of the wheel FH, and if the diameter of the axle G is one-tenth of the diameter of the wheel, a power of 1 exerted at P will raife a weight of 2400 fufpended at the lower block of the four pulleys. fufpended at A, will be in equilibrio with n placed at Cefcnption -Append, to Ter- Machines. S « Xtf FA ers. Fig. 2. 6. Tidier1 s Balance. Fidler’s ba- 47^ The balance reprefented in fig. 3. was made lance. by Fidler for the Royal Inftitution, and does not differ Fig. 3. much from thofe which have been conllruCfed by Ramfden and Troughton. The middle column A can be railed at pleafure by the nut B, and fupoorts the round ends of the axis in the forks at its upper extremity, in order to remove the preffure on the iharp edges of the axis within the forks. C and D are pillars which occafion- ally fupport the fcales, and may be elevated or deprei- fed by turning the nut E. The ferew F raifes or ds- prefles a weight within the conical beam, for the pur- pofe of regulating the polition of the centre of gravity, qphe graduated arc G meafures the extent of the viola¬ tions. See Young's Nat. Phil. vol. i. p. 765- 7. Improvement on the Balance. Improve- 472. An improvement on the balance is reprefented menton jn ^ where DC is a micrometer fecew fixed to the ^ arm FA, fo that when it is turned round by the nut D, it neither anproaches to, nor recedes from, the centie of motion F. The ferew DC works in a female ferew in the fmall weight «, and by revolving in one direc¬ tion, carries this weight from S to R, and thus gives the preponderance to the fcale G. I he receffion of tne weight n from the centre F is meafured as in the com- moii micrometer, and a weight x placed in the icale the ba lance. Fig: 5- any diftance S n. when x— gufon's Lettures. 8. Machine for Jhewing the Compofition of torces. 473. The part BEFC is made to draw other parts into Machine the wooden fquare ABCD. The pulley FI is joined compofitioR to BEFC fp as to turn on an axis which will be^at H0fforces, when the fquare BEFC is pulhed in, and at/> when itFig.4. is drawn out. A ball G is made to Hide on the wire k which is fixed to BEFC, and the thread ot attached to the ball goes over the pullev to I, where it is fixed. Now, when the piece BEFC is palled out, the pulley, wire, and ball, move along with it, in the direction DCF, and it is evident that the ball G will Hide gra¬ dually up the wire k. It is therefore afted upon by two forces ; one in the direction GFI, and the other m the diredion GC, and will be found at the end of the motion at £•, having moved in the direftion G^, the diagonal of a parallelogram whofe fides are GH, GC. 8. Smeaton's Machine for experiments on Windmill Sails. 474. In the experiments with this machine, the fails Apparatus were carried round in the circumference of a ciicle, that the fame effeft w-as produced as if the wind hadftruck ^ the fails at reil with the velocity which was then given them. In the pyramidal frame ABC is fixed to the axis DE, which carries the arm FG with the iails GI. By pulling the rope Z, which coils round the barrel H, a motion of rotation is given to the lails, fo that they revolve in the circumference of a circle, whole radius is DI. At L is fixed a cord which paffes round the pul¬ leys M, N, O, and coils round a fmall cylinder on the axis of the fails and raifes the fcale C, in which diffe¬ rent weights are placed for trying the power of the fails, and which, being in the direction of the axis DE, is not affe&ed by the circular motion of the arm DG. The fcale C is kept fteady by the pillars Q.^R> an(l prevented from fwinging by the chains S, 1, which hang loofely round the pillars. VX is a pendulum compoied of tw o leaden balls moveable upon a wooden rod, fo that they can be adjufted to vibrate in any given time. The pendulum hangs upon a cylindrical wire, on which it vibrates as on a rolling axis. 9. Smeaton's Machine for experiments on Rotatory Motion. 4-75. This machine is exhibited in fig. 1. where the Apparatus vertical axis NB is turned by the rope M palling over the pulley R, and carrying the fcale S. The axis NB tjon> •carries twro equal leaden weights K, D, moveable at plate pleafure on the horizontal bar. Fa I. 1 ne upper pait N ofcccxxvm the axis is one half the diameter of the part M, fo that ^ ‘A when the rope is made to wind round N, it atts at half the diftance from the axis, at .which it adts wh/n coiled round M.—When the rope is wound round N, the fame force will produce in the lame time but half the velocity which is produced wFen the rope coils round M, the fituaticn of the leaden weights being the fame : But when the weights K, L are removed to a double diftance from the axis, a quadruple force will be required in order to produce an equal angular velo¬ city in a given time. Chaw, MECHANICS. 134 D efcriptioi^ of Machines. Chap. II. Machines for various purpsfes. 1. Promfs Condenfer of Forces. denferof0"’ 476' Tlle objca ?f machine is to obtain a maxi- forces. mum f ffecl from an impeding power which is fubjecl to Plate variation in its intenfity. Let us fuppofe that wind is the cccxxvm. fir ft mover, and that O, O is the vertical axis of a wind- mill; e, e, e, c, are feveral radii ifluing from this axis, and carrying a wiper b d, which acts upon the corref- pcnding wipers af and give a motion of rotation to the axis a, a, a, a to which they are attached. The wipers b d, a f muft be fo conftrufted that when ^ d ceafes to prefs on one wiper a f it fhall at the lame moment begin to act upon the next wiper. Each of the . axes a, a, a, a, carries a drum 11 r r, round wdiich is coiled a cord tp F, pa fling over the pulley p, snd fupporting a weight O which can be placed at dif¬ ferent diilances from G on the lever EG. The axes , a, tf, a alfo pafs through the pinions qq, to which they are not fixed ; but thefe pinions carry ratchet v...eels thht bear againft the teeth r r, fo that when the weight if mes, the rope merely coils round the drum w uhout moving the pinion q q. But when the viper b dceafes to aft upon af the weight O defeends, and then the toothed wheel r r a£ls againfl: the ratchet, ^0 that O cannot defeend without turning the pinion q q along with the drum. The pinion qq drives the wheel t? b, which again drives the wheel CE by means or the bevelled teeth CD, and elevates the load at P. Hence, when the axis OO is put in motion by the wind acling on the fails, it will firft raife a number of weights £) fufticient to^ put the machine in motion, and will continue to raife new weights while thofe Before raifed are faliep, fo that the motion once imprefled will be continued. 2. Portable Stone Crane, for loading and unloading Carts. Portable rp, . . > ftone crane.. * h,s crane ls mounted on a wooden ftage, and Eg-4. is to conftrutfted that it may betaken to pieces. The frame A, A, A, A is about ten feet high, nine feet long and nine feet wide. The wheels B, B are of iron and about three feet in diameter. The pinion D that is fixed to the axis of the firft wheel B is eight inches diameter and the other pinion C is about the fame dia¬ meter. When the Hones are fufpended to the rone that rods round the barrel, the workman turns a winch on the axis of the wheel C, and raifes or lowers the weight according to the diiedion in which he turns it. Portable „ . S ^Me Celhr Crane. eellar 47°‘ ^ “!S orane is reprefented in fig. 5. where A A crane. are two wooden fupports about fix feet high, which’are ‘S- 5- jomted at E, and conne£led by the iron cylinder C and the wooden bar D. The fupports A, A are faftened to the edge of the cellar by the iron prongs E, E and the two ropes which fupport the barrel and Pafs round it are fixed to the iron damp G, G. Thefe repes coil round the cylindrical bar F, which is put in motion by the winch K, driving the pinion I about four inches dia¬ meter, which gives motion to the wheel H, about three feet m diameter. The barrel, therefore, will rife or aceordmg to the direction in which the winch is 4. Weighing Crane. Defcnption 479. This crane reprefented in fig. 6. was invented ^-at:lnnes. by Mr Andrews, and weighs the body at the time that "1^ it is railing it. 1 he weight W is elevated by means of HCCXXX. the levers M, N, O, P which coil the rope HR round Fig. 6. the barrel H. The jib ED ftands on a horizontal AE^ews,s beam moveable in a vertical plane round the centre hA, and the diftance of the upright beam E from the centre of. motion A is TV of BE. The weight of the body \\ is then afeertamed by the weight at B, wdiich keeps it in equiiibrio. The piece of wood C prcjecis from the vertical beam CT ' 1 ' beam from riling too high. weighing crane. in order to prevent the 5. Gilpin's Crane. 480. In Eg. I. where this machine is reprefented, Gilpin’s AB is the perpendicular Hand, formed of two oaken crane, planks let into call iron mortifes C, D : Between thefe planks is fixed the barrel E with fpiral grooves on its C_CCXXIX- fm-face, on which the chain RL windL' When the F‘S'r’ winch N is put in motion it drives the pinion O, which 4’ 5' again drives the wheel P, on whole axis is fixed the bairel fi, fo that the chain is coiled round the barrel and the weight raifed. A fetfion of this part of the machinery is fhewn in fig. 2. Figure 3. ihews an en- larged.view of part of the barrel, and part of the chain lying in its proper polition in the fpiral grooves or channels. In order to prevent the chain from twilling when it is-wound upon the barrel, the lower edge of one link lies in the groove, and the next link upon the furface of the barrel. This will be better und'erflood .rom fig. 4. Y\hich is a fe&ion of the barrel F, and liicws the manner in which one link lies within it, and the other link on its outfide. The old method of working chains is exhibited in fig. 5. For a full ac¬ count of this ufeful invention, fee Nicholfon’s Journal vol. xv. p. 126. ’ 6. Bramah's Jib for Cranes. • 14?Ih7 *Je natltre invention, for which we are Bramah’s indebted to the ingenious Mr Bramah, may be eafily ftb. underftood from a bare infpeaion of fig. 6. which re-Fi^5, prefents a jib attached to the wall of a warehoufe. The jib turns on a perforated axis or pillar. The rope by which the weight is raifed after palling over two pulleys, goes through the perforated axis, and is conduced over another pulley to the barrel of the crane, which is not reprefented in the figure. In jibs of the common con- .ruction which turn in two folid gudgeons, the rone patles over the upper gudgeon, and is confined between two vertical rollers ; but the bending of the rope oc- cafions a great deal ofiiiaion, and produces a conftant ettort to bring the arm of the jib into a pofition parallel to the inner part of the rope. 7- Gottlieb's Carriage Crane. 482. This machine, which is ufeful for carrying lame P!ate fiones where carts and horfes cannot be eafilv obtain^ CCCXXIX' rfi07 T7 f? <*.«“' ^ aPrW. jo fets of wheels belonging'to the carriage, fo that two crane.2' men one afting at each winch A, A give motion to the loaded carnage- The pinion B, fix inches in dia¬ meter turns the wheel C, three feet in diameter. The wheel C gives motion to the pinion D one foot in dia¬ meter, M E C H Defcriptionmeter, which works into two wheels E, E three feet fix inches diameter, and are fixed on the wheels of the Machines. « carnage. 8. Common 'Jack. Common 4^3- ^'^e comrnon worm jack is reprefented in fig. 8, jack. and is impelled by the weight W, which is fufpended to Fig- 8. a rope paffing through the pulleys V, R, and rolling round the barrel When the barrel is put in motion by the action of the weight, it drives the wheel KL of Oo teeth, by means of a catch fixed to AB, which lays hold of the crofs bars in KL. The wheel KL drives the pinion M of 15 teeth, fixed on the axis of the wheel N of 30 teeth, which gives motion to the end- lefs (crew O, and the fly-wrheel P. On the axis of the wheel KL is fixed the pulley DG, which by means of a rope gives motion to the fpit. The axis ET is fixed in the barrel AC \ and as this axis is hollow, both it and the barrel turn round upon the axis ED, fo that the rope may be coiled round the barrel by the winch K without moving the wheel K. 9. Loading and Unloading Machine. Loading 484. This portable machine, invented by Mr Daviskif and unload- Windfor, is put in motion by the winch A, which dmr*3' drives the two endlels {crews C, C. Theie fcrews Pirr.^. move the wheels E, E, and confequently the barrels connefted with them, fo that the ropes F, E paffing over the pulleys G, G are coiled round the barrels, and the load H which thcfe ropes fupport is railed into the frame R,R, which thews a part of the cart. The barrels and wheels are contained in an iron box L, the fides of which are removed in the figure. 10. Vauloue's Pile Engine. ’Vauloue's pile engine. Plate cccxxx. Fig. 1. Fig. 7. 485. The horfes which work this engine are yoked at S, S, and by moving the wheel B and drum C, which are locked together, raife the follower CH, (car¬ rying the ram O by the handle R,) by means of the rope HH which coils round the drum. When the fol¬ lower G reaches the top of the frame, the upper legs of the tongs H are clofed by preffing agajnft the adja¬ cent beams ; and their lower legs are opened, fo that they drop the ram Q, which falls and ftrikes the pile. When G is at the top of the frame, the crooked handle 6, of the follower G, preffes aghinft the cords a, a, which raife the end of the lever L (fee fig. 2.) round m as a centre, and by depreffing the extremity N, and confequently the baTS, S, unlock the drum C and the wheel 8, fo that the follower G falls by it ; weight and A N I C S. .to Lizes the ram R. As foon as she follower drops, the Defeription horfes would tumble down, having no refittance to ^ overcome, were not this prevented by the fly O, which * RC is moved by the -wheel B and trundle X, and oppofes a fufficient refiftance to the horfes till the follower again feizes the ram. When the follower falls, the weight L (fig. 2.) puflies up the bolt Y into the drum C, and locks the wheel and the drum;—and the fame operation is afterwards repeated. See Fergufori's LeEl. vol. i. p. 118. 11. Bunce's Pile Engine. 486. A fide view of this engine is (hewn in fig. 3, 4. Buncc’s It confifls of two endlefs ropes or chains A, connected Pf*6 engm.e»' by crofs pieces of iron B, B, &c. (fig. 4.) which pafs^1^'^ round the wheel C, the crofs pieces falling into corre- fponding crofs grooves, cut in the periphery of the wheel. When the man at S, therefore, drives the wheel m by means of the pinion />, he moves alfo the wheel C fixed on the axis of m, and makes the double ropes revolve upon the wheels C, D. The wheel D is fixed at the end of a lever DHK, whofe centre of mo¬ tion is H, a fixed point in the beam FT. Now, when the ram L (fig. 3, 5.) is fixed to one of the crofs' pieces B by the hook M, the weight of the ram, adding by the rope, moves the lever DK round H, and brings the wheel D to G, fo that, by turning the winch, the ram L (fig. 3.) is railed in the vertical line LRG. But when it reaches R, the prcje&ing piece R difen- gages the ram from the crols piece B, by ftriking the bar \ and as the weight is removed from the extre¬ mity E of the lever, the counterpoife I brings it back from G to its old pofition at F, and the ram falls with¬ out interfering with the chain. When the hook is def- cending, it is prevented from catching the rape by means of the piece of wTood N fufpended from the hook hi at O ; for being fpecifically lighter than the iron weight L, and moving with lefs velocity, it does not come in contadl with L till the ram is flopped at the end of its path. When N, therefore falls upon L, it depreffes the extremity M of the hook, and therefore brings the hook over one of the crofs pieces B, by which the ram is again raifed. 487. For the defeription of a great variety of uftful machines, the reader is referred to the iccond volume of Mr Gregory’s Mechanics, and to Dr Young’s Natural Philofophy, a work of great merit, which would have been more particularly noticed if it had reached us be¬ fore the hiftorical part of this article was printed off.— See alfo Hydrodynamics, Marly, Machine at, Mill, Ramsden, and V/ATik lVorks. I N D E X. Abutments, conflruclion of, N° JEpinus's property of the lever, d'Mlembert's principle of dynamics, equilibrium of, catenarian, of equilibration, Mtwood’s machine B. 336 64 22 316 3J9 334 460 Balance, its properties, Iisj 2 Balance, K uh ne’s, Magellan’s, Ludlam’s, Fidler’s improvement on it, Bevelled wheels, Borel/i, works of, c. N* 151 23 2 153 471 472 407 14 Caftftane, defeription of one, 368 Carriages, wheel, or. the couikucllon of, 439 Cellar crane, Centre of inertia, or gravity, how to find it, N° 4, 154, 20tf Centrobaryc method, 206, 208 Collijion, laws of, diicovered by Wren, otc. 12 of hard bodies, 248—258 - of elaftic bodies, 258—279 of imperfeClly elaflic bodies, 279 . Condcnfer of forces, Conical l 1 36 Conical pendulum, N° 394 Corfervaiion of afllve forces difcover- ed by Huygens, 19 generalifed by D. Ber¬ noulli, ib. Coulomb ox\ the force of torfion, 27, 343 —357 * on friflion, 27, 372 on the rigidity of ropes, 382 on the Orength of men, 421 Crane, carriage, Gilpin’s, 48° cellar, 47^ weighing, 479 Croivn wheels, 410 Curves, motion of bodies along, 217 of cjiuckeft defcent, 231 Cycloid, ifochronifm of, difcovered by Huygens, 11 properties of it, 232 the propgr curve for the teeth of rackwork, 411 Ci/cloidal pendulum, properties of, 236 Cylinders, friftion of loaded ones 372 D. .Dcwer, equilibrium of, 339 E. machine for explaining the flat- nefs at its poles, Epicycloids the proper curves for the teeth of wheels, 395 interior, 397 exterior, ib. method of forming them, 406 F. Tidier"1 s balance, Fly wheels, 383 Forces, adlive, difpute about them, Frifiion wheels, 377 Fufee of a watch, its conftruftion, 99 G. Galileo, difcoveries of, refpefting the fcience of motion, 8 Gottlieb"'s antiattrition axletree, 377 Gravity, centre of, 154—201 force of, 2 47 Gregory, Olinthus, his Treatife on Mechanics recommended, 28 H. de la Hire, on the teeth of wheels, 17 Horfes, ftrength of, 423 method in which they exert it, 449 Huygens, difcovefies of, 11, 19 I. Jack, common, 483 Jib, Bramah’s, 481 Itnpuljion. See Colli/ion, Inclined plane, properties of it. . 69 its ufe in praftical mechanics, 83 planes, motion of bodies along, 2T7 Inertia, centre of. 134—201 Involutes proper for the teeth of wheels, 405 L. Lever, properties of, 53—69 MECHANICS. Lever, various modes of deducing its fundamental property, N° 63 yEpinus’s property of, 65 compound, 64 M. Machine, Atwood’s, loading and unloading, for firewing the flatnefs at the poles of the earth, for trying the flrength of materials, in which all the mechanical powers are combined, for rotatory motion, for weighing, Machinery, conffrudfion of, 35^ fimplification of, 3^ firfl movers of, 4^ Machines, fimple, 3° compound, 89 maximum effefls of, 298, 359 Mechanics defined, 1 hi dory of, 2 treat: le on, Mechanical powers, machine in which they are combined, Men, ftrength of, according to various authors, 41 8, &c. Merfennus, problems propofed by him, 1 3 Mills driven by water and wind in¬ vented, 5 Motion not propagated inftantaneouf- ly, 295, 296 N. Newton, Sir Ifaac, his difcoveries, 18 O. ' Ofcillation of pendulums, 236 P. Parallelogram of forces difcovered by Stevinus, 6 demonftrated by D. Ber- nouilli, 20 of forces, machine for explaining it, 473 Parent on the maximum effedfs of machines, 16 on wind-mills, 43O Pendulum, conical, 394 PercuJJion. See Collijion. Piers, condruftion of, 336 Pile engine, Vauloue’s, 485 Bunce’s, 486 . Prong's condenfer of forces, 476 Pulley, properties of it, 100 R. Rackwork, teeth of, 41 I Reflexion of bodies after collifion, 283—293 Rope machine, its properties, 84 Ropes, rigidity of, 382 Rotatory motion, three axes of, dif¬ covered by Segner, 26 Smeaton’s apparatus for, 475 s. Screw, properties of it, Na 131 Mr Hunter’s double one, J37 its ufe in mechanics, 140 Semicycloid, the curve of iwifteft de¬ fcent, 231 Smeaton on wind-mill fails, 430 Stampers, on the wipers of, 411 Statcra, Roman, 47 JDaniih and Swedifti, 217 Steam, the power of, as a firft mover, 425> 427 engine invented, 10 improved by Savary, Newcomen, Watt, &c. ib. Steelyard, 47 Strength of materials, machine for try¬ ing it, 469 of men, 41 ^ of hoifes, 424 Sutton on wind-mill fails, 434 T. Table of the ftrength of firft movers, 425 of the ftrength of men, 418 Teeth of wheels, how to form them, 395 ol rackwork, how to iorm them,4il Toricelli, labours of, 9 Torflon, force of, 27, 343—357 Tradiion, line of, 449 w. Water mills, invention of, 5 Wedge, properties of it, I 21 machine for (hewing its pro¬ perties, Wheel and axle, its properties, Q3 Wheels, on the formation of the teeth of, . 395 bevelled method of forming their teeth, 407 crowm, 410 friction, 374 . 383 Wheel carriages, on the conftru£fion of, . . 439 on the pofition of their wheels, 447 on the fize and form of their w'heels, 439 on the pofition of their centre of gravity, 452 Wind, the power of, as a firtt mover, 425 326 Wind-mills, invention of, 5 defcription of one, 428 fails, on the pofition of, 430 on the efftdf of, 433 form given them by Mr Sutton, 434 horizontal, 435 comparifon between hori¬ zontal and vertical ones, 438 fails Smeaton’s apparatus for determining their pow¬ er, 574 Wipers of (tampers, how to form them. 419 ■ J 1 MECHANISM, M V. (’ l! AX !(’ S. / Plate C C O X 1 M K C HA NIC S . Plate C C C X \rll. I > ' \ I . ( Plate C C C XX . « » '— . . \ v MEG [i Mechanifm MECHANISM, either the conftru&ion or the ma¬ ll chinery employed in any thing j as the mechanifm of Redden- barometer, of the microfcope, &c. ■ a^-' ■ MECHOACAN, a province of Mexico, or New Spain, in America, bounded on the north by Pa- nuco and Guadalajara, on the eaft by Panuco and Mexico Proper, on the fouth by the Pacific ocean, and on the weft by Guadalajara and the South fea. It is about 200 miles in circumference. The foil is exceedingly fertile; and the climate fo wholefome, that the Spaniards imagine it to be pofleffed of fome peculiarly reftorative quality j for which reafon the lick and infirm flock to it from all quarters. The commodities are fulphur, indigo, farfaparilla, faflafras, cacao, vanelloes, ambergris, hides, wool, cotton, filk, fugar, the root mechoacan or white jalap, and filver. This province formed an independent kingdom at the time Mexico wras reduced by Cortez. The fovereign had long been the inveterate enemy of the Mexicans, and was confidered, next to the republic of Tlafcala, as the moft formidable barrier againft the extenfion of the imperial frontier. However, he fubmitted to Cor¬ tez without ftriking a blow, being intimidated by the wonders he had perfoimed with a handful of men 5 and thus Mechoacan became a province of the Spanidr em¬ pire, and a valuable addition to Mexico. The coun¬ try at that time was exceedingly populous, but the na¬ tives are now much thinned $ and that rather by the luxury and effeminacy introduced by the Spaniards, than by their tyranny. The capital of the province is alfo called Mechoacan by the natives, but Valladolid by the Spaniards. Mechcacan, or White *Jalap, in the materia me- dica, the root of an American fpecies of convolvulus brought from Mechoacan, a province of Mexico, in thin flices like jalap, but larger, and of a whitilh co¬ lour. It was firft introduced into Europe about the year 1524 as a purgative : but fince jalap became known, mechoacan has been little employed. MECKLENBURG, a duchy of Germany, con¬ taining thofe of Schwerin and Guftro, is bounded by Pomerania on the eaft, by part of the marquifate of Brandenburg and the duchy of Lunenburg on the fouth, the Baltic on the north, and Holftein and Saxe Lawenburg on the weft. Their greateft length is about 135 miles, and greateft breadth upwards of go. With refpeft to the foil, much cannot be faid in favour of it, as it confifts in general, either of fand, or large and defolate heaths interfperfed wdth moors, woods, fens, and lakes. It yields very little w7heat, and not a great deal of oats, rye, and barley j but breeds a confiderable number of ftieep and cattle, has plenty of filh, with ftone quarries, fait fprings, alum, iron, and fome copper. The principal rivers here are the Elde and Stor, which fall into the Elbe as it glides along the borders of this country to the fouth- weft ; the Reckenitz, wdiich difcharges itfelf into the Baltic ; as do the Peene, the Warno, and the Stope- nitz. This country has only one harbour on the Bal¬ tic, namely that of Roftock. In both duchies, ex- clufive of Roftock, are 45 great and fmall cities, with three convents, and a great number of manors and farms, belonging either to the duke, the nobility, or convents. The peafants are in a ftate of villenage $ but the nobility enjoy verv confiderable privileges. You XIII. Part I. 37 1 MEG The ftates are compofed of the nobility and towns ; Mecklen- and the diets, which are fummoned annually, are held burg, alternately at Sternberg and Malehin. The duchy 1'V'l-eC(->”lum,J of Schwerin appoints four provincial counfellors, and that of Guftro as many 5 who rank according to fe- niority, wuth the duke’s actual privy counfellors, as their marftials do with the colonels. The lefier com¬ mittee reprefents the whole body of the nobility and commons, by wdiom the members are chofen freely and without controul, and no edidt relative to the whole country can be published without their confent, or in prejudice of their rights. The inhabitants of this country are moftly Lutherans, under their fuper- intendants. There are alfo fome Calvinifts and Ro¬ man Catholics. Belides the grammar fchools in the towms, there is an univerfity at Roitock. The com¬ modities of the duchy are corn, flax, hemp, hops, wax, honey, cattle, butter, cheele, wool, and wood, a part of which is exported } but hardly any manu- fadlures. Of the houfe of Mecklenburg, there are two lines ftill fubfifting, viz. that of Schwerin and that of Strelitz. The latter commenced in Duke Adolphus Frederick II. younger brother of the duke of Schwerin, and grand¬ father of Adolphus Frederick IV. who entered on the government in 1752, and whofe family received a great additional luftre by his Britannic majefty’s taking his fecond lifter for his confort, and by her own great me¬ rit and noble deportment in that high llation. Be- fides the duchy of Strelitz, to this duke belong the principality of Ratzeburg, with the lordlhip of Star- gard, the ancient commanderies of Miro and Neme- ro, and a yearly penfion of 9000 dollars out of the Boitzenburg toll. The title afiumed by both the dukes is duke of Mecklenburg ; prince ofWenden, Schwe¬ rin, and Ratzburg ; count of Schwerin and the country of Roflock, and lord of Stargard. By the agreement con¬ cluded at Wittftock in 1442, the eleflor of Branden¬ burg, on the extindlion of the male line of the dukes of Mecklenburg, is entitled to their whole fucceflion. The duke of Schwerin has two votes both in the diet of the empire and that of the circle. The matricular affeffment for the duchies of Schwerin and Guftro is 40 horfe and 67 foot, or 748 florins monthly, includ- / ing what is paid by Sweden for Wifmar, and the bai¬ liwicks of Poll and Neuklofter. To the chamber of Wetzlar, thefe two duchies pay each 243 rix dollars, 43 kruitzers. For the government of Mecklenburg, the adminiftration of juftice, and the management of the revenue, there is the privy council of regency, the demefne chamber, the high and provincial court of ju¬ ftice, to which appeals lie in moft caufes, both from the confiftory and the inferior civil courts, and which are common to both the dukes. As to the revenues, thofe of the Schwerin line muft be very confiderable, thofe arifing from the demefne bailiwicks and regalia alone amounting to 300,000 rix dollars per annum. There is a tax on land that produces no contemptible fum, and that called the princefs''s tax is fixed at 20,000 rix dollars : befides all thefe, there are alfo free gifts.. The whole revenues of the Strelitz branch are eftimated at 120,000 rix dollars. Each of thefe priaces main¬ tains a body of troops. MECONIUM, the excrement contained in the in- teftiues of an infant at its birth. £ MEDALS. [ 138 ] M E D A L S. Utility of ‘TY/f’EDAL, denotes a piece of metal in the form them in Hi- 1>-J. 0f coin, fuch as was either current money among , {toryJ , the ancients, or ftruck on any particular occafion, in order to preferve to poderity the portrait of fome great perfon, or the memory of fome illultrious adtion. Scaliger derives the word medal from the Arabic methalia; a fort of coin with a human head upon it. But the opinion of Voffius is generally received ; viz. that it comes from metallum, “ metal j” of which fub- ftancfc medals are commonly made. Sect. I. Utility of Medals in Hiftory, and various other Sciences. There are few lludies of more importance to hi- flory than that of medals j the foie evidence we can have of the veracity of a hiftorian being only fuch collateral documents as are evident to every body, and cannot be falfified. In modern times, thefe are found in public memoirs, inllruftions to ambaffadors, and date papers of various kinds. Such memorials, how¬ ever, are fubjedl to various accidents, and befides com¬ monly remain in the countries where they are firft publilhed, and cannot therefore give to the world at large that perfedf and entire fatisfadlion which ought to be derived from genuine hiftory ; fo that more durable and widely diffufed monuments are ftill to be wiflied for. Such are public buildings, infcrip- tions, and ftatues 5 but thefe, excepting a few inftances of the two lad, are always confined to particular countries 5 fo that medals alone remain as infallible documents of truth, capable of being diffufed over all countries in the world, and of remaining though the ! lateft ages. Various The firff who fhowed the importance of medals in rntcHS 0U a<'certain'nS tlie dates, and arranging the order of events, in ancient hiftory, by means of medals, was Vaillant, in his Hiftory of the Kings of Syria, print¬ ed at Paris in 1681. By medals alone, he has been enabled to fix the chronology and important events of niftory, in the three moft ancient kingdoms of the world, viz. Egypt, Syria, and Parthia. Many coins have been difcovered fince his time, which confirm the recounts he has given. Pie was followed in this me¬ thod by Father Hardouin, though with lefs fuccefs. Hardouin’s bert work is -his Herodiades, or Series of Succeflors to Herod king of Judaea. The fame plan was purfued by Noris, in his learned Treatife on the Syro-Macedonian princes, and by Bayer in his Hi¬ ftory of Ofrhoene, as w^ell as byFroelicb, in the work Entitled Annales Regum et Rerum Syria-, Vien. 17 54, and another named Kevenhullers Regum veterum Nu~ mifmata Anecdota, auB. Ferrara, Vien. 1752, 4to, of which Froelich was properly the author. Corfini and Cary likewife publilhed works of a fimilar nature j the former in 1744, De Minn fan, alicrumque Anne nice Keg ten?, Nummis, &c. ; the latter in 1752, Htfloire des K°is de Thrace, el du Bfphore Cimmerien, eclaircie par les Mcdatlles. The ftudy of the Greek coins does not Ihow the Utility of- dates of events, though it illuilrates the chronology thfm in Hi- of reigns. This defeat, however, is abundantly fup- ftory’ &cc*, plied by thofe of Rome, which commonly mark the ^ date of the prince’s conlulftiip, the year of his tri-Ofthe bunician power 5 giving alfo, upon the reverfe, the re- Greek prefentation or poetical fymbol of fome grand event. co’n?“ The year of the tribunician power is fometimes ima¬ gined by antiquaries to be fynonymous with that of the emperor’s reign : but this is not the cafe j and Mr Pinkerton is at fome pains to fet them right ii> this refpech He finds fault with Julius Caefar, when he affumed the fovereign authority, for taking upon him the title of Perpetual Diiftator, as being fynony¬ mous with that of king or abfolute governor, which the Romans abhorred. “ He ought (fays our author), under the difguife of fome fupreme magiftrate of an¬ nual eleflion, to have lulled the people with a dream, that they might terminate his povrer when they pleafedj or that he himfelf wmuld refign it, when the neceflities of ftate which had required his temporary elevation had fubfided.” To this error Mr Pinkerton aferibes Method the affaflination of the di&ator, and commends the ufed by Air. policy of Auguftus, who, with far inferior abilities, Kuftus to continued in poffeffion of the moft abfolute authority fecure his as long as he lived. The tribunefhip was an office Ofpower* annual ele&ion; and if put into the hands of any others than plebeians, muft have been the fupreme pow-er of the ftate, as it belonged to that office to put a negative upon every public meafure whatever. Au¬ guftus, being of fenatorial rank, could not affume this office : but he invefted himfelf with the tribunician power, w'hich had the advantages of appearing to be only, a temporary fupremacy, though in truth it was continued during his whole lifetime. Towards the end of his reign, he frequently affumed his deftined fucceffor, liberius, for his colleague, though in the beginning he had enjoyed it alone. This, with his aitifice .of refigning his power every ten years, and reaffuming it at the defire, as wTas pretended, of the fenate, fecured his fovereignty as long as he lived His example w'as followed by his fucceflors ; fo that moft of them have the infeription Tribunicia Potejlate upon their medals, with the date affixed to it thus, lr. Pot. 'Mil. Yet though this date generally im¬ plies the year of the emperor’s reign, it fometimes happens that the emperor, by fpecial favour from a for¬ mer prince, had been endowed with this title before he. came to the throne, as being the fucceflbr to that prince, of which we have already given an inftance in I iberius. Befides the tribunician power, the empe¬ rors very frequently enjoyed that of the confuls •, and the. date, of their confulfhip is frequently expreffed in their coins. The office of Pontifex Maximus was likewife af¬ fumed by the Roman emperors, in order to fecure them- felves in their authority ; which, Mr Pinkerton ob- ferves, was one of the moll efficacious artifices they could have fallen upon. “ In the Greek heroic times (fays M E B Utility of (fays he), king and pried were carefully united in one them in Hi-perfon . ancl w1nen fovereigns arofe in Denmark and ,ilory. occ. ^ gwecjen> the fame plan was followed, as appears from Snorro, and other writers. Nothing could lend more fecurity to the perfon of the monarch than an office of fupreme fanflity, which alfo confirmed his power by all the terrors of fuperftition. Even the Chrilfian fydern was afterwards debafed by a mock alliance with government $ though it be clear from the whole New Teftament, that fuch an alliance is fubverfive of its genuine infiitution, and the greateft of all its corrup¬ tions. But the Roman Catholic clergy, in the dark ages, were the authors of ‘ no church no king,’ for their own intereft ; while the Roman emperors only fought to firengthen their power by the dark awe of fuperftition. The title of Pontifex Maximus was fo important, that it was retained even by the Chriftian emperors till the time of Gratian. Its influence in the date was, indeed, prodigious. Cicero obferves, that to this office were fubjeft, temples, altars, penates, gods, houfes, wealth, and fortune of the people.— That of augur is alfo borne by many emperors; and its authority was fuch, that by the law of the twelve tables no public bufinefs could be tranfafted without a declaration from the augur concerning its event.— The proconfular power was alfo given to Auguftus and the other emperors. It conferred a direft autho¬ rity over all the provinces, and implied the emperor to be chief proconful, or governor of each, and of all. Another fpecial power affigned to the emperors, but not occurring on coins, was the ‘Jus Relationis Tertice, Quarto;, &c. or the right of making three or four mo¬ tions in the fenate on the fame day, while the fenators could only propofe one. Hence our author infers, that medals afford the mod authentic documents of the Roman hiitory, in particular, that could have been invented by man.— The hiflories of Nerva and Trajan are much better elucidated by medals than by authors ; for the hiilory of Suetonius ends with Domitian, and the Hiflor'ue .AuguJJa Scriptures begin with Adrian : fo that the reigns of the two emperors juft mentioned are almoft unknown ; and Mr Pinkerton is furprifed that none of the learned have attempted to fupply the defer!.— “ Capitolinus (fays he), in his life of Maximinus Ju¬ nior, is quite puzzled to know if Maximus and Pu- pienus were two emperors, or two names for the fame. Had he happened on any of thofe coins which bear M. Cl. Pupienus Maximus Aug. he would have feen at once that Maximus was only another name for Pupienus.” Ufe of me- Medals are ufeful in other fciences befides hiftory. dais in geo- In geography, vre find the fituation of towns de- graphy. termined by their vicinity to fome noted river, moun¬ tain, &c. Thus, MAFNHTftN STHTAOT ffiows that Magnefia tvas fituated under Mount Sipylus. In like manner, it is fliown from a medal, that Ephefus flood on the river Cayfter ; and there is extant a medal, bear- in an infcription, which fignifies Alexandria on the Scamander •, a name given to Troy by Alexander the Great. The reverfe has upon it the famous Apollo 5 Smintheus of Homer. In natural hiftory alfo, medals hiftorv11*1 are ufeful chiefly from the coins ftruck on the celebra¬ tion of the fecular games, in which the figures of various animals are preferved 5 and thus it may very A L S. 139 often be determined whether any animal be known to Utility of the ancients or not. On many of the Greek medals are feveral uncommon plants and animals. Thus, on T-’.. V moft of the medals of Cyrene is the figure of the ce¬ lebrated Sy/phium ; and on thofe of Tyre, the Ihell-fiih from which the famous Tyrian purple was procured. 6 By means of medals, alfo, the exadl delineations of In architec. many noble edifices are preferved, though not even a1111’6, veftige of their ruins be now exifting ; fo that the ufes of them to the architedt are very confiderable. To In fine the connoiffeur they are abfolutely neceffary •, becaufe arts. by them alone he is enabled to aferibe ancient bulls and llatues to their proper perfons, with multitudes of other points of knowledge which cannot be other- wife determined. The elucidations of obfeure paf- fages in ancient authors by means of medals are fo numerous and well known, that it is needleis to infill upon them. Mr Addifon has treated the connexion betwixt me¬ dals and poetry at confiderable length •, but Mr Pin¬ kerton finds fault with him for preferring the Latin to the Greek poets. He obferves alfo, that the know¬ ledge of Greek medals is moft neceffary for a fculp- 3 tor, and perhaps an architedl •, but an acquaintance Ijat'n mer~ with Latin ones is preferable for a poet, or perhaps painter. The reafon of this difference is, that the former generally have on the obverfe the head of fome king, god, or goddefs, of exquifite relief and work- manftiip •, but the reverfe feldom affords much fancy of fymbol in the early Greek coins 5 and in the impe¬ rial Greek coins, is chiefly impreffed with the temples df their deities. To a perfon of poetical imagination, however, the Roman coins afford the greateft enter¬ tainment, from the fine perfonifications and fymbols to be found on their reverfes •, of which our author gives the following inffances : 9 “ Happiness has fometimes the caduceus, or wand ”erk)n,fi<::i- of Mercury, which Cicero, 1. OJfic. tells us was thought^1 to procure every with. She has, in a gold coin of Se- ‘ ni verus, heads of poppy, to exprefs that our prime blifs lies in oblivion of misfortune. “ Hope is reprefented as a fprightly girl, walking quickly, and looking ftraight forward. With her left hand the holds up her garments, that they may not im¬ pede the rapidity of her pace •, while in her right hand the holds forth the bud of a flower *, an emblem infi¬ nitely more fine than the trite one of an anchor, which is the fymbol of Patience, and not of Hope. This perfonification, with fome others, muft have been very familiar to the ancie,nts for often in this, and in a few more inftances, no name, as Spes Aug. or the like, is inferted in the legend. “ Abundance is imagined as a fedate matron, with a cornucopias in her hands, of which fne fcatters the fruits, and does not hold up her cornucopiae and keep the contents to herfelf, as many modern poets and painters make her do. “ The emperor Titus, having caufe to import a great fupply of corn during a fcarcity at Rome, that fupply, or the Annona, is finely reprefented as a fe¬ date lady, with a filled cornucopiae in her left hand, which (he holds upright, to indicate that (he does not, however, mean to fcatter it, as Abundance has a title to do, but to give it to Equity to deal out. This laft particular is ftiown by her holding a little image of S 2 • Equity, MO MED w.lity cf Equity, known by ber fcales, and hajla pura, or point- ^toi-11 s/c1’ ^Pear) ber right band, over a baiket filled with ■ ^ wheat. Behind the Annona is the prow of a (hip decked with flowers, to imply that the corn was brought by fea (from Africa), and that the fhips had had a prof- perous voyage. The beft poet in the world would not have given us a finer train of imagery *, the belt painter would have been puzzled to exprefs fo much matter in fo fmall a compafs. “ Security ftands leaning upon a pillar, indica¬ tive of her being free from all defigns and purfuits j and the pollure itfelf correfponds to her name. Ho¬ race, in delcribing the wife man, mentions his being teres atque rotundas ; round and polifhed, againft all the rules of chance : an idea feemingly derived from the column upon which this ideal lady reclines. “ The emblems of Piety, Modesty, and the like, are equally appofite and poetical. “ The happinefs of the ftate is pi&ured by a {hip. failing before a profperous breeze: an image than which the fuperlative genius of Gray could find none more exquilite ; and he has accordingly ufed it in his moft capital produflion “ The Bard,” with due fuc- cefs. “ The diflerent countries of the then known world are alfo delineated with great poetical imagery. It affords patriotic fatisfaftion in particular to a Briton, to fee his native ifland often reprefented upon the ear- lieft imperial coins fitting on a globe, with a fymbol of military power, the labarum, in her hand, and the ocean rolling under her feet. An emblem almofl prophetic of the vaft power which her dominion over the fea will always give her, provided flie exerts her elemeht of empire with due vigour and perfeverance. “ Coins alfo prefent us with Achaia, Africa, Ala- mannia, Alexandria, Arabia, Armenia, Afia, Bithy- nia, Cappadocia, Dacia, Dardania, Egypt, Gallia, Hifpania, Italia, Judtea, Macedon, Mauritania, Pan¬ noma, Parthia, Phrygia, Sarmatia, Sicily, Scythia, Syria, and the rivers Danube, Nile, Rhine, Tyber. This perfonification of provinces feems to have arifen from the figures of provinces carried in triumphs ; as the perfonification of our old poets fprung from the ideal perfem aftually reprefented in the myfterial plays. “ There is one colonial medal of rude execution of Auguftus and Agrippa, which has a high claim to merit in difplaying the ancient poetical imagery. It is infcribed Imp. and Dm. f. and on the reverfe, the conqueft of Egypt is reprefented by the metaphor of a crocodile, an animal almoft peculiar to that country, and at that period efteemed altogether fo ; which is’ chained to a palm tree, at once a native of the country 10 and fymbolic of vidfory. Medals ufe- “ As the reverfes are fo ufeful for knowledge of perfonification, fymbols of countries and a&ions, and the like 5 fo the portraits to be feen on old coins are no lefs important to a painter 5 the high merit of a great number of them, in every charafter, juftly entit¬ ling them to be regarded as the beft ftudies in the world. Not to mention, that, to an hiftoric painter, the fci- ence of ancient medals is abfolutely neceffary, that he may delineate his perfonages with the features they really bore while in exiftence. This can only be at- taiqed in this way, or from ftatues and bufts 5 any one fni to a painter A L S. of which will coft as much as hundreds of medals j Entertain- and indeed a colle&ion of fuch is only attainable by ment tr‘In princes. The fame things which render the ftudy of medals1 important to a painter, do ftill more fo to a fculptor ; ir and in this particular, the ftudy of the Greek coins is Eo a fculp- remarkably ufeful. The fldil of the Greeks in thetor* art of fculpture has always been admired throughout the world ; and on their coins the heads of feveral dei¬ ties are reprefented in the moft exquifite alto relievo. Our author therefore thinks it ftrange, that the Gre¬ cian coins Ihould have hitherto been fo little attended to by men of learning and tafte. They may have been looked upon, he fuppofes, as belonging only to the province of the antiquary j but he affures us, that the Greek medals will afford fatisfaftion to the perfons who value them only as pieces of workmanfhip. In moft refpefts, they greatly excel thofe of Rome even in its beft times ; which our author fuppofes to have been from the days of Auguftus to Adrian. “ In the days °f Adrian, in particular (fays he), the Roman mint feems to have been the very feat of art and genius j witnefs the vaft number of exquifite perfonifications, en¬ graven with equal workmanfhip, which fwarm on the medals of that prince. Yet from his time down to Pofthumus, coins of admirable workmanftiip are to be found. Thofe of the Fauftinas and Lucilla deferve particular mention. There is one, and not an uncom¬ mon one, of the latter in great brafs, which yields to nothing of the kind. The reverfe is a Venus with the name around her. The portrait of the obverfe feems to fpring from the field of the coin ; it looks and breathes, nay talks, if you truft your eyes. The coins of Tarfus are extremely remarkable for a kind of per- fpeftive in the figures, as Froelich obferves. On others aie found triumphal arches, temples, fountains, aque- dufts, amphitheatres, circi, hippodromes, palaces, bafili- cas, columns and obelilks, baths, fea-ports, pharofes, and the like. Thefe furniih much pleafure and inftruftion to the architeft, and ferve to form his tafte to the an¬ cient manner; that manner which unites perfeft fimpli- city with fublimity and grace j that manner which every age admires, in proportion as it has genius to imi¬ tate.” 0 Sect. II. Entertainment arifiug from the Study of Medals. Besides the purpofes which the ftudy of medals anfwers in the ufeful arts, a great variety of fources of entertainment are to be found in it. Mr Pinkerton obferves, that the moft barbarous nations are more pleafed vyith the rudeft efforts of art, than with the moft admirable works of nature ; and that in propor¬ tion as the powers of the mind are large and various, fuch are alfo the pleafures which it receive? from thofe fuperlative produftions of art, which can only be the offspring of vaft genius. Hence works of art are agreeable both to the enlightened and to the ignorant. 1 he chief ,amufement, therefore, which attends the ftudy of medals, originates from the ftrength and fpi- nt, the finifti and beauty, which the engraver has dif- played in the execution of them. It befides gives a kind of perfonal acquaintance wfith the perfons of whom they are the reprefentaiions. Portraits have always been- MED Entertain- been highly entertaining to mankind j and our author went from js 0f 0pin}on? that the love of them gave rife both to painting and fculpture. They are nowhere to be y. - ^ ■ found fo ancient, io numerous, and fo wTell preferved as in medals. Amufement is alfo derived even from the reprefentations of ideal heads and perfons ) nay, even from the minuted fymbols. Thus the Greek coins of cities prefent us with heads of deities of exquifite workmanfhip, apparently copied from ftatues or paint¬ ings •, fo that we may even guefs at the works of A- pelles and Praxiteles from fome of the Greek medals. Their reverfes afford dill greater variety •, there being fcarce an objedf either in art or nature which is not reprefented upon fome of them : ^and to the fatisfac- tion arifing from a view of thefe, we may likewife add that of beholding, in a lively manner, t)ie dreffes, man¬ ners and cudoms, religious and civil ceremonies, of the ancients : fo that from medals we may obtain an intereding hidory of manners j which, though very lately cultivated, may perhaps afford the mod ufeful and entertaining of all the provinces of hidory. 12 There is a very condderable difference betwixt the Difference of medals and that of a mere antiquary. The medallift1 ^atter frecluent^y feems to take delight in coins mere- and anti- ty proportion to their rud and deformity •, fo that quary. it is often a '"'recommendation of fome of their pieces, that neither portrait, reverfe, nor legend, can be dif- covered ; at lead in fuch manner as can be intelligibly explained. “ The delight of the antiquarid (fays Mr Pinkerton), may be called a depraved appetite of the mind, which feeds on trafh, and fills itfelf with empti- nefs. It is perhaps a mere childifh curiofity mingled with caprice and hypochondricifm. Againd this cha¬ racter the ridicule of Severus is particularly {hot, but with little effect ; for our antiquids exceed in vifions and nonfenfe. I fay antiquijls ; for the name of anti¬ quary is facred. By antiquary, in foreign countries, is implied a man who illudrates-their ancient law's, manners, poetry ; but efpecially their ancient hidory. There, men of the mod elevated minds are antiquaries; as Muratori, Leibnitz, Montefquieu, Du Bos. Here men of talents will not doop, forfooth, to dudies the mod important to their country, but leave its anti¬ quities to chance. Every thing is important but our hidory •, and we are profound in every ancient matter that is fuperficial; and fuperficial in what is profound. Even England cannot boad of one general hidorian, but truds to the inaccuracy of Rapin, and the igno¬ rant neatnefs of Hume. It is therefore no wonder that the dudy of antiquity is here ridiculous, though mod important in other countries; none requiring greater talents, learning, or indudry. But the hido- ric antiquary has the pleafure of benefiting fociety, and enlightening whole nations, while the medalhc has only an innocent amufement. This amufemeht, con- fidered merely as rifing from antiquarian objedls, has not been explained, though felt by mod people, and more by the learned. It feems analogical with that which we derive from an extenfive profpedl : for as the mind delights to expand itfelf into didant places, fo alfo into didaM times. We conneft ourfelves wuth thefe times, and feel as it were a double exidence. The paffions are Angularly affe£fed by minute circumdances, though mute to generalities *, and the relicks of an¬ tiquity imprefs us more than its general hidory,” A L S. Sect. 111. Hi/lory of Medals. 141 Hiftory. The ftudy of medals is not of very ancient date: None of the claflic writers give any account of collec¬ tions of them •, though indeed many little particulars are paffed without notice by them. In the times of the Greeks, a colledlion of fuch coins as then exided mud have been but little regarded, as confid¬ ing only of thofe druck by the numerous little dates which at that time ufed the Greek charafters and lan¬ guage. Hence they would have had an air of domedic coinage, and no attention would have been paid to them, however exquifite their workmandiip might have been. The little intercourfe at that time carried on betwixt the different provinces alfo, greatly impeded any communication of knowledge to thofe who wrote hidories j fo that it is no wonder to find any fmall colleftions that might then have exided al- . together unnoticed by them. * 13 Almod as foon as any communication was opened Greek coins between the Greeks and Romans, the latter treated the arts of the Greeks with all due refpedf and ap-mans< plaufe. Their coins were imitated by the Romans, and preferved in cabinets by the fenators among their choiced treafures. Suetonius informs us, that on fo- lemn occafions Augudus was accudomed to prefent his friends with medals of foreign dates and princes, along with other valuable tedimonies of bis frienddnp. In a more advanced period of the Roman empire, however, individuals would undoubtedly form collec¬ tions of coins peculiar to their own date $ for Dr Stukeley, in his Medallic Hidory of Caraufius, in¬ forms us, that a complete feries of diver coins was lately found in Britain, containing all the emperors down to Caraufius inclufively. From Banduri w7e alfo know, that certain Greek coins were fpecially preferved by the Romans \ and it appears from their code, that ancient gold and filver coins were made ufe of indead of gems; to which didindlion thofe of Sicily were particularly entitled. From the decline of the Roman empire till towards the end of the fifth centu¬ ry, almod all branches of literature were involved in darknefs, and the medallic fcience among the red. While the Chridian dominion of Condantinople laded, indeed, almod all the arts and fciences may be faid to have been kept within its own boundaries j though the Arabs and eadern nations had fome arts and fci¬ ences of their own : but after the dedru&ion of the1 imperial city by the Turks, the Greeks were once more compelled to become fathers to the European fcience. Even before this time, indeed, fome vediges of a revival of literature had appeared in Italy ; “ and fo intimate and neceffary a connexion (fays Mr Pin¬ kerton), has now the dudy of medals with that of an-, cient erudition, that on the earlied appearance of a re¬ vival of the latter, the former was alfo difclofed.” 14 The fird among the moderns who began to ftudy Collefffors the metallic fcience was Petrarch. Being defired by °f me!, the maiden, was a name often applied to the te¬ tradrachm, and which would feem to apply to thofe of Athens •, though there are coins of other cities with the head of Proferpine, and the word to which it would appear more applicable in our author’s opi¬ nion. Xs^&iyt, the Jhell, was the name of another coin, from its type. A Sicilian coin was named As^gsrior, from Gelon’s wife. A tetradrachm w7as named K^9r«T£<7«u?, and had eight or hemidrachms. The Tgeiwa», fo called from its country Troizene, had Pallas on one fide and a trident on the reverie. A L S. The hemiobolion was the of Lacedemon ; and Ancient the fcoXAvSoj is fuppofed to have been equal to the M°ney- Roman feftertius or quarter drachma. The cystophori ' v were coins with the myftic cheft or hamper of Bacchus upon them, out of which a ferpent rifes ; and are much celebrated in antiquity. We are told by Livy, that Marcus Acilius, in his triumph over Antiochus and the iTitolians, carried off 248,000 of them; Cneius Man¬ lius Vulfo in that over Gallo-Graecia had 2,0,000 j and Lucius Emiiius Regillus, in his naval triumph over the fleets of Antiochus, had 131,300. Cicero like¬ wife mentions his being pofleffed of a vaft fum in them. The moft: probable opinion concerning them feems to be, that they are all filver tetradrachms *, fuch as be¬ long to the cities of Apamea and Laodicea in Phry¬ gia 5 Pergamus in Myfia j Sardis and Tralles in Ly¬ dia ; and Ephefus: but it is a miftake to afcribe any to Crete. Mr Pinkerton thinks it abfurd to imagine that Crete, a fmall ifland, ftiould ftrike fuch vaft num¬ bers of coins 5 though Cicero mentions his being in pofieflion of an immenfe treafure in them at the time he xvas governor of Afia Minor. “ It is moft: likely (fays Mr Pinkerton), that his wealth flrould be in the coin of the country to wdrich he belonged. But w7hat had thefe triumphs or Cicero’s government to do with Cretan money ? But indeed the coins themfelves, as above noticed, eftablifti the fa£L” ^ Another fet of coins famous in antiquity w7ere thofe Coins of of Cyzicus in Myfia, wdiich w7ere of gold *, but they Cyzicas^ are now almoft entirely vanfthed by being recoined in other forms. The voy.to-y.x,, or money of Slry- andes, w7ho was made governor of Egypt by Cam- byfes, is made mention of by Hefychius; but none of them, as far as is known, have reached our times. They muft have been marked with Perfian charaflers, if with any. The coin of Queen Philiflis is mentioned by the fame worker, and many" of thefe piece* are ftill extant 5 but we know not where this queen reigned, nor does there feem to be any method of finding it out. Mr Pinkerton inclines to believe, that fhe pre- fided over Sicily j and as a confirmation of that .fup- pofition, mentions fome infcriptions of BASIAIS2AS ‘MAIZTIAOS or the Gradini of the theatre at Syracufe j but which appear not older than the Roman times. Some authors are of opinion, that fhe reigned in Cof- fara or Malta ; which our author thinks much more improbable. The moft particular attention with regard to the Athenian names and ftandard of coins is due to thofe of Athens j coins, and it is remarkable, that moft: of them which have reached us are of a very late period, wuth the names of magiftrates infcribed upon them. Some of thefe bear the name of Mithridates ; and few are older than the era of that prince ; who, it is w7ell knowm, took the city of Athens in his war with the Romans. I fu- fpeft (fays Mr Pinkerton), that no Athenian coins of filver are pofterior to Sylla’s infamous deftrudfion of that city 5 an event the more remarkable, as Salluft tells us, that Sylla was learned in Greek. Indeed Ca¬ ligula, Nero, and moft: of the pefts of fociety, have been learned men, in fpite of a noted axiom of Ovid, Scd inyenuas didicijfe feliciter antes Emollit mores, nec fttiit c[fe feros. It is ftill more remarkable, that the fabric of Athe¬ nian MED Ancient Money. - 3^ Greek cop¬ per money. man coins is almSift univerTally very rude : a lingular circumftance, if v:c reflefl how much the arts flourilh- ed there. It can only be accounted for from the ex¬ cellence of their artifts being fuch as to occalion all the good Ones to be called into other countries, and none but the bad left at home. In like manner, the coins llruck at Rome in the imperial times are excel¬ lent, as being done by the belt Greek artifts *, while thole of Greece, though famous at that time for pro¬ ducing miraculous artills, are during that period com¬ monly of very mean execution. The opulence of A- thens in her days of glory was very great •, owing in an eminent degree to her rich commerce with the kingdoms on the Euxine fea, carried on chiefly from Delos, which belonged to Athens, and was the grand centre of that trade.” Hence it has become matter of furprife to Neumann, that when there are fo many coins of Mycene, an iiland even proverbially poor, there fhould be none of Delos. But Mr Pinker¬ ton accounts for this from Mycene’s being a free Hate, and Delos fubject to Athens. “ It may be wrell fup- pofed (fays he), that Athens had a mint at Delos j and fuch Athenian coins as have fymhols of Apollo, Diana, or Latona, were ftruck in this ifland.” The copper money of the Greeks is next in anti¬ quity to the filver. Mr Pinkerton is of opinion, that it was not ufed at Athens till the 26th year of the Pe- loponnefian war ; about 404 years before Chrift, and 300 after filver was lirfl: coined there. The firft cop¬ per coins were thofe of Gelo of Syracufe, about 490 B. C. Ofthechal- ,^e c^a^cos °f brafs, of which eight went to the CUSt filver obolus, feems to have been the firfl: kind of Greek coin. At firft it was looked upon as of fo little confequence, that it became proverbial ■, and to fay that a thing wTas not worth a cha/cos, was equivalent to faying that it was worth nothing. As the Greeks be¬ came poor, however, even this diminutive coin was fubdivided into two, four, nay eight or fmall coins $ but our author cenfures very feverely thofe who have given an account of thofe divifions. “ Pol¬ lux, and Suidas copying from him (fays he), tell us, that there were feven lepta to one chalcos; a number the molt unlikely that can be, from its indivifibility and incapacity of proportion. “ Pollux lived in the time of Commodus, fo was too late to be of the fmalleft authority : Suidas is four or five centuries later, and out of the queftion. Pliny tells us, that there were ten chalet to the obolus ; Diodo- r„us and Cleopatra that there rvere fix ; Ifidorus fays there were four: and if fuch writers differ about the larger denomination, we may well imagine that the fimaller equally varied in different fiates ; an idea fup- ported by thefe undeniable witneffes, the coins which remain. Moft of the Greek copper coin which has reached our times confifts of chalci *, the lepta being io fmall as to be much more liable to be loft.” In Dr Hunter’s cabinet, however, there are feveral of the di- lepta of Athens : and from being ftamped with the reprefentation of two owls, feem to be the fame with the filver diobolus : “ a circumftance (fays Mr Pinker¬ ton), of itfelf fufficient to confute Pollux ; for a dilep¬ ton can form no part of feven j a number indeed which never appeared in any coinage of the fame metals, and is contradictory to common fenfe. It may be obferv- A L S. ed, that the whole brafs coins of Athens publifhed by Dr Combe are reducible to four fizes, which may be the lepton, dilepton, tetraleptoti or hemichalcos, and chalcos. The firft is not above the fize of one of King Lepton, James I.’s farthing tokens ; the laft about that of our cldepton, common farthing.” The lepta was alfo called ^•c" as being change for the poor. The Ktllxfits, perhaps fo called from the figure of a wolf upon it, was the coin of a particular ftate, and if of brafs muft have weighed three chalci. The other names of the copper coins of Greece are but little known. Lycurgus ordered iron money to be coined at Sparta ; but fo periihable is thi& metal, that none of that kind of money has reached our times. After the conqueft of Greece by the Romans, moft; of the coins of that country diminiftied very much in their value, the gold coinage being totally difeonti- nued : though fome of the barbarous kings who ufed the Greek charafter were permitted to coin gold, but they ufed the Roman model •, and the ftandard ufed by the few cities in Afia who fpoke the Greek language in the times of the emperors is entirely un¬ known. Copper feems to have been the only metal coined at that time by the Greeks themfelves 3 and that upon the Roman ftandard, then univerfal through the empire, that there might be no impediment to the circulation of currency. They retained, however, fome of their own terms, ufing them along with thofe of the Romans. The ajfarion or qjjarium of Rome, the name of the diminiftied as, being 16 to the drachma or denarius, the obolus was fo much diminilhed in va¬ lue as to be ftruck in brafs not much larger than the old chalcus, and valued at between two and three af- faria 3 which was indeed its ancient rate as to the drachma. This appears from the copper coins of Chios, which have their names marked upon them. The brafs obolus, at firft equal in fize to the Roman feftertius or large brafs, leffens by degrees to about the fize of a filver drachma. From the badnefs of the imperial coinage iu Greece alfo, it appears that brafs was very fcarce in that country, as well as in all the cities ufitig the Greek charadlers 3 being found moftly 3Q in the weftern countries of the Roman empire. The Era of the time of this declenfion in fize of the Greek coins is dedenlioa by Mr Pinkerton fuppofed to have been from Au- Greek cojB guftus down to Gallienus. He is of opinion, however, age< that the copper obolus, at firft above the fize of large brafs, was ufed in Greece about the time of its firfl: fubjeftion to Rome 3 and that the lepta ceafing, the chalci came in their room, with the dichalcus and the hemiobolion of brafs. 4® With refpefl to the gold coins of the Greeks, Mr Gold coins Pinkerton is of opinion that none of that metal was<-'reecc.’ coined before the time of Philip of Macedon, as none have reached our times prior to the reign of that mo¬ narch. From a paffage in Thucydides our author con¬ cludes, that in the beginning of the Peloponnefian war the Athenians had no gold coin. Mentioning the treafure in the Acropolis or citadel of Athens, at the commencement of that war, the hiftorian mentions filver coin, and gold and filver in bullion 3 and had any of the gold been in coin, he would certainly have mentioned it. Philip began his reign about 68 years after the beginning of the Peloponnefian war ; and we can fcarce fuppofe that any city would have pre- T 2 ceded 148 M E D Ancier.t ceded the elegant and wealthy Athens in the coining of , Money- gold. Notwithflanding, however, this deficiency of gold Gold com- coin among the Greeks, it is certain that the coinage c-d early in of gold had taken place in Sicily long before ; as we ^icdy. have gold coins of Gelo about 491 B. C. of Hiero I. 478, and of Uionyfins I. in 404, all ufing the Greek characters; though not to be ranked among the gold coins of Greece, as Philip caufed his to be. Gold coins of Syracufe even appear of the third clafs of an¬ tiquity, or with an indented fquare, and a fmall figure »n one of its fegments. Gold coins are ufed in the cities of Brettium, Tarentum, and throughout Magna Graecia j alfo in Panticapaea in Thrace, and likewife £!ofa in that country j but not in Tufcany, as is com¬ monly believed, though Neumann proves that they wrere ftruck by Brutus, and are unqueftionably as ancient as the Greek coins. The Thebans and Athenians pro¬ bably coined the firil gold after Philip had fet them the example, and wdren they were attempting to refift the projefts of that enterprifing monarch. The Ai,to- lians probably coined their gold during the time of their greateft power, about a century after Philip, and when they were combating the power of Aratus and the Achasan league. “ There is (fays Mr Pinkerton) but one ifu^vo-cs of Thebes, much worn, in Dr Hun¬ ter’s cabinet, and weighing but 59 grains j and per¬ haps not above two or three or gold didrachms of Athens in the world ; one of which is alfo in the collection of Dr Hunter, and weighs 132! grains. It appears to be more modern than the reign of Phi¬ lip. That monarch having got poffeffion of the mines of Philippi in Thrace, improved them fo much, that they proctuced him annually above a thoufand talents of gold, or 2,88o,oool. of our money. From this gold the firft coins named from the monarch, Philippi, were itruck. They were marked with his portrait , and for many ages after wrere fo numerous, that they were common in the Roman empire ; whence the name Philippi became at length common to gold, fil- yer, and at laft even hrafs coins of their fize. Even in the time of Philip gold was very fcarce in Greece ; but after the Phocians had plundered the temple of Delphos, this precious metal which had been valu¬ ed as gems, and confecrated only to the decoration of the temples of the gods, began to be known among the Greeks. The comparative value of gold and fd- yer, however, feem to have been at that time very dif¬ ferent from what they are now. Herodotus values gold at 13 times its weight in filver; Plato in his Hipparchus at 1 2 } and even the low value of 10 to 1 feems to have been the dated value in Greece, though in Rome the plenty of filver from the Spanifh mines made the value of gold to be much higher •, and there is no reafon to think that it was ever valued in that city at lefs than 12 times its weight in filver. The Philippus x^vrof, gold piece, orJlater, is a didrachm, and is the tnoft common of all the ancient coins. Mr Pinkerton is of opinion that it w'ent for 20 filver drachms^ on its firft appearance •, but in latter times for 25 Greek drachmae or Roman denarii. There are proofs of the Philippi being didrachms, both from the writings of ancient authors and from numbers of the coins themfelves, which remain to this day j and that the ^vvos, or principal gold coin of Greece, was of A L S. the fame weight, is alfo evident from ancient writings. Ancient. It was anciently worth about 15s. but valuing gold Money, now at the medium price of 4I. per ounce, it is worth v_ ' J about • 20s. The or half the former coin, fcarcely occurs of the coinage of Philip and Alexander, though it does of Hiero I. of Syracufe and of King Pyrrhus. It pafted for ten filver drachmas, and was valued only at 7s. 6d. though now worth 10s. There was another divifion of this kind worth about 5s. There were befides fome lefler divifions of gold coins, which could not be worth above two drachmas. Thefe were coined in Gyrene 5 and there were befides feveral old gold coins of Afia Minor, the value of which is now unknown. Our author fuppofcs that they were coined not with relation to their weight as parts of the drachma, but merely to make them correfpond with fo many filver pieces as was neceffary. There are alfo larger coins than the the St%£v &-c* meafures, fee. and half a third; whence the feftertius came at laft to be the grand eftimate of Roman mo¬ ney. The as being at firft the largeft, and indeed the only Roman coin, the word fejlertius means fefertius as, or “ two afes and an half.” On the firft coining of filver, the denarius of ten afes wTas ftruck in the mold common and convenient denary divifion of money, or that by tens j the feftertius being of courfe two afes and an half. But the denarius being afterwards efti¬ mated at 16 afes, the name feftertius was ftill applied to a quarter of the denarius, though it now contained four afes. The term fejlertius was applied to ail fums not exceeding 1000 feftertii, or 81. 6s. 8d.; but for greater fums the mode of the feftertius was likewife altered, though not to exclude the former. Very large fums. MED Ancient Money. Whence the Re¬ mans deri¬ ved their coinage. fums of money were eftimated by the hundred weight of brafs j for the Romans were at firft unacquainted with the talent. The bundled weight, by way of eminence, tvas diftinguilbed by the name of pondusy and fejlertium pondus became a phrafe for two hundred weight and an half. Mr Pinkerton is of opinion, that we may value the as libralis of ancient Rome at about eightpence Englilh. Eftimating the as there¬ fore at a pound weight, the Jejlei'tium pondus was equal to iooo fejiertii, or 81. 6s. 8d.; and by coincidence which our author fuppofes to have been the effe£t of defign, as foon as the filver coinage appeared, the fejiertium centum denariorum was always equal to 81. 6s. 8d. alfo. The word feftertium itfelf, however, feems to have been unknown prior to the coinage ef filver money at Rome : the pondera gravis ceris being fuffi- cient before that time for all the purpofes of a flate in which money was fo fcarce. But however this may be, the pondus or hundred weight of brafs was precile- ly worth 100 denarii, or a pound of filver.* As the great feftertium was always valued at iooo of the fmaller, or 81. 6s. 8d. we never find one feftertium men¬ tioned in authors, but two, three, or more \ ten thou- fand of them being equal to 83,333!. 6s. 8d. The ftates from which the Romans may be fuppo- fed firft to have derived their coinage, were the Etruf- cans and the Greek colonies in Magna Graecia and Sicily. Jofeph Scaliger, Gronovius, &c. contend that it was from the Sicilians that the Romans firft derived their knowledge of money; but Mr Pinkerton argues that it was from the Etrufcans. In confirmation of his opinion, he appeals to the ftate of the Roman te- ritories in the time of Servius Tullius, who is look¬ ed upon to have been the firft wrho coined money at Rome. At that time the whole Roman dominion did not extend beyond ten miles round the city j and was entirely furrounded by the Etrufcan and Latin ftates 5 Cumae being the next Greek colony to it that was of any confequence, and which was in the neigh¬ bourhood of Naples, at about the diftance of 150 miles. Our author alks, Is it reafonable to think that the Romans received the ufe of money from the Etrufcans and Latins who were their neighbours, or from the Greeks, who w7ere at a diftance, and at that time, as far as appears from their hiltory, abfolutely unknown to them ? “ If this argument (adds he), is ftrong with regard to the neareft Grecian colonies, what muft it be with refpefl to Sicily, an ifland 300 miles diftant from Rome, where it was not known, at that time, if a boat went by land or water ?/’ Argu¬ ments, however, for this opinion have been derived from the fimilarity betwixt the Sicilian and Roman coins •, which Mr Pinkerton now proceeds to examine. The Greek pound in Sicily was called A which was divided into an half and quarter, named Qfue-oQbXtoi and j the latter of which is ftiown by Du Cange to have been a fmall brafs coin, as the other is fuppofed to have been by Mr Pinkerton.— Befides thefe, the follis was divided into eight oboli, 16 3 MEDALS. aflaria or lepta, and 32 noumia, though in common Ancient computation it contained 40 of thefe laft. This coin, Money- notwithftanding fo many divifions, was of no more v value than a halfpenny. Mr Pinkerton controverts an opinion, common among medallifts, that the largeft brafs coin or follis of the lower empire had 40 fmall coins, expreffed by the letter M upon it j the next had 30, expreffed by the letter A •, the half by the letter K j and the quar¬ ter marked I, which contained only 10. Mr Pinker¬ ton informs us, that he has three coins of Anaftafius, all marked M in large $ one of them weighs more than half an ounce ; the fecond 40 grains lefs j and the third of 160 grains, or one third of an ounce ; but the fize is fo very unequal, that the laft, which is very thick, does not appear above half the fize of the firft. There are pieces of Juftinian which weigh a whole ounce j but the fize of copper was increafed as the filver became fcarcer j and the value of the coinage cannot be deduced from the weight of the coins, as it is plain that cur own coinage is not of half the value with regard to the metal. A great number of medal¬ lions were ftruck by Conftantius II. but there is no other copper larger than the half ounce, excepting that of Anaftafius, when the follis began to be ftruck larger. All medalifts allowr the others to be medallions. The metal employed in thefe very fmall coins, though at firft of brafs, was always a bafe and refufe kind ; but copper is generally made ufe of in the parts of the" as from the earlieft times to the lateft j and if brafs be fometimes employed, it is never fuch as ap¬ pears in the feftertii and dupondiarii, which is very fine and beautiful, but only the refufe. “ Yellow brafs of the right fort (fays Mr Pinkerton), feems totally to have ceafed in the Roman coinage with the fefter¬ tius, under Gallienus, though a few fmall coins of very bad metal appear under that hue as late as Ju- lian II.” _ _ 62 Silver was coined in Rome only as late as the 485thRoman year of the city, or 266 B. C. Varro indeed fpeaksfilver* of filver having been coined by Servius Tullius, and the libella having been once in filver j but Pliny’s au¬ thority muft be accounted of more weight than that of this author, as he miftakes the Xitbx of Sicily for Roman coins, having been current at Rome during the time of the firft Punic war. Even Pliny, accord¬ ing to our author, very frequently miftakes with regard to matters much antecedent to his own time 5 and among the moderns he criticifes feverely Erafmus and Hume. “ Erafmus (fays he), who had been in Eng¬ land for fome time, talks of leaden money being ufed here.” Not even a leaden token was ftruck in the reign of Henry VIII. 5 yet his authority has been fol¬ lowed with due deference to fo great a name 5 for how could Erafmus, who muft have feen the matter with his own eyes, affert a direft falfehood ? To give a later inftance in a writer of reputation, Mr Hume, in Vol. VI. of his hiftory, has thefe words, in treating of the reign of lames I. “ It appears that copper halfpence and farthings began to be coined in this reign. Tradefmen had commonly carried on their re¬ tail bufinefs by leaden tokens. The fmall filver penny was foon loft $ and at this time was nowhere to be found.” Copper halfpence and farthings were not ftruck till Charles II. 1.672; there were fmall tokens for Ancient Money. 6.3. Denarii when firft coined. 64 Value of the dena¬ rius and its parts. M E D for farthings ftruck In copper by James I. but not one for the halfpenny. The filver farthings had ceafed with Edward VI. but the filver halfpence continued the foie coinstill Charles II. It was by copper tokens that fmall bufinefs was carried on. The filver penny was much ufed till the end of the reign of George I. and fo far from being nowhere to be found, is fuper- abundant of every reign fince that period, not except¬ ing even the prefent reign of George III. From thefe inftances the reader may judge how ftrangely writers of all ages blunder, when treating a fubjeft of which they are entirely ignorant.” The firft filver denarii coined at Rome, are fup- pofed by our author to have been thofe which are im- prefled with the Roma ; and he inclines to account thofe the moft ancient which have a double female head on the one fide, and on the reverfe Jupiter in a car, with Victory holding the reins, and the word Roma indented in a rude and lingular manner. The double female head feems to denote Rome, in imita¬ tion of the Janus then upon the as. There are 15 of thefe in the cabinet of Dr Hunter; one of the largeft weighs pBJ; grains : and the red, which feem to be of greateft antiquity, are of various weights betwixt that and 84 ; the fmaller and more modern weigh 58 or 59 grains; but Mr Pinkerton is of opinion, that the large ones are of the very firft Roman coinage, and ftruck during that interval of time betwixt the coin¬ age of the firft filver denarius and the as of two ounces. He takes the indentation of the word Roma to be a mark of great antiquity $ fuch a mode being fcarcely known any where elfe, except in Caulonia, Crotona, and other towns of Italy ; all of them allowed to be ftruck at leaft 400 B. C. As thefe large coins are not double denarii, they mull have been rtruck prior to the fmall ones j and Neumann has given an account of one of them recoined by Trajan, in which the inden¬ tation of Ro?viA is carefully preferved. The firft de¬ narius was in value 10 afes, when the as weighed three ounces 5 and allowing 90 grains at a medium for one of thefe large denarii, the proportion of copper to filver muft have been as 1 to 160: but when the as fell to one ounce, the proportion was as 1 to 80 ; when it fell to half an ounce, fo that 16 afes went to the de¬ narius, the proportion was as 1 to 64, at which it re¬ mained. Copper wdth us, in coinage, is to filver as 1 to 40 •, but in aftual value as 1 to 72. At Rome the denarius was worth 8d. j the quina- rius 4d. j and the feftertius, whether filver or brafs, 2d. The denarius is the coin from which our penny is de¬ rived, and w7as the chief filver coin in Rome for 600 years. According to Celfus, feven denarii w?ent to the Roman ounce, which in metals did not exceed 430 grains 5 but as all the denarii hitherto met with weigh at a medium only 60 grains, this would feem to make the Roman ounce only 420 grains ; though perhaps this deficiency may be accounted for from the unavoidable wafte of metal even in the beft preferved of thefe coins. According to this proportion the Ro¬ man pound contained 84 denarii *, but in tale there was a very confiderable excefs j for no fewer than 100 denarii went to the Roman pound. The Greek ounce appears to have been confiderably larger than that of Rome, containing about 528 grains; yet not- withftanding this apparently great odds, the difference in the coins was fo final], that the Greek money wnet Vol. XIII. Part I. A L S. 153 current in Rome, and the Roman in (Greece. The Ancient denarius at firft went for 10 affes, and was marked X: Money, it was afterwards raifed to 16 ; which Mr Pinkerton fuppofes to have been about 175 B. C. Some are met with bearing the number XVI. nay, with every number up to CCCCLXXVI. Thefe large numbers are fuppofed to have been mint-marks of fome kind or other. After being raifed to 16 afes, it continu¬ ed at the fame value till the time of Gallienus ; fo that till that time we are to look upon its conftituent parts to be 16 afes or affaria, eight dupondii, four brafs feftertii, and two filver quinarii. Under the emperor Severus, however, or his fucceffor Caracalla, denarii were ftruck of two fizes, one of them a third heavier than the common; which we muft of confequence fuppofe to have borne a third more value. This large piece obtained the name of argenteus, and argenteus PhilippuS) or the “filver Philip;” the name of Philip having become common to almoft every coin. The common denarii now7 began to be termed minuti and argenli Philippi minutuh, &x\ to exprefs their being fmaller than the reft. Some have imagined that the large denarii were of the fame value with the fmall, only of worfe metal; but Mr Pinkerton obferves, that among the few which have any difference of metal, the imalleft are always the worft. The firft mention of the minuti is in the time of Alexander Severus, who reduced the price of pork from eight minuti at Rome to two and to one. The minutus argentcus of that age was about 40 grains; and from the badnefs of the metal was not worth above 4d. of cur money. Thus the price of meat was by this prince reduced firft to 8d. and then to 4d. gy According to Zozimus and other writers, the pu-Reftoratio’* rity of the Roman coin was reftored by Aurelian t °/pu- but Mr Pinkerton controverts this opinion ; thinking 01 . , , .q 7 . ,0 Roman it more probable, that he only made the attempt wxth-co^ns> out fuccefs; or that his reformation might be entirely confined to gold, on which there is an evident change after the time of this emperor. His fucceffor Taci¬ tus is faid to have allowed no brafs to be mixed with filver upon any account ; yet the few coins of this emperor are very much alloyed. We are certain, however, that the emperor Dioclefian reftored the fil¬ ver to its ancient purity ; the denarii ftruck in his reign being very fmall indeed, but of as fine filver as the moft ancient coins of the empire. After Gor¬ dian III. the fmall denarius entirely vanished, while the large one w7as fo much diminilhed, that it refem- bled the tninutus, or fmall one of Caracalla, in fize. Gallienus introduced the denarii errei inftead of the fef¬ tertii. The argenteus, though reduced more than one third in fize, contained fix denarii serei, the old ftand- ard of feftertii. According to the writers of this pe¬ riod, and fome time afterwards, the denarius or ar¬ genteus contained 60 affaria ; whence it follows, that each denarius sereus had 10 ; and from this it probably had its name. The affaria are of the fixe of the ar- gentei already mentioned ; and fhow the copper to have retained nearly its old proportion of value to the filver, viz. 1 to 60. ^ A larger filver coin w7as introduced by Conftan-Reforma- tine I. who accommodated the new money to the tion of the pound of gold in fuch a manner, that 1000 of the for-filver Cbm mer in tale were equal to the latter in value ; fo that this new piece frem thence obtained the name of the ’ * U milliarevjis 54 Ancient Monev. 67 Account of the fmall Roman coins. M E D mUHarcvlis or “ thoufander.” Its tveight at a medi- um is 70 grams, or 70 to the pound of filver : but Mr Pinkerton is of opinion, that it might have contained 72 grains, of which two have no.v periihed by the foftnefs of the filver ; that the pound contained 7 2 j or that two of the number might be allowed for coinage j while the alloy alone would pay for coining gold. The code fays, that .60 went to the pound ; but the numbers of this are quite corrupt. The miltiarenjis was •worth about a {hilling fterling. The argentei or de¬ narii, however, were ftill the mofl: common currency ; and having been originally rated at too to the pound of filver in tale, they from thence began to be called centenionales, or “ hundreders.” Thofe of Con- ilantine I. and II. Conftans, and Conftantius, weigh from 50 grains down to 40; thofe of Julian and Jovian, from 40 to 30 , and of the fucceeding emperors from that time to Juftinian, from 30 to 20. Under Hera- clius they ceafed entirely ; and, from Juftinian to th«ir total abolition, [tad been brought down from 15 to 10 grains. A like decreafe of weight took place in the milliarenfis ; thofe of Conftantine and Conflans being above 70 grains in weight 5 thofe of Arcadius not above 60 ; and the milliarenfis of Juftinian not more than 30 grains ; but, from the weight of thofe in Dr Hunter’s cabinet, Mr Pinkerton deduces the medium to have been exadlly 7oT8T grains. Thefe coins were alfo called majorince. The fmaller filver coins of Rome tvere, 1. The qui- narius, at firft called viBoriatus, from the image of Vic¬ tory on its reverfe ; and which it continued to bear from firft to laft. Its original value was five afes, but it was afterwards railed to eight, when the value of the denarius increafed to 16. According to Pliny, it was firft coined in confequence of the lex C/odia, about the 523th year of Rome. Some are of opinion, that it was called under the Conftantinopolitan empire, becaufe it wras worth a xi^xtioi of gold, 144 of which went to the ounce : but this is denied by Mr Pinkerton, becaufe, at the time that the word xi^xrtov firft appears in hiftory, the denarius did not weigh above 30 grains •, and of confequence, as 25 muft have gone to the gold folidus, of which there rvere fix in the ounce, 130 denarii muft have gone to the ounce of gold. He is therefore of opinion, that the word x,i£X7;t>v, was only another name for the denarius when much reduced in fize ; probably owing to the great fcarcity of filver in Conftantinople, though in the fame city there was plenty of gold j and of confequence, the gold folidus w^s never diminilhed. “ For Montef- quieu (fays our author) has well obferved, that gold muft be common where filver is rare. Hence gold was the common regulation of accounts in the Eaftern empire.” The ^ixs^xTiev met with in ancient authors, according to Mr Pinkerton, was merely an improper name for the milliarenjis; when, on account of the fcarcity of filver, the denarius was reduced, and no milliarenfes coined : fo that the current milliarenfis of former reigns happened to be doable to the denarius or centenonialis. The quinarius diminilhes in fize along with the other coins : thofe of Auguftus weigh¬ ing 30 grains, of Severns 23, of Conftantine I. 29, of Juftinian 12, and of Heraclius only 3, A new filver coinage leems to have taken place after the days of this emperor j as the little we then meet with, A L S. which in the beft cabinets fcarce exceeds a dozen of Ancient coins, confifts entirely of large unfhapely pieces of M°ney. . coarfe metal. 2. The confular denarius had alfo four filver fefter-Divifions of tii, till the as fell to half an ounce, when it was thought the dena- proper to coin the feftertius in brafs, as it continued rms‘ to be ever afterwards. “ The very laft filver fefter- tius (fays Mr Pinkerton) wThich appears, is one with a head of Mercury, and PI. S. •, on the reverfe a caduceus P. SEPVLLIVS $ who appears to be the P. SEPVLLivs macer of the denarii of Julius Caefar. If fo, as is moft probable, the feftertius was coined in filver down to Auguftus ; and it is of courfe not to be expefted that any of brafs can appear till Auguftus, under wdrom they are adlually quite common. I have in¬ deed feen no coin which could be a confular brafs fe¬ ftertius ; and though w;e have certainly brafs dupondii of Caefar, yet it is reafonable to infer, that the brafs feftertius w7as firft coined by Auguftus. Not one filver feftertius appears during the w'hole imperial period, yet we know7 that the feftertius was the mort common of all filver coins. The confular feftertii of filver, marked H. S. are not uncommon, nor the quinarii ; but the latter are very fcarce of all the emperors, if we except one inftance, the ASIA RECEPTA of Au- guftus- . . “ The Roman gold coinage was ftill later than that Rom.m of filver. Pliny tells us, that “ gold was coined 62goltl- years after filver ; and the fcruple went for 60 fefler- ces. It was afterwards thought proper to coin 40 pieces out of the pound of gold. And our princes have by degrees diminifhed their weight to 43 in the pound.” This account is confirmed by the pieces which ftill remain ; for u7e have that very coin weigh¬ ing a fcruple, wdiich went for 20 fefterces. On one fide is the head of Mars, and on the other an eagle j and it is marked xx. We have another coin of the fame kind, but double, marked xxxx ; and its triple, marked \^x or 60 j the ■<]/ being the old numeral charafler for 30.” Mr Pinkerton, the difeoverer of this, treats other medallifts with great afperity. Sa- vot and Hardouin are mentioned by name y the latter (he fays) is “ ignorant of common fenfe j” and nei¬ ther he nor Savot could explain it but by reading backward ; put the for the Roman V, and thus mak¬ ing it xv. Other readings have been given by vari¬ ous medallifts, but none have hit upon the true one excepting our author, though the coin itfelf fed to it ; being juft three times the weight of that marked xx. We have likewife half the largeft coin, which is mark¬ ed XXX, and which weighs 26 grains the fmalleft is only 175-j the XXXX weighs 34; and the LX or drachma 33. There is alfo the didrachm of this coin¬ age, of 106 grains. 7 becaufe under him and his fucceffor lian. Probus, the common aureus was of too grains, a fize confined to thofe emperors : there are likewife halves of about 50 grains *, and double aurei, commonly of very fine workmanflrip, of upwards of 200 grains. In the time of Gallienus, the precious metal was fo common, that this emperor vied in magnificence with Nero and Pleiiogabalus. Aurelian, who plundered the rich city of Palmyra, and thus became mafter of the treafures of the eat!, obtained fucli a profufion of gold, that he looked upon it to be produced by nature in greater plenty than filver. It is remarkable, that du¬ ring this emperor’s reign there was a rebellion among, the money coiners, which could not be quelled but by the deftrublion of feveral thoufands j which Mr Pin¬ kerton afcribes to his having ordered the gold to be reftored to its former fize, but to go for no more lilver than it formerly did. “ So very little filver (fays he) occurs of this period, that it is plain no altera¬ tion in the filver produced the war with the mo- neyers ; and in the brafs he made no change ; or if he nad, it were firange that fuch commotions fliould a rife about fo trifling a metal. But if, as appears from the coins, he ordered the aureus, which had fallen to 80 grains, to be raffed to about 100, it is no wonder that the contractors ihould be in an uproar ; for a whole quarter of their coinage, amounting as would feem, to all their profits, was lofl. Aurelian judged, tnat when he found gold fo common in the eaft, it A L S. wTas equally fo in the weft ; and that the moneyers muff have made a moft exorbitant profit j but his ideas on this fubjeff were partial and unjuft : and after his fhort reign, which did net exceed five months after the alteration, the gold returned to its former courfe ; though a few pieces occur of Aurelian’s ftandard, flruck, as would feem, in the commencement of the reign of Probus his fuccefl.br. From this time to that of Conftantine I. the aureus weighed between 70 and 80 grains; but in his reign it was changed for the folidus, of which fix went to the ounce of gold, which w'ent for 14 milliarenfes, and 25 denarii as before ; the value of filver being now to .gold as 14 to 1. This nerv coin continued of the fame, value to the final downfal of the Conftantinopo- litan empire •, gold being always very plentiful in that city, though filver became more and more fcarce. The folidus was worth 12s. fterling. Here again our au¬ thor moft feverely criticifes Mr Clarke and Mr Raper : the former (he fays) with refpedl to the value of gold in the time of Conftantine I. “ has left all his fenfes behind him. In page 267, he abfurdly afferts, that 20 denarii went to the folidus in the time of Theo- dofius I. and proceeds with this deplorabla error to the end of his work. He then tells uq that only 14 denarii went to the folidus under Conftantine I. &c.” To Mr Raper, however, he is a little more merciful, as he owns, that “ though he (Mr Raper) has ft range- ly confounded the milliarenfis with the denarius, he has yet kept common fenfe for his guide.” Mr Pin¬ kerton, indeed, argues with great probability, “ that had any change in the coinage taken place between the time of Conftantine and Theodofius I. that is, in lefs than 50 years, the laws of that period, which are all in the Theodofian code, muft have noticed it.” To this and other arguments upon the fubjeft, Mr Pinkerton adds the following obfervation upon the va¬ lue of gold and filver : “ As a ftate advances to its height, gold increafes in value •, and as a ftate declines, it decreafes, providing the metals are kept on a par as to purity. Hence we may argue, that gold decreafed in its relation to filver perhaps four or five centuries, furniftied moft European kingdoms with gold in coin, which otherwife would, from their want of arts and of intercourfe with the caff, then the grand feminary of that metal, have almoft been ignorant of what gold was. Thefe gold coins were called Bezants^ in Eu¬ rope, becaufe fent from Byzantium or Conftantinople •, and were folidi of the old fcale, fix to the ounce. In Byzantine writers, the folidus is alfo called nomifma, or “ the coin j” cn/Jinos, becaufe of gold ; hyperperos, from its being refined with fire, or fror?! its being of bright gold flaming like fire. The fol'idi alfo, as the aurei formerly, received names from the princes whofe portraits they bore ; as Michelati, Manuelati. Solidus is a term ufed alfo for the aureus by Apulelus, who lived in the time of Antoninus the Philofopher j nay, as early as in the praetorian edi6Is of the time of Trajan. It wa^ then a diftin<5tion from the femittis or half. In the time of Valerian, when aurei of different fizes had been introduced, it became neceflary to dillinguilh the particular aurei meant. Hence in the Imperial Re- feripts, published by the Hijlorue Augvjlee Scriptures, Valerian ufes the term Bhiiippeos i\oJlri vultus, for the common aurei. Amrehnn ufes the fame term aurei U 2 Philippei, 156 MED Ancient Philippei, for the aurei which he had reftored to their , lvIe”cy- , fize in fome degree. Gallienus ufes aurei Valeriani for his father’s coins. A'/rei Antoniniani are likewife put by Valerian for coins of the early Antonini, of fuperior llandard to any then ufed. Divifion of I” the firft gold coinage at Rome, the aureus was the aureus, divided into four parts; the femiffis of 60 fellertii ; the tremifiis, or third, of 40; the fourth, the name of which is not mentioned, of 30; and the fcrupulum of 20. But in a fliort time all of thefe fell into difufe, except the femiflis or half, which is extremely fcarce ; fo that it is probable that few have been flruck. It is an erroneous opinion (according to Mr Pinkerton), that the femilBs was called a denarius aureus. The aureus itfelf indeed had this name ; but the name of quinanus is applied to the femiflis with greater proprie¬ ty than the former. Trientes, or tremiffis of gold, are found of Valerian and his fon Gallienus, and weigh about 30 grains. Thofe of Salonina the wife of Gal¬ lienus weigh 33 grains. Under the Conllantinopo- litan empire, tremiffes again make their appearance ; and from the time of Valentinian downwards, the thirds are the moft common coins of gold, being worth about 4s. fterling. The femiffis is likewife mention¬ ed, but none occur earlier than the time of Bafilifcus. The gold tremiffis was the pattern of the French and Spaniih gold coins; as the filver denarius, in its dimi- 73 niffied Hate, was of the Gothic and Saxon penny. Account of We (hall clofe this account of the Roman money the Roman with fome remarks concerning the mint, and method coining 01 co’na£e- This at firft feems to have been under the dire£1 ion of the quaeftor. About the time that filver was firft coined in Rome, viz. about 266 B. C. the triumviri moneta/es were created. They were at firft of fen at orial rank, but were by Auguftus chofen from among the equeftrian ; and the title of triumviri was continued till after the time of Caracalla ; but under Aurelian there was probably but one mafter of the mint, called rationahs; and Mr Pinkerton is of opi¬ nion that the change took place under Gallienus. He feems alfo to have permitted the provincial cities to coin gold and filver, as well as to have altered the form of the mints in the capital, and to have ordered them all to ftrike money with Latin legends, and of the fame forms ; as in his time we firft meet with coins with mint marks of cities and offices. The violent in- furredftion which took place in his reign has already been mentioned, as well as its probable caufe; and Mr Gibbon has fhown, that the concealed enemies of Au¬ relian took fuch advantage of this infurredtion, that it coft 7000 of his beft troops before it could be quelled. About this time the procurator monetce feems to have fucceeded the rationalis as diredtor of the mint. In the colonies, the diredlion of the mint feems to have been given to the decemviri, whofe names frequently occur on colonial coins; “ which (fays Mr Pinkerton), though generally of rude invention, and ruder execu¬ tion, are yet often interefting and important.” The engraving of the ancient dies ufed in coinage was a work, of much genius and labour ; and at Rome Greek artifts were generally employed in it ; but it has been thought a matter of great furprife, that fcarce any two anment coins are to be found exadtly the fame. Hence fome antiquaries have imagined, that only, a fingle coin was thrown off from each die. M, A L S. Beauvais informs us, that the only two Roman impe- Ancient rial coins of the firft times w hich he had feen per- Money- ^ fedtly alike were thofe of the emperor Galba. It is, v however, the opinion of the beft judges, that a perfedt fimilarity betwixt two medals is a very great reafon for fuppofing one of them to be forged. “ It muft tilfo be obferved (fays Pdfi Pinkerton), that the difterences in coins, apparently from the lame die, are often fo minute as to efcape an eye not ufed to microfcopic ob- fervations of this fort. But it would be furprifing if any two ancient coins wTere now found ftruck with the fame die ; for out of each million iffued, not above one has reached us. Dies foon give way by the vio¬ lence of the wrork ; and the ancients had no puncheons nor matrices, but were forced to engrave many dies for the fame coin. Even in our mint, upon fending for a (hilling’s worth of new halfpence, it will appear that three or four dies have been uled. Sometimes the ' obverfe of the die gives way, fometimes the reverfe; but among us it is renewed by puncheons, though with variations in the lettering or other minute ftrokes ;. w hile the ancients wrere forced to recur to another die differently engraven. The engravers of the die were called calatores ; other officers employed in the mint were the fpcclatores, expeclatorcs, or nummularii. The melters w’ere ftyled fufarii, jlatuarii, and Jlaturarii; thofe who adjufted the weight wrere called cequatorcs mo- netarum; thofe who put the pieces into the die fup- pojito res, and thofe who ftruck them malleatores. At the head of each office wras an officer named primice- rius, and the foreman was named optio et exatlory In order to affift the high relief on the coins, the metal, after being melted and refined, was caft into bullets, as appears from the ancient coins not being cut or filed on the edges, but often cradked, and al¬ ways rough and unequal. Thefe bullets were then put into the die, and received the impreffion by re¬ peated ftrokes of the hammer, though fometimes a machine appears to have been ufed for this purpofe : for Boiterue informs us, that there was a picture of the Roman mintage in a grotto near Baiae, where a machine w7as reprefented holding up a large (tone as if to let it fall fuddenly, and ftrike the coin at once. None of the ancient money wTas caft in moulds, except¬ ing the moft ancient and very large Roman brafs, commonly called weights, and other Italian pieces of that fort ; all the reft being mere forgeries of ancient and modern times. Some Roman moulds which have been found are a proof of this ; and from thefe fome medallifts have erroneoufly imagined that the an¬ cients firft caft their money in moulds, and then (lamp- ed it, in order to make the impreffion more clear and (harp. The ancients had fome knowledge of the method of crenating the edges of their coins, which they did by cutting out regular notches upon them; and of this kind we find fome of the Syrian and ancient con- fular coins, with a few others. The former were caft in this fhape, and then ftruck ; but the latter were crenated by incifion, to prevent forgery, by (flowing the mfide of the metal : however, the ancient forgers alfo found out a method of imitating this ; for Mr Pin¬ kerton informs us, that he had a Roman confular coin, of which the incifions, like the reft, were plated with filver over the copper. Sect.- ?4 , Erafs and copper beft preserved by the run: that covers them. 75 Ditterent kinds of this ruft. 16 Medals liow dimi¬ ni thed in v*i!ue. MED Sect. VI. Of the Prefervalion of Medals. We now come to confider what it is that diftin- guifhes one medal from another, and why fome are fo highly prized more than others. This, in general, befides its genuinenefs, confifts in the high degree of prefervation in which it is. This, by Mr Pinkerton, is called the confervation of medals, and is by him re¬ garded as good and as perfeB. In this, he fays that a true judge is fo nice, that he will rejedt even the rareil: coins if in the leaf! defaced either in the figures or legend. Some, however, are obliged to content themfelves with thofe which are a little rubbed, while thofe of fuperior tafte and abilities have in their ca¬ binets only fuch as are in the very ftate in which they came from the mint; and fuch, he fays, are the ca¬ binets of Sir Robert Auftin, and Mr Walpole, of Roman filver, at Strawberryhill. It is abfolutely ne- ceifary, however, that a coin be in what is called good prefervation ; which in the Greek or Roman empe¬ rors, and the colonial coins, is fuppofed to be when the legends can be read with fome difficulty ; but when the confervation is perfeft, and the coin juft as it came from the mint, even the moft common coins are valuable. The fine ruft, like varffiffi, which covers the fur- face of brafs and copper coins, is found to be the beft preferver of them •, and is brought on by lying in a certain kind of foil. Gold cannot be contaminated but by iron mold, which happens when the coin lies in a foil impregnated with iron j but lilver is fufcep- tible of various kinds of ruft, principally green and red *, both of which yield to vinegar. In gold and filver coins the ruft muft be removed, as being preju¬ dicial *, but in brafs and copper it is prefervative and ornamental ; a circumftance taken notice of by the ancients. “ This fine ruft (fays Mr Pinkerton), which is indeed a natural varniffi not imitable by the art of man, is fometimes a delicate blue, like that of a tur- quoife ; fometimes of a bronze brown, equal to that obfervable in ancient ftatues of bronze, and fo highly prized ; and fometimes of an exquifite green, a little on the azure hue, which laft is the moft beautiful of all. It is alfo found of a fine purple, of olive, and of a cream colour or pale yellow7 : wffiich laft is exqui¬ fite, and fhow7s the impreffion to as much advantage as paper of cream colour, ufed in all great foreign prefles, does copperplates and printing. The Neapo¬ litan patina (the ruft in queftion) is of a light green ; and wffien free from excrefcence or blemiffi is very beautiful. Sometimes the purple patina gleams through an upper coat of another colour, writh as fine effeft as a variegated filk or gem. In a few inftances a ruft of a deeper green is found ; and it is fometimes fpot- ted with the red or bronze (hade, which gives it o;uite the appearance of the Eaft Indian ftone called the bloodJlone. Thefe rufts are all, wffien the real produft of time, as hard as the metal itfelf, and preferve it much better than any artificial varnifh could have done; concealing at the fame time not the moft minute par¬ ticle of the impreffion of the coin.” The value of medals is lowered when any of the letters of the legend are mifplaced ; as a iufpicion of forgery is thus induced. Such is the cafe with many of thofe of Claudius Gothxcus. The fame, or even A L S, 157 greater, diminution in value takes place in fuch coins Preferva- as have not been well fixed in the die, which has oc-, t‘or1, . cafioned their flipping under the ftrokes of the ham- v f mer, and thus made a double or triple image. Many coins of this kind are found in wffiich the one fide is perfectly w7ell formed, but the other blundered in the manner juft mentioned. Another blemiffi, but of fmaller moment, and wffiich to fome may be rather a recommendation, is when the workmen through in¬ attention have put another coin into the die without taking out the former. Thus the coin is convex on one fide, and concave on the other, having the fame figure upon both its fides. 77 The medals faid by the judges in this fcience to be Counter. countermarhed are very rare, and highly valued. They have a fmall ftamp imprefled upon them, in fome an 1 head, in others a few leters, fuch as Aug : N. pro¬ bus, &c. which marks are fuppofed to imply an al¬ teration in the value of the coin ; as w7as the cafe with the coumermarked coins of Henry VIII. and Queen Mary of Scotland. Some have a fmall hole through them ; fometimes with a little ring fattened in it, hav¬ ing been ufed as ornaments; but this makes no al¬ teration in their value. Neither is it any diminution in the value of a coin that it is fplit at the edges ; for coins of undoubted antiquity have often been found in this ftate, the caufe of which has been already explain¬ ed. On the contrary, this cracking is generally con- iidered as a great merit ; but Mr Pinkerton (ufpedls that one of thefe cracked coins has given rile to an error with refpedl to the wife of Caraulius who reigned for fome time in Britain. The infer!ption is read oriuna Aug : and there is a crack in the medal juft before the O of oriuna. Without this crack Mr Pin¬ kerton fuppofes that it would have been read For- tuna Aug. 7 s Some particular foils have the property of giving Silver ancU filver a yellow colour as if it had been gilt. It natu- g0^ h°w rally acquires a black colour through time, which any fulphureous vapour will bring on in a few minutes. From its being fo fufceptible of injuries, it was al¬ ways mixed by the ancients with much alloy, in or¬ der to harden it. Hence the impreffions of the ancient filver coins remain perfedl to this day, wffiile thofe of modern coins are obliterated in a few years. On this account Mr Pinkerton expreflfes a wiffi, that modern ftates would allow a much greater proportion of alloy in their filver coin than they ufually do. As gold admits of no ruft except that from iron above-mention¬ ed, the coins of this metal are generally in perfedt confervation, and frefti as from the mint. To cleanfe gold coins from this ruft, it. is beft to How to - fteep them in aquafortis, which, though a very power-c!ean^e ful folvent of other metals, has no eftedl upon gold. t*'rrnj Silver may be cleanfed by fteeping for a day or two in vinegar, but more effe&ually by boiling in water with three parts of tartar and one of fea fait ; on both thefe metals, however, the ruft is always in fpots, and never forms an entire incruftation as on brafs or copper. The coins of thefe two metals muft never be cleanfed, as they would thus be rendered full of fmall holes eaten by the ruft. Sometimes, however, they are found fo totally obfeured with ruft, that no¬ thing can be difeovered upon them ; in which cafe it is beft to clear them with a graver ; but it may alfo be done by boiling them for 24 hours in water with- thre© tarnifhed,. 19 •J 5 o How to di ftinguifti true from counter¬ feits. So Why an¬ cient coins are in fuch a high hate of pre fervation. Si Number of ancient coins. •tln-ce phr«of tartar and one of alum; not fea fait as in filver coins. he high ft ate of prefervation in vrhich ancient coins are u'.ually found, is thus accounted for by Mr Hancarville. He obferves, that the chief reafon is the cuilom of the ancients always to bury one or more coins with their dead, in order to pay for their paf- fage over the river Styx. “ From Phidon of Argos (fays he) to Conflantine I. are 36 generations : and fiom Magna Graecia to the Euphrates, from Cyrene to the Euxine fea, Grecian arts prevailed, and the inhabitants amounted to about 30,000,000. ’There died, therefore, in that time and region, not lefs than ten theufand millions of people, all of whom had coins of one fort or other buried with them. The tombs were facred and untouched ; and afterwards negleffed, till modem curiofity or chance began to difclofe them. The mn of Tlavia Valentina, in Mr Towlev’s capital collebfion, contained feven brafs coins of Antoninus Pius and Heliogabalus. Such are generally black, from being burnt with the dead. The beft and frefli- eft coins were ufed on thefe occafions from refpeft to the dead ; and hence their fine confervation. At Sy- racufe a fkeleton was found in a tomb, with a beauti- juI gold coin in its mouth ; and innumerable other in- ilances might be given, for hardly is a funeral urn found without coins. Other incidents alfo confpire to lurnifli us with numbers of ancient coins, though the above-recited circumftance be the chief caufe of perfeff confervation. In Sicily, the filver coins with the head of Proferpine were found in fuch numbers as to weigh 600 French livres or pounds. In the 16th century, 60,000 Roman coins were found at Modena, thought to be a military cheft hid after the battle of Bedriacum, when Otho was defeated by Vi- telhus. Near Breft, in the year 1760, between 20 and 30,000 Roman coins were found. A treafure of gold coins of Lyfimachus was found at Deva on the Mams ; and Strabo, lib. vii. and Paufan. in Attic, tell that he was defeated by the Get* ; at which time this treafure feems to have fallen into their hands.” Thus Mr Pinkerton, from the authority of Mr Hancarville and others : but confidering thefe vaft numbers of coins found in various places, it feems fur- pnfing how fo few fhould now remain in the cabinets of tne curious, as the fame author informs us that the whom of the different ancient coins known to us amount only to about 80,000, though he owns, that the calculation cannot be efteemed accurate. SECT. VII. How to dijlinguijh true Medals from coun¬ terfeits. . T.HE di/Mt and the mo ft important thing m tne whole fcience of medals is the method of di- itinguilhmg the true from the counterfeit. The value put Uj on ancient coins made the forgery of them al- mo coeval with the fcience itfelf; and as no laws in- JC . a P'Jyffihment upon fuch forgers, men of great gen.us and abilities have undertaken the trade : but wnetner to the real detriment of the fcience or not, is matter of mme doubt ; for if only exaeff copies of genuine medals are fold for the originals, the Lpofi- courted^ver ; but the cafe nmft be ac- / ddureut, if people take it upon them to forge medals which never exifted. At firit the fer- •M E E> A L S. feits. geries were extremely grofs ; and medals were forged How to di- of Priam, of Ariitotle, Artemifia, Flannibal, and moft ftinguifh of the other illuftrious perfonages of antiquity. Moft tmp of thele wrere done in fuch a manner, that the fraud c0l,nter~ could eafily be difeovered ; but others have impofed even upon very learned men. Mr Pinkerton mentions a remarkable medal of the emperor Heraclius, repre- fenting him in a chariot on the reverfe, with Greek and Latin inferiptions, which Jofeph Scaliger and Lipfius imagined to have been ftruck in his own time, but which was certainly iffued in Italy in the icth century. “ Other learned men (fays our author) have been ttrangely milled, when fpeaking of coins; for to be learned in one fubjeft excludes not grofs ignorance in others. Budaeus, de Affe, quotes a denarius of Cicero, M. tull. Erafmus, in one of his Epiftles tells us with great gravity, that the gold coin of Bmtus ft ruck in Thrace, KOZS2N, bears the patriarch Noah coming out of the ark with his two fons, and takes the Roman eagle for the dove with the’olive branch. Winkelman, in his letters informs us, that the fmall brafs piece with Virgil’s head, reverfe’ epo is undoubtedly ancient Roman ; and adds, that no knowledge of coins can be had . out of Rome: but Winkelman, fo converfant in ftatues, knew nothing of qoins. It is from other artifts and other produc¬ tions that any danger of deceit arifes. And there is no wonder that even the Ikilful are milled by fuch artifts as have ufed this trade ; for among them appear c- the names of Vidor Gambello, Giovani del Cavino, Coins fbr- f., ., PAr)UAN, and his fon Aleffandro Bafliano ex- likewife of Padua, Benvenuto Cellini, AleffandroceIlent ar" Greco, Leo Aretino, Jacobo da Frezzo, FederigotlftS' Bonzagna, and Giovani Jacopo, his brother ; Sebaf- tiano Plumbo, Valerio de Vizenza, Gorlams, a Ger¬ man, Carteron of Flolland, and others, all or moft of them of the 16th century ; and Cavino the Paduan who is the moft famous, lived in the middle of that century. The forgeries of Cavino are' held m no little efteem, being of wonderful execution. His and thofe of Carteron are the moft numerous many of the ether artifts here mentioned not hav- mg lorged above two or three coins. Later forgers were Dervieu of Florence who confined himfelf to medallions, and Cogornier who gave coins of the 20 tyrants in fmall brafs. The chief part of the forgeries 01 Greek medals which have come to my knowledge are of the firft mentioned, and a very grofs kind, repre- fenting perfons who could never appear upon coin, uch as Priam, Alaeas, Plato, Alcibiades, Artemifia and others. The real Greek coins were very little known or valued till the works of Goltzius appeared which were happily pofterior to the tera of the grand forgers. . Why later forgers have feldom thought of counterfeiting them cannot be eafily accounted for if u is not ©wing to the rnafter!y workmanlhip of the ori¬ ginals, which lets all imitation at defiance. Forgeries, icwever, of moft ancient coins may be met with, and 01 the Greek among the reft. 1 he forgeries are more confpicuous among the Re-Horan for- man medals than any other kind of coins ; but we are genes more not to look upon ail thefe as the work of modern (0nli)icu0’>s artifis. On the contrary, we are affured that manytban G"eek* of them were fabricated in the times of the Romans themielves, fome of them being even held in more efti- mation than the genuine coins themfelves, on account 1 of §5 Imperial medals. MED How to di-of their being plated, and otherwife executed in a ftinguifli manner to which modern forgers could never attain, true from jrven tpe anc;ents held fome of tbefe counterfeits in feits " foci1 eftimation, that Pliny informs us there were fre- i quently many true denarii given for one falfe one.”— Caracalla is faid to have coined money of copper and lead plated w;ith fdver ; and plated coins, the work of ancient forgers, occur of many Greek cities and princes •, nay, there are even forgeries of barbaric coins. “ Some Roman coins (fays Mr Pinkerton), are found of iron or lead plated with brafs, perhaps trials of the fkill of the forger. Iron is the molt com¬ mon j but one decurfio of Nero is known of lead plated with copper. Neumann jultly obferves, that no hifto- ric faith can be put in plated coins, and that molt faulty reveries, &c. arife from plated coins not being noticed as fuch. Even of the Roman confular coins Denarius of not very many have ever been forged. The celebrated Brutus. lilver denarius of Brutus, with the cap of liberty and two daggers, is the chief inftance of a confular coin of which a counterfeit is known. But it is eafily re¬ jected by this mark : in the true coin the cap of liber¬ ty is below the guard or hilt of the daggers 5 in the falfe, the top of it rifes above that hilt.” The imperial feries of medals is the grand objeCt of modern medallic forgeries 5 and the deception was at firft extended to the molt eminent writers upon the fubjeCt. The counterfeits are by Mr Pinkerton divided into lix clafles. I. Such as are known to be imitations, but valued on account of the artilts by whom they are executed. In this clafs the medals of the Paduan rank highelt ; the others being fo numerous, that a complete feries of imperial medals of almolt every kind, nay almolt of every medallion, may be formed from among them. In France, particularly, by far the greater part of the ca¬ binets are filled with counterfeits of this kind. They are diftinguifhed from fuch as are genuine by the fol¬ lowing marks : I. The counterfeits are almoft uni- verfally thinner. 2. They are never worn or damaged. 3. The letters are modern. 4. They are either deili- tute of varnilh entirely, or have a falfe one, which is eafily known by its being black, fliining, and greafy, and very eafily hurt with the touch of a needle, while the varnifh of ancient medals is as hard as the metal itfelf. Inflead of the greafy black varnilh above mentioned, indeed, they have fometimes a light green one, fpotted with a kind of iron marks, and is com- pofed of fulphur, verdigrife, and vinegar. It may frequently be diftinguifhed by the hairftrokes of the pencil with which it was laid on being vilible upon it. 5. The fides are either filed or too much fmoothed by art, or bear the marks of a fmall hammer. 6. The counterfeits are always exaftly circular, which is not the cafe with ancient medals, efpecially after the time of Trajan. The Paduan forgeries may be diftinguifhed from Series how thofe Gf inferior artifts by the following marks: 1. The known. former are feldom thinner than the ancient. 2. They very feldom appear as wmrn or damaged, but the others very frequently, efpecially in the reverfe, and legend of the reverfe, which fometimes, as in forged Othos, appear as half confumed by time. 3. The letters in mould* taken from the antique coins have the rudenefs of antiquity. 4. Falfe varnifh is commonly light green 36 Paduan for- A L S. 159 or black, and ftiines too much or too little. 5. The How to di- fides of forged coins are frequently quite fmooth, and undiftinguifhable from the ancient, though to accom- plifh this requires but little art. 6. Counterfeit me¬ dals are frequently as irregular in their form as the genuine *, but the Paduan are generally circular, though falfe coins have often little pieces cut oft, in perfefl imitation of the genuine. 7. In caft coins the letters do not go (harp down into the medal, and have no fix¬ ed outline their minute angles, as well as thofe of the drapery, are commonly filled up, and have not the iharpnefs of the genuine kind. Where the letters or figures are faint, the coin is greatly to be fufpefted. gy The letters form the great criterion of medals, the Letters the ancient being very rude, but the modern otherwife j principal the reafon of which, according to Cellini, is, that the^'^j°afH ancients engraved all their matrices with the graver or burin, while 'the modern, forgers ftrike theirs with a punch. gg According to Vico, the falfe patina is green, black, Vico’s ac- ruffet, brown, gray, and iron colour. The green is count of made from verdigrife, the black is the fmoke of ful- Patana* phur, the gray is made of chalk fteeped in urine, the coin being left for fome days in the mixture. The rul- fet is next to the natural, by reafon of its being a kind of froth which the fire forces from ancient coins j but when falfe, it ftiines too much. To make it they frequently took the large brafs coins of the Ptolemies, which were often corroded, and made them red hot in the fire ; put the coins upon them, and a fine patina adhered. Our author does not fay in what manner the iron-coloured patina was made. “ Sometimes (adds he) they take an old defaced coin, covered with real patina, and ftamp it anew' *, but the patina is then too bright in the cavities, and too dull in the protu¬ berances. The trial of brals coins with the tongue is not to be defpifed ; for if modern the patina taftes bitter or pungent, while if ancient it is quite taftelefs.” Mr Pinkerton informs us, that all medallions from Julius Casfar to Adrian are much to be fulpedlen of forgery 5 the true medals of the firft 14 emperors be¬ ing exceedingly valuable, and to be found only in the cabinets of princes. sq II. The fecond clafs of counterfeit medals contains Meda's caft thofe caft from moulds taken from the Paduan forge- *ra;:' thd ries, and others done by eminent matters. Thefe are f1 ' 'ur" fometimes more difficult to be difcovered than the for-'’ mer, becaufe in cafting them they can give any degree of thicknefs they pleafe \ and, filling the fmall land- holes with maftic, they retouch the letters with a gra¬ ver, and cover the whole with varnifh. The inllruc- tions already given for the former clafs, however, are alfo ufeful for thofe of the fecond, with this addition, that medals of this clafs are generally lighter than the genuine, becaufe fire rarefies the metal in fome degree-, while that which is itruck is rather ccnden'ed by the ftrokes. In gold and filver medals there cannot be any deception of this kind 5 becaufe thefe metals ad¬ mit not of patina, and confequently the varniffi 'e- trays the impofition. The marks of the file on the margin of thofe of the fecond clafs are a certain fign of forgery ; though thefe do not always indicate he forgery to be of modern date, becaufe the Romans often filed the edges of coins to accommodate the:n to the purpofes of ornament, as quarter guineas are lonm- times i6o MEDAL S. tique. 91 Ancient me da is re¬ touched. How to d:- times put into the bottora of punch ladles. It is com- true^froni mon to *m’tate t^e holes of medals made by time by counter- means of aquafortis j but this deftroys the fides of feits. a coin more effectually than if it had been eat into 1 ' ~'T—J naturally. The fraud, however, is not eafily diftin- 90 guiihed. Medals caft IJI. Medals cajl in moulds from an antique.—In this ^o”1 an an-mode fome forgers, as Beauvais informs us, have been fo very careful, that they would melt a common me¬ dal of the emperor whom they meant to counterfeit, left the quality of the metal fliould betray them. “ This (fays Mr Pinkerton), has been done in the fil- ver Septimius Severus, with the reverfe ©f a trium¬ phal arch, for which a common coin of the fame prince has been melted j and in other inftances. Putting me¬ tals in the fire or upon hot iron to cleanfe them, gives them an appearance of being caft 5 for fome fpots of the metal being fofter than the reft will run, which makes this one of the worft methods of cleaning medals.— The dire&ions given for difcovering the two former deceptions hold good alfo in this. IV. Ancient medals retouched and altered.—This is a clafs of counterfeits more difficult to be difcovered than any other. “ The art (fays Mr Pinkerton) ex¬ erted in this clafs is aftoniftiing 5 and a connoiffeur is the lefs apt to fufpeift it, becaufe the coins themfelves are in fadl ancient. The acute minds of the Italian artifts exerted themfelves in this way, when the other forgeries became common and known. With graving tools they alter the portraits, the reverfes, and the in- fcnptions themfelves, in a furprifing manner. Of a Claudius ftruck at Arftioch they make an Otho *, of a Fauftina, a Titiana $ of a Julia Severa, a Didia Clara ; of a Macrinus, a Pefcennius, &c. Give them a Marcus Aurelius, he ftarts up a Pertinax, by thicken¬ ing the beard a little, and enlarging the nofe. In fhort, wherever there is the leaft refemblance in perfons, re¬ verfes, or legends, an artift may from a trivial me¬ dal generate a moft fcarce and valuable one. This fraud is diftinguifhable by the falfe varnilfi which fome- times mafks it; but, above all, by the letters of the legend, which are always altered. Though this be fometimes done with an artifice almoft miraculous, yet moft commonly the charafters ftraggle, are difunited, and pot in a line.” In counterfeits of this kind fometimes the obverfe is not touched, but the reverfe made hollow, and filled with maftic coloured like the coin, and engraven with fuch device and legend as was moft likely to bring a great price $ others are only retouched in fome minute parts, by which, however, the value of the coin is much diminifhed. “ Againft all thefe arts (fays Mr Pinkerton), fevere fcrutiny muft be made by the pur- chafer upon the medal itfelf •, and the inveftigation and opinion of eminent antiquaries had upon its being al¬ tered, or genuine as it is. iffued from the mint. V. Medals imprejfed with new devices, or folder ed. In the firft article of this clafs the reverfes have been totally filed off, and new ones impreffed with a die and hammer. This is done by putting the face or obverfe, whichever is not touched, jupon different folds of pafteboard, afterwards applying the die and link¬ ing it with a hammer. The forgery in this clafs is very eafily difcovered, as the devices and infcriptions on the counterfeits are known not to exift on true 4 92 Medals with new devices, or foldered. medals: as the Pons ./Elius on the reverfe of Adrian : How to di - the Expeditio Judaica of the fame emperor, &c. The difference of fabrication in the face or reverfe wall be difcovered at the firft glance by any perfon of Ikill. The foldered medals confift of two halves belong¬ ing to different medals, fawed through the middle and then joined with folder. This mode of counterfeiting is common in filver and brafs coins. “ They will take an Antoninus, for example, and faw off the re¬ verfe, then folder to the obverfe wEich they have treat¬ ed in the fame manner. This makes a medal, which, from an unknowing puchafer, will bring a hundred times the price of the two coins which compofe it. When the deceit is ufed in brafs coins, they take care that the metals be of one hue j though indeed fome pretenders in this wray fometimes folder copper and brafs together, which at once reveals the deceit. Me¬ dals which have a portrait on each fide, and which are generally valuable, are the moft liable to a fufpi- cion of this fraud. To a very nice eye the minute ring of folder is always vifible 5 and upon inferting a graver, the fabrication falls into halves.” In the fame manner reverfes are fometimes foldered to faces not originally belonging to them ; as one men¬ tioned by Pere Jobert, of Domitian with an amphi¬ theatre, a reverfe of Titus joined to it. Another art is fometimes made ufe of in this kind of counterfeits, of which there is an inftance of the temple of Janus upon Nero’s medals j where the middle brafs is taken off, and inferted in a cavity made in the middle of a large coin of that prince. In the coins of the lower empire, however, the reverfes of medals are fometimes fo connected with their obverfes, that a mfpicion of forgery fometimes occurs without any foundation. They are met with moft commonly after the time of Gallienus, when fuch a number of ufurpers arofe, that it was difficult to obtain an exadl portrait of their fea¬ tures \ the coiners had not time, therefore, to ftrike a medal for thefe as they could have done for other emperors who reigned longer. Hence, on the reverfe of a medal of Marius, who reigned only three days, there is pacator orris, which fhows that at that time they had reverfes ready fabricated, to be applied as occafion might require. VI. Plated medals, or thofe which have clfts.—It has Plated me. been already remarked, that many true medals are dais, Sco. cracked in the edges j owing to the repeated ftrokes of the hammer, and the little degree of duflility which the metal poffeffes. This the forgers attempt to imi¬ tate by a file j but it is eafy to diftinguiih betwixt the natural and artificial cleft by means of a fmali needle. The natural cleft is wdde at the extremity, and appears to have a kind of almoft imperceptible filaments; the edges of the crack correfponding with each other in a manner wEich no art can imitate. The plated medals which have been forged In an¬ cient times were long fuppofed to be capable of refift- ing every effort of modern imitation •, but of late years, “ fome ingenious rogues (fays Mr Pinkerton), thought of piercing falfe medals of filver with a red- hot needle, which gave a blacknefs to the infide of the coin, and made it appear plated to an injudicious eye. This fraud is eafily diftinguiftied by feraping the infide of the metaL” It is, however, very difficult to diftinguiih 93 MEDALS. 161 94 Mr Pmker ton's direc¬ tions for knowing medals. 95 Forgeries of modern coins. - diftingulfli the forgeries of rude money when not caft ; and our author gives no other dire&ion than to confult a fkilful medallift. Indeed, notwithftanding all the dire£Hons already given, this feems to be a refource which cannot by any means with fafety be neglected. A real and practical knowledge of coins “ is only to be acquired (fays he) by feeing a great number, and comparing the forged with the genuine. It cannot therefore be too much recommended to the young connoiileur, who wilhes to acquire forne knowledge in this way, to vifit all the fales and cabinets he can, and to look upon all ancient medals with a very microfco- pic eye. By thefe means only is to be acquired that ready knowledge vhich enables at firft glance to pro¬ nounce upon a forgery, however ingenious. Nor let the fcience of medals be from this concluded to be un¬ certain •, for no knowledge is more certain and imme¬ diate, when it is properly ftudied by examination of the real objefts. A man who buys coins, trufling merely to his theoretic perufal of medallic books, will find himfelf wofully miftaken. He ought to ftudy Coins firfl, where only they can be fiudied, in them- felves. Nor can it be matter of wonder or implica¬ tion of caprice, that a medallift of ikill (hould at one perception pronounce upon the veracity or falfehood of a medal 5 for the powers of the human eye, em¬ ployed in cert in lines of fcience, are amazing. Hence a iludent can diftinguifti a book among a thoufand fi- milar, and quite alike to every other eye : hence a fhepherd can difcern, &c. j hence the medallift can fav in an inllant, ‘ this is a true coin, and this is a falfe,’ though to other people no diftimftion be percep¬ tible.” Forgeries of modern coins and medals, Mr Pinker¬ ton obferves, are almoft as numerous as of the ancient. The fatiric coin of Louis XII. Per dam Balylonis NOMEN, is a remarkable inftance : the falfe coin is larger than the true, and bears date 1512. The rude coins of the middle ages are very eafily forged, and forgeries have accordingly become common. Forged coins of Alfred and other early princes of England have ap¬ peared, feme of which have been done with great art. “ The two noted Englilh pennies of Rich. I. fays our author, are of this ftamp 5 and yet have impofed upon Meftrs Folkes and Snelling, who have publifhed them as genuine in the two beft books upon Engiilh coins. But they were fabricated by a Mr White of New- gate-ftreet, a noted colle&or, who contaminated an otherwife fair charaiSter by fuch praftices. Such for¬ geries, though eafy, require a fkill in the hiftory and coinage of the times, which luckily can hardly fall to the lot of a common Jew or mechanic forger. But the pradlice is deteftable, were no gain propofed : and they who ftoop to it muft fuppofe, that to embarrafs the path of any fcience with forgery and futility, im¬ plies no infamy. In forgeries of ancient coin, the fiftion is perhaps fufticiently atoned for by the vaft Ikill required •, and the artift may plaufibly allege, that his intention was not to deceive, hut to excite his ut- moft powers, by an attempt to rival the ancient ma¬ ilers. But no poftible apology can be made for for¬ ging the rude money of more modern times. I he crime is certainly greater than that which leads the common coiner to the gallows 5 inafmuch as it is com- VOL. XIII. Part I. mitted with more eafe, and the profit is incomparably Va‘u"* larger.” ^ Sect. VIII. Of the Value of Medals. Ale ancient poins and medals, though equally ge¬ nuine, are not equally valuable. In medals as well as in every thing elfe, the fcarcity of a coin ftamps a value upon it which cannot otherwife be derived from its intrinfic worth. There are four vor five degrees of rarity reckoned up j the higheft of which is called unique. The caufe is generally aferibed to the few- nefs of number thrown off originally, or to their having been called in, and recoined in another form. To the former caufe Mr Pinkerton aferibes the fcarcity of the copper of Otho and the gold of Pefcennius Niger 5 to the latter that of the coinage of Caligula ; “ though this laft (fays he) is not of lingular rarity ; which Ihows that even the power of the Roman lenate could not annihilate an eftablilhed money ; and that the firft caufe of rarity, arifing from the fmall quantity originally ftruck, ought to be regarded as the principal.” 9^ In the ancient cities Mr Pinkerton aferibes the fear- [he*fcarcity city of coin to the poverty or fmallnefs of the ftate j of medals but the fcarcity of ancient regal and imperial coins m ancient arifes principally from the fhortnefs of the reign j andc^ties* fometimes from the fuperabundance of money before, which rendered it almoft unneceffary to coin any money during the reign of the prince. An example of this we have in the fcarcity of the fhillings of George HI. which Ihows that fhortnefs of reign does not always occafion a fcarcity of coin ; and thus the coins of Harold II. who did not reign a year, are very numerous, while thofe of Richard I. who reigned ten, are almoft unique. ^ Sometimes the rareft coins lole their value, and be-R-are c°ins come common. This our author aferibes to the high {°metlmes price given for them, which tempts the poffeffors to common bring them to market; but chiefly to the difeovering and vice of hoards of them. The former caufe took place with verfa. Queen Anne’s farthings, fome of which formerly fold at five guineas ; nay, if wm could believe the newfpa- pers, one of them was fome years ago fold for 960I. ; the latter with the coins of Canute, the Danifh king of England ; which were very rare till a hoard of them was difeovered in the Orkneys. As difeoveries of this kind, however, produce a temporary plenty, fo when they are difperfed the former fcarcity returns j while, on the other hand, fome of the common coins become rare through the mere circumftance of negledf. 9S As double the number of copper coins of Greek Silver coins cities are to be met with that there are of filver, the^nw^at latter are of confequence much more efteemed : butefteemef/*" the reverfe is the cafe with thofe of the Greek princes. All the Greek civic coins of filver are very rare, ex¬ cepting thofe of Athens, Corinth, Meffana, Dyrrha- chium, Maflilia, Syracufe, and fome others. Of the Greek monarchic coins, the moft rare are the tetra- drachms of the kings of Syria, the Ptolemies, the fo- vereigns of Macedon and Bithynia, excepting thofe of Alexander the Great and Lyfimachus. Thofe of the kings of Cappadocia are of a fmall fize, and fcarce to be met with. Of thofe of Numidia and Mauritania the coins of Juba, the father, are common : but thofe X 162 V a'ue. 99 Greek cop per coins. 100 Roman con ftiiar coins. 101 I.eaJen Ro man coins. 102 Cf coins blundered in the mintage. MED of the Ion, and nephew Ptolemy, fcarce. Coins of the kings of Sicily, Parthia, and Judcea, are rare 5 the laft very much fo. We meet with no coins of the kings of Arabia and Comagene except in brafs 5 thofe o: the kings of Bofphorus are in eleftrum, and a few in brafs, but all of them rare; as are likewife thofe ot Philetenis king of Pergamus, and of the kings of Pontus. In the year 1777, a coin of Mithridates fold for 26I. 5s. Didrachms of all kings and cities are fcarce excepting thofe of Corinth and her colonies •, but the gold coins of Philip of Macedon, Alexander the Great, and Lyfimachus, as has already been ob- ferved, are common. The lilver tetradrachms of all kings bear a very high price. The didrachm of Alex¬ ander the Great is one ol the fcarceft of the fmaller Greek filver coins j fome of the other princes are not uncommon. In moil; cafes the copper money of the Greek mo¬ narch? is fcarce ; but that of Hiero I. of Syracufe is uncommonly plenty, as well as that of feveral of the Ptolemies. I he moft rare of the confular Roman coins are thofe reftored by Trajan : of the others the gold confular coins are the moft rare, and the filver the moft com¬ mon ; excepting the coin of Brutus with the cap of liberty, already mentioned, with fome others. Some of the Roman imperial coins are very fcarce, particu¬ larly thofe of Otho in brafs j nor indeed does he occur at all on any coin ftruck at Rome : but the reafon of this may with great probability be fuppofed to have been the ftiortnefs of his reign. His portrait upon the brafs coins of Egypt and Antioch is very bad ; as well as almoft all the other imperial coins of Greek cities. The heft likenefs is on his gold and filver coins \ trie latter of which are very common. The Greek and Egyptian coins are all of fmall or middling fizes, and have reverfes of various kinds: thofe of An¬ tioch have Latin legends, as well as moft of the other imperial coins of Antioch. They have no other reverfe but the SC in a wreath •, excepting in one inftance or two of the large and middle brafs, where the infcrip- tions are in Greek. Latin coins of Otho in brafs, with figures on the reverfe, are certainly falfe ; though in the cabinet of D’Ennery at Paris there was an Otho in middle brafs reftored by Titus, which was efteemed genuine by connoiffeurs. The leaden corns of Rome are very fcarce : IVtoft of them are pieces ftruck or caft on occafion of the faturnalia; others are tickets for feftivals and exhi¬ bitions, both private and public. The common tickets for theatres were made of lead, as were the contorniati ; perpetual tickets, like the Engliih filver tickets for the opera. Leaden medallions are alfo found below the foundations of pillars and other public buildings, in order to perpetuate the memory of the founders. From the time of Auguftus aRo we find that leaden feals were ufed. The work(of Ticorini upon this fub- jedf, entitled Piombi Antiochi, is much recommended by Mr Pinkerton. The Roman coins, which have been blundered in the manner formerly mentioned, are very rare, and un- defervedly valued by the connoilTeurs. The blunders in the legends of thefe coins, which in all probability are the mexe effedls of accident, have been fo far mif- taken by fome medajlifts, that they have given rife to A L S. imaginary emperors who never exifted. A coin of Purehafe. Iauftina, which has on the reverfe sousti. s. c. puz- v zled all the German antiquaries, till at laft Klotz gave it the following facetious interpretation : Swe otntu mi¬ litate feBamini tantas ineptias. Tc^ d he heptarchic coins of England are generally rare, Heptarchic except thofe c-a\\c& Jhjcas, which are very common, nscoir,s of well as thofe of Burgred king of Mercia. The coinsEngIanc3' of Alfred which bear his hurt are fcarce, and his other money much more fo. Thofe of Hardyknute are fo rare, that it was even denied that they had an exift- ence •, but Mr Pinkerton informs us, that there are three in the Britfth mufeum, upon all of which the name HARTHCANUT is quite legible. No Engliih coins of King John are to be met with, though there are fome Iriih ones $ and only French coins of Richard I. i^eake (fays Mr Pinkerton), made a itrange blun¬ der in aferibing coins of different kings with two faces, and otherwife fpoiled in the ftamping, to this prince 5 in which, as ulual, he has been followed by a miffed number.” Coins of Alexander II. of Scotland are rather fcarce,Scottifli but thofe of Alexander III. are more plentiful. Thofe coins- of John Baliol are rare, and none of Edward Baliol are to be found. Sect. IX. Of the Pur chafe of Medals. Medals are to be had at the ihops of goldfmiths and filverfmiths, with thofe who deal in curiofities &c. but in great cities there are profefled dealers in them., j he heft method of purchafing medals, howr- ever, is that of buying whole cabinets, which are every year expoied to auftion in London. In thefe the rare medals are fold by themfelves 5 but the common ones are put up in large lots, fo that the dealers commonly purchafe them. Mr Pinkerton thinks it would be better that medals were fold one by one ■, becaufe a lot is often valued and purchafed for the fake of a Angle coin j while the others feparately w’ould fell for perhaps four times the price of the wLole lot. “ If any man of common fenfe and honeffy (fays Mr Pin¬ kerton), wTere to take up the trade of felling coins in London, he wTould make a fortune in a Ihort time. This profitable bufinefs is now in the hands of one or two dealers, wLo ruin their own irtereft by making an ele¬ gant ftudy a trade of knavery and impofition. ^ If they buy 300 coins for 10s. they will alk 3s. for one of the worlt of them ! nay, fell forged coins as true to the ig¬ norant. .The fimpletons complain of want of bufinefs. A knave is always a fool.” The gold coins of Carthage, Cyrene, and Syracufe, Price°of are worth about twice their intrinfic value as metal j gold coins but the other gold civic coins from 5I. to 30I. each.ofCRr' The only gold coins of Athens certainly known tothase’ &C‘ exift are two lately procured by the king. One of thefe remains in poflefficn of his majelly, but the other was given by the queen to Dr Hunter. There was another in the Britiih mufeum, but fufpedled not to be genuine. Dr Hunter’s coin, then, if fold, would bear the higheft price that could be expefted for a coin. . The filver coins of Syracufe, Dyrrhachium, Maffi-of fiver lia, Athens, and a few other ftates, are common j the coins', drachmas and coins of leffer ffze are worth about five M E D Purchafe. fi ve ftiilltngs j the didrachms, tetradrachras, &c. from ' v——' live to ten, according to their fize and beauty 5 the larged, as might naturally be expefted, being more valuable than the fmall ones. The tetradrachms, when of cities whofe coins are common, are worth from 7s. 6d. to il. is. ; but it is impoffible to put a value upon the rare civic coins $ ten guineas have been given for Tc^ a (ingle one. Greek cop- The Greek copper coins are common, and are al- per coins. moft a]l Qf kind called fmall brafs; the middle fize being fcarce, and the largeft in the ages prior to the Roman emperors extremely fo. The common Greek coins of brafs bring from 3d. to i8d. according to their prefervation •, but w’hen of cities, whofe coins are rare, much higher prices are given. “ The want of a few cities, however (fays Mr Pinkerton), is not thought to injure a colledtion *, as indeed new names are difco- Vered every dozen of years, fo that no afiortment can be perfeft. To this it is owing that the rarity of the ^ g Grecian civic coins is not much attended to.” Gold coins hThe gold coins of Philip and Alexander the Great bf Philip being very common, bear but from five to ten (hillings andAlexan- above their intrinfic value ; but thofe of the other der' princes, being rare, fell from 3I. to 30I. each, or even more. The tetradrachms are the deareft of the filver mo¬ narchic money, felling from five to ten (hillings •, and if very rare, from 3I. to 30I. Half thefe prices may be obtained for the drachmas, and the other denomi¬ nations in proportion. GVeckcop- Th6 Greek copper coins are for the moft part fcar- per coins1 cer than the filver, except the Syro-Grecian, which more rare are common, and almoft all of the fize called fmall than the brafs. “ They ought (fays Mr Pinkerton), to bear a a high price •, but the metal and fimilarity to the cop¬ per civic coins, which are common, keep their adtual purchafe moderate, if the feller is not well inftrudled, and the buyer able and willing to pay the price of rarity.” The name of weights given to the ancient Roman afes is, according to our author, exceedingly impro¬ per ; as that people had weights of lead and brafs fides, without the lead appearance of a portrait upon therti. Thefe denote the weight by a certain number of knobs; and have likewife fmall fleurettes engraved upon them. According to Mr Pinkerton, whenever we meet with a piece of metal (lamped on both fides w'ith buds and figures, we may lay it down as a certain rule that it is a coin ; but when (lightly ornamented and marked up¬ on one fide only, we may with equal certainty conclude I10 it to be a weight. Price of the The ancient Roman afes are worth from 2S. to 2I. ancient Ro- according to the fingularity of their devices. Confu- man afes. ]ar g.0]j col'ns are worth from il. to 5I. Pompey with his fons 21I. and the two Bruti 25I. The filver coins are univerfally worth from a (hilling to half a crown, excepting that of the cap of liberty and a few others, which, if genuine, will bring from 10s. to 5I. The con- fular copper bears an equal price with the filver, but is more rare j the confular filver coins redored by Tra¬ jan are worth zcs. each. With regard to the Roman imperial coins, it is to be obferved, that fome of thofe which belong to princes whofe coins are numerous, may yet be rendered ex¬ tremely valuable by uncommon reverfes. Mr Pinker- fi!ver. of m Hilderic Barbaric coins. thofe and worth 10s. j the gold of Theo- the the A L S. 163 ton particularly points out that of Augudus, with the Arrange- legend C. Mari vs Trogvs, which is worth three ment- guineas, though the filver coins of that prince in ge¬ neral are not worth above a (hilling. In like manner, the common gold coins of Trajan are not worth above twenty (hillings; while thofe with Bajilica U/pia, Forum Trajani, Divi Nerva et Trajanus, Paler, Divi Nerva et Platina Aug. ProfeBio Aug. Regna AJfignata, Rex Parthus, and fome others, bear from three to fix pounds. The ticket medals belong to the Roman fenate, and are worth from three to ten (hillings. The forged coins and medallions of the Paduan fell from one to three drillings each. Of the coins of other nations, king of the Vandals are in filver, the finall brafs of Athanaric, 3s. 5 doric 2I. •, the fecond brafs of Theodahat 5s. fecond brafs of Badueta rare, and worth 10s. third brafs, 3s. The Britiih coins are very rare, and worth from ten drillings to two guineas each, fome- times much more. Medals with unknown charafters are always fcarce and dear. Saxon pennies of the heptarchy are rare, and worth from ten drillings to ten pounds, according to their fcarcity and preferva¬ tion. The coins of the Englidr kings are common 5 thofe of Edward the Confeffor, in particular j others are rare, and worth from ten drillings to two guineas, while two of Hardyknute are wmrth no lefs than ten guineas. The gold medals of Henry, in 1545, and the coronation of Edward, are wmrth 20I. each : the Mary of Trezzo, 3I, •, Simon’s head of Thurloe in gold is worth 12I. ; his oval medal in gold upon Blake’s naval vidlory at fea is worth 30I. j and his trial piece, if brought to a fale, would, in M1' Pinker¬ ton’s opinion, bring a ftill higher price. The medals of Queen Anne, which are intrinfically worth about two guineas and a half, fell for about 3I. each j the filver, of the fize of a crown piece, fell for 10s. and the copper from five to ten drillings. Dafiier’s copper pieces fell from twro to five drillings, and a few bear a higher price. 1 II3 The Scottiflr gold coins fell higher than the Eng- Gold coins lidt, but the others are on a par. The drilling of Mary of Scotland. with the bud is rare, and fells for no lefs than 30], $ the half 3I.; and the royal 5I. 5s. The French tef- toon of Francis and Mary brings lol. 10s. and the Scottidr one of Mary and Henry would bring 50I. as wmuld alfo the medal of James IV. The coronation medal of Francii and Mary is worth 20I. Briot’s co¬ ronation medal fold in 1755 only for two guineas at Dr Mead’s fale 5 but would now bring 20I. if fold ac¬ cording to rarity. 1x3 The Englifii coins firuck in Ireland are of much the Englifh. fame price w'ith thofe of the native country *, but the f°ins (truck St Patrick’s halfpence and farthings are rather fcarce,111 Ire^anc*' and the rare crown of white metal is worth 4I. The gun-money of James II. and all other Iri(h coins are very common. SECT. X. Arrangement of Medals, with the Inf rue-' tion to be derivedfrom them. Having thus given a full account of every thing in general relative to medals, we mud now come to fome particulars refpedting their arrangement, and the enter-* X 2 tainment ’ 164 MED ArT|tn&~ ^a*nment which a medallift rriay expedl from the trouble ^ment, •(_. an(;j eXpence ;s a|. jn ng a colledfion. It has already been obferved, that one of the prin¬ cipal ufes of medals is the elucidation of ancient hi¬ ll ory. Hence the arrangement of his medals is the firlt thing that mull occur in the formation of a cabi¬ net, The moll ancient medals with which we are ac¬ quainted are thofe of Alexander I. of Macedon, who began to reign about 501 years before Chrilf, The feries ought of confequence to begin with him, and to be fucceeded by the medals of Sicily, Caria, Cyprus, Heraclia, and Pontus. Then follow Egypt, Syria, the Cimmerian Bofphorus, Thrace, Bithynia, Par- thia, Armenia, Damafcus, Cappadocia, Paphlagonia, Pergamus, Galatia, Cilicia, Sparta, Pteonia, Epirus, Illyricum, Gaul, and the Alps, including the fpace of time from Alexander the Great to the birth of Chrilf, and which is to be accounted the third medallic feries of ancient monarchs. The lalt feries gees down to the fourth century, including fome of the monarchs of Thrace, Bofphorus, and Parthia, with thofe of Comagene, Edelfa or Ofrhoene, Mauritania, and Ju- dma. A moll diifindl feries is formed by the Roman emperors, from Julius Csefar to the dellrudlion of Rome by the Goths ; nay, for a much longer period, were it not that towards the latter part of it the coins become fo barbarous as to dettroy the beauty of the collection. Many feries may be formed of modern po- 114 tentates. Diadem an jgy means 0f medals we can with great certainty ancient em* i * i • ^ * blem of determine tne various ornaments worn by ancient fovereign princes as badges of diltindlion. The Grecian kings authority, have generally the diadem, without any other orna¬ ment ; and though in general the fide of the face is prefented to view, yet in fome very ancient Greek and Roman confular coins, full faces of excellent work- manlhip are met with. On feveral coins allb two or three faces are to be feen, and thefe are always account¬ ed very valuable. • 4 The diadem, which was no more than a ribbon tied round the head with a floating knot behind, adorns all the Grecian princes from firit to lall, and is almoit an infallible mark of fovereign power. In the Roman confular coins it is feen in conjundtion with Numa and Ancus, but never afterwards till the time of Licinius, the colleague of Conftantine. Dioclefian, indeed, ac¬ cording to Mr Gibbon, firlt wore the diadem, but his portrait upon coins is never adorned with it. So great an averfion had the Romans to kingly power, that they rather allowed their emperors to affume the ra¬ diated crown, the fymbol of divinity, than to wear a diadem ; but, after the time ©f Conftantine, it becomes common. 1 he radiated crown appears firlt on the pofthumous coins of Auguftus as a mark of deifica¬ tion, but in fomewhat more than a century became common. The laurel crown, at firft a badge of conqueft, was afterwards permitted by the fenate to be worn by Ju¬ lius Csefar, in order to hide the baldnefs of his head. From him all the emperors appear with it on their medals, even to our own times. It the lower empire the crown is fometirtts held by a hand above the head, as a ximrk of piety. Bolides■ thfcfe, the naval, mural, and civic crowns appear on the medals both of empe- zors and other eminent men, to denote ther great • ac- A L S. tion«. The laurel croxvn is alfo fomethnes worn by Arrange- he Greek princes. The Arfacidse of Parthia wear ment> a kind of laih round the head, with their hair in rows v of curls like a wig. The Armenian kings have the t/ara, a kind of cap which was efteemed the badge of imperial power in the eaft. Conical caps are feen on the medals of Xerxes, a petty prince of Armenia, and Juba the father, the former having a diadem around it. 115 The impious vanity of Alexander and his fucceffors Symbols of in affuming divine honours is manifeft on their medals, <)‘,;v‘rat7 on where various fymbols of divinity are met with. Some AA;?nde^ of them have an horn behind their ear, either to de- and h;s fuc- note their ftrength, or that they were the fuccelTors ofceflbrs. Alexander, to whom this badge might be applied as the fen of Jupiter Ammon. This, however, Mr Pinkerton obferves, is the only one of thefe fymbols which certainly denotes an earthly fovereign, it being doubted whether the reft are not all figures of gods.—. According to Eckhet, even the horn and diadem be¬ long to Bacchus, who invented the latter to cure his headaches •, and, according to the lame author, the only monarch who appears on coins with the horn is Lyfimachus. We are informed, however, by Plutarch, that Pyrrhus had a creft of goats horns to his helmet j and the goat, we know, w7as a fymbol of Macedon. Perhaps the fucceiTors of Alexander wore this badge of the horn in confequence. The helmet likewife fre¬ quently appears on the heads of fovereigns, and Con¬ ftantine I. has helmets of various forms curioully or¬ namented. The diadem is worn by moft of the Greek queens, by Orodaltis, daughter of Lycomedes, king of Bithynia j and though the Roman emprefies never appear with it, yet this is more than compenfated by the variety of their headdreffes. Sometimes the bull of an emprefs is fupported by a crefcent, to imply that Ihe was the moon, as her hulband was the fun of the ftate. The toga, or vail drawn over the face, at firft implied that the perfon was inverted with the pontifical office ; and accordingly we find it on the bulls of Julius Crefar, while pontifex maximus. It likewife implies the au- gurlhip, the augurs having a particular kind of gown called /arui, with which they covered their heads when obferving an omen. In latter times this implies only confecration, and is common in coins of empreffes. It is firft met with on the coins of Claudius Gothicus as the mark of confecration of an emperor. The nimbus, or glory, now appropriated to faints, has been already mentioned. It is as ancient as Auguftus, but is not to be met with on many of the imperial medals, even after it began to be appropriated to them. There is a curious coin, which has upon the reverfe of the common piece, w’ith the head of Rome, Urbs Roma, in large brafs, Conftantine I. fitting amid Viflories and genii, with a triple crown upon his head for Eu¬ rope, Alia, and Africa, w’ith the legend Securitas Romas. . rl6 In general only the bull is given upon medals, Portraits though fometimes half the body or more ; in which upon me- latter cafe the hands often appear with enfigns of ma- jelly in them ; fuch as the globe, faid to have been in¬ troduced by Auguftus as a fymbol of univerfal domi¬ nion the feeptre, fometimes confounded with the con¬ fular ftaff j a roll of parchment, the fymbol of legiila- tiys M E D Arrange- tire power , and an handkerpliief, cxpreflive of the power nient,&c. over the public games, where the emperor gave the vlignal. Some princes hold a thunderbolt, fhowing that their power on earth was ec|ual to that of Jupiter m heaven j while others hold an image of Victory. Medals likewife afford a good number of portraits of illuftrious men 5 but they cannot eafily be arranged in chronological order, fo that a feries of them is not to be expected. It is likewife vain to attempt the formation of a feries of gods and goddeffes to be found on ancient coins. Mr Pinkerton thinks it much bet¬ ter to arrange them under the feveral cities or kings whofe names'they bear. A collection of the portraits of illuftrious men may likewife be formed from medals XI7 Reveries of Greek and Roman eoins. of modern date. Xhe reverfes of ancient Greek and Roman coins afford an infinite variety of inftrudlion and amufement. They contain figures of deities at full length, with their attributes and fymbols, public fymbols and diver- fions, plants, animals, &c. &c. and in (hort almoft every objeft of nature or art. borne have the por¬ trait of the queen, fon, or daughter of the prince whofe image appears on the face obverfe *, and thefe are efteemed highly by antiquaries, not only becaufe every coin ftamped with portraits on both fides is ac¬ counted valuable, but becaufe they render it certain that the perfon reprefented on the reverfe was the wife, fon, or daughter of him who appears on the obverfe $ by which means they aftift greatly in the ad¬ juring of a feries. Some, however, with two portraits are common, as Auguftus, the reverfe of Caligula ; and Marcus Aurelius, reverfe of Antoninus Pius. We find more art and defign in the reverfes of the Roman medals than of the Greek $ but on the other hand, the latter have more exquifite relief and work- manlhip. The very ancient coins have no reverfes, excepting a rude mark llruck into the metal, refem- bling that of an inftrument with four blunt points on which the coin was ftruck } and was owing to its hav¬ ing been fixed by fuch an inftrument on that fide to receive the impreffion upon the other. lo. this fucceeds the image of a dolphin, or fome Imall animal, in one of the departments of the rude mark, or in an hollow fquare : and this again is fucceeded by a more perfeft image, without any mark of the hollow fquare. Some of the Greek coins are hollow in the reverfe, as thofe of Caulonia, Crotona, Metapontum, and fome other ancient cities of Magna Graecia. About 500 B. C. perfeft reverfes appear on the Greek coins, of exquifite relief and workmanlhip. li Xhe veiy inuf- cles of men and animals (fays Mr Pinkerton), are feen, and will bear infpeaion with the largeft magnifier as ancient gems. Xhe ancients certainly had not eyes different from ours; and it is clear that they mull have magnified objefts. A drop of water forms a micro- fcope ; and it is probable this was the only one of tne ancients. To Greek artirts we are indebted for the beauty of the Roman imperial coins-', and thefe are fo highly finilhed, that on fome reverfes, as that of Nero’s decurfion, the adventus and progvejfio of va¬ rious emperors, the fundator pacts of Severus, the fea¬ tures of the emperor, riding or walking, are as exaft as on the obverfe. But though the belt Greek ar- tifts were called to Rome, yet the Greek coins under A L S. 165 the Roman emperors are fometimes well executed, Arrange- and always full of variety and curiofity. No Roman ,mentj ^'c'. or Etrufcan coins have been found of the globular form, or indented on the reverfe like the early Greek. The firft Greek are fmall pieces of filver, while the Roman are large maffes of copper. The former are ftruck \ the latter call in moulds. The reverfes of the Roman coins are very uniform, the prow of a Ihip, a car, or the like, till about the year 100 B. C. when various reverfes appear on their conlular coins in all metals. The variety and beauty of the Roman impe¬ rial reverfes are well known. dLhe medalift much va¬ lues thofe which have a number of figures *, as the VuelU Faujliniavte, of Fauftina, a gold coin no larger than a fixpence, which has 12 figures j that of Irajan, regna ajpgnata, has four ; the congiartum of Nerva five the allocution of Trajan feven 5 of Hadrian 10 ; of Probus I 2. Some Roman medals have fmall figures on both fides, as the Jpollini fantto of Julian II. Such have not received any peculiar name among the medal- lifts. Others have only a reverfe, as the noted fpintri. ati, which have numerals I. II. &c. on the ob¬ verfe.” The names of the deities reprefented on the rever- ri?. . fes of Greek coins are never expreffed ; perhaps, as MfOGhe dei- Pinkerton fuppofes, out of piety, a fymbolical repre-J^pon fentation of their attributes being all that they thought ancient proper to delineate 5 but the Roman coins always ex-coins, prefs the name, frequently with an adjunft, as VENERI Victrici, &c. In others, the name of the empe¬ ror or emprefs is added ; as Pudicitite AuGUSTiE, round an image of modefty} Vxrtus Augusti, a legend for an image of virtue. The principal fymbols of the divine attributes to be met with on the Greek medals are as follow : 1. Jupiter is known on the coins of Alexander the Great by his eagle and thunderbolts ; but when the figure occurs only on the obverfes of coins, he is di- ftinguilhed by a laurel crown, and placid bearded coun¬ tenance. Jupiter Ammon is known by the ram’s horn twilling round his ear } a fymbol of power and ftrengtb, affumed by fome of the fucceffors of Alex¬ ander the Great, particularly by Lyfimachus.. 2. Neptune is known by his trident, dolphin, or be¬ ing drawn by fea horfes} but he is feldom met with on the Grecian coins. 3. Apollo is diftinguilhed by an harp, branch of laurel, or tripod •, and fometimes by a bow and arrows.. In the character of the fun, his head is furrounded with rays ; but when the bull only occurs, he has a fair young face, and Js crowned with laurel. He is frequent on the coins ol the Syrian-princes. 4. Mars is dillinguilhed by his armour, and fome¬ times by a trophy on his Ihoulders. His head is armed with a helmet, and has a ferocious counte¬ nance. 3. Mercury is reprefented as a youth, with a. fmall cap on his head, wings behind his ears and on his feet.,- He is known by the cap, which refembles a fmall hat, and the wings. He appears alfo with the caduceus, or wand twined with ierpents, and the marfupium, or purfe, which he holds in his hand. 6. vEfculapius is known by his bulky beard, and his leaning on a club with a lerpent twilled round it.. He 166 M E D Arrange- He fometimes occurs with Lis wife Hygeia or Health, n.ent, &lc. their fon Telefphorus or Convalelcence between them. 7. Bacchus is known by his crown of ivy or vine, his diadem and horn, with a tiger and fatyrs around him. 8. The figure of Hercules is common on the coins of Alexander the Great, and has frequently been mif- taken for that of the prince himfelf. He appears fometimes as a youth and fometimes with a beard. He is known by the club, lion’s Ikin, and remarkable apparent ftrength j fometimefc he has a cup in his hand ; and a poplar tree, as a fymbol of vigour, is fometimes added to the portrait. 9. The Egyptian Serapis is known by his bulky beard, and a mealure upon his head. 10. Apis is delineated in the form of a bull, with a flower of the lotos, the water lily of the Nile, fup- pofed by Macrobius to be a fymbol of creation ; and Jamblichus tells us, that Ofiris was thought to have his throne in it. 11. Harpocrates, the god of Silence, appears with his finger on his mouth •, fometimes with the liftrum in his left hand j a fymbol common to moil of the Egyp¬ tian deities. 12. Canopus, another Egyptian deity, appears in the fhape of a human head placed on a kind of pitch¬ er. “ This deified pitcher (fays Mr Pinkerton), feems to refer to an anecdote of ancient fuperftition, which, I believe, is recorded by Plutarch. It feems fome Per- fxan and Egyptian priefts had a contefl which of their deities had the fuperiority. The Egyptian faid, that a Angle vafe, facred to Serapis, would extinguilh the whole power of the Perfian deity of fire. The ex¬ periment was tried 5 and the wily Egyptian, boring holes in the vale and Hopping them with wax, afterwards filled the vafe with water; wdaich, gulhing through the holes as the wax melted, extinguilhed the Perfian deity. Hence the vafe was deified.’’ 13. The Holy Senate and Holy People, appear fre¬ quently on the Greek imperial coins, fometimes repre- fented as old men with beards, at others as youths. The goddefles reprefented on medals are, 1. Juno, reprefented by a beautiful young woman, iometimes with a diadem, fometimes without any badge, which is reckoned a fufficient difiin61ion, as the other goddeffes all wear badges. Sometimes’fhe appears as the goddefs ef marriage ; and is then veiled to the middle, and fometimes to the toes. She is known by the peacock, a bird facred to her from the fable of Argus. 2. Minerva is very common on the coins of Alex¬ ander the Great; and her bull has been miftaken by the celebrated painter Le Brun for the hero himfelf She is very eafily dillinguifhed by the helmet. Her fymbols are, her armour 5 the fpear in her right hand -and the aegis, with a Medufa’s head, in her" left • an owl commonly Handing by her. 3. Diana of Ephefus is commonly reprefented on the vjreek imperial coins ; and appears with a great num- ber of breads, fuppofed to denote univerfal Nature. She is fupported by two deer, and carries a pannier of fruit upon her head. The bufl of this goddefs is known -by the crefcent on her brow, and fometimes by the bow and quiver at her fide. 2 A L S. 4. Venus is known by an apple, the prize of beauty, Arran-e- in her hand. Sometimes Hie is difiinguifiied only by me! t, ixc. her total want of drefs ; but is always to be known by ' ^ her extraordinary beauty, and is fometimes adorned with pearls about the neck. 5. Cupid is fometimes met with on the Syrian coins, and is known by his infancy and wings. 6. Cybele is known by a turreted crown and lion ; or is fcen in a chariot drawn by lions. 7. Ceres is known by her garland-of wheat, and is common on the Sicilian coins ; that ifland being re¬ markable for its fertility. Sometimes (he has two fer- pents by her, and is fometimes drawn in a chariot by them. She. carries in her hands the torches with which Hie is fabled to have gone in fearch of her daughter Proferpine. .8. Proferpine herfelf is fometimes met with on coins, with the name of xogjj, or the girl. 9- The Egyptian Ifis has a bud or flower on her head } a fymbol of the perpetual bloom of the inhabi¬ tants of heaven. She carries alfo a fiflrum in her hand. 10. The Sidonian Allarte appears on a globe fup¬ ported on a chariot with two wheels, and drawn by two horfes. J I hefe are the deities mofi commonly reprefented on the Greek coins. Ihe more uncommon are, Saturn with his fcythe, or wuth a hook on the HeracHan coins } \ ulcan with his tongs on the reverfe of a coin of. Thyatira, reprefented at work in the prefence of Minerva. Adranus, a Sicilian god, is fometimes re- prefente.d on coins with a dog. Anubis, an Egyp¬ tian deity, has a dog’s head. Atis is known by his Phrygian bonnet 5 Caflor and Pollux by a flar on the head of each j Dis, by his old face, difhevelled hair ana beaid, and a hook j Flora by her crown of flow¬ ers 5 Nemefis by her wheel; and Pan by his horns and ears belonging to fome kind of beafi. There are likewife to be found on medals many Table of different fymbols by themfelves ; of the mofl remark- f>'niboli- able of which, we fliall give the following table, with their fignifications: Symbols. 1. Vafes with fprigs, 2. Small chefl or hamper, with a ferpent leaping out, 3- Anchor on Seleucian medals. 4. Apollo on Syrian coins, on an inverted hamper, 5- Bee, ... 6. Laurel, - 7. Reed, - 8. Ivy and grapes, 9. Poppy, 10. Corn, - „ _ 11. Owl and olive, 1 2. Dove, - I3* Signification. Solemn games, f Myflic rites of \ Bacchus, f Coin ffruck at Antioch, where an an¬ chor was dug jj- Covered tripod. {Ariffeus the Ion of Apol¬ lo. Apollo. A river. Bacchus, y Ceres and Pro- / ferpine. Ceres. Minerva. Venus. Arrange¬ ment, See. I3- M- I5- 16. 17- 18. 19. 20. 21. 22. 23* 24. 26. 27. 28. 29. 3°- 31* 3,2. 33- 34- 35- 36. 37- 38- 39- 40. 41* 42. 43- 44. 45- MED Symbols. Torch, Mudnis, or conic done, t Significations. { 5 Diana, Ceres, or Profer- pine. The fun, Belus, or Venus. Symbols of Countries, &c. Pomegranate flowers, Owl, Pegafus, - . _ Wolf’s head, Bull’s head, Minotaur’s head and labyrinth, Horfe’s head, Lion, - - - Tortoife, - - > Sphinx, - - Three legs joined, as in the Ifle of Man money, Horfe, - The crefcent, Bull, Enfign, with the letters Col. Bull, Caduceus, - - - Cornucopiae, Pontifical hat, Parazonium, Globe on an altar with three ftars, - Fort and gate, Tribuli, a kind of chevaux de frize, - Altar or tripod, Dolphin, - Le6liflernia, Lituus, or twilled wand, Apex, or cap with firings, Thenfa, or chariot employed to carry images, Peacock, - Eagle, Rhodes. Athens. Cbrinth. Argos. Boeotia. Crete. Pharfalia. Marfeilles. Peloponnefus. Scio. { { { { Theffaly. Byzantium (a). Suppofed to be a river. Acolony drawn from one le¬ gion. Apis, flrength or fecurity. Peace and con¬ cord. Abundance. Priellhood. Batoon of com¬ mand. The world pre- ferved by the gods for the three fons of Conllant. I. Security. } Unknown. { Piety. Apollo. Fellivals. Augurlhip. Pontificate. Con fee ration of an emprefs. Ditto. Confecration of an emperor. A L S. rtfy The legends put upon medals are defigned as ex- Arrange- planations of them ; but as the compafs of even the ,ment’ large!! coins does not admit of any great length of I20 infeription, it has always been found neceffary to ufe Legends of abbreviations ; and in readily decyphering thefc lies a medals, confiderable part of the difficulty of the fcience. This, however, is greater in the Roman than in the Greek medals \ for the Greeks commonly infert as much of the word as is lufficient to enable us eafily to under- ftand its meaning ; but it is common for thofe who at¬ tempt to explain letters that do not often occur, to 121 . fall into very ridiculous errors. Of this Mr Pinker- ^ ton gives a mol! remarkable inllance in Fortunius Li- ofFor- cetus, a learned man, who finding upon a coin of A- tunlus Lice- drian the letters, r. IA fignifying the 14th year of that tus. emperor’s reign, imagined that they fignified Litcer- nas invenit Delta ; “ Delta invented lanthorns j” and thence aferibed the origin of lanthorns to the Egyp¬ tians. Tables explaining the meaning of the abbrevi¬ ations found upon medals have been publilhed by Pa- tin, Urfatus, and others. Sect. XL Of Medallions, Me da lets, &c. Besides the ordinary coins of the ancients, which paffed in common circulation through the> country, there were others of a larger fize, which are now term¬ ed medallions. Thefe were ftruck on the commence¬ ment of the reign of a new emperor and other folemn occafions: frequently alfo, by the Greeks in particular, as monuments of gratitude or of flattery. Sometimes they were mere trial or pattern pieces; and thofe abound after the time of Maximian, with the words Tres MoneUe on the reverfe. The common opinion is, that all the Roman pieces of gold exceeding the denarius aureus, all in filver exceeding the denarius, and all in brafs exceeding the feftertius, went under the denomination of medallions: but Mr Pinkerton thinks that many of thefe large pieces went in circula¬ tion, though not very commonly, as our five and two guinea pieces, filver crowns, &c; do in this country. The fineft medallions were prefented by the mint maf- ters to the emperor, and by the emperor to his friends, as fpecimens of fine workmanffiip. The bell we have at prefent are of brafs, and many of them compofed of two forts of metal ; the centre being copper, with a ring of brafs around it, or the contrary ; and the infeription is fometimes confined to one of the metals, fometimes not. There is a remarkable difference be¬ tween the Greek and Roman medallions in point of thicknefs •, the latter being frequently three or four lines thick, while the other feldom exceed one. Very few medallions, however, were ftruck by the Greeks before the time of the Roman emperors ; but the Greek medallions of the emperors are more numerous tha (a) This appears on the early coins of Byzantium, with the legend BTZANTIN. 2QT. “ the preferver of By¬ zantium.” The reafon of this was, that when Philip of Macedon befieged the city, and was about to ftorm it in a cloudy night, the moon fhone out on a fudden and difeovered him j by which means the inhabitants had time to collect their forces and repulfe him. The Turks on entering Conllantinople, found this badge in many places; and fulpefting fome magical power in it, aflumed the fymbol, and its power, to themfelves) fo that the crefcent is now the chief Turkilh enfign. - L 168 MED Medal- thofe of the Romans themfelves. All thefe pieces, ^lions &(. however, are of fuch high price that few private per- fons are able to purchafe them. In the laft century Chriftina queen of Sweden procured about 300. In the king of France’s colledlion there are x 200 ; a num¬ ber formerly fuppofed not to exiil ; and Dr Hunter’s colle<5i:ion contains about 400, exclufive of the Egyp¬ tian. Befides thefe large pieces, there are fmaller ones, of a fize fomewhat larger than our half-crowns ; and by Italian medallifts are called medaglion cini, or fmall medallions. They are ftill fcarcer than the large kind. Ofmed i- There is Hill a third kind, which have almofi: efca- Jets. ped the notice of medallifts, viz. the fmall coins or tnijjilia fcattered among the 'people on lolemn occa- fions; fuch as thofe ftruck for the flaves on account of the faturnalia *, counters for gaming •, tickets for baths and feafts j tokens in copper and in lead, &c. Thefe are diftinguifhed by Mr Pinkerton by the name of medalcts. Many, or perhaps almoft all, of thofe ftruck for the faturnalia were fatirical ; as the Haves had then a licenfe to ridicule not only their mafters but any perfon whatever. Mr Pinkerton mentions one of the moft common pieces of this kind, which has on the obverfe the head of an old woman veiled, with a laurel crown ; the reverfe only s. c. within a wreath. Baudelot is of opinion that it is the head of Acca Laurentia, the nurfe of Romulus, to whom a feftival was ordained. “ Perhaps (fays Mr Pinkerton), it was ftruck in ridicule of Julius Caefar j for the man¬ ner of the laurel crown, and its high appearance over the head, perfeftly referable that of Julius on his coins.” Some have a ftxip upon one fide ; on the reverfe T, or a crofs, which was the image of Priapus; and oc- cafioned many falfe inveftives againft the firlt Chrif- tians, w’ho paid fuch refpeft to the crofs. Some pieces have the heads of the emperors upon one fide j on the reverfe only numerals, III. IV. V. &c. and the _ noted fpintriati of Tacitus. Both thefe kinds appear tickets for the baths, as the number feems to denote the particular bath. Some have the head of a girl, with a veflel ufed at the baths in her hand. The fpintriati .are fo immodeft, that few will bear mention. But fame are merely ludicrous j as on§ which has an afs with a bell about his neck, and a foldier riding him j another wfth two figures hoifting a woman in a balket into the air. Of thofe that wdll juft bear mention, is a man with titles around him, as chief of the games j and a woman in ridicule of the modeft bath-girl above mentioned. There is alfo one marked xix, on which appears an imperator triumphing in a car: this car is placed on the back of a camel; and behind the impe- I23 rator is a monkey mimicking him. Of the con- A fourth clafs of medals are called contorniati itom Sorniati. the Italian contorniato, “ encircled becaufe of the hollow circle which commonly runs around them. They are diftinguilhed from medallions by their thin- nefs, faint relief, reverfes fometimes in relief, fome- times hollow; and in general by the inferiority in their wftjrkmanfhip. The opinions of medallifts con¬ cerning theie pieces are very various $ fome fuppofe them to have been ftruck by Gallienus to the memory ©f illuftrious men and celebrated athlctce^ at the time A L S. that he caufed all the confecration coins of his pre- Medal- deceffbrs to be reftored ; others aferibe their invention Jlons» ^ to Greece, &c. but Mr Pinkerton is of opinion that they were only tickets for places at public games. Many of them, notwithftanding their inferior w’ork- manfhip, are very valuable on account of their pre- ferving the portraits of fome ifluftrious authors of an¬ tiquity, nowhere elfe to be found. Mach depend- ance, however, cannot be put on the portraits of Greek authors and eminent men found upon fome of them $ for though we know that the bulls of Salluft, Horace, &c. muft have been ftruck when their per- fons were freftr in the memory of the artifts, yet it was otherwife with Homer, Solon, Pythagoras, &c. w hich are to be found on fome of them. Even thefe, however, are valuable, as being ancient and perhaps traditional portraits of thefe great men. The laft; whofe portraits are fuppofed to have been delineated in this w'ay, are Apollonius Tyaneus who tlourifhed in the time of Domitian, and Apuleius in that of Marcus Antoninus. Mr Pinkerton thinks it a con¬ firmation of his opinion concerning thefe medals, that the reveifes always contain fome device alluding to public games, as that of a charioteer driving a cha¬ riot, &c. Sect. XII. DireBions for making Cabinets. We muft: now proceed to the laft part of our fub- jedl, viz. that of giving dire£tions for the formation of cabinets. As we have already feen that the forma¬ tion of any one muft be attended with very confider- able expence, it is neceffary for every one wrho at¬ tempts this to proportion the cabinet to his own cir- cumftances. There are, properly fpeaking, three kinds of cabinets. 1. Thofe meant to contain a coin of every fort that has been iffued from the mint in every age and country •, but this, which may be called the large and complete cabinet, is not to be purchafed by private perfons. That of Dr Hunter already men¬ tioned is perhaps one of the beft private cabinets ever known ; and coft 23,000!. but as many duplicates were fold as coft 2000!. by which means the expence was reduced to 2i,oool. The vaft colleftion made by the king of France coil upwards of ioo,oool. 2. The fmaller cabinet may be fuppofed to coniift only of middle and fmall Roman brafs, Englilh pennies, groats, &c. with a few medals of the more valuable kind, and may be fuppofed to incur an expence pf from 200I. to iooqI. 3. The fmalleft kind is called a cafket of me¬ dals, and does not confift of above 1000 at moft of va¬ rious kinds ; and ccnfequently the expence muft depend on the pleafure of the proprietor. In the formation of the grand cabinet, it muft be obferved that the Greek medals of every denomina¬ tion do not admit of any arrangement by the metals like the Roman j not any regular feries of this kind being met with even in the moft opulent cabinets. Hence in all colledlions the civic coins are ranged ac¬ cording to an alphabetical order •, and the monarchic in a chronological one. The fame rule is to be ob¬ ferved in the Roman confular medals 5 they are ranged, like the coins of the Greek cities, in an alphabetical feries of the families. The Roman imperial coins are only 4 MED DireAions only tliofe capable of being arranged according to fizes for making an(j meta;[s> Even from this muft be excepted the . (-'at31^net:>- minimi, or very fmalleft coins; which are fo fcarce, that the only regular feries of them in the world is that belonging to the king of Spain, which was form¬ ed by a moll (kilful French medallifr, and conlilts of all the metals. The arrangement of a grand cabinet, according to Mr Pinkerton, is as follows. “ I. The coins of cities and of free dates in alpha¬ betical order: whether uling Greek, Roman, Punic, Etrufcan, or Spanifh charadlers. “ II. Kings in chronological feries, both as to foun¬ dation of empire and feniority of reign. “ III. Heroes, heroines, founders of empires, and cities. “ IV. Other illulfrious perfons. “ V. Roman afes. VI. Coins of families, commonly called confular. “ VII. Imperial medallions. ‘‘ VIII. Imperial gold. “ IX. Imperial minimi of all metals. X. Imperial lilver. “ XI. Imperial firil brafs. “ XII. Second brafs. XIII. Third brafs. “ XIV. Colonial coins, which are all of brafs. “ XV. Greek cities under the emperors, of all me¬ tals and fizes. In a fmaller cabinet they may be put with the Roman, according to their metal and fize. Thofe without the emperor’s head go to clafs I. though ftruck in Roman times. 4‘ XVI. Egyptian coins ftruck under the Roman emperors, of all metals and fizes. They are moftly of a bafe metal called by the French patin ; it is a kind of pot-metal or brittle brafs. “ XVII. Contorniati, or ticket medals. “ XVIII. Coins of Gothic princes, &c. infcribed with Roman chan-afters. “ XIX. Coins of fouthern nations ufing uncommon alphabets; as the Perfian, Punic, Etrufcan, and Spa- nifh. “ XX. Coins of northern nations ufing uncommon charafters, as the Runic and German. “ In the modern part no feries can be formed of copper that will go back above two centuries *, but Se¬ quences (chronological feries) of gold and filver may be arranged of all the different empires, kingdoms, and ftates, as far as their feveral coinages wall allow. Thofe of England and France will be the moft perfefl. Mo¬ dern filver is commonly arranged in thtee fequences ; the dollar, the groat, and the penny fizes. The me¬ dals of each modern country ought of courfe to be feparated 5 though it is befx to arrange each fet in chronological order, let their fize of metal be what they will. It may be remarked here, that our modern medals, of the fize of a tea-faucer, are only fo many monuments of barbarifm. The ancient medallions are alraoft univerfally but little larger than our crown- piece, though three or four of them may extend to about two inches diameter, but very many modern me¬ dals to four inches and more. A large medal always declares an ignorant prince or an ignorant artift. Into the iize of a crown-piece the ancients threw more mira¬ cles in this way than will ever appear in thefe mon- ftrous productions.” VoL.XlII. Part I. A L S. , 169 Thefe directions will likewife apply to the forma- Ancient tion of a cabinet of the fecond kind : but if the col- <-‘oins- ledtor means to form a feries of large Roman brafs, he v~ will find the coins of four or five emperors fo fcarce as not to be attainable in that feries, even at any price. He muft therefore fupply their places with middle brafs, as is allowed with regard to Otho, even in the heft cabinets j there not being above three coins of that emperor in large brafs known in the world : whereas of the middle brafs, two or three hundred may exift. For this reafon Mr Pinkerton concludes, that in cabinets of the fecond clafs, the colledlor may mingle the large and fecond brafs together as he thinks proper, in order to fave expence ; though it would not do fo well to unite fuch difproportionate fizes as the large and fmall. “ In the fmall iequence, however (fays he), there can be no harm in his mix¬ ing gold, filver, and brafs, as chance or curiofity may lead him to purchafe any of thefe metals. And though your ft arched bigotted medallift may fneer becaufe fuch a fequence would controvert his formal and narrow way of thinking, common fenfe will authorize us to laugh at the pedant in our turn, and to pronounce fuch a feries more various, rich, and interefting, than if the colledlor had arranged only one metal, and rejeCed a curious article becaufe he d:d not collect gold or filver. In like manner, if, in the modern part of the fmaller cabinet, any coin of a feries is of high price, or of bad impreffion, there can be no impropriety in putting anather of the fame reign, which is cheaper, or bet¬ ter executed, though of a different denomination or of a little larger fize. In ftiort, the collector has no rules but in the Greek cities and Roman families, to obferve alphabetical order and chronology in every thing elfe. Tables of Ancient Coins.- The moft ancient coins, according to Froelich, are diftinguhhed by tbe following marks, which he ac¬ counts infallible. 1. Their oval circumference, and globulcus fwelling fiiape. 2. Antiquity of alphabet. 3. The characters being retrograde, or the firft divi- fion of the legend in the common ftyle, while the next is retrograde. 4. The indented fquare already deferib- ed. 5. The fimple ftrufture of the mintage. 6. Some of the very old coins are hollowed on the reverfe, with the image impreffed on the front. 7. The drefs, fym- bols, &c. frequently of the rudeft defign and exe¬ cution. Table I. Ancient Greek Coins. 1. Thofe without impreflion. 2. With one or more hollow indented marks on one fide, and an impreflion in relief on the other.—Of Chal- cedon on the Hellefpont, Lebos, Abdera in Thrace, Acanthus in Macedon, thofe faid to belong to E^iiim in Achaia. This clafs continues from about 900 to 700 B. C. 3. With an indented fquare divided into fegments, having a fmall figure in one of them ; the reft blank, with a figure in relief on the obverfe.—Of Syracufe and other places adjacent.—Continue from 700 to 600 B. C. | Y 4. Coins 170 MED 4. Coins hollow on the reverfe, with figures in relief on the obverle.—Or Caulonia, Crotona, Metapontum, &c. Suppofed by feme to be a local coinage of Mag¬ na Graeciaj but probably of equal antiquity with the former. 5. Coins in which a fquare die is ufed on one or both Tides.—Of Athens, Cyrene, Argos, &c.—Of Alexander I. and Archelaus I. of Macedon. Difufed in the reign of the latter about 420 B. Ci 6. Complete coins, both in obverfe and reverfe, oc¬ cur firit in Sicily in ' the time of Gelo, about 401 B. C. 7. Coins ot Alexander the Great and his fucceffors. About the time of this hero the Greek coins began to attain to perfection, and were ftruck of uncommon beauty. It is remarkable, that on the coins of this monarch his own image feldom occurs. The only one yet found of Alexander with his portrait upon it, and firuck during his reign, is a lilver hemi- drachm in Dr Hunter’s cabinet, which is reprefented Plate CCCXXXI. N° 3. After his death many coins bear his portrait. Trebellius Pollio informs us, that ibme coins, particularly thofe of Alexander, ufed to be worn as amulets ; and many medals are met with in cabinets, bored feemingly with that intention. 8. Coins of the Succefiors of Alexander.—Thofe of the Syrian monarchs almoil equal the coins of Alex¬ ander lnmrelf in beauty. Thofe of Antiochus VI. are fuppofed to be the moft perfedt patterns of male beauty to be met with any where. The Egyptian Ptolemies are fomewhat inferior. 9. The coins of the Arfacidae of Parthia done by Greek wo kmen. 10. 1 he Greek imperial coins, being fuch as have the head of an emperor or emprefs : fuch as have not thefe impreffions being clalfed with the civic coins, though ftruck under the Roman power. None of the imperial coins occur in gold. Of lilver there are thofe of Antioch, Tyre, Sidon, Tarfus, Berytus, Csefarea. Egyptian filver coins of bafe metal. Syrian filver coins, which fometimes bear on the reverfe the club of Her¬ cules. or the Tyrian Ihell-fifh. Thofe of Sidon bear toe image of the goddefs Aftarte, or her chariot. Thofe o‘ Caefarea in Cappadocia of better work than the Syrian Lycian coins of good workmanlhip : on the reverfe two harps and an owl fitting upon them. Silver coins of Gelon in Sarmatia reiembling the Sy¬ rian. I he fituation of this town is very much un¬ known. It feems to have been iituated on the north of the Euxine fea, where fome Sarmatic or Sclavonic tribes were mingled with the Scythians or Goths. The Greek imperial brafs coins are very numerous. A feries of almoft all the emperors may be bad from thofe of Antioch, with a Latin legend on the obverfe and Greek on the reverfe. Thofe of Bithynia and Phrygia remarkable for good workmanftiip. The coins of Tarfus remarkable for their curious view's of ob- je&s, almoft in perfpedlive. The Egyptian coins, from the time of Auguftus to Nero, are worfe exe¬ cuted than afterwards. From Nero to Commodus they are frequently of admirable worktnanfhip, and in a peculiar ftyle, diftinft both from the Greek and Ro¬ man. From the time of Commodus they decline, and are loft after the reign of Conftantius I. The Egyp¬ tian brafs coins of the Roman period are likewife of ex- A L S. cellent workmanftiip, efpecially in the time of Antoni- Ancient nus Pius. Coins. Table II. Roman Coins. I. The confular coins, called alfo the coins of fami¬ lies, and arranged alphabetically in cabinets, accord¬ ing to the names of the families which appear on them. They are, 1. Brafs Coins.— I hefe confift chiefly of large pieces of rude workmanship without any interefting imagery. In cabinets they are generally kept in boxes apart by themfelves. The as bears the head of Janus; the le- mis ot Jupiter with S ; the triens of Minerva with four cyphers; the quadrans of Hercules with three cy¬ phers ; the fextans of Mercury with two cyphers ; and the uncia bears the head of Rome with one cy¬ pher. In all thefe pieces the prow of a ftiip is con- fiantly the figure on the reverfe, with very few excep¬ tions. Sometimes indeed they have a ftiell, two heads of barley, a frog, an anchor, or a dog, on the reverfe. About the time of Julius Csefar both the obverfes and the reverfes of the coins began to be altered. 2. Silver.—Of this the denarius was the firft and principal coin. It was ftamped originally with X, denoting' that the value was ten ales. On the reverfe was Caftor and Pollux, or a chariot of Victory. Af¬ terwards the bufts of various deities make their appear¬ ance ; and in the feventh century of Rome the por¬ traits ol illuftrio.us peifons deceafed are met with : but till the time of Julius Caefar no figure of any livinp- perfon is to be met with ; Julius himfelf being the firit who alfumed that honour. The workmanftiip on the beft and worft filver is much the fame. J. lie reverfes are very curious, and point cut many remarkable events in Roman hiftory 5 but none of thefe occur till about a century before the Chriftian era. The large denarii, ■with Roma, are the moft ancient 5 and fome of thefe bear the Pelafgic A, not the Roman. The filver fef- tertii have a head of Mercury, with a caduceus on the reverfe. The quinarii have always a head of Jupiter, with a Victory on the reverfe. 3. Gold—Moft of thefe are of great value. The number of thefe exceeds not 100 ; thofe of brafs 2CO ; and of filver 2000. The aureus is the general gold coin 5 but two or three gold femiffes of families likewife occur. II. Roman imperial coins. 1. Brafs,—This is of three fixes; large, middle, and final]. The firft forms a moft beautiful feries, but very expenfive. The various colours of the pati¬ na have the fineft effefft. It is the moft important of all the Roman coins, and exceeds even the gold in value. The middle brafs is next in value to the former ; and in it are many rare and curious coins, particular¬ ly interefting to Britons, as elucidating the hiftory of the illand. Of thefe are the triumphal arch of Clau¬ dius ; the Exerc. Britannicus of Adrian ; the coins of Antoninu:. Pius, Cornmodus, Severus, with a Vi ft or v, Victoria Britan.: but efpecially thofe perfonifying the country Britannia. “ The num¬ ber of Roman coins relating to Britain (fays Mr Pin¬ kerton) is remarkable, more than 20 having been ftruck at various times; while thofe perfonifying Italy, Gaul, Spain, M E D Ancient Spain, and other regions of the empire, exceed not four Coin*. or fix at for each country.” Only one country y vies with Britain, and that is Dacia on the extreme north eaft of the empire, as Britain on the extreme north-vveil. No doubt this circumftance of remote- nefs in thefe two countries recommended them to this particular attention,- as more expreffive of the Roman power. The fmall brafs fcries abounds alfo with curious coins. They are fcarce till the time of Valerian and Galiienus, but very common afterwards. Mr Pinker¬ ton recommends, therefore, to forin a feries in filver as w'ell as brafs j both being the cheapeft of all the Romm coins. “ In this feries (fays he), it is a com¬ mon fault to arrange many coins which have been plat- e* with gold or filver, the forgeries of ancient times, but which time has worn off either wholly or in part.” All real brafs coins have the s. c. till the time of Gal¬ iienus 5 as the fenate alone had the power of ftriking brafs, while the emperor himfelf had that of gold and lilver. When the S. c. therefore, is wanting, the coin was certainly once plated ; as, in general, the different type and fabric, being thofe of gold and filver, fufficiently ihow themfelves. With Pertinax, A. D. 192, there is a temporary ceffation of fmall brafs •, nor after him do any princes occur in that feries till Valerian, A. D. 2 54, excepting Trajanus Decius, A. D. 250 only. After Valerian the feries is conti¬ nuous and common. The brafs coinage gradually de¬ clined in fize from the time of Severus •, fo that parts of the as could not be flruck, or at lead it wras held unnecedary to- drike them. Trajanus Decius attempt¬ ed in vain to redore the coinage •, and Valerian and Galiienus wTere forced to iffue denarii aerei and fmall alTaria. The feries of large and of middle brafs are of two fixed and known fizes •, the former about that of Our crown, the latter of the half crown : though after Severus they gradually leffen. But the fmall brafs takes in all parts of the as and every brafs coin not larger than our {hilling belongs to this feries. The minimi, indeed, or very fmalled, it is proper to keep apart. The coins of Julius Cuefar in this fize are of peculiarly fine workmandnp. They bear his portrait reverie of Augudus, or the reverfe has a crocodile Egypto capta. There are feveral with Mark An¬ tony, and fome writh Cleopatra •, but the more com¬ mon pieces are thofe with only numerals on the obverfe, which go the length of XIII ; probably tickets for the baths. A great many occur in the time of Nero of w'hich Mr Pinkerton particularizes one which has 41 on the reverfe a table ornamented with griffins and other devices. Upon it is placed a wrreath of laurel, and a beautiful vafe, of which the emboffed human figures are fo minute, and finiihed fo furprifingly, as to damp thefe coins the mod exquifite produftions of the an¬ cient mint.” From the time of Nero to that of Ve- fpafian no fmall brafs occurs : but there are many of this emperor and of his fon Titus j while Domitian has as many as Nero, and Domitia his wife has al- mod as many. Succeeding emperors to the time of Pertinax have alfo many brafs coins ^ but from his time to that of Valerian there are no real fmall brafs, excepting thofe of Trajanus Decius. After Galiienus there are a great many coins of this kind ; and Mr Pinkerton mentions one in Dr Hunter’s cabinet, of A L s. 171 an unknown perfon named Nigrianus. The coin feems ^Y^nt to have been druck at Carthage j and our author con- ■ eludes that he was an African nlurper, father to Ni- grinianus. 2. Silver.—This feries is very complete, and the cheaped ot any •, efpecially as the fmall brafs becomes a fine fupplement to it : the latter being had in plenty when the filver become fcarce, and the filver being plentiful w'hen the brafs is fcarce. 3. Gold.—The Roman imperial gold coins form a feries of great beauty and perfeftion 5 but on account of their great price, are beyond the purchafe of private perfons. 4. The colonial coins occur only in brafs ; none, ex¬ cepting that of Ncmaufus, having a right to coin filver. They begin in Spain with Julius Caefar and Antony, and ceafe with Caligula, who took away the privilege of coinage from the Spanilh colonies. The mod beau¬ tiful are thofe of Corinth. The other remarkable co¬ lonial coins are thofe of Emerita, liice, Terraco, Caf- fandria, Babba, Berytus, Casfarea, Patr&e, Emiia, He¬ liopolis or Balbec, Ptolemais, Sidon, Tyre, Deulton, Dium, Troas, Rhefaina, Neapolis of Samaria, which bears a reprefentation of Mount Gerizzim wuth the temple on it, Hippo in Africa, &c. On many of thefe coins we meet with fine reprefentations of temples, triumphal arches, gods, goddeffes, and illudrious per¬ fons. But coins with thofe reprefentations are by no means common j the colonial coins till the time of Trajan bearing only a plough, or fome other fimple badge of a colony. Camelodunum is the only colony in Britain of which we have any coins. 5. The minimi.—This includes the fmalled: coins of all denominations, mod of which do not exceed the fize of a filver penny. They are the mod curious of all } but no feries of them was ever formed by any per¬ fon except the abbe Rothelin, whofe colledjtion form¬ ed of all metals palfed to the queen of Spain. The reafon of the fcarcity of thefe fmall coins is probably their diminutive fize j by reafon of which they are modly lod. It is furprifing that numbers of Roman coins are found through all countries once fubjecl to that power¬ ful people. Some have been met with in the Ork¬ neys, and many in the mod remote parts of Europe, Alia, and Africa, known to the ancients. Table III. Coins of other ancient Nations. 1. The Lydians appear to have invented coinage ; though, perhaps, this honour may be difputed with them by the Greeks. 2. 'The Aflfyrians, Medes, Babylonians, Phoenicians, and Egyptians, had no coins. In the mouths of the mummies are only thin, undamped, and round pieces of gold, to pay Charon’s fare. 3. No Indian or Chinefe coins are to be met with till a very late period ; and even then fo rude as fcarce to be worth notice. Voltaire mentions a colletlion of ancient Chinefe and Indian corns made by the emperor of China in 1700; but Mr Pinkerton fuppofes it to have confided only of the Greek and Roman money which had been introduced into thefe countries. 4 The Lydian coins have no legends ; fo that mere conje&ure only determines the ancient coins of ele&rum Y 2 and J72 MED an^ filver tound in A6a, ?.ncl different from the Per- ‘ t j fian, to belong to Lydia. Croefus coined gold into a form which he called /Inters; and Mr Pinkerton mentions a very ancient gold coin in Dr Hunter’s ca¬ binet, which he fuppofes to have been one of thefe. It has a globous figure, with indented marks on one fide, and on the other a man kneeling, with « fiih held out m the left hand, and a fword depending in the right. It weighs four drachms j which Jofephus tells us was the weight of the Lydian gold coins. In the fame col- leftion are other gold coins little inferior in antiquity ; the moll ancient of which, our author fuppofes, may have been coined by the cities of Afia Minor, as coin¬ age palled through them to Greece. They are of ad¬ mirable workmanlhip, and as much fuperior to the belt Sicilian coins, as the latter are to all the reft in the world. 1 hefe gold coins are all extremely pale j owing to the want of knowledge in refining gold. 5. Perfian coins.—Thefe W'ere firft ftruck by Darius Hyftafpes, whence they had the name of darics. They are of gold, and generally have the figure of an archer: they weigh about four drachms $ and fome occur with the indented mark on one fide, while others have figures upon both. The filver coins have generally a king in a chariot of two horfes, with a charioteer, and forsetimes another figure on foot be¬ hind, on the obverfe : while the reverie prefents a {hip, fometimes a ram, bull, or other animal. The gold coins, which only had the title of darics, are extreme¬ ly fcarce, having been melted down, as is fuppofed, and recoined by Alexander the Great on his conqueft of Afia. There is a fecond feries of Perfian coins beginning with Artaxares, or Artaxerxes, who overthrew the Parthian monarchy about the year 210. Thefe are large and thin, with the king’s buff on one fide and the altar of Mithras on the other j generally with a human figure on each fide. Thefe coins continue till the year 636, when Perfia was conquered by the Sa¬ racens. Thefe have ' only Perfian letters upon them, which have never been explained by any antiquaries. Mr Pinkerton fays that they leem to partake of the ancient Greek, Gothic, and Alanic. 6. The Hebrew fhekels, originally didrachms, but after the time of the Maccabees tetradrachms, are al- moft all forgeries of modern Jews, as well as the brafs coins with Samaritan characters upon them. They have all a fprig upon one fide and a vafe on the other. Mr Pinkerton fays, that the admiffion of one of them into a cabinet would almoit be a difgrace to it. 7. Phoenician and Punic coins are very interefling on account of the great power and wealth of thefe na¬ tions. The alphabets have been cleared by their rela¬ tion to the Hebrew and Syriac languages. 8. The coins of Palmyra come under the fame de¬ nomination with the former, Palmyra being a Syrian city. 9. The Etrufcan coins have the characters of that nation, which have been explained by their affinity to the Pelafgic, or oldeft Greek and Latin. 10. I he Spanith coins are inferibed with two or three alphabets allied to the old Greek or Punic 5 but the inicriptions have not been fufficiently explained. 11. Gaulifli coins.—Thefe are numerous j but the moil ancient have no legends j and even after the A L S. Greek letters were introduced into Gaul by a colony MAera at Marfeilles, the legends are very difficult to be ex- Com¬ plained. 1 .11 -- y— 1 2. Britifh coins.—From a paflhge in Csefar’s Com¬ mentaries, it has been inferred that the Britons ufed fome kind of coins even in his time. IVIr Pinkerton in¬ forms us, that foroe rude coins of copper very much mingled with tin are frequently found .in England; which, he fuppofes, may be fome of the ancient Bri- tiih money. 1 hey are of the fize of a didrachm, the common form of the nummus aureus among the an¬ cients. After the time of Caefar, coinage increafed among the Britons ; and there are many found of Cu- nobelinus mentioned in the Roman hiftory. PToft of thefe have on one fide cuno, with an ear of wheat, a horfe, a kind of head of Janus, or other fymbol; mid have frequently alfo the letters camu ; fuppofed to mean Camelodunum. Sometimes the word Tascia occurs ; the meaning of which has not yet been ex¬ plained. 13. Gothic coins of France, Italy, and Spain, to the time of Charles the Great. Thefe have the Roman chara&ers upon them. The Italian coins are moftly of the fize ot fmall brafs ; and in this way we meet with coins of Athalaric, Iheodahat, Witigez, and other Gothic princes. Many others occur, the inferip- tions of which, though meant for Roman, are fo per¬ verted as to be illegibly. Table IV. Modern Coins. 1. Of Japan.—Thefe are thin plates of gold and filver, of an oval figure, with fmall marks or figures ftamped on them. 2. China.—Thefe are only copper, about the fize of a farthing, with a fquare hole in the middle to put them on firings. The inferiptions on them do not exprefs the name of the fovereign, but the year of his reign ; as the happy year, the illu/lrious year, &c. * 3. The Tartarian coins are rude, having only in¬ feriptions upon them; and they are all pofterior to the time of Jenghiz khan. 4. Coins of Thibet, Pegu, and Siam, are much the fame, prefenting only inferiptions without any figures. They are alfo of late date. 5. India.—Some old coins have been found in the neighbourhood of Calcutta, of gold, filver, copper, and tin, all mixed together. Thefe have commonly a war¬ rior with a fword on one fide, and an Indian female idol on the other, of the fame form with the celebrated fculptures in the ifland of Elephanta ; but it is impof- fible to tell what antiquity they are of. The modern coins, are the pagoda of gold, worth little more than fix fhillings ; the roupee of filver upwards of two fnil- hngs ; and the caffi, of copper. There is a remarkable fet of roupees, which fhow the twelve figns; a lion on one, a bull on another, &c. but the occafion on which they -were ftruck is unknovfn. The other coins of India have generally Perfian inferiptions upon them. 6. Periia—The Perfic coins fince its conqueft by the Arabs continue on the Arabian model. 7- Arabia. Some coins of the petty princes of Arabia are met with as old as the imperial ages of Rome; but till the time of Haroun Alrafhid, no re¬ gular MED Modern" gular coinage appears in die vail empire of the Sara* Coins. cens> Even then the reverfe has only an infcription, —"'v ' and the obverfe is copied from any Greek or Syrian coin which happened to fall in the moneyer’s way. The later Arabian coins are moftly iilver, with the name and titles of the prince on one fide, and fome infcription from the Koran on the other. The more modern coins of this country are in the (hape of a filh- hook, with Arabic infcriptions. 8. Turkey.—No regular coinage was formed by the Turks till they became mailers of Conftantinople. They refemble thofe of Perfia and Arabia, having merely infcriptions on both Tides. 9. The coins of the African Hates, at leaft fuch as profefs the Mohammedan religion, have merely infcrip¬ tions without any figures : thofe of the internal parts are unknown •, and no coinage was ufed among the Mexicans and Peruvians, the only civilized nations in America ; but La Hontan mentions an American fa- vage who had a fquare medal of copper depending from his neck. Mr Pinkerton fuppofes it to have come from Japan. 10. Modern Italic coins. Befides the Gothic prin¬ ces mentioned in the former table, the exarchs of Ra¬ venna coined money with the infcription Felix Ra¬ venna, See. The Lombards iffued no coins, but there are fome Hill extant of Charlemagne. The follow¬ ing lift (hows the origin of the coinage in various Ita¬ lian Hates. Rome.—Papal coinage originates with Hadrian I. Size of lilver pennies, with the Pope’s name on one fide, and Scos Petrus on the other. No coins appear from 975 to IC99, excepting of Leo IX. In 1303 appear pennies of the fenate and people of Rome, with Peter on the one fide and Paul on the other. There are groats of Clement V. with his portrait three quarters length 5 but the fide-head begins with Sixtus V. in 1470. Gold was firft coined by John XXII. in 1316. The coins of Alexander VI. Julias II. and Leo X. are remarkable for beauty and elegance. Milan. Coinage began with Charlemagne. The firft coin of the family of Vifconti occurs in 1330 un¬ der Azo. The let finilhes with Louis XII. Naples. Coinage begins in 840 and 880, with Duke Sergius and Bilhop Athanafius. The next coins are of Roger of Sicily, and Roger II. in 1I3°> William I. II. and Tancred. Naples and Sicily were fubdued in 1194 by the emperor of Germany; in 1255 Manfred appears; in 1 266 Charles of Provence ; and others till Jo.at in 1414" a^er which follow tne houfe of Arragon, and later kings. Venice begins in the Ioth century. The firft coins are filver pennies marked Veneci. Then follow the coins of Henrico Dandulo in 1192, of Ziani in 1205, &c. Gold was firft coined at Venice in 1280, and copper in 1471 ; but the filver groats are as old as JI92. _ . - , 1 Florence. Silver was coined here m the 12th cen¬ tury, or before ; but in 1252 the firft gold coins ftruck in Europe after the 8th century made their ap¬ pearance, and were named florins from the flower of the lily noon them. They were imitated by the popes, by France, and England. They have on one fide St John the Baptift Handing, on the other a large A L S. 173 fleur de lis, and it is not doubted that the French fleurs Modern de lis took their origin from thefe coins. They weigh , Co^ns- , a drachm, and are no lefs than 24 carats fine, accord- in? to Italian writers, and are worth about 12 IhiL o ' lings. Geneva firft began to coin money in 1129, under the government of Conrad. Thofe of the dukes of Savoy began in the fame century. Aquileia. Coins were ifiued from this city by the patriarchs from 1204 to 1440. Ferrara. Coins of the marquifes from 134c. 11. French coins. During the race of Clovis, from 490 till 751, the coins are chiefly gold trientes% with fome flolidi and flemifles. The former are of good workmanfhip, with the heads of kings. Ihe reverfe has a crofs, with the name of the town where they were ftruck. The coins of the fecond race begin with Pepin in 751, and continue till Hugh Capet in 987. The coins of the firft race are elegant, but thofe of the fe¬ cond entirely the reverfe, being almoft all filver pen¬ nies, and feldom bearing the portrait of the king. Thofe of Charlemagne have only Garqlus in the field; while the reverfe bears R. F. or fome fuch in¬ fcription ; though one piece ftruck at Rome has a rude buft of him. The coins of Louis le Debonnaire are better done. The third race begins with Hugh Capet in 9^7» and extends to this time. Fhe coinage did not begin to improve till 1 226 under St Louis, when the groat appears. Its name in Italian is groflb, in French in Englifh groat, or great com ; fo called from its iize in comparifon with the penny ; and it palled from Ita¬ ly to France, to Germany, and to England. After the conqueft of France by the Englilh, bafe coins of many kinds were introduced ; and in the year I574» in the time of Henry III. copper was firft introduced into the French coinage. Befides thefe, the other re¬ markable coins of France are, the blancs or billon groats, firft iflued in 134^ ? e('us a couronne, or crowns of gold, fo called from the crown on one fide, and begun by Charles VI. in 1384 } thofe ol Ann oi Bretagne in 1498 : the teflon, or piece with the king’s head, of Louis XII; the Henri of Henry II. with Gaul fitting in armour, and a Victory in her hand. There are many coins of Cardinal Bourbon, ele61ed king in 1589 ; and in 1642, Louis XIV. takes the title of Catalonia; Princeps. The firft louis d'or made its appearance in 1640 ; but fuch was the poverty of France, if we believe certain au¬ thors, that in 1719 the duke of Orleans regent ftruck copper for filver. 12. Spanilh coins. The moft early feries of thefe confifts almoft entirely of trientes, finely done. On one fide they have the head of the kmg with his name, and on the other a crofs, with the name of the town, commonly in Bsetica, or the foutn part of Spain, where there were a great many Roman colonies, and which was fertile to a proverb. Ihe Moreique coins of Spain, like thofe of the reft of the Mohammedan Hate1-, prefent us ©nly with infipid infcriptions on both fides. Indeed the Mohammedan religion, by its abfo- lute refufal to allow the reprefentation of any living creature, has prevented the progrefs of coinage in any degree throughout thofe regions which it has over- fpread. 174 MED Modern j^rtad. The infcriptions on the ailcient Spanifli coins , Co^r>s- are in the Cufic or old Arabic charaiders. 13. Portugal. No defcription of the coins of this kingdom has yet appeared. 14. Germany. No account of the German coins has been publiihed j though it is well known that not only the emperors, but many of the cities, particular¬ ly thofe called Hanfe-towns, iffued money ; and many of the coins iffued by the cities were fuperior in ele¬ gance even to thofe iffued by the emperors. 15. Denmark. Here the coinage begins with Ca¬ nute the Great in 1014. The pieces are at firft ex¬ tremely rude, ornamented only with rings and Runic characters. Thefe are fucceeded by copper pieces, fome of w'hich have a crofs, others a paftoral ftaff, on one fide, with the letter A on the other. Later coins have ftrokes mi, &c. all round them ; but thofe of Harold, Hardicanute, and Magnus Bonus, in 1041, are of neat wmtkmanfhip, and have the portraits of the princes at half length. The coins of Nicolas, or Niel, as he is called by the Danes, are rude, as well as thofe of Wajdemar I. and the celebrated Margaret. In 1376 Olaf cau^d money to be ftruck with a grinning full Tee, with a crowned O upon the other fide. “ The Swedes (fays Mr Pinkerton) took thefe coins extremely ill, as they thought they grinned at them.” Silver was firft coined in Denmark by Philippa queen of Eric, and daughter to Henry IV. of Eng¬ land. 16. Sweden. The coinage of this kingdom began in 818 under Biorno, on the plan of Charlemagne. The coins are marked with a crofs. Next follow thofe of Olaf in 1019 ; which Mr Pinkerton fuppofes to have been the firft true Swedifh coins ; and that the art of coinage firft paffed from England into Den¬ mark in the time of Canute the Great, and from Den¬ mark into Sweden. Thefe coins were ftruck on the Englifh model. During the time that Sweden was fubjeft to Denmark, or miferably haraffed by the Danes, the coins of both kingdoms were the fame 5 but after the time of Guftavus Vafa many elegant pieces appear. In 1634, dollars were coined with the portrait of Guftavus Adolphus, who was killed two years before : on the reverfe they have the arms of Sweden, with the chemical marks of mercury and fulphur. In 1716, 1717, and 1718, Charles XII. being in extreme want of money, iffued fmall copper coins with Saturn, Jupiter, Mars, &c. upon them/to go for dollars; and on account of this fcheme, Ba¬ ron Goertz, the fuggeftor of it, was brought to the block. 17. Norway. The coins of this country begin with Olaaf in 1006 ; after which time there are vari¬ ous coins of other princes; but copper was not coined till the year 1343. Befides the coins already mentioned, there are ec- clefiaftic coins of France, Germany, Denmark, Swe¬ den, Norway, &c. Thofe of Denmark and Sweden are numerous, but the Norwegian coins of this deno¬ mination are rare. Mr Pinkerton deferibes a filver one in his poffeffion as having arms and a mitre, with the infeription on one fide, Sanctus Olaws Rex Norvey ; on the reverfe, Olaws Dei Gra. Arcep. Np’sEN, meaning Nidrosiensis, or archbifhop of s Nidros, now Drontheim. A L S. 18. Bohemia. The coinage of this kingdom ap- Modem pears at a very early date, viz. in the year 9C9, under Coins- Duke Boleflaus I. Thefe coins are followed by others of Boleilaus II. and Emma his wife in 970 ; of Bo¬ leflaus III. in JC02; Jaromir in IC20 5 Udalrich in 1030, and other princes. The bracleate money of Ot- tocar I. was coined in 1197. 19. Poland. lire coinage of this country is nearlv as ancient as that of Bohemia. The coins are on the German model, but no particular account of them has been published. 20. Ruftia. None of the Ruffian money appears to be more ancient than the 13th century. The firft are the kopecks or filver pennies, w'hich have upon them rude figures of animals on one fide, and a man Hand¬ ing with a bow or Ipear on the other. There are like'- wife coins of Mofcow ftruck by Ariftoteles the archi- teft in 1482. The roubles or dollars and their hhlfs. There are fome of the impoftor Demetrius in 1605, which are very fcarce. 21. Pruflia. The firft Pruffan coins were ftruck at Culm by the Teutonic knights in 1230. Thev were filver pennies, and upon the German plan. In the next century w^ere ftruck {hillings, groats, and Jchots ; the laft were the largeft,’ and are extremely rare. They have the Pruffian flfield, an eagle fur¬ mounting a crofs, with a rofe-thaped border, moneta DOMINORUM Prussia: : on the reverfe is a crofs fieu- rie, within a border of a fimilar kind, having the in- feription honor magistri, justitiam diliget.—- Gold coins were ftruck in the fame century. In the time of Copernicus the money was fo debafed that 12 or 13 marks were worth but one of pure filver. . 22, England. The Englilh coins are of various kinds. 1 ft. Hcptarchic. Thefe are only of tw'o forts, viz, thejkeat'a or penny of filver, and the Jiyca of copper.* Few of the pennies appear till after the year 700 ; though fome are met wdth which bear the name of Ethelbert 1. king of Kent, as old as 560. At firft they had only rude figures of ferpents, but in latter times legends were likewife added. Moft of thefe pennies have pagan fymbols upon them. The ilyca w^as only coined in Northumberland, and w’as a very fmall piece, about the value of half a farthing. 2d. Coins of the chief monarchs of England. Mr Pinkerton denies that an end wras put to the heptar- chy by Egbert in 832, as is commonly fuppofed j tnough he owns that he was chief monarch of the coun¬ try, as^ feveral others had been before him. Edgar, wffo reigned in 959, according to him, was the firft king of England ; and the coins of the chief monarchs form almoft a complete feries from the time of Eg¬ bert to Edgar. Ibe only chief monarch of whom there are no coins is Ethelbald, who reigned in 857. Moft of thefe coins bear rude portraits ; but the re- verfes are fometimes curious and interefting. Some have views of cathedrals and other buildings 5 particu¬ larly one of Edward the Elder in 900 ; which has the cathedral of York with three row s of windows, round arched as the other Saxon and Norman buildings ; the Gothic arch being quite unknown till after the i 2th century. Some coins of Anlaf king of Northumber¬ land have the famous raven, the Danifh enfign : and thofe 2 M E D Modem tliofe of other princes have frequently very curious re- C0'1™' verfes. 3d. Ecclcjiqftic coins appear of the archbiOiops of Canterbury, Wulfred in 804, Ceolnoth in 830, and Piegmund in 889. 4th. Coins of the kings of England. The filver pen¬ ny, which had begun during the heptarchy, continued to be the general coin after the kingdom had ben n united under one head *, and extends in a continued feries from Egbert almoit to the prefent reign. The only kings wanting are Edmund Iron fide, Richard I. and John. At firif the penny weighed 224- gtains : but towards the clofe of the reign of Edward III. it fell to 18 grains; and in that of Edward IV. to 12. In the time of Edward VI. it was diminiihed to 8 grains; and in Queen Elizabeth’s reign to 7TT; at which it Hill continues. Halfpennies and farthings wrere firft ftruck in filver by Edward I. in 1280; the former continued to the time of the commonwealth, but the latter ceafed with Edward VI. The groat w7as introduced by Edwrard III. in 1334, and continues to this day, though not in common circulation. The half-groat or two pence is of the lame date, and alfo continues to the prefent time. Shillings were firll coined by Henry VII. in 1503. At firll it was called tejioon, from the tejle, tete, or head of the king upon it ; the name Jhi/ling being derived from the German fchelliag; under wThich appellation coins had been ftruck at Hamburgh in 1407. The crown was firft coined in its prefent form by Plenry VIII. Formerly it had appeared only in gold, whence the phrafe of crowns of gold ; though thefe indeed were the largeft gold coins known for a long time in France and other countries on the continent, being worth about 10s. fterling. They had their name from the crown ftamped on one fide, and were firft coined by Charles VI. in 1384, and continued till the time of I jouis XIV. The half-crown, fixpence, and three¬ pence, were coined by Edward VI. In 1558 Queen Elizabeth coined three halfpenny, and in 1561 three farthing pieces ; but they w7ere difeontinued in 1582. From the year 1601 to the prefent time the coins of England remain the fame. Gold was coined in England by Henry III. in 1 257 ; the piece was called a gold penny, and was lar¬ ger than the filver one ; and the execution is by no means bad for the time. The feries of gold coinage, however, commences properly from Edward III. In 1344, this monarch firft ftruck florins, in imitation of thofe in Italy ; and it is remarkable, that though thefe coins at the time they were firfl iffued bore only fix flhiiiings value, they are now intrinfically worth 19s; I;> much has the value of gold increafed fince that time. The half and quarter florin were ftruck at the fame time, but only the laft has been found. The florin, however, being found inconvenient, gave place to the noble of 6s. 8d. value, and exa£Ily half a mark. The latter had its name flrom being a limited fum in accounts ; and was eight ounces in weight, two thirds of the money pound. It is lometimes alfo called feli- brci, as being one half of the commercial pound of 16 ounces. 1 he noble had its name from the nobility of the metal ; the gold of which it v,7as coined being of the fineft fo;t. Sometimes was called rofe nob/e: A L S. from both Tides being impaled in an undulating circle. Modern It continued with the half and quarter noble to be the Coin3, only gold coin tUl the angels of Edward IV. appeared v in 1465. Thefe had their name from being ftamped with the image of Michael and the dragon. The an- gelites of 3s. 4d. value tvere fubftituted in their place. In 1527 Henry VIII. added to the gold coined the crown and half-crown at their prefent value ; and the fame year he gave fovereigns of 2 2s. 6d. and ryals of its. 3d. angels at 7s. 6d. and nobles at their old value of 6s. 8d. In 1546 he caufed fovereigns to be coined of the value of 20s. and half-fovereigns in proportion. His gold crown is about the fize of our {hilling, and the half-crown of fixpence, but thin. All his coins, however, gold as well as filver, are much debafed ; and it was not without much labour and trouble that Ed¬ ward VI. brought it back to its former ftandard. On the union of the two crowns, James gave the fovereign the name of unite; the value continuing of 20s. as before. He coined alfo rofe-ryals of 30s. value, fpur- ryals of 15s. angels of 10s. and angelets of 5s. Un¬ der the commomvealth, the fovereign got the name of the twenty-Jhi/hng piece, and continued current till the coinage of guineas. Thefe were fo called from their being coined of Guinea gold, and were at firft only to go for 20s. though by an univerfal but tacit confent they always palled for 21s. Half-guineas, double guineas, and five guinea pieces, were alfo coined dur¬ ing the fame reign ; which ftill continue, though the two latter are not in common circulation. Quarter guineas were coined by George I. and likewife by his prefent majefty ; but they were found fo trouble- fome on account of their fmall fize, that they were flop¬ ped within a year or two, when received at the bank of England, and thus are not to be met with at pre¬ fent. A few pieces of 7s. value have likewife been coined, and are known by the lion above the helmet ; but none have been iffued. In 1688 the guinea rofe to 2is. 6d. and continued to increafe in value till 1696, when it was as high as 30s. ; but after the re¬ coinage in 1697 and 1698 it fell by degrees, and in 1717 was at its old ftandard of 2 is. and at that time filver was fixed at its prefent ftandard value, viz. as 1 to 15 4- in weight. Though the firft money coined in Britain, as we have already obferved, was copper, yet, excepting the Northumbrian ftycas, no copper coin w7as found in England from the time of the Saxon conqueft till the year 1672. An averfion to a copper coinage it feems was prevalent throughout the nation ; and Queen Eli¬ zabeth, who without hefitation ufed bale money for Ireland, yet fcrupled at coining copper for England. This want of fmall coin occafioned fuch an increale of private tokens for halfpennies and farthings, that it be¬ came a ferious object to government; and in 159 4 a cop¬ per coinage was ferioufly thought of. This year a fmall copper coin was ftruck about the fize of a filver two¬ pence, w7ith the queen’s monogram on one fide, and a rofe on the other ; the running legend on both (ides being, the pledge of a halfpenny. Of this there are patterns both in copper and filver, but both of them foon fell into difufe. On the iprh of May 1613, King James by., royal proclamation iffued farthing tokens. They are generally of the fame fize with the tWQ pence? with two feeptres io faltiej: furmounted . with 4 Ut 176 M E D Modern with a cfowfl, and tlie harp upon the other ; with an Coins, intention, as it would feem, that if they were refufed v in England they might pafs in Ireland. In 1635 Charles I. coined thofe with the rofe inftead of the harp ; but the circulation of thefe was entirely flopped by the vaft number of counterfeits which appeared, and by the king’s death in 1648. After this the pri¬ vate tokens began again to be circulated, till put a flop to by the coinage of farthings in 167 2. The workman- fliip of the tokens is quite contemptible. In 1672 the halfpence as well as the farthings which had been flruck two years before began to circulate. They were of pure Swediih copper, the dies engraved by Roettier j and they continued till the year 1684, when home difputes aroi'e about the copper lately obtained from the Englilh mines. Tin farthings were coined with a flud of copper in the centre, and infcribed round the edge as the crown pieces, with nummorum famulus. J685 or j686. In 1685 halfpence of the fame kind were coined ; and the tin coinage continued till the year 1692, to the value of more than 65,000!; but next year the tin was all called in by government, and the copper coinage recommenced. The farthings of Queen Anne are all trial pieces, excepting thole of 3^714, the laft year of her reign. “They are (fays Mr Pinkerton) of exquifite workmanfltip, exceeding moft copper coins either ancient or modern, and will do honour to the engraver Mr Crcker to the end of time.” The one, whofe reverfe is Peace in a car, pax missa per orbem, is the moft efteemed ; and next to it the BRITANNIA under a portal. The other half¬ pence and farthings are lefs valuable. 23. Scotland. Silver pennies of Alexander I. wdio reigned in 1107, are believed to exift ; and there cer¬ tainly are fome of Alexander II. in 1214. There are Jikewife coins of David in 1124; but perhaps none of Malcom IV. his fucceffor, whofe reign wras very fliort. There are many coins of William I. in 1165; and a large hoard of his pennies was found at Invernefs in 1780. The money of Scotland continued to be of the farce value with that of England till the country was drain¬ ed by the vaft ranfom of David II. after which it be¬ came neceffary to reduce its ftze; and fo much did this diminution affedt England, that Edward III. found himfelf obliged to leffen the Englifti coin alfo. The diminution of the Scottilh coin, however, continued Hill to go on until it became impraclicable to keep par with that of England. In the firfl; year of Ro¬ bert III. it pafled only for one half of its nominal value in England : in 1393, Richard II. ordered it only to go for the weight of the genuine snetal it contained. In 1600 it had funk to fuch a degree as to pafs only for a twelfth part of the Englilh money, and conti¬ nued at that low ebb till the coinage of Scotland was entirely cancelled by the union of the twu king¬ doms. Of fil-ver coins we have only pennies till the year 1293, when Edward I. having coined halfpeace and farthings, Alexander III. of Scotland coined alfo halfpence, of which we have a fewq but no farthings are to be met with ; but there are fdver farthings of Robert I. and David II. The latter introduced the groat and half-groat, which completed the fet of Scot¬ tilh ftlver. It continued unaltered till the tim of 3 A L 5. Queen Mary, when they all ceafed to be coined in Modem ftlver, on account of the high price of that metal. C°“1S' In 1553 {hillings were firfl coined, writh the buft of the queen on one fide and the arms of France and Scotland on the other. The fdver crown was firfl; coined in 1565, which went for 30s. Scots; Idler pieces of 20s. and 10s. having likewife been flruck, and marks of filver, worth 3s. 4d. Englifti, wrere alfo coined about the fame time. Thefe coins have upon them the marks xxx. xx. x. to denote their value. They are commonly called Cruickflone dollars, from the palm-tree upon them, miftak-en for a remarkable yew at Cruickflone near Glafgow*, wdiere Henry Darn- ly refided. It is defcribed, however, in the act as a palm, with a “ {hell padoc” (a tortoife) crawling up. This alludes to Dandy’s marriage with the queen, as the motto from Propertius Dat Gloria Vires alfo implies. The motto Nemo me impune lacesset firfl appears on the Scottifli coins in I57^> an<^ ^n* ventiph is given to the celebrated Buchanan. In 15^ the crown of an ounce weight went for 40s. Scots, and was accordingly marked XL. ; in 159? ^'e mark was L. the Scottilh money being then only one-tenth of the Englifti : the mark w^as LX in 1601, the value being then reduced to one twelfth, at which it has ever fince continued. In the time of Charles I half marks, 40 and 20 penny pieces, wTere coined. In 1675 the Scottifli dollars firft appeared, in value 56s. Scots, with halves and quarters of proportional value. In 1686, James VII. coined 60s. 40s. 20s. 10s. and 5s. pieces ; but only thofe of 40s. and I os. are known, with thefe numbers under the buft. At the union of the kingdoms, all the Scottifti coins ivere called in, and recoined at Edinburgh, with the mark E under the bull t« diflinguifli it : fince which there has been no coinage in Scotland. The Scottifli filver coins are in general equal, if not fuperior, in the workmanftiip to the Englifti. Gold was firfl: iflued by Robert II. about 30 years after Edivard III. of England had coined the fame metal in that country. The pieces were at firft called St Andrews, from the figure of that tutelar faint upon the crofs, and who appears on the obverfe with the arms of Scotland, and on the reverfe a lion in a Afield. The lion was another name for the largeft gold coin in Scotland, from the arms of the kingdom upon it. The next was the unicorn, under James III. ; which were followed by the bonnet-pieces of James V. Thefe laft are of admirable workmanfhip, being almoft equal to the ancient coins in this refpeft. In imita¬ tion of the French, the monarch we fpeak of dimi- niftied the fize of the coin without leffening its wreight; an improvement not adopted by the Englifti for a whole century. The laft gold coined in Scotland was the piftole and half piftole, of twelve and fix pounds Scots. Thefe coins have the fun under the head. The gold coins of Scotland fell in the fame proportion with the filver. The copper coinage of Scotland is of more early date than that of England. It was preceded by mo¬ ney of bil/on, or copper waflied with filver, called black money. James III. firft coined black farthings in 1466; and this .is recorded by hiftorians as one of his greateft faults. This kind of coinage, however, con* tinued as late as the reign of James VI. In his time MED ^fodefa the true copper coinage began; but as the value of Coins. Scottilh money had now declined almoft to the ut- J” v moft, the pieces fuddenly affumed a form almoit re- fembling that of the French coins. The bodle fo called from Bothwell the mintmalter, being equal in fize to the linrd, and worth two pennies Scottilh, was ftruck. The billon coin, formerly called has piece, and worth fix pennies Scots, was now coined in cop¬ per, and termed the baw-bee. Thus it correfponded wich the French half fol and Englilh halfpenny, the Scots penny being now equivalent to the French de¬ nier. Some pieces named Atkinfons were coined by James VI. in 1582, when the Scottifh money was to the Englifh as 1 to 8 j but on its being {till farther reduced, they went for 8 pennies, a third more than the value of the baw-bee. Befides thefe there were the hardie and plack, the former being worth three and the latter four pennies Scots. This coinage con¬ tinued through the reigns of Charles I. and II. but Scottilh coins of the former are, perhaps, the fcarcefi: of any. 24. Ireland. The firft coins introduced into this king¬ dom feem to have been thole of the Danes, and which have only a number of ftrokes around them inftead of letters. In the tenth century, however, this coinage had been confiderably improved •, and in 930 and 994. there are pennies ftruck in Dublin, w'ith the infcrip- tion on Dvfli or Dyfli, Duflin or Dyjlin being the Danilh name of that city. There are likewife coins of the I nth princes themfelves, and of the Englilh monarchs, ftruck in Ireland as early as the ninth cen¬ tury 5 and it is aflerted by fome, that Ireland even in thefe days had been conquered by England •, of which indeed, thefe coins leem to be a proof. None of the Iriih coins of Henry II. are to be met with, but w'e have fome of the coins of John; aud from'his time to that of Henry V. the Iriih coins are known by a triangle enclofing the king’s head, wdiich appears alfo upon the coins of other nations at this period. The harp does not appear upon the Iriih coins till the time of Henry VIII. Till the time of this monarch, the Englilh and Irilh coins are the fame ; but the fame de- bafement of the coin which at that time took place in England extended alfo to Ireland ; but in 1601 copper halfpence and farthings were coined alfo for this king¬ dom. Thefe circulated in Ireland wdien James VI. ilfued his farthing-tokens of copper, the latter being of two fizes, that if they failed in England they might be fent to Ireland as pennies and halfpence. In 1635 a mint wras eftablilhed in Dublin by Charles I. but it wTas flopped by the Iiilh maffacre, and the many di- fturbances which follow’ed ; fince which time the fcheme has not been refumed. After the mafiacre, St Pa¬ trick’s halfpence and farthings were coined by the Pa- pilts, bearing the legends FloreA.T Rex, and on the reverfe Ecce Grex ; on the farthing Quiescat Peeks. Copper tokens w’ere ftruck by towns and tradefmen, as in England and Scotland. In 1680, half¬ pence and farthings were iflued by authority, wnth the harp and date. In 1689, James H. having invaded Ireland, inftituted a mint, and coined {hillings and half-crowns of all the refufe metal he could find, par¬ ticularly fome brafs guns were employed, whence the coinage is commonly called gun-money. Even this metal, howrever, foon became fo fcarce, that a diminu- VOL. XIII. Part I. A L S. tion in its fize is quite apparent from June 1689 to July 1690; and as the month of their mintage is marked upon them, this decreafe is eafily perceived. In March 1690, pennies of lead mixed with tin were iffued ; and on the 15th of June the fame year, crowns of white metal were coined ; but thefe are now very fcarce. In 1722, the patent for coining halfpence and farthings was given to William Wood, which excited fuch difcontent in Ireland. From the imall fize allow¬ ed by the patent to thefe pieces, it was fuppofed that the patentee would have gained 6o,oool. but as he caufed them to be ftruck of a fize {till fmaller, his gains were eftimated at ioo,oool. The coins, how'- ever, are of admirable w-orkmanftnp, and very fine copper, bearing the beft portrait of King George I. to be found any where. Sir Ifaac Newton, at that time at the head of the mint, declared that they were fuperior to the Englifti coins in every thing except the fize. In 1737 the Iriftr halfpence and farthings, with the harp on the reverfe, were coined, and continue to the prefent time. In 1 760, there was luch a fcarcity of copper coin, that fome private perlons applied for leave to coin halfpence, w'hich appeared with a very bad portrait of George II. and the words Voce Po- puli around it. No gold or filver has been coined in Ireland fince the mafiacre of 1641. 177 Modern Medal?. Table V. Modern Medals, properly fo called. 1. Scottifh medals. Thefe take the lead in the pre¬ fent article, the firft modern medals of gold being thofe of David II. ftruck between the years 1330 and J37Q. Only two of them are known to exift ; one in the col- leblion of Mr Barker of Birmingham, and the other in that of Dr Hunter. In 1487, there is a medal of James III. fent to the fhrine of St Amboife in France. It is deferibed as of two inches and a third in diame¬ ter ; the weight near twro ounces; having on the ob- verfe a beardlefs king, with long hair, fitting on a throne, holding in one hand a naked fvvord ; in the other a fhie!d, with the Scottifh arms. On the bor¬ ders of the canopy above the throne is an inlcription in Gothic letters, in Ml deffen, being corrupt French for In my defence; a common motto in the Scottifh arms. Above the canopy is Villa Eer- wichi : the reverfe bears St Andrew and his crofs, SALVUM FAC POPULUM TUUM DOMINE, There is alfo a medal of James IV. in the collar of St Michael, having on the reverfe a Doric pillar furmounted by a young Janus, Handing on a hill, beyond w'hich is the fea, and land on either fide. This, however, is by fome fufpe&ed to be a forgery. The moft remarkable Scottifh medals are thofe of the unfortunate Mary. The firft is properly French, having been iffued at her coronation as queen of France, along with her hufband King Francis 1]^ On the obverfe of this piece there are portraits of Francis and Mary, face to face, with three legends around them, the outermoft containing their titles; the middle one the following fentence : Hora Nona DOMINUS J. H. S. EXPIRAVIT HELLI CLAMANS ; the innermoft the name of the city (Paris). On the re¬ verfe are the arms of France and Scotland. Fine tertoons were alfo coined upon the fame plan, and are now fo rare that Dr Hunter gave ten guineas for one £ which 188 MED Modern which is in his collefKon. The fame portraits appear < *Vlfc-la-s- ^ on t]le {nie crown of Mary and Henry, in 1565, which is fo rare as -to be efteemed a medal of the higheft va¬ lue ; and Mr Pinkerton imagines, that if offered to fale it would bring 40 or 50 guineas. Another remarkable medal of Mary reprefents her full faced, and weeping, with the infcription, O God GRANT PATIENCE IN THAT I SUFFER VRANG. The xeverfe has in the centre, (^UHO CAN compare with ME IN GRIEF, I DIE AND DAR NOCHT SEEK RE- EIEF; with this legend around, Hourt NOT THE (figure of a heart) qUHAls JOY THOU ART. There are alfb many counters of this unfortunate princefs, being thin filver pieces of the fize of a fhilling. “ They all appear (fays Mr Pinkerton) to have been done in Fiance by the dire&ion of Mary, who was fond of de¬ vices. Her cruel captivity could not debar her from intercourfe wdth her friends in France, who mult with pleafure have executed her orders, as affording her a little confolatlon,” The coronation medal of Charles I. flruck at Edin¬ burgh for his inauguration, June 18. 1663, is remark¬ able as being the only one ever coined of Scottith gold, and the firft in Britain iiruck with a legend on the edge. With refpeft to the workmanfhip, it is inferior to Simon’s. Of thefe medals only three are known to exifl, of which one is in the Mufeum. It is not un¬ common in filver ; in which cafe it fometimes wants the legend on the edge. 2. Italian medals. Thefe appear in the 15th cen¬ tury, and from that time fucceflively in moll Euro¬ pean countries. Vittore Pifano, a painter of Verona, is celebrated as the reftorer of the art, but it remains to be accounted for how the medals of King David, already mentioned, came to exift fo long before. Mr Pinkerton conliders this artiil rather as an inventor than a retlorer, his medals having no refemblance to the ancient coins, as being large, and all caff. They were firft modelled in wax, then a mould taken from the model in fine fand and other ingredients. After a good call: was procured, it was touched up, and made a model for the reft. Thefe medals of Pifano, are almoft always 'm^crVoed. Opus Pifani PiEloris. The portraits of a great number of illuftrious men were done by him in this manner j and in the Britifti Mu¬ feum is a large brafs medal of Pifano by himfelf.— Other artlfts were Boldu, Marefcotto, Matthaeus de Paftus, Sperandes, Mifaldone, &c. Towards the end of the century, however, the medals began to affbme a more elegant appearance; and the papal ones are not only the moft elegant but the moft ancient feries of all the modern medals. The improvement began' in the reign of Alexander VI. fo famous for his own crimes, and thofe of his nephew Ctefar Borgia. His fucceffors, Julius II. Leo X. Hadrian VI. and Cle¬ ment VIE had many of their medals defigned by Ra¬ phael, Julio Romano, and other eminent painters, and the engraving executed by artifts of equal merit. Among thefe were the celebrated Cellini, and the noted Paduan forgers of Roman coins, Cavino and Bafliano. In 1644, Cormanni, a medallic artift, was imprifoned cn account of a piece which reprefented the Pope up- ©n one fide, and Olympia Maidalchina, the relation of his holinefs, on the other. The unfortunate Cor- Kianni poifoned kimfelf. About this time the family A L S. of the Hamerani, originally from Germany, begati to Modern engrave the papal medals; which they did with fur- Medals. prifing merit for feveral generations. Each of the daughters did a fine medal, as we are informed by Venuti. Betides the papal medals, many have been iiTued by the various ftates of Italy. There are medals of Fre¬ deric II. of Sicily in 1501, of feveral Venetian gene¬ rals in 1509, of Alfonfo duke of Ferrara in 1311, and of the celebrated Andrew Dona in 1528. 3. French medals. Till the reign of Louis XIV. the medals of this country are neither fine nor nume¬ rous 5 but this monarch exceeds ail modern princes in this way. Many of his pieces are well defigned and executed, though objectionable on account of their falfehood. 4. Danifh medals. Thefe appear of Chriftian II. in 1516, of Frederic and Sophia in 1532, of Frede- ric I. and Chriftian III. in bonnets worn in the 16th century. The elephant of the houfe of Oldenburg is frequent upon Daniih medals. 5. Swedifh medals. Thefe begin with Guftavus Vafa } and feveral of Chriftina are likewife to be met with. There are alfo fome curious ones of Charles XII. 6. Dutch medals. Thefe begin in 1566; and many of them are remarkable for maps and plans, which mult be very interefting to pofterity. “ Had the Greeks and Romans (fays Mr Pinkei'ton) given us maps and plans, wdiat a fine fyftem of ancient geography and topo¬ graphy a cabinet of medals muft have been !” 7. Medals of Spain, Portugal, and Germany. The Spanifti medals began with Gonfalo in 1503, many of which are curious and interefting. Finder Charles V. there are many curious Spaniih medals; but thofe of Germany begin with Frederic in 1453. They are ex¬ tremely numerous 5 as we may eaftly fuppofe from the greatnefs of the empire, and the various ftates which compofe it. There is a famous medal of Sebaftian king of Portugal, famous for his unfortunate expedi¬ tion into Africa in 1578 j with his bull, full face, and three quarters in length. On the reverfe is a ftiell-fifh in the fea, with the moon and feven ftars, bearing the infcription Serena Calsa fa vent. There is alfo a curious lezenge-fhaped coin of the fame with the arms of Portugal, and the king’s name and title : On the reverfe is a crofs with the infcription In hoc signo VINCES, 1578. 8. Satiric medals. Thefe began almoft as foon as the knowledge of the art of coining medals was revived. They feem to have been almoft unknown to the an¬ cients. One indeed of the emperor Gallienus is fup- pofed to have been fatiric. It has on the front the emperor’s buft, with the infcription GallienjE AUG. the reverfe is Peace in a car, Pax Ubique ; but this has been proved to be only a blundered coin. Some other ancient medals, however, are not liable to this objedfion. The firft modern fatiric medal publiftied was that of Frederic king of Sicily in 1501, againft his antagonift Ferdinand king of Spain. It has on one fide the head of Ferdinand, with the infcription Ferdinandus r. ar. vetus vulpes orbis ; on the reverfe. a wolf carrying off a fheep, Jvgvm mevm SVAVE EST ET onvs mevm eeve. Many others have been (truck, of which the wit would now perhaps be difficult MED Modern difficult to be found out : but of all nations the Dutch Medals, molt diftinguilhed themfelves in this way ; and paid very dear for their conduct, as they brought upon themfelves by one or two fatiric medals the whole power of France under Louis XIV. 9. Englilh medals. The firft of thefe is in the duke of Devonihire’s collection. It is of a large lize, and done on the plan of the early Italian medals. It has on the reverfe the arms of Kendal, with the infcrip- tion TEMPORE OBSIDIONIS TURCORUM, MCCCCLXXX. On the other fide is a portrait wjjth 10 KENDAL RHODI tvrcvpellerivs. It was found laft century in Knaref- borough forelt j but Mr Pinkerton has no doubt ef its having been done in Italy. The next is that of Henry VIII. in 1545, and is of gold, larger than the crown-piece, with the king’s head upon the obverfe, and three legends within each other, including his titles, &c. The reverfe contains two infcriptions, de¬ claring him to be the head of the church j the one in Plehrew, the other in Greek. It was imitated exaftly by Edward VI. whofe coronation medal is the firfl we have. There are two medals of Philip and Mary, whofe execution is tolerably good j but thofe of Eli¬ zabeth are very poor. There are good medals of James I. .and his queen ; with a fine one of Charles I. atid Plenrietta, though the workmanlhip is much in¬ ferior to the antique. There are many good medals of Charles, with various devices upon their reverfes. Under the commonwealth the celebrated Simon pro¬ duced medals which are defervedly reckoned the molt admirable pieces of modern workmanlliip. There are many good medals of Charles II. James II. and Wil¬ liam III. Some are alfo found of James after his ab¬ dication. Some fine gold, filver, and copper medals, w’ere iffued in the time of Queen Anne ; the tvro lalt affording a feries of all the great actions of the duke of Marlborough. About the year 1740, a feries of medals was engraved in London by Daffier, a native of Geneva, containing all the kings of England j being 36 in number. They are done upon fine copper, and executed with great tafte. There are befides many medals of private perfons in England j fo that it may jufily be faid, that this country for medals exceeds al- molt every other in Europe. To this account of modern coins and medals we {hall add that of another fet called Jiege pieces, and which were iffued during the time of a fiege in cafes of urgent neceffity. Thefe were formed of any kind of metal; fometimes of no metal *, and Patin mentions a remarkable one ftruck at Leyden in 1574, when the place was befieged by the Spaniards. It w'as of thick paper or pafieboard, having a lion rampant, wdth this infcription, PVGNO PRO PATRIA, 1574; and on the reverfe, LVGDVNUM Batavorvm. There are various fiege-pieces of Charles I. both in gold and filver, fome of the latter being of the value of 20 {hillings. The nummi braBeati are a fpecies of modern coins fomewhat between counters and money ; and have their name from the word BRACTEA, a fpangle or thin bit of metal. They are commonly little thin plates of filver, {lamped as would feem with wooden dies up- A L S. 179 on one fide only, wriih the rude impreffion off various Abbrevia- figures and infcriptions. Moll of them are ecclefiaftic, tI0ns' , and wTere flruck in Germany, Switzerland, Denmark, Sweden, Norway, and a few in Poland. They con¬ tinued to be in ufe in Germany till the end of the 1 5th century j and fome are Hill ufed in Switzerland at this day. Table of Abbreviations ufed in the Legends of Me¬ dals ; from Mr Pinkerton. GREEK COINS. A. A. Athens, Argos, Aulus, Afylum 5 primi or firfi; as Elpiruw A. Arists “ Ephelians, firit people of Alia. A. Abaffus, Abdera, Aby- dus on Hellefponc AB. Abydus in Egypt ABT. Abydus on Hellef- pont A©. A0E. Athens AIT. Aigina AITOSno Aigofpotamos AI A. ^Elius, ^SLlra Capito¬ lina AIN. ^dEnos AK.—AKPATAN. Agri- gentum AKI Acilium AKT. Adlium AAE. Alexandria AM. Amyntas AMBP. Ambracia A MO I. Amphilochia AN©. AvdvTnarov, Proconful ANTIS. Antiffa ANA. Anadloria ANTI. Antium AN. Ancyra ANT. Antoninus, Antioch AS. Axus in Crete AON. Aonitae AOTE. Avenio, Pe/L AIT. Appius AITA. Apamea AITO. Apollonia A OTA. Aptara AP. Aiadus, Harma APFE. Argennos APT. Argos API. Aricanda APIM. Ariminum AP2I. Arfinoe AFT. Aryca APX. A^-gu^ivs or Ag%ey, high prielt or magiltrate AEIAPX. Afiarchae, prefi- dents of the games of Alia (b) Z 2 AS. Afylum A. S. rigoroi Zvateti, Firft of Syria ASK. Afcalon AT. Atabyrium ATAP. Atarnce ATT. Augultus ATPHA. Aurelius AT ATT. AvTMgeiTog Em¬ peror ATTON. Avrovo[s.oi, enjoy¬ ing their own laws AOI. Aphyta AOP. Africanus AX. Achaii B. B. BeyAjjj, Council: Bery- tus: Bithynia BAFHAAO Bagadaonia BAA. Valerius BH. Berytus BITON. Bitontum BOI. Bceotia BPTN. Brundufium BT. Byzantium F. F. PP. FPAM. Grammati¬ cus, or keeper of the re¬ cords F. Gaius, or Caius F A. Gallus, Gallerius, Gal- lienus F. Tvcoetpov, Uluftrious FEA. Gelas FEP. Germanicus FN. Gneius FOPTT. Gortyna FPA. Graviica A. A. Decimus, Dymae AAK. Dacicus AAM. Damafcus AAP- Durdanum AH. Av/zos, the people AHMAPX. ESOTS. with '1 ribunitian power AE. Decelia AEK. Decius AEP. (b) Ihere were a!lo Syriarchre, Lyciarchae, Galatarchae, Bithyniarehae, Cappadociarchae, &c. Morel. Spec, D 180 Abbrevia- AEP. Derbe in Lycaonia tions- AH. Delos AI. Diofpolis APE. Drepanum ATP. Dyrrhachiura E. E. Eryce E. EPEE. Erefus EAET. Eleufis EAET0. EAst^E^o*, Free EITI, Epidaurus EPI. Eriza in Caria EPX. Erchia EFT. Erythree ET ETO. Eravj, Year ET. Etenna in Pamphylia EX. E^«t;«-. EE. Ephefus Z. ZA. Zacynthus ZANKA. Zancle, Meffa- na anciently fo called H. H- Elium HP. HySjUeyaf, Prendent HPAK. Heraclea ©. ©A. Thafus 0E. Thefpiae ©E2. Theffalonica ©E. ©HE. Thebee I. I. IEP. Sacred lEPAHT. Hyerapytha IKAP. Hiccara IAI. Ilium IOT. Julis, a city, or Julius IOTA. Julia I HA. Hippana IP. Irene Inf. Pellerin. IE. Ifus, Iftiaea K. K. Caius; Kotiors?, Quintus K. KAIE. Ceefar K. K. Ko. Philip, Phceftus, Pbi- luntium €>A. Phafelis AP. Pharfalus I. Vibius, PhilippopoBs INE. Phineium •PA. Flavius OK. Phocaeum ^>OTA. Fulvia OT. Phycus in Cyrene X. X. Chios XAA. Chalcis XEP. Cherfonefus XI. Chytri in Crete Abbrevfa- tions. Greet Numerals. A. B. r. A. E. or Z. H. ©. I. K. A. M. N. E. O. R. 10. 20. 3°* 40. 5°. 6o. 7°. 8o. q or n 90. V. 100. E.or C 200. T. T. X. £2. q- 30°. 400. 500. 600. 700. 800. goo. Example, MED Abbrevla- Examples. I is 10: add A to I, and IA makes u: , tions- fo IB, 12 i IF, 13, &c. K is 20, KA, 21, &c. PI A v makes in. The Engliili word air marks the grand initial numerals. On coins the numerals are often pla¬ ced in retrograde order ; which makes no difference in the value, as every letter is appropriated to its num¬ ber. Thus TAT or TAT imply the fame, 333. But this advantage being unknown to the Roman numerals and Arabic cyphers, is apt to puzzle the beginner. ROMAN COINS. A A. aulus : in the exergue it implies the firft mint, as ant. A. coined at An¬ tioch in the firft mint A. A. A. F. F. Auro, Ar- gento, ALre, Flando, Feriundo A. or AN. Annus A. a. Apollo Augufti A. F. A N. Auli filius, Au- li nepos ABN. Abnepos act. Adtiacus, or Aftium AD. FRV. EMV. Ad fruges emundas adiab. Adiabenicus ADOP. Adoptatus ADQ. Adquifita ADV. Adventus aed. Aides aed. p. AEdilitia poteftate AED. s. Aides facrae AED. CVR. Aidilis Curulis AED. pl. Aidilis Plebis AEL. AElius AEM. or AIMIL. Aimilius AET. Aiternitas AFR. Africa, or Africanus ALBIN. AlBINUS ALIM. ITAL. Alimenta Ita¬ lic ANN. AVG. Annona Au¬ gufti A. N. F. F. Annum Novum Fauftum Felicem ANic. Anicius ANN. DCCCLXIIII. NAT. VRB. P. CIR. CON. An¬ no 864 Natali Urbis Populo Circenfes confti- tuti ANT. avg. Antonius Au- gur ant. Antonius, or Anto¬ ninus ap. Appius A. p. F. Argento Publico Feriundo A. POP. FRVG. AC. A Po¬ pulo Fruges Acceptae AO. or aql. Aquilius aqva mar. Aqua Martia ARAB. adq_. Arabia Ad- quifita ARR. Arrius avg. Augur, Auguftus, Augufta AVG. D. F. Auguftus Divi Filius AVGG. Two Augufti AVGGG. Three Augufti AVR. or AVREL. Aurelius B. B. The mark of the fecond mint in any city bon. event. Bonus Even- tus B. R. P. nat. Bono Reipub- licse Nato BRIT. BrITANNICUS ERVT. Brutus c. c. Caius, Colonia c. A. Casfarea Augufta c. cae. or caes. Caefar CAESS. Caefares carth. Carthage CEN. Cenfor cens. P. Cenfor Perpetuus CEST. Ceftius, or Ceftia- nus CIR. CON. Circum Condi- dit, or Circenfes Con- ceffit CIV1B. ET SIGN. MILIT. A. parth. recvp. Civibus et Signis Militaribus a Parthis Recuperatis CN. Cneius coel. Coelius. con. OB. Conftantinopoli Obfignata, or Conftan¬ tinopoli Officina fecun- da, or Conflata Obryzo col. Colonia con. svo. Confervatori fuo CONCORD, Concordia CL. v. Clypeus Vctivus comm. Commodus CLOD. Clod'us cl. or clavd. Claudius cos. Conful coss. Confules A L S. 181 corn. Cornelius CVR. x. F. Curavit Dena- rium Faciendum D. D. Decimus, Divus, De- fignatus DAC. Dacicus D. F. Dacia felix D. M. Diis Manibus des. or desig. Defignatus DICT. Didlator DOMIT. Domitianus D. N. Dominus nofter did. Didius D, P. Dii Penates Dv. Divus E. EID. mar. Idus Martiae EX. cons. D. Ex Confenfu Decuriorum ex. s. c. Ex Senatus Con- fulto EQ. ordin. Equeftris Or- dinis. EX. A. PV. Ex Argento, or Audloritate Publica EXER. Exercitus ETR. Etrufcus F. F. Filius, or Filia, orFelix, or Faciundum, or Fecit FEL. Felix FELlc. Felicitas FL. Flavius FLAM. Flamen FORT. RED. Fortunse Re- duci FOVRI. Fourius for Furius FONT. Fonteius frvgif. Frugiferae(Cere- ri) FVL. Fulvius FVLG. Fulgerator G. G. Gneius, Genius, Gau- dium ga. Gaditanus G. D. Germanicus Dacicus GEN. Genius germ. Germanicus gl. e. R. Gloria Exercitus Romani gl. p. R. Gloria Populi Romani GOTH. Gothicus G. P. R. Genio Populi Ro¬ mani G. T. A. Genius Tutelaris JEgypti, or Africae H. HEL. Helvius HEL. Heliopolis her. Herennius, or He- rennia . H®. Honos Abbrevia- HS. Seftertius , t'°ns‘ , I. Imperator, Jovi, Julius ian. clv. Janum clufit for claufit imp. Imperator impp. Imperatores I. s. M. R. Juno Sofpita* Mater or Magna Re¬ gina _ IT. Italia, Iterum ITE. Iterum ivl. Julius or Julia 1 vst. Julius I-l. s. Seftertius I. o. M. sacr. Jovi Opti¬ mo, Maximo, Sacrum II. vir. Duumvir III. vir. r. p. c. Triumvir Reipublicae Conftituen-- dae mi. vir. a. p. f. Quatu- orvir, or Quatuorviri, Auro, or Argento, or ALre, Publico Feriundo IVN. Junior L. L. Lucius lat. Latinus leg. propr. Legatus Pro-' praetoris LEG. I. &c. Legio Prima, &.C. lep. Lepidus LENT. CVR. x. P. Lentu- lus Curavit Denarium Faciundum LIBERO P. Libero Patri lib. pvb. Libertas Publica Lie. Licinius L. s. DEN. Lucius Sicinius Dentatus lvc. Lucifera lvd. cir. Ludi Circenfes LVD. E£>. Ludi Equeftres LVD. SAEC. F. Ludos Ste- culares Fecit M. M. Marcus, or Marius MAR, CL. Marcellus Clo- dius M. F. Marci Filius M. otacil. Marcia Ota- cilia MAG. or MAGN. Magnus MAC. Macellum max. Maximus mar. Martia (aqua) MAX. VLT. Marti Ultori mes. Meflius metal. Metallum min at. Minatius Miner. Minerva M. M. I. V. I 82 Abbrevia- M/ M. I. V. Municipes Mu- . 1: 005, nicipii Julii Uticenfis ^ MON. or MONET. Moneta N. N. Nepos or Nofler N. c. NobilifRmus Ccefar NAT. VRB. Natalis Urbis NET. Nepos net. red. Neptuno Re- dilci o. o. Optimo OB. c. s. O’o Gives Serva- tos OF. OfRcina OPEL. Opelius ORB. terr. Orbis Terra- rum P. P. or POT. Poteflate PAC. ORB. TER. Pacatori Orbis Terrarum papi. Papius or Papirius parth. Parthicus Perp. Perpetuus pert, or pertin. Pertinax PESO. Pefcennius P. F. Pius Felix plaet. Plastonius P. L. N. Pecunia Londini Notata P. lon. s. Pecunia Londi- ni Signata P. M. or PONT. MAX. Pon- tifex Maximus pomp. Pompeius p. p. Pater Patrim PR. Praetor p. R. Populus Romanus PRAEF. CLAS. ET. OR MA- rit. Praefedtus Claffis et Orae Maritimae princ. I went. Princeps Juventutis priv. Privernum PROC. Proconful PRON. Pronepos prop. Propraator proq_. Proquaellor prov. deor. Providentia Deorum PVPIEN. Pupienus . H £L Quintus, or Quaeftor Q. c. m. p i. Quintus Cae- cilius Metellus Pius Im- perator Q. desig. Quaeftor Defig- natus p. Quaedor Praetorius Q. PR.QuaeftorProvincialis R. r. Roma, Reftituit recep. Receptis, or Re- MED REST. Reflituti ROM. et avg. Romae et Auguflo R. P. Refpublica S. saec. avr. Saeculum Au- reum saec. FEL. SaeculiFelicitas sal. Salus sall. SallufHa SARM. Sarmaticus s. C. Senatus Confulto scip. asia. Scipio Afiati- cus sec. orb. Securitas Orbis sec. perp. Securitas Per- petua sec. temp. Securitas Tem- porum sen. Senior sept. Septimius ser. Servius SEV. Severus SEX. Sextus sic. v. sic x. Sicut Quin- quennalia, fic Decenna- lia SIG. Signis s. M. Signata Moneta s. P. q. r. Senatus Popu- lufque Romanus stabil. Stabilita (terra) svl. Sulla. T. T. Titus, Tribunus ter. Terentius, or Terti- um temp. Temporum Tl. Tiberium tr. or TREY. Treveris TREE. Trebonianus TR. mil. Tribunus Milita- ris TR. p. or TRIB. POT. Tri- bunicia Poteftate V. V. Ouintum v. c. Vir Clariflimus vesp. Vefpafianus vib. Vibius vict. Vidloria Vli. vir. epvl. Septemvir Epulonum VIL. pvb. Villa Publica VIRT. Virtus VN. mr. Venerandae Me¬ moriae VOT, X. MVLT. XX. Votis Decennalibus Multipli- catis Vicennalibus X. x. Decern, Denarius XV. VIR. SACR. FAC. Quin- decim Vir Sacris Faci- undis. 4 A L S. Abbreviations on the Exergue ; from Boudiiri and Mo- naldini. Pinkerton. A. Officina Prima ALE. Alexandria AMB. Antiochenfis Mone¬ ta Secundae Officinae AN, ANT. ANTI. Antiochia ANB. Antiocbiae Secunda Officina : to ANH. An- tiochiae Odtavia OiTicina A. p. l. (In officina) Pri¬ ma percuffa Lugduni AQ. aql. Aquileioe A£K o. B. F. Aquileiae Of¬ ficinae Secundae Fabrica AQ^. P. s. Aquileiee Pecu¬ nia Signata A. ar. arl. Arelate A. sisc. Prima (in officina) Sifciae B. sirm. Secunda Sirmii B. s. l. c. Secunda Signa¬ ta Lugduni c. 0. Conftantinopoli No¬ na comob. Conflata Moneta Obryzo. Only on gold or filver from a gold die CON. Condantinopoli conob. Condata Obryzo. Only on gold. CONS. Condantinopoli KART. Carthago K. o. Carthaginenfis Offi¬ cina L. LC. LVC. LVG. Lucdu- ni, Lugduni L. LON. Londini L. p. Lugdunenfis vel Lon- dinenlis Pecunia lvc. p. s. Lugduni Pecu¬ nia Signata mbps. Mediolani Pecunia Signata M. K. v. T. Moneta Kar- taginenfis Urbs (in offi¬ cina) Tertia M. l. Moneta Lugdunen¬ fis vel Londinenfis mostt. Moneta Officinae Secundae Treverorum mstr. Moneta Signata Treveris o. Officina off. in. const. Officina Tertia Condantinopoli pare. Percufla or Pecunia Arelate plon. Pecunia Londinen¬ fis plvg. Pecunia Lugdunen¬ fis P. R. Pecunia Roman a-, or Percuffa Romae P. T. Pecunia Treverenfis q. ar. Quindta Arelatenfis (officina) R. ro. rom. Romse ra. Ravennae ROPS. Romce Pecunia Sig¬ nata s. ar. Signata Arelate s. const. Signata Conftan¬ tinopoli sis. Sifciae ss. p. Sifcienfis Pecunia SISC. v. Sifcia Urbs sma. Signata Moneta An- tiochiae s. M. HER. Signata Mone¬ ta Heracleae s. M. N. Signata Moneta Nicomediae s. M. r. Signa'ca Moneta Romae s. T. Signata Treveris tesob. Teffalonicae Offici¬ na Secunda theopo. Theopoli TR. Treveris trob. Treverris Officina Secunda A Li/i of Roman Colonies whofe Coins remain ; and Ab¬ breviations on thefe Coins. Abdera in Spain Acci in Spain Achulla in Africa AElia Capitolina in Judaea Agrippina in Germany Antiochia in Pifidia in Syria Apamea in Bithynia Arna in Theffaly Aftigi in Spain Babba in Mauritania Tin- gitana Beiytus in Phoenicia Bilbihs in Spain Boftra in Arabia Bracara Augufta in Spain Buthrotum in Epirus Cabellio in Gaul Caffar-Augufta in Spain Caefarea in Paleftine Calagurris Abbievia- Calagurris in Spain t tions. Calpe in Spain -y—— £ama]ocjurmm jn Carrhae in Mefopctaraia Carteia in Spain Carthago in Africa Carthago Nova in Spain Cafcantum in Spain Caffandria in Macedon Celfa in Spain Clunia in Spain Coillu in Nutnidia Comana in Cappadocia Corinthus in Greece Cremna in Pi fid i a Culla in Thrace Damafcus in Ccelefyria Dertofa in Spain Deultcn in Thrace Diuna in Macedon Ebora in Spain Edeffa in Mefopotamia Emerita in Spain Emefa in Phoenicia Ergavica in Spain Germe in Galatia Graccuris in Spain Eladrumetum in Africa Heliopolis in Coelefyria Hippo Regius in Africa Iconium in Lycaonia Uerda in Spain Hiergavonia in Spain llleci in Spain lol in Mauritania Italica in Spain Lselia in Spain Laodicea in Syria Leptis in Africa Lugdunum in Gaul Neapolis in Paleftine MED Nemaufus in Gaul Nefibis in Mefopotamia Norba Ctefarea in Mauri¬ tania Obulco in Spain Oea in Africa Olba in Pamphylia Ofca in Spain Olicarda in Spain Panormus in Sicily Parium in Myfia Parlais in Lycaonia Patricia (^Corduba) in Spain Pella in Macedon Philippi in Macedon Philippopolls in Arabia Ptolemais in Phoenicia Rhefsena in Mefopotamia Romula (Hifpalis) in Spain Rufcino in Gaul Sabaria in Hungary Saguntum in Spain Sebafre in Paleftine Segobriga in Spain Sidon in Phoenicia Singara in Mefopotamia Sinope in Pontus Stobi in Macedon Tarraco in Spain Theflal'onica in Macedon Tradufla (Julia) in Spain Troas in Phrygia Turiafo in Spain Tyana in Cappadocia Tyrus in Phoenicia Valentia in Spain Vienna in Gaul Viminacium in Moefta Utica in Africa ‘ Abbreviations on Colonial Coins. acci. Accitana Colonia, Guadix in Spain ADI. Adjutrix legio ael. mvn. coel. iElium Municipium Coela, near Sef- tos on the Hel/efpont AST. Aftigitana, Eceja in Andalufia B. a. Braccara Augufti, Brogue in Portugal c. A. Ctefarea Antiochice c. A. A. p. or patr. Colonia Augufta Arot; Patrenfis CAB. Cabellio c, A. bvt. Colonia Augufti Buthrotum, in Epirus C. A. C. Colonia Augufta Caefarea c. A. i. Colonia Augufta Julia, Cadiz, C. A. E. Colonia Aug. Emerita, Merida CAL. Calagurris, Calahorra in Spain c. A. o. A. F. Colonia Antoniana Oea Aug. Felix, Tri¬ poli in Africa A L S. i S3 c. A. it. MET. SID. Colonia Amelia Pia Metropolis Abbievia- Sidon _ tlons- , c. a. R. Colonia Augufta Rauracorum, or Colonia Afta Regia : Augft in Switzerland, or Aft near Xeres de la Frontera in Spain c. c. a. Colonia Caefarea Augufta, Saragojfa in Spa n C. C. COL. LUG. Claudia Copia Colonia Lugdunemis c. c. 1. B. Colonia Campeftris Julia Babba, in Mauri¬ tania C. c. 1. B. D. D. Colonia Campeftris Julia Babba, De- creto Decurionum C. c. 1. h. P. A. Colonia Concordia Julia Hadrumetina, Pia Augufta c. civ. D. D. P. Corona Civica data Decreto Publico C. C. N. A. Colonia Carthago Nova Augufta c. c. N. c. D. D. Colonia Concordia, Norba Csefareana, Decreto Decurionum C. cor. Colonia Corinthus c. c. T. Ducentefima RemilTa C. c. s. Colonia Claudia Sabaria, in Hungary C. F. P. D. Colonia Flavia Pacenfts Develtum, Devel- tum in Thrace C. G. I. H. P. a. Colonia Gcmella- Julia Hadriana, Pa- riana, Augufta c. 1. c. A. Colonia Julia Concordia, Apamea c. I. a. d. Colonia Julia Augufta Dertona, Torlona near Milan c. 1. av. Coionia Julia Aug. Cadiz, c. 1. avg. F. sin. Colonia Julia Augufta Felix Sinope c. 1. B. Colonia Julia Baiba, in Mauritania C. I. C. A. P. A. Colonia Julia Carthago Augufta Pia Antiqua, or Corinth, or Carthago Nova C. I. CAL. Colonia Julia Calpe, Gibraltar c. I. F. Colonia Julia Felix, Cadiz c. 1. G. A. Colonia Julia Gemella (c) Augufta c. 1. 1. A. Colonia Immunis Illici Augufta, Elehe in Spain. c. I. N. C. Colonia Julia Norba Cmfareana, or Alcan¬ tara : fometimes it means Col. Julia Nova Carthago c. 1. v. Colonia Julia Valentia, Valencia in Spain C. v. T. Colonia Victrix Tarraco c. L. 1. cor. Colonia Laus Julia Corinthus c. l. 1. N. avg. Colonia Laus Julia Nova Augufta, Laus or Lodi in Lucania c. M. l. Colonia Metropolis Laodicea, in Coelefyria CO. DAM. METRO. Colonia Damafcus Metropolis cohh. pret. vii. P. \T. F. Cohorles Prcetorianae Sep- timum Piae, Sextum Felices COH. I. CR. Cohors prima Cretenfis COM. FRET. PHIL. Cohors Prsetoriana Philippenfmm COL. AEL- A. H. MET. Colonia-/Elia Augufta Hadru¬ metina Metropolis, in Africa col. ael. CAP. comm. P. F. Colonia ALlia Capitolina Commodiana Pia Felix COL. ALEX, trgas. Colonia Alexandriana Troas col.amas. or ams. Colonia Amaftriana, in Paphlagonia col. ant. Antioch in Pifidia col. arelat. sextan. Colonia Arelate Sextanorum, Arles col. ast. avg. Colonia Aftingitana Augufta, Eceja in Spain. col. (c) Gemella implies a colony drawn from two others. 184 MEDALS. Abbrevla- COL. AVG. FEL. BER. Colonia Augufta Felix Berytus i t‘°ns' . COL. AVG. FIR. Colonia Aug. firma, Eceja COL. AVG. IVL. PHILIP. Colonia Augurta Julia Philip- penfis COL. AVG. PAT. TREVIR. Colonia Augufta Paterna Trevirorum, Treves in Germany, fent from Paternum in Italy COL. AVR. KAR. comm. P. F. Colonia Aurelia Karrhae Commodiana Pia Felix, or Carneatum Commagene, or Carrhce in sljia C®L. B. a. Colonia Braccara Augufla, Braque col. bryt. L, v. Colonia Berytus Legio Quinta * COL. CABE. Colonia Cabellio. COL. caes. avg. Colonia Caefarea Augufta, in Balefine COL. camalOj^VN. Cclonia Camalodunura, England col. casilin. Colonia Cafilinum, Cqftella%o in Italy col. cl. ptol. Colouia Claudia Ptolemais, Acre in Phoenicia col. DAMAS. metro. Colonia Damafcus Metropolis col. F. i. a. p. earcin Colonia Flavia Julia Augufta Pia, Barcino or Barcelona col. FL. pac. hevlt. Colonia Flavia Pacenfis Deultum, Dev el turn in Thrace COL. HA. ME. T Colonia Hadriana Mercurialis Thae- nitana, Mercuriali, Fermo in Italy, and Thenes in Africa COL. H. (or HEL.) leg. H. Colonia Heliopolis Legio Heliopolitana col. iiel. i. o. M. H. Colonia Heliopolis Jovi Optimo Maximo Heliopolitano COL. IVL. AVG. c. l. F. COMAN. Colonia Julia Augufta Concordia Invitfta Felix Comanorum, drawn from Concordia in Italy, andfnit to Comana in Cappadocia COL. ivl.! AVG. FEL. cremna. Colonia Julia Augufta Felix Cremna, in Pamphylia COL. IVL. CER. SAC. AVG. FEE. CAP. OECVM. ISE. HEL. Colonia Julia Certamen Sacrum Auguftum Felix Capitolenum Oecumenicum Ifelafticum Heliopolita- num COL. IVL. CONC. APAM. avg. d. D. Colonia Julia Con- cordia Apamea Augufta Decreto Deoarionum COL. IVL. PATER. NAR. Colonia Julia Paterna Narbo- nenlis col. nem. Colonia Nemaufus COL. niceph. cond. Colonia Nicephorium Condita, in Mefopotamia COL. patr. Colonia Patrenfts or Patricia, Patras in Greece, or Cordova in Spain COL. P. F. AVG. F. caes. met. Colonia Pnma Flavia Aug. Felix Caefarea Metropolis, in Palfline. COL. P. FL. AVG. CAES. METROP. P. s. Y. fame as above, P. s. P. is Provinciee Syrite Paleftinae. col. pr. f. A. Caesar. Colonia Prima Flavia Augufta Caefarea, in Palejline COL. R. f. AUG. FL. c. metrop. Colcnia Romana Felix Aug. Flavia Caefarea Metropolis. The fame col. ROM. Colonia Romulea, or Seville col. rom. lvg. Colonia Romana Lugdunum col. Rvs. leg. vi. Colonia Rufcino Legio Sexta, RonfilIon in France COL. sabar. Colonia Saburiae COL. SABAS. Sebafte, in Palefine ,col. ser. g. neapol. Colonia Servii Galbae Neapolis, in Palejline col. v. i. celsa, or col. vie. ivl. celsa. Colonia Vidlrix Julia Celfa, Kelfa in Spain COL. VIC. IVL. LEP. Colonia Vielrix Julia Leptis, z.1 Africa COL. vim. an. i. or II, Colonia Viminacium Anno primo, Widin in Servia coi . vlp. tra. Colonia Ulpia Trajana : Kellen, or Warhal in Tranflvania co. p. F. coe. metro. Colonia Prima Flavia Caefarea Metropolis co. p. i. a. Colonia Pacenfis Julia Augufta, or Col. OeJaviana c. R. i. f. s. Colonia Romana Julia Felix Sinope C. T. T. Colonia Togata Tarraco c. v. il. Colonia Viftrix Iliice, Elche in Spain D. Decuriones D. c. a. Divus Csef. Aug. DERT. Dertofa gen. col. ner. patr. Genio Coloniae Neronianae Fa- trenfis Explana¬ tion of Plates. G. L. s. Genio Loci Sacrum M. H. Illergavonia dyrt. Municipium Hibera Iller- gavonia Dertofa, Tortofa in Catalonia M. m. i. v. Municipes Municipii Julii Uticenfis M. r. Municipium Ravennatium mvn. cal. ivl. Municipium Calagurris Julia, in Spain mvn. clvn. Municipium Clunia, Crunna in Spain mvn. fane. jEL. Municipium Faneftre Aelium, Fano mvn. stob. Municipium Stobenfe, Stobi in Macedon MV. tv. Municipium Turiafo, in Spain N. tr, alexandriane col. bostr. Nervise Trojanee Alexandrians Colonise Boftrae, in Palejline SEP. col. laVD. Septimia Colonia Laudicea, or Lao- dicea sep. tyr. met. Septima Tyrus Metropolis. Explanation of the Plates. Fig. i. A Perfian daric 2. A drachm of Egina 3. A filver hemidrachm of Alexander the Great 4. Tigranes the younger of Armenia, with his After 5. One of the coins of the Arfacidae of Parthia 6. A coin of the Saflanidae of Perfia. Firlt pub- liihed by Mr Pinkerton 7. Denarius of Cneius Pompey from Mr Pinkerton, reverfe. Received by Spain 8. A brafs coin of Cunobelinus 9. Pefcennius Niger. Struck at Antioch; u- nique. In Dr Hunter’s cabinet ; publilhed by Mr Pinkerton 10. A filver coin of Caraufius 11. Reverfe of Claudius in firft brafs 12. Reverfe of Adrian 13. Of Antoninus Pius 14. Of Commodus 15. Of Severus 16. & Saxon penny 17. A Saxon ftyca 18. 19. Ancient pennies, fuppofed to be ScCttifh 20. A penny of William of Scotland 21. A penny of Robert the Great 2 2. An Irilh penny Plates CCGXXXf. and CCCXXXIi 3 23. The M E D Explana¬ tion of Plates. 23. The gold penny of Henry III. 24. The large noble of the firft coinage of Ed¬ ward III. 25. The gold medal of David II. of Scotland A L S. 26. The ryal of Queen Mary of Scotland 27. Letters on Anglo-Saxon coins 28. Abbreviations on ditto 29. Monetarius 185 Explana¬ tion of Plates. MED Medallion Imprefftons of Medals. See Casting. MEDALLION, or MedalioN, a medal of an ex¬ traordinary fize, fuppofed to be anciently ftruck. by the emperors for their friends, and for foreign princes and ambaffadors. But, that the fmallnefs of their num¬ ber might not endanger the lofs of the devices they bore, the Romans generally took, care to damp the fub]e£l of them upon their ordinary coins. Medallions, in refpedl of the other coins, were the fame as modern medals in refpefl of modern money : they were exempted from all commerce, and had no other value than what was fet upon them by the fancy of the owner. Medallions are fo fcarce, that there cannot be any fet made of them, even though the me¬ tals and fizes Ihould be mixed prumifcuoufly. MEDEA, in fabulous hiftory, a celebrated forcerefs, daughter of .ZEetes king of Colchis. Her mother’s name, according to the more received opinion of He- fiod and Hyginus, was Idyia, or, according to others, Ephyre, Hecate, Afterodia, Antiope, and Neasra. She was the niece of Circe. When Jafon came to Colchis in quell of the golden fleece, Medea became enamoured of him, and it w^as* to her well direfted labours that the Argonauts owed their prefervation. Medea had an interview with her lover in the temple of Hecate } where they bound themfelves by the molt folemn oaths to eternaTfidelity. No fooner had Jafon overcome all the difficulties which iEetes had placed in his way, than Medea embarked with the conquerors for Greece. To flop the purfuit of her father, Ihe tore to pieces her brother Abfyrtus, and left his mangled limbs in the way through which iEetes was to pafs. This ad of barbarity, fome have attributed to Jafon, and not to her. When Jafon reached lolchos his na¬ tive country, the return and vidories of the Argo- nauts were celebrated with univerfal rejoicings : but iEton the father of Jafon was unable to aflift at the folemnity on account of the infirmities of his age. Medea, at her hufnand’s requeft, removed the weak- nefs of ALfon ; and by drawing away the blood from his veins, and filling them again with the juice of cer¬ tain herbs, Ihe reftored him to the vigour and fpright- linefs of youth. This fudden change in AJon afto- nHired the inhabitants of lolchos •, and the daughters of Pelias were alfo defirous to lee their father reltored by the fame power to the vigour of youth. Medea, willing to revenge the injuries wffiich her hulband’s fa¬ mily had fuffered from Pelias, increafed their curi- ofity •, and betrayed them into the murder of their fa¬ ther as preparatory to his rejuvenefcence, which {he afterwards refufed to accompliih. This adlion great¬ ly irritated the people of lolchos j and Medea with her hufband fled to Corinth to avoid their refentment. Here they lived for 10 years with mutual attachment, when the love of Jafon for Glance the king’s daugh- Vojl. XIII. Part I. MED ter interrupted their harmony, and Medea was divor- Medaliioa ced. Medea revenged the infidelity of Jafon, by cau Me(pa. fing the death of Glance, and the deftru£Hon of her ~~v family. She alfo killed two of her children in jffieir father’s prefence ; and when Jafon attempted to punifh the barbarity of the mother, fhe fled through the air upon a chariot drawn by wunged dragons. From Co¬ rinth Medea came to Athens, where, after {he had un¬ dergone the neceffary purification of her murder, Ihe married King zEgeus, or (according to others) lived in an adulterous manner with him. From her conduct with /Egeus, Medea had a fon who was called Medus. Soon after, when Thefeus wiihed to make himfelf known to his father, Medea, jealous of his fame and fearful of his power, attempted to poifon him at a feafl: which had been prepared for his entertainment. Her attempts, however, failed of fuccefs, and the fight of the fword which Thefeus wore by his fide convin¬ ced ALgeus that the ftranger againft whofe life he had fo bafely confpired was his own fon. The father and the fon were reconciled j and Medea, to avoid the puniflunent which her wickednefs deferved, mount¬ ed her fiery chariot and difappeared through the air. She came to Colchis j where, according to fome, flic was reconciled to Jafon, who had fought her in her na¬ tive country after her fudden departure from Corinth. She died at Colchis, as Juftin mentions, when {he had been reftored to the confidence of her family. After death ihe married Achilles in the- Elyfian fields, ac¬ cording to the tradition mentioned by Simonides. The murder of Mermerus and Pheres, the youngeft of Jafon’s children by Medea, is not to be attributed to the mother, according to Elian j but to the Corin¬ thians, who affaflinated them in the temple of Juno Acraea. To avoid the refentment of the gods, and to deliver themfelves from the peftilence w'hich vifited their country after fo horrid a maffacre, they engaged the poet Euripides for five talents to wnite a tragedy, which cleared them of the murder, and reprefented Medea as the cruel aflafiin of her own children. And befides, that this opinion might be the better credit¬ ed, feftivals were appointed, in which the mother was reprefented with all the barbarity of a fury murdering her own fons. MEDEOLA, climbing African asparagus, a genus of plants belonging to the hexandria clafs, and in the natural method ranking under the 11th order, Sar- mentaccce See Botany Index. MEDIA, now the province of GhilaN in Perfia, once the feat of a potent empire, was. bounded, ac¬ cording to Ptolemy, on the north by part of the Caf~ pian fea j on the fouth by Perfis, Sufiana, and Affynaj on the eaft by Parthia and Hyrcania 5 and on the weft by Armenia Major. It was anciently divided into fe~ veral provinces, viz, Tropatene, Charomithrene, Da- ^ a rites, M E E [ r! viteS, Marciar.s, Amariacc, and Syro-Mcdia. By a — Y-—— Jajer divifion, however, all thefe were reduced to two j the one called Media Magna, the other Media Atro- pa!w, or fimply Atropaiene. Media Magna was bound¬ ed by Perils, Parthia, Hyrcania, the Hyrcanisn fea, and Atropatene, and contained the cities of Ecbatan, Laodicea, Apamea, Raga, Rageia or Ragea, &tc. Atrcpatene lay between tire Cafpian mountains and the Cafpian fea. This country originally took its name from Midai, the third fon of Japhet ; as is plain from Scripture, where the Medes are conftantly called Madai. Among profane authors, fome derive the name Media, from one Medus the fon of Jafon and Medea } ethers from a city called Media. Sextus Rufus tells us that in his time it was called Med'ena, and from others we learn that it was alfo called Aria. The molt probable hi- fiory of the Medes is as follows. This people lived in fubjedbon to the Affyrians till the reign of Sennacherib, when they threw off the yoke, and lived for fome time in a date of anarchy. But at laft, rapine and violence, the natural confequences of fuch a fituation, prevailed fo much that they were con- ffrained to have recourfe to fome kind of government, that they might be enabled to live in fafety. Accord¬ ingly, about 699 B. C. one Dejoces having procured himfelf to be cholen king, united the fcattered tribes into which the Medes were at that time divided ; and having applied bimfelf as much as poffible to the civi¬ lization of his barbarous fubjedfs, left the throne to his fon Phraortes, after a reign of 53 years. The new king, who was of a warlike and enterpri- fing difpofition, fubdued almoft ail the Upper Alia ly¬ ing between Mount Taurus and the river Halys which runs through Cappadocia into the Buxine fea. Elated with this good fuccefs, he invaded Affyria, the empire of which was now much declined, and greatly weak¬ ened by the revolt of many nations which had follow¬ ed the example of the Medes. Nebuchadonofor or Chyniladan, however, the reigning prince, having af- fembled what forces he could, engaged Phraortes, de¬ feated, took him prifoner, and put him to death ; af¬ ter which, entering Media, he laid wade the country, took the metropolis of Ecbatan itfelf, and levelled it with the ground. On the death of Phraortes, his fon Cyaxares was placed on the throne. He was no lefs valiant and enter- priling than his father, and had better fuccefs againft the Affyrians. With the remains of that army which had been defeated under his father, he not only drove the conquerors out of Media, but obliged Chvniladan to ffiut himfelf up in Nineveh. To this place he im¬ mediately laid clofe liege •, but vfas obliged to give over the enterprife on account of an irruption of the Scy¬ thians into his own country. Cyaxares engaged thefe mew enemies with great refolution ; but was utterly defeated •, and the conquerors overran not only all Me¬ dia, but the greateft part of Upper Alia, extending their conquefts into Syria, and as far as the confines of Egypt. They continued mailers of all this vaft 5 ] M E D traft of country for 28 years, till at lafl Media was McJlana delivered from their yoke by a general mafia ere at the il inftigation of Cyaxares. Medicinal After this deliverance, the Medes foon repoffeffed ^,‘ings'-. themfelves of the territories they had loft ; and once more extended their frontiers to the river Halys, their ancient boundary to the wefhvard. After this we find the Medes engaged in a war with the Lydians j which, however, ended without any remarkable tranfadlion : but on the conclufion or it, Cyaxares having entered into a llncl alliance with Nebuchadnezzar king of Ba¬ bylon, returned in Conjunction with the Babylonians beiore Ninevei : which they took and levelled with the ground, putting moll of the inhabitants to the fword. After this viRory the Babylonian and Median em¬ pires feem to have been united : however, after the death of Nebuchadnezzar, or rather in his lifetime, a war enfued, which was not extinguilhed but by the. diffolution of the Babylonian empire. The Medes, un¬ der Aftyages the fon of Cyaxares I. withftood the power ol the Babylonian monarchs : and under Cyrus and Cyaxares II. utterly dellroyed their empire by the taking of Babylon, as is related under that article. After the death of Cyaxares, the kingdom fell to Cy¬ rus, by whom the feat of the empire was transferred to Persia, under which article the hiftory of Media now falls to be conlidered, as alfo the manners, &c. of the inhabitants. MEDIANA, the name of a vein or little veffel, made by the union of the cephalic and bafilic, in the bend of the elbow. MEDIASTINUM, in Anatomy, a double mem¬ brane, formed by a duplicature of the pleura ; ferving to divide the thorax and the lungs into two parts, and to fuftain the vilcera, and prevent their falling from one fide of the thorax to the other. See Anatomy N° 117. MEDIATE, or Intermediate, femething that Hands betwixt and connects tw-o or more terms confi- dered as extremes; in which fenfe it Hands oppofed to immediate. MEDIATOR, a perfon that manages or tranfafls between two parties at variance, in order to reconcile them. The wmrd, in Scripture, is applied, 1. To Jefus ChriH, who is the only interceffor and peace-maker between God and man, (1 Tim. ii. 5.) 2. To Mofes, who interpofed between the Lord and his people, to declare unto them his word \ (Deut. v, 5. iii. 19.) MEDIC AGO, Snail-trefoil, a genus of plants belonging to the diadelphia clafs, and in the natural method ranking under the 3 2d order, Papilionacecd. See Botany Index. For the properties and culture of Lucern, a fpecies of this genus, fee Agriculture, Index. MEDICINAL, any thing belonging to medicine. MhDiciNAL Springs, a general name for any fountain the waters of which are of ufe for removing certain dis¬ orders. They are commonly either chalybeate or ful- phureous. See Springs and Water. MEDICINE, r 187 ] MEDICINE. ■jV/TEDiCINE is the art of preventing, caring, or alleviating, thofe difeafes to which the human fpecies are fubjected. History of Medicine. ©rigin of The fabulous hiflory of the ancients derives this art medicine immediately from their gods 5 and, even among the Jew”^tlie m0£^erns’ ^ome are opinion that it may juflly be confrdered as of divine revelation. But without adopt¬ ing any fuppofition of which no probable evidence can be given, we may conclude that mankind were naturally led to it from cafual obfervation on the dif¬ eafes to which they found thcmfelves fubje&ed 5 and that therefore, to a certain degree at leaft, it is as an¬ cient as the human race. But at what period it began to be pradlifed as an art, by particular individuals fol¬ lowing it as a profeffion, is not known. The moft an¬ cient phyficians we read of were thofe who embalmed the patriarch Jacob by order of his fon Jofeph. The facred writer ftyles thefe phylicians fervants to Jofeph : whence we may be affured that they were not priefls, as the hrlt phyficians are generally fuppofed to have been ; for in that age we know the Egyptian priefts were in fuch high favour, that they retained their li¬ berty, when, through a public calamity, all the reft of the people w^ere made Haves to the prince. It is not probable, therefore, that among the Egyp¬ tians religion and medicine were originally conjoined j and if we fuppofe the Jew's not to have invented the art, but received it from fome other nation, it is as little probable that the priefts of that nation were their phy- ' licians as tbofe of Egypt. That the Jewilh phyficians were abfolutely diftinift from their priefts, is very certain. Yet as the Jews re- fided for fuch a long time in Egypt, it is probable they w'ould retain many of the Egyptian cuftoms, from which it would be very difficult to free them. We read, how’ever, that when King Afa was difeafed in his feet, “ he fought not to the Lord, but to the phyftcians.” Hence w’e may conclude, that among the Jews the medical art was looked upon as a mere human invention ; and it was thought that the Deity never cured dileafes by making people acquainted with the virtues of this or that herb, but only by his miraculous power. That the fame opinion prevailed among the nations who were neighbours to the Jew's, is alio probable from what we read of Ahaziah king of Judah, who having fent meffengers to inquire of Baal- zebub god of Ekron concerning his difeafe, he did not defire any remedy from him or his priefts, but fimply to know whether he ftiould recover or not. W hat feems molt probable on this fubjecl therefore is, that religion and medicine came to be mixed toge¬ ther only in confequence of that degeneracy into ig¬ norance and fuperftition which took place among all nations. . The Egyptians, we know, came at laft to be funk in the mofl: ridiculous and abfiird fuperftition ; and then, indeed, it is not wonderr,ul that we Ihould find their priefts commencing phyficians, and mingling r#rig!r! ^ charms, incantations, &c. with their remedies. That .Med‘cine', this was the cafe, long after the days of Jofeph, w'e are very certain ; and indeed it feems as natural for ig¬ norance and barbarifm to combine religion with phv- fic, as it is for a civilized and enlightened people to keep them feparate. Hence we fee, that among all modern barbarians their priefts or conjurors are their only phyficians. 2 \Ve are fo little acquainted with the ftate of phyfic Among the among the Egyptians, that it is needlefs to fay much Egyptians*1 concerning them. They attributed the invention of medicine, as they did allb that of many other arts, to Thoth, the Hermes or Mercury of the Greeks. He is faid to have written many things in hieroglyphic characters upon certain pillars, in order to perpetuate his knowledge, and render it ufeful to others. Thefe were tranferibed by Agathodemon, or the fecond Mer¬ cury, the father of Tat, who is faid to have compofed books of them, that wmre kept in the moft facred places of the Egyptian temples. The exiftence of fuch a perfon, however, is very doubtful, and many of the books afciibed to him were accounted forgeries as long ago as the days of Galen 5 there is alfo great reafon to fufpedl that thofe books were written many ages after Hermes, and wffien phyfic had made confiderable ad¬ vances. Many of the books attributed to him are tri¬ fling and ridiculous *, and though fometimes he is allow¬ ed to have all the honour of ‘nventing the art, he is on other occafions obliged to Ihare it with Ofiris, Ifis, and Apis or Serapis. After all, the Egyptian phyfic appears to have been little elle than a collection of abfurd fuperftitions. Ori- gen informs us, that they believed there were 36 de¬ mons, or gods of the air, who divided the human body among them *, that they had names for each of them ; and that by invoking them according to the part affect- , ed, the patient ms cured. Of natural medicines we hear none recommended by the father of Egyptian phy¬ fic ; except the herb moly, which he gave to Ulyffes in order to fecure him from the enchantments of Circe ; and the herb mercury, of which he firft difeovered the ufe. His fucceffors made ufe of venefection, cathartics, emetics, and clyfters. There is ns proof, however, that this practice was eflabliffied by Hermes-; on the con¬ trary, the Egyptians themfelves pretended that the firft hint of thofe remedies w’as taken from fome ob- fervaiions on brute animals. Venefection was taught them by the hippopotamus, which is Lid to perform this operation upon itfelf. On certain occafions, he comes out of the river, and ftrikes his leg againft a fharp-pqinted reed. As he takes care to direct the ftroke againft a vein, the confequence muft be a con¬ fiderable effufion of blood ; and this being fuffered to run as long as the creature thinks proper, lie at iaft flops up the orifice with mud. The hint of clyfters was taken from, the Ibis, a bird which is faid to give itfelf clyfters wdth its bill, Sec. They ufed venefection, however, but very little, probably on account of the A a 2 warmth i8S M E D I Origin of warmtli of the climate \ and the exhibition of the re- Medicine. above mentioned, joined with abftinence, formed ^ ~ the moft of their practice. Among the The Greeks too had feveral perfons to whom they Greeks. attributed the invention of phyiic, particularly Pro¬ metheus, Apollo or Paean, and iEfculapius j which iaft was the moll celebrated of any. But here we mull obferve, that as the Greeks were a very warlike people, their phyiic feevns to have been little elfe than what is now called furgery, or the cure of wounds, frac¬ tures, &c. Hence iEfculapius, and his pupils Chi¬ ron, Machaon, and Podalirius, are celebrated by Ho¬ mer only for their fkill in curing thefe, without any mention of their attempting the cures of internal dil- eafes. We are not, however, to fuppofe that they confined themfelves entirely to furgery. They no doubt would occafionally prefcribe for internal difor- ders ; but as they were moll frequently converfant with wounds, we may naturally fuppofe the greatell part of their fkill to have confilled in knowing how to cure thefe. If we may believe the poets, indeed, the know¬ ledge of medicine feems to have been very generally diffufed. Almoft all the heroes of antiquity are re¬ ported to have been phyflcians as well as warriors. Moft of them were taught phyfic by the centaur Chi¬ ron. From him Hercules received inftrudiions in the medicinal art, in which he is find to have been no leis expert than in feats of arms. Several plants were call¬ ed by his name ; from which fome think it probable that he found out their virtues, though others are of opinion that they bore the name of this renowned hero on account of their great efficacy in removing difeafes. Arifireus king of Arcadia rvas alfo one of Chiron s fcholars 5 and is fuppofed to have difcovcred the ufe of the drug called Jilphiutny by fome thought to be afa- foetida. Thefeus, Telaman, Jafon, Peleus, and his foil Achilles, were all renowned for their knowledge in the art of phyfic. The laft is faid to have difcovered the ufe of verdegrife in cleanfing foul ulcers. All of them, however, feem to have been inferior in knowledge to Palamedes, who hindered the plague from coming into the Grecian camp after it had ravaged moft of the cities of the Hellefpont, and even Troy itfelf. His method was to confine his foldiers to a fpare diet, and to oolige them to ufe much exercife. The pradlice of thefe ancient Greek phyficians, not- withftanding the praifes bellowed on them by their poets, feems to have been very limited, and in lome cafes even pernicious. All the external remedies applied to Homer’s wounded heroes were fomentations; while inwardly their phyficians gave them wine, fometimes mingled with cheefe feraped down. A great deal of their phyfic alfo confifted in charms, incantations, amu¬ lets, &c. of which, as they are common to all fuperfti- mous and ignorant nations, it is fuperfluous to take any farther notice. In this way the art of medicine continued among the Greeks for many ages. As its firft profeffors knew nothing of the animal economy, and as little of the theory of difeafes, it is plain, that whatever they did mufl have been in confequence of mere random trials, ©r empiricifm, in the ftridl and proper fenfe of the word. Indeed, it is evidently impolfible that this or almoft any other art could originate from another fource than trials of this kind. Accordingly, we find, Hippo¬ crates. CINE. Hiftory. that fome ancient nations were accuftomed to expofe their fick in temples, and by the fides of highways, that they might receive the advice ot every one who ^ pa fled. Among the Greeks, however, Atfculapius ^fcuia. was reckoned the moft eminent pradliuoner of his time,pius. and his name continued to be revered after his death. He was ranked amongll the gods; and the principal knowledge of the medical art remained with his fa¬ mily to the time of Hippocrates, who reckoned himfelf the feventeenth in a lineal defeent from iEfculapius, and who was truly the firft who treated of medicine in a regular and rational manner. 5 Hippocrates, who is fuppofed te have lived 40oHjppo- years before the birth of Chrift, is the moft ancientrrates* • author whole writings exprefsly on the fubjedl of the medical art are preferred; and he is therefore juft ly confidered as the father of phyfic. All the accounts which w'e have prior to this time, if not evidently fa¬ bulous, are at the utmoft highly conjedlural. Even the medical know-ledge- of Pythagoras, fo much cele¬ brated as a philofopher, can hardly be confidered as refting on any other foundation. But from the time of Hippocrates, medicine, feparated from philofophy and religion, feems to have aflumed the form of a ici- ence, and to have been pradlifed as a profefticn. It may not, therefore, be improper to give a particular account of the ftate of medical fcience as tranfinit- ted to us in his writings. The writings of Hippo¬ crates, however, it may be remarked, are even more than preferved. Many things have been reprefented as written by Hippocrates which are probably fpurious. Nor is it wonderful that attempts ftiould have been g made to increafe the value of manuferipts, by attribut- His writ¬ ing them to a name of fuch eminence. But although Eg5* what are tranfmitted to us under the title of his works may have been written by different hands, yet the pre- fumption is, that moft, if not all of them, are of nearly as early a date, and contain the prevailing opinions of thofe times. According to the moft authentic accounts, Hippo¬ crates was a native of the ifland of Cos, and born in the beginning of the 88th Olympiad. In the writings tranfmitted to us as his, we find a general principle adopted, to which he gives the name of Nature. To this principle he aferibes a mighty power. “ Nature (fays he) is of itfelf fufficient to every animal. She performs every thing that is necefiary to them, with¬ out needing the leaft inftrudlion from any one how to do it.” Upon this footing, as if Nature had been a principle endowed with knowledge, he gives her the title of jujl; and aferibes virtues or powders to her, which are her fervants, and by means of w'hich ftie performs all her operations in the bodies ©f animals : and diftributes the blood, fpirits, and heat, through all parts of the body, which by thele means receive life and fenfation. And in other places he tells us, that it is this faculty which gives nourifhment, prefervation, and growth, to all things. 7 The manner in w’hich nature adls, or commands her His idea fubfervient power to adl, is by attradling what is of nature, good and agreeable to each fpecies, and by retaining, preparing, and changing it j and on the other fide in rejedling whatever is fuperfluous or hurtful, after flie has feparated it from the good. This is the foundation of the dodlrhie of depuration, concoction, and crifis in fevers. cafe. His divi- ilons of difeafes. Hiftory. M E D I Hippo- fevers, fo mach lafifted upon by Hippocrates and many crates, otner pbyilcians. He fuppofes alfo, that every thing n -v }las an inclination to be joined to what agrees with it, and to remove from every thing contrary to it j and likewife that there is an affinity between the feveral parts of the body, by which they mutually fympp- thize with each other. When he comes to explain what this principle called nature is, he is obliged to * refolve it into heat, which, he fays, appears to have 8 fomething immortal in it. _ r r rr nfthe cmi- As far as he attempts to explain the caufes or 011- fes of dii- cafe, he refers much to the humours of the body, par¬ ticularly to the blood and the bile. He treats alfo of the effe61s of deep, watchings, exercife, and reft, and all the benefit or mifchief we may receive from them. Of all the caufes of difeafes, however, mentioned by Hippocrates, the molt general are diet and air. On the fubjea of diet he has compofed feveral books, and in the choice of this he was exaftly caretul j and the more fo, as his praftice turned almoft wholly upon it. He alfo confidered the air very much j he examined what winds blew ordinarily or extraordinarily he con¬ fidered the irregularity of the feafons, the rifing. and fetting of ftars, or the time of certain conftellations 5 alfo the time of the folftices, and of the equinoxes; thofe days, in his opinion, producing great alterations in certain diftempers. He does not, however, pretend to explain how, from thefe caufes, that variety of diftempers anfes which is daily to be obferved. All that can be ga¬ thered from him with regard to this is, that the different caufes above mentioned, when applied to the diifeient parts of the body, produce a great variety of diftem¬ pers. Some of thefe diftempers he accounted mortal, others dangerous, and the reft eafily curaule, according to the caufe from whence they fpring, and the parts on which they fall. In feveral places abo he diftin- guilhes difeafes, from the time of their duration into acute cr Jhort, and chronical or long. He likewife di- ftinguifties difeafes by the particular places where they prevail, whether ordinary or extraordinary. I he firft, that is, thofe that are frequent and familiar to certain places, he called endemic difeafes \ and the latter, which ravaged extraordinarily fometimes in one place, ibmetimes in another, which feized great numbeis at certain times, he called epidemic, that is, popular dif¬ eafes ; and of this kind the moft terrible is the plague. He likewife mentions a third kind, the oppofite of the former \ and theie he calls fporadic, or ftraggling difeafes : thefe laft include all the different forts ot dff- tempers which invade at any one feafon, which are fometirnes of one fort, and fometimes of another. He diftinguiftied between thofe difeafes which are heredi¬ tary, or born with us, and thofe which are conti-afted afterwards 5 ,and likewife between thofe of a kindly and thofe of a malignant nature, the former of which are eafily and frequently cured, but the latter give t e phyficians a great deal of trouble, and are feldom over¬ come by all their care. Hippocrates remarked four ftagcs in diftempers \ viz. the beginning of the diieafe, its augmentation, its ftale or height, and its declination. In iuch difeafes as terminate fatally, death comes in place of tne decli¬ nation. In the third ftagc, therefore, the change is moft confide ruble, as it determitiss the fbt£ of the CINE. perfon ; and this is moft commonly done by means of a crijis. By thisword he underftood any hidden change in ficknefs, whether for the better or for the worfe, whether health or death fucceed immediately. Such a change, he fays, is made at that time by nature, either abfolving or condemning the patient. Hence we may conclude, that Hippocrates imagined diieafes to be on¬ ly a difturbance of the animal economy, witn which Nature wras perpetually at variance, and ufing her ift- moft endeavours to expel the offending caufe. Her manner of a£ling on thefe occafions is to reduce 10 their natural ftate thofe humours whole difcord occafions tne difturbance of the whole body, whether in relation to their quantity, quality, mixture, motion, or any other way in which they become offenfive. The principal means employed by nature for this end is what Hippo- ro crates calls concoclion. By this he underftood the His cpinioa bringing the morbific matter lodged in the humours to ef a .i.i-i luch a ftate, as to be eafily fitted for expulsion by what¬ ever means nature might think moft proper. When matters are brought to this pafs, whatever is fuperfiu- ous or hurtful immediately empties itfelf, or nature points out to phyficians the way by which fuch an eva¬ cuation is to be accompliihed. Ihe crifis takes place either by bleeding, ftool, vomit, fweat, urine, tumors or abfceffes, fcabs, pimples, fpots, &c. But thefe evacua¬ tions are not to be looked upon as the effedls of a true crifis, unlefs they are in confiderable quantity j fmali difcharges not being fufficient to make a crifis. On the contrary, fmall difcharges are a fign that natuie is depreffed by the load of humours, and that Ihe lets them go through weaknefs and continual irritation. What comes forth in this manner is crude, became the dift temper is yet too ftrong } and while matters remain in this ftate, nothing but a bad or imperfedt crifis is to be expe&ed. This (hows that the diftemper triumphs, or at leaf! is equal in ftrength to nature, which prognofti- cates death, or a prolongation of the difeafe. In this laft cafe, however, nature otten has an opportunity of attempting a new crifis more happy than the for¬ mer, after having made frefh efforts to advance the concodlion of the humours.— It nauft here be obferved, however, that, according to Hippocrates, concodtion cannot be made but in a certain time, as every fruit has a limited time to ripen \ for he compares the humours which natuie has digefted to fruits come to* maturity. The time required for concodlion depends on the ,, differences among diftempers mentioned above. In thofe which Hippocrates calls very acute, the digeftion or crifis happens by the fourth day} in thofe which are only acute, it happens on the 7LE Jtth, or 14th day j which laft is the longed period generally allowed by Hippocrates in diftempers that are truly acute : though in fome places he ftretches it to the 20th or 21 ft, nay, fometimes to the 40th or 60th day. All difeafes that exceed this laft term are called chroni¬ cal. And while in thofe difeafes that exceed 14 days,; he confiders every fourth day as critical, or at lead; re¬ markable, by which we may judge whether the crifis on the following fourth day will be favourable or not; fo in thofe which run from 20 to 40 he reckons only the fevenths, and in thofe that exceed 40.be begins to- reckon by 20. Beyond the 123th be thinks that the nyrcib?r of days has no power over the crifis. They M E D I are tnen referred to the general changes of the feafons; lome terminating about the equinoxes ; others about the iolilices j others about the rifing or fetting of the ua,s or certain conftellations j or if numbers have yet any place, he reckons by months, or even whole years. 1 bus (lie lays), certain difeafes in children have their crills in the feventh month after their birth, and others m their feventh or even their 14th year. I. hough Hippocrates mentions the 21ft as one of the critical days in acute didempers, as already noticed >et, in other places of his works, he mentions alfo the 20th. 1 ne reafon he gives for this in one of thofe places of his work is, that the days of ficknefs were not quite entire. In general, however, he is much attach- e^.; to tne odd days: infomuch that in one of his apho- in’ms he tells us, “ 1 he fweats that come out upon the 3d, 5th, 7th, gth, nth, 14th, 17th, 21ft, 27th, 3id, !jr 34-'1 days, are beneacial 5 but thole that come out upon other days fignify that the fick drall be brought low, that his difeafe diall be very tedious, and that he iiiad be fubjedf to relapfes.” He further fays, “ That the fever which leaves the dek upon any but an odd day is ufually apt to relapfe.” Sometimes, however, ‘e comedes that it ss otherwife 5 and he gives an in¬ dance of a falutary cribs happening on the bxth day. But thefe are very rare indances, and therefore cannot, m his opinion, overthrow the general rule. Befides the ends, however, or the change which de¬ termines the fate of the patient, Hippocrates often ipeaks of another, which only changes the fpecies of the didemper, without reboring the patient to health j as when a vertigo is turned to an epilepfy, a tertian fever to a quartan, or to a continued, &c. But what has chiedy contributed to procure the S-rg- FT re/pea generally paid to Hippocrates, is his in- j-rU7 111 °bfemng lbe moft minute circumdances of difeaies, and his exadlnefs in nicely defcriblng every thing that happened before, and every accident that appeared at the fame time with them ; and likewife what appeared to give eafe, and what to increafe the malady : which is what we call writing the hi/lory of a dfe-nfe.—Thus he not only didinguilhed one difeafe frem another by the dgns which properly belonged to each j but by comparing the fame fort of didemper which happened to feveral perfons, and the accidents wmich ufually appeared before and after, he could often foretel a difeafe before it began, and afterwards give a right judgement of the event of it. By this way. of prognodicating, he came to be exceedingly admired : and this, he carried to fuch a height, that it may judly be faid to be his mader-piece ; and Cel- lus who lived after him, remarks, that fucceeding phyficians, though they found out feveral new thingl relating to the. management of difeafes, yet were obli¬ ged to the writings of Hippocrates for all that they ■Knew of dgns. J The firft thing Hippocrates conddered, when called t:o a patient, was. his looks.—It was a good fiyn with mm to nave a vifage refembling that of a perfon in health, and the fame with what the dek man had be¬ fore be was attacked by the difeafe. As it varied 10m this fo much, the greater danger was appre- hended. Ine following is the defection which he gives of the looks of a dying man.—« When a pa¬ rent (fays he) has Ids nofe lharp, his eyes funk, his 3 11 His accura¬ cy in pn jipftics; 'F rom the look: C 1 N E. Hifloiy. temples hollow, his ears cold and contrafted, the {kin Rippo- o[ his forehead tenfe and dry, and the colour of his crates. face tending to a pale-green, or lead colour, one may v pronounce for certain that death is very near at hand j unlefs the ftrength of the patient has been exhauded all. at once by long watchings, or by a looienefs, or being a long time without eating.” This obferva- tion has been confirmed by fucceeding phyficians, who have, from him, denominated it the Hippocratic face. The lips hanging relaxed and cold, are like¬ wife looked upon by Hippocrates as a confirmation of the foregoing prognodic. He took alfo his figns from the difpodtion of the eyes in particular. When a patient cannot bear the light 5 when he fheds tears, involuntarily ; when, in deeping, fome part of the white of the eye is feen, unlefs he ufually deeps after that manner, or has a loofenefs upon him : thefe dgns, as well as the foregoing ones, prognodicate danger! The eyes deadened, as it were with a mid fpread oveif them, or tneir brightnefs loll, likewife prefages death, or great weaknefs. The eyes fparkllng, fierce, and fixed, denote the patient to be delirious, or that he foon will be feized with a frenzy. When the patient fees any tiling red, and like fparks of fire and lightning pafs before his eyes, you may expedl an haemorrhagy ; and this often happens before thofe crifes which are to be attended by a lofs of blood. The condition of the patient, is alfo diown by his From die pofline in bed. If you find him lying on one fide P°fiure in his. body, neck, legs, and arms, a little contra£ted, bed ’ which is the podure of a man in health, it is a good %n : on the contrary, if he lies on his back, his arms dretched out, and his legs hanging down, it is a fign of great weaknefs ; and particularly when the patient fiides or lets himielt fall down towards the feet^ it de- notes the approach of death. W7hen a patient in a burning fever is continually feeling about with Ills’ ' hands and fingers, and moves them up before his face and eyes as if he was going to take away fomethino- that paffed before them ; or on his bed-coverino-, as if he was picking or fearching for little draws, or Bakina away .fome filth, cr drawing out little docks of wool • ad this is a lign that he is delirious, and that he will die. ^ Am on gd the other figns of a prefent or ap¬ proaching delirium he alfo adds this: When a patient who naturally fpeaks little begins to talk more than he ufed to do, or when one that talks much becomes filent, this change is to be reckoned a fort of delirium or is a fgn that the patient will foon fall into one! The frequent trembling or darting of the tendons of the vend, prefage likewife a delirium. As to the differ¬ ent forts of delirium, Hippocrates is much more afraid of thofe that run upon mournful fubjedls, than fuch as are accompanied with mirth. When a patient breathes fad, and is opprelfed, it is From re- a.dgn that he is in pain, and that the parts above the Ration; diaphragm .are inflamed. Breathing long, or when the patient is.a.great while in taking"his breath, (hows him to be delirious ; but eafy and natural refpiration is always a good dgn In acute difeafes. Hippocrates de¬ pended much on refpiration in making his prognodics 7 and therefore has taken care in feveral places to\lefcribe the different manner of a patient’s breathirm. Contf- tinual watchings in acute difeafes^ are figniTof prefent pain, or a delirium near at hand. Hippocrates. Hiflory. Urine. MED! Hippo- Hippocrates alfo drew figns from all excrements, crates‘ -whatever they are, that are feparated from the body Fro^ex" maI1, H10^ remarkable progr.oftics, however, crementiti- 'vere from the urine. The patient’s urine, in his opi- ousdilchar-nion, is beft when the fediment is white, foft to the ges> touch, and of an equal conhftence. If it continue fo during the courfe of the diilemper, and till the time of the crifis, the patient is in no danger, and will foon be well. This is what Hippocrates called concocled urine, or what denotes the concodtion of the humours; and he obferved, that this concoction of the urine feldom appeared thoroughly, but on the days of the crilis which happily, put an end to the diftemper. 41 We -ought (faid Hippocrates) to compare the urine with the purulent matter which runs from ulcers. *As the pus, which is white, and of the fame quality with the fediment of the urine we are jw fpeaking of, is a fign that the ulcer is on the point of cloiing-, io that which is clear, and of another colour than white, and of an ill fmell, is a fign that the ulcer is virulent, and in the fame manner difficult to be cured : the urines that are like this we have deferibed are only thofe which may be named good ; all the reft are ill, and differ from one another only in the degrees of more and lefs. The firft never appear but when na¬ ture has overcome the difeafe ; and are a fign of the concoclion of humours, without which you cannot hope for a certain cure. On tbe contrary, the laft are made as long as the crudity remains, and the humours con¬ tinue unconcodled. Among the urines of this laft fort, the beft are reddifh, with a fediment that is foft and of an equal confiftence ; which denotes, that tbe difeafe will be fomewhat tedious, but without danger. The worft are thofe which are very red, and at the fame time clear and without fediment ; or that are muddy and troubled in the making. In urine there is often a fort of cloud hanging in the veffel in which it is received *, the higher this rifes, or the farther diftant it is from the bottom, or the more different from the colour of the laudable fediment abovementioned, the more there is of crudity. That which is yellow, or of a fandy colour, denotes abundance of bile 5 that which is black is the worft, efpecially if it has an ill fmell, and is either altogether muddy or altogether clear. That whofe fediment is like large ground wheat, or little flakes or fcales fpread one upon another, or bran, prefages ill, efpecially the laft. The fat or oil that fometimes fwims upon the top of the urine, and ap¬ pears in a form fomething like a fpider’s web, is a fign of a confumption of the flefh and folid parts. The ma¬ king of a great quantity of urine is the fign of a cri- fis, and fometimes the quality of it (hows how the blad¬ der is affedled. We muft alfo obferve, that Hippo¬ crates compared the ftate of the tongue with the urine j that is to fay, when the tongue was yellow, and char¬ ged with bile, the urine he knew muft of courfe be of the fame colour j and when the tongue was red and moift, the urine was of its natural colour. Among his prognoftics from the excretions by ftool are the following. Thofe that are foft, yellowilh, of fome confiftence, and not of an extraordinary ill fmell, that anfwer to the quantity of what is taken inwardly, and that are voided at the ufual hours, are the beft of all. They ouirht alfo to be of a thicker confiftence when the diftemper is near the crifis j and it ought to Ip! Hippo¬ crates. Faeces. C J N E. V be taken for a good prognoftic, wnen fome worms, par¬ ticularly tbe round and long, are evacuated at the fame , time with them. The prognofis, however, may ftill be v favourable, though the matter excreted be thin and liquid, provided it make not too much noife in coming out, and the evacuation be not in a fmall quantity nor too often 5 nor in fo great abundance, nor lb often, as to make the patient faint. All matter that is watery, vvlute, of a pale green or red colour, or frothy and vifeous, is bad. That which is blackifli, or of a livid hue, is the meft pernicious. That which is pure black, and nothing elfe out a difeharge of black bile, always prognofticates very ill j this humour, from What part foever it comes, fhowing the ill difpofition of the intef- tmes. The matter that is of fcveral different colours, denotes the length of the diftemper; and, at the fame time, that it may be of dangerous confequence. Hip¬ pocrates places in the,fame clafs the matter that is bilious or yellow, and mixed with blood, or green and black, or like the dregs or ferapings of the guts. The ftools that confift of pure bile, or entirely of phlegm, he alfo looks upon to be very bad. _ Matter ejected by vomiting ought to be mixed with bile and phlegm ; where one of tbefe humours only is obferved, it is worfe. lhat winch is black, livid, green, or of the colour of a leek, indicates alarming confequen- ces. The fame is to be faid of that which fmells very ill ; and if at the fame time it be livid, death is not far oft. The vomiting of blood is very often a mortal fymp- tom. I he fpitiings which give cafe in difeafes of the lungsExpeclo- and in p leu rifle 9, are thofe that come up readily and ration, without, difficulty ; and it is good if they be mixed at tbe beginning with much yellow : but if they appear off the fame colour, or are red, a great while after the be¬ ginning of the diftemper, if they are fait and acrimonious, and caufe violent coughings, they are not good. Spittings purely yellow are bad ; and thofe that are white, vifeous, and frothy, give no eafe. Whitenefs is a good fign of concotftion in regard to fpittings; but they ought not at all to be vifeous, nor too thick, nor too clear. We may make the fame judgment of the ex¬ crements or the nofe according to their conco&ion and crudity. Spittings that are brack, green, and red, are of very had confequence. In inflammations of the- lungs, thofe that are mixed w ith bile and blood prefage well if they appear at the beginning, but are bad If. they , arife not about the feventh day. But the worft fign in theffi diftempers is, when there is no expeftora- t:cn at all, and the too great quantity of matter that is ready to be difeharged this way makes a rattling in the breaft. After {pitting of blood, the difeharge of pu¬ rulent matter often follows, which brings on a confump- tion, and at laft death. A kind good fweat is that which arifes on the day Swea.u or the crifis, and is difeharged in abundance all over the body, and at the fame time from all parts of the body, and thus carries off the fever : A cold fvveat is alarming, eipecially in acute fevers, for in others it is only a fign of long continuance. When the patient fweats no where but on the head and neck it is a fign that tbe difeafe will be long and dangerous. A gentle fweat in fome particular part, of the head and breaft, for inftance, gives no relief, but denotes the.feat of the diftemper, or the weaknefs of the part. This It) 2 Erora the puife. M E D I This kind of fweat was called by Hippocrates ephidro- Jis. The hypochondria, or the abdomen in general, ought always to be foft and even, as well on the right fide as on the left. When there is any hardnefs or un- evennefs in thoie parts, or heat and fwellings, or when the patient cannot endure to have it touched, it is a fign the inteftines are indifpofed. Hippocrates alfo inquired into the ftate of the pulfe, or the beating of the arteries. The moft ancient phy- ficians, however, and even Hippocrates himfelf, for a long time, by this word underlfood the violent pulia¬ tion that is felt in an inflamed part, without putting the fingers to it. It is obferved by Galen, and other phyficians, that Hippocrates touches on the fubjefl of the pulfe more (lightly than any other on which he treats. But that our celebrated phyfician underftood fomething even on this fubjeft, is eafily gathered from feveral paffages in his writings j as when he obferves, that in acute fevers the pulfe is very quick and very great; and when he makes mention, in the fame place, of trembling pulfes, and thofe lhat beat flowly. He likewife obferves, that in fome difeafes incident to wo¬ men, when the pulfe ftrikes the finger faintly, and in a languilhing manner, it is a fign of approaching death. He remarks alfo, in the Coacce Pramotiones, that he whole vein, that is to fay, whofe artery of the elbow, beats, is juft going to run mad, or elfe that the perfon is at that time very much under the influence of anger. From this account of Hippocrates, it will appear, that he was not near fo much taken up with reafoning on the phenomena of difeafes, as with reporting them. He was content to obferve thefe phenomena accurately, to difiinguifh difeafes by them, and judged of the event by comparing them exadlly together. For his (kill in prognoftics he was indeed very remarkable, as we have already mentioned, infomuch that he and his pupils were looked upon by the vulgar as prophets. What adds very much to his reputation is, that he lived in an age when phyfic was altogether buried in fuperftition, and yet he did not fuflfer himfelf to be carried away by it; on the contrary, on many occafions, he expreffes his abhorrence of it. Having thus feen in what Hippocrates makes the difference between health and iicknefs to confift, and likewife the moft remarkable figns from whence he drew his prognoftics, we muft now confider the means ra he prefcribed for the prefervation of health, and the His maxims cure cf difeafes. One of his principal maxims was That, to preferve health, we ought not to over- of health, charge ourfelves with too much eating, nor negleft the ufe of exercife and labour. In the next place, That we ought by no means to accuftom ourfelves to too nice and exa6I a method of living; becaufe thofe who have once begun to a£t by this rule, if they vary in the leaft from it, find themfelves very ill; which does not happen to thofe who take a little more liberty, and live fomewhat more irregularly. Notwithftanding this he does not negleft to inquire diligently into the articles which thofe who were in health ufed for food in his time. Here we cannot help taking notice of the pro¬ digious difparity between the delicacy of the people in our days and in thofe of Hippocrates: for he takes great pains to tell the difference between the flclh of a dog. Hippo¬ crates. Diet. CINE. Hiftory. a fox, a horfe, and an ais j which he woind_not have done if at that time they had not been uieti for viftuals, t at leaft by the common people. Befides thefe, how¬ ever, Hippocrates fpeaks of all other kinds of provifion that are now' in ufe j for example, falads, milk, whey, cheeie, flefh as well of birds as of four-footed beatls^ frefli and fait fifli, eggs, all kinds of pulfe, and the dif¬ ferent kinds of grain we feed on, as well as the different forts of bread that are made of it. He alfo fpeaks very often of a fort of liquid food, or broth, made of barley- meal, or fome other grain, which they fteeped for fome time, and then boiled in water. With regard to drink, be takes a great deal of pains to diitinguifh the good waters from the bad. The belt, in his opinion, ought to be clear, light, without fmell or tafte, and taken out of the fountains that turn towards the eaft. Ihe fait waters, thofe that he evils hard, and thofe that rife out of fenny ground, are the w'orft of all} he condemns alfo thofe that come from melted fnow. But though Hip¬ pocrates makes all thofe diftinhtions, he adviies thole who are in health to drink of the firft water that comes in their way. He fpeaks alfo of alum waters, and thole that are hot •, but does not enlarge upon their qualities* He advifes to mix wine with an equal quantity of water: and this (he fays) is the juft proportion ; by uiing which the wine will expel w'hat is hurtful to the body, and the water will ferve to temper the acrimony of the humours. For thofe that are in health, and likewife for fuch Exercife. as are lick, Hippocrates advifes exerciie. The books, however, which treat on this fubje£l, M. Le Clerc conjectures to have been written by Herodicus, who firft introduced gymnaftic exercife into medicine, and who is laid by Hippocrates himfelf to have killed leve- ral people by forcing them to walk while they were af- flidted with fevers and other imflammatory diforders. The advices given in them confift chiefly in dire&ions for the times in which we ought to walk, and the con¬ dition we ought to be in before it} when we ought to walk flowly, and when to run, &c. ; and all this with defign to bring the body down, or diffipate the hu¬ mours. Wreftling, although a violent exercife, is numbered with the refl. In the fame place alfo mention is made of a play of the hands and fingers, which was thought good for health, and called chi~ ronomie ; and of another diverfion which was perform¬ ed round a fort of ball hung up, which they called. con/cus, and which they (truck forward with both their hands. With regard to thofe things which ought to be fe- Excretions, parated from, or retained in the human body, Hippocra¬ tes obferves, that people ought to take great care not to load themfelves with excrements, or keep them in too long 5 and befides the exercife above-mentioned, which carries off one part of them, and which he pre- fcribes chiefly on this account, he advifes people to excite and roufe up nature when (lie flagged, and did not endeavour to expel the reft, or take care of the im¬ pediments by which (lie was refilled. For this reafon he prefcribed meats proper for loofening the belly ; and when thefe were not fufficient, he direded the uie of clyfters and fuppofitones. For thin and emaciated perfons he direded clyfters compoled only of milk and oily unduous fubilances, which they mixed with a de- codion 2 Hiftory. MED! co&ion of cliick-peafe ; but for fuch as were plethoric, they only made ufe of fait or fea-water. As a prefervative againft diftempers, Hippocrates alfo advifed the ufe of vomits, which he directed to be taken once or twice a month during the time of winter and fpring. The moft limple of thefe were made of a deco&icn of hyflbp, with an addition of a little vine¬ gar and fait. He made thofe that were of a ftrong and vigorous conflitvtion take^this liquor in a morning fad¬ ing j but fuch as were thin and weakly took it after flipper.—Venery, in his opinion, is wholefome, pro¬ vided people confult their flrength, and do not pur- fue it to excefs j which he finds fault with on all occa- fions, and would have excefs avoided alfo in relation to ileep and watching. In his writings are likewife to be found feveral remarks concerning good and bad air j and he makes it appear that the good or bad difpofi- tion of this element does not depend folely on the dif¬ ference of the climate, but on the filuation of every place in particular. He fpeaks alfo of tbe good and bad effects of the paflions, and recommends moderation in regard to them. From what we have already related concerning the opinions of Hippocrates, it may naturally be concluded, that for the moft part he would be contented with obferv- ing what the ftrength of nature is able to accompliftr without being aflifted by the phyfician. That this was really the cafe, may be eafily perceived from a perufal of his books entitled, “ Of epidemical diftempers which are, as it were, journals of the praflice of Hippo¬ crates : for there we find him often doing nothing more than defcribing the fymptoms of a diftemper, and in¬ forming us what has happened to the patient day after day, even to his death or recovery, v ithout fpeaking a word of any kind of remedy. Sometimes, however, he did indeed make ufe of remedies j but thefe were ex¬ ceedingly fimple and few, in comparifon of what have been given by fucceeding practitioners. Thefe remedies v,e {hall prefently confider, after we have given an abridgement of the principal maxims on which his prac- 13 tice was founded. His maxims Hippocrates afferted in the firft place, That contra¬ ries, or oppofites, are the remedies for each other; and this maxim he explains by an aphorifm j in w hich he fays, that evacuations cure thofe diftempers w'hich come from repletion, and repletion thofe that are caufed by evacuation. So heat is deftroyed by cold, and cold by heat, &c. In the fecond place, he aflerted that phyfic is an addition of wjhat is wanting, and a fubtradfion or retrenchment of what is fuperfluous : an axiom which is thus explained, that there are fome juices or humours, which in particular cafes ought to be evacuated, or driven out of the body, or dried up ; and fome others W'hich ought to be reftored to the body, or caufed to be produced there again. As to the method to be taken for this addition or retrenchment, he gives this general caution, That you ought to be careful how you fill up, or evacuate, all at once, or too quickly, or too much ; and that it is equally dangerous to beat or cool again on a fudden ; or rather, you ought not to do it : every thing that runs to an excefs being an enemy to nature. In the fourth place, Hippocrates allowed that we ought iometimes to dilate, and fometimes to lock up : to dilate, or open the paflages by which the humours are voided naturally, when they are not fufficlentlv opened, or when VOL. XIII. Part I. for the cure of dif- siiles. C I N E. they are clofed ; and, on the contrary, to lock up or ftraiten the pafiages that are relaxed, w hen the juices that pafs there ought not to pafs, or when they pafs in too great quantity. He adds, that we ought fometimes to fmooth, and fometimes to make rough ; fometimes to harden, and fometimes to foften again, fometimes to make more fine or fupple ; fometimes to thicken ; fometimes to roufe up, and at other times to ftupify or take away the fenfej all in relation to the folid parts of the body, or to the humours. He gives alfo this farther leffon. That we ought to have regard to the courle the humours take, from whence they come, and whither they go j and in confequence of that, when they go where they ought not, that we make them take a turn about, or carry them another way, almoft like the turning the courfe of a river : or, upon other cccalions, that we endeavour if poftiLle to recal, or make the lame humours return back again ; drawing upward fuch as have a tendency downward, and drawing downward fuch as tend upward. We ought alfo uo carry oft, by con¬ venient ways, that which is neceflary to be carried off j and not let the humours once evacuated enter into the veffels again. Hippocrates gives alfo the follow ing inftruc- tion, That when we do any thing according to realon, though the fuccefs be not anfwrerable, we ought not eafily, or too hafti y, to alter the manner of afting, as long as the reafons for it are yet good. But as this maxim might fometimes prove deceitful, he gives the following as a corrector to it : “ WTe ought (fays he) to mind with a great deal of attention wdhat gives eafe, and what creates pain ; what is ealily lupported, and what cannot be endured.” We ought not to do any thing rafldy ; but ought often to paufe, or w'ait, without doing any thing: by this way, if you do the patient no good, you will at leaft do him no hurt. Thefe are the principal and moft general maxims of the pra&ice of Hippocrates, and which proceed up¬ on the luppofition laid down at the beginning, v.z^ that nature cures difeafes. We next proceed to con¬ fider particularly the remedies employed by him, wduch will ferve to give us further inftru&ions concerning his practice. T93 Hippo¬ crates. Diet was the firft, the principal, and often the only remedy made ufe of by this great phyfician to anfwer ^ep£ting all the circumftances that are neceffary in order tobat5 lI12' caufe the patient receive benefit from it, among which the following are the principal. The patient that bathes himfelf muft remain fliil and quiet in his place without {peaking while the affiflants throw water over his head or are wiping him dry ; for which laft pur- pofe he defired them to keep fponges, inftead of that inftrument called by the ancients Jlrtgil, which ferved to rub off from the ikin the dirt and naftinefs left upon it by the unguents and oils with which they anointed themielves. He muft alfo take care not to catch cold j and muft not bathe immediately after eating and drinking, nor eat or drink immediately alter coming out of the bath. Regard muft alfo be had whether the patient has been accuftomed to bathe while in health, and whether he has been benefited or hurt by it. Laftly, he muft abftain from the bath when the body is too open, or too coftive, or when he is too weak ; or if he has an inclination to vomit, a great lefs of appetite, or bleeds at the nofe. The advantage of the bath, according to Hippocrates, confifts in moi¬ ftening and refreihing, taking away wearinefs, making the ikin foft and the joints pliant 5 in provoking urine, and opening the other excretories. He allows two baths in a day to thofe who have been accuftomed to. it in health. lg In chronical diftempers Hippocrates approved very His maxims much of exercile, though he did not allow it in acute refpe tention be made ufe of fuppofitories and clyders. The former were compounded of honey, the juice of the herb mercury, of nitre, powder of colocynth, and other fharp ingredients, to irritate the anus. Thefe they formed into a ball, or into a long cylindrical mafs like- a finger. The cly ders he made ufe of for fick people were fometimes the fame with thofe already mention¬ ed as preventives for people in health. At other times he mixed the decoftion of herbs with nitre, honey, and oil, or other ingredients, according as he imagined he could by that means attracf, wadi, irritate, or foften* The quantity of liquor he ordered was about 36 ounces j from which it is probable he did not intend that it fhould all be ufcd at one time. On fome occafions Hippocrates propofed to purge the head alone. This practice he employed, after pur-, ging the reft of the body, in an apoplexy, inveterate B b 2 pains j,cj6 Hippo¬ crates. 20 His maxims refoedting blood-iet- ting. M E 1) I pains of the head, a certain fort of jaundice, a con- fumption, and the greateft part of chronical diftem- pers. For that purpofe he made ufe of the juices of ieveral plants, as celery, to which he fometimes added aromatic drugs, making the patients fnuff up this mix¬ ture into their noftrils. Fie ufed alfo powders com¬ pounded of myrrh, the dowers of brafs, and white hellebore, which he caufed them put uo into the nofe, to make them fneeze, and to draw the phlegm from the brain. For the fame purpofe alfp he ufed what he calls tetragomn, that is, “ fomething having four angles j” but what this was, is now altogether un¬ known, and was fo even in the days of Galen. The latter phyfician, however, conjectures it to be antimo¬ ny, or certain dakes found in it. a In the diftemper called empyema (or a collection of matter in the bread), he made ufe of a very rough me¬ dicine. He commanded the patient to draw in his tongue as much as he was able ; and when that was done, he endeavoured to put into the hollow of the lungs a liquor that irritated the part, which railing- a violent cough, forced the lungs to difcharge the purulent matter contained in them. The materials that he ufed for this purpofe' were of different forts ; fometiraes he took the root of arum, which he ordered to be boiled with a little fait, in a fufficient quantity of wa¬ ter and oil 3 diffolving a little honey in it. At other times, when he intended to purge more ftrongly, he took the dowers of copper and hellebore 3 after that he (hook the patient violently by the Ihoulders, the better to loofen the pus. This remedy, according to Galen, he received from the Cnidian phyficians 3 and it has never been ufed by the fucceeding ones, probably becaufe the patients could not fuffer it. Blood-letting was another method of evacuation pretty much ufed by Hippocrates. Another aim he had in this, beddes the mere evacuation, was to divert or recal the courfe of the blood when he imagined it was going where it ought not. A third end of bleed¬ ing was to procure a free motion of the blood and fpi- rits. Hippocrates had alfo a fourth intention for bleed¬ ing, and this was refrellunent. So in the iliac paflion, he orders bleeding in the arm and in the head 3 to the end, fays he, that the fuperior venter, or the bread, may ceafe to be overheated. With regard to this eva¬ cuation, his conduct was much the fame as to purging, in refpect of time and perfons. We ought, fays he, to let blood in acute difeafes, when they are violent, if the party be lufty and in the dower of his age. We ought alfo to have regard to the time, both in refpeCt to the difeafe and to the feafon in which we let blood. He alfo informs us, that blood ought to be let in great pains, and particularly in indammations. iVmong thefe he reckons fuch as fall upon the principal vifcera, as the liver, lungs, and fpleen, as alio the quinfy and pleurify, if the pain of the latter be above the dia¬ phragm. In thefe cafes he would have the patients blooded till they faint, efpecially if the pain be very acute ; or rather he advifes that the orifice thould not be clofed till the colour of the blood alters, fo that from livid it turn red, or from red livid. In a quinfy he blooded in both arms at once. Difficulty of breathing he alfo reckons among the diilempers that require hleqJing 3 and he mentions another fort of inflamma- C I N E. Hiltory, tion of the lungs, which he calls a fwelling or tumor Hippo- of the lungs arifing from heat 3 in which cafe he ad- cmes' , vifes to bleed in all parts of the body 3 and direfis it particularly by the arms, tongue, and noftrils. To make bleeding the more ufeful in all pains, he d'recied to open the vein neared; the part affeffed 3 in a pleurify he direfts to take blood from the arm of the fide affec¬ ted 3 and for the fame reafon, in pains of the head, he direfts the veins of the nofe and forehead to be opened. When the pain was not urgent, and bleeding was ad- vifed by way of prevention, he diredted the blood to be taken from the parts fartheft off, with a defign to divert the blood infenfibly from the feat of pain. The higheil burning fevers, which ihow neither ligns of in¬ flammation nor pain, he does not rank among thofe diftempers which require bleeding. On the contrary, he maintains that a fever itfelf is in fome cales a reafon againd bleeding. If any one, fays he, has an ulcer in the head, he muff bleed, unlefs he has a fever. Fie fays further, thofe that lofe their fpeech of a ludden muff be blooded, unlefs they have a fever. Perhaps he was afraid of bleeding in feveis, becaule he fuppofed that they were produced by the bile and pituita, which grew hot, and afterwards heated the whole body, which is, fays he, what we call fever, and which, in his opinion, cannot well be evacuated by bleeding. In other places alfo he looks upon the prefence or abun¬ dance of bile to be an objection to bleeding 3 and he orders to forbear venefefrion even in a pleuriiy, if there be bile. To this we muff add, that Hippocrates di- ftinguiihed very particularly between a fever which followed no other diffemper, but was itfelf the original malady, and a fever which came upon inflammation. In the early ages of phyfic, the firft only wTere proper¬ ly called fevers : the others' took their names from the parts affected 3 as pleurify, peripneumomj, hepatitis, ne¬ phritis, See. which names fignify that the pleura, the lungs, the liver, or the kidneys, are difeafed, but do not intimate the fever which accompanies the difeafe.. In this latter fort of fever Hippocrates conftantly or¬ dered bleeding, but not in the former. Hence, in his books on- Epidemic Diflempers, we find but lew di- reflions for bleeding in the acute diftempers, and par¬ ticularly in the great number of continual and burning fevers there treated of. In the nrft and third book we find but one Angle inftance of bleeding, and that in a pleurify 3 in which, top, he flaid till the eighth day of the diftemper. Galen, however, and moil o- ther commentators on Flippocrates, are of opinion, that he generally blooded his patients plentifully in the beginning of acute diforders, though he takes no no¬ tice of it in his writings. But had this been the cafe, he would not perhaps have had the opportunity of feeing fo many fevers terminate by crifes, or natural evacua¬ tions, which happen of themfelves on certain days. Hippocrates, in faft, laid fo much weight upon the. afliftance of nature and the method of diet, which was his favourite medicine, that he thought if they took care to diet the patients according to rule, they might leave the reft to nature. Thefe are his principles, from which he never deviates 3 fo that his writings on Epidemical Difeafes feem to have been compofed only with an intention to leave to pofterity an ex- aft model of management in purfuance of thefe prin¬ ciples. With Hiftory. M E D I Hippo- Witli regard to the rules laid down by Hippocrates crates. •f0-r bleedinp', ive muft farther take notice, that in all V -y- difeafes which had their feat above the liver, he blood¬ ed in the arm, or in feme of the upper parts of the body •, but for thofe that were fituated below it he opened the veins of the foot, ankle, or ham. If the belly was too loofe, and bleeding was at the lame time thought neceffary, he ordered the loofetiefs to be flop¬ ped before bleeding. Aim oft all thefe inftances, however, regard fcarce any thing but acute diftempers 5 but we find feveral concerning chronical difeafes. “ A young man com¬ plained of great pain in his belly, with a rumbling while he was fading, which ceafed after eating : this pain and rumbling continuing, his meat did him no good ; but, on the contrary, he daily wrafted and grew lean. Several medicines, as well purges as vomits, were given him in vain. At length it was refolved to bleed him by. intervals, firft in one arm and then in the other, till he had fcarcely any blood left, and by this method he v/as perfedlly cured.” Hippocrates let blood alfo in a dropfy, even in a tympany 5 and in both cafes he preferibes bleeding in the arm. In a difeafe occaftoned by an overgrown fpleen, he propofes bleeding feveral times repeated at a vein of the arm which he calls the fplenetic ; and in one fpecies of jaundice, he propofes bleeding under the tongue. On feme occalions he took away great quan¬ tities of blood, as appears from what we have already obferved. Sometimes he continued the blooding till the patient fainted : at other times he would blood in both arms at once ; at others, he did it in feveral pla¬ ces of the body, and at feveral times. The veins he opened were thofe ol the arm, the hands, the ankles on both Tides, the hams, the forehead, behind the head, the tongue, the nofe, behind the ears, under the breafts, and thofe of the arms ; befides which, he burnt others, and opened feveral arteries. He likewife ufed cup- ping-veffels, with intent to recal or withdraw the humours which fell upon any part. Sometimes he contented himfelf with the bare attradlion made by the cupping-veffels, but fometimes alfo he made fcarifications. 21 When bleeding and purging, which were the prin- His maximscipal and moft general means ufed by Hippocrates refpeAing for taking off a plethora, proved infufficient for that awHudod PurP0^» ^e had recourfe to diuretics and fudorifics. fits. UCU ~ The former were of different forts, according to the conftitution of the perfons : fometimes baths, and fometimes fweet wine, were employed to provoke urine 5 fometimes the nourifhment which w!e take con¬ tributes to it : and amongft thofe herbs which are commonly eaten, Hippocrates recommends garlic, leeks, onions, cucumbers, melons, gourds, fennel, and all other things which have a biting tafte and a ftrong fraell. With thefe he numbers honey, mixed with water or vinegar, and all fait meats. But, on fome occafions, he took four cantharides, and, pulling off their wings and feet, gave them in wine and honey. Thefe reme¬ dies were given in a great number of ciiiomcai di¬ ftempers after purging, when he thought the blood w'as overcharged with a fort of moifture which he cabs ichor ; or in fuppreflfions of urine, and when it w7as made in lefs quantity than it ought. There were alfo fome cafes in which he would force fweat as well as CINE. 197 urine ; but he neither mentions the difeafes in wdiich Hippo- fudorifics are proper, nor lets us know what medicines , , are to be ufed for this purpofe, except in one fingle paffage, where he mentions fweating, by pouring upon the head a great quantity of water till the feet i'weat •, that is, till the fweat diffufes itfelf over the whole body, running from head to foot. After this he ivould have them eat boiled meat, and drink pure wane, and being well covered wdth clothes, lay themfelves down to reft. The difeafe for which he propofes the above mention¬ ed remedv is a fever 3 which is not, according to him, produced by bile or pituita, but by mere laffitude, or feme other fimilar caufe 3 from whence we may con¬ clude that he did not approve of fweating in any other kind of fever. Other remedies which Hippocrates tells us he made life of were thofe that purged neither bile nor phlegm, but a£t by cooling, drying, heating, moiitening, or by doling and thickening, refolving and diflipating. Thefe medicines, however, he does not particularly mention 3 and it is probable they were only fome particular kinds of food. To thefe he joined hypnotics,, or iach things as procure fleep 3 but thefe laft were ufed very leldom, and, it is moft probable, were only different prepara¬ tions of poppies. £ j , Laftly, befides the medicines already mentioned, j ^ j j which ailed in a fenlible manner, Hippociatcs made cl‘fics> L ufe of others called fpecifics ; whole action he did not underfland, and for the ufe of which he could give no reafon but his own experience, or that of other phyii- cians. Thefe he had learned from his predeceffors the defeendants of iEfculapius, who, being etnpirics, did not trouble themfelves about inquiring into the ope¬ ration of remedies, provided their patients were cured. Of the external remedies preferibed by Hippo- ^ 23 crates, fomentations were the chief. Thefe w7ere ofIIls two kinds. The one was a fort of bath, in which the^n^ppica“ patient fat in a veffel full of a decodlion of limples appropriated to his malady 3 fo that the part affected was leaked in the decodlion. This w7as chiefly ufed in diftempers of the w’omb, of the arms, the bladder, the reins, and generally all the parts below the dia¬ phragm. The fecond way of fomenting was, to take 2 ^ warm water and put it into a fkin or bladder, or even Fomenta- into a copper or earthen veffel, and to apply it to the tkms. part affefted 3 as, for example, in a plcurify. They ufed likewife a large fponge, which they dipped in the w^ater or other hot liquor, and fqueezed out part of the liquor before they applied it. The fame ufe they made of barley, vetches, or bran, which wrere boiled in fonie proper liquor, and applied in a linen bag. Thefe are called moijl fomentations. The dry ones wTere made of fait or millet, heated confiderably, and applied to the part. Another kind of fomenta¬ tion was the vapour of lome hot liquor 3 an in fiance of which w7e find in Bis firft book of the Diftempers of Wo¬ men. He caft, at feveral times, bits of red-hot iron into urine, and, covering up the patient clofe, caufed her to receive the fleam below. His defign in thefe kinds of fomentations was to warm the part, to re- folve or diffipate, and draw out the peccant matter, to mollify and affuage pain, to open the paffages, or even to fhut them, according as the fomentations were emol¬ lient or aftringent. Fumigations- 198 - M E D I Hippo- Fumigations were likewife very often ufed by Hip- , C1^s‘ , pocrates. In the quinfy, he burned hyffop with 2- fulphur and pitch, and caufed the fmoke to be drawn Fumiga- into the throat by a funnel 5 and by this means he »ons. brought away abundance of phlegm through the mouth and through the nofe. For this purpofe he took nitre, marjoram, and crefs-feeds, which he boiled in water, vinegar, and oil, and, while it was on the fire, caufed the patient to draw in the fleam by a pipe. In his works we find a great number of fumigants for the diftempers of women, to promote the menftrual flux, to check it, to help conception, and to eafe pains in the matrix, or the fuffocation of it. On thefe oc- cafions he ufed fuch aromatics as were then known, viz. cinnamon, caflia, myrrh, and feveral odoriferous plants *, likewife fome minerals, fuch as -nitre, fulphur, and pitch, and caufed the patient to receive the va- pours through a funnel into the uterus. Gargles. Gargles, a kind of fomentations for the mouth, were alfo known to Hippocrates. In the quinfy he ufed a gargle made of marjoram, favory, celery, mint, and nitre, boiled with water and a little vinegar. When this was ftrained, they added honey to it, and 2j waflied their mouths frequently wuth it. ©ils and v Oils and ointments were likewife much ufed by ointments. Hippocrates, with a view to mollify and abate pain, to ripen boils, refolve tumours, refrelh after wearinefs, make the body fupple, &c. For this purpofe, fome- times pure oil of olives was ufed ; fometimes certain fimples were infufed in it, as the leaves of myrtle and rofes j and the latter kind of oil was in much requeft among the ancients. There were other forts of oils fometimes in ufe, however, which were much more compounded. Hippocrates fpeaks of one named Sufi- num, which was made of the flowers of the iris, of fome aromatics, and of an ointment of narciffus made with the flowers of narciffus and aromatics infuftd in oil. But the mofl compounded of all his ointments w>as that called netopon, which he made particularly for women ; and confided of a great number of ingredi- •ents. Another ointment, to which he gave the name ©f ceratum, was compofed of oil and wax. An oint¬ ment which he recommends for the foftening a tu¬ mor, and the cleanfing a wound, was made by the following receipt : “ Take the quantity of a nut of the ' marrow7 or fat of a fheep, of maftic or turpentine the quantity of a bean, and as much wax ; melt tbefe over a fire, wnth oil of rofes, for a ceratum.” Sometimes he added pitch and wrax, and, with a fufficient quanti¬ ty of oil, made a compofition fomewhat more confiflent 2S than the former, which he called cerapiffits. flataplafins. Cataplafms we re a fort of remedies lefs confiftent than the two former. They were made of pow'ders or herbs fteeped or boiled in water or fome other li¬ quor, to which fometimes oil was added. They were tiled with a view to foften or refolve tumors, ripen ab- feeffes, &c. though they had alfo cooling cataplafms made of the leaves of beets or oak, fig or olive-trees, 29 boiled in wuter. •ollyria. Laftly, To complete the catalogue of the external remedies ufed by Hippocrates, vve (hall mention a fort of medicine called collyrium. It was compounded of powrders, to which was added a fmall quantity of lome ointment, or juice of a plant, to make a folid or dry mafs) the form of which was long and round, CINE. Hiltory. wThich w7as kept for ufe. Another compofition of much Hippo- the fame nature was a fort of lozenge of the bignefs of crates- a fmall piece of money, which was burnt upon coals' -J for a perfume, and powdered for particular ufes. In his works we find likewife deferiptions of pow’ders for feveral ufes, to take off fungous flelh, and to blow into the eyes in ophthalmies, &c. Thefe were almoft all the medicines ufed by Hip¬ pocrates for external purpofes. The compound me¬ dicines given inwardly were either liquid, fohd, or lambative. The liquid ones were prepared either by deco&ion or infufion in a proper liquor, which, when ffrained, were kept lor u!e j or by macerating certain' powders in luch liquors, and fo taking them toge¬ ther, or by mixing different kinds of liquors toge¬ ther. The folid medicines confifted of juices infpif- fated ; of gums, refins, or powders, made up with them or wbth honey, or fomething proper to give the neceffary confiftence to the medicine. Thefe were made up in a form and quantity fit to be fw7allowed with eaie. The lambative wras of a confiflence be- tween lolid and fluid ; and the patients were obliged to keep it for fome time to diffolve in the mouth, that they might fwallow7 it leifurely. This remedy w7as ufed to take off the acrimony of thofe humours which fometimes fall upon this part, and provoke coughing and other inconveniences. The bafis of this laft com¬ pofition was honey. It is worth our obfervation, that the compound medicines of Hippocrates were but very few, and compofed only of four or five ingredients at moft ; and that he not only underflood pharmacy, or the art of compounding medicines, but prepared fuch as he ufed himfelf, or caufed his fervants prepare them in his houfe by his direflions. We have thus given fome account of the ftate of medicine as pradlifed and taught by Hippocrates, who, as we have already obferved, has for many ages been juflly confidered as the father of phyfic. For when vve attend to the ftate in which he found medicine, and the condition in which he left it, we can hardly beflow fufficient admiration on the judgement and accuracy of bis obfervations. After a life fpent in unwearied induf- try, he is faid to have died at Lariffa, a city in Thef- faly, in the 101ft year of his age, 361 years before the birth of Chrift. After the days of Hippocrates, medicine in ancient Greece gradually derived improvement from the la¬ bour of other phyficians of eminence. And we may particularly mention three to whom ks future progrefs feems to have been not a little indebted, viz. Praxago- ras, Erafiftratus, and Herophilus. 'I he firft phyfician of eminence who differed confi- Praxagoras. derably in his practice from Hippocrates w7as Praxa¬ goras. Ccelius Aurelianus acquaints us, that he made great ufe of vomits in his pradlice, infomuch as to ex¬ hibit them in the iliac palTiun till the excrements were dilcharged by the mouth. In this diflemper he alfo advifed, when all other means failed, to open the belly, cut the inteftine, take out the indurated faeces, and then to few up all again; but this practice has not probably been followed by any fubfequent phyfi¬ cian. Erafiftratus was a phyfician of great eminence, folates, and flouriffied in the time of Seleucus, one of the fuveeffors of Alexander the Great. According to Galen, Hiftory. M E D I ;Erafiftratus, Galen, he entirely banifhed venefeftion from medi- v'*' cine 5 though feme affirm that he did not totally dif- card it, but only ufed it lefs frequently than other phyficiansc His reafons for difapproving of venefec- tion are as follow: It is difficult to fucceed in vene- feftion, becaufe we cannot always fee the vein we in¬ tend to open, and becaufe we are not fure but we may open an artery inftead of a vein. We cannot afeertain the true quantity to be taken. If we take too little, the intention is by no means anfwered : if we take too much, we run a rilk of deilroying the patient. The evacuation of the venous blood alfo is fucceeded by that of the fpirits, which on that occa- fion he fuppofes to pafs from the arteries into the veins. It muft likewife, he contends, be obferved, that as the inflammation is formed in the arteries by the blood coagulated in their orifices, venefe&ion muft of courfe be ufelefs and of no eflfefl. As Erafiftratus did not approve of venefeflion, fo neither did he of purgatives, excepting very rarely, but exhibited clyfters and vomits ; as did alfo his ma¬ iler Chryfippus. He was of opinion, however, that the clyfters iliould be mild 5 and condemned the large quantity and acrid quality of thofe ufed by preceding practitioners. The realon why purgatives were not much ufed by him was, that he imagined purging and venefeflion could anfvver no other purpofe than dimi- niffiing the fulnefs of the veflels ; and for this purpofe he afferted that there were more effeCual means than either phlebotomy or purging. He afferted that the humours difeharged by cathartics were not the fame in the body that they appeared after the difeharge ; but that the medicines changed their nature, and produced a kind of corruption in them. This opinion has fince been embraced by a great number of phyficians. He did not believe that purgatives afled by attra&ion ; but fubftituted in the place of this principle what Mr Le Clerc imagines to be the fame with Ariftotle’s fuga vacm. The principal remedy fubftituted by him in place of purging and venefedtion was abftinence. When this, in conjun&ion with clyfters and vomits, was not fufticient to eradicate the difeafe, he then had rccourfe to exercife. A1*l this was done with a view „ to diminifh plenitude, which, according to him, was the rtioft frequent caufe of all difeafes. Galen alfo in¬ forms us, that Erafiftratus had fo great an opinion of the virtues of fuccory in difeafes of the vifeera and lower belly, and efpecially in thofe of the liver, that he took particular pains to deferibe the method of boiling it, which was, to boil it in water till it was tender ; then to put it into boiling water a fecond time, in order to deftroy its bitternefs: afterwards to take it out of the water, and preftrve it in a veffel with oil *, and laftly, when it is to be ufed, add a little weak vinegar to it. Nay, fo minute and circumftantial was Erafiftratus with regard to the preparation of his favourite fuccory, that . he gave orders to tie feveral of the plants together, be¬ caufe that was the more commodious method of boil¬ ing them. The reft of Erafiftratus’s practice confided aim. A entirely of regimen ; to which he added fome topical remedies fuch as cataplafms, fomentations, and unCHons. In {hurt, as he could neither endure com¬ pounded medicines, nor fupe. ftitious and fitie-fpun rea- fonings-, he reduced medicine to a very Ample and com¬ pendious art. <5 I N E. i9> With regard to furgery, Erafiftratus appears to Herophilus. have been very bold 5 and as an anatomift he is faid to v—' have been exceedingly cruel, infomuch that he is re- prefented by fome as having diffecled criminals while yet alive*. In a feirrhous liver, or in tumors oi* that organ, Coelius Aurelianus obferves, that Erafiftra-t0n ^ ^' tus made an incifion through the fkin and integu¬ ments, and having opened the abdomen he applied medicines immediately to the part aflfecled. But though he was thus bold in performing operations on the liver, yet he did net approve of the paracentefis or tapping in the dropfy j becaufe (faid he) the waters being eva¬ cuated, the liver, which is inflamed and become hard like a ftone, is more prelfed by the adjacent parts which the waters kept at a diftance from it, fo that by this means the patient dies. He declared alfo againft drawing teeth which were not loofe j, and ufed to tell thofe who talked with him on this operation. That in the temple of Apollo there was to be feen an inftrument of lead for drawing teeth ) in order to infi- nuate that we muft not attempt the extirpation of any but fuch as are loofe, and call for no greater force for their extirpation than what may be fuppofed in an in¬ ftrument of lead. 32 Herophilus, the difciple of Praxagoras, and contem- Herophilus, porary of Erafiftratus, followed a lefs fimple pra£tice : he made fo great ufe of medicines both fimple and compound, that neither he nor his difciples would un¬ dertake the cure of any diforder without them. He feems alfo to have been the firft who treated accurately t of the doftrine of pulfes, of which Hippocrates had but a fuperficial knowledge. Galen, however, affirms, that on this fubjefl he involved himfelf in difficulties and ad¬ vanced abfurdities } which indeed we are not greatly to wonder at, confidering the time in which he lived. He took notice of a clifeafe at that time pretty rare, and to which he aferibes certain fudden deaths. Pie calls it a palfy of the heart; and perhaps it may be the fame difeale with what is now termed the angina peBoris. According to Celfus, it was about this time that medicine was firft; divided into three branches, viz. the dietetic, the pharmaceutical, and the chirurgical medi¬ cine. 'Phe firft of thefe employed a proper regimen in the cure of difealesj the fecond, medicines j and the third, the operation of the hands. The fame au¬ thor informs us, that thefe three branches became now the bufinefs of as many diftinsft clafles of men ; fo that from this time we may date the origin of the three profeffions of phyficians, apothecaries, and fur- geons.—Before this divifion, thofe called physicians dif¬ eharged all the feveral offices belonging to the three profeffions; and there were only two kinds of them, Viz. one called ct^Tinroyixoi, who only gave their ad¬ vice to the patients, and direffions to thofe of an infe¬ rior clafs, who were called ^yifuov^ypi, and worked wfith their hands either in the performing operations, or in the compofition and application of remedies. 33 - The firft: grand revolution which happened in the T^e medicinal art after the days of Herophilus and Erafi-™* ftratus was occafioned by the founding of the empiric feff by Serapion of Alexandria about 287 years before ,Ch5ia- , P™"?0? fint° d°gmfifts and empiricsSerai^a,. had mdeeci fubfifted before ; but about this time the latter party began to grow ftreng, and to have cham- plons 200 MEDICINE. Senpion. pions ppbliciy auertinp; its caufe. Galen informs us, that Serapion uied Hippocrates very ill in his writ¬ ings, in which he difcovered an excefs of pride, felf- fufficiency, and contempt for all the phylicians that went before him. We have fome Iketches of his pra£lice in Coelius Aurelianus, from which we may infer that he retained the medicines of Hippocrates and the other phyficians who went before him, though he rtjefled their reafoning. We know not what argu¬ ments he advanced for the fupport of his fentiments, fince his works are loft, as well as thofe of the other empirics; and we fhould know nothing at all of any of them, if their adverfaries had not quoted them in order to confute them. The empirics admitted only one general method of obtaining fkill in the medical art, which was by ex¬ perience, called by the Greeks From this word they took their name, and refuled to be called after the founder or any champion of their feft. They defined experience a knowledge derived from the evidence of fenfe. It was either fortuitous, or acquired by defign. For acquiring pra&ical Ikill they recommended ivhat they called rn^r traflion. This laft principle Afclepiades denied in v every infiance, even in that ol the loaditone and fteel, imagining that this phenomenon proceeded from a concourfe of corpufcles, and a particular difpofition or modification of their pores. He alio maintained, that nothing happened or was produced without feme caufe ; and that what was called nature was in reality no more than matter and motion. From this laft; prin¬ ciple he inferred that Hippocrates knew not what he faid when he fpoke of Nature as an intelligent being, and aferibed qualities of different kinds to her. For the fame reafon he ridiculed the dohtrine ot Hippo¬ crates w ith regard to crifes; and afferted that the termination of difeafes might be as well accounted for from mere matter and motion. He maintained, that we w^ere deceived if we imagined that nature always did good 5 fince it was evident that Ihe often did a great deal of harm. As for the days particularly fixed upon by Flippocrates for criles, or thofe on wffiich w7e ufually oblerve a change either for the bet¬ ter or the worfe, Afclepiades denied that inch altera¬ tions happened on thofe days rather than on others. Nay, he afferted that the crifis did not happen at any time of its owm accord, or by the particular determi¬ nation of nature for the cure of the diforder, but that it depended rather on the addrefs and dexterity of the phyfician ; that we ought never to wait till a diftem- per terminates of its own accord, but that the phyfi¬ cian by his care and medicines muff haften on and ad¬ vance the cure.-—According to him, Flippocrates and other ancient phyficians attended their patients rather with a view to obferve in what manner they died than in order to cure them ; and this under pretence that Nature ought to do all herielf, without any affift. ance. According to Afclepiades, the particular affemblage of the various corpufcles above mentioned, and repre- fented as of different figures, is the reafon wffiy there are 1’everal pores or interfaces within the common mafs, formed by th’efe corpulcles; and why thefe pores are of a different fize. This being taken for granted, as thefe pores are in all the bodies we obferve, it muff of courfe follow that the human body has lome pecu¬ liar to itfelf, which, as wrell as thofe of all other bo¬ dies, contain certain minute bodies, which- pafs and re- pafs by thofe pores that communicate with each other j and as thefe pores or interftices are larger or fmaller, fo the corpufcles which pafs through them differ pro- portionably as to largenefs and minutenefs. The blood confilts of the largeft of thefe corpufcles, and the ipirits, or the heat, of the fmalleft. From thefe principles he infers, that as long as the corpufcles are freely received by the pores, the body remains in its natural Hate •, and on the contrary, it begins to recede from that ftate, when the corpulcles find any obflacle to their paffage. Flealth therefore depends on the juft proportion between the pores and the corpufcles they are deftined to receive and tranimit j as difeafes, on the contrary, proceed from a difpropor- tion between thefe pores and the corpufcles. The moft; ufual obftacle on this occafion proceeds from the cor¬ pufcles embracing each other, and being retained in fome of their ordinary paffages, whether thefe ccrpuf- cles Hiftory. M E D I Afclepi- cles arrive in too large a number, are of irregular fi- a<^eg' , gures, move too fait or too {low, &c. s Among the difeafes produced by the corpufcles flopping of their own accord, Afclepiades reckoned phrenfies, lethargies, pleurifles, and burning fevers. Pains, in particular, are claffed among the accidents which derive their origin from a ftagnation of the largeft of all the corpufcles of which the blood con- fifts. Among the diforders produced by the bad flate and difpofition of the pores, he placed deliquiums, lan¬ guors, extenuations, leannefs,' and dropfies. Thefe laft diforders he thought proceeded from the pores being too much relaxed and opened : the dropfy in particular, he thinks, proceeds from the flefh being perforated wnth various fmall holes, which convert the nourflhment received into them into water. Hunger, and efpecially that fpecies of it called fames canina, proceeds from an opening of the large pores of the ftomach and belly ; and third from an opening of their fmall ones. Upon the fame principles he account¬ ed for intermittent fevers. According to him, quoti¬ dian fevers are caufed by a retention of the largeft eorpufcles, thofe of the tertian kind by a retention of corpufcles fomewhat fmaller, and quartan fevers are produced by a retention of the fmalleft corpufcles of all. The pra£lice of Afclepiades was fuited to remove thefe imaginary caufes of diforders. He compofed a book concerning common remedies, which he princi- *pally reduced to three, viz. geftation, fri&ion, and the ufe of wine. By various exercifes he propofed to render the pores more open, and to make the juices and fmall bodies, which caufe difeafes by their reten¬ tion, pafs more freely ; and while the former phy- ficians had not recourfe to geftation till towards the end of long-continued diforders, and when the patients, though entirely free from fever, were yet coo weak to take fufficient exercife by walking, Afclepiades ufed geftation from the very beginning of the mold burn¬ ing fevers. He laid it down as a maxim, that one fever was to be cured by another j that the ftrengfh of the patient was to be exhaufted by making him watch and endure third: to fuch a degree, that, for the two firft days of the diforder, he would not allow them to cool their mouths with a drop of water. Celfus abb obferves, that though Afclepiades treated his patients like a butcher during the firft days of the diforder, he indul¬ ged them fo far afterwards as even to give directions for making their beds in the fofteft manner. On fe- veral occaftons Afclepiades ufed frictions to open the pores. The dropfy was one of the diftempers in which this remedy was ufed \ but the moft lingular attempt was, by this means, to lull phrenetic patients afleep. But though he enjoined exercife fo much to the fick, he denied it to thofe in health ; a conduft not a little furprifing and extraordinary. He allowed wine freely to patients in fevers, provided the violence of the dif- temper was fomewhat abated. Nor did he forbid it to thofe who were afflifted with a phrenfy : nay, he or¬ dered them to drink it till they were intoxicated, pre¬ tending by that means to make them fleep ; becaufe, he faid, wine had a narcotic quality and procured fleep, which he thought abfolutely neceffary for thole who la- bouied under that diforder. To lethargic patients he ufed it on purpofe to excite them, and roufe their fen- VOL. XIII. Part I. CINE. 20: fes: he alfo made them fmell ftrong-fcented fubftan- Afclepi- ces, fuch as vinegar, caftor, and rue, in order to make ades’ &c- them freeze ; and applied to their heads cataplafms of ^ r nauftard made up with vinegar. Befides thefe remedies, Afclepiades enjoined his pa¬ tients abftinence to an extreme degree. For the firft three days, according to Celfus, he allowed them no aliment whatever j but on the fourth began to give them victuals. According to Caslius Aurelianus, how¬ ever, he began to nourilh his patients as foon as the acceflion of the difeafe was diminiflied, not waiting till an entire remiflion; giving to fome aliments on the firft, to fome on the fecond, to fome on the third, and fo on to the feventh day. It feems almoft incredible to us, that people flrould be able to fall till this laft mentioned term ; but Celfus affures us, that ab¬ ftinence till the feventh day wTas enjoined even by the predeceflbrs of Afclepiades. The next great revolution which happened in the medicinal art, was brought about by Themifon, the difciple of Afclepiades, who lived not long before the time of Celfus, during the end of the reign of Auguf- tus, or beginning of that of Tiberius. The fed found¬ ed by him was called methodic, becaufe he endeavoured Methodic to find a method of rendering medicine more eafy than feet formerly. _ He maintained, that a knowledge of the caufes of Themifon. difeafes was not neceffary, provided we have a due re¬ gard to what difeafes have in common and analogous to one another. In confequence of this principle, he di¬ vided all difeafes into two, or at moft three, kinds. I he firft included difeafes arifing from ftrifture the fecond, thofe arifing from relaxation ; and the third, thofe of a mixed nature, or fuch as partook both of ftricture and relaxation. Themifon alfo afferted, that difeafes are fometimes acute, and fometimes chronical; that for a certain time they increafe j that at a certain time they are at their height; and that at laft they were obferved to dimi- nifli. Acute difeafes, therefore, according to him, mull be treated in one way, and chronical difeafes in. another j one method mull be followed with fuch as are in their augmentation, another with fuch as are at their height, and a third with fuch as are in their de- clenfion. He afferted, that the whole of medicine con¬ fided in the obfervation of that fmall number of rules which are founded upon things altogether evident. He laid, that all diforders, whatever their nature was, if included under any of the kinds above mentioned, ought to be treated precifely in the fame way, in what¬ ever country and with whatever fymptoms they hap¬ pen to arife. Upon thefe principles, he defined me¬ dicine to be a method of conducing to the knowledge of what difeafes have in common with each other. Themifon was old when he laid the foundation of the methodic fed! ; and it was only brought to perfec¬ tion by Theffalus, who lived under the emperor Nero. TheifulDS- Galen and Pliny accufe this phyfician ef intolerable in- folence and vanity, and report that he gave himfelf the air of defpifing all other phyficians ; and fo intole¬ rable was his vanity, that he affumed the title of the conqueror of physicians, which he caufed to be put up¬ on his tomb in the Appian way. Never was moun¬ tebank (fays Pliny) attended by a greater number of C c fp eel a tors 39 Soranus; 40 Celias. 202 fv Theffalus, fpeclators than Theffalus had generally about him ; , oi'c_' and this eircumflance is the lei's to bp wondered at, it vve confider that he promifed to teach the whole art of medicine in lefs than fix months. In reality, the art might be learned much fooner if it comprehended no more than what the methodics thought neceflary : for they cut oil the examination of the caufes of difeafes followed by the dogmatics j and fubftituted in the room of the laborious obfervations of the empirics, in¬ dications drawn from the analogy of difeales, and the mutual refemblanee they bear to each other. The mold ikilful of all the methodic fe£l, and he who put the lalt hand to it, was Soranus. He lived under the emperors Trajan and Adrian, and was a native of Ephefiis. One of the moft celebrated medical writers of an¬ tiquity was Celfus, whom we have already had oc- cafion to mention. Moft writers agree that he lived in the time of Tiberius, but his country is uncertain. It is even difputed whether or not he was a profeffed phyfician. Certain it is, however, that his books on medicine are the moft valuable of all the ancients next to thofe of Hippocrates. From the latter, indeed, he has taken fo much, as to acquire the name of the La¬ tin Hippocrates; but he has not attached himfelf to him fo clofely as to rejeft the affiftance of other au¬ thors. In many particulars he has preferred Afcle- piades. With him he laughs at the critical days of Hippocrates, and afcribes the invention of them to a foolilh and luperftitious attachment to the Pythago¬ rean do&rine of numbers. He alfo rejected the doc¬ trine of Hippocrates with regard to venefebtion, of which he made a much more general ufe $ but did not take away fo much blood at a time, thinking it much better to repeat the operation than weaken the patient by too great an evacuation at once. He ufed cupping alfo much more frequently, and differed from him with re¬ gard to purgatives. In the beginning of diforders, he faid, the patients ought to endure hunger and third: : but afterwards they were to be nourithed with good aliments; of which, however, they were not to take too much, nor fill themfelves fuddenly, after having faded long. He does not fpecify how long the pa¬ tient ought to prattlfe abdinence ; but affirms, that in this particular 'it is neceffary to have a regard to the difeafe, the patient, the feafon, the climate, and other circumdances of a like nature. The figns drawn from the pulfe he looked upon to be very precarious and un¬ certain. “ Some (fays he) lay great drefs upon the beating of the veins or the arteries ; which is a deceit¬ ful circumdance, fince that beating is dow or quick, and varies very much, according to the age, fex, and conditution of the patient. It even fometimes happens that the pulfe is weak and languid when the domach is difcrdered, or in the beginning of a fever. On the contrary, the pulfe is often high, and in a violent com¬ motion, when one has been expofed to the fun, or comes out of a bath, or from ufing exercife ; or when one is under the influence of anger, fear, or any other paflion. Beddes, the pulfe is eafily changed by the arrival of the phyfician, in confequence of the patient’s anxiety to know what judgement he will pafs upon his cafe. Io prevent this, the phyfician mud not feel the patient’s pulfe on his fird arrival: he mud fird fit down by him, affume a cheerful air, inform himfelf of his con- /I EDICT N E. Hiftory. dition ; and if he is under any dread, endeavour to re-Cdfus, &c. move it by encouraging difcourfe j after which he may "•“'"v examine the beating of the artery. This neverthelefs does not hinder us from concluding, that if the fight of the phyfician alone can produce fo remarkable a change in the pulfe, a thoufand other caules may pro¬ duce the fame effect.” But although Celfus thought for himfelf, and in not a few particulars differed from his predeceffors, yet in his writings, which are not only1 dill preferved, but have gone through almod innu¬ merable editions, we have a compendious view of the praflice of almoit all his predeceffors : and he treats of the healing art in all its branches, whether per¬ formed mann, viciu, vel medicamentis. His writings, therefore, will naturally be confulted by every one who wilhes either to become acquainted with the practice of the ancients prior to the fall of the Roman empire, or to read medical Latin in its greateft pu- rity- . . 41 About the 13 id year after Chrid, in the reign of Galen. the emperor Adrian, lived the celebrated Galen, a na¬ tive of Pergamus, whofe name makes fuch a confpicu- ous figure in the hidory of phyfic. At this time the dogmatic, empiric, methodic, and other fe£ts, had each their abettors. The methodics were held in great edeem, and looked upon to be fuperior to the dogmatics, who were drangely divided among them¬ felves, fotne of them following Hippocrates, others Erafidratus, and others Afclepiades. The empirics made the lead condderable figure of any. Galen un¬ dertook the reformation of medicine, and refiored dogmatifm. He feems to have been of that feft which was called eclediic, from their choofing out of different authors ivhat they edeemed good in them, without being particularly attached to any one more than the red. This declaration he indeed lets out with ; but, notwithdanding this, he follows Hippocrates much more than any other, or rather follows nobody elfe but him. Though before his time feveral phyli- cians had commented on the works of Hippocrates, yet Galen pretends that none of them had underdood his meaning. His fird attempt therefore was to explain the works of Hippocrates ; with which view he wrote a great deal, and after this fet about compofing a fy- dem of his own. In one of his books entitled, “ Of the edablidiment of medicine,” he defines the art to be one which teaches to preferve health and cure difeafes. In another book, however, he propoles the following definition : “ Medicine (lays he) is a fcience which teaches what is lound, and what is not fo ; and what is of an indifferent nature, or holds a medium between what is found and what is the reverfe.” Fie affirmed, that there are three things which conditute the object of medicine, and which the phyfician ought to confider as found, as not found, or of a neutral and indifferent nature. Thefe are the body itfelf, the figns, and the caufes. He edeems the human body found, when it is in a good date or habit with regard to the Ample parts of which it is compofed, and when befides there is a jud proportion between the organs formed of thefe Am¬ ple parts. On the contrary, the body is reckoned to be unfound, when it recedes from this date, and the jud proportion above mentioned. It is in a date of neutrality or indifference, when it is in a medium be¬ tween foundnefs and its oppofite date. The falutary Hiftory. M E D X Galen. fignS are fucli as indicate prefent health, and prognofti- Cate that the man rnay remain in that ftate for fome time to come. The infalubrious figns, on the contrary, indicate a prefent diforder, or lay a foundation for ful- pefling the approach of one. The neutral figns, or fuch as are of an indifferent nature, denote neither health-nor indifpofition, either for the prefent, or for the time to come. In like manner he fpeaks of caufes falutary, unfalutary, and indifferent. * Thefe three difpofitions of the human body, that is, foundnefs, its reverfe, and a neutral ftate, comprehend all the differences between health and diforder or in¬ difpofition : and each of thefe three dates or difpo¬ fitions has a certain extent peculiar to itfelf. A found habit of body, according to the definition of it already given, is very rare, and perhaps never to be met with ; but this does not hinder us to fuppofe fuch a model for regulating our judgement with refpeft to different con- fiitutions. On this principle Galen eftablithes eight ether principal conllitutions, all of which differ more or lefs from the perfect model above mentioned. The four firft are fuch as have one of the four qualities of hot, cold, moift, or dry, prevailing in too great a degree •, and accordingly receive their denomination from that quality which prevails over the reft. The four other fpecies of conftitutions receive their deno¬ minations from a combination of the above mentioned ; fo that, according to his definition, there may be a hot and dry, a hot and moift, a cold and moift, and a cold and dry, conftitution. Befides thefe differences, there are certain others which refult from occult and latent caufes, and which, by Galen, are faid to arife from an idiofyncrafy of conftitution. It is owing to this idiofyncrafy that fome have an averfion to one kind of aliment and fome to another •, that fome cannot en¬ dure particular fmells, &c. But though thefe eight laft-mentioned conllitutions fall Ihort of the perfec¬ tion of the firft, it does not thence follow, that thofe to whom they belong are to be claffed among the va¬ letudinary and difeafed. A difeafe only begins when the deviation becomes fo great as to hinder the due adfion of fome parts. Galen deferibes at great length the figns of a good or bad conftitution, as well as thofe of what he calls a neutral habit. Thefe figns are drawn from the origi¬ nal qualities of cold, hot, moift, and dry, and from their juft proportion or difproportion with refpedl to the bulk, figure, and fituation, of the organical parts. With Hippocrates he eftablifties three principles of an animal body \ the parts, the humours, and the fpirits. By the parts he properly meant no more than the fo- lid parts; and thefe he divided into fimilar and orga¬ nical. Like Hippocrates, he alfo acknowledged four humours •, the blood, the phlegm, the yellow bile and black bile. He eftabliihed three different kinds of fpirits; the natural, the vital, and the animal. The firft of thefe are, according to him, nothing elfe but a fubtle vapour arifing from the blood, which draws its origin from the liver, the organ or inftrument of fan- guification. After thefe fpirits are conveyed to the heart, thev, in coyundfion with the air we draw into the lungs, become the matter of the fecond ipecies, that is, of the vital fpirits, which are agai» changed into thofe of the animal kind in the brain. He fuppo- fed that thefe three Ipecies of fpirits ferved as inftru- CINE. ments to three kinds of faculties, which refide in the refpeflive parts where thefe faculties are formed. The natural faculty is the firft of thefe, which he placed in the liver, and imagined to prefide over the nutrition, growth, and generation, of the animal. The vital fa¬ culty he lodged in the heart, and fuppofed that by means of the arteries it communicated warmth and life to all the body. The animal faculty, the nobleft of all the three, and with which the reafoning or go¬ verning faculty was joined, according to him, has its feat in the brain : and, by means of the nerves, dif- tributes a power of' motion and fenfation to all the parts, and prefides over all the other faculties. The original fource or principle of motion in all thefe fa¬ culties, Galen, as well as Hippocrates, defines to be Nature. Upon thefe principles Galen defined a difeafe to be “ fuch a preternatural difpofition or affeiftion of the parts of the body, as primarily, and of itfelf, hinders their natural and proper action.” He eftabliihed three principal kinds of difeafes : the firft relates to the fi- milar parts j the fecond, to the organical j and the third is common to both thefe parts. The firft kind of difeafes confifts in the intemperature of the fimilar parts; and this is divided into an intemperature wh/i- out matter, and an intemperature with matter. The firft difeovers itfelf when a part has more or' lefs heat or cold than it 'ought to have without that change of quality in the pait being fupported and maintained by any matter. Thus, for inifance, a perfon’s head may be overheated and indifpofed by being expofed to the heat of the fun, without that heat being maintained by the continuance or congeftion of any hot humour in the part.. The fecond fort of intemperature is when any part is not only rendered hot or cold, but alio fill¬ ed with a hot or cold humour, which are the caufes of the heat or cold felt in the part. Galen alfo ac- know’tdged a fimple intemperature : that is, when one of the original qualities, fuch as heat or cold, exceeds the natural ftandard alone and feparately ; and a com¬ pound intemperature, when two qualities are joined to¬ gether, fuch as heat and drynefs, or coldnefs and humi¬ dity. He alfo eftablilhed an equal and unequal tem¬ perature. The former is that which is equally in all the body, or in any particular part of it, and which creates no pain, becaufe it is become habitual, fuch as drynefs in the heflic conftitution. The latter is diftin- guifhed from the former, in that it does not equally fubfift in the whole of the body, or in the whole of a part. Of this kind of intemperature we have ex¬ amples in certain fevers, where heat and cold, equally, and almoft at the fame time, attack'the fame part; or in other fevers, which render the furface of the body cold as ice, while the internal parts burn with heat; or laftly, in cafes where the ftomach is cold and the liver hot. The fecond kind of diforders, relating to the orga¬ nical parts, refults from irregularities of thefe parts, with refpeft to the number, bulk, figure, fituation, &c.j as when one has fix fingers, or only four ; when one has any part larger or fmaller than it ought to be, &c. The third kind, which is common both to the fimilar and the organical parts, is a folution of continuity, which hap¬ pens when any fimilar or compound part is cut, bruifed, or corroded. C c 3 Like 204 Galen M E D I L.ii-.e Hippocrates, Galen diftinguifhed difeafes into acute and chronical 5 and, with refpedl to their nature and genius, into benign and malignant} alfo into epi¬ demic, endemic, and fporadic. After having diftinguilhed tiie kinds of difeafes, Ga¬ len comes to explain their caufes 5 which he divides into external and internal. The external caufes of difeafes, according to him, are fix things, which contribute to the prefervation of health when they are well difpofed and properly ufed, but produce a contrary effea when they are imprudently ufed or ill difpofed. Thefe fix things are, the air, aliments and drink, motion and reft, lleeping and watching, retention and excretion, and laftly the paffions. All thefe are called thejOro- eatarBic or beginning caufes, becaufe they put in mo¬ tion the internal caufes ; which are of two kinds, the antecedent and the conjunB. The former is difcover- ed only by reafoning 5 and confifts for the molt part in a peccancy of the humours, either by plentitude orcacochymy, i. e. a bad ftate of them. When the humours are in too large a quantity, it is called a plethora ; but we muft obferve, that this word equally denotes too large a quantity of all the humours to- gt tber, or a redundance of one particular humour which prevails over the reft. According to thefe prin¬ ciples, there may be a fanguine, a bilious, a pituitous, or a melancholy pienitude 1 but there is this difference between the fanguine and the three other plenitudes that the blood, which is the matter of the former, may far fuipafs the reft : whereas, if any of the three laft mentioned ones do fo, the cafe is no longer called pleni¬ tude, but cacochymia ; becaufe thefe humours, abound¬ ing more than they ought, corrupt the blood. The caufes he alfo divides into fuch as are manifeft and evi¬ dent, and fuch as are latent and obfcure. The firft are fuch as fpontaneoufty come under the cognizance of our fenfes when they aft or produce their effeas : the fecond are not of themfelves perceptible, but may be difcovered by reafoning: the third fort, i. e. fuch as he calls occult or concealed, cannot be difcovered at all Among this laft he places the caufe of the hydro¬ phobia. J He next proceeds to confider the fymptoms of dif- ™es- A/ymptom he defines to be “ a preternatural affection depending upon a difeafe, or which follows it as a thadow does a body.” He acknowledged three kmds of fymptoms: the firft and moft confiderable of thefe confifted inthe adion of the parts being injured or hindered ; the fecond in a change of the quality of t ie. parts their adtions in the mean time remaininy; entire : the third related to defefts in point of excre¬ tion and retention. After having treated of fymptoms, Galen treats of the 7%™ Qf difeafes. Thefe are divided into dia- gnojhc and prognojlic. The firft are fo called becaufe they enable us to know difeafes, and diftinguifh them from each other They are of two forts, pathognomonic or adjunB. 1 he firft are peculiar to every difeafe make known its precife fpecies, and always accom¬ pany it, fo that they begin and end with it. The lecond are common to feveral difeafes, and only ferve t® point out the difference between difeafes of the lame fpecies. In a pleurify, for inftance, the patho¬ gnomonic figns are a cough, a difficulty of breathing, a f the and a continued fever j the adjuLft C I N E, Hiftoiy* figns are the various forts of matter expectorated, Oribafius, which is fometimes bloody, fometimes bilious, &c. &c. Ihe diagnoftic figns wrere drawn from the defective ~ J or difordered difpofition of the parts, or from the difeafes themfelves 5 fecondly, from the caufes of dif- eafes ; thirdly, from their fymptoms j and laftly, from the_ particular difpofitions of each body, from things which prove prejudicial and thofe that do fervice, and from epidemical difeafes.—The prognoftic fmns he gathered from the fpecies, virulence, and pecufiar genius of the difeafe : but as we have already fpoken fo largely concerning the prognoftics of Hippocrates, it is fuperfluous to be particular on thofe of Galen.— His method of cure differed little from that of Hip¬ pocrates . but from the Ipecimen already given of Galen’s method of teaching the medical art, it is evi¬ dent that his fyftem was little elfe than a colleaion of fpeculations, diftin£Hons, and reafonings 5 whereas that of Hippocrates was founded immediately upon fads which he had either obferved himfelf, or had learned from the obfervation of others. Ihe fyftem of Galen, however, notwithftanding its defeds and abfurdities, remained almoft uncontradid- ed for a very long period. Indeed it may be conlider- ed a.s having been the prevailing fyftem till the inun¬ dation of the Goths and Vandals put an almoft entire flop to the cultivation of letters in Europe. But du¬ ring the general prevalence of the fyftem of Galen, there appeared fome writers to whom medicine was in¬ debted for improvements, at leaft in certain particulars. Among the moft diftinguifhed of thefe we may men¬ tion Oribafius, ^Etius, Alexander, and Paulas. Oribafius fiouriffied about the year 360, and wasoribliL phyfician to the emperor Julian. He fpeaks very ' fully of the effeds of bleeding by way of fcarification, a thing little taken notice of by former writers ; from his own experience he affures us that he had found it fuccefsful in a fuppreffion of the menfes, defluxions of the eyes, headach, and ftraitnefs of breathing even when the perfon was extremely old. He tells his own cafe particularly, when the plague raged in Alia and he himfelf was taken ill. On the fecond day he fcari- fied his leg, and took away two pounds of blood; by which means he entirely recovered, as did feveral others who ufed it. In this author alfo we find the firft defeription of a furprifing and terrible diftemper, which he termed Xvx.xv6^u7rx, a fpecies of melancholy and madnefs, which he deferibes thus. “ The per- fons affedfed get out of their houfes in the night-time, and in every thing imitate wolves, and wander among the fepulchres of the dead till day-break. You may know them by thefe fymptoms: Their looks are pale 5 their eyes heavy, hollowq dry, without the leaft moif- ture of a tear ; their tongue exceedingly parched and dry, no fpittle in their mouth, extreme third: 5 their legs, from the falls and the bruifes they receive full of incurable fores and ulcers.” JEtim lived very near the end of the fifth, or in the beginning of the fixth century. Many paffages in his writings ferve to fhow us how much the aflual and potential cautery were ufed by the phyficians of that age. In a pally, he fays, that he ffiould not at all hefitate to make an efehar either way, and this in fe¬ veral places one in the nape, where the fpinal mar¬ row takes its rife, two on each fide of it; three or four Hiftory. M E D I Alexander, four on tke top of the head* one juft in the middle, M~nu ' and three others round it. He adds, that in this cafe, if the ulcers continue running a coniiderable time, he fliould not doubt of a perfedf recovery. He is ftiil more particular when he comes to order this applica¬ tion for an inveterate afthma, after all other remedies have been tried in vain. One, he fays, ftiould be made on each ftde near the middle of the joining of the cla¬ vicle, taking care not to touch the wind-pipe : two other little ones are then to be made near the carotids under the chin, one on each fide, fo that the cauftic may penetrate no further than the Ikin ; two others under the breafts, between the third and fourth ribs} and again, two more backwards towards the fifth and fixth ribs. Befides thefe there ought to be one in the middle of the thorax, near the beginning of the xiphoid cartilage, over the orifice of the ftomach 5 one on each fide between the eighth and ninth ribs; and three others in the back, one in the middle, and the two others juft below it, on each fide of the vertebrae. Thofe below the neck ought to be pretty large, not very fu- perficial, not very deep : and all thefe ulcers ftiould be kept open for a very long time. ^Etius takes notice of the wTorms bred in different parts of the body called dracuncuh, which w’ere un¬ known to Galen. He feems alfo to be the firft Greek writer among the Chriftians, who gives us any fpeci- men of medicinal fpells and charms ; fuch as that of. a finger of St Blafius for removing a bone which fticks in the throat, and another in relation to a fiftula. He gives a remedy for the gout, which he calls the grand drier ; the patient is to ufe it for a whole year, and obferve the following diet each month. “ In September, he muft eat and drink milk : In Oflober, he. muft eat garlic j in November, abftain from ba¬ thing ; in December, he muft eat no cabbage j in January, he is to take a glals of pure wine in the morning j in February, to eat no beet; in March, to mix fweet things both in eatables and drinkables; in April, not to eat horfe-radifti, nor in May the fiftt called pohjpus ; in June, he is to drink cold water in a morning j in July, to avoid venery; and laftlv, in Auguft, to eat no mallows.” Hus may fufticiently fhow the quackery of thofe times, and how fuperftition ^ was beginning to mix itfelf with the art. Alexander. Alexander, w'ho flouriftred in the reign of Juftinian, is a more original author than either of the two for¬ mer. He confines himfelf direftly to the defcribing the figns of difeafes, and the methods of cure, with¬ out meddling with anatomy, the materia medica, or forgery, as all the reft did. He employs a whole book in. treating of the gout. One method he takes of relieving this difeafe is by purging ; and in moft of the purges he recommends hermodadlyls, of which he has a great opinion* In a caufus, or burning fever, where the bile is predominant, the matter fit for eva¬ cuation,. and the fever not violent, he prefers purging to bleeding, and fays that he has often ordered purging in acute fevers with forprifing foccefs. In the caufus alfo, if a fyncope happens from crude and redundant humours, he recommends bleeding. In a lyncope fuc- ceeding the foppreflion of any ufoal evacuation, he re¬ commends bleeding, with fridlions. The diagnoftics upon which he founds this pradfice are the following : viz. a face paler and more fwelled than ufoal, a bloated C r N E. * * 205 habit ol body, with a frnall fiuggiih pulfe, having long Arabian intervals between the ftrokes. In tertian, and much Ffoficians-< more in quartan fevers, he recommends vomits above all other remedies, and affirms that by this remedy alone he has cured the moft inveterate quartans. On the bulimus, or canine appetite/ he makes a new ob- fervation, viz. that it is fometimes caufed by worms. He mentions the cafe of a woman who laboured un¬ der this ravenous appetite, and had a perpetual gnaw¬ ing at her ftomach and pain in her head : after taking hiera, foe voided a worm above a dozen of cubits long, and was entirely cured of her complaints.—He is alfo the firft author who takes notice of rhubarb; which he recommends in a weaknefs of the liver and in dyfentery.—Alexander is recommended byDrFreind as one of the bell praftical writers among the ancients, and well w'orthy the perufal of any modern. 45 . Paulus was byrn in the ifiand Atgina, and lived in^>llu^us* the 7th century. He tranfcribes a great deal from Alexander and other phyficians. His defcriptions are fiiort and accurate. He treats particularly of women’s diforders; and feems to be the firft inftance upon re¬ cord of a profeffed man-midvoife, for fo he was called by the Arabians : and accordingly he begins his book wdth the diforders incident to pregnant women. He « treats alio very hilly of forgery ; and gives fome direc¬ tions, according to Dr Freind, not to' be found in the more ancient writers. ^5 After the downfal of the Roman empire, and whenArabi?n the inundation of Goths and Vandals had almoft completely exterminated literature of every kind in .Europe, medicine, though a pradical art, ftiared the fame fate with more abilraft fciences. Learning in general, baniffied from the feat of arms, took refuge among the eaftern nations, where the arts of peace ftill continued to be cultivated. To the Arabian phy¬ ficians, as they have been called, we are indebted both for the prefervation of medical fcience, as it fobfifted among the Greeks and Romans, and likewife for the defcription of fome new difeafes, particularly the Imall- pox. Among the moft eminent of the Arabians, we 4y may mention Rhafes, Avicenna, Albucafis, and Aven-Miafes. zoar. But of their writings it would be tedious, and is unneceffary, to give any particular account.—They W'ere for the moft part, indeed, only copiers of the Greeks. We are, however, indebted to them for fome improvements. . They were the firft who introduced chemical remedies, though of thefe they ufed but few, nor did they make any confiderable progrefs in the chemical art. Anatomy w'as not in the leaft improved by them, nor did forgery receive any advancement till the time of Albucafis, who lived probably in the 12th century. rlhey added a great deal to botany and the materia medica, by the introduction of new drugs, of the aromatic kind efpecially, from the eaft, many of which are of confiderable ufe They alfo found out the way of making fugar ; and by help of that, fyrups 5 which two new materials are of great ufe in mixing up compound medicines. With regard to their practice, in fome few particu¬ lars they deviated from the Greeks. Their purging medicines were much milder than thofe formerly in ule 5 and even when they did prefcribe the old ones, they gave them in a much lefs dole than the Greek and Roman phyficians. I he fame reflection may ue made concerning Arabian Phyucians 48 College of Salernum. 49 Ccnftan- tiae. 60 State of medicine in the 15th and 16th •enturies. 51 Sweating fickneis in ^England. M fi O I cohcernlv;g t’hexr manner of bleeding, which was never to that exeeltive degree praclifed by the Greeks. They cetdated from Hippocrates, however, in one very trivial circumftance, which produced a violent controverfy. The queftion was, Whether blood in a pleurify ought to be drawn from the arm of the affefted fide or the oppofite ? Hippocrates had direfted it to be drawn from the arm of the afiefted fide ; but the Arabians, following fome other ancient phyficians, ordered it to be drawn from the oppofite one. Such was the igno¬ rance of thofe ages, that the univerfity of Salamanca in Spain made a decree, that no one fiiould dare to let blood but in the contrary arm ; and endeavoured to procure an edict from the emperor Charles V. to fecond it ; alleging that the other method was of no lefs per¬ nicious conlequence to medicine, than Luther’s herefy had been to religion. In conlequence of the general deca^ of learning in the weftern parts of the world, the Greek writers were entirely neglefted, becaufe nobody could read the lan¬ guage ; and the Arabians, though principally copiers from them, enjoyed all the reputation that was due to the others. T he Arabian phyfic w'as introduced into Europe very early, with the mod extravagant ap- plaufe : and not only this, but other branches of their learning, came into repute in the weft 5 infomuch that in the nth century, the ftudies of natural philofophy and the liberal arts wrere called the Jhidies of the Sara¬ cens. This wras owing partly to the crufades under¬ taken againft them by the European princes 5 and partly to the fettlement of the Moors in Spain, and the intercourfe they and other Arabians had with the Italians. For, long before the time of the crufades, probably in the middle of the 7th century, there were Hebrew, Arabic, and Latin profeffors of -phyfic fettled at Salernum : which place foon grew into fuch credit, that Charles the Great thought proper to found a college there in the year 802 j the only one at that time in Europe. Conftantine the African flouriftied there towards the latter end of the nth century. He xvas a native of Carthage 3 but travelled into the eaft, and fpent 30 years in Babylon and Bagdad, by which means he became mafter of the oriental languages and learning. He returned to Carthage; but being in¬ formed of an attempt againft his life, made his efcape into Apulia, where he was recommended to Robert Guifcard, created in 1060 duke of that country, who made him his fecretary. He was reputed to be very well verfed in the Greek, as well as in the eaftern tongues 3 and feems to have been the firft who intro¬ duced either the Greek or Arabian phyfic into Italy. His works, however, contain nothing that is new, or material; though he was then accounted a very learned man. _ From this time to the end of the 15th and begin¬ ning of the 16th century, the hiftory of phyfic fur- nifties us with no interefting particulars. This period, however, is famous for the introduflion of chemiftry into medicine, and the defeription of three new dif- tempers, the fvveating ficknefs, the venereal difeafe, ana the feurvy. The fweating ficknefs began in 1485 in the army of Henry VII. upon his landing at Mil- ford-haven, and fpread itlelf at London from the 21ft of September to the end of Oddober, It returned there five times, and always in fiimmerj firft in 149^, then 3 C I N E. Hiftory. in 1506, afterwards in' 1517, when it was fo violent Modems, that it killed many in the fpace of three hours, fo that numbers of the nobility died, and of the commonalty in feveral towns often the one-half perilhed. It ap¬ peared the fourth time in 1528, and then proved mor¬ tal in fix hours 3 many of the courtiers died of it, and Henry VIII. himfelf was in danger. In 1520, and only then, it infefted ^the Netherlands and Germany, in which laft country it did much mifehief. 'The lalt return of it was in 1551, and in Wefiminfter it carried off 120 in a day. Dr Cains deferibes it as a pefiilent contagious fever, of the duration of one natural day 3 the fweat he Reckoned to be only a natural fymptom, or crifis of the diftemper. It firft affedted fome par¬ ticular part, attended with inward heat and burning, unquenchable thirft, reftleffnefs, ficknefs at ftomach, but feldom vomiting, beadach, delirium, then faint- nefs, and exceftive drowfinefs. The pulfe was quick and vehement, and the breath fliort and laborious.— Children, poor and old people, were rarely fubjebt to it. Of others, fcarce any efcapcd the attack, and moft of them died. Even by travelling into France or Flan¬ ders they did not efcape 3 and what is ftill more ftrange, the Scots were faid not to be affe£led 3 abroad the Englilh only were feized, and foreigners in England were free. x'M firft the phyficians were much puzzled how to treat this difeafe. The only cure they ever found, however, was to carry on the fweat for a long time 3 for, if flopped, it was dangerous or fatal. The way, therefore, -was for the patient to lie ftill, and not expofe himfelf to cold. If nature was not ftrong enough to force out the fweat, it was neceffary to af- fift her by art, with clothes, wine, &c. The violence of the diftemper was over in 15 hours 3 but there was no fecurity for the patient till 24 were paffed. In fome ftrong conftitutions there was a neceffity to re¬ peat the fweating, even to j 2 times. The removing out of bed was attended with great danger 3 fome who had not fweated enough fell into very bad fevers.— No flefh meat was to be allowed in all the time of the diftemper 3 nor drink for the firft five hours. In the ft vent h, the difternper increafed 3 in the ninth the de¬ lirium came on, and deep was by all means to be avoid¬ ed. However terrible this diftemper appeared at firft, it feldom proved obftinate, if treated in the above-men¬ tioned manner. ?2 In the beginning of the 16th century, the famous Paracelfus. chemift Paracelfus introduced a new fyftern into me¬ dicine, founded on the principles of chemiftry. The Galenical fyftem had prevailed till his time 5 but the prapHce had greatly degenerated, and was become quite trifling and frivolous. The phyficians in geiaeral rejedt- ed the ufe of opium, mercury, and other efficacious re¬ medies. Paracelfus, who made ufe of thefe, had therefore greatly the advantage over them 3 and now all things relating to medicine were explained on ima¬ ginary chemical principles. It will eafily be conceived that a praclice founded in this manner could be no other than the moft dangerous quackery. At this time, however, it was neceffary ; for now a new dif¬ eafe overran the world, and threatened greater de- ftrudlion than almoft all the old ones put together, both by the violence of its fymptoms, and its baffling the moft powerful remedies at that time known.— This was the venereal difeafe, which is fuppofed to have been •» imported Hiftory. M E D I Modems, imported from the Weft Indies by the companions of ’ v Chriftopher Columbus. Its firft remarkable appear¬ ed ance was at the liege of Naples in 1494, from whence rf^he^ve-'0it was foon after propagated through Europe, Ada, nerealdif- and Africa. The fymptoms with which it made the eafe. attack at that time were exceedingly violent, much more fo than they are at prefent; and confequently were utterly unconquerable by the Galenifts. The quacks and chemids, who boldly ventured on mer¬ cury, though they no doubt deftroyed numbers by their excedive ufe of it, yet ftiowed that a remedy for this terrible diftemper was at laft found out, and that a proper method of treating it might foon be fallen upon. Shortly after, the Weft Indian fpecific, guaia- cum, was difeovered : the materia medica was enriched with that and many other valuable medicines, both from the Eaft and Weft Indies: which contributed confiderably to the improvement of the practice of phyfic. At this period, as fea voyages of confiderable duration were more frequent, the feurvy became a more common diftemper, and -was of ccurfe more ac¬ curately deferibed. But probably, from fuppofed a- nalogy to the contagions which at that time w'ere new in Europe, very erroneous ideas were entertained with regard to its being of an infedh'ous nature : And it is not impoflible, that from its being attended alfo with ulcers, it was on fome occaftons confounded with lyphi- ,, litic complaints. Progrefs of The revival of learning, which now took place medicine in throughout Europe, the appearance of thefe new dif- 4he 17th tempers, and the natural fondnefs of maukind for novelty, contributed greatly to promote the advance¬ ment ot medicine as well as other fciences. While at the fame time, the introdu&ion of the art of print¬ ing rendered the communication of new opinions as well as new pradices fo eafy a matter, that to enume¬ rate even the names of thofe who have been juftly ren¬ dered eminent for medical knowledge would be a very tedious talk. It was not, however, till 1628 that Dr William Harvey of London demonftrated and commu¬ nicated to the public one of the molt important dif- coveries refpe&ing the animal economy, the circula¬ tion of the blood. This difeovery, more effedually than any reafoning, overturned all the fyItems which had fubfifted prior -to that time. It may juftly be rec¬ koned the molt important difeovery that has hitherto been made in the healing art : for there can be no doubt that it puts the explanation of the phenomena of the animal body, both in a ftate of health and dif- eafe, on a more folid and rational footing than for¬ merly. It has not, however, prevented the rife of numerous fanciful and abfurd fyftems. Thefe, though falhionable for a Ihort time, and ftrenuoufly fupported by blind adherents, have yet in no long period fallen into deferved contempt. And notwithftanding the, abilities and induftry of Stahl, Hoffman, Boerhaave, and 18th centuries. 55 IDifcovery ©f the cir- culatisn. C I N E. 207 and Cullen, we may confidently venture to affert that Moderns. no general fyftem has yet been propofed which is not1 v 1 liable to innumerable and unfurmountable objections. Very great progrefs has indeed been made in explain¬ ing the philofophy of the human body, from alcer- taining by decilive experiment the influence of the cir¬ culating, the nervous, and the lymphatic fyftems in the animal economy. But every attempt hitherto made to eftablifh any general theory in medicine, that is to conduCI the cure of every difeafe on a few gene¬ ral principles, has equally deviated from truth with thofe of Hippocrates and Galen ; and has equally tended to miftead thofe who have adopted it. Many fyftems of our own days, fuch for example as that of Brown, though adopted with enthufiafm by the young and inexperienced, have evidently been attended with the moft pernicious confequences in praCtice. Indeed we may with confidence venture to affert, that from the very nature of the fubjeft itfelf, medicine does not admit of fuch fimplicity. No one can deny that the human body confifts of a very great number of diffe¬ rent parts, both folids and liuids. It is, however, equally certain, that each of thefe is from many diffe¬ rent caufes liable to deviations from the found ftate. And although fome {light changes may take place without what can be called a morbid affc&ion, yet we well know, that every change taking place to a certain degree in any one part will neceffarily and unavoidably produce an affeClion of the whole. Hence we may without hefitation venture to affirm, that eve¬ ry general theory which can be propofed, attempting to explain the phenomena, and conduct the cure of all dileafes on a few general principles, though for fome time it may have ftrenuous advocates, will yet in the end be found to be both ill-grounded and per¬ nicious. The art of medicine has been much more ufehilly improved by careful attention to the hiftory, theory, and practice of particular difeafes, and by endeavour¬ ing to afeertain from cautious obfervation the fymp¬ toms by which they are to be diliinguithed, the caufes by which they are induced, and the means by which they are to be prevented, alleviated, or cured. On this footing, therefore, we ftiall endeavour to give a brief account of at leaft the moft important affedions to which the human body is fuhjedcd, delivering what appear to us to be the beft eftabiiftied fads and obfer- vations refpeding each. / ‘ But before entering on the confideration of parti¬ cular difeafes, or what has commonly been ftyted the pradice of medicine, it is neceffary to give a gene¬ ral view of the moft important fundions of the animal body, and of the chief morbid affedions to which they are fubjeded ; a branch which has ufually been named the Theory or Inftitutions of Medicine. Theory of Medicine, or an Account of the principal Funaions of the Animal Body. WHILE the fundions of living animals, but par¬ ticularly of the human ipecies, are very numerous, the accounts given of thefe both in a ftate of health and 4i- feafe are very various. Without, therefore, pretending to enumerate the contradidory opinions of different au¬ thors, we ill all here prefent the reader with a view of this • fubjed, j c. !03 MEDICINE. FimcKons of the Body, . -56 Divifion of the func¬ tions into a- nimal, vital and na¬ tural. .57 . DiftindHon of difeales into Pimple and com¬ pound. 58 Symptoms. 59 Predifpo- nent caufe. fuhjccl, chiefly exlracled from the ConfpeBus Medicince ■ Theoretic# of Dr James Gregory, who has collected from other writers the opinions at preient molt gene¬ rally adopted. In this work, which was firlt publifhed in 1780, and afterwards reprinted under an enlarged form in 1782, Br Gregory introduces his fubjedt by obfer- ’ving, that fome functions of the human body relate to itfelf only, and others to external things. To the latter clafs belong thofe which by phyficians are call¬ ed the animal fu?iBions ; to which are to be referred all our fenfes, as well as the power of voluntary motion, by which we become acquainted with the univerfe, and enjoy this earth. Among the fundtions which relate to the body, fome have been named vital, fuch as the circulation of the blood and refpifation ; be- caufe, without the conftant continuance of thefe life cannot fubfilt; others, intended for repai ing the wafte of the fyilem, have been termed the natural func¬ tions : for by the conllant attrition of the folids and the evaporation of the fluid parts of the body, we fland in need of nourilhment to fupply this wafte j after which the putrid and excrementitious parts muft be thrown out by the proper paffages. The digeftion of the food, fecretion of the humours, and excretion of the putrid parts of the food, are referred to this clafs \ which, though neceflary to life, may yet be interrupted for a confiderable time without dan¬ ger. This divifion of the fundlions into animal, vital, and natural, is of very ancient date, and is perhaps one of the beft that has yet been propofed. A difeafe takes place, when the body has fo far declined from a found ftate, that its fumftions are either quite impeded, or performed with difficulty. A difeafe therefore may happen to any part of the body either folid or fluid, or to any one of the func¬ tions : and thofe may occur either fingly, or feveral of them may be difeafed at the fame time 5 whence the diftin&ion of difeafes into Jimple and compound. We have examples of the moft Ample kinds of difeafes, in the rupture or other injury of any of the corporeal organs, by which means they become lefs fit for performing their offices ; or, though the organs themfelves fhould remain found, if the folids or fluids have degenerated from a healthy ftate 5 or if, having loft their proper qualities, they have acquired others of a different, perhaps of a noxious nature j or laftly, if the moving powers fhall become too wreak or too ftrong, or direft their force in a way contrary to what nature requires. The moft Ample difeafes are either produclive of others, or of fymptoms, by which alone they become known to us. Every thing in which a fick perfon is obferved to differ from one in health is called a fymptom ; and the moft remarkable of thefe fymptoms, w'hich moft conftantly appear, define and conftitute the difeafe. The caufes of difeafes are various ; often obfeure, and fometimes totally unknown. The moft full and perfect proximate caufe is that which, when pre- fent, produces a difeafe, when taken away removes it, and when changed, changes it.—There are alfo remote caules, which phyficians have been accuftomed to divide into the predifponent and exciting ones. The Theory. Caufes of Difeafes. 60 former are thofe which only render the body fit for a difeafe, or w'hich put it into fuch a ftate that it wall readily receive one. The exciting caufe is that which immediately produces the difeafe in a body already dif- pofed to receive it. The predifponent caufe is always inherent in theExeitin body itfelf, though perhaps it originally came from caufe. without j thus heat or cold, a very fparing or a very luxurious diet, and many other particulars, may operate as caufes of predifpofition, inducing plethora, inanition, or the like. But the exciting caufe may either come from within or without. From the combined aflion of the predifponent and exciting caufes comes the proximate caufe, which nei¬ ther of the twm taken fingly is often able to produce.— f1 A body predifpofed to difeafe therefore has already declined fomewhat from a ftate of perfeft health, al¬ though none of its funflions are impeded in fuch a man¬ ner that wre can truly fay the perfon is difeafed. Yet fometimes the predifponent caufe, by continuing long, may arrive at fuch a height, that it alone, without the addition of any exciting caufe, may produce a real dif¬ eafe.—The exciting caufe alfo, though it ihould not be able immediately to bring on a difeafe j yet if it continues long, will by degrees deftroy the ftrongeft conftitution, and render it liable to various difeafes j becaufe it either produces a predifponent caufe, or is converted into it, fo that the fame thing may fometimes be an exciting caufe, fometimes a predifponent one, or rather a caufe of predifpofition ; of which the incle¬ mencies of the wreather, floth, luxury, &c. are ex¬ amples. -A Difeafes, hoxvever, feem to have their origin from Hereditajy the very conftitution of the animal machine j and difeales., hence many difeafes are common to every body wffien a proper exciting caufe occurs, though fome people are much more liable to certain dileafes than others. Some are hereditary 5 for as healthy parents natural¬ ly produce healthy children, fo difeafed parents as naturally produce a difeafed offspring. Some of thefe difeafes appear in the earlieft infancy •, others occur equally at all ages; nor are there wanting fome wdiich lurk unfufpefled even to the lateft old age, at laft breaking out with the utmoft violence. Some di¬ feafes are born with us, even though they have no pro¬ per foundation in our conttitution, as when a foetus re¬ ceives fome hurt by an injury done to the mother; while others, neither born with us nor having any foundation in the conftitution, are fucked in with the nurfe’s milk. Many difeafes accompany the different ftages of life •, and hence fome are proper to infancy, youth, andfrorn old age. Some alfo are proper to each of the fexes : and fex. efpecially the female fex, proceeding, no doubt, from the general cenllitution of the body, but particularly from the ftate of the parts fubfervient to generation. Hence the difeafes peculiar to virgins, to menftruating W'omen, to women with child, to lying-in wromen, to nurfes, and to old women. The climate itfelf, under 64 and every Difeafes vrhieh people live, produces fome difeafes , climate has a tendency to produce particular difeafes,from c^~ either from its excefs of heat or cold, or from the mu-lllate’ lability of the weather. An immenfe number of difeafes alfo may be produced by impure air, or fuch as is load¬ ed with putrid, marffiy, and other noxious vapours. The fame I Theory. M E D I Caufcs of Dfeafei. : Difeafes from acci dents. 66 Difeafes from paf- fions of the v wind. fame tlvnj may happen likewife from corrupted aliment, whether meat or drink 5 though even the beft and moft nutritious aliment will hurt if taken in too great quan¬ tity 5 not to mention poifons, which are endowed with luch pernicious qualities, that even when taken in a very fmall quantity they produce the moft grievous difeafes, or perhaps even death itfelf. Laltly, from innumeiacle accidents and dangers to which mankind are expofed, they frequently come off with broken limbs, wounds, and contufions, fometimes quite incu¬ rable 5 and thefe misfortunes, though proceeding from an external cauie at firft, often terminate in internal difeafes. Hitherto we have mentioned only the dangers which come from without; but thofe are not lefs, nor fewer in number, which come from within. At every breath, man pours forth a deadly poifon both to himfelf and others. Neitner are the effluvia of the lungs alone hurt¬ ful . there flows out from every pore of the body a mofl fubtile and poifonous matter, perhaps of a putref- cent nature, wnich being long accumulated, and not a no wed to diffufe itfelf through the air, infedls the body with melt grievous difeafes ; nor does it flop l.e.e, out produces a contagion which fpreads devafta- non tar and wide among mankind. From too much or too littie exercife of our animal powers alfo no imall danger enfues. By inactivity either of body or iuind, tne vigour of both is impaired 3 nor is the dan¬ ger much lefs from too great employment. By mode- 2 ate ufe, all the faculties of the mind, as well as all the parts of the body, are improved and ftrengthened 3 and here nature has appointed certain limits, fo that exercife can neither be too much neglefted, nor too much increafed, with impunity. Hence thofe who ufe violent exercife, as w’ell as thofe who fpend their time in fioth and idlenefs, are equally liable to difeafes; but eacn to diieafes of a different kind : and hence alfo the l.aa effeCls of too great or too little employment of the mental pow'ers. Befides the dangers aniing from thofe aClions of the bouy and mind which are in our own power, there are ot.ieis ariflng from thofe w'hich are quite involuntary. 1 nus, paffions of the mind, either when carried to too great excefs, or when long continued, equally deftroy tne health ; nay, wall even fometimes bring on hidden death. S.eep alfo, which is of the greatelf fervice in reftoring the exhaufted ftrength of ‘the body, proves noxious either from its too great or too little quantity. In the moft healthy body, alfo, many things always require to be evacuated. The retention of thefe is luitful, as well as too profufe an evacuation, or the ex¬ cretion of thofe things either fpontaneoufly or artifi- aaily which nature direCls to be retained. As the foud parts lometimes become flabby, foft, almoft dif- foived, and unfit for their proper offices 3 fo the fluids are fometimes infpiffated, and formed even into the hardeft folid maffes. Hence impeded aClions of the oigans, vehement pain, various and grievous difeafes. ^alliy, fome animals are to be reckoned among the cau.es of difeafes : fuch particularly, as fupport their life at the expence of others : and thefe either invade vis 10m without,, or take up their refidence within tne body, gnawing the bowels while the perfon is yet alive not only with great danger and diftrefs Vol. XIII. Part I. CINE. . 2O0 to the patient, but lometimes even producing death Animal itfelf. ° Solids. Man, however, is not left w ithout defence againft' ^ fo many and fo great dangers. The human body is pof- Ffr mldica- felled of a moft wonderful power, by w'bich it preferves^fr itfelf from difeafes, keeps off many, and in a very fhorH"^- time cures fome already begun, while others are by the fame means more flowly brought to a happy con- clulion. This power, called the autocrateia, or vis mc- dicatrix natures, is w^ell knowm both to phyficians and philofophers. This alone is often fufficient for curing many difeafes, and is of fervice in all. Nay, even the beft medicines operate only by exciting and properly direding this force 3 for no medicine will aft on a dead caicale. But though phylicians juftly put confidence in this power, and though it generally cures difeafes of a flighter nature, it is not to be thought that thofe of the more grievous kind are to be left to the unaflifted efforts of the vis mcdicatrix. Phyficians therefore have a twofold error to avoid, either defpifing the powers of nature too much, or putting too great con¬ fidence in them 3 becaufe in many difeafes thefe ef¬ forts are either too feeble or too violent, infomuch that fometimes they are more to be dreaded than even the difeafe itfelf. So far therefore is it from being the duty of a phyfician always to follow the footfteps of nature, that it is often neceffary for him to take a di- retf ly contrary courfe, and oppofe her efforts with all his might. ^ After a general view of the funaions of the ani-Chemical mal body, of the nature and caufes of difeafe, and ofana*ybisof the powers by which thefe are to be combated, Dr ^ Gregory proceed* to treat of the folid materials ofS which the body is formed. He tells us, that the animal folid, W'hen chemically examined, yields earth, oil, fait, water, phlogifton or inflammable air, and a great quantity of mephitic air. Thefe elements are found in various proportions in the different parts of the body 3 and hence thefe parts are endowed wifh very different mechanical powers, from the hardeft: and moft folid bone to the foft and almoft fluid retina. . Nay, it is principally in this difference of proportion between the quantities of the different elements, that the difference between the folid and fluid parts of the animal confill, the former ha¬ ving much more earth and lefs water in their compo- fition than the latter. The cohefion, he thinks/ is owing to fomething like a chemical attradion of’the elements for one another ; and its caufe is neither to be fought for in the gluten, fixed air, nor earth. This attradhon, however, is not fo ftrong but that even during life the body tends to diflblution 3 and imme¬ diately after death putrefa&ion commences, provided only .there be as much moifture in it as will allow an inteftine motion to go on. 'I he greater the heat, the fooner. does putrefaction take place, and with the great¬ er rapidity does it proceed 5 the mephitic air flies oft', and together with it certain faline particles 5 after which, the cohefion of the body being totally deftroyed the whole falls into a putrid colluvies, of w’hich at length all the volatile parts being diflipated, nothin/ but the earth is left behind. This analyfis, he. owns, is far from being perfeCl, and is by no means in the language of modern chemif- d try. . the animal rfolids. 210 Animal Solids. 69. Qualities of the animal foiicb. 70 Eaufes af- fedting the iplids. M E D I try. But no modern chemift has ever been able, by combining the chemical principles of flelh, to repro¬ duce a compound any thing like what the flelh ori¬ ginally was : yet, however imperfeft the analyfis may be, it ftill has the advantage of fhowing in fome meafure the nature and caufes of certain difeafes, and thus leads phyficians to the knowledge of proper reme¬ dies. The folid parts are fitted for the purpofes of life in three feveral ways ; namely, by their cohefion, their flexibility, and their elafticity, all of which are various in the various parts of the body. Moft of the functions of life confift in various motions. In fome the molt violent and powerful motions are required 5 and there¬ fore fuch a degree of cohefion is neceflary in thefe parts as will be fufficient for allowing them to perform their offices without any danger of laceration. It is therefore neceffary that fome of the folid parts ffiould be more flexible than others j and it is likewife necef¬ fary that thefe parts, along with their flexibility, Ihould have a power of recovering their former fhape and fituation, after the removal of the force by which they were altered. Thefe variations in flexibility, within certain li¬ mits, feldom produce any material confequence with regard to the health : though fometimes, by exceed¬ ing the proper bounds, they may bring on real and very dangerous difeafes ; and this either by an excefs or diminution of their cohefion, flexibility, or elalfictty. By augmenting the cohelion, the elafticity is alfo for the moft part augmented, but the ftexibility diminiihed ; by diminiftiing the cohefion, the flexibility becomes greater, but the elafticity is diminifhed. The caufe of thefe affeftions, though various, may be reduced to the following heads. Either the che¬ mical compofition of the matter itfelf is changed } or, the compolition remaining the fame, the particles of the folid may be fo difpofed, that they ftiall more or lefs ftrongly attradft one another. As to the compofition, almoft all the elements my exift in the body in an un¬ due proportion, and thus each contribute its (hare to the general diforder. But of many of thefe things we know very little ; only it is apparent, that the fluid parts, which confift chiefly of water, and the folid, which are made up of various elements, are often in very different proportions: the more water, the lefs is the cohefion or elaflicity, but the greater the flexibility; and the reverfe happens, if the folid or earthy part pre¬ dominates. The remote caufes of thefe different ftates, whether predifponent or exciting, are very various. In the firft place, idiofyncrafy itfelf, or the innate conftitution of the body, contributes very much to produce the above- mentioned effedls. Some have naturally a much harder and drier temperament of the body than others; men, for inftance, more than women; which can with the utmoft difficulty, indeed fcarce by any means what¬ ever, admit of an alteration. The fame thing takes place at different periods of life; for, from firft to laft, the human body becomes always drier and more rigid. Much alfo depends on the diet made ufe of, which al¬ ways produces a correfponding Mate of the folids in proportion to its being more or lefs watery. Neither are there wanting ftrong reafons for believing, that cot only the habut of the body, but even the difpofi- CINE. Theory. tion of the mind, depends very much on the diet we Animal make ufe of. The good or bad conco61ion of the ali- Solids. ^ ment alfo, the application of the nourifhment prepared from it, and likewife the ftate of the air with regard to moifture or drynefs, affedt the temperament of the body not a little ; and hence thofe who inhabit mountains or dry countries, are very different from the inhabitants of low mariliy places. Laftly, the manner of living contributes fomewhat to this effeft: Exercife preffes out and exhales the moifture of the body, if in too great quantity ; on the contrary, floth and lazinefs produce an effebl diredlly oppolite, and caufe a redundancy of fluid. But, putting the chemical compofition of the folid parts out of the queflion altogether, they may be af- fetled by many other caufes. The condeufation, for inftance, or compreffion of the particles, whether by mechanical caufes or by means of cold or heat, makes a confiderable alteration in the ftrength and elafticity of every folid body. How much mechanical preffure contributes to this may be underftood from the expe¬ riments of Sir Clifton Wintringham: and hence alfo are we to deduce the reafon of many fafts of the high- eft importance in the animal economy ; namely, the growth, ftate, decreafe of the body ; its rigidity daily increafing ; and at laft the unavoidable death incident to old age from a continuance of the fame caufes. Perhaps the different denfity of the folids is in fome meafure owing to Nature herfelf; but it feems to de¬ pend more on the powers of exercife or inaflivity in changing the ftate of the folids, the effefts of which on the body whether good or bad, may hence be ealily underftood. Heat relaxes and expands all bodies, but cold ren¬ ders them more denfe and hard ; the effects of which on the human body are well known to raift people. Though the body is found to preferve a certain de¬ gree of heat almoft in every fituation, yet its furface muft unavoidably be affe&ed by the temperature of the circumambient atmofphere ; and we have not the leaft reafon to doubt that every part of the body may thus feel the effects of that temperature. What a difference is there between one who, expofed to the fouth wind, becomes lazy and languid, fcarce able to drag along his limbs ; and one who feels the force of the cold north wind, which renders the whole body alert, ftrohg, and fit for a£lion ? That thefe various caufes, each of which is capable of affefling the conftitution of the body when taken fing- ly, will produce much greater effefts when combined, is fufficiently evident. The experiments of Bryan Ro- binfon, the effects of the warm bath, and indeed daily ex¬ perience, ffiow it fully. It is not yet certainly known what is the ultimate ftrufture of the minuteft parts of the animal-folid ; whe¬ ther it confifts of ftraight fibres or threads, whofe length is very confiderable in proportion to their breadth, vari- oufly interwoven with one another, as Boerhaave fup- pofes; or of fpiral ones, admirably convoluted and in¬ terwoven with one another, as fome microfcopical ex¬ periments feem to {how ; or whether the cellular tex¬ ture be formed of fibres or lamina, and from thence the greateft part of the body, as the celebrated Haller hath endeavoured to prove. The Theory. M E D I Animal The cellular texture is obferved throughout the Solids, whole body: it furrounds and connects the fibres * themfelves, which are fufficiently apparent in many Cellular of the organs j and {lightly joins the different parts texture. which ought to have any kind of motion upon the neighbouring ones. By a condenfation of this fubftance alfo, the ftrongeft, and what feem the thinneft, mem¬ branes are formed $ the molt fimple of which being accurately examined, difcover the cellular ltru£ture. This cellular fubftance fometimes iucreafes to a furpri- fing degree, and all parts formed of it, membranes, veffels, &c. efpecially by a gentle diftenfion ; for a fudden and violent diftenfion either breaks it altoge¬ ther, or renders it thinner. Sometimes alfo it grows between neighbouring parts, and joins thofe which na- - ture has left free. Preternatural concretions of this kind are often obferved after an inflammation of the lungs or of the abdominal vifcera j and thefe new membranes are found to be truly cellular, 'l ifts fub¬ ftance, when cut, or by any other means divided, grows together of its owm accord •, but if, by reafon of very great inflammation and fuppuration, a large portion of the cellular texture has been deftroyed, it is never again completely renewed, and an ugly fear is left. It is even faid, that this fubftance, in certain cafes, is capable of joining the parts either of the fame body with one another, or of a foreign body with them ; and upon this, if on any foundation, refts the art of Taliacotius and that of tranfplanting teeth, lately fo much talked of. The cellular texture is in fome places merely a kind of net-work, in others filled with fat. Wherever too great bulk or compreflxon would have been inconve¬ nient or dangerous, as in the head, lungs, eyes, eye¬ brow's, penis, ferotum, &c. there it collects no fat, but is lax, and purely reticulated; but between the mufcles of the body and limbs below the {kin, in the abdomen, efpecially in the omentum and about the kidneys, very much fat is fecreted and collected. Animal fat. The fat is principally a pure animal oil, not very dif¬ ferent from the exprefled and mild vegetable ones; du¬ ring life it is fluid, but of different degrees of thick- nefs in different parts of the body. It is fecreted from the blood, and is often fuddenly reabforbed into it, though pure oil is very rarely obferved in the blood. It is indeed very probable, that oil, by digeftion, partly in the primae viae, and partly in the lungs, is converted into gluten, and this again into oil by means of fecretion j though no glandular organs fecreting the fat can be ftiown by anatomifts. It is however, probable, that there are fuch organs ; and that the cellular texture has fome peculiar ftrutfture in thofe parts which are deftined to contain the fat already fecreted, without fuffering it to pafs into other places j for it never paffes into thofe parts which are purely re¬ ticulated, although the cellular texture is eafily per¬ meable by air or water over the whole body from head to foot. The fat is augmented by the ufe of much animal- food, or of any other that is oily and nouriftiing, pro¬ vided the digeftion be good •, by the ufe of ftrong drink, efpecially malt-liquor ; by much reft of body and mind, much fleep and inaftivity, caftration, cold, repeated bloodletting, and in general by whatever di- minifhes the vital and animal powers. Much, howT- ever, depends on the conllitution of the body itfelfj CINE; • 21i nor is is poftible to fatten a human creature at pleafure Animal like an ox. A certain degree of fatnefs, according to So|lds' . the age of the perfon, is a fign and effedt of good health j but w'hen too great, it becomes a difeafe of itielf, and the caufe of other difeafes. It may al¬ ways be very certainly removed by ftrong exercife, little fleep, and a fpare diet. The fat commonly makes up a confiderable part of the bulk of the body, and fometimes by far the greateft part. Its ufe feems to be to make the motion of the body more eafy and free, by leffening the fri&ion of the moving parts, and thus preventing the abralion of the folids, which would other wife happen. It is alio of ufe to hinder the parts from growing together, w'hich fometimes happens, when by an ulcer or any other accident a part of the cellular texture containing the fat is de¬ ftroyed. Befides all this, the fat contributes not a little to the beauty of the body, by filling up the . large interftices between the mufcles, which wrould otherwife give the perfon a deformed and {hocking ap- pearace. It is thought to be nutritious, when ab- forbed from its cells into die blood ; but of this we have no certain proof. It feems to “have fome power of defending from the cold •, at leaft, nature has be¬ llowed it in very great quantity on thote animals which inhabit the colder regions, as whales, bears, &.c. 73 Thofe parts of the body wdfich enjoy fenfe and mo-Vltall0" bility, are called /iw/ig or viia/ folids. They are the hd'J> brain, cerebellum, medulla oblongata, fpinal marrow, the nerves arifing from thefe and diffufed throughout . the whole body, and which are diftributed through the various organs of fenfe and through the mufcles, and laitly the mufcles themfelves. Senfation is much more general than mobility, as being common to all the parts already mentioned. Mobility is proper to the mufeu- lar fibres alone : wherever there is fenfation, therefore, we may believe that there are nerves 5 and wherever there is mobility, we may believe that mufcular fibres exirt. Nay, even mobility itfelf feems to originate from the connexion which the mufcles have with the nerves j for foon after the nerves are comprefl'ed, or ti¬ ed, or cut, the mufcles to which they are diftributed lofe their faculties ; which happens, too, when the brain itfelf, or the origin of the nerves, is affefled. Some reckon that the mufcles are produced from the nerves, and confift of the fame kind of matter. Both in¬ deed have a ftmilar ftrudlure, as being fibrous and of a white colour: for the mrafcles when well freed from the blood, of which they contain a great abundance, are of this colour as well as the nerves; neither can the ner¬ vous fibres by any means be diftinguiflied from the muf¬ cular fibres themfelves. Both have alfo fenfation 5 and both ftimulants and fedatives a£t in the fame manner, whether they be applied to the mufcles themfelves or to the nerves. Thefe circumftances have led Dr Cullen and many others to confider the mufcular fibre as being merely a continuation of nerve. But to this opinion there are many ftrong objections j though there can be no doubt that the contraction of the mufcular fibre is intimately connected with nervous influence. It is difficult for us to difcover the origin of many parts of the body, or to afeertain whether they are produced all at the fdme time or one after another : yet it muft be owned, that many of the mufcular parts are obferved to have attained a remarkable degree of D d 2 . ftrengtlrj M E D I 74 Seme of ifding. 212 ’SSr1 flrenStll» wIlile the brain is ftill foft and almoft fluid j ' 1— ' that the action of thefe mufcular parts is required for the action and growth of the brain. The mufcles are alio of a much firmer contexture than the nerves; and enjoy a power of their own, namely, that of irri- tabdity, of which the nerves never participate. Of ne- ceflity, therefore, either the mufcles mult be conftruc- ted of fome kind of matter different from that of the nerves j or if both are made of the fame materials, iheir organization mufl: be exceedingly different. But if the fubftance of the mufcles and nerves be totally dif¬ ferent, we may eafily be convinced that much of the one is always mixed with the ether 5 for it is impof- fible to prick a mufcle, even with the fmallefl: needle, without wounding or lacerating many nervous fibres at the fame time. Since, therefore, there is fuch a clo.e connexion between the mufcles and nerves both as to their fundions and firu&ure, they are defer- vediy reckoned by phyfiologifls to be parts of the fame genus, called the genus nervofum. or nervous x\ltei treating of fenfe in general, Dr Gregory pro¬ ceeds to confider particularly each of the fenfes°both*ex¬ ternal and internal. He begins with the fenfe of feel¬ ing, as being the moft fimple, and at the fame time in common to every part of the nervous fyftem. In fome places, however,, it is much more acute than in others •, 111 toe ^n> inftance, and efpecially in the points of the fingers. Thefe are reckoned to have nervouspapil- kc, which by. the influx of the blood are fomewhat erec¬ ted in the a&ion of.contaft, in order to give a more acute leniation ; though indeed this opinion fecms rather to be founded on a conje..es tne motion of the blood. In many fevers, ty¬ phus, for inftance, the nervous fyftem itfelf is much fooner and more affeCIed than the blood’s motion; and though the morbid affe&ions of the nervous fyftem are as invifible to the fenfes as the healthy ftate of it, the fymptoms of its injuries plainly fhow that its aCtion, or excitement, as fome call it, is unequal and inordinate. In this w-ay, too, delirium is produced by feveral poifons. 1 he pathology of melancholy and mania is much more obfeure ; as coming on without any fever, or di- fturbance in the blood’s motion. Often alfo they are hereditary, depending on the original ftru&ure of the body, efpecially of the brain ; the fault of which, how¬ ever, cannot be detected by the niceft anatomift. But it is well known, that various difeafes of the brain, obftruclions, tumors, either of the brain itfelf, or of the cranium prefling upon it, any injury done to the head, and, as fome phyficians relate, the hardnefs and orynefs or the brain, and fome peculiar irritations af- feCting the nervous fyftem, are capable of bringing on this malady. And indeed fo great are the irritations affetfing the nervous fyftem in mad people, that they often fleep little or none for a long time. Yet even this fo defective and imperfea knowledge of the dif- Vol. XIII. Part I. MEDICINE. 217 Idiotifm. 85 Melancho¬ ly and ma- &ia. eafes of the brain and nerves, is by no means free from difficulties. For though we know that the brain, or a certain part of it, is hurt, or that it is irritated by a fwelling, or a pointed bone growing into it, nobody can foretel how great, or what may be the nature of the malady from fuch a hurt: for examples are not wanting of people wffio, after lofing a large part of the brain, have recovered and lived a long time ; there are many inftances alfo of perfons who have perceived no. inconvenience from a large portion of that vifeus being corrupted, until at length they have fallen fud- denly down and died in convulfions. g6 Another difeafe of the internal fenfes, quite differ-Idiotifm. cut from thefe, is fatuity or idiotifm. Ihofe are call¬ ed idiots who are deftitute either of judgement or me¬ mory, or elfe have thefe faculties unequal to the com¬ mon offices of life. A weak memory, however, is by no means effential to idiotifm. For there are fome in¬ ftances of idiots who have had very correCl and very extenfive memories. A kind of idiotifm is natural and common to all infants ; neither is it to be accounted a difeafe ; but if it laft beyond the ftate of infancy, it is a real difeafe, and for the moft part incurable. It has the fame caufes with the other difeafes of the in¬ ternal fenfes; although thefe can fcarcely be deteCled by the eye or by the knife of the anatomift. It fre¬ quently accompanies, or is the effeCt of, epilepfy. Hence,, if the epilepfy derives its origin from caufes not feated in the head, as from worms lodging in the in- teftines, the fatuity may be cured by diflodging thefe, and.removing the epilepfy. It is not unlikely that the fatuity of children, and the dotage of old men, may arife from the brain being in the former too foft, and in the latter too hard ; or perhaps in the one cafe not evolved, and in the other fomewhat decayed. 8 The mufcular power may be difeafed in a great num-Diforders ber of ways. The mobility itfelf may be too great •ln muf- but this muft be carefully diftinguiffied from vigour!cuIar By mobility is meant the eafe with which the niufcularP0Wer‘ fibres are excited into contradlion. The vigour, on the other hand, is that power with which the contraftion is performed. They are fometimes joined, but more frequently fep.arate, and for the moft part the exceffes of each are owing to contrary caules gg 1 00 great mobility is when motions are excited by Mobilitv. a very flight ftimulus, or when very violent motions are . produced by the cuftomary ftimulus. A certain habit of body, fometimes hereditary, renders people liable to this difeafe. Women have a greater ftiare of mobility than men. Infants have a great deal of mo¬ bility, often too great ; youth has lefs than infancy, but more than man’s eftate ; though old age has com¬ monly too little. A lazy, fedentary life, full diet, a fuppreffion of the ufual evacuations, fulnefs of the blood-veffels, and fometimes their being fuddenly emptied, laxity, flaccidity of the folids in general, but fometim.es too great a tenfion of the moving fibres, the ufe of diluents, efpecially when warm, or heat applied in any manner, produce too great mobility. And this may be either general or particular, according as the caufes have been applied to the wffiole body, or only to a part of it. 3 . Vig°ur in general is rarely morbid ; although fome-Vigour, times certain mufcular parts appear to have too great ftrenatk in snaffiacs arjd phrenitics, an immenfe c Itrength ftrength. 90 Torpor. 218 M E D I Diforders in ftrength is obferved in all the mufcles, efpecially in thofe the Mufcu- ferve for voluntary motion ; this is not unjuftly kr Pcwer. recj