Sst ot es Bp SSS pope os =a tenets See ; my TRANSACTIONS OF THE ROYAL SOCIETY OF EDINBURGH. Lp, Votre fetter Tih - ED IN oB.U-R GH: PRINTED FOR T. CADELL JUN. AND W: DAVIES (SUCCESSORS TO MR CADELL) IN THE STRAND, LONDON, ae 32 AND J. DICKSON, AND E. BALFOUR, EDINBURGH, ————_—_—=——_—_—_— MDCC XCcVIItI. . « ; : AUR ae fai: A OAR i Gans ae gee.) er eS.) Sagwag sa ava ol 11a. 40%, CRIA 6 2.) es 460 MOd CORATS THT Hi (AAPA AM OF endzaagoue) ee A) i 8) MD eee APOTIAE Ge GAR eOer IG 1 es it Soe ian om TUNED N 2 CE ae ad ~ ‘ “A ] . f y ; ’ i : < i 4 ~ s « a 2 Z a ‘ ¥ wD - CONTENTS FOURTH VOLUME. POAC et AIS TOR Yof- the SOCIETY. Four Theorems for refolving all the Cafes of Plane and Spheri- cal Triangles, by the Reverend Mr Fither, - Page. 4. Differtation on the Philofophy of oe Heat, and Fire, by Dr Hutton, . = - - vB Improvement of the Mercurial bee by Mr Keith, be 17. Experiments on the Effects of Opium on the Living Animal, by Dr Wilfon, = - -- - 18... On the Diurnal Variations of the Barometer, by Dr Balfour of Calcutta, - ~ - 255. On the Sulpburating of ie by Dr Hiaton, - 27. New Obfervatory at Aberdeen, ~ 29. Mak ee N Dat X., Office. Bearers of the Society; - - = ar. List of MEemsBeERs, continued from the third Volume, - Ba, - MEMBERS DECEASED, -. = - 36. Donations, = * = at 38. I. Biographical Account of Lord Abercromby, . (1). NH. Biographical Account of William ret Efq; of Wood- | heufelee, ~ - - (47): Ill. Biogra-- vi 4 EO IN eT ied 6-6, MW. Bzggraphical Account of Mr William Hamilton, late Profeffor of Anatomy and see in the Univerfity of | Glafgow, = = - Page (35). IV. Biographical Account of John Racback, MeuDi = (65). i ae Py od Daeg 3 PAPERS READ BEFORE THE SOCIETY: he PAPERS OF THE PHYSICAL CLASS. I. Account of a Mineral from Strontian, and of a peculiar Species of Earth which it contains. By Thomas Charles Hope, Profeffor * Ae Medicine in the Uni- verfity of Glafgow, Page 3. Il. Obfervations on the Natural Ht sffory of Guiana. By William Lochead, Efq; - = 4I. Ill. On the Principles of the Antecedental Calculus. By , James Glenie, Efq; - = 65. IV. Obfervations on the Trigonometrical Tables of the Brab~ mins. By John Playfair, Profeffor of Mathematics in the Univerfity of Edinburgh, - - 8 3. V. Some Geometrical Porifms, with Examples of their Ap- plication to the Solution of Problems. By Mr Wil- liam Wallace, Afiflant-Teacher of the Mathematics in the Academy of Perth, ~ - 107. V+. On the Latitude and Longitude of Aberdeen. By An- — drew Mackay, LL. D. & F. R. S. Edin. - 135: VI. * Now Joint Profeffor of Chemiftry in the Univerfity of Edinburgh. + By miftake No. V. is repeated. COIN ee. BING Ts, Se VI. dn Account of certain Motions which fmall lighied Wicks acquire, when fwimming on a Bafon of Oil. By Patrick Wilfon, F. R. S. Edin. and Profeffor of Vil Praétical Aftronomy in the Univerfity of Glafgow, Page 163: VII. Account of a Singular Halo of the Moon. By William Hall, Efq; of Whitehall, F. R. S. Edin. “ VII. A New Series for the Rectification of the Ellipfis, with Obfervations on the Evolution of a certain Algebraic Formula. By James Ivory, A. M. as IX. Mineralogical Defcription of the Mountain of Gibral- — tar. By Major Imrie. . - X. Defcription of a Thermometer, which marks the great- eff Degree of Heat and Cold from one Time of Ob- fervation to another.. By Alexander Keith, Big: F.R. S. & F. A. S. Edin. . XI. Defeription of a Barometer which marks the Rife and Fall of the Mercury from two different Times of Ob- Jervation. By Alexander Keith, Efq; F. R. S. & F. A. 5, Edin. : ss = XII.- Meteorological Abfiradt for the Years 1794 1705; 1796, « “ II. PAPERS OF THE LITERARY CLASS. ¥. On the Origin and Principles of Gothic Architecture. By ‘Sir James Hall, Bart. F. R. & A. S. S. Edin. - II. M. CHEVALIER’s Tableau de la Plaine de Troye idlu- Jtrated and confirmed from the Obfervations of fub- Sequent Travellers and others. By Andrew Dalzel, M.A. F.R.S. Edin. Profeffor of Greek in the Univerfity of Edinburgh, - - 174. 177: 1g!. 209. 213. 2g. ADVER- ADVERTISEMENT. Edinburgh, February. 15. 1798. AT a Meeting of the Council of the Royal Society it was,. this day, Re/olved, That a Publication of Papers, communicated to the Society, fhall hereafter be made annually, whether fuch Papers be fufficient to form an entire Volume, or only a Part. of a Volume. TRANS- ffi JG OF Of Ren pS PY a 8 Na Bre a ONS aa a FICHE Third Volume of thefe Tran/actions brings down the _ Hiftory of the Society no farther than the end of the year 1792, though it contains feveral Papers that are of a later date. Phyf. Cl. Dr Monro read a paper, entitled, Obfervations on ae the Mufcles, and particularly on the Effects of the Oblique Fi- ps Monro on d the muicles, an bres.. This paper is inferted in the Third Volume of the Tranf- onthe efiedtsof actions, Part II. No. XIII. p. 250. Hae cli Be Lit. Cl. Mr Stewart read the firft part of his Biographical ‘Jan. aI. Account of the late ADam Smrru, LL. D.. [See Vol. I. Hitt. osehc . ? Smith, P- 55-1] 5 a. 2: Lit, 61793: "Mas. 2ae Eiographical account of Dr Smith. April 3. Mr Playfair on porifms. Mr Fither on *trigonometry. 4 HISTORY of the SOCIETY. Lit. Cl, Mr Stewart read the remainder of the Biographi- cal Account of the late ADAm SmiTH, LL. D. ~ Phyf. Cl. Mr Puayratr read fome Obfervations on Porifms, additional to thofe formerly communicated. Thefe were in- tended to prove, that the propofitions called Porifms do not, as fome mathematicians have alleged, involve in them any viola- tion of the daw of continuity. ‘This fubje@ belongs to the fecond part of the paper, No. VII. of the preceding volume; which fe- cond part has not yet been fully communicated to the Society. Ar this meeting was alfo read a paper on Trigonometry, entitled, An Eafy and General Method for, folving all the Cafes of Plane and Spherical Triangles, by the Reverend WALTER FisHER, minifter at Cranftoun. Ir has long been an object with mathematicians to reduce the rules of trigonometry to the fmalleft number poflible, and to give them the form moft eafily retained in the memory. Lord Napier, whofe difcoveries have fo much facilitated and abrid- ged the labour of numerical calculation, applied himfelf to fim- plify the rules of trigonometry with great fuccefs. He in- vented the rule of the Circular Parts, which gives an apparent unity to theorems, where a real unity is wanting, and is per- haps the moft fortunate attempt toward an artificial memory that has been made by any of the moderns. Various improvements of this rule have fince been pro- pofed. That of M. Pincre# is one of the beft: He retains Lord Napier’s arrangement of the circular parts, and reduces the rules of fpherical trigonometry to four; the two firft of which are NapPrer’s, and the other two a generalization of the common theorems refpeCting the fegments, into which the perpendicular, drawn to any fide of a fpherical triangle, di- vides that fide, and alfo the angle from which it is drawn. See Mem. HISTORY of the SOCIETY. c Mem. Acad. Sciences, 1756, p. 301. ‘There is a fifth rule, it muft be obferved, neceflary for the cafe, when the three fides, or three angles of the triangle, are given, as this cafe refufes to fubmit to NAPIER’s rule in any form of it. © Tue author of the paper, now communicated to the Society, has alfo been fuccefsful in his attempt to render the rules of tri- gonometry eafily retained in the memory. He employs the circular parts, and makes ufe of fewer rules than M. PINGRE, as he has only four, including one for the cafe juft mentioned. Tue theorems Mr FisHER employs are’not new, but they are judicioufly feleéted, and are lefs embarrafling in the ap- plication than either thofe of Napier or PINGRE. They are as ‘little as poflible fubje& to ambiguity ; they do not require the letting fall a perpendicular, and res apply both to plane and {pherical triangles. 1. M denotes the middle part of the triangle, and muft al- ways be affumed betwixt two given parts. It is either a fide or the fupplement of an angle. 2. A and a are the two parts adjacent to the middle, and of a different denomination from it. : 3- O and o denote the two parts oppofite to the adjacent parts, and of the fame denomination with the middle part. 4. lis the laft or moft diftant part, and of a different deno- mination from the middle part. THEOR. 1793- OV, As Dr Hope on a mineral from Strontian. 6 HISTORY of the SOCIETY. TEL foe . ; Pe ae A NE ire ae THEOR. . I, Sin ars : fin peers ; tan Oa 3 tan 258 2 . 2 2 THEOR. II. Tan. Gage ose Os eee 2 2 2 THEOR. i Sin AX fina:1:: —— x fin —— fi m Mr FisHEer recommends, for the purpofe of remembering thefe rules, to commit to memory the words Sao, Satom, Tao, Sarfalm, formed from the abreviation of the terms of the above proportions. It is obvious that thefe four theorems apply to plane triangles, providing that, inftead of the fine or tangent of a fide, you take the fide itfelf. Phyf. Cl. Dr Hore read a paper, giving an account of a Mi- neral from Strontian in Argylefhire, and of a Peculiar Species of Earth contained in it. A fhort abftract of this paper was in- ferted HISTORY of the SOCIETY. : ferted in the laft volume of the Tranfactions. The paper it- felf is the firft of the Phyfical Clafs in this volume. [See Part II. Pte | Phyf. Cl. Dr Monro read a paper, being Experiments on the Nervous Syftem with Opium and Metalline Subftances, with a view of determining the Nature and Effects of Animal Electricity. This paper is publifhed feparately. AT this meeting a paper was alfo communicated from AN- prew Mackay, LL. D. containing an Account of a Series of Obfervations, made by him in the Obfervatory at Aberdeen, for determining the Latitude of that place. Dr Mackay alfo promifed to fend his Obfervations for de- termining the Longitude of the Obfervatory. Thefe were not received till September 1796. Both papers are inferted in this volume, Part II. Hs or Vip. P35. Dr James ANDERSON read a paper, entitled, Obfervations on Peat Mofs. ‘This paper has been publifhed feparately. Phyf. Cl. A paper was read from Mr Locueap, F. R. S. Edin. on the Natural Hiftory of Guiana. It is inferted in this volume, Part II. No. II. p. 41. Phyf. Cl. Dr Wurron read the firft part of a paper, being a Differtation on the Philofophy of Light, Heat, and Fire. This paper, which confifted of feveral parts, was read at the different Meetings of the Society in May, June, July, Auguft, and De- cember, of this year. It has been fince publifhed feparately in one volume 8vo. ‘The following abftra@t contains an account of 1793> Dec. 2. Dr Monro on the nervous fy- ftem. Dr Mackay on the latitude of Aberdeen. = 1794. Jan. 6. Dr Anderfon on peat mois. March 3. Mr Lochead on the natural hi tory of Guiana» April 7, Dr Hutton on the philofophy of light, heat, and fire. 8 HISTORY of the SOCIETY. of the object of the PaePaow: he of fome of the remlodivie employed in it. Dr Hutton was led into the fpeculations contained in the Differtation, by an account of two experiments made by M M. DE SAussuRE and PicreT of Geneva. In the firft of thefe experi- ments, two concave {pecula were placed oppofite and parallel to one another, about twelve feet diftant; and in the focus of one of them was a ball of iron, which had been heated to incandefcence, but allowed to cool till it was no longer luminous, even in the dark, In the focus of the other fpeculum a thermometer was placed, which prefently rofe 8° (of ReEaumur’s fcale) above another that {tood near it, but without the focus. Voyages dans les Alpes, tom. LI. § 926. To account for this phenomenon, M. DE Saussure fuppofes, that there exifts what M. Lambert and fome other philofophers have called radiant heat, and that this heat may be obfcure, and not accompanied with light.. This radiant heat he conceives to be reflected in the fame manner that lights, and by that means to have produced the effect on a thermometer that has juft been defcribed. To this folution Dr Hutton objects, alleging, that it afcribes properties or capacities to heat which are inconfiftent altogether with our notions of it. We know heat only as a quality of bodies, and as acting either in expanding them, when it is call- ed fenfible heat, or in giving them fluidity, when it is termed la- tent heat. We never perceive it as exifting in any other fhape, and therefore, to fuppofe it capable of moving through fpace, independently of body, and of being reflected from a polifhed furface, is to afcribe to heat properties not predicable of it, and quite inconfiftent with its nature, fo far as we have information concerning it. Dr Hutton therefore propofes another explanation. From experiments which he had made, long fince, he had found that the HISTORY of the SOCIETY. 9 the different fpecies of light, when of equal intenfity, as eftima- ted by the eye, are of unequal intenfity when their effect is meafured by the thermometer. In thefe experiments he ren- dered light of different colours equally intenfe to the eye, by increafing or diminifhing the diftance from’ the luminous body, till he could juft read by the light of it. In this way he compared the red light from a fire of coals, with the white light of flame, and found, that while they were equally powerful in affording vifion, the red was incomparably the moft powerful in producing heat. Wuen a body, therefore, is heated to incandefcence, like the iron ball in M. pe Saussure’s experiment, it emits at firft the white or compound light, but as it cools, the light which it emits becomes of the red fpecies, and this is the laft that difap- pears. As the body cools, therefore, the power of its light, to produce heat, increafes in proportion to its power to afford vi- fion, and, therefore, when this laft vanifhes, or ceafes entirely, the other may {till remain in a certain degree. Thus, in the experiment juft defcribed, the iron ball, after it had loft all light to the eye, continued to emit rays of light, which, though they made no impreflion on the organ of vifion, had power to pro- duce heat, and expand the mercury in the thermometer. To the principle, therefore, of the irradiation of obfcure heat, by which M. DE Saussure explains the above phenomenon, Dr Hutron fubftitutes that of ob/cure, or invifible light, which, though it be in appearance more paradoxical, is in reality free from the very {trong objections which prefs againft the other hypothefis. WE mutt not omit to obferve, that M. Picret varied the ex- periment, by placing a matrafs full of boiling water, inftead of the iron ball, in the focus of one of the fpecula. The thermome- ter im the other was ftill affe¢ted, and raifed a little more than a degree. The irradiation of invifible light explains this alfo; for it _is natural to fuppofe, that fuch an irradiation takes place from Vou. EV. b all 10 AYTSTORY of. the. SOCTEMF. all bodies, when above a certain temperature, whether they be im the act of cooling down from incandefcence or not. Tue fame ingenious and accurate obferver, made another change in the circumftances of the experiment, by fmoking the bulb of the thermometer; in confequence of which it was heat- _ ed fooner, and rofe higher than before. This appearance is per- feftly conformable to Dr Hurron’s theory, and feems quite inconfiftent with the other. ‘The black coating of the bulb, by its well known property of abforbing light, tended to accelerate and increafe the effect of the light in heating the thermometer ; but the fame coating being of fmoke, and a very bad con- ductor of heat, muft have oppofed the tranfmiffion of heat through the glafs, and have both retarded and diminithed its effect. | NoTHING, indeed, can be more unlike than the laws which ufually regulate the propagation of light and heat. To move with extreme velocity through the tranfparent fubftance of fome bodies, without heating them in any fenfible degree; to be reflected from the furfaces of others, without entering them at all; and, laftly, to be abforbed by certain bodies, neither pafling through them, nor being reflected from them, thefe are the properties of light. . Heat, on the other hand, is lowly pro- pagated through .all bodies, combines with them intimately in its paflage, and often remains at reft without any motion what- ever. is THE converfion of thefe experiments, which was very inge- nioufly imagined by M. Prictert, led to a fact ftill more fingu- lar and unexpected. Inftead of. the heated body, he placed a matrafs, with ice in the focus of one of the fpecula ; the confe- quence was, that the thermometer in the focus of the other was fenfibly depreffed.. When the cold was increafed, by pouring nitrous acid on the ice, the depreffion of the thermometer was alfo increafed. | To HISTORY of the SOCIETY. it To account for this phenomenon, M. Pictrer tonfiders the thermometer as the body irradiating heat, and the matrafs with the ice as the body which receives it, fo that the experiment 1s the fame with the former, only that the ob{cure heat moves in the contrary direction. MOTTE Tuts explanation, however, is not only liable to the objec- tions that have been made, in general, to the fuppofition of ra- diant and obfcure heat, but it involves in it new difficulties. It implies, for inftance, that the irradiation from the heated body is affected by the ftate of the body which receives that irradia- tion, a principle furely contrary to all analogy. In the irradia- tion of light from a luminous body, nothing fimilar to this is obferved: Whether the light of a candle: fall on a white wall, by which it is reflected, or on a black wall, by which it is ab- forbed, no difference is produced in the quantity of light emit- ed, but it remains in both cafes the fame. In no cafe, it fhould feem, can the quantity of the radiating matter depend on the condition of the recipient bodies ; yet, according to the prece- ding explanation, a body muft be fuppofed to irradiate heat more copioufly when the body on which the irradiation falls is cold than when it is hot; a fuppofition which, being, as has been faid, contrary to analogy, cannot be admitted. THE Doctor next proceeds to offer his own explanation, but with the diffidence that ought to accompany every attempt to account for a phenomenon fo fingular as this, and having fo little analogy with any other fact that relates to the communication of heat. He fuppofes that all bodies irradiate invifible light, when they are of an ordinary temperature, and that this irradiation di- minifhes as their heat diminifhes. The temperature of the thermometer, therefore, in the above experiment, is to be confi- dered, like that of all other bodies, as being maintained by the . action of two caufes, viz. the irradiation of invifible light from the furrrounding bodies, and the communication of heat from — b 2 them 12 HISTORY of the SOCIETY. them by contact. ‘The thermometer, therefore, that is placed in the focus of one of the mirrors, in the above experiment, will be affe@ted by any body whatfoever that is placed in the focus of the other. If that body be cooled below the tempera- ture of the furrounding bodies, lefs light wall be irradiated from it, and refleéted on the thermometer ; the thermometer, there- fore, will be deprefled, till the influx of heat from the air, or other bodies with which it is in contaét, fupply the deficiency. This, however, is thrown out rather as a queftion to be refol- ved by future obfervations, than as a theory already eftablith- ed. The experiments by which it muft ftand or fall are not indeed difficult to be imagined. They are however of extreme delicacy in the performance; and Dr Hurron, who, in differ- ing from the philofophers of Geneva, does eae to the accu- racy and judgment with which they have conduéted their in- quiries, exprelles a with, that the {kill and ingenuity of M. Pic- TLT were again directed toward this object. By the preceding inquiry, Dr Hutron was led to pes the connection between light and fire, as well as between hght and heat ; a fubject which he had formerly treated of in feve- ral papers read before the Royal Society, and afterwards pu- blifhed in his chemical differtations. In thefe he objected to the theory of fire as laid down by M. LavoisizR, and the French chemifts ; acknowledging, at the fame time, that the oxygenating of bodies, by vital air, is to be ranked among the greateft difcoveries in phyfics. It is a difco- very, however, in his opinion, that will by no means explain all the phenomena of burning, by which the exiftence of fome other caufe is clearly pointed out, belide the decompofition of the vital air, and the extrication of the calorique or latent beat, which maintained: the air in a ftate of fluidity. The arguments in fupport of this aflertion, which Dr Hutron, employs here, are founded, on the appearances exhibited by bodies; burning without HISTORY of th SOCIETY. ry without flame, and burning with flame ; that is, on the pheno- mena of combuftion and inflammation. In the combuftion of a piece of charcoal, two diftinct effects may be traced, viz. 1. The oxygenating of the carbonic fub- {ftance, by which fixed air is produced, or carbonic acid in an elaftic ftate; 2. The production of a great quantity of light and heat, while the charcoal is undergoing this change. It is with refpect to this laft part of the procefs only that different opinions are entertained, The phlogiftic theory maintains, that in the oxygenation of the carbonic {fubftance by the vital air, the phlogiftic matter of that fubftance is fet free from combi- nation with it, and in making its efcape exhibits the phenomena of light and heat. Tue antiphlogiftic theory, on the other hand, fuppofes, that, by the decompofition or the condenfation which the vital air undergoes, while it oxygenates the carbonic fubftance, the la- tent heat is transferred to that fubftance, and produces light and fire. | | Now, if it can be fhewn that a burning coal, though placed ya circumftances the moft favourable for its oxygenation, may meverthelefs lofe its heat, and ceafe to burn entirely, it is cer- tain, that it is net alone by the calorigue of the vital air that the fire is fapported. Let then a confolidated piece of charcoal, fuch as the mineral kingdom, in many places, affords in great perfec- tion, be heated to the higheft degree of incandefcence, and expofed, infulated, to the atmofpheric air. Here every condi- tion is united favourable to the oxygenation of the coal, a fuf- ficient quantity of heat, and free accefs of air. If the heat, fup- pled from the decompofition of the vital air, were able to main- tain the heat of the coal, it would continue to burn; but the fat is, that, in fuch a fituation as is here defcribed, the coal dofes, its heat, and at is at laft extinguifhed. It is. plain, there- 14 HISTORY of the SOCLETY. fore, that more heat is loft by communication with the atmof phere than is acquired from the decompofition of the vital air. Now, let the experiment be fo far varied, that the incandef- cent coal, inftead of being fufpended fingly in the atmofphere, is furrounded with other burning coals, that are likewife fufpend- ed, and at fuch a diftance from it as to leave room for the free paflage of a current of air: We know, with certainty, that the central coal will now continue to burn as long as thofe that fur- round it are incandefcent, or emit a certain degree of light. But the circumftances of the coal, in this experiment, are in nothing more favourable to the receiving of heat from the decompofi- tion of the vital air than they were in the former ; for if it be faid, that the air afcends through the greater mafs of burning matter, with more rapidity than before, and fo depofits more of the calorique, it muft be remembered, that it alfo abftraéts more heat from the coals, juft in the fame proportion, or in propor- tion to its rapidity. If then the antiphlogiftic theory be true, the heat acquired by the coal, in the one of thefe experiments, fhould be to the heat abftraéted from it, in the fame ratio that the heat, acquired in the other experiment, is to the heat abftract- -ed. But this does not hold; for the heat acquired, in the firft experiment, is lefs than the heat abftracted, and in the fecond it is not lefs, but is either equal, or greater. Therefore the anti- phlogiftic theory is not true; that is to fay, the theory which derives the fupply of heat, in burning secs Gerke — the calorique of the vital air. We muft therefore admit another caufe, before we can fully explain combuftion ; and this can be no other than the extrica- tion of the phlogiftic matter of the body which is oxygenated, the converfion of that matter into Here, and then the proaee tion of heat. In the phenomena of inflammation, Dr Hutton thinks that the proofs of his theory of fire are no lefs conclufive than in thofe HISTORY of, the SOCIETY. LS thofe of combuftion. . The inconceivable rapidity with which fire is propagated through an inflammable and tranfparent va- pour, is among the moft remarkable.of thofe phenomena, and is certainly inconfiftent with the new theory of burning, and indeed with every other that makes fire to be produced by heat alone. Let.an inflammable fluid. be heated till it boil, and to the top of the column of vapour emitted from it let the {malleft fpark of flame be applied. .The vapour is kindled, and, how- ever high the column, the flame defcends in an inftant to the furface of the inflammable fubftance, and {ets fire to it. Now, it is impoflible that mere, heat could, defcend in this manner, againft the ftream of vapour that is continually rifing from the boiling fluid. ,This is quite contrary to the laws by which it is ufually propagated; and it fhould feem, that the fat can on- ly be accounted for by the celerity with which light moves through tranfparent, bodies, and by fuppofing that the extrica- tion of light is the immediate caufe of burning. THE above inftance is conformable to the experience of every day : Another example, which Dr Hutton gives of the, celerity with. which fire is propagated. through an inflammable and - tranfparent -vapour,;is.more, fingular, and may, perhaps be thought. hypothetical, but. it is at leaft a very happy application of his theory. This example is the meteor, which was feen in 17 8 3, over all Great Britain, and as far fouth as Paris. There can be no doubt, fays he, that this was a {tream of inflammable va- pour which had iffued from the mineral regions: of Iceland, at ‘that time laid wafte by fubterraneous er uptions. "This train of inflammable vapour,,about 60: miles high in the atmofphere, had been kindled at. the north end, probably by an eleétrical {park, and the. ‘inflammation ran: the {pace of feveral hundred. miles, (at leaft_1900), in a minute of time, or little more. | Tuus the inflammation. of a body of pure vapour, in contact with the atmofpheric air, is made with-a rapidity quite incon, fiftent: 16 BESFORYK of me SO0TRTY. fiftent with the propagation of heat. Inftances, ftill more re- markable, of the rapid progrefs of fire, are found in the inflam- mation of fuch vapours, when mixed with that proportion of vital air which is neceflary for decompofing the phlogiftie fub- ftance. ) Own the whole, Dr Hutron concludes, that in no cafe is the light which appears in burning, an effect of the heat obtained from the decompofition of vital air, but that it is the extrication of phlogifton, of fixed light, or a certain modification of the fo- Jar fubftance, which had exifted in the inflammable bodies, and had been chemically combined with their elements. It appears alfo, that it is light which is immediately produced in burning, and that it is only mediately that heat is excited: This is true both of combuftible bodies which burn in an affociated ftate, and of thofe inflammable fubftances where the emerging light heats both the infammable body, and the contiguous atmofphe- ric fluid. THE Doétor proceeds to explain, more at large, his notions of the folar fubftance, of which he conceives light, heat, phlo- gifton, and electricity, to be fo many different modifications. His notions on this fubject are very peculiar, as he conceives the folar matter to be without gravitation, without inertia, and, it may be added, without extenfion. ‘The nature of this ab- {tract does not admit of entering further on the argument: It is fuffcient to remark, that the theory of seat feems to be arrived at a point where it muft almoft unavoidably ftand ftill, till fome experiments fhall determine how far the gravitation of bodies is affe€ted by the heat, whether fenfible or latent, that is contained in-them. The experiments already made, though ingenioufly contrived, and ably executed, are not fufficient to decide a queftion of fuch extreme delicacy; nor does it feem probable, that, without having recourfe to the pendulum, a fa- tisfatory folution of the difficulty will ever be obtained. Phyf: HISTORY of the SOCIETY. 17 Phyf. Cl. Dr Monro read a paper, concerning the Commu- ‘nication of the Ventricles of the Brain with one another, in Man and Quadrupeds. This paper is publifhed in Dr Monro’s book, entitled, Three Treatifes, &c. Me Keirtu alfo communicated an Improvement of the Mer- curial Level, defcribed in the Second Volume of the Tranfactions of the Society. THIs improvement confifts in a contrivance for avoiding the trouble of pouring the mercury out and into the level, every time it is ufed. Befide the canal of communication at the bot- tom, between the two upright columns of mercuty, on which the flots fwim, (fee Vol. II. Part II. No. III.), there is, in the new conftru€tion of the inftrument, another canal, parallel to the former, cut in the upper part of the wood, which allows the air to circulate freely, according as the mercury below rifés or falls. The whole is made perfectly clofe, fo that no air can get admittance. THE inftrument‘may be carried about in this manner, with the mercury remaining in it; and though by agitation that fluid calcines, and is converted into’a grey powder, this only happens when it has free accefs to vital air ; and as all fuch ac- cefs is here prevented, the mercury will not lofe its metallic luftre. Ff THE level, in this form of it, as it requires no previous ad- yaftment, is very commodious, and, when much accuracy is not required, may be ufed with advantage. Phyf. Cl. Dr ANDERSON read a paper, entitled, Obfervations on Wool-bearing Animals, Phyf. Cl. Mr PLAyFAiR communicated an Abftra@ of a Journal of the Weather, kept at his Houfe in Windmill Street, ‘Vox, IV. c for 1794. Aug. 18, Dr Monro on the communica- tion of the ven- tricles of the brain. Mr Keith on an improvement of the mercurial ~ level. 1795 Jan. 5. Dr Anderfon on wool-bear- ing animals. Feb. 2. Mr Playfair on: the weather of. 1794» 179 5« Feb. 2. Dr Anderfon on the making of indigo. Extract of a letter from W. Hall, Efq; March 2. Dr Wilson on the effects of opium on the living animal. 18 HISTORY of the-SOCIETY. for the year 1794. This abftract, with thofe for 1795 and 1796, make the laft of the Phyfical papers in this volume. Ar this meeting Dr ANDERSON alfo read a paper on the Ma- king of Indigo at Tranquebar, by Dr ANDERsoN of Madras. An extract of a letter from W. Haut, Efq; of Whitehall, Berwickfhire, was read, giving an Account of a Great Degree of Cold which he had obferved on the Evening of the 22d of January, when the Thermometer ftood between 5 and 6 degrees below o of FAHRENHEIT’S {cale. Phy. Gl. Dr ALEXANDER WILSON read the firft part of a pa- per, concerning the Effects of Opium on the Living Animal. This paper has been publifhed feparately: An abftract of it follows. Tue difference in the refults of the experiments that have been made to afcertain the effeéts of opium, and the inconfiftency — of the conclufions deduced from them, led Dr Wixsown to enter on the experimental inveftigation contained in this paper. The firft point which he endeavours to afcertain is, whether opi- um, applied to the internal furface of the heart, is capable of fo affecting its nerves, as to act on thofe of every part of the body, producing the general convulfions obferved on injecting a folution of this drug into the heart or blood-veffels. It “ap- _ pears from his experiments, that the only effects of the applica- tion of opium to the internal furface of the heart, are thofe of interrupting its motion, and deftroying its irritability ; and that when convulfions fucceed, they are owing to the opium being conveyed along the aorta, and immediately applied to the brain. It has alfo been afferted, that opium, applied to diftant parts of the body, is capable of affecting the motion of the heart, through the medium of the nervous fyftem. Injected into the cavity of . . the HISTORY iof the SOCTETY. 19 the abdomen, for inftance, it almoft immediately impairs the _ action of the heart. It is only, however, when applied to an extenfive furface that it has this effect; and if Dr Witson’s obfervations be juft, this effect is not produced through the me- dium of the nervous fyftem; but is the confequence of the opium deftroying the mufcular power, and, confequently, the circulation in thofe veflels to which it is applied; thus fud- denly diminifhing the fupply of blood to the heart, and at the fame time oppofing an additional obftacle to its perfect evacua- tion. The experiments, next related; demon{trate that opium, immediately applied to the brain itfelf, although it excites vio- lent and univerfal convulfions in all the mufcles of voluntary motion, is incapable of affecting at all the contractions of the heart. It even appears, from thefe experiments, that although. opium be applied at the fame time to the brain and fpinal mar- _ row of a frog, in confequence of which, (if the folution employ- ed be ftrong), the animal inftantly expires, as if thunderftruck, the motion of the heart is not in the leaft affected by it. It continues to beat with the fame frequency and force after, as it did before, the application of the opium. We arrive, then, at this conclufion, that opium, applied to a diftant part of the body, does not affect the motion of the heart, through the medium of the nervous fyftem; nor, on the other hand, does opium, ap- plied to the heart, affect any other part of the body, through the fame medium, But the heart is not the only mufcle, which opium, applied to a diftant part, feems incapable of affecting through this medium. Many confiderations render it highly probable, that the fame is true of all the mufcles of involuntary motion, without exception. That it is fo of the mufcular coat _-of the alimentary canal, which, next to the heart, may be con- fidered the chief -of this clafs of mufcles, appears from the ex- periments next related. On comparing the experiments above alluded to, with thofe in which opium thrown into the ftomach C2 and. e 20 HISTORY of the SOCIETY. and inteftines, the cavity of the abdomen, &c. is found to-produce convulfions, it appears probable, that in the latter cafes, as in the former, the convuifions do not proceed from any action of the opium on the nerves of the part to which we apply it, but from its being received into the fanguiferous fyftem, and im- mediately applied to the brain. The experiments which follow, in the treatife, confirm this conjecture. On comparing toge- ther all the experiments there related, and thofe alluded to in the introduction, it appears, that the various effects of opium on living animals may be divided into three claffes. The firft comprehending its action on the nerves of the part to which it is applied, not differing effentially from that of any other local irritation. The fecond comprehending its effe¢éts on the heart and blood-veffels ; that of increafing their a€tion, when applied in a fmall quantity; and that of impairing, or altogether deftroy- ‘ing their power of action, when applied to them more freely. The third comprehending its effects, when immediately applied to the brain; which, when the dofe is moderate, are impaired fenfibility, languor, fleep; when applied more fully, convul- fions and death. In all its effects on the living animal body, opium has much, in common with other fubftances, but at the fame time fomething in each peculiar to itfelf. It may appear an omiflion, Dr Wison obferves, that he has not ranked among the effects of opium, received into the fyftem, thofe which it feems to produce on the mufcles of voluntary motion. In fome of the foregoing experiments, the irritability of thefe mufcles was found much impaired after death, although the opium was not applied dire@ly to the mufcles themfelves. But it appears, both from an experiment related in the Treatife, and others alluded to, that the impaired irritability of thefe muf- cles is owing, not to any direct action of the opium on them, but to the violent convulfions excited in them, in confequence of the opium being applied to the brain. THE HISTORY of the SOCIETY. on eg Tue dodtrine of the fympathy of the nerves has been fo much employed in accounting for the effects of opium, that Dr Witson judged it proper to make fome obfervations upon it ; in which he endeavours to prove, that no fuch law of the ani- mal ceconomy exifts; and that all the phenomena, which have | been referred to. this fuppofed law, depend on certain changes taking place in the /enforium commune, In an appendix, he relates fome experiments, made with a view to determine the manner in which tobacco a¢ts on living animals. From thefe experiments it appears, that the fymptoms which tobacco produces, when thrown into the heart, are the fame with thofe excited by its immediate application to the brain. That thefe fymptoms, when the tobacco is exhibited in the for- mer way, proceed from no action of the tobacco on-the nerves of the heart, but from its being conveyed along the aorta, and - immediately applied to the brain; fince they do not follow its injection into the heart, when the aorta is previoufly fecured by ligature ; although it was found, that interrupting the circula- tion does not unfit the nervous fyftem from undergoing the change neceffary for the production of fuch fymptoms. It, alfo appears from thefe experiments, that tobacco produces the fame effects, though more flowly, when thrown into the ftomach and inteftines as when thrown into the heart: That in the former cafe, as in the latter, they are ftill to be afcribed to the tobacco being received into the fanguiferous fyftem, and immediately applied to the brain ; and that the effects of this drug, when it acts merely on the nerves of the part to which it is applied, do not effentially differ from thofe of any {trong topical irritation, It may alfo be collected from thefe experiments, that the pree fence of tobacco in the fyftem, like that of opium, only affects the irritability of the mufcles of voluntary motion, when it pro- duces convulfions in them ; 2. ¢. when it is applied in confider- able 1795+ April 6, Mr Playfair on the trigonome- try of the Brah- mins. May 5- Mr Wilfon on motions of wicks in a ba- fon of oil, June rt. Dr Wilfon on the effects of opium on the living animal. Dr Anderfon on making chinam. June 15. Mr Marfhall on the Argonautic expedition, Aug. 3. Mr Keith on different ther- mometeis. Nov. 2. Dr Monro on the internal hy- drocephalus. “ 22 HISTORY of the SOCIETY. able quantity to the brain. It appears, therefore, that the modus operandi of tobacco, on the living animal body, 1s in every in- f{tance analogous to that of opium. Phyf. Cl. Mr PLAyrair read a paper on the Trigonometry of the Brahmins. ‘The paper is inferted in this volume, Part IL. No. IV. p. 83. Phyf. Cl. Mr Pray¥Farik communicated a letter from Mr Profeflor Witson of Glafgow, giving an Account of certain Motions obferved in {mall lighted Wicks, when made to fwim on a Bafon of Oil, or any other Fluid which can maintain Flame. [See this volume, Part II. No. VI. p. 163.] Phyf. Cl. Dr ALEXANDER WILSON read the remaining part of his paper on the Effects of Opium on the Living Animal. Dr James ANDERSON alfo read an Account of the Method of making Chinam at Madras, communicated by Dr ANDERSON of Madras. Lit. Cl. Mr Dauzet read an Effay on the Argonautic Ex- pedition, by the Reverend Mr Esenezer MarsnHatt, Minifter at Cockpen. Phyf. Cl. Mr Ketru read a Defcription of different Ther- ‘mometers, accompanied with figures, by which the Degree of Heat may be recorded for every hour and minute throughout the year. Phy/f. C7, Dr Monro read a paper on thé Internal Hydrocepha- lus. This, with fome other papers, already mentioned, by the fame Author, have been publithed feparately ; and as an account of the HISTORY of the SOCIETY. 23 the difcoveries, which Dr Monro has made in the Structure of the Brain, the Ear, &c. could not be fufficiently underftood without the numerous plates by which they are illuftrated, it is unneceflary to attempt any detail of their contents. Pby/. Cl. A paper, by Dr BALrour of Calcutta, was com- municated, on the Diurnal Variations of the Barometer. Dr Batrour’s Obfervations, on the Diurnal Variations of the Barometer, were made at Calcutta, and communicated to the Afiatic Society in 1794. A copy of them, which he fent to a friend in Edinburgh, was the paper now read in the Royal Society. Tue fituation in which thefe obfervations were made, entitles them to peculiar attention; for it is well known, that, between and near the tropics, the barometer is very fteady, and free from thofe great and fudden changes that take place in higher lati- ‘tudes. It is in fuch fituations, therefore, that the fmaller periodi- cal variations of the barometer, if they exift at all, are likely to be difcovered, as being feparate from thofe accidental irregulari- ties with which they muft be complicated in our northern cli- mates. j Dr Batrovur’s diligence, in obferving the barometer, has al- fo been fingularly great. He impofed on himfelf the tafk of obferving the ftate of that inftrument every half hour, for an entire lunation, from the new moon on the 31{t of March, to that of the 29th of April 1794. THE refult was, the difcovery of a periodical variation in the _barometer, confifting of two ofcillations, which it performs re- gularly every twenty-four hours. 1. ON every day, that Dr Batrour obferved, with fcarce any exception, the barometer conftantly fell between ten at night. 1796. Jan. 4, Dr Balfour on the diurnal va- riations of the barometer. a4 HISTORY of the SOCIETY. night and fix in the morning; and this it did progreflively, without any intermediate rifing but in one inftance, 2, BETWEEN fix and ten in the morning the barometer con- ftantly rofe; it alfo did fo. progreflyvely, and rarely with any intermediate falling. 3. BETWEEN ten in the morning and fix at night the bere meter fell progreflively, without a fingle exception. 4. Lastxy, between fix and ten at night the barometer rofe progreflively, without any intermediate falling, except in one in- Hance. THESE are Dr BALFour’s general conclufions ; and, accord- ingly, on caf{ting an eye over the table into which he has redu- ced his obfervations, one is immediately {truck with the ap- pearance of two maxima, viz. at ten at night and ten in the morning ; and, again, two minima, alfo diametrically oppofite to one another, at fix in the morning and fix at night. THE quantity of thefe diurnal variations is not very confider- able, but fufficient, at the fame time, to leave no doubt of their reality. The difference between the contiguous maximum and ' minimum is fometimes ;'5 of an inch, eotae 4 in general it is lefs than half that quantity. Ir does not appear that the above variations have any rela~ tion to the heat and cold of the atmofphere, or to the changes of the temperature of the mercury in the barometer, though, with refpect to this laft, we are not furnifhed with fufficient information. Tit thefe obfervations are further multiplied and extended, it will be in vain to attempt any explanation of the fads to which they relate. It feems not improbable, however, that they are connected with the reciprocations of the fea arid land winds, during the day and night, or with the heating and cooling of the fuperincumbent atmofphere. It would be of great ufe to have HISTORY of th SOCIETY. 25 have the obfervations repeated at different feafons of the year. An. obferyer equally affiduous with Dr Baxrour will not be eafily found; but it will perhaps be fufficient to obferve the barometer er three hours, and particularly at the ftationary points.. Ir is proper to remark here, that fome obfervations of a fimi- lar fort have been made in Europe; where, though the fituation is far lefs favourable, than in India, for difcovering the true — law of fuch minute variations, refults have been obtained tole- rably confiftent with one another, yet differing confiderably. from thofe that are ftated above. A-sERIEs of fuch obfervations was inftituted by M. PLANER ef Erfort in Germany, and is defcribed in the Ephemerides of the Meteorological Society at Manheim for 1783. Before thefe obfervations, it had been remarked, that when the barometer is. rifing, it ftands lower at, noon than at any other time of the day, and higher.at the fame hour when it is defcending. M. PLANER’s obfervations feem to extend and modify this conclu- fion ; for they make it appear, that between ten and two, both of the day and night, that is, for two hours before, and two hours after the fun is on the meridian, the elevations and depreflions of the mercury are lefs than at. any other time of the day ; and that between fix and ten in the morning, and, again, between fix and ten, at night, thefe elevations and depreffions. are the greateft.. The fame rule feems to be confirmed by the obferva- tions of M. CoTTE.in.France, of which he has given an account in the Journal de Phyfique for 1792 and 1794. THESE laft conclufions feem to indicate fome. periodical re-. tardation of the movement of the mercury in the barometer, whether afcending or defcending; but it is difficult to form, any notion of the force by which fueh an effect can be produced.. Perhaps the only general inference that is yet deducible, frong comparing all the circumftances, is, that certain diurnal va- Vou. IV. ad riations: 1796. Feb. 1. Mr Playfair on the weather of 1795- Feb. 15. Biographical account of Lord Abercromby. March 7. Mr Wallace on geometrical po- rifms. March 21.— Biographical account of Dr Robertfon. April 4. Biographical account of Dr Roebuck. May 2. Extract of 9 letter from W, Hall, Efq; 26 HISTORY of the SOCIETY. riations of the barometer do actually exift; that more infor- mation on the fubject is neceflary before any explanation of them can be attempted ; and that it is in the countries lying near to the equator that we are to look for thefe periodical variations leaft interrupted and obfcured by accidental irregula- rities. * Phyf. Cl. Mr Prayratr read an Account of the Weather for 1795, extracted from his Journal kept for the Society. Lit, Cl. Mr Mackenzie read his Biographical Account of Lord AzercromsBy. [See Hiftory of the Society, Appendix, p- (1)}- | Phyf. Ci. A paper was communicated, containing Certain Geometrical Porifms, with their Application ‘to the Solution of Problems, by Mr Witit1am Wat tace, Affiftant-teacher of the Mathematics in the Academy of Perth. [See this volume, Part II. No. V. p. 107.] ) Lit. Cl. Mr Stewart read the firft part of his peal aaa Account of the late Dr ROBERTSON. Phyf. Cl. A Biographical Account of the late Dr RoEBucK was read, communicated by Mr Profeflor JARDINE of the Uni- verfity of Glafgow. [See Hift. Appen. No. IV. p. (65)]- Phyf. Cl. An Extra& of a Letter from Mr Hatt to Sir JAMEs Hatt, Bart. was read, giving an Account of an Extraordinary Halo of the Moon, obferved on the 18th of February laft. [See this Volume, Part II. No. VIL p. 173.] } Phyf. HISTORY of the SOCIETY. 27 Phyf. Cl. Mr Stewart read a paper by Dr Hutton, viz. An Examination of a New Phenomenon which occurs in the fulphu- rating of Metals, with an Attempt to explain that Phenomenon. AN account that was given, fome time ago, in the Literary Journals, of certain experiments made in Holland on the ful- phurating of metals, gave rife to this communication. Accord- ing to that account, when metallic filings are mixed with ful- phur, and expofed in a clofe veffel to a certain degree of heat, the mafs kindles, and burns not only without vital air, but in any air whatfoever, or even in a vacuum. In the experiment, as thus reprefented, Dr Hutton readily faw a ftrong argument againft the theory which explains the phenomena of fire by the extrication of the calorigue of vital air; and in this light he con- fidered it in the end of the Differtation on the Philofophy of Light, &c. of which an abftract has been already given. Dr Hope ha- ving however fuggefted to him, that, in making the experiment, he had feen reafon to doubt the reality of the inflammation, they agreed to repeat the experiments together. Dr Hutton was then convinced that this fact had been mifreprefented, or rather mif- underftood ; and therefore thought it neceffary, in this paper, to correct the error into which he had been led by that mifre- prefentation, defcribing the real appearances, and endeavouring to explain them on known principles. ‘“ In doing this,” fays he, “T fhall deftroy the argument which the experiment feemed to afford againft the doctrine of calerique, but | fhal!l have no rea- fon to change the conclufion that I formed againft that. doc- trine, founded on facts that are univerfally acknowledged.” Tue fact, as thefe gentleman obferved it, is this: The metal and fulphur being mixed in due proportions,.and expofed to heat in a clofe glafs veffel, the fulphur firft melts, then undergoes a kind of ebullition, emitting vapours which condenfe in the up- per part of the veffel, and are a fublimation of the fulphur. © In d 2 this. 1796. May 9. Dr Hutton on the fulphura- ting of metals. 28 HIS TORT sof the SOOTY this {ftate, and while the heat communicated was {till under that of incandefcence, there appeared in the bottom, or hotteft part of the mafs, an incandefcent f{pot, which increafed in fize. The glafs veflel was now removed from the fire, and carried into a dark room, that the light emitted from it might be the more accurately obferved. There the incandefcence was plainly per- ceived, fpreading from the place where it firft began, and gain- ing ground continually, till the whole became very luminous, The heat, when thus diffufed through the mafs, begins inftantly to diminifh, and the body quickly cools, as a fimilar mafs of any other fubftance would do. Thefe are the appearances obferved in the experiment; and are what Dr Huttow proceeds to ex- plain. . | IT is evident that the incandefcence, which has juft been de- {cribed, is an operation proceeding from the mafs itfelf, and not from the intenfity of the heat communicated to it, for that heat is not. fenfibly incandefcept ; whereas the heat which the mafs acquires, after the veffel is removed from the fire, 1s confider- ably luminous. We have here, therefore, a fpecies of kindling like that of burning bodies; but, at the fame time, diftinctly different from it. In burning, a phlogiftic fubftance is decom- pofed, by means of the oxygenating principle; and the matter of light, which was contained in that fubftance, being fet at liberty, _ is emitted in the form of light, and heats thofe bodies by which it happens to be extinguifhed or abforbed. But, in this experi- ment, though the mafs is a phlogiftic fubftance, there is no de- compofition of the phlogifton, no appearance of inflammation ; fo that its incandefcence proceeds from another caufe than that which operates in burning. On attending to the circumftances, however, we fhall perhaps difcover that the phenomena of this experiment are not anomalous, but follow a rule, exemplified in many initances, though not precifely with the fame appear- ances. THIS HISTORY of the SOCIETY. 29 Turs rule feems to be no other than that which regulates the extrication ef latent heat, when bodies pafs from a fluid to a folid ftate, though this cafe is fomewhat more complicated than ufual, and attended with circumiftances that are yet but imper- feétly underftood. It muft therefore be confidered, whether the fources of latent heat in the bodies, here combined, be fuch as we can reafenably fuppofe adequate to the effect produced. Frrst, then, we have the latent heat of the fulphur, when it is fimply in its melted ftate ; it has then an aqueous or perfect fluidity, to which the quantity of its latent heat neceflarily cor- refponds. But this is not precifely the flate in which the ful- phur combines with the metal; for before that happens, and while the fenfible heat increafes, the fulphur becomes vifcid, and lofes its perfect fluidity. We have nothing with which we can compare this phenomenon, or by which we can eftimate the latent heat now contained in the fulphur. There is how- _ever reafon to think, that this heat is of the fpecies which Dr Hutton, in his Differtations on fubjeéts in Natural Philofophy, diftinguifhes by the name of the latent heat of ductility. The reafon for this fuppofition is, that when the fulphur, in its vifcid ftate, is plunged into cold water, it does not concrete into its ufual, hard, friable, and cryftallized ftru€ture, but is changed into a tranfparent du@tile mafs. This ftate it feems to owe to the la- tent heat contained in it; for after fome hours expofure to cold, | it gradually lofes its ductility, and undergoes another change of ftruéture, fo as to refume its ordinary appearance, as if it had been concreted and cryftallized from the ftate of fimple fluidity. But the fulphur alfo emits another fpecies of heat, on its com- bination with the metallic fubftance. This is what may be called the conftitutional heat of a body, or that by which its volume is preferved in oppofition to any force endeavouring to diminifh » 40 HISTORY of the SOCIETH diminifh it. The volume of the fulphur is obvioufly much diminifhed on its combination with the metal ; and therefore a quantity of its con/litutional heat muft be expelled, correfpond- ing to the condenfation or diminution of bulk which it has un- dergone. This quantity may be very great; but it is what at prefent our fcience has not the proper means of eftimating. ~ Sucw are the fources of heat contained in the fulphur. The metal alfo, by lofing its ductility, may emit a certain quantity of latent heat, and may thus contribute to increafe the fenfible heat of the compound mafs. The quantity of this effect, like the former, it is difficult to eftimate. | THESE, then, are the different f{pecies of latent heat, which may be fuppofed to emerge, and become fenfible, on the com- bination of the fulphur and the metal in the preceding experi- ment, and on the inftantaneous concretion of the compound mafs. The confequence of this muft be, that the mafs already heated, from without, nearly to a red heat, having this addi- tional heat communicated, muft become incandefcent, and emit light. This muft happen, even if the latent heat emerging fhould be but in a very fmall quantity; and thus the leading fact of the incandefcence feems to be fufficiently accounted for. It may alfo be ufeful to remark, that there are other cafes in which incandefcence feems to be produced, on the principle here afligned, though not perhaps in a degree equally remark- able. In the affaying of filver on the teft, when the lead is fufh- ciently feparated, fo as to leave the filver ftill fluid, but in a degree of heat inferior to what is required to melt it, or to preferve its fluidity, the button of filver inftantly concretes, and appears at the fame time much more luminous. Here + there is evidently no caufe that operates, but the latent heat of fluidity, emitted, as on all occafions, when concretion takes place ; HISTORY of the SOCIETY. 31 place; and had the filver been here, in the loweft degree of in- candefcence, or the higheft degree of obfcure heat, the pheno- menon would have been as remarkable as in the fulphurating of metals. On the fame principle it feems to be, that, ina very common, but very inftructive experiment, a bar of cold iron is made in- candefcent, by hammering it with a certain degree of rapidity and force, fo that the condenfation may be fufficiently quick to expel the heat all at the fame time, or nearly fo. In this cafe, it is the latent heat of ductility that is made to appear, as in the congelation of water it is the latent heat of fluidity. Tron alfo furnifhes another example of the fame kind, where the incandefcence is very confpicuous, but where the procefs is not fo fimple as in the former inftances, becaufe a part of the light is probably produced from another caufe. This example is found in the converfion of pig iron into malleable iron by Mr Corte’s procefs, viz. by keeping the iron melted in a re- verbatory furnace, and expofed, by being agitated, to the influ- ence of the atmofphere. When the caft iron comes in this man- ner to its malleable f{tate,it quickly difplays the brighteft incan- defcence poflible, coagulating, at the fame time, from its melted ftate. Now, there can be no doubt that this extreme incandef- cence arifes from the commutation of latent into fenfible heat, and the commutation of that heat again into light, in which {tate it is emitted by the incandefcent body. In this cafe, how- ever, it is probable, that there is alfo light emitted immediately on the principle of burning, and that the iron is in part fcori- fied, by being oxygenated and lofing its phlogifton. But this alfo is in a great meafure owing to the extreme heat produced by the congelation of the iron; for the heat of melted iron is not alone fufficient for that effect. THE theory above laid down will enable us to explain all the different fteps in the complicated procefs of the fulphurating of gz HISTORY of the SOCIETY. of metals. When the mixture of the metal and fulphur is ex- pofed to heat, and the fulphur melted, it is not immediately combined with the metal; for it requires a greater degree of heat, and one which is perhaps nearly that of incipient incandef- cence, to produce the compound fubftance of the fulphurated metal. The moment, however, that this combination is form+ ed, that part of the mafs, in which it began, lofes its fluidity, ~ and is made to concrete, and at the fame time becomes ftrong= ly incandefcent. In this ftate, if the glafs veflel be removed from the fire, the procefs of the combination of the fulphur with the metal will be carried on, as has been defcribed above.. For the firft incandefcent part is that which had been moft im-- mediately expofed to the heat of the burning coals, and had, by that means, acquired the temperature neceflary for the combr- nation of the two fubftances ; but at this time the part imme- diately contiguous to the concreted portion of the mafs is in the next degree of heat; confequently, upon the emerging of the latent heat of the firft portian, this fecond portion, having its heat increafed, is made to combine, and, by its inftant con- folidation, produces incandefcence. This incandefcence of the fecond portion produces a like effect upon the third ; and thus the heat, combination, concretion, and incandefcence,. {pread. quickly through the whole mafs, without any further affiftance from external fire. In all this there is fo great a refemblance to. the phenomena: of burning, that fome attention is neceflary to enable an obfer- ver to diftinguifh the one procefs from the other. WHEN a mafs of charcoal, properly prepared for combutftion,, is kindled in one part by the heat of incandefcence, the oxyge- nation begins, attended with the decompofition of phlogifton, and the emiffion of the fixed light. The neighbouring parts being then heated, by the light emitted from the firft kindled part, are alfo kindled themfelves, and ferve to augment both ! the HISTORY of the SOCIETY. 25 the intenfity of the heat and the extent of the burning. In this manner the parts of the mafs are kindled in fucceflion, until the whole is incandefcent ; it is at the fame time gradually confu- med, the vital air uniting with the carbonic principle, and this laft being deferted by the fixed light of the phlogifton. In the fulphurated mafs, though there be the fame appear- ance of ignition propagated fucceflively from a central point to the adjacent parts, yet it is not real ignition, but fimple in- candefcence, produced from the extrication of latent heat, in the manner already explained. It is diftinguifhed from ignition by this circumftance: that, as foon as the incandefcence has fpread over the whole mafs, there is an end of the generation of heat, and the fulphurated metal cools from its incandefcent ftate, like any other incombuftible body heated to the fame degree. In the whole procefs there is no oxygenation; no production of fixed or carbonic air ; no apparent wafte ; nor any thing emit- ted from the mafs, except the light of incandefcence. Tuus, Dr Hutton concludes, that, in the procefs of the ful- phurating of metals, we perceive the action of the fame laws as in the converfion of water into ice, and muft explain both on the great principle, by the difcovery of which ‘his friend Dr BLAck rendered fo important a fervice, not to chemittry alone, but to many other branches of natural philofophy. HE is aware, however, that an explanation of it will alfo be attempted by fome chemifts, on the principle of the change of the capacity for heat ; an explanation which he confiders as ex- tremely fallacious and unphilofophical. When he applies thefe epithets to the doctrine of the capacities for heat, he does not mean to object to the phrafe, capacity for heat, or to the ap- plication of that phrafe to exprefs a mere matter of fact, viz. the difference of the fpecific heat of bodies, or the unequal quantities of theat contained in different fubftances, when their Vou. IV. e | mafles 26 HISTORY of the SOCIETY mafles and temperatures are equal. But what Dr HutTown calls fallacious and unphilofophical is, the afligning the change in the capacity of a body for heat, as the caufe of the abforp- tion or emiffion of heat, at the moment when that change takes place. This fuppofition is grounded, as he contends, on a falfe view of the facts concerning the tranfition of water from a hard to a fluid ftate, or the contrary. The chemitts, for example, who maintain this doctrine, hold, that when water is cooled down to a certain temperature, it neceflarily freezes and becomes ice, a fubftance that has a much lefs capacity for heat than water has; on which account a certain quantity of the heat contained in the water is expelled, and enters into the fur- rounding bodies... Now in all this it is fuppofed, that water, at a certain temperature, is neceflarily changed. into ice, which is by no means true; becaufe it is well-known, that water may be cooled feveral degrees below what is:called the point of con- gelation without lofing its fluidity. Dr Hurron tells us, that he has found means to cool it no lefs than 30° below that tempe- rature, without its being changed into ice. Though it be true, therefore, that water muft be cooled to a certain temperature before it can freeze, it is not true, converfely, that it does freeze whenever it is cooled to that temperature. It follows, as a ne- ceflary confequence, that fomething elf befide a change of tem- perature is effential to congelation, and is the caufe of that won- derful change which water undergoes in pafling from a fluid to a folid ftate. The feparation of the latent heat feems a caufe more adequate to the effect, and ferves to explain the cooling of. the water below the point of congelation, without the lofs of its fluidity, becaufe this only happens when the efcape of the la- tent heat is prevented. . Tuat the heat, abforbed by the water, is the true caufe of its fluidity, appears from the facility with which this. hypothetis explains HISTORY of the SOCIETY. 2 explains all the other phenomena of congelation. There is, as has juft, been faid, a-certain fixed temperature, at which water and ice are,convertible into one another. At this temperature, however, a mixed body of ice and water may remain for ever without any of the water being congealed, or any of the ice melted ; but let there be added to this'compound mafs a quan~ tity of heat, by communication from a warm body, and there is a certain quantity of the ice melted, while the mafs remains in its former temperature. Now, if we meafure the quantity of the heat, communicated to this compound mafs, without chan- ging its temperature, and alfo the quantity of ice melted, that.is, the quantity of fluidity produced, it will be found that they are in all cafes proportional to one another, and have therefore the relation of caufe and effect. This certainly amounts to no Jefs than a full demonftration, that the heat abforbed, or ren- dered infenfible to the thermometer, is the caufe of fluidity. To fay, that the change of the capacity for heat is the caufe of the abforption of the heat, is, in fact, to affirm, that the fluidity of the water is the caufe of that abforption, and, of confequence, leaves the fluidity as a phenomenon without a caufe: for it has been fhown that mere change of temperature is not the caufe of it. Dr Hurton has been remarkably happy in his explanation of the manner in which heat produces fluidity. Heat, fays he, has two diftinct effects on body: The one of thefe confifts in its power of diftending the fubftance of the body, or increafing its volume, and this is the effect that is meafured diretly by the thermometer: The other effect of heat is to move the par- ticles of hard bodies on their axes, and by this rotatory mo- tion to feparate their poles of attraGtion, which were united in their ftate of hardnefs and folidity. The particles of the body, in confequence of this rotatory motion, are in a ftate ; €52 of 1796. June 20. Biographical account of Tytler, Efq; July 4. Dr Walker’s ftatiftical ac- count of Col- lngton. Nov, 7. Mr Ivory on the rectification of the ellipfis, Dr Mackay’s determination of” the longitude of the Obfervatory. at Aberdeen, 28 || § HISTORY of the SOCIETY. of equilibrium ; they have no difpofition to cohere together, and are ready to obey the impreffion of the fmalleft force. Sucu are the ideas which Dr Hutron had formed on the fulphuration of metals, and the theory by which it muft be ex- plained ; and they are rendered more interefting, by being the Jaft communication made by that ingenious and profound phi- lofopher. Lit. Cl. Mr Mackenzie read a Biographical Account of the late Wittiam TyTLeER, Efq; of Woodhoufelee. [Hiftory, No. II. p. (17)]. Phyf. Cl. Some Paflages from Dr WALKER’S Statiftical Ac- count of the parifh of Collington were read. Phyf. Cl. Mr Playfair communicated an Extract of a Let- ter from James Ivory, A. M. containing a New Series for the- Rectification of the Ellipfis. [See Part I. of this volume, Noi VIN. pi 77] At this Meeting Dr Macxay’s Determination of the Longi- tude of the Obfervatory at Aberdeen was alfo communicated: [Part II. of this volume, No. V. p. 140.] Tae eftablifhment of a New Obfervatory, where there are fo few as in Scotland, is an event of too much importance, ia the literary hiftory of the country, to be pafled over without notice: The eftablifhment of that at Aberdeen ought the more to be re- corded, that it does great honour to the public fpirit and fcien- tific zeal of the Principal and Profeffors of the Marifhall Col- lege, and of the other gentlemen by whofe voluntary fub- fcription it was brought about. From the fuads which their fubfcription afforded, an Obfervatory was built in 1781, on a part of the Caftle Hill, which was given in a prefent to the College HISTORY of th SOCIETY. ~ 2g College by the Magiftrates and Town-Council of Aberdeen. The building confifted of three rooms, two of which, forming the wings, were circular, about 12 feet in diameter, with co- nical roofs. The eaftermoft of thefe was for the quadrant, and had its roof moveable, and furnifhed with flits; the weftern. was the tranfit room ; its roof had flits, but was not moveable ; the room in the middle ferved for the accommodation of the aftronomer. THE inftruments, with which the Obfervatory was furnifh- nifhed, were a tranfit inftrument by RaMsDEN ; a moveable aftronomical quadrant, of 2 foot radius, by MacuLtocu ; an equatorial inftrument by Sisson and RAMSDEN ; an achroma- tic telefcope and a divided object glafs micrometer by, Dot- LOND; an aftronomical clock, with a gridiron pendulum, by Mariorre. To thefe were added an ailiftant clock by Gabby, Aberdeen ; an alarm clock ; a barometer and thermometer, the two laft by Mitier, Edinburgh. Tue tranfit infument, and the equatorial, were prefents from the late Earl of Bure, at that time Chancellor of the Univerfity. They are both inftruments of great value; the tranfit, in particular, is faid to be of fingular excellence, and: _ altogether worthy of the great artift by whom it was conftruét- ed. ; . Tue Obfervatory, however, fuch as it is here defcribed, has been but of fhort continuance. About three years ago bar- racks were built‘on the Caftle Hill, immediately to the north of the Obfervatory ; and.as it appeared to be of confequence, that the ground occupied by the latter fhould belong to the bar- racks, it was purchafed by Government, and the Obfervatory demolifhed. It is to be rebuilt, however, on an improved plan,. and in a fituation where it will be lefs incommoded by the vi- cinity of the town than formerly, and where, it is hoped, the feries 30. HISTORY of the SOCIETY. feries of obfervations may, be continued, which Dr Mackay has begun with fo much diligence and accuracy. | AccorpinG to Dr Mackay, the latitude, from a mean of 64 obfervations of the fun’s meridian altitude, is 57°. 9.1’, or becaufe the fun’s femidiameter, taken from the. Nautical Alma- nac, is about 13” too. great, it is more exactly 57°. 8’. 5947, and this agrees to + of a fecond with the mean of 8 obfervations of the meridian altitudes of fixed ftars. Tue longitude, determined alfo by a mean of feveral obfer- vations, is ob. 8’. 32” of time, or 2°. 8’ weft of Greenwich. HENCE it appears, that the beft maps and charts require fome correction in the pofition they aflign to Aberdeen, and proba- bly to a great part of the eaft coaft of Scotland. AINSLEy’s map places Aberdeen in latitude 57°. 5’. 9’, which is 3’. 50” too far fouth: It is however very exact in the longitude, which it makes 1°. 6’ eaft of Edinburgh; fo that, reckoning the longi- tude of Edinburgh 3°. 14’. 45” weft of Greenwich, as it is near~ ly, there remains 2° 8’. 45° W. for the longitude of Aberdeen. M. pE ta RocHETTE, in a chart of the north fea, conftruct- ed with great fkill and accuracy, lays down Aberdeen in lati- tude 57°. 5, and in longitude 2°. 21. 31” weft from Green- wich ; fo that there is an error of nearly 4’ in the latitude, and 13/ in the longitude. It is likely that the latter affects the pofi- tion of the coaft for a confiderable extent. ieee Phy/. Ci. A Report concerning the Weather in 1796 was Mr Playfair on Communicated by Mr Piayrarr, [See this volume, the laft the weather of 1796. Article of Part II. ~APPEN. ao eect gecrelbans IN. Sin A Dnretd sri Pie OrFricE-BEARERS of.the SocIEeTy. Office-bearersof OrFice-BEARERS eleéted for\ the enfuing Year, at the General the sociey, Meeting held for that Purpofe, 25th November 1793. Prefident. His Grace the Duke of BuccLEUGH. Vice-Prefidents. Lord Dunfinnan. | Right Hon. Henry Dundas. Secretary. Treafurer. Profeffor Yobe Robifon. | Mr Alexander Keith. Phyf. Cl. Counfellors. Ee. Ch Mr Benjamin Bell. Lord Craig. : Mr Greenfield. General Fletcher Campbell. Mr George Ferguffon. Mr Mackenzie. Dr Gregory. _ Lord. Dreghorn. Dr Rutherford: Commiffioner Edgar. Profeflor Stewart. Mr David Hume. OFFICE- 32 HISTORY of the SOCIETY. Office-bearersof _ OrFicE-BEARERS of the SOCIETY. the Society. PuysIcay Crass. Prefidents. Dr Black. { Dr Home. Dr Mutton. | Dr Monro. Secretaries. Profeffor Playfair. | Dr Walker. LitTERARY CLAss. Prefidents. Mr Baron Gordon. | Dr Augh Blair. Sir William Miller. | Dr Adam Ferguffon. Secretaries. Mr Frafer Tytler. | Profeffor Dalzel. Ar the General Meetings in 1794, 1795,.and 1796, the fame office-bearers were eleéted. LIST LIST of Mempers or Fettows of the Royat Society of EDINBURGH, continued from the third Volume. (Hiftory of the Society, Appendix. ] THE following Members were elected at the General Meeting, Jan. 27. 1794. NON-RESIDENT, The Reverend Fobn a adie of Brookhill, county of Cavan, “Ireland. L. The Reverend Dacre Carlyle, A.M. L. James Glenie, E{q; F. R. S. Lond. P, THE following were elected at the General Meeting, Jan. 26. 1795» RESIDENT. The Reverend George Baird, D. D. Principal of the Univerfity of Edinburgh. Robert Hamilton, E{q3 Advocate. The Reverend Thomas Hardy, D. D. Profeflor of Church Hitory in the Univerfity of Edinburgh. Francis Humberfion Mackenzie, E{q; of Seaforth. Alexander Phillip Wilfon, M. D. Phyfician in Edinburgh. Vou. 1V, f NON= Members cho- fen, Jan. 27. 4794- Members cho- en, Jan. 26. 1795+ Members cho- fen, June 27. 1796, 344) TSF ORS of Shee SOC TRI. NON-RESIDENT. Fobn Cooper, M. D. Phyfician at Fochabers. Willam Garfhore, Ef{q; of London. fobn Gillies, LL. D. F. R. S. London, and Hiftoriographer to his Majefty for Scotland. FOREIGN. Fobn Godfrey Smeiffer, A. M. & F. R. S. London. Ga/fper Voght, Efq; of Hamburgh. THE following were elected at the General Meeting, June 27. 1796. | RESIDENT. Lieutenant-Colonel Alexander Dirom, Fo &R..S. London. , F, The Right Honourable Lord Fincafile. P. The Reverend Sir Henry Moncrieff-Wellwood, Bart. D. D. L. Patrick Murray, Eq; of Ochtertyre, Advocate. P. NON-RESIDENT. Andrew Berry, M.D. Madras. P. Sir Heary Englefield, Bart. F. R. S. London. P. Dr freer, Profeflor of Medicine.in the Univerfity of Glafgow. P.. Dr James Gafcoigne, Phyfician at Plymouth. P. Richard Kirwan, Efq; F. R. S. London. P. FOREIGN. Mark Auguftus Pictet, Profeffor of Philofophy in the Academy of Geneva. . P: : M. P. Prevof, Honorary Profeffor in the Academy of Geneva. P. THE APPENDIX. 35 TuE following were elected at the General Meeting, June 26. Members cho. fen, June 26, wee ies RESIDENT. Robert Beatfon, E{q; of Kilrie. P. Dr Andrew Duncan junior. P. NON-RESIDENT. The Reverend Walter Fi/ber, Minifter at Cranftoun. - P. The Rev. George Gleig, LL. D. Epifcopal Minifter at Stirling. Z. Charles Hatchett, Efq; F. R. S. London. _ P. Major James Rennel, F. R. S. Lond. P. FOREIGN. Fobn Fepcot, M. D. F. R. Coll. of Phyficians at Stockholm, and Profeffor of the Practice of Medicine at Upfal. P. f 2 LIST Members decea- .15'T of MEMBERS who have died fince the Publication of the laft Volume. Colonel Edmonjtone of Newton. June 24. 1793. Honourable James Veitch of Elliock, (Lord Elliock), one of the Senators of the College of Juftice. July 1. 1793. Honourable Francis Garden, (Lord Garden/tone), one of the Se- nators of the College of Juftice. July 22. 1793. Abraham Guyot of Neuchatel. May 22. 1794. ohn Roebuck, M.D. July 16. 1794. Reverend Dr Be//, Minifter at Coldftream. Auguft 9. 1794. Right Honourable Lord Daer. Nov. 5. 1794. Charles Scott, M. D. Phyfician in London. Sir William Fones, one of the Judges of the Supreme Court at Bengal, and Prefident of the Afiatic Society. Alexander Gerard, D. D. Profeffor of Divinity, King’s College, Aberdeen. Jan. 22. 1795. Sir Francis Kinloch of Gilmerton. April 16. 1795: Rev. Yobn Main, D. D. Minifter at Newton. May 13. 1795: William Smellie, Printer in Edinburgh. June 24. 1795. _ Adair Crawford, M. D. Phyfician to St Thomas’s Hofpital, Lon- don, and Profeffor of Chemiftry in the Academy at Wool- wich. Auguft 5. 1795. Honourable Alexander Abercromby, (Lord From STRONTIAN. 28 are delicate flender prifms, fometimes two inches long, having a foft filky appearance. If the refrigeration has been very gra- dual, the prifms will be formed lefs delicate, and of a more di- ftinguifhable fhape. All of them are hexagonal, fome having all their fides equal, others having two broad fides, with two in- tervening narrow ones, while another fort is feen with three broad alternating with three narrow fides. At one time they end abruptly, at another an obtufe trihedral pyramid terminates them, and now and then they are feen pointed like a needle. 29. By the facility of cryftallization, and by the peculiar form of the cryftals, this earthy falt may be eafily detected wherever it exifts in folution. For this purpofe, put a few drops on a plate of glafs, and the muriate will foon difcover itfelf by fhooting into its long flender needles, which are often difpofed in a radiated form. 30. Turse cryftals, after they are thoroughly dried, fuffer little change from expofure to air, yet when the atmofphere is greatly loaded with moifture, they are apt to deliquefce. ‘Their folubility in water is great. At temperature 60, one ounce of diftilled water is capable of diffolving one ounce, four drachms and one fcruple. To the fame quantity of diftilled water, kept boiling on a fand bath, I added in fucceffive portions four ounces of the falt, which became fluid, and I imagine I might have added any quantity more with the fame event, as the tem- perature of the folution, when boiling, feems fufficient to ena- ble the water of cryftallization itfelf to diffolve the faline mat- ter. 31. IF into a faturated folution, fome {trong muriatic acid be: thrown, a precipitation inftantly happens. The matter that falls down is the falt in fmall needle form cryftals, and the fe-. paration of them from the water arifes from the force with which the acid attracts the fluid, being greater than that exert-. ed by the falt to retain its folvent. 32; THE i4 ACCOUNT of a MINERAL 32. Tue tafte of the falt 1s peculiar, fharp and penetrating. When urged quickly by heat, the muriate of Strontites under- goes the aqueous fufion, and by lofing the water of cryftalliza- tion, and with it 42 per cent. of its weight, becomes a white powder, which, as foon as the crucible is heated to rednefs, melts. A quantity of this falt was kept in the red heat of a ftrong open fire, occafionally enlivened by bellows, for above an hour. It had been in perfect fufion, yet its acid was not expelled. It could not, however, when contained in a fmall {poon of platina placed upon charcoal, endure, without decom- pofition, the ftronger heat excited by the blowpipe. With Acetous Acid. 33- Orpinary diftilled vinegar diffolves the Strontian fof- fil, after being reduced to a very fine powder, but with no great energy- An effervefcence, as ufual, accompanies the diflolu- tion. The liquid acetite is tranfparent, and without colour. It changes, though flowly, the colour of violet teft papers to a green. By fpontaneous evaporation, it dries up into a friable falt, compofed of minute cryftals. THEsE are perfiftent, though expofed to the atmofphere. They render green the vegetable colours. They feem to be nearly equally foluble in hot and cold water; for a quantity of water, kept in a ftate of ebullition, which diffolved them at the rate of 196 grains fer ounce, depofited no cryftals on cooling. With Oxalic Acid. 34. THE Strontian mineral muft be in fine powder, elfe it will remain untouched by this acid. When finely pulverized fpar is thrown into oxalic acid, an oxalate of little folubility is generated, which falls to the bottom of the vefiel, under the form Fron STRONTIAN. 15 form of a white powder. This acid, poured into Strontitic wa- ter, unites with the earth, and precipitates with it. 35. Tuis is one of the moft infipid, and one of the moft in- foluble of the combinations into which Strontites enters. Ten grains were boiled in four ounces of diftilled water for fome minutes, there remained undiflolved fully nine grains. The clear liquor had the flighteft poffible degree of milkinefs produ- ced in. it, on the addition of fulphuric acid, or of carbonate of. potafs, By heat the oxalic acid is deftroyed, and the earth re-- mains partly pure and partly united to carbonic acid.. Web artaneinvideids 36. Wits this acid the mineral exhibits appearances nearly: fimilar to thofe now defcribed. There is however, for a fhort: period, an extremely feeble effervefcence. Here I may remark, that for the fake of promoting the union of Strontites with: the weaker acids, I frequently employ what I call the artificial’ carbonate of Strontites, by which I mean this earth precipitated from an acid by an effervefcent alkali. On this powder the acid: of tartar acts with vigour. When.dropped into Strontitic wa-. ter, it carries down the Strontites in union with it. 37. THE tartrite is nearly infipid. I boiled ten grains of it: in four ounces of diftilled water; fix grains were diflolved. This folution, after it had ftood fome weeks in a clofe phial, depofited during frofty weather feveral fmall but very regular: cryftals, the form of which isa triangular table, having the: edges and angles fharp and well defined. Thefe cryftals under- go no alteration from expofure to the air. When acted upon by heat, they at firft {well and are puffed up after the manner of. borax, and at length with ignition lofe their acid, which is the: firft change that the powdery tartrite fuffers under. fimilar treat-- ment. With) 16 ACCOUNT of a MINERAL With Fluoric Acid. 38. SCARCELY any perceivable effervefcence happens when Strontian fpar is thrown into acid of fluor. It is brifk if the artificial carbonate be ufed, but little is diffolved, as the fluate falls to the bottom. Fluor acid occafions a milkinefs in Stronti- tic water by the formation of a fluate, which is poflefled of nearly the fame folubility as the preceding. With Phofphoric Acid. 39. Turs acid attacks the fpar, though in a folid form, but the progrefs of the effervefcence and folution is exceffively flow. A bit, weighing two or three grains, was not completely diffol- ved in twenty-four hours, though the difengagement of carbo- nic acid went on without interruption. The folution continues clear as long as the acid is confiderably in excefs; but as foon as the point of faturation approaches, it becomes thick, from the depofition of a white powdery phofphate. When the acid of phofphorus is dropped into Strontitic water, a precipitate ap- pears, which is rediffolved when the acid comes to be redun- dant. The phofphate, if perfeCtly neutral, has little folubility in water. Ten grains of it, treated with four ounces of boil- ing diftilled water, left a refiduum of nine grains. 3 With Succinic Acid. 40. THE acid of amber, diffolved in water, aflaults, but with no remarkable activity, the artificial carbonate of Strontites.. A clear folution refults, which, by {pontaneous evaporation, yields a cryftalline fuccinate, which is perfiftent in the air. 3 With From STRONTIAN. 17 > | With Acid of Arfenic. ai. Tue arfenic acid diffolves with tardinefs fmall but felid pieces of the foffil. With the artificial carbonate the effervef- cence is lively. In either cafe, the compound continues dif- folved till the acid is almoft faturated, when the liquor grows thick, from the depofition of a white powder, which is the ar- fenicate. A precipitate is formed by pouring Strontitic water on acid of arfenic; but agitation makes it difappear. This happens till the acid is nearly faturated ; after which the preci- pitate will not be taken up, unlefs upon the addition of fuch a quantity of acid as fhall make it predominate. The arfenic acid being dropped into Strontitic water, a copious precipitate defcends to the bottom, which vanifhes when the acid comes to prevail. 42. Havine diluted a quantity of this acid with about twice its volume of water, I threw into it the artificial carbonate to nearly perfect faturation. A clear folution refulted, which evaporated on a plate of glafs, gave a gelatinous fubftance, that by longer expofure to the air dried into a white powder. Cry- {talline forms fhowed themfelves on the infide of a glafs, which contained fome of the folution after it had ftood for fome time. It is fomewhat curious, and deferving of notice, that this folu- tion lets fall the greater part of the arfenicate it contains as foon as it is made to boil by the application of heat. Tue arfenicate fully neutralized is only in a fmall degree fo- luble in water ; an ounce of which, when boiling, takes up ra- ther more than.a grain. With Boracic Acid. 43. To the acid of borax diffolved in hot water, I added a _Minute portion of artificial carbonate of Strontites; a flight Vor,lV. ear effervefcence 18 BIC COUNT of a MINERAL effervefcence and folution took place ; and this happened when fimilar fparing quantities were thrown in for two or three times, after which the powder united with gentle effervefcence, and fell to the bottom. I poured Strontitic water into a fimilar folution of the acid; at firft no difturbance of tranfparency was obfervable, but when the point of faturation was not far diftant, a copious precipitate appeared. This I wafhed with cold water, that feems to act little upon it, and diffolved it in boiling, of which it requires about an hundred and thirty times its own weight. The folution changes to a green, the co- lour of paper {tained with the juice of violets. With Carbonic Acid. 44. THE combination of Strontites with carbonic acid we have in the Strontian mineral, the properties of which I have been detailing. The earth, foluble in water, becomes fcarcely fo by uniting with this acid. With an excefs of acid its folu- bility increafes confiderably, as is the cafe with barytes and lime. The folution of Strontites is precipitated by water im- pregnated with carbonic acid, and the precipitate is rediffolved by the addition of more of the fame fluid. 45. STRONTITES, and all its combinations, poflefs a remark- able property, and one which I long confidered as peculiar to them: I allude to the quality of tinging the flame of combu- {tible bodies of a red colour. The muriate has this power in the moft eminent degree. Its effects are well exhibited by put- ting a portion of the falt on the wick of a candle; it caufes the flame to affume a beautiful deep blood-red colour. All the other compounds, and Strontites itfelf, occafion more or lefs of the fame appearance. The nitrate approaches the neareft to the muriate ; and it is in confequence of this property that the de- flagration of this falt with an inflammable fubftance exhibits fo brilliant and vivid a red flame. It isa pretty experiment to ex- tinguifh Fron STRONTIAN. ig tineuifh a candle by means of carbonic acid gas, as it iflues from a brifkly effervefcing folution of the {par in muriatic acid. After the nitrate, comes Strontites in cryftals; the acetite holds the next place. Thofe that follow give but a faint tinge of red. I fhall enumerate them in the order of their power: Tartrite, fulphate, oxalate, fluate, arfenicate, carbonate, phofphate and borate; the effect of the two laft is extremely feeble *. 46. Ir is worthy of remark, that a certain portion of humi- dity is abfolutely requifite to enable thefe fubftances to alter the hue of the flame. By way of illuftration, dry by a gentle heat the moft powerful of them all, the muriate, and by that bring it to the ftate of a dry white powder. In this condition it will not affect the flame; moiften it, and inftantly you reftore its former power. This holds true with regard to all the reft; fo much fo indeed, that thofe which have not much moifture in their compofition will not affect the flame without an addition of humidity. This is the cafe with the fulphate, tartrite, oxa- late, phofphate, arfenicate, borate, fluate, carbonate and cal- cined {par. Nay, itis even true with refpect to the acetite, though in a cryftalline form. | 47. Aut the combinations of Strontites wich different acids, excepting the carbonate, are decompofed by the three alkalis in their ordinary effervefcent ftate, by virtue, in part, of a dou- ble elective attraQion. When a folution of carbonate of po- tafs, for example, is dropped into the muriate, at firft a tranf- parent gelatinous precipitate is formed, which, upon agitation, after further additions of alkali, acquires a white curdy appear- ance. Similar phenomena accompany the precipitations by the carbonates of foda and ammoniat ; no effervefcence attends any of them. ‘The precipitate, when dried, proves to be a white C2 fubtle * The beautiful experiment with the muriate was firft mentioned to me in the 1787, by an ingenious gentleman, Mr Asn, who was then ftudying phytic at Edin- burgh. ~~ we 20 ACCOUNT of a MINERAL. fubtle powder, and is what I have hitherto denominated the ar- tificial carbonate. In diluted muriatic acid, I diffolved 200 grains of Strontian mineral, and then added falt of tartar, which had run per deliquium as long as it occafioned any preci- pitate. By the teft of fulphuric acid, I difcovered that the al- kali had feparated the whole of the earth, which was well walhed, and afterwards dried before a fire, being towards the conclufion of the exficcation brought very near the bars; it weighed 198 grains. This deficit of two grains I afcribe to ac- cidental lofs, as during wafhing, by adhering to the filter, We. ‘The artificial carbonate pofleffes all the chemical qualities of the native, with this difference, that it parts with its acid more readily when urged by heat. 48. Tue pruffiate of potafs and of lime did not difturb the tranfparency of a folution of a pure colourlefs mafs of Stron- tian mineral in nitric acid. Sometimes, however, thefe fub- {tances threw down from folutions in the muriatic acid a fpa~ ring precipitate of a blue colour, which denotes the exiftence of a minute portion of iron in fome fpecimens. The precipitate is moft abundant when a coloured fpar has been employed; whence I| conclude, that the colour which the fpar occafionally exhibits is adventitious, and is owing to the iron it contains. ~ 49. Wir fulphur, Strontites combines into an hepar. Equal weights of calcined Strontian mineral and flowers of fulphur were triturated together, and expofed to heat in a covered cru- cible. The heat was continued till a few minutes after the blue flame had ceafed to appear at the chinks of the cover. The mafs had been in fufion. Being pulverifed, part was thrown into muriatic acid; an effervefcence enfued, and the hepatic odour became offenfive. Boiling water was poured on the remaining portion; a yellow-coloured fluid refulted, which was decompofed by acids, and gave with acetite of lead a very abundant black precipitate. In the humid way likewife a he- par may be formed. On -a mixture of equal parts of flowers of From STRONTIAN. 21 of fulphur and cryftals of Strontites, I poured fome hot wa- ter, which I caufed to boil for fome time. A liquid hepar, of a dark yellowifh brown colour, was the produdt, and fhowed the fame qualities as the preceding. | 50. CrysTats of Strontites were diffolved, but fparingly by’ alcohol.. The tinéture was of a yellow colour, and burned. with a reddifh flame.. 51. Havince detailed all the properties of the Strontian mi- neral, and of its earthy bafe, with which I have made myfelf acquainted, my next object fhall be to confider, and, if poili- ble, to determine, whether this earth be really different and diftinét from all thofe that are already known. There are two kinds to which the Strontitic. bafis bears in its properties no in- confiderable refemblance, I mean barytes and lime; yet it feems- to me to differ as much from both of them as they differ the one from the other. In. external. appearance, it. muft be ac- knowledged, fome fimilarity is obfervable among the native: carbonates of thefe earths. The Strontian foffil refembles moft the barytic fpar. Indeed this is fo much the cafe, that many perfons admitted it into their collections as the. aérated barytes. Nay, a French chemift. of fome note, M. PeLLerizR, informs us, that having analyzed a mafs, which he received from the Honourable Mr.Grevit_e, he did. not publith the refult. for the reafon, ‘‘ qu’elle ne m’avoit fourni rien de particulier *.”’ 52. THESE two productions of nature agree in exceeding other earthy fpars in f{pecific gravity ; in retaining their carbo- nic acid, unlefs when urged by a very intenfe heat; in dif- folving when. cauftic in water; in affording the pure earth. in. cryftals ; in diffolving in acids with nearly fimilar phe- nomena; in forming falts of difficult folubility with feve- ral.of the acids, and cryftallizable ones with the nitric and muriatic. In thefe refpects a ftrong analogy prevails: between them, yet it is but an analogy ; for in the points now’ enumerated,', * Ann, de Chem. t. 10. p. 188. 20 ACCOUNT of a MINERAL enumerated, as well as in others, a confiderable difference aQually prevails. 53- luetr fpecific gravities differ, that of native carbonate of barytes being 4.338, while that of Strontitic fpar goes from 3.650 to 3.726. The laft mentioned parts with its acid fome- what more readily, and without being fufed itfelf, or acting fo powerfully on the clay of the crucible ; and when calcined, it imbibes moifture with much greater avidity, fplitting with more heat and noife. There fubfifts a greater difference be- tween the folubility of pure Strontites in hot and cold water than of barytes * ; moreover, the forms of their cryftals dif- agree widely. Strontites generates with fulphuric acid a lefs ponderous and more foluble earthy falt than barytes. It is true that both barytes and Strontites form cryftallizable falts when combined with nitric or muriatic acids, but the cryftals have no fimilarity either in property or afpect. Thofe, into the com- pofition of which Strontites enters, fuffer changes from expo- fure to the air, which do not happen to the nitrate or muriate of barytes, and they are vaftly more foluble in water. In the figure of the cryftals alfo the difference is very remarkable. A {trong and weighty argument in favour of the diftiné nature of thefe earths is furnifhed by the circumftance, that folutions of Strontites in acids fuffer no decompofition from pruffiate of lime or potafs ; for here I put out of confideration the change that is occafionally produced when the minute portion of iron is prefent; while, as every body knows, a prominent and dif- criminating feature of barytes is its precipitation by either of thefe fubftances. A mark of diftinétion not lefs decided is the quality that Strontites and its compounds poflefs of tinging the flame of combuftible bodies of a red colour; a property that does * T have, fince this paper was read, difcovered that the difference of folubility of barytes in hot and in cold water is fully as remarkable as that of Strontites. This mark of diftinétion confequently mutt be rejected. From STRONTIAN. 23 does not belong to barytes, the muriate of which gives a very faint greenifh hue. To thefe add, what affuredly carries great weight with it, that thefe fubftances do by no means agree in the order of their attractions. On the whole, I think it abun- dantly manifeft, that the foffil from Strontian is not aérated barytes, and that it has not this earth for its bafis. 54. Ir has been above remarked, that this mineral occafionally affumes the appearance of fome forts of calcareous fpar ; andit has likewife been noticed, that fome analogy prevails between the properties of their component earths. In no circumftance does this appear fo ftrongly as in the quality of tinging flame, which I have difcovered to_belong alfo to the compounds of lime, though in a much fmaller degree. The muriate of lime gives the flame of a candle, when applied in the manner for- merly defcribed, a red colour, which is confiderably lefs vivid and brilliant than that produced by muriate of Strontites, and fhort of that occafioned by the nitrate of this fubftance. It is eafy, however, to fhow, that Strontites and lime materially dif- fer. The fpecific gravity of the Strontian far exceeds that of calcareous {par, which is commonly about 2.700. The former retains its carbonic acid much more obftinately in the fire. But the incomparably greater folubility of the pure earth in hot water, and its cryftallizing, are characters of themfelves fuffi- cient to difcriminate Strontites from lime, and I fhall only fur- ther obferve, that Strontites forms a lefs foluble compound with fulphuric acid, yields a cryftallizable nitrate and muriate, and difplays a power of attraction different from lime ; whence I reckon it certain, that the earth of Strontian mineral is not lime. | 55. L Neep not draw a parallel between the appearance and properties of this foflil and any of the other earthy bodies, as . it is not in the moft diftant degree like any of them. 56. Ir perhaps deferves notice, that the mineral I have been treating of, though different from the native carbonates of ba- rytes 24 ACCOUNT of a MINERAL rytes and lime, holds a fort of intermediate fpace, and forms a kind of link between them. To illuftrate what I mean, I may obferve, that in fpecific gravity, fufibility, capability of decom- pofition by heat, and in the folubility of the compounds it forms, it {tands in the middle. Thus, heavier than calcareous and lighter than barytic {par, it is more eafily melted than the one, lefs fo than the other. When fubjecied to heat, it parts with its carbonic acid more readily than barytes, lefs fo than lime. The fulphate, nitrate and muriate of it are all more fo- luble than the fame falts of barytes, and lefs foluble than thofe of lime. In one refpect ‘indeed it exceeds both, and that is, folubility in hot water, which perhaps is fo great as may make fome perfons, over fond of nice diftin¢tions, deny it a piace among the earths altogether *. : 57. Turis kind of intermediate fituation fhall perchance in- duce fome to imagine, that this earth is a peculiar combination of the other two. At firft, I confefs, when this idea fuggefted itfelf to me, I did not deem it improbable ; but now, after full inveftigation, I muft reject the notion. This, I hope, I do with good reafon, fince I have found that, like the acknowledg- ed fimple earths, this fubftance bears repeated folutions, cry- ftallizations and precipitations, without fhowing the {malleft difpofition to a feparation of principles; and fince the means that difunite an artificial mixture of the two earths, fuch as diffolving in muriatic acid and cryftallizing, or precipitating by pruffiate of potafs or lime, have no effect in occafioning a disjunction of its parts. 58. As the earthy bafis of the Strontian fpar poffeffes re- markable qualities that are peculiar to it, and forms with acids combinations unlike thofe generated by the known earths, and differs from all of them in the order of its attraGiions, I can- not hefitate to conclude, that it is an earth /wi generis, a new Bigs: and * Vide note to 53. From STRONTIAN. 25 -and diftin genus. It belongs decidedly to the ancient order of them called alkaline or abforbent, of which the moft abun- dant fpecies, the calcareous earth, has been long known. To my illuftrious mafter in chemiftry, Dr BLack, we are indebted for eftablifhing the diftin@ nature of magnefia. Dr Gaun -and Mr Scuzece have the merit of difcovering barytes. 59. CONSIDERING it as a peculiar earth, I thought it necef- fary to give it aname: I have called it Strontites, from the place where it was found; a mode of derivation, in my opi- nion, fully as proper as from any quality it may poffefs, which isthe prefent fafhion. My reafon is, that I think there is lefs chance of difcovering two new earths in the fame fpot, than of finding two poffeffed of the fame property any where. The denomination, however, is of little moment, provided it be well underftood what it is intended to denote, and there be no room for miftake. 60. To complete the hiftory of Strontites, it remains for me to {tate what I have difcovered refpecting the order of its at- tractions. I fhall begin with pointing out the order in which the principal acids attract it, and then I fhall fhow the place due to its attraction among thofe of other fubftances for acids. 61. SunpuHuric acid attracts Strontites with the greate{t force ; for when added to a folution of the nitrate, muriate, . tartrite, arfenicate, fuccinate, fluate, acetite and borate, it in- {tantly caufes a difturbance of tranfparency, and a white pre- cipitate falls to the bottom. When poured upon the oxalate, which is fcarcely foluble in water, and permitted to remain for fome hours upon it, this acid expels the oxalic, and takes its place. JI may here remark, that the precipitates formed by the falphuric acid do not defcend fo rapidly as the ponderous ful- phate of barytes ; they have oftentimes in their fall more the appearance of fulphate of lime, On this account, Strontites, though a good one, is by no means fo delicate a teft of the pre- fence of this acid as barytes, nor can it be employed altogether Vout. IV. D with 26 ACCOUNT of a MINERAL with the fame advantage in the purification of nitric and mu- riatic acids from the fulphuric. 62. THe acid of fugar, or oxalic acid, follows the fsliphuwvib. This acid takes the new earth from all the folutions above men- tioned, and with it f2!!s in a powdery form, excepting from the fluate. Icis acurions faét, that the oxalate is foluble in mu- riatic acid with partial decompofition. I obtained an oxalate by dropping the acid of fugar into muriate of Strontites, which _ I wathed well with cold water, and dried. I then introduced it into muriatic acid, that did not diffolve it till a very little di- ftilled water was added. The folution, in a few hours, had depofited a fmall quantity of cryftals, which I dried on blotting paper. They were perfiftent in the air, they diflolved in wa- ter, and imparted to it the tafte of oxalic acid. This fluid was not difturbed in its tranfparency by fulphuric acid, and it oe- cafioned in lime water a copious precipitate of very little fo- lubility ; whence I inferred thefe cryftals were oxalic acid, and their form did not contradict the conclufion. On evaporating the liquor from which they had been depofited, I procured a powdery oxalate and cryftallized muriate. The reafon of this partial decompofition I cannot at prefent affign; it cannot be explained in the fame way that the partial decompofition.of ful- phate of potafs or foda by nitric or muriatic acid is fags ee for. 63. Tue third place belongs to ee tartarous acid, which de- compofes and caufes a milkinefs in the folutions of the earth in nitric, muriatic, fuccinic, arfenic, boracic and acetous acids. 64. THEN comes the acid of fluor, which precipitates ‘the earth from its folution in all the acids I have tried, excepting the three already mentioned as exceeding it in force. It is re- markable, that a folution of fluate is not rendered turbid by oxalic acid, though it be certain, that the oxalic has the ftronger attra@tion; perhaps a triple compound is formed. 65. Nitric From STRONTIAN. 27 65. Nrrrice acid holds the next place). When this acid, in a {tate of concentration, is poured into a faturated folution of the muriate, a precipitate immediately defcends. This confifts of minute cryftals of the nitrate. An aflufion of water reftores fluidity. The liquor on evaporation affords the nitrate in cry- ftals. - 66. Murtatic acid, as ufual, fucceeds the nitric. As it forms a very foluble compound with Strontites, the decompofi- tions accomplifhed by it are made apparent by evaporation. The phofphate,of Strontites is diffolved readily by this acid. The liquor, when the moifture is diflfipated by a very gentle heat, yields cryftals of the muriate and phofphoric acid in a concrete ftate. The arfenicate is taken up ftill more readily ; and from the folution, by an evaporation not pufhed fo far as to deprive the arfenic acid of its humidity, are obtained cry- {tals of the muriate. The borate diffolved in this acid exhibits phenomena fimilar to the phofphate. By adding this acid to the acetite, and evaporating, we get the muriate. Succinic acid, if it do not rank before the two laft men- tioned acids, without doubt, holds the place immediately fol- lowing. 67. PHospHoRIc acid comes next in order. It makes no change in the combinations containing any of the acids already noticed, but inftantly throws down a precipitate from the ace- tite, arfenicate and borates With regard to the two laft of thefe, care muft be taken not to add more phofphoric acid than is fufficient, elfe the precipitate will be inftantly rediffolved, and will elude obfervation. 68. Arter phofphoric ftands acetous acid, which unque- ftionably has a feebler attraction than any of the preceding, and I think a greater than the acid of arfenic, becaufe this acid, dropped into the acetite, ‘difturbs not the tranfparency. Boracic acid follows the arfenic, and laft of all comes carbo- D2 nic 28 ACCOUNT of a MINERAL nic acid, which is expelled by all the others, as appears from the narration already given. Order of Attractions among the Principal Acids for Strontites. STRONTITES. Sulphuric acid. Oxalic. Tartarous. Fluoric. Nitric. _ Muriatic. Succinic. Phofphoric. Acetous. Arfenic. Boracic. Carbonic. 69. THE attraction of the new earth for acids ranks high. For fulphuric acid, barytes has unqueftionably a ftronger at- traction than Strontites. I added barytic water to a folution of fulphate of Strontites; and though only an extremely minute portion of this earthy falt be contained in the fluid, yet an im- mediate milkinefs end precipitation was the confequence. This earth however comes next; for I find that, when I pour Stron- titic water into folutions of fulphate of potafs, of foda, or of lime, the liquor becomes turbid, and the Strontitic fulphate falls to the bottom. : 40. I HAVE not afcertained how the attraction of Strontites ftands with oxalic acid further than that the force of its attrac- tion for this acid is fuperior to that of potafs, and confequently of all thofe fubftances that are inferior to it. 3 71. THE ' From STRONTIAN. 29 71. Tue earth attracts tartarous acid more forcibly than al- kalis do. Add Strontitic water to tartrite of potafs, and tartrite of Strontites will defcend; but its attraction is weaker than that of barytes or lime, for the folutions of either of thefe earths renders tartrite of Strontites turbid. The fame place is due to this earth in its attraétion for fluoric acid as with acid of tartar; barytes and lime exceed it, potafs is feebler. 42. WiTH refpect to nitric and muriatic acids, the order feems foméwhat different. Here fixed alkalis appear to predo- minate. Yet of this, after feveral trials, I was fomewhat un- certain, in confequerice of peculiar phenomena that occur. When abfolutely cauftic potafs is dropped into a diluted folu- tion of muriate of Strontites, tranfparent cryftalline flakes ap- pear ; but long before all the earth is.difengaged, the alkali ceafes to occafion more precipitation, and it may be afterwards added in quantity, without producing any vifible effect. If, however, an effervefcent alkali be now poured in, a copious. curdy precipitate will be formed. Two hundred grains of Strontian fpar were diffolved in muriatic acid. To the folution, diluted with more than an equal quantity of diftilled water, L added potafs, till it no longer occafioned depofition. I permit- ted the precipitate to fubfide, and then poured in fome potafs, which caufed no vifible change. ‘The clear liquor was decant- ed off, and the remaining portion filtered. The precipitate, when colle@ted and weighed, amounted only to 24 grains, With the clear liquor, I mixed carbonate of potafs, and I ob- tained an abundant white precipitate This I wathed, and dried by a gentle heat ; it weighed 170 grains. On another occafion, I diffolved a fimilar quantity of the mineral in the fame acid, and after dilution I added the alkali very flowly. The matter feparated aflumed the form of quadrilateral Jamellar cryftals, fome of which, unattached to any others, fhowed. the wedge fhaped margin like an ordinary cryftal of Strontites ; frequently they adhered to each other, fometimes appearing in arborefcent ; ; figures. 32 ACCOUNT of a MINERAL figures. I continued to pour in potafs as long as any precipi- tation followed, and I certainly confumed more alkali than would have been fufficient to faturate the whole of the acid. The cryftalline depofite, when dried quickly, effervefced very feebly with muriatic acid ; it was much more abundant than the former; it weighed 74 grains. From the fupernatant h- quor, carbonate of potafs feparated effervefcent Strontites to the amount, when dry, of 132 grains. The matter ‘thrown down by potafs, when diffolved in muriatic acid, cryftallizes in every refpect like ordinary muriated Strontites. It is alfo fo- luble in water, and generates Strontitic water. From thefe ex- periments it appears, that potafs precipitates only a portion of the Strontites, which is in the ftate of cryftals, and that this portion is variable in quantity, which imagine in fome mea- fure depends upon the ftate of dilution. How this comes to pafs it is not eafy to fay. I am difpofed to afcribe it either to the production of a triple compound, or to the folubility of Strontites in pure alkali. The weight of the two precipitates, in neither experiment, exactly amounted to that of the {par employed; nor was this to be expected. In the former it was deficient by fix grains, in the latter it exceeded by as much. The deficit of the one may arife in part from the lofs of matter adhering to the filter, but principally from the heat employed in drying, expelling too much moifture from the firft precipi- tate. 4 priort, it might be imagined, that there should always be a deficiency, fince part of the earth is difengaged in its pure ftate, as invariably happens with lime. Inftead_ of this, how- ever, in the latter experiment there was rather an increafe of weight. This I impute to the cryftalline form in which the Strontites is feparated ; for in this ftate it is united to a greater weight of water than it contains of both carbonic acid and wa- ter when it is effervefcent.. 73. THE impracticability of precipitating all the Strontites from muriatic acid, fuggefted fome doubts whether the alkali . 2 . . really Fron STRONTIAN. alae really poffeffed a ftronger attraction or not. Thefe were remo- ved by the refult of the following experiments: I difiolved a quantity of nitrate of potafs in boiling water, and threw in fome mafles of recently calcined Strontites. The heat genera- ted commenced an ebullition, which I prolonged by the heat of a fand bath, the mouth of ‘the flafk being ftopped by a perfo- rated cork. During the cooling, cryftals of Strontites were de- pofited. I next diffipated by boiling much of the water of the clear fluid, managing the operation fo that the atmofpherical air fhould have as little accefs as pofliblé. By this procets I-ob- tained cryftals of nitre, intermixed with a fmall quantity of cryftallized strontites. I performed a fimilar experiment with a folution of muriate of foda, and the refult only differed in this, that the cryftals of common falt were depofited during the evaporation of the liquor, and thofe of Strontites, for the fe- cond time, during the fubfequent refrigeration ; whence the in- ference is deducible, that Strontites cannot detach the nitric or muriatic acid from the alkalis with which they are united in faltpetre and fea falt. 74. THE attraction of barytes for muriatic acid exceeds that of the new earth. Toa folution of Strontitic muriate I added fome native carbonate of barytes lately calcined and re- duced to fine powder.’ Soon marks of decompofition were ap-_ parent, and the liquor confifted of muriate of barytes. Mu- riated barytes, on the other hand, fuffers no change from the earth [ have been defcribing. The attraction of lime for this acid is feebler than that of Strontites. Muriate of lime became muriate of Strontites. fome time after I had introduced the powder of calcined Strontian {par into it. Ammoniac was in- ftantly difengaged from the muriatic acid by Strontites. _ 75. Porass attracts acetous acid more forcibly than Stron- tites, and diilodges it. 76. Puospaoric acid is*one of thofé’ that prefer Strontites to alkalis. Strontitic water immediately caufes a precipitation 1M: 32 ACCOUNT of a MINERAL in phofphate of potafs or foda. Strontites in its turn gives place to lime and barytes. 77. THE fame order as in the preceding is olbteraea with re- gard to the acid of arfenic. 78. BoraTeE of Strontites fuffers no vifible seadae from lime-water or potafs, but is turned muddy inftantly by bary- tic water. A folution of borax is decompofed by diffolved Strontites. mr 2 79. THE attraction of Strontites for carbonic acid is power- ful. It renders mild alkalis cauftic, and becomes thereby itfelf a carbonate. I was defirous of determining the relative attrac- tions of barytes, lime and Strontites for this acid, but found it not an eafy matter. The difficulty proceeds from all the three being entirely or nearly equal in power. BERGMAN was not able to decide between the two firft of them. In hopes of af- certaining this point, with artificial carbonate of Strontites in fubtle powder, I mixed a quantity of barytic and of lime wa- ter, and kept them in phials accurately clofed. I had the: bot- tles fkaken very often during a week. At the expiration of this time, I decanted carefully from both the fupernatant fluid, and faturated it with marine acid. ‘The liquor of the one, treated in this manner, gave, on evaporation, muriate of ba- rytes ; from the other I obtained muriate of lime. Thefe ex- periments feem to fhow, that Strontites will not yield carbonic acid to either of thefe earths. Again, when Strontitic water, poured upon the carbonates of barytes and of lime, is managed in the fame manner as the former, the clear liquors, faturated with the fame acid, afford, both of them, muriate of Strontites. This earth confequently had not taken the fixed air from either. Since then neither lime nor barytes can attract carbonic acid from Strontites, and fince this acid will not defert either of thefe to combine with Strontites, I am led .to the conclufion, that the forces of their attraction are equal, or very nearly fo. This alfo appears from the following experiments: Into a mix- ture From STRONTIAN. 33 ture of nearly equal parts of Strontitic and barytic waters, I threw diftilled water impregnated with a quantity of fixed air lefs than was fufficient to faturate either of the earths. I fhook the whole well for fome time, in the expectation that the earth, whofe attraction preponderated, would attach to itfelf all the acid, and become infoluble. On examination, however, I found, that the precipitate confifted of the carbonates of both. When a folution of lime, inftead of barytes was ufed, the event was fimilar. 80, STRONTITES precipitates metallic calces from their folu- tions in acids, but with no particular phenomena. When Strontitic water is poured into a folution of muriate of mercu- ry, a brownifh yellow precipitate, like to that produced by ba- rytic or lime water. prefents itfelf. The fame fluid caufes a dark green precipitate in fulphate of iron, a greyifh white in fulphate of zinc, a light blue in fulphate of copper, and a white one in acetite of lead. T ABLE to fhow the Place due to Strontites in the Order of Attractions. 4 Tartarous. Sulphuric Acid. Oxalic. Fluoric. Nitric. Barytes Barytes Lime Lime Barytes ‘Strontites Lime ? ~ Barytes Barytes Potafs Potafs Strontites Strontites Strontites re, 2 Soda Potafs Potafs Potafs Strontites Lime Soda Soda Soda Lime Muriatic. Phofphoric. Arfenic. Boracie. Carbonte. Barytes Lime Lime Barytes Lime Barytes Strontites Potafs _ Barytes Barytes Lime g > Potafs Soda — Strontites - Strontites Strontites Soda Strontites Potafs Potafs Potafs Lime Soda Soda Soda Vou. IV. E To 34 ACCOUNT of a MINERAL TREE Pe RR ER ree To make a {mall addition to the hiftory of barytes, and to correct a miftake that has prevailed refpecting the native com- bination with carbonic acid, I beg leave to add a few words. 1. Aut the chemifts who have made native carbonate of ba- rytes the fubject of their experiments, concur in aflerting, that the carbonic acid cannot be difengaged from it by heat alone ; and upon this fuppofed fact, a theory of pretty extenfive applica- tion has been founded. Dr WITHERING, in his admirable paper, Phil. Tranf. vol. Ixxiv. p. 298. fays, ‘‘ It is very remarkable, that *“ the terra ponderofa {par in its native ftate will not burn to lime. “ When urged with a ftronger fire, it melts and unites to the cru- ““ cible, but does not become cauftic.” ‘“ May we not conjec- ture then, that as cauftic lime cannot unite to fixed air with- out the intervention of moifture, and as this fpar feems to contain no water in its compofition, that it is the want of ‘“* water which prevents the fixed air affuming its elaftic aérial “ ftate.”” This fuppofition becomes, in his opinion, {till more probable from the circumftance, that the artificial aérated terra ponderofa, which contains water, lofes its fixed air by the ac- tion of heat. ; 2. Dr PriEsTLEY adopted this notion, and adds his teftimony to the fat upon which it refts. In the Phil. Tranf. vol. Ixxviii. p- 152. we have the following words: “ Terra ponderofa aérata ** gives no fixed air by mere heat. But I find, that when “ fteam is fent over it in a red heat in an earthen tube, fixed “* air is produced with the greateft rapidity, and in the fame “‘ quantity, as_when it is diflolved in fpirit of falt, and making “ the experiment with the greateft care, I find that fixed air * confifts sé From STRONTIAN, 35 * Gonfifts of about half its weight of water.” From thefe ob- fervations Dr PriestLey infers, that water enters into the com- pofition of fixed air, nay, that it is this ingredient which is effential to the aériform condition of the acid. He extends the - idea to all aérial fluids, and hence draws a futile argument againft Mr Cavenpisn’s glorious difcovery of the compofition of water. 3. Iv is unneceflary to tranfcribe the words of Mr Warr junior, who {peaks on the authority of Mr Jos1:au WeDGEwooD junior, to nearly the fame purpofe. or thofe of M. Sacer, Four- croy and PELLETIER, who ftrangely aflert, that this fubfiance is abfolutely unchangeable by heat. _ 4. From this general opinion, however, I am obliged to dif- fent, having found, that the fixed air can be expelled from the Native aérated barytes by heat alone, if fufficiently intenfe; a circumftance that muft prove fatal to the theory founded on its fuppofed impradticability. The heat which anfwers this pur- pofe is that of a fmith’s forge, when the fire is fkilfully ma- naged. By its afliftance, I have oftentimes deprived the bary- tic fpar of its acid either entirely or nearly fo. 5. I NEED not detail the particulars of more than of one expe- riment. In feveral trials, however, it may not be improper to remark, I was difappointed, in confequence of the barytes, vehe- mently heated, acting as a flux on the clay of the crucible, cor- roding holes in it and making its efcape, leaving as its only ve- ftige a green-coloured vitreous glazing on the infide of the cru- cible. At firft I employed crucibles made of pure Stourbridge clay, but was, from the circumftance this moment mentioned, obliged to have recourfe to thofe compofed of black lead, which are able to refift and confine the heated {par ; yet fometimes I fucceeded even with thofe of clay. 6. A soLip and pure mafs of the fpar, weighing 338.4 gtains, was put into a black lead crucible, having a lid of the E2 fame 36 ACCOUNT of a MINERAL fame fubftance fitted to it. The crucible, gradually heated, was kept in the {trong fire of a fmith’s forge for the fpace of half an hour, when it became very foft. On breaking it after it had cooled, indubitable proofs appeared of the mafs having undergone complete fufion. From being previoufly angulated, it now accommodated itfelf to the thape of the crucible, and encrufted the bottom and fides of it a little way up. ‘The cruft externally, where it flightly adhered to the crucible, was of a dark greyifh colour, internally it had a greenifh fhade. The matter was light, fpungy and porous like pumice {ftone, and being carefully colle@ted weighed only 261 grains. The {par had therefore loft 77.4 grains, which is at the rate of “ per cent. nearly. 47. THE calcined mafs imbibed water with a hiffing noife and confiderable increafe of temperature, but without fwelling or fplitting like lime, and was foluble in this fluid. On dropping it into diluted muriatic acid, a very flight effervefcence took place; but this foon ceafed, and the diffolution proceeded in perfect quiet. The folution had a greenifh catft. 8. From another mafs, weighing 530.5 grains, I expelled 136.5 grains or 25.60 per cent. and ftill it was not altogether non-effervefcent. I however obtained it once abfolutely cau- ftic or free from carbonic acid, having employed a crucible of Stourbridge clay, which endures a ftronger heat than the black Jead. But I could not in this cafe afcertain the lofs of weight, as part of the mafs had efcaped through a hole it had made for itfelf. 9. Even by the common blowpipe and candle, a part of the acid may be difengaged. Suppofing that the heat excited by this inftrument, employed in the ufual way, would be very in- adequate to produce the defired effect, I tried pure air, in the manner I had feen M. LavorsiEr ufe it. This mode confifts in directing a flream of oxygenous gas againft ignited charcoal, From STRONTIAN. 37 and produces an extreme intenfity of heat. By this heat the fpar was rapidly melted, but finking into the pores of the charcoal, it eluded further impreffion. I then had recourfe to the ordinary blowpipe. The fmall mafs readily melted, and on being kept in fufion for fome time, boiled with fo much violence as to fcatter around it minute particles of the liquid matter. After two or three minutes, it was kept fluid with more difficulty; and, finally, it covered the furface of the charcoal with a thin powdery cruft. Though it ftill effervefced brifkly with muriatic acid, a portion of the fixed air had been feparated ; for a part of it, thrown into diftilled water, impart- ed to it the power of changing to a green violet teft-papers, and the water acquired a cruft on its furface from expofure to the air. ro. THESE experiments, I hope, fatisfactorily fhow, that the Native carbonate of barytes can be decompofed by heat alone, and further afford proof of the infufficiency of the theory that has been deduced from the fuppofed impoflibility of accomplifh- ing it. 11. I Have found that barytes is vaftly more foluble in hot. than in cold water, and that it is depofited from the former im the {tate of cryftals. To obtain thefe I commonly employ the calcined barytic fpar, and the mode I follow confifts in throw- ing into water, that has juft ceafed to boil, fome pieces of a re- cently burned mafs. The heat that is generated caufes the wa- ter to boil, and I prolong the ebullition for a little time. The clear part of the liquor being decanted off and permitted to cool, depofits fooner or later a quantity of cryftals. The fhape and appearance of thefe vary confiderably, according to the ra- pidity with which they have been formed, and this depends: upon the greater or fmaller quantity taken up by the hot wa- _ ter over what can be retained by it when cold; the moft fatu-. rated yielding cryftals the moft {peedily, the lefs fo not for feve-. ral days.. ; £2; THE. 38 ACCOUNT of 4 MINERAL 12. Tue cryftal in its perfect condition feems to be a flatted hexagonal prifm, having two broad fides, with two intervening narrow ones, and terminated at either end by a quadrangular pyramid, which, in fome cafes, conftitutes the larger part of the cryftal. When the cryftallization goes on at great leifure, the eryftals are often diftinG and folid, of no inconfiderable magni- tude ; but more commonly with a quicker depofition, they are more flender and delicate. and are attached to each other in fuch a manner as to aflume a foliaceous form of beautiful appear- ance, refembling fome of the fern tribe in their pinnated frons, to fpeak botanically ; but in this arrangement, a confiderable diverfity occafionally happens. 13. THE cryftals obtained from calcined barytic fpar, in the manner now defcribed, diffolve in water, and impart the qua- lities of barytic water; they change vegetable colours to a green, they unite with acids without effervefcence, and gene- rate with the muriatic and fulphuric, compounds fimilar to the fulphate and muriate of barytes; hence I infer they confift of pure barytes. 14. THESE cryftals are perfectly tranfparent and colourlefs, but when expofed to the air, become white, opaque and effer- vefcent, lofing during this change nearly 30 per cent. of their weight. Subjected to the heat of boiling water, they undergo the aqueous fufion and become fluid ; from which ftate, if al- lowed to cool flowly, they concrete into a folid cryftalline mafs. When a ftronger heat is applied, and continued tll all the moi- fture is diffipated, there remains a white powder, lighter by one half than the cryftals employed, which, urged by the heat produced by the blowpipe, is melted with more difficulty than the native carbonate. 15. THe folubility of thefe cryftals in water furprifed me a good deal. One ounce of diftilled water, at temperature 60, diffolves almoft twenty-five grains, while boiling water appears to | I be From STRONTIAN. 39 * a Be apable of diffolving any quantity of qian, however great. _ This arifes from the circumftance, that the earth becomes fo xtremely foluble at an elevated temperature, that the water of yftallization itfelf, which fcarcely furpafles the weight of the arytes, when heated to the two hundred and twelfth degree, able to get the folution of the earth without the affift-_ Hi 6. In this amazing folubuity barytes and Strontites nearly ee, but materially differ from lime, which, fo far as I can cover, is diffolved as {paringly by hot water as it is by TE. re ets ae / . ' s ght a ey 4” i ae a ( 1 ‘ ’ ei. ae ’ me pan ri et AA alk + ofthat ea id phlei: }i2h de) cnea 3 41) oe oli “st dee” ; pyrene on Sah aot (2 Hughsticesy Pata Ao aU | pe ners ie y | J lifeirecmae ‘hj ioe Sascoh neg Hel Sa aged Riscsapepasti ; suckin ithebinragle phos shih” aerit tropes ir, | gett! fee tl cdl ai mS ae rie i ete etic ata Peta on a a a nut a Gait aekgienta aa cies 7 ea jh me cage dina: eal aE ‘en mn A ie SO Te aid z yeah sad hint yj tears tiie a sete Wirt peste! ie ais i Ht in ; is ce oe 4 Nps sth ail grat ee ay fi ot a in mi , 2 bettas wet nce ey ¢ II. OpservaTions on the NaTuRAL History of Guiana: In a Letter from WitLi4m LocHEAD, E/q; F.R.S. EDIN. to the Rev. Dr WALKER, F.R.S. Evin. Regius Profeffor of Natural Hiftory in the Univerfity of EDINBURGH. [Read March 3. 1794] DEAR SIR, LLOW me at prefent to trouble you with a few gene- ral obfervations on natural hiftory, which I had an op- portunity of making while on a botanical excurfion, with my friend Mr ANDERSON, to the Dutch colony of Demerary. Gui- ana is a country but little known in Europe, though its animals and vegetables have added confiderably to the catalogue of na- tural productions. It is not however the organic kingdom which I mean at prefent to touch upon; all I aim at is to give you fome idea of the face of the country, as leading to the know- ledge of its formation and prefent ftate. It is not a field for the mineralogift, as its interior is unexplored. But to the geolo- gift, who wifhes to trace revolutions of the latef{t date, it is not uninterefting to contemplate fuch a recent and fingular coun- try as Guiana. I NEED not inform you, that under Guiana is comprehended all the coaft of South America from the Amazons to the Oroo- _ noko ; that it trends nearly N. W. and S. E.; that it is in gene- ral a very low and flat country, efpecially the Dutch or wefter- moft part of it; and that it is watered jby feveral rivers and creeks, which rife in a chain of mountains running nearly E. Vor. IV. F and. = 42 NATURAL HISTORY and W. and dividing Guiana from the inland parts of South . America, which form the banks of the Amazons and its nu- merous branches. Coa/t.—No coaft can be more eafy to make than that of Gui- ana. ‘The changed colour of the water indicates foundings long before you make the land, and you may run on in feven , fathoms before you can difcover it from the deck. The bottom is at that diftance a foft mud. All along the coaft near Deme- rary, you have only about two fathom at.a good league from the fhore ; to leeward of Effequebo, it deepens ftill more gra- dually. In {tanding off or on five or fix miles, you will hardly deepen or fhallow the water as many feet. When a high fea fets in upon fuch a coaift, it 1s eafy to conceive, that at a very confiderable diftance from the land it muft be affected by 'the bottom. The interval betwixt wave and wave becomes more diftina. As they roll .on i fucceflion, the lower part is re- tarded, the upper furface accelerated, each billow of courfe be~- comes {teeper and more abrupt, till at laft at gradually ends m a breaker, when it has come to the depth’of only a few feet. Thefe rollers, as they are called, are the dread of feamen, efpe- cially betwixt Effequebo and Pomeroon, where the water is fhallow, and ‘the bearing ‘of the coaft very much north and fouth, expofes it fully to the aétion of the trade-winds. In fmall craft, thofe acquainted with the navigation do not hefitate to run along the coaft, even among the rollers themfelves ; but veflels drawing ‘from ‘eight ‘to twelve ‘feet water, efpecially if the fwell be heavy and it falls calm, can hardly getoff. If an- chor and cables fail, they drift ‘on till they are faft in the mud, and there they will continue, fometimes-for weeks together, be- fore they ‘go to pieces. The fea-water ‘becomes ‘exceedingly thick and muddy within a few leagues ‘from the coaft.of De- merary, as much or more fo than the Thames is at London. A firanger would naturally take this for the difcharge of large flooded Of GUIANA. 43 flooded rivers after a rainy feafon. By and by I fhall explain the true caufe of it. | On approaching the continent of South America, a change on the face of the /fty will ftrike the attentive obferver. The clouds become lefs diftint from each other, and the intervals between them lefs:clear., They are blended into one another as. it were, and fuffufed more generally over the atmofphere. They appear to be furcharged with vapour, or to have a fetonger difpofition to depofit it. _ THERE is a particular, prevailing appearance of the heavens within the tropics when you are at a diftance from continents | or very high iflands, which has fo often ftruck me that I won- der it has not been taken notice of. I call it a tropical /ky, and thus defcribe it. The clouds:in fine weather are in a fingle feries or ftratum, failing away regularly withthe trade-wind. They are {mall and diftintly feparated from each other. The inter- vals or fky above them of a clear azure. The lower furface of the clouds is. perfectly horizontal. As the temperature is commonly. very equal over the fea, the condenfation takes place every where at an.equal height'from the furface of the water. In the clouds that are over-head, you. cannot indeed perceive this ; but it becomes more and more vifible as the eye recedes from the zenith. The lower limb of each diftant cloud. appears perfectly level. and-well: defined, brighter than the fuperincum- bent part. - Ata diftance, nothing is to be feen but thefe. limbs clofer and clofer,in.gradation one behind, the other; and the whole horizon round refembles the roof of a ftage;,with an in- finity of half dropt curtains as far as the eye can reach. In two voyages from Europe, I have met with this tropical {ky as far,north as Cape Finifterre. It came with a fair wind, which continued with us like a regular trade-wind,accompanied with the fame appearance of the clouds, till we made the Weft Indies. In running down. the trade-winds, every one has an opportunity of verifying this defcription, and muft be, ftruck with the beauties PZ which Ad NATURAL HISTORY which this fky prefents at the fetting of the fun. The inhabi- tants of the lower iflands may alfo be well acquainted with it. In the higher ones, the attraction of the mountains ever forms fets of clouds of other appearances, as being produced by other caufes. With our prefent knowledge of meteorology, hardly any other caufe can be affigned for the phenomena above men- tioned, than the conftant equal temperature that every where prevails on the intertropical feas. One analogous fact however may be mentioned ; the exceedingly fmall range of the baro- meter in the torrid zone. Does the fame caufe regulate fo ex- actly the height of the clouds, and maintain the uniform fu- fpenfion of the mercury ? We might almoft fufpect it did, were it not well known, that the barometer varies as little upon con- tinents, and in the vicinity of mountains, in thefe regions as elfewhere, though the condenfation of vapours is in fuch cafes much more irregular. Upon the continent you will frequently obferve this tropical fky alfo, efpecially in fine fettled weather ; but much more commonly you will find the fky there, and even before you make the coaft, covered with heavy large dark clouds in fome places, and in others, at a greater height, the ferene dappled fky, fo often feen in Europe. Winds.—Tue trade-wind generally prevails all the day long,. and on the fea-coaft feldom fails even at night ; but in lefs than fifty miles up the river it is a dead calm at night, and the breeze is not able to penetrate fo far till towards noon. Still farther up we had whole days of a ftark calm, and the heat very intenfe. Dews, fogs and temperature.—Tur dews, following the law which they generally obferve, are very heavy when and wherever there is but little wind, and the hotter the day and evening, they fall the more copioufly ; they were of courfe more abundant up the river than near the fea-coaft. The exhalations in the day-time from — Of GUIANA. 45 from a hot and mifty country covered with vegetables being very great, the condenfation occafioned by the abfence of the fun, and the cold accompanying that condenfation, are in pro- portion. Near the coaft the diurnal difference of temperature is but trifling, the conftant trade-wind preferving in the air nearly the fame medium of heat as in the body of the ocean; but far up the river the range of the thermometer was very great. The heat of the day was intolerable. In the fhade it was fre- quently above go°. This, when there is no breeze, forces you into the woods for fhelter. ‘Towards evening it cools; during the night the cold increafes, and is greateft about five in the morn- ing. The thermometer would then be from 72° to 74°. The body of the river being large enough to retain its heat, the eva- poration goes on from its furface through the night, and is condenfed into thick fog, which hangs over it, and is feldom difperfed before eight or ten next day. While the air was as above in the morning at 72°, the water along-fide gave 80° to 83°, and feldom rofe two degrees higher at noon-day. We had _an opportunity of verifying an obfervation made by the few inhabitants who live far up the river Demerary; that when it feels very cool.in the morning before day-break, they are fure of fine weather; when, on the contrary, it feels warm, they expect rain. They fleep in hammocks, and the houfes they have are pervious enough to the air, fo they are fenfibly affected by any change in its temperature. Seafons.—As to the feafons, it is not an eafy matter, from the accounts given by the colonifts, to afcertain them exactly. All feem to agree, that fince cultivation has been fomewhat extended, they are not fo regular as before ; that the dry feafon encroaches on the rainy, and that during the latter, they have often feve- ral dry days in fucceflion, The account given by Dr Ban- _ CROFT was the one generally allowed; that it is dry about the equinox, and rainy about the folftices; that of confequence they 46 NATURAL HISTORY they have two wet and two dry feafons every year. We thought it difficult to reconcile this with the account given of the fea- fons of other countries in fimilar climates, and with what ac- tually takes place in the Carib iflands. I will give you my ideas on the fubjeét. It is within the tropics a very general rule, that the vicinity of the fun brings the rainy feafon. To the northward of the line therefore this muft be in our fummer months. Itis another mvartable law, that.as in lunar influences, fo in the change of feafons produced by the fun, fome time is neceflary after the maximum of the ‘caufe to produce the full effect. The higheft tides are not till two or three days after the full and change. The greateft heat of the day is' two hours after noon, and the hotteft months in Europe are July'and Au- guft, not June, when the fun is,higheft. Among the Weft India iflands, the full effet of the fun’s vicinity is ftill later. I have found Auguft, and more efpecially September, to be the . hotteft months in the year, and they are accordingly the height of the rainy feafon. It begins thus: No fooner has: the’ fun come to the northward, and begun to be vertical among the iflands in April and May, than ‘his force is felt, the fly is more difturbed, the wind is ‘more frequently from the fouthward and in {qualls, and now and then there are heavy fhowers. In June the fame effects continue, and increafe in July, when the proper rainy feafon may be. faid to begin, and’ continues. in force more or lefs till the middle of O&ober. Auguft and Sep- tember, with part of July and O@ober, when thefe effects are at their greateft height, are ftyled the hurricane months, and by the French P?’hivernage. During them, the full force*of the great haminary which diftributes light and life, however necedf- {ary, feems fometimes too’ much for nature.’ She is opprefied and fickens; her ref{piration is difordered by intenfe heat ; fome- times calms, fometimes heavy fqualls ; the agitated elements vent themfelves in lightning, with thunder and torrents of rain, or are fometimes thrown out into thofe horrid: convulfions,. hurri- rox canes, Uf GUIANA » ‘47 canes which feem to threaten inftant diffolution. Guiana is . happily free from thefe fcourges of the Antilles. Their force has lately been partially felt at Tobago, which was thought be- yond-their reach. In Trinidad, the greateft ftorms they have hitherto experienced, do not deferve the name of hurricanes ; and to the fouthward, on the main of America, they are utterly unknown. The difference then. between Guiana and the iflands is this: In the former, the rainy feafon fets in earlier, as indeed the fun is fooner vertical, Their principal rains are in the end of April, in May, June and July. They are alfo fooner over ; for Auguft, September and O@tober, and I believe part of July, are commonly fair weather. But again, November in part, De- cember, January and February, reckoned dry months among the iflands, are in Guiana a fecond rainy feafon. The caufe of this I take to be as follows: North-eafterly winds, pretty tiff, cold, and bleak comparatively in thefe climates, are frequent among the iflands during the winter months, They are well known by the name of Norths. They are often accompanied with rain, but it is not very heavy, nor thought of confe- quence enough to give the denomination of a rainy feafon. Thefe winds we know to reach as far as the coaft of Guiana ; and there I have reafon to believe they are productive of more rain than in the iflands. The face of a large continent, and its effects upon the atmofphere, may very probably make them give up more of their humidity than they do among the An- tilles, though, at the fame time, their force and bleaknefs may not be fo much felt. If this conjecture hits the truth, the fol- lowing ought to be corollaries, and are left to future obferva- tion. In this rainy feafon, when the fun is near the fouthern folftice, their rams will be with pretty fteady northerly*breezes on the coaft. They may be of longer continuance at a time, but they will not be fo heavy as thofe of fummer, and they will be chiefly on the fea-coaft, and probably will not extend a great way up the country. It remains even a query with me, 3 | whether ‘ 48 NATURAL HISTORY whether the rain that accompanies the norths among the iflands, efpecially thofe moft remote from the line, be not generally in a greater proportion than is commonly fuppofed. Country.—I WILL now endeavour to give you fome idea of _ the face of the country. Though, as is well known, Guiana is flat and {wampy, yet it affords to the attentive eye an in- terefting variety. The fea-coaft is little, if at all, raifed above the level of high water, and it continues at this level for many miles inland. It is properly an immenfe woody fwamp, never dry in the drieft feafon, covered with feveral feet of water in the wet. Next the fhore, as far as the brackifh water extends, it is covered with mangroves, which grow toa confiderable height, and form a thick fhade. They are elevated on their branchy intermingled roots from the bare wet clay or mud, on which there is fcarcely one herb or plant, but which feems to be all in motion, from the prodigious number of crabs which make: their holes in it. Further on, when the under-water is frefh, you meet with a new fet of vegetables, principally {mall trees, which, from their fituation, are obliged to adopt the habits of mangroves, having the bottom of their trunks fup- ported three or four feet above ground by their ramified roots. Several climbing plants are. mixed with them. Arunis, in great variety and profufion, emerge from the water, or embrace the ftems of the trees ; and feveral broad-leafed plants of the hexandria and triandria claffes, affift the Arunis in forming an herbage. In all this low part of Demerary, there is not one tree of a large fize, nor ‘among them all above two or three fpecies which can be applied to ufe as timber. Proceeding ftill up the river, its banks are found generally to raife themfelves above the level of the water; and when you have gone up one tide, (betwixt twenty and thirty miles), they are fo high, that there is no farther occafion for dams to keep the plantations from being overflowed at high water, as below ; canals. Of GUIANA. 49 canals or ditches are fufficient to drain the land, which is ftill perfectly flat. The trees are here different in fpecies and larger in fize than below, and the woods are much more practicable. As they are drier, the ground has acquired a regular fort of fur- face, and there is neither that plexus of roots, nor the fame number of vines, (the common name in the Weft Indies for _all climbing plants), to entangle thofe who choofe to traverfe them. The foil here is generally a ftiff, cold, reddifh clay, mixed a-top with a portion of vegetable mould. THE fand-hills prefent to the admiring eye a fcene very dif- ferent from what it had been accuftomed to below. The firft you meet with upon the Demerary, is upwards of thirty miles from the mouth of the river, and on the right hand afcending, or on its weftern fhore. There are of them further down in the country, but not clofe by the river-fide. This one is the extremity of a ridge which extends to the weftward {feveral miles. As you afcend the river, you meet with many more of the fame kind on both fides, whofe direCtion feems likewife to be eaft and weft, or nearly at right-angles with the average courfe of the ftream. They vary from 50 to 100, 150, or 200 feet of perpendicular height above the level of the river and the intervening flat country. Their breadth and extent varies fometimes only a few hundred paces, fometimes many miles. Their length is great; with fome interruptions, I have reafon to believe they are generally continued from one fide of the colony to the other, only interfected in different places by the rivers and their branches. They confift of a pure filiceous fand, fo white that it dazzles the eyes, commonly fine grained and loofe, but not unfrequently mixed with little ftrata of coarfer pebbles, moftly quartz, and fometimes concreted into a proper fand-ftone. In the laft cafe, a black or reddifh tinge is IN Many cafes communicated to it, from clay, decayed vege- tables, or other extraneous matter. There is no regular ftratifi- cation to be found in it, more than what is common to all Vot. IV. i fands, 50 . NATURAL HISTORY fands, the produce of depofitions of different dates, and as they are of different materials, thicker in one place, thinner in another, fometimes horizontal, but oftener inclined, and convex or con- cave according to circumftances. We could meet with no ap- pearance of fhells or other marine produ¢tions, but in a few places, pieces of broken vegetables buried in the fand where it was concreted. They were black as all the foffil vegetables that I have ever féen in fand-ftone. Upon, and by the fides of the fand-hills, grows the moft valuable timber of thefe colonies. The trees there are of a good fize, and very clear of obftructing underwood or vines. ‘The Wallabba, (Parivoa grandiflora of Aublet); the Sipiri or green-heart, (a new fpecies of laurel) ; the Coumarou or Tonquzbean-tree, Coumarouna odorata of Aublet ; the Mora, valuable for boat-timbers, and many others, whofe wood is equally hard and beautiful. ConTINUING to afcénd the river, the fand-hills become ra- ther more frequent, but the intervals ftill remain a perfec flat, though now feveral feet above the level of the ftream, and the, foil is ftill a {tiff clay. Hitherto the river is deep all over, ge- nerally from two to five fathoms; the bottom is mud or clay, and the fhores on either fide at low water covered with ooze. About 130 miles up, however, or juft before it begins to fhal- low, the bottom is covered with banks of a hard white or brown fand. It was a problem for fome time whence all this fand originated in fuch a country. It was foon folved. Lea- ving here the veffel that had hitherto carried us, we proceeded in a canoe ; and at about 160 or 170 miles diftance from the mouth of the river, we met with the firft proper hills of folid materials. The neareft to us was a rock of granite projecting into the ftream, whofe direction it gave a change to at this place, and it ferved for a landmg-place to the higheft piece of cleared land upon the river next to the poft-holders. It was part of a low ridge of the fame ftone which crofled the country, probably te Berbia or beyond it, and was fucceeded by many other feries of ‘ | hills Of GUIANA. 5) hills more inland, and as far as we could examine them, of the fame matcrials. The granite was both of the red and the gray kinds, but chiefly of the latter. A number of feams or dikes croffed it here and there in all diredtions, not diftin@lly fepa- rate, but firmly united to the reft, making as it were but one body with it, and confifting of the fame materials diffe- rently modified. ‘Their component parts were generally {mail- er; they were more compact and clofer in the texture than what furrounded them; and where they had been equally ex- pofed to the action of the weather, they appeared to have born it much better than the furrounding granite. The origin of» the fand was now accounted for. This ftone, in fome cafes ex- ceedingly firm and durable, is in others very liable to decay ;. and the wafh of thefe enormous chains of hills was able to fur- nifh abundance of fuch fand as we had met with below. The granite afforded many varieties, indeed every fhade, from large and diftin@t grained, to that whofe component parts of felt- f{par, {chorl or quartz, were fo {mall as to refemble pretty com- pact, compound lavas, or fome of our mixed whin-{tones in Scotland. All thefe varieties would be found at no great di- ftance from each other. I brought fome fpecimens, from Ti- ger’s berg, a hill about 500 feet perpendicular height, which have every appearance of having undergone the action of fire. They .refemble half-vitrified {coriz, and would be taken for- them, but that they were actually broken off from the granite, and difcover all its parts in the fracture. The fummit of this hill is irregular, with feveral pits and holes among the rocks. A little higher than it, and I fuppofe nearly about 200 miles from the fea, you meet what are called the Falls. They are only five or fix rapids, within the fpace of a mile or two, form- ed by ledges of very clofe-grained gray granite that run acrofs the river. There are breaks in each of them, through which the dextrous Indians are able, in their light canoes, to pafs up at any feafon, even the drieft ; and when the river is {welled by Grea the 52 NAFURAL HISTORY the rains, they become totally obliterated. Two days journey, or two and a half above this, is the great fall, where the ftream comes over the face of a rock, as we were informed, twenty feet high. Savannahs. —SavANNAHS, ever fince the difcovery of Ame-. rica, have been known to occupy large {paces in the fouthern. parts of that continent. They are to be met with abundantly m Guiana, and are of two kinds very diftinét from each other, , the wet and the dry. Of the former, many are extenfive as. the. eye can reach, immenfe verdant plains occupying- the. whole. face of a country, with or without a few ftraggling infulated . patches of wood. In the dry feafon, they appear. meadows. of long grafs or reeds, and are feldom practicable for any diftance, for the bottom is very rarely dry. In the wet feafon, they are all one entire plain of water, over the furface of. which the grafs ftill rifes, but which may be every where navigated in the cou- rialls or canoes. ‘Towards the end of the drought, the Indians fet fire tothem. The young growth which fucceeds attraéts the. deer, and the native, on the return of the half-deucalion days, purfues them in his little bark-acrofs their former plains. The foil upon thefe favannahs can neither be very deep nor very good ; yet water may be always commanded, and labour and induftry might convert thefe deferts into rice-fields. It is. a queftion whether the days of flavery willever fee that event. The culture of this ufeful vegetable, which in the eaft has: for ages been the ftanding food of millions, brings too moderate.a. return, at leaft in an infant colony, for the-rapacious agricultu- ral fyf{tem of the Weft Indies. — Tue dry favannahsare neither fo frequent nor: fo extenfive, yet we have paffed through fome of them feveral leagues in circumfe- rence. They are formed along the flats on the top'of the fand ridges, and covered by a very thin coat of verdure. They re- femble, exactly enough, fome of the bare moors in Scotland. Many Of GUIANA. 53 Many beautiful plants of the clafs gynandria are their chief orna- ments, as is alfo the orchis, which grows in fimilar fituations with’ you. Some Melaftomas, and more Rhexias, fupply the place, and. bear fomewhat of the habit of the Erice ; for your Sedums and. Saxifrages is the little Sauvagefia ; and in hollows of the fame fa- vannahs, where moifture prevails, what I never could have ex- » pected to fee within five degrees of the line, and not more than go or 100 feet above the level of the fea, the Drofera lifts its: humble head from.a bed of the Sphagnum palutftre. BEsIDEs thefe two. kinds, there are alfo what we may deno- minate 4alf-favannahs, formed upon the tops of fand-hills, higher and more irregular than in the cafe of thofe juft de- feribed. Some of thefe are alfo very extenfive. Few herbaceous- vegetables are to be met with upon them. Broad {paces of arid’. fand are interfected by clumps of fhrubery. Nothing grows . to the height of a tree; but a particular fet of. plants, different _ from thofe in other parts of the country, find fubfiftence-enough . to rife to fifteen or thirty feet. How nature, after all her ef- forts, fhould have. failed to induce a foil: upon thefe, is furpri- fing. It appears chiefly owing to-the great porofity of the fand, which every where admits- the decayed vegetable matter deftined for that purpofe, to be carried: down through it, and filtered off by rain. Even thofe fand-hills which are covered | by tall-trees, {till thew proofs. of this. The trifling layer of mould formed upon them is-exceedingly:thin. When cleared - they are very barren; and when you dig in them to a-great depth, you ftill find fmall portions of black. vegetable earth dif- perfed among the fand.. What corroborates the above fuppofi- tion, is the appearance of. the fprings.. Abundance of thefe are found-gufhing out copioufly round the verges of the hills ; and notwithftanding the extreme whitenefs: and purity of the fand from whence they flow, there is not one in an hundred whofe © waters are limpid. They come out not muddy, but of a. brownifh colour, very much like the. water which runs from ; peat=.~ 54 NATURAL HISTORY peat-mofles, and they are certainly tinged by the fame caufe. The rotten leaves of trees, and other decayed parts of vegeta~ bles on the hills, inftead of being colleted on the furface to form foil, are wafhed down into the fandy ftrata by every rain ; fo that the refervoirs of the fprings, and the water which pro- ceeds from them, is always coloured with thefe fubftances. There _ follows a corollary alfo from this general principle, and when compared with facts I believe it will hold good :, The more the fand is concreted into {tone in any of the hills, the more and better will be the foil upon them. Where clay in fmall beds, or in a certain proportion, is mixed with the fand, the vegeta~- ble mould will likewife be better retained. Rivers.—\ Wiki next give you what general obfervations I have ‘been able to make upon the rivers and creeks of this part of America. The courfe of nearly all thofe of Guiana is from fouth to north. They originate in a chain of hills running eaft and weit, which feparates Guiana from the country on the Ama- zons, and likewife gives rife, on its fouth fide,. to the numerous branches which fall into that river. The Demerary is a confi- derable ftream, equal, if not fuperior to the Thames ; yet it is by no means among the largeft of them. The Effequebo is five times larger at its mouth, forming a whole Archipelago of iflands ; but its {tream foon divides, and, on account of rocks, {hallows and rapids, none of its branches are navigable fo high up as the former. Moft of the particulars I am now to give you muft be underftood as applying to the Demerary. The bar, if it may be fo called, is common to this with many other rivers, which difcharge themfelves into a fhallow fea; but full with circumftances in the prefent cafe which diftinguifh it from others, where the bottom is not mud but fand. It does not run like a fingle narrow ridge, acrofs, or nearly acrofs the mouth of the river, but it is of great extent, and is properly a con- tinuation of the mud-bank which runs all along the coaft. .To the eaft and weft, and for two miles or more in the offing, you have Of GUIANA. 55 have ten or twelve feet water with the utmoft uniformity, and ftanding in with the mouth of the river open, you neither deepen nor fhallow till you enter it, when you find two, three, four or five fathom, and it continues to average that depth for a long way, fo that any veffel which can enter, may, for draught of water, proceed up the river for roo miles or more.. Tue mouth of the Effequebo, from the fand-hills and rocks being very near it, is exceedingly different. Three large iflands. prefent themfelves in a breaft, and divide its entrance into four channels. The length of thefe iflands is with the current, fouth and north ; and from the tail or north end of each of them, as alfo. from the banks of the main on either fide, run out fand-banks to a: good diftance. They are perfectly firm, quick in very few {pots,, and the body of them is above the level of low water. On the outfide of them you have the continuation of the mud-banks and fhallow water as above, only that the entranee of thefe channels is: {till fhallower than that of the Demerary.. The {treat of this river runs very brown and muddy, and the fea is {tained with it for’ fome leagues off A ftranger naturally imputes this-to the wafhings of a large flat country, or the ftirring up of the muddy bottom by the tides. The latter may in part be a: caufe, though I believe it contributes. to it but very little, and the former, in a ftate of uncultivation, none at all. On afcend- ing forty miles or fo, you find the water clear again, or rather of a darkifh hue, and fo it continues above that. I was at firft at a lofs how to account for this, but,, from a number of cir- cumftances,. was foon led to conclude, that the thicknefs, and. light brown colour of the water near the mouth of the river: and on the coaft, were almoft entirely the effect of cultivation. . -Numberlefs ditches and canals have been opened by the inhabi-. tants, which are receiving or difcharging water every tide, and each particular piece on a plantation is every way interfeted with open little drains, which communicate with thefe ditches.. In digging and hoeing this clayey foil, much of it is fufpended: in: 56 NATURAL HISTORY ‘in the water, and carried off by the current of the tides. Nothing can be more certain, than that all up the river, and in all the creeks which difcharge themfelves into it, the colour of the water is conftantly clear or blackifh, even in the rainy fea- fon, when it is fwollen. On confidering thefe circumftances, I have been led to this general conclufion, which is fubmitted to the proof of obfervation in different parts of the world. The reddifh brown colour, fo common in frefhes of rivers, in Europe, and we may add every where, is almoft entirely the effect of cultivation ; and the natural colour of rivers, even in the higheft and longeft continued floods, where all the country is {till in woods or paftures, is ever that of a very dark brown, or blackifh, pretty much like that of the ftreams which rife among peat-mofles, but rather more diluted. It is compara- tively very clear, and depofits but a trifling fediment. The other is thick and opaque, and its fediment copious. Thus is man, in his little workings, made, in a fmall degree, one of the engineers of nature. We cannot doubt, that entire ftrata will owe to him their exiftence, accumulated in a feries of ages at the bottom of the fea, and deftined, in future revolutions, to act a more diftinguifhed part. It may be curious too to con- fider the differences that may be expected betwixt the {trata formed by thefe different depofitions, which may be fuppofed between them to have been the origin of moft of the clays upon our globe. Clay, earth or loam, ftirred up by the la- bourer, gives rife to the one; minutely decayed parts of ve- getables form the body of the other. Ir muft alfo be obferved, that clearing the ground along the coaft, by cutting down the trees, and opening ditches for the difcharge of water, has expofed the land very much to the wafhing of the fea. The roots of the mangroves formed a plexus able to refift its force; and the former equal, and very flow deepening of the water, prevented its making a ftrong ; impreflion Of GUIANA. 87 impreffion on any place. The difcharge from the-ditches at low water cut out channels in. the mud, and left the fides of thefe channels more expofed to the returning waves, which here beat continually upon a lee-fhore. We find therefore on the coaft, that the fea has made here and there confiderable en- croachments, which generally begin on the weft fide of the canals or ditches, as being the moft acted upon by the waves. The mouth of the Demerary itfelf furnifhes us with a ftrong inftance. That river is now nearly twice as wide as it was when the country firft began to be cleared; the fea and the ftream together having fince that {wept away a large portion of land from the weftern fhore. Crecks.—A NuMBER of creeks fall into the Demerary on both fides, but fo fmall that they bear no proportion to the fize of the river. You can hardly diftinguifh their mouths in the woods which overhang the banks. They are fo narrow that it is difficult to run a fmall boat in them; yet you will find in them throughout from two and a half to four fathom _-water, and they run winding fo far back that it will take five, fix, eight hours, or more, to carry you up to their heads, where they terminate in {mall ftreams from among the fand-hills. The banks of the creeks at their mouths are of the fame height as thofe of the river clofe by, from five perhaps to twelve feet above the water in the dry feafon. As you afcend the creek, you might naturally expect to find them rife. It is however the very reverfe ; they become gradually lower and lower, till at laft all round them is a fwamp; and the trees on each fide in like manner become fmaller and {maller, and of different fpecies from what they were. It is now in fhort exactly a mangrove fwamp, with this difference, that the water is quite frefh, the vegetables are not the fame, and there are abundance of arunis and other low herbaceous plants. A little higher up, Vou. IV. H you 58 NATURAL HISTORY you lofe the wood altogether, and find yourfelf in a beautifuk — deep canal, winding through a {pacious wet favannah, which is fometimes many leagues in circumference. The firft time - we went up one of thefe creeks, (called Camouni), I was fur- prifed at this appearance, and thought it muft be a mere local circumftance peculiar to it. We found afterwards the fame in one or two more inftances, and were fatisfied upon enquiry, that it is common to them all. It was natural to look for an explanation of this phenomenon, and I foon found it in one of thofe laws, which probably extend to all rivers fubject to frequent inundations. It has been obferved, in particular, of | the Ganges *, that the banks of that river are higher than the adjacent lands at a diftance from the ftream, owing, no doubt, to the annual depofitions of mud, t¥c. during the {well of the river. Apply the fame rule to the Demerary, and the difficulty will be folved. The wet favannah behind, and the fwampy woods around them, are the body of the low country at its natural level, fcarcely a foot or two above the fea. Whatever additional height the land has in the vi- cinity of the river, from the time you have afcended about twenty miles or fo, is all acquired. It has arifen from the fedi- ment of the river during the rainy feafon, when the country is overflowed fo as that all the lower part of it is under water. This depofition muft be always more copious, in proportion as it is nearer the ftream, where additional quantities are always brought, and where it is kept in motion both by the current and the tide. Every thing which we afterwards faw confirmed this theory, and nothing more dire¢tly than the canals which run out at right angles from the river. Some of thefe extend four miles. inward, and they prove to a demonftration, that the land becomes lower and lower the farther you. recede from the _* Account of the Ganges, &c.. Phil, Tranf. 1781, by M. RenvE Lt. Of GUIANA, 56 the river. The maps of the colonies confirm it; for in all of them the main body of the low land of Guiana is laid down as favannah, and the woody country, which a ftranger or fuperfi- cial obferver would fuppofe to be the whole or much the greater part of it, is in fact only a border on the fides of the rivers and of the fea, but of confiderable breadth, more or lefs, in proportion to the fize of the adjoining river, or, which is generally the fame thing, to the acquired height and extent of the foil on either bank. It followed as a confequence, and, as far as we had opportunities of obferving, we found it to be the cafe, that the low land was fomewhat higher, and continued fo farther down, about the Effequebo than the Demerary ; the woods con- fequently were of greater extent. We found, befides, in the foil adjoining the Effequebo, at leaft upon the eaft fide, a mix- ture of fand. ‘The river is full of fand-banks; and it appears, that the finer parts of even this lefs fufpenfible fubftance are raifed by the floods and carried among the adjacent woods to be depofited with the mud. The Mahayka, a fmall river or creek which falls into the fea about twenty or thirty miles to the eaft- ward of the Demerary, though it runs a long way up the country, and fpreads into many branches, has but a very nar~ row, and often interrupted border of wood upon its banks; it runs through an immenfe favannah, and fo do its branches, with little or no wood, till they approach the fand-hills. The Deltas of the river of Oroonoko, and its numerous mouths, make a figure even in the map of the world. It is to be regretted, that its noble ftream has been fo long hid from fcience. What I learned in Trinidad from a gentleman, who had failed from its mouth to the Angufturas, about 300 miles up, confirms and illuftrates, in the fulleft manner, the above general rule) The weftern mouths of it oppofite Trinidad, are navigable only for launches drawing fix or feven feet wa-: Hiv ter. ee) NATURAL HISTORY ter. At and oppofite them, the bottom is fhallow and mud- dy, and the coaft a low mangrove fwamp, refembling, in all refpedts, that of Guiana. You muft afcend thofe branches feveral days before you reach the main ftream; and in doing fo, you find the fame phenomena as in afcending the Deme- rary, but in a ftill greater degree. At firft you have the man- grove, or fome fimilar {wamp, and behind it on both fides for about twenty leagues, the land, if you can call it fo, hardly emerging from the water. Afterwards the ground appears ; and, as you go up, rifes {till higher and higher on the banks above the common level of the ftream. The trees become, in the fame manner, of different {pecies, and much taller than they were below, The channel in which you are, from being wide, grows narrower by degrees. It is from about one and a half to three-fourths of a mile broad near the entrance ; and, when it joins the main ftream, is not more than about 200 yards. It has then acquired a confiderable depth, and the banks may be about twenty feet high. Along the main ftream of the ri- ver, or Boca de Nafios, the gradual rife, and other circume ftances attending it, are quite fimilar. All this height of the bank, I can make no doubt, is entirely acquired ground, form- ed by the fediment of the floods, greater near the ftreams than at a diftance from them; and though I have no knowledge of the nature of the land in the deltas and their vicinity, I would not hefitate to fay, that great part of the interior body of each ifland, and moft probably of the main on either fide, where it is low country, confifts of nothing elfe than wet favannahs. Ficods, BEFORE we leave the rivers, it may be proper to take notice of their floods. In no inftance of a large river does the univerfal law within the tropics fail, that they annually overflow their banks for a certain feafon, What was a prodigy * . im ae of GUIANA. 61 in the Nile during the infancy of {cience, is now a well known phenomenon to every inhabitant of a continent in the torrid zone. From the fituation of the river Amazons, it amounts to a certainty, that the Demerary, Effequebo, and other rivers of Guiana, cannot originate very far up in the continent of South America. This is confirmed by what I could learn of the rife and duration of the floods of thefe two rivers. En- "quiring about them at the plantations below, is to little pur- pofe, for there the floods are hardly difcernible ; but by the poftholder and the fettlers fartheft up, I was informed, that they are there fenfible enough, and that, independent of all partial fwells from accidental rains, the Demerary generally rofe every year in the month of June, and continued high through July and part of Auguft.° The rife there, upon the whole, might be about twelve feet; it is fufficient to lay the level parts of the country under water, and to render the woods, that cover them in feveral places, paflable in canoes. We could have wifhed for more exact information. This, how-. ever, was fufficient to prove, that the rivers. did not rife very far inland, elfe the floods would have been later in the year ; but at the fame time that they were of extent enough to fol- low the rule of all confiderable intertropical rivers, fo.as to have a flood in the raimy feafon, that is, in the months when the fun is upon the fame fide of the line on. which they have their origin and courfe. THE great Oroonoko, | have been informed, begins to rife a: littl. in May, it continues increafing through the fummer months, and the inundation.is at its height in September. At. that time, as far up as the Angufturas, the rife is about forty feet perpendicular above the low water-mark. It diminifhes as you defcend till about the mouth, where it is only a very few feet. Tides: 62 NATURAL HISTORY Tides are of the utmoft confequence to the inhabitants of the coaft of Guiana. They enable them to drain a country which otherwife could never have been cleared, and they af- certain their journeys which are made by water up and down the rivers, and even along the coaft. At the mouth of the Demerary, it is high water at about half paft five, at new and full moon. The rife in fpring tides, a little way up, is twelve feet, or more, above low water-mark. ‘The tide runs very rapidly near the mouth of the river, feldom lefs than four or five miles in the hour. It continues to run with force for a long way up, and was fufficient, without wind, to carry us up or down at 150 miles from the mouth. Above that it be- comes feebler ; and-for a confiderable diftance below the rapids, though there is a fenfible rife and fall of two or three feet, yet, even in the dry feafon, the current is conftantly down, only more gentle during the rife or flood, and there alfo the conti- nuance of the rife is very fhort, not more than two or three hours. Some obfervations upon the Soi/ of the different parts of the country, may be the fubject of a future communication. I will only add at prefent, what I think has more than con- _ jectural foundation, wz. That this moft recent of countries, together with the large additional parts {till forming on its coaft, appear to be the productions of two of the greateft rivers on the globe, the Amazons and the Oroonoko. If you caft your eye upon the map, you will obferve from Cayenne to the bottom of the gulph of Paria, this immenfe tract of fwamp, formed by the fediment of thefe rivers, and a fimilar tra@t of fhallow muddy coaft, which their continued operation will one day elevate. ‘The fediment of the Amazons is- carried down thus to leeward (the weftward) by the conftant currents, - which Of GUIANA. 63 which fet along from the fouthward and the coaft of Brafil. That of the Oroonoko is detained, and allowed to fettle near its mouths, by the oppofite iflands of Trinidad, and ftill more by the mountains on the main, which are only feparated from that ifland by the Bocos del Drago. The coaft of Guiana has remained as it were the great eddy or refting-place for the wafhings of great part of South America for ages; and its own comparatively {mall ftreams have but modified here and there the grand depofit. W. LocuuHEAD. IIE. - : 7 Ate: Base i ; - wrest, ui “in Mink bint ie ie shay Cue Behe MMi mea i “pe fs Aus ary Foner MEA RRR, ‘s i Wel 1yU RE a Yes ee] Seal BAY sat qe Hine fh Se es hey, be rstast wit) i enyrete ae Ta, ora pier teed 2 tebe Beye. erwrcity valet. ei Ree ee aE Ae gel: hit nats pias er sale hide: Parle the ¥ i Resbaee! te i : Tigh rey’ 7 eae *. “ y ; ¥e iis OnE Rnaee! Sah teat ie aes | gw nat ty heat ‘Agta: be (dardet et ee Biles kt ee Peg 3 van iy! ir) Fee fon Ah allo: i Sie -Geheeriabaie ogee er mbt! teaehent whi ty; nn roth. iar Svawre ra Bre Wht, Chis atte: taane Das: aa ie baptt baat: : PAAR jane si +paladut mad poet). hocrhisig but | ae BLE tis, Hg ew ha pepe el igre whe pinichit wih i ae “6h By, Oe Tapes oh weeks hee KA Wey don 7.08 pena lbh Bi a BT aan ry er Made oY ffias 1s aie A aetinty SSP pete alee tate hgh aie Rais va “" Sgt debs ee ten ave ot’ besa “Shute i or He ey wt ‘make cae, aaah, & fie | 8 hay 4 a ee i Ps YY >) Lat minal hail oe Shee tse G tenella c ats} Pe ae Ae hi inten at I Fah: Te. We upri ms . 4 i \ 4 : = | ‘ape cs | co ‘. +i oF (2% 5 Walnae, cba ‘ ; sh , \" c= . % \ ri a | . 5 \ 4 Ill. 4 fhort Paper on the Principies of the ANTECEDENTAL CatcuLus. By {AMES GLENIE, E/g; M.A. F.R.S. Lonp. & EDIN. [Read Dec. 1. 1794.] EVERAL of my friends have fuggefted to me the propriety of publifhing fomething of the kind now offered to the Society, obferving, that the great brevity with which the ‘ Antecedental Calculus is written, and the very concife form in which it is delivered to the public, may lead fome to form erroneous opinions refpecting the principles on which it is founded. In compliance partly with their requeft, I have drawn up this fhort paper, which I hope will remove even the - poffibility of mifconception on that head, and convince every intelligent reader, that the antecedental calculus has the fame geometrical principles for its ground-work, that the formulz in the Univerfal Comparifon themfelves have, from which I origi-' nally derived it more than twenty years ago. In the third page of that treatife, I have fhewn from the © firft formula in the third theorem of my Univerfal Comparifon, that, when R and Q are any two given magnitudes of the fame kind, and A, N, B are any homogeneous magnitudes, the ex- cefs of the magnitude, which has to B a ratio having to the ratio of A+-N to B the ratio of R to Q, above the magnitude, Vou. IV. I which 66 - On the PRINCIPLES of the which has to B a ratio, having to the ratio of A to B the fame ratio of R to Q, is geometrically exprefled by R acca ie R—Q_ ee R R--Q_ R-2 R-3Q, A - re — .« ——. —— ANB + ie Sew res et aati bis ae fa ae or, which comes to the fame thing, that the expreffion, RR dgle a a Reekigse | A— + —., A=. N+ —. ZA. TN’*+ &c. . 2 Qi MQ Qe a RD GE Oe so. > eaeendnamne oO : Danie Wee geometrical expreflion, Or gee Qa i R— A—B R—Q R- Aa Bie ASA SS aca rae +&c. by the afore- faid geometrical expreflion. In the fame page, I have fhewn, that the excefs of the mag- nitude, which has to B a ratio, having to the ratio of A to B the ratio of R to Q, above the magnitude, which has to B a ra- tio having to the ratio of A—N to B the ratio of R to Q, is geometrically exprefled by RRO, RK RO R201 ge. of g Song Agen tee K—O_ , or, which comes to Q the fame thing, that the expreflion, x R q RQ , AcB R-QR2Q , ADBy mere Q CA, B + Q . 2Q A B 4+- &e; LX= ©. ; ceeds ANTECEDENTAL CALCULUS. 67 ceeds the geometrical expreflion, ne Reo VRS , rs ene erg Sa are TE Oa CBE SS RIES A ree ee: -aforefaid geometrical expreflion. Ir is almoft unneceflary to obferve, that the two expreffions, which have refpectively to B ratios, having to the ratios of A-+4N to B, and A—N to B the ratio of R to Q, give us: Ro SO yt BROS, RO eh be Ean A Soe ee for the geo- oO metrical magnitude, which has to B a ratio, having to the ratio of A=N to B the ratio of R to Q. But as this expreflion muft vary indefinitely with the endlefs variations in the quantity of the magnitude B, its geometrical ftandard of comparifon, fo, when we fuppofe it to become numerical, we get an indefinite number of arithmetical formulz, referring to different ftandards of comparifon. For B may be then reprefented by 1, 25 35 45 5s &c. I, ¥ 2, Y 3; v Ay: V5, &c. or &c. &c. fine limite. And in that particular cafe, when it is reprefented by 1 or unit, this geometrical formula gives the arithmetical one, (put- ting r and q for R and Q,) eee A NG OD A Tt Ant N 34 + &e. ; + q7 4 q q 29 q Fina Ogi ag dasa which 68 On the PRINCIPLES of the which has to 1, or unit, a ratio having to the ratio of A+N to 1 the ratio of ry tog. Init A, N, 7,9, may be any numerical or arithmetical magnitudes whatever, whole, fractional, furd or mixed. ‘This formula, or antecedent, is exactly what is com- monly called the Binomial Theorem. Ir we fuppofe B to be reprefented by 2, we derive immedi- ately from this geometrical antecedent or formula, the following arithmetical one : Ra A ee ee eee q 2 Z 2q 2 med, ras? of g which has to 2 a ratio having to the ratio of A+N to 2, the ra- tio of 7 to 4. To fuch arithmetical formule there is no end or limit. And this I take to be the true and fyftematic method of deriving them, viz. from geometrical antecedents or formule, when they are fuppofed to become numerical. WHEN I or unit is the ftandard of comparifon, its various combinations with itfelf and the other numerical magnitudes, do not appear in the formula or antecedent. This circumftance renders it of all others the moft commodious for common ufe in algebra and arithmetic, though the leaft calculated of any for fhewing the rationalia or ground-work of the various opera- tions in thefe two fciences. For when the formula or antece- dent fhows the different combinations of the confequent or ftandard of comparifon with itfelf and the other numerical. magnitudes, it is a fort of language announcing or exhibiting the reafons of its formation. Ir is evident, that half the excefs of the two geometrical expreflions taken together, which have refpectively to B ratios, having to the ratios of A+-N to B and A—N to B, the ratio of in oe R to Q, above twice 0: or twice the magnitude, which Q has ANTECEDENTAE CALCULUS. 69 has to Ba ratio having to the ratio of A to B the fame ratio of _R to Q, is truly exprefled by R RHQ ,RaQvs, R RQ ze R-3Q_,R- Raley a 10 aa. 2G, a (OTM un ONO 4Q ears and that half the difference of thefe exprefflions is R RQ, R RQ R2Q, RQ ee ee ~N3 + &e. BerorE I proceed farther, however, in the confideration of thefe expreffions, it may not perhaps be improper to premife the few following lemmata, which are almoft too evident to re- quire demonftration. LEMMA L _Ir any ratio be compounded with its inverfe, or the inverfe of any ratio the fame with it, the compofition produces a ratio of equality. ‘ For of the three magnitudes A, B, A, by the definition of compound ratio, (5. Evc. Srmson’s edit.), the ratio of A to B, compounded with the ratio of B to A, is the ratio of A to A, or a ratio of equality ; and if the ratio of C to D be equal to, or the fame with the ratio of A to B, its inverfe, D to C, is equal to, or the fame with the ratio of B to A, (Prop. B. ibid.) : Therefore, (Prop. F. Euc. 5. Simson’s edit.), the ratio of A to B, compounded with the ratio of D to C, is the fame with the 3 ratio 70 On the PRINCIPLES of the ratio of A to B compounded with the ratio of B to A, or a ra- tio of equality. Q. E. D: LEMMA IL. Ir with the inverfe of any ratio there be compounded a ratio greater than it, the compofition produces a ratio of greater ine- quality, or a ratio of which the antecedent is greater than the confequent ; and if with the inverfe of any ratio, there be com- pounded a ratio lefs than it, the compofition produces a ratio of lefs inequality, or a ratio of which the antecedent is lefs than the confequent. | Frrst, Let the ratio of C to D be greater than that of A to B. Then (10. Euc. 5.) the magnitude, which BA DCE has to D the ratio of A to B, is lefs than C. If E therefore be that magnitude, the ratio of | C to D, compounded with the ratio of B to A, is the fame with the ratio of C to D, com- pounded with the ratio of D to E, (Propofi- | tions B. and F. 5. Euc. Sim.). Wherefore, the ratio produced by compounding the ratio of C to D with that of B to A, is the fame with the ratio of Cto E. But fince C is greater than FE, the ratio of C to E is greater than that of .E to E,: (10. Etc. 5.), or.a ratio of equality. Q.E. D, SECONDLY, ee ———————— ANTECEDENTAL CALCULUS. FE Seconpty, Let the ratio of F to D be lefs than that of A to B. Then (10. Eve. 5.) the magnitude, which B AD F E has to D the fame ratio with that of A to B, | is greater than F. If E therefore be that | magnitude, the ratio of F to D, compounded with the ratio of B to A, is the fame with the | ratio of F to D, compounded with the ratio | of D to EF, (Propofitions B. and F. 5. Euc. | Sim.). Wherefore the ratio produced by - compounding the ratio of F to D with that of B to A, is the fame with the ratio of F to E. But fince F is lefs than FE, the ratio of F to E is lefs than that of E to E, (10. Euc. 5.), or a ratio of equality. Q.E.D. LEM M Ze IIT. Ir any ratio be compounded with a ratio of equality, it is not altered thereby. For the ratio of C to D, compounded with the ratio of A to A, is the fame with the ratio of C to D, compounded with the ratio of D to D, (Prop. F. 5. Sim. Euc.), which, by the defini- tion of compound ratio, is that of CtoD. Q.E.D. . TuEsE three Lemmata are alfo evident from Formula 1.. Theorem 1. Univerfal Comparifon. Cor. From this and Lemma 1. with the definition of com- pound ratio, itis evident, that if with any ratio there be com- pounded a greater one, there arifes a ratio greater than it; and that, if with any ratio there be compounded a lefs one, there arifes a ratio lefs than it. 1 } Oe ee L EM 92 On the PRINCIPLES of the LEMMA IV. Ir from any magnitude there be taken the half, and from the remainder its half, and fo on, the halves fo taken, be their number ever fo great, are together lefs than the magnitude. | Cc D Ey EF A———— SB For let AB be any magnitude, AC the half of AB, CD the half of CB, DE the half of DB, EF the half of EB, and fo on. THEN it is manifeft, that AC, together with CD and DE and EF, &c. are lefs than AB, from which they are taken. Q. E.D. Cor. 1. The ratio of AB to the fucceflive halves AC, CD, DE, EF, &c. taken together, be their number ever fo great, is greater than a ratio of equality; and the ratio of any one of the terms to all the fucceeding ones taken together, be their - number ever fo great, is greater than a ratio of equality. Cor. 2. Hence it follows, that of any feries or fucceffion of terms, in which the half of each term has to the immediately fucceeding one a ratio of equality, each term has to all the fuc- ceeding ones, be their number ever fo great, a ratio greater than that of equality. Cor. 3. Hence it alfo follows, that if CD, inftead of one half, be one third of AC or CB, DE one fourth of CD, EF one fifth of DE, and fo on, the ratio of any term to all the fucceeding ones taken together, exceeds a ratio of equality more than the ratio it has to the fame number of fucceeding terms, be that number ever fo great, exceeds it, when each term has to the. immediately fucceeding one the ratio of two to one, SCHOLIUM. ANTECEDENTAL CALCULUS. 73 Scuotium. In like manner is it fhewn, that, if AC bea third part of AB, CD of AC, DE of CD, EF of DE, and: fo on, the ratio of each term to all the fucceeding ones taken together, be their number ever fo great, exceeds the ratio of two to one; ‘and, in general, if the ratios AB to AC, AC to CD, CD to DE, DE to EF, &c. be refpectively the fame with that of A to N, that the ratio of each term to all the fucceeding ones, be their number ever fo great, exceeds the ratio of A—N to. N. This is alfo evident from the well known method of finding the aggre- gates of geometrical progreflions; and if the ratio of AC. to: CD be greater than that of AB to AC, the ratio of CD to DE greater than that of AC to CD, and fo on, the ratio of any term to all the fucceeding ones, be their number ever fo great, exceeds the ratio. of A—N to N, more, than the ratio it has to the fame number of fucceeding terms, exceeds it, when each term has to. the immediately fucceeding one the ratio of A to N. I now proceed to prove, that each of the general geometrical. expreflions in p. 3. Autecedental Calculus, viz. RRQ. R RHQ R22 R RQ RaQ >» R-3Q. ~A—_—N , é TA: -N3 + &ce. or a, ae oie Gan eee pet oes _ and. R RQ. RRQ RQ, R RQR1Q RGQ., —. A——_"N -—. a A. N+ — ; - &e: ea Sg geen 8 1) eT gag hed) wit ps Q R R-@ has to N’a ratio nearer to the ratio of & a to B than any: i given or afligned ratio, or than by any given or afligned. mag- | nitude, when A+N' and A-—-N have either to A or B ratios: nearer to that of equality than any sinha or afligned ratio, or. Won. LV. K than: a4 On the PRINCIPLES of the than by any given, or afligned magnitude, and. R and Q are twe given magnitudes of the fame kind. PROPOSITION L ‘In this cafe, the firft term in each of thefe general expref- fions has to twice the fecond, the fecond to thrice the thifd, the third to four times the fourth, the fourth to five times the fifth, and fo on, a ratio greater than-.any given ratio. For, if this be denied, let C and D be two given homogene- ous magnitudes, and let:the ratio of C to D be greater. In each; the ratio of the firft term to. twice the fecond, is that ‘of A to SSN, and its inverfe SON, or (N+ SF) ; to A, is the ratio compounded of the ratios of R—Q to Q, and N to A, (For. 1. Theor. 1. Univerfal Comparifon). Now, the ratio compounded of this ratio, and that of C to D, is a ratio compounded of the three ratios C to D, R—Q to Q,; and N to A. But, fince R and Q are given magnitudes, R—Q is a gi- ‘ven magnitude, (4. Euc. Data), and the ratio of R—-Q to Qa given ratio, (1. Data). Wherefore the ratio compounded of the ratios of C to D and R—Q to Q,; is alfo given, (67. Data). This ratio, however, compounded with that of N to A, is the fame : R— with the ratio compounded of C to D, and eon to, A,. \ Emet fince that of A to N is by the hypothefis greater than any given ratio, the ratio compounded of C to D and R—Q to Q, com- pounded with that of N to A, produces a ratio of lefs inequa- Dc Sik pinin ~N 18 lity, (Lemma 2.). Confequently, the ratio of A to greater than any given ratio C to D. Wherefore, the fuppofi- tion, ANTECEDENTAL CALCULUS. 75 fition, that any given ratio C to D is greater than it, is ab- furd. AnD, fince the ratio of the fecond term to thrice the third, is that of A to = N, it is proved exaétly in the fame manner, that this ratio is greater than any given ratio. And precifely in the fame way is it demonftrated, that the ratio of the third term to four times the fourth, is greater than any given ratio ; and fo on. Cor. 1. If R—Q be equal to Q, the ratio compounded of” € to D, and R—Q to Q, is the fame with that of C to D, (Lem- ma 3.); and if R—Q be greater or lefs than Q, the ratio com- pounded of C to D and R—Q to Q, is accordingly greater or lefs than that of C to D, (Cor. to Lemma 3.). nar Aeve Ba tary culight Oe | ne oa, “QO. pe B16 UG pee2@ ‘ ~N, &c. are lefs than any given or: Cor. 2. The magnitudes afligned magnitude. Cor. 3. The ratio of each term to all the fucceeding ones, be their number ever fo great, is greater than any given ratio, . (Scholium to Lemma 4.). Cor. 4. The magnitudes a tS Sny, At SON, &c. have refpectively to A-ratios nearer to that of equality than any given Tatio, or than by any given magnitude. Cor. 5. The magnitude which has to B a ratio, having to the ratio of A to B the ratio of R to Q, has to twice the firft term, in each of thefe general geometrical expreflions, a ratio greater than any given ratio. K 2 PRO- 76 On thee PRINCIPLES of the PROPOSITION IL THE ratio of each of thefe two general geometrical expref- R—Q a i a R ee fions to N, is nearer to the ratio of QU ped to B than any given or affigned ratio. For, fince the firft term in each has to twice the fecond a ra- tio greater than any given or afligned ratio, (Prop. 1.), and the fecond has to all the fucceeding terms, be their number ever fo great, a ratio greater than any given ratio, (Cor. 3. Prop. 1.) the ratio of the firft term to all the fucceeding ones is a fortiort greater than any given ratio, being greater than that of A to = -N. Wherefore each of thefe expreflions has to the firft term a ratio nearer to that of equality than any given or aflign- ed ratio, or than by any given or afligned magnitude, (Cor. 4. Prop. 1.). Confequently the ratios which thefe expreflions have to N, are nearer to the ratio of the firft term in each to N, than any given or afligned ratio. But the ratio of the firft term in R-Q : R Q each to N, is that of oO" See” B. Therefore, &c. Q.E.D. - OTHERWISE: In the firft expreflion, the firft term, with twice the fecond, is much greater than the whole of it, (Cor. 3. Prop. 1.), and confequently has to N a greater ratio than the expreffion itfelf has to N, (8.E. 5.). But this ratio exceeds the ratio of the firft term to N lefs than any given or afligned ratio. For, if the ra- t1o ANTECEDENTAL CALCULUS. 79 tio of the firft term to N be decompounded with it, or its in- verfe, the ratio of N to the firft term, be compounded with it, there arifes the ratio of A +A to A, which (Cor. 4. Prop. 1.) is nearer to a ratio of equality than any given ratio. Iw the fecond, the excefs of the firft term above twice the fe- cond is lefs than the whole expreffion, and confequently has to N a lefs ratio than the expreflion itfelf has to N, (8. E. 5.). But if with it the ratio of N to the firft term be compounded, there arifes the ratio of A ASSN to A, which (Cor. 4. Prop. 1.) is nearer to a ratio of equality than any given ratio. Q.E.D, OTHERWISE: Ir it be denied, that each expreffion has to N a ratio nearer to the ratio of its firft term to N than any given ratio, let the ra- tio of two given magnitudes C and D be nearer to it, and let the ratio of Bto E, compounded with that of the firft term to Ate Q pea | : ° a Le ot N, or with the given ratio or to B, be equal to the gi- ven ratioC to D. But the magnitude, which has to B the ra- tio compounded of thefe two ratios, is (For. 1. Theorem t. Univerfal Comparifon), UTR ota pee = to B, which is greater than the ratio of the firft term to N, and lefs than the ratio of the firft expreflion to N, by the fuppofition, and confequently lefs than the ratio of the firft term with twice the 98 On the PRINCIPLES of the R—Q oma: the fecond to N. Therefore ee eee is lefs than Q GR = - R2Q Acre R RQ ues * -R Q . Oo heen N. But fince the ratio of a = a E,, Q being compounded of the firft term to N, and oe to E, is the fame with the ratio of C to D, E is a given magnitude, (2. Data), and B—E a given magnitude, (4. Data). Wherefore the given RO: R-2Q See els RRO “0 magnitude, a ae E> is lefs than cn Feet re Q which (Cor. 2. Prop. 1.) is lefs than any given magnitude, which is abfurd, In like manner is it demonftrated, that the ratio of the fe- cond expreffion to N, is nearer to the ratio of its firft term to, N than any given ratio. Q.E. D. SCHOLIUM.. IF the fame reafoning be applied to the expreflion, De ose: SO Sh ee ae ~N +— calli ak Nal which is half Q the difference of the two geometrical expreffions that have re{pectively to B ratios having to the ratios of A+N to B, jand A—N to B, the ratio of R to Q, we get the ratio of the firft term to twice the fecond, the fame with that of A _ to ReQs RR N’ Ce Lorre —, and the ratio of the fecond to four times the third, - ANTECEDENTAL CALCULUS. 79 third the fame with that of A to SE and. A on. THE general expreflion, (p. 5. Antecedental Calculus), gives A.N+C.M+M.N oo B the ratio, that is produced by compounding the ratio of C+N _ . to D with that of A+M to B, above the magnitude, which has to B the ratio compounded of the ratios of A to B and C to D. But it is demonftrated in the fame manner as above, that if A+M and C+N have refpedctively to A and C ratios nearer to that of equality than any given or afligned ratio, or than by any given or afligned magnitude, this expreffion alfo has to A.N + C.M for the excefs of the magnitude, which has to a ratio nearer to that of equality than any given ra- tio, or than by any given magnitude. And the demonftration is exactly the fame, when any number of ratios are compounded. In like manner, if the ratio of C+N to D be decompounded | with that of A-++M to B, we get the difference between the ex- preffion thence arifing, and the magnitude which has to B the ratio produced by decompounding the ratio of C to D with that CD.M—AD.N ot ; of A to B, equal to Kee Geen) a: But it 1s readily demon- {trated, as above, that if A+M and C++N have refpectively to A and C ratios nearer to that of equality than any given or aflign- ed ratio, or than by any given or afligned magnitude, this ex- cae CD.M — AD,N : preffion. alfo has te ——~gr———~ a ratio nearer to that of equa- lity than any given ratio, or than by any given or afligned mag- nitude. | Ir is manifeft then, that in this calculus no indefinitely {mall or infinitely little magnitudes are fuppofed, but only magni- tudes lefs than any that may be given or affigned, and ratios _mearer to that of equality than any that may be given or aflign- ed, 80 On the PRINCIPLES of the ed, and that it is equally geometrical with the method of ex- hauftions of the ancients, who never fuppofed lines, furfaces, or folids, to be refolved into indefinitely fmall or infinitely little elements. The expreflion infinitely little magnitude indeed im- plies a contradiction. For what has magnitude cannot be infi- nitely little. THIS geometrical danseini: though 1 it has no connection with the various modifications of motion, is equally convenient in its application with the method of fluxions, (which is unqueftiona- bly a branch of general arithmetical proportion, in which 1 or unit is the common ftandard of comparifon, as well as the con- fequent of every ratio compounded, or decompounded). EXAMPLE I. In the circle ATB, (Fig. I. Pl. I.) let the diameter AB be re- prefented by D, TE perpendicular to it by Y, and AE by X. Then {1 3. E. 6.) Y* is equal to the re@tangle DK—X’. But the antecedental of Y° is 2YY, and that of DX —X’ is DX—2XX, (p. 6. Antecedental Calculus). Wherefore D—2X is to 2Y as ¥ to X, that is, as TE to CE, (p.g. zt. Cal.). Confequently CE is a third proportional to EO and TE. EXAMPLE fF. To find the furface of the fphere of which ATBA is a great circle, (Fig. I. Pl. I.). Tue furface of the fpherical fegment, cut off by the circle, of which TE is the radius, has to the fquare on any given line B, a ratio compounded of the circumference of faid.circle to B, and of the antecedental of the curve AT to B, (Ant. Cal. p. 9.) But the antecedental of the curve is a fourth proportional to 2YD and | ANTECEDENTAL CALCULUS. 81 and. x, (ibidem). Wherefore, if 2YXp reprefent faid circum- ference, the antecedental of the fpherical fegment is pDX, of which the antecedent is PDX. EXAM PL Be Ti, Ir it be required to draw a tangent to the parabola (Fig. a. Pl. 1.) ATG at the point T ; let the latus rectum be seopeented by L. Then L.X is equal, to Y" ? and L. x to 2¥Y. Where- fore L is to 2Y (2TE) as ¥ to X, that is, (Ant. Cal. p. Q.) a6 TE to CE, which is confequently equal to twice AE. EXAMPLE IV. _ In finding the area of the parabola, fince K is equal to or YX, equal to 2YY Bis 2Y Y 2X3 3, the antecedent of which is oie or its equal ZXXY. | \ OTHERWISE: THE ratios of the antecedentals of the area AET, and the re€tangle under AE, and any given line B to the fquare on B, are YX and BX to B’, But YX is equal to = , the antece- 2Y3 & dent of which is =” “or its equal — x XY; and the antece- dent of BX is BX. Wherefore eh area of the parabola is two thirds of the rectangle AE, ET. VoL. IV. : L ' E X~ 82 On the PRINCIPLES, &c. EXAMPLE V. So to divide a ftraight line AB, that the reangle under the two parts AC, CB {hall be the greateft poflible. : | ae EL ree Let AB bereprefented by A, AC by X, and confequently CB by A—X. Then the rectangle. AC, CB is equal to AX—X’, the antecedental of which is AX—2XX, which, when fup- pofed equivalent to nothing, (according to Ant. Cal. p. 7.) gives A equal to 2X, or AC equal to CB. To multiply examples would be ufelefs. I will take an op- portunity, as foon as I conveniently can, of applying this cal- culus to feveral phyfical problems of importance, and particularly fome refpecting the refiftance of fluids ; and will fhew, that as it furnifhes a much greater variety of ways for exprefling antece- dentals than the fluxionary calculus does for fluxions, fo it wilt open new and extenfive rules for finding antecedents, as yet altogether unknown in the inverfe method of fluxions. ALTHOUGH the notation be in reality of no importance, I a e ~ prefer x. Y, &c. to X, Y, &c. as more indicative of the ori- gin of this mode of reafoning, which was derived from an exa- mination of the antecedents of ratios in general geometrical comparifon. 1 4 iM 2 - if . ; a _™ : BY; Os-~ IV. OpsERVATIONS on the TRIGONOMETRICAL TABLEs of the BrAuMINS. By FoHN PLATFAIR, F. R.S. Evin. and Profeffor of Mathematics in the Univerfity of Edinburgh. [Read April 6. 1795.] 1. JN the fecond volume of the Afatic Refearches, an extract is given from the Surya Siddbanta, the ancient book which has been long, though obfcurely, pointed out as the fource of the aftronomical knowledge of the Brahmins. The Surya Siddhanta is in the Sanfcrit language: It is one ofthe Saftras, or infpired writings of the Hindoos, and is called the Jyotith, or Aftronomical, Saftra. It profeffes, as we learn from Mr Davis, the ingenious tranflator, to be a revelation from heaven, communicated to MeEyaA, a man of great fanctity, about four millions of years ago, toward the clofe of the Satya Jug, or of the Golden Age of the Indian mythologifts; a period at which man is faid to have been incomparably better than he is at pre- fent ; when his ftature exceeded twenty-one cubits, and his life extended to ten thoufand years. INTERWOVEN, however, with all thefe extravagant fiGtiions, this fingular book contains a very fober and rational fyf{tem of aftro- nomical calculation ; and even the principles and rules of trigo- nometry, a {cience of all others the moft remote from fable, and the leaft fufceptible of poetical decoration. It is on the con- ae a ftruction 84 OBSERVATIONS on the ftruGtion of the tables contained in this trigonometry, that [I ° now beg leave to offer a few remarks. 2. Ir is neceflary to begin with obferving, that the cir- cumference of the circle is here divided into 360 equal parts, each of which is again fubdivided into 60, and fo on. The fame divifion was followed by the Greek mathematicians ; and this coincidence is the more to be remarked, that it re- lates to a matter of arbitrary arrangement, and one by no means neceflarily connected with the properties of the circle. There are indeed fome very obvious properties of that curve, that make it, though not neceflary, at leaft convenient, that the number of parts, into which the circumference is divided, fhould be a number divifible both by 3 and by 4, that is, that it fhould be a multiple of 12 ; but nothing more precife can be determin- ed from the nature of the curve itfelf. The agreement of two nations, therefore, in dividing the circumference of the circle precifely in the fame manner, as it cannot well be attri- buted to chance, muft be fuppofed to refult from fome communi- cation having taken place between them, if it were not that ano- ther very probable caufe may be afligned for it. In Greece, and — no doubt in every other country, the divifion of the circle, i ito equal parts, is of a much older date than the origin of trigono- metry, and muft be as ancient as the firft circular inftruments ufed for meafuring angles in the heavens. ‘The inventors of thofe inftruments naturally fought to make the divifions on them correfpond to the fpace which the fun defcribed daily in the. ecliptic ; and they could eafily difcover, without any very pre-. cife knowledge of the length of the folar year, that this. might be nearly effected by making each of them the 36oth part of the whole circumference. Accordingly the famous circle of OsyMAND1IAsS, in Egypt, defcribed by HERopotus, was divided into 360 equal parts. THis: TRIGONOMETRY of th BRAHMINS., 85 . Tuts principle may therefore have guided the aftronomers, both of the Eaft and of the Weft, to the fame divifion of the circle, without any intercourfe having taken place between them. It has certainly directed the Chinefe in their divifion, though it has led them to adopt one different from the Hindoo and Egyp- tian aftronomers. They divide the circle into 365 parts and 4, which can have no other origin than the fun’s annual motion : and fome fuch divifion as this; may perhaps have been the firft that was employed by other nations, who changed it however to the number 360, which nearly anfwered the fame purpofe, and had befides the great advantage of being divifible into ma- ny aliquot parts. The Chinefe, again, with whom the {ciences became ftationary almoft from their birth, have never attempt-. ed to improve on the method that firft occurred to them. 3. THE next thing to be mentioned, is alfo a matter. of arbi- trary arrangement, but one in which the Brahmins follow a method peculiar to themfelves. They exprefs the radius of the circle in parts of the circumference, and fuppofe it equal to. 3438 minutes, or Goths of a degree. In this they are quite fin- gular. Proxtemy, and the Greek mathematicians, after dividing the circumference, as we have already defcribed, fuppofed the radius to be divided into 60. equal parts, without feeking to af- certain, in this divifion, any thing of the relation of the dia- meter to the circumference :. and thus, throughout the whole of their tables, the chords are expreffed in fexagefimals of the ra- dius, and the arches in fexagefimals of the circumference. They had therefore two: meafures, and two units; one for the circum~- ference, and another for the diameter. The Hindoo mathema~ ticians, again, have but one meafure and one unit for both, v7z. a minute of a degree, or one of thofe parts whereof the circum- ference contains 21600. From this identity of meafures, they derive no inconfiderable advantage in many calculations, though. it muft be confefled, that the meafuring of a ftraight line, the radius,, 86. OBSERVATIONS on the radius, or diameter of a circle, by parts of a curve line, namely, the circumference, is a refinement not at all obvious, and has probably been fuggefted to them by fome very particular view, which they have taken, of the nature and properties of the cir- cle. As to the accuracy of the meafure here affigned to the radius, v7z. 3438 of the parts of which the circumference con- tains 21600, it is as great as can be attained, without taking in {maller divifions than minutes, or 6oths of a degree. It is true to the neareft minute, and this is all the exactnefs aimed at in thefe trigonometrical tables. It muft not however be fuppofed, that the author of them meant to affert, that the circumference is to the radius, either accurately or even very nearly, as 21600 to 3438. I have fhewn, in another place *, from the Inftitutes of AKBAR, that the Brahmins knew the ratio of the diameter to the circumference to great exaétnefs, and fuppofed it to be that of 1 to 3.1416, which is much nearer than the preceding. Cal- culating, as we may fuppofe, by this or fome other proportion, not lefs exact, the authors of the tables found, that the radi- us contained in truth 3437’. 44%. 48’, &c.; and as the frac- - tion of a minute is here more, than a half, they took, as their conftant cuftom is, the integer next above, and called the radius 3438 minutes. The method by which they came to fuch an accurate knowledge of the ratio of the diameter to the circum- ference, may have been founded on the fame theorems which were fubfervient to the conftruction of their trigonometrical tables +. . 4. THESE tables are two, the one of fines, and the other of verfed fines. The fine of an arch they call cramajya or jyapinda, and the verfed fine utcramajya. They alfo make ufe of the co- fine or bhujajya. Thefe terms feem all to be derived from the word jya, which fignifies the chord of an arch, from which the name * Tranf. R. S. Edin. vol. II. p. 185. Phyf. Cl. + See Note, § 6. TRIGONOMETRY of the BRAHMINS. 87 name of the radius, or fine of go°, viz. #rijya, is alfo taken. This regularity in their trigonometrical language, is a circum- ftance not unworthy of remark. But what is of more confe- quence to be obferved,'is, that the ufe of fines, as it was un- known to the Greeks, who calculated by help of the chords, forms a ftriking difference between the Indian trigonometry and theirs. The ufe of the fine, inftead of the chord, is an improve- ment which our modern trigonometry owes, as we have hither- to been taught to believe, to the Arabs ; and it is certainly one of the acquifitions which the mathematical f{ciences made, when, on their expulfion from Europe, they took refuge in the Eaft. But whether the Arabs are the authors of this invention, or whether they themfelves received it, as they did the numerical characters, from India, is a queftion, which a more perfect knowledge of Hindoo literature will probably enable us to re-. folve. . No mention is made in this trigonometry, of tangents or fe-. cants; a circumftance not wonderful, when we confider that the ufe of thefe was introduced in Europe no longer ago than the middle of the fixteenth century. It is, on the other hand, not a little fingular, that we fhould find a table of verfed fines in the ‘Surya Siddhanta; for neither the Greek nor the Arabian ma- thematicians, had any fuch, nor had we, in modern Europe, till. after the time of PeTiscus, who wrote about the end of the cen- tury juft mentioned. 5- NEXT, as to the extent and accuracy of thefe tables. The firft of them exhibits the fines to every twenty-fourth part of the quadrant, that is, the fine of 3°. 45’, and of all the multiples pena arch) wiz. 7°. 30',° 11°, 15°, Cc. up to Oo". Phe“table of” verfed fines does the fame. In each, the fine, or verfed fine, is expreffed in minutes of the circumference, but without any frac- tions of a minute, either decimal or fexagefimal; and, agreeably to the obfervation already made, when the fraction that ought tO 88 OBSERVATIONS on the to have been fet down is greater than 4, the integer next greater is placed in the table. ‘Thus the fine 3°: 45’ being, when accu- rately expreffed in their way, 224’. 49”, is put down 225’; and fo of the reft. The numbers, therefore, in thefe tables, are only fo far exact as never to differ more than half a minute from the truth, and this very limited degree of accuracy gives no doubt to their trigonometry the appearafice of an infant fcience: But when, on the other hand, we confider the principles and rules of their calculations, rather than the numbers actually calculated, we find the marks of a fcience in full vigour and maturity: and we will acknowledge, that the Hindoo mathematicians did not fatisfy themfelves with the degree of accuracy above mentioned, from any incapacity of attaining to greater exactnefs. » THEIR rules for con{tructing their tables of fines, may be re- duced to two, vz. the one for finding the fine of the leaft arch in the table, that of 3°. 45’, and the other for finding the fines of the multiples of that arch, its triple, quadruple, tc. Both of thefe Mr Davis has tranflated, judging very rightly, that it was impoflible to give two more curious {pecimens of the geometri- cal knowledge of the Hindoo philofophers: the firft is extracted from a commentary on the Surya Siddhanta; the other from the Surya Siddhanta itfelf. 6. WiTH refpect to the firft, the method proceeds by the con- tinual bifection of the arch of 30°, and correfpondent extrac- tions of the {quare root, to find the fine and co-fine of the half, the fourth part, the eighth part, and fo on, of that arch. The rule, when the fine of an arch is given, to find that of half the arch, is precifely the fame with our own : “ The fine of an arch — being given, find the co-fine, and thence the verfed fine, of the fame arch : then multiply half the radius into the verfed fine, and the fquare root of the produét is the fine of half the given arch.” Now, as the fine of 30°, was well known to thofe mathemati- cians to be half the radius, it was of confequence given: thence, by TRIGONOMETRY of the BRAHMINS. 97 by the rule juft laid down, was found the fine of 15°, then of 7°. 30, and laftly of 3°. 45’, which is the fine required. Thus the fine of 3°. 45’ would be found equal to 224’, 44”, as above obferved, and, the fine of 7°. 30’, equal to 448’. 39”, and, taking the neareft integers, the firft was made equal to 225, and the fe- cond to 449*. 7. WueEN, by the bifections that have juft been defcribed, the fine of 3°: 45, or of 225’, was found equal to 224’, the reft of the table was conftructed by a rule, that, for its fimplicity and elegance, as well as for fome other reafons, is entitled to particular attention. It is as follows: “ Divide the firft jya- pinda, 225’ by 225; the quotient 1, deducted from the divi- dend, leaves 224°, which added to the firft jyapinda, or fine, gives the fecond, or the fine of 7°. 30’, equal to 449. Divide the fecond jyapinda, which is thus found, by 225, and dedu& 2, the neareft integer to the quotient, from the former remain- der 224’, and this new remainder 222‘, added to the fecond jya- pinda, will give the third jyapinda equal to 671’. Divide this laft by 225, and fubtract 3, the neareft integer to the quotient, from the former remainder 222’, and there will be left 219, . | M which, * By fuch continual bifections, the Hindoo mathematicians, like thofe of Europe before the invention of infinite feries, may have approximated to the ratio of the * - diameter-to the circumference, and found it to be nearly that of 1 to 3.1416 as above obferved. A much lefs degree of geometrical knowledge than they pofleffed, would inform them, that fmall arches are nearly equal to their fines, and that the fmaller they are, the nearer is this equality to the truth. If, therefore, they affumed the radius equal to 1, or any number at pleafure, after carrying the bifeGtion of the arch of 30, two fteps farther than in the above conftruction, they would find the fine of the 384th part of the circle, which, therefore, multiplied by 384, would nearly be equal to the circumference itfelf, and would aétually give the proportion of 1 to 3.14159, as fomewhat greater than that of the diameter to the circumfe- tence. By carrying the bifections farther, they might verify this calculation, or eftimate the degree of its exaétnefs, and might affume the ratio of 1 to 3.1416 as more fimple than that juft mentioned, and fufficiently near to the truth, 98 OBSERVATIONS on the which, added to the third jyapinda, gives the fourth; and fo on unto the twenty-fourth or laft.” Ir is not immediately obvious on what geometrical principle this rule is founded, but a flight change in the enunciation will remove the difficulty. The remainder, it muft be ob- ferved, from which the quotient is always directed to be taken away, is the difference between the two fines laft computed; and hence the rule may be exprefled more generally: Divide any fine by 225, and fubtract the quotient, or the integer neareft the quotient, from the difference between that fine and the fine next lefs ; the remainder is the difference between the fame fine and the fine next greater ; and therefore if it be added to the former, will give the latter. If then, (fig. 3. Pl. I), GA, GC, GE, be three contiguous arches in the table, of which the dif- ferences AC, CE, of confequence are equal, and of which the fines are AB, CD, and EF, the rule, as laft ftated, gives us CD—AB— i for the difference between CD and EF, and therefore EF= CRED a Meas =? 2cD—— AB, and al! ‘fo EF-+-AB=CD (2-)= cp(:). But 225 is the fine of 225 the arch 3°. 45’, and 449 of twice that arch, as already fhewn; and, therefore, according to this rule, if there be three arches, — of which the common difference is 3°. 45’, the fine of the mean arch will always have to the fum of the fines of the ex- treme arches, a given ratio, that namely, which the fine of 3°. 45° has to the fine of twice 3°. 45’, or of 7°. 30°; now, this is a true propofition ; and therefore we are in pofleffion of the principle on which the Hindoo canon is conftructed. 8. THE geometrical theorem, which is thus fhewn to be the foundation of the trigonometry of Hindoftan, may alfo be more generally enunciated. ‘“ If there be three arches in arithmetical progreflion, the fine of the middle arch is to the fum of the fines of ¥ TRIGONOMETRY of the BRAHMINS. 99 of. the two extreme arches, as the fine of the difference of the arches to the fine of twice that difference.” This theorem is well known. in Europe; it is juftly reckoned a very remarkable pro- perty of the circle ; and it,ferves to fhew, that the numbers in a table of fines conftitute a feries, in which every term is formed exactly in the fame way, from the two preceding terms, v7z. by multiplying the laft by a certain, conftant number, and fub- tracting the laft but one from the produdt. g. Now, it is worth remarking, that this property of the table of fines, which has been fo long known in the Eaft, was not ob- ferved by the mathematicians of Europe till about two hundred years ago. The theorem, indeed, concerning the circle, from which it is deduced, under one fhape or another, has been known to them from an early period, and may be traced up to the writings of Euci1p, where a propofition nearly related to it forms the 97th of the Data: “ If a ftraight line be drawn with- in a circle given in magnitude, cutting off a fegment containing - a given angle, and if the angle in the fegment be bifected by a ftraight line produced till it meet the circumference ; the ftraight lines, which contain the given angle, fhall both of them together have a given ratio to the ftraight line which bifects the angle.” This is not precifely the fame with the theorem which has been fhewn to be the foundation of the Hindoo rule, but differs from it only by affirming a certain relation to hold among the chords of arches, which the other affirms to hold of their fines. It is given by Evcuip as ufeful for the con- -ftrudtion of geometrical problems; and trigonometry being then unknown, he probably did not think of any other applica- tion of it. But what may feem extraordinary is, that when, about 400 years afterwards, Protemy, the aftronomer, con- ftructed a fet of trigonometrical tables, he never confidered Eu- CLIp’s theorem, though he was probably not ignorant of it, as * having any conneétion with the matter he had in hand. Ee M2. therefore, 100 OBSERVATIONS on the therefore, founded his calculations on another propofition, con- taining a property of quadrilateral figures infcribed in a circle, which he feems to have inveftigated on purpofe, and which is ftill diftinguifhed by his name. This propofition comprehends in faét Evcuip’s, and of courfe the Hindoo theorem, as a par- ticular cafe; and though this cafe would have been the moft ufeful to ProLemy, of all others, it appears to have efcaped his obfervation ; on which account he did not perceive that every number in his tables might be calculated from the two preceding numbers, by an operation extremely fimple, and every where the fame; and therefore his method of con{tru€ting them is infinitely more operofe and complicated than it needed to have been. Nor only did this efcape ProLemy, but it remained un- noticed by the mathematicians, both Europeans and Arabians, who came after him, though they applied the force of their minds to nothing more than to trigonometry, and actually enriched that fcience by a great number of valuable difcoveries, They continued to conftruct their tables by the fame methods which Protemy had employed, till about the end of the fix- teenth century, when the theorem in queftion, or that on which the Hindoo ruleis founded, was difcovered by VireTa. \We are however ignorant by what train of reafoning that excellent geo- meter difcovered it; for though it is publifhed im his Treati/fe on Angular Sections, it appears there not with his own demon- ftration, but with one given by an ingenious mathematician. of our own country, ALEXANDER ANDERSON of’: Aberdeen.. It was then regarded as a theorem entirely new, and f know not. that any of the geometers of that age remarked its affinity to the propofitions of Evctip and Protemy. ‘It was oon after applied in Europe, as it had been fo many ages: before in Hin- doftan, and quickly gave to the conftruction of ‘the trigonome- trical canon all the fimplicity which at feems capable of attaining. From all this, Ihink it might fairly be-concluded, evenif we od had ‘\ TRIGONOMETRY of th BRAHMINS. 10t had no knowledge of the antiquity of the Surya Siddhanta, that the trigonometry contained in it is not borrowed from Greece or Arabia, as its fundamental rule was unknown to the geometers of both thofe countries, and is greatly preferable to that which they employed. ) 10. CONSIDERABLE light may perhaps hereafter be thrown -on this argument, if it be found that the Surya Siddhanta con- tains a demonftration of this rule. It does not appear, however,, from the fragment we are.in’ pofleffion of, that any explanation ‘of the rule is given, either in that work, or in the commentary. Indeed I am not certain that the Surya Siddhanta contains any thing but rules and maxims, or that the author of it condefcends. to give any demonftrations of the propofitions which he enun- ciates. He may have felt himfelf relieved from the neceflity of doing fo, by his claim to infpiration ; and as he probably valued himfelf more on the character of a prophet, than-of a geometer, he may rather have inclined to exercife the faith, than the rea- ‘fon, of his difciples. However that be, by the rule above explained, the Brah- mins have computed a fet of tables, limited indeed in their accu- racy, but extremely fimple and compendious. ‘The rule is eafily remembered by one who has been accuftomed to. numeri- cal calculation, and is fuch, that, by help of it, he may at any time compofe for himfelf a complete fet of trigonometrical _tables, in a few hours, without the affiftance of any book what- ever. For the purpofe of rendering it thus fimple, the con- ‘wivance of méafuring the radius, and all the fines, in parts of ‘the circumference, feems to have been adopted: if we follow any other method, the rule, though it remain the fame in reality,. will aflume a form much lefs eafy to be retained in the me-- mory*. It has the appearance, lake nia Onbes things in the mt 4 : {cience _* Turis feems to me the moft probable reafon that can be affigned for the mea- faring of the radius, and the other ftraight lines in the circle, in parts of the circum- x xerence, JO2 OBSERVATIONS on the fcience of thofe eaftern nations, of being drawn up by one who was more deeply verfed in the fubje& than may be at firft ima- gined, and who knew much more than he thought it neceflary to communicate. It is probably a compendium, formed by fome ancient adept in geometry, for the ufe of others who were mere- ly practical calculators. 11. Ir we were not already acquainted with the high anti- quity of the aftronomy of Indoftan, nothing could appear more fingular, than to find a fyftem of trigonometry, fo perfect in its principles, in a book fo ancient as the Surya Siddhanta. The antiquity of that book, the oldeft of the Saftras, can fcarce be accounted lefs than 2000 years before our exra, even if we fol- low the very moderate fyftem of Indian chronology laid down by Sir Wittiam Jones *. Now, if we fuppofe its antiquity to be no higher than this, though it bears in itfelf internal marks of an age {till more remote J, yet it will fufficiently excite our won- der, to find it contain the principles of a fcience, of which the firft rudiments ference. It is remarkable that the Hindoos fhould have been thus led, at fo early a period, to put in practice a method, the fame in the moft material point, with one which has been but lately fuggefted in Europe as an important improvement in tri- gonometrical calculation. In the Phil. Tranf. for 1783, Dr Hutton of Woolwich propofed to divide the circumference, not into degrees, as is ufually done, but into decimals of the radius; and he has pointed out how the prefent trigonometrical ta- bles might be accommodated to this new divifion, with the leaft poffible labour, in a paper which difplays that intimate acquaintance with the refources, both of the na- merical and algebraic calculus, for which he is fo much diftinguifhed. His plan is, in one refpedt, the fame with the Hindoo method, for it ufes the fame unit to exprefs both the circumference and the diameter; in another refpe& it differs from it, v7z. in making the radius the unit, while the other afflumes for an unit the 36oth part of the circumference. Dr Hutton’s plan has never been executed, though it cer- tainly would be of advantage to have, befides the ordinary trigonometrical tables, others conftruéted according to that plan. * Afiatic Refearches, vol. II. p. riz, &c. + The obliquity:of the ecliptic is ftated at 24° in the Surya Siddhanta, as in all the.other aftronomical tables of the Hindoos which we are yet acquainted with. (Tranf. TRIGONOMETRY of the BRAHMINS. 103 rudiments are not older in Greece than 130 years before our era.. The bare exiftence of trigonometrical tables, though they belong undoubtedly to a very elementary branch of fcience, yet argues a ftate of greater advancement in the mathematics than may at firft. be imagined, and neceflarily fuppofes the application of geome- trical reafoning to fome of the more difficult problems of aftro- nomy and geography. As long as the furveying of land, and the ordinary menfura- tion of furfaces and folids, are the only pra¢tical arts to which the geometer applies his fpeculations, he will naturally content himfelf with conftructing his figures and plans by means of a feale, and an inftrument for meafuring angles, as by doing fo he may attain to all the accuracy he can defire. But when, in the figures that are to be thus delineated, the fides happen to be extremely unequal, and fome of the angles very acute, or very obtufe, graphical operations become inaccurate, and a very {mall error in the meafuring of one thing produces an enormous error in the eftimation of fome other. Lines, therefore, that extend over _a great tract of the earth’s furface, and much more thofe that extend to the heavens, cannot be compared with the fmaller lines, which we have an opportunity of meafuring, by the bare con- {truction: (Tranf. R. S. Edin. vol. II. p. 164.) Mr Davis concludes from this, (Afiatic Re- fearches, vol. If. p. 238), that if the obliquity diminith, at the rate of 50” in a hun- dred years, the Surya Siddhanta is at prefent about 3840 years old, which goes back. nearly 2000 years before the Chriftian era. But the diminution of the obliquity of the ecliptic, ts fuppofed confiderably too rapid in this calculation. According to Mayer it is 46" in a century; and according to De la Granee, (Mem. Berlin 1782), at a medium no more than 30”. This laft is moft to be depended on, as it proceeds on an accurate inquiry into the law of the fecular variation of the obliquity, that variation being by no means uniform. Let us however take the mean, viz. 38”, and the obliquity at the beginning of the prefent century having been 23°. 28’. 41”, we fhall have 5020 years for the age of the Surya Siddhanta, reckoned from that: date, or about 3300 years before Curist, which is near the era of the Caly Yung... 104 OBSERVATIONS on the ftruction of triangles and parallelograms ; and when ever fuch comparifons are to be made, fome other method mutt be fought for. It was precifely in fuch circumftances, that the inventive genius of Hipparcuus fuggefted the application of arithmetic to afcertain thofe ratios among the fides and angles of figures, which pure geometry afforded no method of exprefling. This union of geometry and arithmetic did not happen, however, till each of thefe fciences feparately had made great progrefs ; for before the days of Hiprarcuus, EucLip, ARCHIMEDES, and ApPpoLonius, had all flourifhed in fucceflion, and had pro- duced thofe immortal works, of which the luftre has not been ob- {cured by the higheft improvements of later ages. In the progrefs of fcience, therefore, the invention of trigonometry is to be confi- dered as a ftep of great importance, and of confiderable diffi- culty. It is an application of arithmetic to geometry, with which we are now too familiar, to perceive all the merit of the inventor; but a little reflection will convince us, that he, who firft formed the idea of exhibiting, in arithmetical tables, the ra- tios of the fides and angles of all poffible triangles, and contrived the means of conftructing fuch tables, muft have been a man of profound thought, and of extenfive knowledge. However ancient, therefore, any book may be, in which we meet with a fyftem of trigonometry, we may be affured, that it was not written in the infancy of fcience. 12. As we cannot therefore fuppofe the art of trigonometri- cal calculation to have been introduced till after a long pre- paration of other acquifitions, both geometrical and _atftro- nomical, we muft reckon far back from the date of the Surya Siddhanta, before we come to the origin of the mathemati- cal fciences in India. In Greece, the conftellations were firft reprefented on the fphere, if we take a medium between the chronology of Newron, and that which is now ge- nerally TRIGONOMETRY Gf the ‘BRAHMINS. TOs nerally received, about 1140 years before the Chriftian xra® ; and Hirrarcuus invented trigonometry 130 years before ea fame xra. Even among the Greeks, therefore, an) interval,, of ‘at leaft:1000 years, elapfed fromthe firft obfervations in aftro- momy, to the invention of trigonometry; and we have furely no reafon to fuppofe, that the pr es of knowledge ‘has bese more rapid in other countries. A THOUSAND years therefore muft be added to va age of the Surya Siddhanta, which we fuppofe here to be» 2000 before CuRIsT, in order that we may reach the origin of the fciences an ‘Hindoftan, and this brings us very nearly to the celebrated era of the Caly Yug, to which M. Baitty has already referred the conftru@tion of the aftronomical tables of that country. And here, I cannot help obferving, in juftice to an author, of whofe talents and genius the world has been fo unfeafonably and fo cruelly deprived, that his opinions, with refpect to this gra, appear to have been often mifunderftood. It certainly was not his intention to affert, that the Caly Yug was a real era, confidered with refpect to the mythology of India, or even that at fo remote a period the religion of Brahma had an exift- ence. ‘The religious and civil inftitutions of Hindoftan, as they now exift, may be all pofterior to this date, and their antiquity 1s probably to be determined from principles that are not the ob- jects of aftronomical difcuffion. All, -I think, therefore, that M. Baittiy meant to affirm, and certainly all that is neceflary to his fyftem, is, that the Caly Yug, or the year 3102 before our era, marks a point in the duration of the world, before which N the * The {phere of Curron and Muszus was conftrusted, according to Newton, ‘about the year 936 before Curist, (NEwTon’s Chron. chap. i. § 30). According to the fyftem generally received, the ancient fphere, defcribed by Evroxus, was conftruéted about 1350 years before Curist, (Dr Prayrarr’s Chronology, p. 37): The medium is 1143. 106 OBSERVATIONS, &c. the foundations of aftronomy were laid in the Eaft, and thofe obfervations made, from which the tables of the Brahmins have been compofed. . On this, however, and on many more of the particulars of the hiftory of thofe remote ages, great additional light will un-. doubtedly be thrown, by the complete tranflation of the Surya. Siddhanta. From the fpecimen which Mr Davis has given, we can neither doubt of the importance of fuch a work, nor of his abilities to execute it; and we truift, that, to the zeal and libe-- rality of our brethren of the Afiatic Society, the learned world will foon be indebted for the poffeflion of this ineftimable trea-- fure., V. Some GEOMETRICAL Porisms, with ExamPLes of their APPLICATION to the SoLuTION of ProsptEMs. By Mr WILLIAM WALLACE, Affiftant-Teacher of the Mathematics in the Academy of Perth. Communicated by Mr PLAYFAIR. [Read March 7. 1796.} E nature of thofe mathematical propofitions, which were called Porifms by the ancient geometers, is now no longer a ‘matter of uncertainty. The relation which they bear to other mathematical truths, the way in which they may at firft have been obferved, the kind of analyfis to be employed in their in- veftigation, their application to the folution of problems, have all been confidered by fome eminent mathematicians of the pre- fent age. THESE propofitions appear to have been held in high eftima- tion by the mathematicians of antiquity, becaufe of their great ufe in the analyfis of difficult problems, as we learn from the writings of Parpus of Alexandria: And fome fpecimens, which Jate inquirers into this fubjeét have given us, of their applica+ tion to the folution of problems, feem to juftify his very high character of them. _ Tue following paper contains fome porifms intimately con- nected with each other, and which feem capable of being ap- plied to the folution of a number of gcometrical problems. Ex- N a. amples 108 GEOMETRICAL PORISMS.. amples of their application are added, fome of which are pro- blems that have been long known, and others are new ; but the conftructions of the former, it is believed, differ from any hi- therto. publifhed. Althoughthere are feveral of thefeexamples, in appearance, little related to each other, yet their folutions are. effected by the fame general principle, which is alfo the founda-. tion all the porifins. PROP. Il. PORISM, Fig. 4, 5. Sura LET AB, AC, be two ftraight lines given by onnon lec B, be given points in thefe lines, a point H may be found, fuch, that any circle whatfoever pafling through A, the in- terfeCtion of the given lines, and H the point which may be found, fhall cut off from the given lines fegments BD, CE, adjacent to.the given points, and having: to. >-each. other the given ratio of « to PB, Sirpeaae the porifm to be true, and that,the point H is found. If a circle be defcribed through H,.A, and B one of the given © points, it muft alfo, pafs. through C the other given point, that the propofition may. be univerfally true. Therefore H is in the circumference of a given circle. Join BH, CH, DH, EH. The angle DHE is equal to DAE, that is, to. BHC, (fig. 4.) or DHE is the fupplement of DAE, (fig. 5.) and therefore equal to BHC; hence BHD is equal to CHE, but BDH is equal to CEH, there- fore the triangles BDH, CEH, are equiangular, and BH is to HC as BD to CE, that is by hypothefis in the given ratio of « to @; therefore if BC be joined, the triangle BHC is given in {pe- cies, and BC being given, BH and HC are given; therefore the ‘point H is given, which was to be found. _ Ir the fegments BD, CE, cut off from the given lines, lie in the fame dir ection with refpect to AB, AC, (fig..4.) the point H > will . %, . P ¢ \ - : sf ~— _— ee ee ree GEOMETRICAL PORISMS. Tog will be in the fame fegment of the circle with the angle BAC; but if BD, CE, lie in contrary directions to AB, AC, (fig. 5.) then H will be in that fegment of the circle upon which BAC ftands. THE point H will be found by the following conftruction : Defcribe a circle through the points A, B,C. Join BC, which divide at G, fo that BG may be to GC in the given ratio of BD to CE, that is of « to 8, and if the fegments to be cut off are to lie in the fame direction with AB, AC, find F the vertex of the fegment upon which the angle BAC ftands, (fig. 4.) ; but if BD, CE are to lie in oppofite direCtions, (fig. 5.) find F the vertex of the fegment BAC, and in either cafe join FG, which produce to ' meet the circle in H the point to be found ; that is, if any circle be defcribed through H and A to meet the given lines in D and E,'BD.is to CE ase to6.) Join HB, HC, HD, HE. The tri- angles BDH, CEH are. fimilar, for the angle BDH is equal, to CEH, and becaufe the angle BHC is equal to DHE, therefore ‘BHD is equal to CHE; hence BD is to CE as BH to HC, that ‘is, (becaufe HG bifects the angle BHC), as BG to GC, or as «. $20) p. % Ir is-evident that the point H may be alfo. found, by taking ~ any fegments BD, CE, in the given ratio of a to 3, and defcrib- ‘ing a circle through the points D, A, E, to meet the circle BAFC in H the point required. If the given lines be parallel, and the ‘points B, C, alfo the ratio of BD to CE, (fig. 6.) given as-before, the indeterminate circle will be ‘changed into a ftraight line paf- fing through a given point H, which will be without the given lines, or between them, according as BD, CE, are to lie in the fame, or in-contrary, direétions with AB, AC. » PROP. IE . 110 GEOMETRICAL PORISMS. PROP. IL PORISM, Fig. 7. PLI. Let AF, AG be two ftraight lines given by pofition, a point H{ may be found, fuch, that any circle whatfoever defcri- -bed through it, and A the interfeétion of the given ines, to meet them in D and E, fhall cut off from them feg- ments AD, AE, whofe fum fhall-be a given line M. Suppose the porifm to be true, and that the point is found, ‘and circle deferibed as above, let given points B, C be fo taken, that BA and AC-may be together equal to DA and AE, that is, by hypothefis to the given line M, then BD will be equal to CE. If a circle be defcribed through the given points A, B, C, by hy- pothefis it will meet the circle pafling through A, D, E, in H the point which ‘may be found. Join BH, CH, DH, EH. The ‘angle BHC is equal to DHE, each being the fupplement of BAC, therefore BHD is equal to CHE; now, HDB is equal to HEC, and BD is equal to CE, therefore the triangle HBD is equal to HCE, and BH 1s equal to CH, alfo DH to EH ; hence the angle BAH is equal to CAH, and H is in a ftraight line bifecting the angle FAG, but it is alfo in the given circle BAC; therefore the point H is given, as was required. Hence this conftruction: Take B and C two given points, fo that BA and AC may be together equal to M, and through A, B, C defcribe a circle. Draw AK bifedting the given angle FAG, and meeting the circle ABC in H the point required, that is, if any circle be defcribed through H and A, to meet the gi- ven lines in D and E, the fum of DA and AE fhall be equal to the fum of BA and AC, that is, by conftrudtion to the given line M. The fynthetical demonftration follows readily from the preceding analyfis. ‘ PROP. III ee ee GEOMETRICAL PORISMS. 11s PROP. UI. PORISM, Fig. 8. Pl. IL. Let AF, AG be two ftraight lines given by pofition, a point H may be found, fuch, that if any circle be defcribed through it, and A the interfeétion of the given lines, to. meet them in D and_E, the difference between AD and AE fhall be equal to a given line N. THE analyfis of this propofition will differ in nothing material from the laft, and the point required may be found thus: Take- B and C, two given points, fo that the difference between BA and. AC may be equal to N.. Through the points A, B, C, de- {cribe a circle. Draw AK bifecting the angle contained by FA one of the given lines, and AL the other line produced at their - interfection, and AK will meet the circle ABC in H the point which may be found; that is, if any circle be deferibed through . H and A, to meet the given lines in D, E, the difference between. AD and AE is equal to N the given line. Join AH, BH, CH, DH. The triangles HCE, HBD are equal to one another in every refpect, for if BC be joined, the angle HBC is.equal to HAL, that is, by conftruction to. HAB, there- fore HB is equal to HC; in the fame way it appears that HD : is equal to HE; now, the angle DHE is, equal to DAE, that is to BHC, therefore BHD is equal to CHE, hence BD is equal to CE, and the difference between DA and AE is the fame with. the difference between BA, AC, which by conftruction is equal, to the given line M.. THEsE two laft_propofitions tse confidered ‘as particular cafes of the following propofition. | PROE TV... 112 GEOMETRICAL PORTSMS. PROP. IV. PORISM, Fig. 4,5. PLL ‘Two ftraight lines AB, AC being given by pofition, and two lines P, Q_ being given in magnitude, a point-H may be found, (fig. 5.) fuch, that any circle deferibed through it and A the interfeCtion of the given lines, to meet them in D, E, fhall cut off from them fegments AD, AE, fo that PXAD+QXAE, fhall be equal to a given fpace. Alfo, the fame things being fuppofed, a point H may be found, (fig. 4.) fo that Px AD —QXAE, thall be See to a given fpace. LET given points B, C, be taken in either cafe agreeing with the hypothefis of the propofition, or fo that PX AB+Q x AC, ( fig. 5.) may be equal to PKAD+Q XAE, -and’ fo hat PXAB—QXAC may be equal to PX AD—Q XAE, (fig. 4:) then, m both cafes, PX BD will be equal to Q XCE ;° there- fore BD is to CE as Q to P, that is, in a given ratio, and the points B, C being given, the point H may be found, (Prop. 13 Construction. Let given points B, C be taken as above direfted, and if PX AD+Q x AE is to be a given fpace, (fig. 5.) find a point H, (Prop. 1.) fo that any circle defcribed through © - A and H may meet the given lines in D, E, fo that BD, CE may lie in contrary directions to AB, AC, and have to each other the given ratio of Q to P, then PX BD will be equal to QXCE, and adding the common fpace PX AB-+QXAE to each, we get PX AD+QX AE, equal to PX AB-+Q*X AC, that is, to the given fpace, as was required. But if Px AD—Q XAE is to be a given fpace, (fig. 4.) find H, (Prop. 1.) fo that any circle paffling through H, A may cut off fegments BD, CE, in the given ratio of Q to P, and lying towards the fame parts with AB, AC, then PXBD is equal to Q x CE, ————— GEOMETRICAL PORISMS. 113 Qx CE, and Px AD —Q xX AE, will be equal to Px AB—Qx AC, that is, by conftruction to the given {pace. LEMMA, Fig.-9. Pl. I. Ir circles be defcribed through A and C any two angles of a triangle ABC, to meet each other at D a point in AC, and the remaining lines AB, BC, in E and F; their other in- terfeCtion H, the remaining angle B, and the points E, F, are in the circumference of a circle. Join DH, EH, FH. The angle AEH is equal to ADH or CFH, that is, BEH is equal to BFH, hence the points H, B, D, F areinacircle. Q. E. D. PROP Vaart OkRis M,. Pip. to. Pim Ler AB, AC, BC be three ftraight lines given by pofition, a point H may be found, fuch, that if any circle be defcri- bed through H, and B the interfeétion of any two of the given lines, to meet them in D and F, and if DF be joined ‘meeting the remaining line at E.. The line DF fhall be divi- ded at E, into fegments having to each other a given ratio. Suppose that the point H is found. Join HA, HB, HC; join alfo HD, HE, HF. Since, by hypothefis, a circle may pafs through the point which is to be found, the interfeGtion of any two of the given lines, and the points where DF meets thefe _ lines, therefore the points H, A, D, E are in a circle, and the an- gle HEF is equal to HAD or HAB; now the points H, B, D, F are fuppofed to be in a circle; fince therefore in the triangle ABC, circles pafs through two of its angles A, B, and meet each other at D, a point in AB, (Lemma.) the points H, C, E, F are alfo 114 GEOMETRICAL PORISMS. alfo in a circle; therefore the angle HCF is equal to HEF, that is, (as has been fhewn), to HAB; hence the point H, which may be found, is in acircle paffing through the points A, B, C, what- ever be the given ratio of DE to. EF. Let this circle be defcribed. . Because the points H, A, D, E are in a circle, the angle HAC is equal to HDE, and becaufe H, C, E, F are in a circle, the angle HFE is equal to HCA; therefore the triangles AHC, DHF are fimilar. In the fame manner it appears, that AHB is fimilar to EHF, and CHB to EHD. " Let AC be divided at K, fo that AK. may be to KC, in the given ratio of DE to EF, the point K will thus be given. Join HK meeting the circle in G. The triangles AHC, DHF being fimilar, and -having AC, DF, fimilarly divided at K, E, the tri- angles AHK, KHC will therefore be fimilar to DHE, EHF, which have been proved fimilar to BHC, AHB; therefore the angle AHB is equal to CHK or CHG, and the arch AB is equal to CG, hence G is a given point, and K being given, the line GH will be given by pofition; therefore the point H is given which was to be found. Construction. Defcribe a circle through the points A, B, C, let AB, BC, be the lines upon which D and F, the extremities of the indeterminate line, are.to be placed, and let AC be the line which is to meet it in E, fo that DE may be to EF, in the given ratio of detoef. Find K, fo that AK may be to KC as de to ef, draw BG parallel to AC, meeting the circle in G, join GK meeting the circle in H, the point which may be found; that is,, if any circle be defcribed through H, and B the interfe¢tion of any two of the given lines, to meet them in D and F, and if DF be joined, meeting the remaining line at E, the line DF fhall be divided at E, fimilarly to the given line def. - Let AH, BH, CH be joined, alfo DH, EH, FH.” The angle HDF or HDE is equal to HBF, that is, to HAE, the points. H, 4, D, E are therefore in a circle, now the points H, 8B, D, F are. ae 1 GEOMETRICAL PORISMS. rs are in a circle, therefore (Lemma.) the points H,T, EF, F are alfo ina circle. The angle HDE is equal to HBC, that is, to HAK, and fince HEF is equal to HCF, therefore HED is equal to HCB, that is, to HGB or HKA; hence the triangles HDE, HAK are fimilar, and fince HFE is equal to HCK, the triangles HEF, HKG are alfo fimilar ; therefore DE is to EF as AK to KG, that is,as detoe/f. Cor. 1. The lines DH, EH, FH contain given angles, and have to each other the given ratios of AH, KH, CH. Cor. 2. The line DF cuts off fegments DA, EK, FC from _ the given lines, adjacent to given points in them, and having to each other the given ratios of HA, HK,HC. For the angles HDB, HEK, HFC are equal among themfelves, and fince BCH or BGH, that is, AKH, is the fupplement of each of the angles HCF, HAD, HKE, the angles HAD, HKE, HCF are equal a- mong themfelves, therefore the triangles HAD, HKE, HCF are fimilar, and AD, KE, CF are proportional to the given lines AH, KH, CH. PRORSOVEO PORES NMP Fig? t1.* Pi ‘i, Let AB, AC, BE, DE be four ftraight lines given by pofi- tion ; a point P may be found, fuch, that if any circle be defcribed through it and B, any of the fix interfections of the given lines, to meet the lines through whofe interfection it pafles in G and L, and if GL be joined, meeting the re- maining lines in H_ and K, the fegments GH, HK, KL have given ratios to one another, which ratios are to be found. Because, by hypothefis, the points P, A, G, H are in a circle, and alfo the points P, F, H, K, it will appear, as in the analyfis of laft propofition, that P is in a circle defcribed about the tri- _ angle ADF; in the fame way it will be found, that P muft be in circles defcribed about each of the triangles ABC, DBE, O 2 | FCE. ie GEOMETRICAL PORISMS. FCE, Therefore, that the propofition may be univerfally true, thefe four circles muft interfeét one another at the fame point. Axsour any two of thefe triangles, as ABC, DBE, let circles be defcribed, the point P muft be at their interfection. Because ADF is a triangle, and through two of its angles A, D, circles are defcribed, meeting each other at B, a point in AD, therefore (Lemma.) P, their other interfeCtion, and the points F, C, E, are in a circle; and becaufe FCE is a triangle, and circles pafs through C, E, two of its angles, and meet each other at B, a point in CE, therefore (Lemma.) the points P, A, D, F are in a circle. Thus, it appears, that circles defcribed about each of the four triangles ADF, ABC, DBE, CFE, pafs through the fame point P as was to be inveftigated. It remains to inquire, whether the ratios of GH, HK, KL to one another be given. Join PB, PC, PE, alfo PG, PH, PK, PL. The angle © GPH is equal to GAH, that is, to BPC, and PGH is equal to PBC, therefore the triangles BPC, GPH are fimilar, and the an- gle PHK is equal to PCE; but HPK is equal to HFK, that 1s, to CFE or CPE, hence the triangles HPK, CPE are fimilar, and PKL is equal to PEL. Now, if PN be drawn, fo that the angle BPN may be equal to GPL, that is, to the given angle GBL, it is evident that the point N is given, and will be in a circle paf- fing through P, and touching AG at B; the angles NPE, LPK will thus be equal, and the triangles NPE, LPK fimilar. Since, therefore, the triangles BPC, CPE, EPN are fimilar to GPH, HPK, KPL, it follows, that BN, GL are fimilarly divided by the given lines CH, EK, therefore the ratios of GH, HK, KL are the fame with the given ratios of BC, CE, EN. Construction. About ABC, DBE any two of the four _ triangles formed by the given lines, let circles be defcribed, they will meet each other at P, the point which is to be found. THRO GH. ees Se ee ee ee Oe GEOMETRICAL PORISMS. Ti7 Turovucu P and B, the interfection of any two of the given lines, let a circle be defcribed to touch one of them at Bb, and cut the other at N, the line BN will be given, and the ratios of GH, HK, KL, the fame with the given ratios of BC, CE, EN to one another. Tue fynthetical demonftration follows readily from the ana--. lyfis, and for the fake of brevity is here omitted. Cor. 1. The lines PG, PH, PK, PL, contain given angles, and have to each the given ratios of PB, PC, PE, PN. Cor, 2. The line GL cuts off from the given lines, fegments BG, CH, EK, NL, adjacent to given points, and having to each other the given ratios of PB, PC, PE, PN. For the points P, A, G, H, being in a circle, the angle PGB is equal to PHC; and fince P, F, H, K, are in a circle, the angle PHC is equal to PKE, which in like manner will be found equal to PLN. Now, the angles PBA, PCF, PEF, PNB are equal among themfelves, there- _ fore their fupplements PEG, PCH, PEK, PNL are equal, and _ the triangles PBG, PCH, PEK, PNL are familar, therefore BG, CH).EK, NE are proportional to the given lines BP, CP, EP, NP. PROP. VI. THEOREM, Kg. 12. Pl. HI. Let PGAB,. PFAC, PEAD, toc, be any. number of given circles, each of which pafles through the fame two points A, P; from.A, either of thefe points let a ftraight line, given by pofition, be drawn, meeting the circles at B, C, D, &c.. and another meeting them at E, F,G, &c. Let ftraight lines GB, FC, ED, téc.. be drawn,. joining thefe points, fo as to form, with the lines paffing through A, triangles GAB, FAC, EAD, &c, in each of the. circles. If, through P, the common interfeétion of the circles, and Q, the interfection of: : 118 GEOMETRICAL PORISMS. of any two of the lines, a circle be defcribed to meet them in K and L, a lime joining KL, and meeting the remaining lines, will be divided by them into fegments HK, KL, LM, MN, We. having to each other given ratios. Ler Q, R, 5, ec. be the remaining interfeétions of GB, FC, ED, c. Becaufe GRE is a triangle, and circles PGAB, PEAD pafs through G, E, two of its angles, and meet at A, a point in GE, the points P, R, B, D, are ina circle, (Lemma.) in’ the fame way it appears, that circles may pafs through P, 8, C, D, and P,Q, B, C, tc. Becaufe it is now proved, that in che tri- angle CDS, a circle may pafs through P, C, B, Q, and. another through P, D,B, R; therefore the points P, S, R, Q, are ina circle. (Lemma.) Thus it may be fhewn, that circles defcribed about each of the triangles, formed by the intercepted fegments of the ftraight lines, will all pafs through the fame point Py From P draw ftraight lines to the points of interfection of one of the given lines, with all the others, as PA, PB, PC, PD, te. Join PH, PK, PL, PM, PN, tc. SincE P, Q, K, L, are in a circle, the angle BKP is equal to CLP ; now, the angles PBG, PCF, are each equal to. PAG; therefore the angles PBK, PCL, are equal, and the triangles PBK, PCL, fimilar ; hence KP is to PL as BP to PC; now the angle KPL is equal to KQL, that is, to BPC; therefore the tri- angles KPL, BPC, are fimilar, and the angle PLM will be equal to PCD. But the points P, S, C, D, having been proved to lie in a circle, if PS be joined, the angle PCD will be equal to PSD, therefore PLM is equal to PSD or PSM, hence the points P, 5, L, M are inacircle. In the fame way it may be fhewn, that P, G, H, K are in a circle, as alfo P, D, M,N, @c. and that the triangles PAH, PDM, tc. are each fimilar to PBK and PCL, and hence that PHK is fimilar to PAB, and PLM to PCD, We. - Through P defcribe a circle to touch AG at A, and meet AD in So aes en a x. or» eee a 4 ‘ 7 GEOMETRICAL PORISMS. Tig in V, which will be a given point, fince GA, AD, are given 2 pofition. Join PV, the angle PVA is equal to PAE or PDS, that is, EP, «D,:M, N being in a circle) to PNM, and PDV is equal to PMN, the triangle PMN is therefore fimilar to PDV ; and fince the angle PVA is equal to PDS, alfo FNV to PMD, the triangles PDM, PVN are fimilar. Thus it appears, that HN and AV are fimilarly divided by the lines BK, CL, DM, &c. ; now, the points A, B, C, D, V, tc. are given; therefore the ratios of HK, KL, LM, MN, tc. to one another are given. Q. E. D. Cor. 1. The lines PH, PK, PL, PM, PN, &c. contain given angles, and have to each other the given ratios of PA, PB, PC, Pee; Se, Cor. 2. The line HN cuts off from the given lines, fegments fae. LG, DM, VN, tc. adjacent to given points, and hav- ing alfo to one another the given ratios of PA, PB, PC, PD, PV, &%c.; for the triangles PAH, PBK, PCL, PDM, PVN, ‘te. have been proved equiangular ; and therefore AH, BK, CL, DM, VN, dc. are proportional to PA, PB, PC, PD, PV, &e. *. PROP. VIII. * Tt may be proper to remark here, that,.in the preceding propofitions, the ftraight lines given by pofition, as well as the indeterminate ftraight line, which is cut by them into fegments, having to each other given ratios, and which alfo cuts off from them fegments adjacent to given points, and having to each other given ra- tios, are tangents to a parabola, of which the point that is required to be found is the: focus, This confideration fuggefls fome curious propofitions, relating to tangents to. the parabola. Some of them have been obferved by Dr Hatxey, in his tranflation of the Seé?zo Ratzonis of APPOLLONIUS. Owner very obvious application of the propofitions above hinted at, is to defcribe-. - parabolas that fhall pafs through given points, and touch ftraight lines given by pofi. tion. 120 GEOMETRICAL PORISMS. PROP. VIL SPO RIS M, Fie rs. Plt Let CA, CB, AB be three ftraight lines given by pofition, a point H may be found, fuch, that if through H, and B, C, any two of the interfections of thefe lines, there be defcribed circles HBEF, HCDE, to meet each other at E, a point in BC, and the remaining lines at Dand F.. If DE, EF, DF be joined, the triangle DEF fhall be fimilar to a given triangle def, and fhall have its angles upon the given lines in a given order. BeEcAusE circles are defcribed through C, B, and meeting each other at E, a point in CB, therefore their other interfection H, the remaining angle A, and the points D, F, are in a circle. (Lemma.) Let a circle be defcribed through H, C, A,’to meet CB in G, and another through H, B, G, to meet AB in K, Join HA, HG, HK, alfoHD, HE, HF. The angles ADH, GEH, KFH, are equal to one another, and the angles CAH, CGH, BKH are equal, therefore HAD, HGE, HKF are equal, and the triangles HAD, HGE, HKF are fimilar ; therefore DH is to HE as AH to HG, and EH is to HF as GH to HK; now, the angles DHE, EHF are equal to DCE, EBF, that is, to AHG, GHK; hence the quadrilateral HDEF is fimilar to HAGK, and the triangle DEF is fimilar to AGK ; now, the an- gles EDF and DEF are given by hypothefis, therefore GAK and AGK are given; but A is a given point, and AK is given. by pofition, therefore AG and the point G are given; therefore GK and the point K are alfo given, and H, the interfection of . the given circles GAC, GBK, will be given, which was to be found. Construction. ‘Take a given point, which, to render the conftruétion more fimple, may be at A, one of the interfections of GEOMETRICAL PORISMS. 121 of the given lines. Let AG, GK be fo drawn as to form a triangle AGK, fimilar to the given triangle def, and having its angles placed upon the given lines, in the given order. Through A, G, any two of its angles, and C, the interfection of the lines upon which they are placed, defcribe a circle; through G, K, and B, the interfeétion of CG, AK, let another circle be defcribed, meeting the former in H, the point to be found, which will alfo be ina circle paffing through K, and touching CA at A. Tue demontftration follows eafily from the preceding analyfis. Cor. tr. The lines HD, HE, HF contain given angles, and have to each other the fame ratios, with the given lines HA, HG, HK. Cor. 2. The lines AD, GE, KF have alfo to each other the given ratios of HA, HG, HK. mek OP. IX,. THEOREM,.Fig,.14..P), Ill Ler Ea, Ed, Fe, Gd, &%c. be any number of ftraight lines given by pofition. Let P bea given point. Through P,. and E, the interfection of any two of the given lines, let a _ circle be defcribed to meet them in A and B ; through P, B, and H, the interfeGtion of BJ, with one of the remaining lines, let a circle be defcribed to meet that line in C. Through P, CG, and K, the interfection of Cc, with one of the remain- ing lines, let a circle be defcribed to meet that line in D, and fo on if there be more lines. Join AB, BC, CD, We. DA. The rectilineal figure ABCD, tc. is given in fpecies. TAKE 4, a given point in EA, through P, E, a, defcribe a circle to meet EB in 4, through P, H, 4, defcribe a circle to meet HAC in ¢, through P, K, c, defcribe a circle to meet KD in d, and fo on if there be more lines. Join Pa, PA, alfo PB, Pd, PC, ) P Pe, 122 GEOMETRICAL PORISMS. Pc, PD, Pd, 8c. Becaufe the points P, E, A; B, are ima circle, the angle PAa is equal to PBJ; now PaA is equal to PJB; for PaE is equal to PdE, the triangles PaA, PJB are therefore fimi- lar. In the fame manner it may be fhewn, that PB is fimilar to PcC, and that again to PdD, tc. Therefore PA is to PB as Pa to Pé,-and PB to PC as Pé to Pc, and PC to PD as Pe to Pd, <%c.; now the angles APB, BPC, CPD, tc. are equal to AEB, BHC; CKD, t&c. that 1s, to aPb, 6Pc, cPd; e.therefore if ali, bc, cd, ‘8c. Ad be joined, the reétilineal figure PABCD, 9c. is fimilar to Padcd, &c; and leaving out the fimilar triangles PAD, Pad, the redtilineal figure ABCD, tc. is fimilar to abcd, tfc. Now the points P, E, a, being given, the circle pafling through them is given; therefore 4 is a given point; in like manner ¢, d, Wc. are given points; therefore the figure aled, We. ~ is given; therefore ABCD, tc. to which it ig fimilar, is given in fpecies. Q. E. D. Cor. 1. The lines PA, PB, PC, PD, €c. contain given an- gles, and have to each other the given ratios of Pa, Pé, Pc, Pd, we Cor. 2. The fegments Aa, Bd, Cc, Dd, tc. of the given lines, adjacent to the given points a, 3, c, d, &&c. have alfo to each other the given ratios of Pa, Pd, Pe, Pd, tc. Cor. 3. If there be any number of ftraight lines given by pofition, there may be innumerable reétilineal figures fimilar to one another, and having their angles upon the ftraight lines given by pofition. PROP.) Kio PO RAS My Pigs ngwiPle 1: Ler A and B be two given points in the circumference of a — given circle. Let Cbea given point in KC, a ftraight line given a eee SS ee GEOMETRICAL PORISMS. 123 piven by pofition. There may be found a ftraight line KD given by pofition, and alfo a given point D in that line, fuch, that if AE, BE be infle@ted to any point in the cir- cumference of the given circle, they fhall cut off from KC, KD, fegments FC, GD, adjacent to the given points, and having to each the given ratio of « to 6. Suppose the line KD, and the point D to be found. If AH, BH be inflected to the circle, fo that AH may pafs through C, then BH muft pafs through D, the point which may be found, otherwife the propofition would not be univerfally true. Now, C being given, the point H, and the line BH, will be given by pofition. Let AL be drawn parallel to KC, then BL muft be parallel to KD, the line to be found ; hence it appears, that the angle GKF is equal to ALB, that is, to GEF; therefore the points E, K, G, F are in a circle, and the angle DGB is equal to CFA; now DBG is equal to CAF; therefore the triangles DBG, CAF are equiangular, and AC is to BD as CF to DG, that is, by hypothefis, as # to 8; now AC is given, and BH is given by pofition, therefore the point D is given, but BDG is equal to the given angle ACF, therefore DG is given by pofi- tion. Construction. Join-AC, meeting the circle in H. Join BH, and, as @ is to 6, fo let AC be to BD. Through H, D, C defcribe a circle to meet FC in K, Join DK; then D is the given point, and DK is the line given by pofition, which are to be found ; that is, if AE, BE be inflected to any point in the circumference, to meet the-given lines in F, G; CF thall be to DG as AC to BD, oras ato 6. The arable wise: 3 is eauily de- rived from the aie. THE foregoing propofitions, in one point of view, may be confidered as exhibiting innumerable folutions of certain geo- metrical problems of the indeterminate kind, to each of which, P.2 if ee 124 GEOMETRICAL PORISMS. if fome condition, unconnected with the hypothefis of the pro- pofition, be added, there will be formed a problem perfeétly li- mited in its nature. Tue method of applying the porifms to the folution of many problems is obvious enough ; and, as fome of thefe may be of a very extenfive nature, and fuch as many others can be reduced to, therefore the utility of the porifms will by this means be greatly extended. The condition that may be joined to the hy- pothefis of each porifmatic propofition, it is evident, may be greatly varied : And, hence, it were eafy to form abundance of problems, differing from any hitherto propofed: but this would extend the paper to too great a length. We fhall therefore on- ly give a few examples, of which, let the firft be the Sectio Ra- tionis of the ancient geometers. ; PR ODP.. XT EO BL BV Fie. 76. Pl atl Two ftraight lines AB, AC are given by pofition, and two points B, C are given in thefe lines. It is required to draw a line through P, a given point, without them, to meet them in D and E, fo that BD may have to CE the gi- ven ratio of M to N. Because the ratio of BD to CE is given; if a circle be de- fcribed through the points A, B, C, there is given a point H in — the circumference, fuch, that the points A, H, D, E are ina circle, (Prop. 1.) therefore if HD, HA be joined, the angle HDP is equal to HAE, that is, toa given angle; now H and P are given points, therefore D is in the circumference of a gi- ven circle, but it is alfo in AB, a line given by pofition ; there- fore D is a given point, and PE is given by pofition, which was to be found. Con- GEOMETRICAL PORISMS. 125 Construction. Through A, B, C defcribe a circle; inflect BH, CH to the circumference, fo that BH may be to CH in the given ratio of BD to CE, or of M to N*, thus H will be a given point. If the fegments BD, CE to be cut off, are to lie in the fame direction with AB, AC, the point H muft be found in the fame fegment with BAC; but if they are to lie in contrary di- rections, then H muft be taken in that feement upon which BAC ftands. Join AH and PH, upon which defcribe a feg- ment of a circle, that may contain an angle equal to HAC, which is given. This circle may cut AB in two points D, 2. Join PD and Fd, meeting the remaining line in E and «; thefe lines cut off fegments BD, CE, or Bd, Cz, having to each other the given ratio of BH to HC, or of M toN. Join HD, HE. Becaufe the angle PDH is by conftruction. equal to HAE, the points A, H, D, E are in a circle; therefore the angle HEA is equal to HDA, that is HDB is equal to HEC; now, HBD is equal to HCE, for HBA is equal to HCA, there- fore the triangles HCE, HBD are fimilar, and BD is to CE as BH to HC, that is, by conftru@tion, as M to N. ‘Ir is evident that this problem may admit of four folutions in general, if there be given no limitation with refpect to the di- rection in which the fegments are to be cut off from the given lines ; but the data may be fuch as to render it capable of three and alfo of two folutions only. THE next example fhall be the Seé#io /patii of the ancients. PRO Po XS "PROBE EM, Fig! rn Ph me Two ftraight lines AB, AC are given by pofition, and two: points B, @ are given in thefe lines. It is required to draw a. * THE manner of doing this has been fhewn in Prop. x. 126 GEOMETRICAL PORISMS. a ftraight line through P, a given point, without them, te meet them in D and E, fo that the rectangle BD, CE may be equal to a given fpace. Suppose that DE is drawn as required. Join PC which will be given in pofition and magnitude. Draw PF parallel to AC, and take F, fo that the rectangle CP, PF may be equal to the given fpace, the point F will therefore be given; draw FL pa- rallel to CP, meeting AB in K, and PD in L, then FL and the point K will both be given by pofition. The triangles LFP, PCE are fimilar; therefore LF is to FP as PC to CE, and the rectangle LF, CE is equal to the rectangle FP, PC, which, by hypothefis, is equal to the rectangle BD, CE, therefore FL is equal to BD ; now, B and F are given points, and BK, FK are lines given by pofition ; therefore (Prop. 1.) if a circle be de- {cribed through K, B, F, there is a given point H in the circum- ference, fuch, that K, H, L, D are in a circle; therefore, if this point be found, and HD, HL, HK joined, the angle HDL is equal to HKL; therefore HDP is equal to HKF, that is, to a given angle; but H and P are given points, therefore D is in the circumference of a given circle; but itis alfo in a ftraight line given by pofition ; therefore D is a given point, and PD is given by pofition, Construction, Join P and GC, either of the given points in the given lines; draw PF parallel to CA, and take F, fo that the given {pace may be the rectangle CP, PF. Draw FL parallel to CP, meeting AB in K, and through the points F, B, K defcribe a circle. Find H in the circumference, fo that BH may be equal to FH. Join HK and HP, upon which defcribe a feg- ment of a circle, that may contain an angle equal to HKF; this circle may meet AB in two points D, d. Join PD and Pd, meet- : ing GEOMETRICAL PORISMS. 127 ing AC in Eande The rectangles BD, CE, and Bod, Ce, are each equal to the given rectangle FP, PC. Let ED meet FK in L, join HL, HD. Becaufe by conftruc- tion the angle HDP is equal to HKF; therefore HDL is equal to HKL;; therefore the points H, K, D, L, are in a circle, and the angle HLK is equal to HDK, that is HLF is equal to HDB, now HFL is equal to HBD, alfo HF is equal to HB; therefore the triangles HFL, HBD are in all refpects equal, and FL 1s equal to BD. Again, the triangles LFP, PCE are fimilar, therefore FL is to FP. as CP to CE, and the re€tangle FL, CE is equal to the rectangle FP, PC, but FL is equal to BD, therefore the rec- tangle BD, CE is equal to the re€tangle FP, PC, that is to the given fpace. In the fame way it may be fhewn that the rec-- canes Bt Ce is equal ta FP, PC. PROP. Mh. PROPS LEM) *Fig. 18: PLiy.: foun ftraight lines DB, DF, CG, BG are given by pofition, it is required todrawa line to meet them in the points N,O,P,Q; fo that the line NQ may be divided at thefe points, fimilar-. ly to a given divided line 2 op q.. . Suppose the line NQ drawn as required. Becaufe DB, DF,. BF are three ftraight lines given by pofition, and that NQ is di-- vided by one of them at O into fegments, having to each other - 4 given ratio, if a circle be defcribed through the points B, D, F, there is & given point E in the circumference, fuch, that the points E, B,.N;Q are in a circle, (Prop. 5.). Again, becaufe CB, CG, BG are three lines given by pofition, and NQ _is-divi-. ded by one of them at P into fegmenits, having to each other a. Given ratio, if a circle be deferibed through B, C, G, there is.a given point Ain the circumference, fuch, that A, N, B, Q are in a circle, (Prop. 's.) |, Thus it appears, that there are given. ‘three 128 GEOMETRICAL PORISMS. three points A, E, B ina circle, pafling through N and Q, there- fore NQ is given by pofition. « | Construction. Let DB, BG be the lines upon which the extremities of NQ are to be placed. About the triangles BDF, BCG, defcribe circles, draw BH parallel to FD, meeting the circle DBF in H, and draw BK parallel to CG, meeting the circle CBG in K. In DF find L, fo that DL may be to LF as no to og, and in CG find M, fo that CM may be to MG as np to pq, jom HL meeting the circle DBF in EF, join alfo KM meeting the circle CBG in A. Through the points A, E, B defcribe a circle meeting DB, BG in N and Q, join NQ_meet- ing the other lines in O and P, and NQ_fhall be divided fimi- larly to 74g. Ir has been proved in Prop. 5. that the point E being found as above, if any circle pafs through E and B, and mect DB, GB in N and Q, the line joining NQ_ fhall be divided at O, fo that NO will be te OQ as DL to LF, that is by conftruction as no to og. Likewife, that the point A being found as above, if any circle be defcribed through A and B, to meet DB, BG in N and Q, the line NQ_ being drawn, fhall be di- vided at P, fo that NP will be to PQ as CM to MG, that is by conf{truction as ap to pg. Hence, it is obvious, that NQ is divided fimilarly to 2 ¢. Ir may be remarked, that the preceding conftruction points out very clearly, a circum{tance which appears to have efcaped the notice of fome Mathematicians that have given folutions of the problem,with a view to its application to Aftronomy. It is that the given ratios of NO, OP, PQ, to one another may be fuch as to render the problem indeterminate. Now, this it is evident will be the cafe, if the points A, E fhall both fall at & the interfe@tion of the circles. This cafe forms Prop. VI. of this paper, fo that it may be fufficient to add here, that the ratios which GEOMETRICAL PORISMS. 129 which render the problem indeterminate, are thofe which are required to be found, in the propofition juft now quoted. PROP, XIV. PROBLEM, Fig. 19. Pl. IV. THREE ftraight lines AB, AC, BD are given by pofition, and P is a given point. It is required to. draw PE to meet BD in E, and PG meeting AB in F, and AC in G, fo that the angle EPG may be given, and fo that EP may have to FG the given ratio of « tof. Suppose the lines drawn as required. In GP take PH equal- to FG, therefore the ratio of EP to PH will be given, now the angle EPH is. given, therefore Hs in a ftraight line given by pofition, (Apoll. Loci Plani, Lib. 1. Prop. 6.) let this line be LC. Bifeét PF in K, then becaufe P is a given point, and AB is given by pofition, the point K will be in a ftraight line given by pofition, (Loci Plani, Lib.1. Prop. 4.) let this line be LM. Becaufe GF is equal to PH, and FK to PK, therefore. GK is equal to KH, but the lines ML, MG, CL are given by _ pofition, therefore, (Prop. 5.) a given point N may be found in the circumference of a circle pafling through M, C, L, fuch, that the points N, M, G, K are in a circle, therefore if this point be found, and NG, NM joined, the angle NGK or NGP is equal to the given angle NML, now N and P are given points, there- fore G isin the circumference of a given circle, but it is alfo in a ftraight line given by pofition, therefore the point G is given. Construction. Find LC a ftraight line given by pofition, fuch, that if PE, PH be drawn meeting BD, CL, and contain- ing an angle EPH equal to the fupplement of the given angle ERG, 130 GEOMETRICAL PORISMS. EPG, the ratio of EP to PH may be the fame with the given ratio of @ to #. (Loci Plani, Prop. 6. Lib. 1.) Find alfo a ftraight line LM given by pofition, fuch, that PF drawn to any point in AB, may be bifected by itin K. Through L, M, C, the interfections of the given lines LM, AC, LC, defcribe a cir- cle. Draw CO parallel to LM, meeting the circle in O; bife@ ML in Q; join OQ meeting the circle in N ; join NM, and inflect NG, PG to AC, fo that the angle NGP may be equal to NML; draw PE, fo that the angle EPG may be fuch as is re- quired. Let GP meet CL in H, and AB in F, alfo LM inK ; join NH, NK, NL. Since NGP is equal to NML, the points N, K, G, M are in a circle, and the angle NKH is equal to NMG or N MC, that is to NLH; therefore the points N, K, L, H are in a circle, and the angle NHK 3 is equal to NLQ; now NKH is equal to NMG or NOC, that is (OC being parallel to ML) to NQL; therefore the triangles NKH, NQL are fimilar. In like manner it ap- pears, that NKG, NQM are fimilar; therefore ML and GH are fimilarly divided at Q and K, but ML is bifeéted at Q; therefore GH is bifected at K; now PF is alfo bifef@tea at K; therefore GF is equal to PH, and EP is to FG as EP to PH, that is, by conftruction, as @ to B. PRO RY AV. PO BY, EW Pie, 20; PRY. Turee ftraight lines AB, AC, BC are given by pofition, and three points D, E, F are given in thefe lines. Itis required to draw a ftraight line GHK to meet them, fo that DG, EH, FK may have to each other the given ratios that P, Qs R have among themfelves. Suppofe GEOMETRICAL PORISMS. 131 Suppose that the line is drawn as required. Becaufe the ra- tio of DG to EH is given, there is given (prop. 1.) a point M in the circumference of a circle pafling through A, D, E, fuch, that | the points A, M, G, H are inacircle. If this point be found, and MG, MH, MD, ME joined, the angle GMH is equal to GAH orto DME. Alfo if MA, DE be joined, the angle MHG is equal to MAG or to MED. Therefore the triangle MHG is fi- m ilar to thegiven triangle MED, and the angle MHG is given. In like manner, becaufe the ratio of EH to FK is given, there is given a point N in the circumference of a circle pafling through E, C, F, fuch, that N, C, H, K are in a circle: If NH, NK, NE, NF, NG, EF be joined, it may be proved, in the fame way, that the triangle NHK is fimilar to NEF, hence the angle NHK is given. Now, the angles MHG, NHK being each proved to be given, the angle MHN is given, and the points M, N_ being alfo given, the point H is in the circumference of a given circle ; but it is alfo in a ftraight line given by pofition ; therefore the point H is given, and the angles MHG, NHK being given, the line GK is given by pofition, which was to be found. Construction. Through the points A, D, E defcribe a cir- cle, and infleé¢t DM, EM to the circumference, fo that DM may be to EM as P to Q. Defcribe alfo a circle through C, E, F, and infleét EN, FN to the circumference, fo that EN may be to FN as Q to R. Join DE, EF, and infle¢tt MH, NH to the ftraight line AE, fo that the angle MHN may be the fupplement of the fum of MED and NEF; draw HG, fo that the angle MHG may be equal to MED; then NHK is equal to NEF. Join MG, MA. Becaufe the angle MHG is equal to MED or to MAG, the points M, A, H, G are in a circle; hence the angle MHE is equal to MGD; now MEH is equal to MDG; for MEA is equal to MDA; therefore the triangles MEH, MDG are fimilar, and DG is to EH as DM to ME, that is as P to Qo: O25. : In 132, |GEOMETRICAL PORISMS, In like manner it may be proved, that becaufe the angle NEF ~is equal to NHK, the points N, C, H, K are’in a circle, and hence that the triangle NEH is fimilar to NFK.;. hence EH is to FK as' EN to FN, that. is as Q toR. Therefore GHK is drawn as required. | PROP. XVI. PROBLEM, Fig: 20. PI. IV. ’ Ir is required-to defcribe a triangle DEF fimilar to a given triangle def, having one of its fides EF pafling through P a given point, and having its angles in a given order up- on three ftraight lines’ AB, AC, BC. given by pofition. Tue conftruétion of this problem follows readily from the 8th propofition, as follows’: Draw AG, GK, fo as to'form a triangle AGK, familar to the given triangle de f, and having its angles: upon the given’ lines in the given order. Turovuca A, G, any two of its angles, and C, the interfection of the lines upon’ which they are placed, defcribe a circle. Through G, K,.and B, the interfeCtion' of GC, KA, defcribe a> circle meeting the former in H. From the points’ Hy, P inflect HE, PE to CB, fo that the angle HEP may be equal to HGR; let PE meet AB in F. Through H, C, E defcribe a circle to meet CA in D:; join DE, DF, and: the triarigle DEF fhall be fi- milar to AGK or to deft Join HD, HF, HA, HK, HB, HC. Becaufe, by conftruction, the angle HEF is equal to HGK or to HBX, the’ points H, B)E, F are in a circle, and the angle FHE is equal to FBE or KHG,. therefore the triangles EHF, GHK are fimilar.. In like’ manzer, becaufe a circle pafles through H, G,; D, E, the angle DHEas‘equal ~ to DCE or AHG, and! HDE is’ equal! to! HCE or HAG, therefore: the. GEOMETRICAL PORISMS. ee the triangles EHD; GHA are fimilar. Now the triangle HEF was proved fimilar to HGK. Therefore the quadrilateral. ELDER is fimilar to HAGK, and the angle DEF is equal to AGK 3, alfo DE is to EF as AG to GK; therefore the triangle DEF is fimi- _lar to AGK or to def, as was required. / PROP. XVII. PROBLEM, Fig. 21. PI. IV. A and B are two given points in the circumference of a gi- ven circle. C and D are two given points in ftraight lines CE, DE given by pofitiom. It is required to inflect AF; BF to the given circumference, meeting the given lines in G _ and H, fo that the reCtangle CG, DH may be equal to:a given fpace. | Because A and B are given points in the circumference of a - given circle, and D is a given point in a line DE given by pofi- tion, a line LM, and a point M in it, both given by pofition, may be found, (prop. 1o.), fo that BF, AF being inflected to amy point in the circumference, meeting the given line DE in H ; and the line LM, which may be found in N, the ratio of DH to MN, may be given. | Suppose the line ML found, fo that MN may be equal to DH, then the rectangle MN, CG is equal to DH, CG, which by hy- pothefis is given. Now A is a given:point, and C, M are given points in ftraight lines given by pofition. Therefore the pro- blem is now reduced to the 12th propofition of this paper. ConsTRucTion. Join B and D, the given point, in the line whofe fegment is to be intercepted by BF. Let BD meet the circle in K; join AK, and take AM equal to BD. Through the points D, M, K defcribe a circle cutting DE in L, and AK in M. Join LM, and from the point A (by prop. 12.) draw a ftraight line to meet CE in G, and LM in N, fo that the rec- tangle 134 GEOMETRICAL PORISMS. _ tangle MN, CG may be equal to that which is to be contained by CG,DH. Let AN meet the circle in F; join BF meeting DE in /H. . : | Tue angle HDB is equal to LMK or AMN, and the angle DBH is equal to MAN; now BD tis equal to AM ; therefore | the triangles BDH, AMN are in all refpeéts equal, and DH is equal to MN. Therefore the rectangle DH, CG is equal to MN, CG, that is, (by conftruction), to the given fpace as requi- red. IT is eafy to fee, how, in like manner, by drawing AGN, fo that CG may be’to MN in a given ratio, (prop. 11.), the lines BF, AF fhall cut off fegments DH, CG, having to each other a given ratio. i LifrccL ge L3G, Lhy. La. . Cow ee ya =f 3 / CE ne met te ay Yo De tie Cie i Uns + " y rs omer. Yon Yay orang 7 Med 2 te ee . : y Pht eee Se WS Soop ened BER hg cope pee ee ts ese | ae oT ee ae ve ' : a) (AK ae gel SS eI 3 a ; BOY NYY Kage. 1M. TE A. 2 Bape, 13° D : ne ae Te es ae Pee aie ud) : La a aa, a / | \ | | | | a nh T mo A, oe uF ' Lt mh a? Me aerk Tha. » E \ an = sem nein V4 -_ a ee a eee! — ie 7 > en Rec ener x : i ° ~ Ce se Mem My hesnainactneaevenneseates- vsiacsiecniiatien bBiastai (aati Doh eae y ¥ ' r Fe M aes ““ hy & Te ppm mst ge ate nee Sm ng V. DETERMINATION of the LATITUDE and LoncitTuDE of the OBSERVATORY at ABERDEEN: In Two Letters from ANDREW Mackar, LL.D. & F. R. S. Epin. to FoHN Piarrair, ¥. R.S. Evin. and Profeffor of Mathematics in the Univerfity of Edinburgh. EBD PE Ro fk. [Read 2d Dec. 1793.] DEAR Sir, Aberdeen, 18th September 1793. OME time ago I promifed to fend you the refult of a feries of obfervations, made to determine the fituation of this place. Having, however, been much hurried of late, I am only able at prefent to tranfmit you the determination of the latitude, deduced from a feries of obfervations of the fun’s meridian ze- nith diftances. With refpect to the longitude, as foon as it 1s in my power, I will reduce fome obfervations of occultations, and of the late folar eclipfe, and fend you the refults. Tue following obfervations of the fun’s meridian zenith di- {tances were made with a moveable quadrant of two feet radius, conftructed by Mr Maccurtitocu of London. ‘This qua- drant has two feparate fets of divifions: the quadrantal arc of the ‘inner fet is divided into ninety degrees as ufual; and the exterior arc is divided into ninety-fix primary divifions ; each of which a 136 | DETERMINATION of the LATITUDE which is fubdivided into eight equal parts; and the vernier gives one thirty-fecond part of a fubdivifion, or 13,18. A micrometer {crew is attached to the vernier, which ferves to re- gulate the motion of the index, and by which, the excefs in fe- conds above the next lefs divifion of the vernier is fhown. Eacu zenith diftance was read off, at leaft, three times, both from the ninety and ninety-fix arcs, and the means of each were taken. hefe ferved as a check on each other ; however, the zenith diftance, as given by the ninety-fix arc only, is ufed for obvious reafons. The ninety-fix arc was found to be about 12” lefs than go° ; and the error of the line of collimation at the vertical radius was about a fecond and a half, fubtra¢tive. As the tranfit inftrument and quadrant were placed in adja- cent rooms, it was therefore in my power to obferve both the fun’s tranfit and zenith diftance the fame day; however, the paf- fage of the fun’s weft limb over the fifth wire, and that of the eaft limb over the firft wire, were by this means loft. Hence, alfo, the zenith diftance of one limb only of the fun could be obferved ; and the true zenith diftance will be affected by the error of the fun’s femidiameter, as given in the Nautical Alma- nac, and by the irradiation, which according to M. pu SEjour, exceeds three feconds. THE middle wire in the telefcope of the quadrant fubtended an angle of no lefs than 20”,6; therefore, as it was fcarce pof- fible to bring the fun’s limb exactly to the middle of the wire, I conf{tantly made the lower edge of the wire a tangent to the fun’s apparent lower limb. ‘The zenith diftances in the follow- ing table are the differences between thofe obferved and the fe- midiameter of the wire, the tenths of a fecond being neglected. THE fifth column of the table contains the error of the line of collimation, combined with that of the ninety-fix arc, taking | it for granted that this arc is accurately divided. In column fixth is the fun’s femidiameter, from the Nautical Almanac, to the I nearelt a ds ee ree ae ne And LONGITUDE of ABERDEEN. 137 neareft fecona? The next column contains the aggregate of the three preceding columns, and is the fun’s apparent central ze- nith diftance. The eighth column contains the mean refraction, anfwering to the apparent zenith diftance of the fun’s limb ; hence the allowance for the contraction of the femidiameter at low altitudes is avoided. The next column contains the mean refraction reduced to the true, by the application of the correc- tions depending on the heights of the barometer and thermo-- meter, as they are found in Table VIII. of my book on the Longitude: In column tenth is the fun’s parallax; and the quan- tities in the two laft columns, applied to thofe in column feventh, give thefe in column eleventh, being the true zenith diftances of the fun’s centre. The following column contains the fun’s declination, reduced to the meridian ofthis place; and in the laft column is the latitude. Vou. IV. R Obferved. 138 DETERMINATION of the LATITUDE Obferved Diftances of the Sun’s Upper Limb-from the Zenith of the Obfervatory,. Err.| Sun’s Ped {> 1786. |H. of | Th.| Zen. dit. |Qua.| Semid. | Appar. Zen.{M.Ref.|Ref. (Par. | True Zenith} Declination | Latitude, ; Rar. +] add. diftance. — | diftance. . B May 17.|29-78 148° |37° 26’ 46] 3" | 15° 5t" 137° 42' 40"lo' 44" [o' 4g” | 5" 137% 43° 19"| 19° 25'49"|57° 9 8” h June 3.130-15 1624 134 2955 |] 3 | 315 49 134 45 471039 |0 359 |5 |34, 46 21 J22 22 49157 9 10 © — 4.|30-26 |60 134 22 5613 | 15 48 [34 38 47}0 39 jo 39 |5 134 39 2X }22 29 52/57 913 © Y — 5-130-36 {6r 134 161413 175 48 134 32 S]o 38 Jo 38 |5 [34 32 38|22 36 31)57 9 9 B — 7-/30-23 [59 [34 4 0)3 | 15 48 134 I9 st]o 38 Jo 38 FS 134 2024 }22 48 39157 9 3 my — 8.}29.09 [553 |33 5845 |3 115 48 [34 14 36]0 38 jo 38 | 5 [34 15 9 |22 54 7157 9 16 }. — 10./ 29-83 1545133 49 8 73, | 15 4834 4 53 to 38) lo 37 15 134 § 23 148) “Anse lcy Gam @ — 1. }3000 153 [33 44 4013 | 35 48 134 © 3rfjo 38 Jo 38 15 (34 £ 4123 8 4|57 9 8 D — 12.[29.98 ]54% 133 40 47|]3 115 48 433 56 38/0 38 Jo 38 | 5 $33 57 12 (23 11 55 9 6 YU — 15.]30.05 [58 133 31 3613 115 47 133 47 26\0 38 10 38 | 5 (33 47 591/23 2% F 9 9 © — 18.137.06 |55 33 262013 115 47 133 42 191/037 (937 | 5 133 42 42 123 26 24 6 6 D — 19-13005 156 135 25 30] 3 115 47 133 41 201057 ]0 37 | 5 133 4% 52123 27 22 9 14 3d — 20.)30-08 |60 [35 24 4513 115 47 |33 4935 ]° 37 1037 |5 133 41 7123 27 56 oom B — 21-130-05 (63 33 24 37]3 115.47 133 4° 2710 37 1037 | 5 |33 40 59123 28 5 9 4 UY — 22.)29-89 |65 |33 245313 | 15 47 133 43 |° 0 36 | 5 {33 4% 14 123 27 49 9 3a %h — 24.\29- ‘ 3 32 |o 936 |5 |33 43 3 |23 26 9 5 © — 25.|29.86 |66 133 28 0 | 3 |15 47 |33 44 © 19 37 |9 36 | 5 9 3 3S — 27.429.65 {58 133 32 2813 | 15 47 133 48 18 ]o 38 Jo 37 | 5 9 6 © July 2.]30-00 |57 133 501313 125-47 [34 6 31]° 38 J|o 38 | 5 9 4 D —- 3-]29-71 163 133 54 5613 | 19 47-134 10 46 Jo 38 10 37 .1 5 5 ¢ So — §.430-29 [617 134 § 52 |3 115 47 134 21 42 ]0 38 Jo 38 | 5 9 13 h — 15.]30-31 [66 }34 22 36 |3 | 5 47 134 38 26 |0 39 |0 39 | 5 8 so a — 18.130.3r 163 135 525613 | 15 47 ]36. 8 46|0 41 jo 41 5 8 57 Q@ — 27.(30.02 |57 |36 26 30 | 3 rg 48 |26* 42 21 /o 42 Yo 42 5 8 58 © 33: ° 5 9 4 2f Aug. 3: 39 26 25 Oo 4 5 9 12 # 4: ° 5 9 g h 5: ° 5 9 6 h 6. I 6 9 2 ) I 6 9 40 pid I 6 8 54 h I 6 9 8 rol I 9 16 3 cr 9 2 QE I 9 128 8 I 9 g 2 9 git 2 8 kh + 8 10) 5 8 2 5 8 © 5 8 gi 5 8 © 5 8 »)) 5 8 ' : fo) Q May 4.29.81 ° D) — 14.| 30.06 ° ad — 22. 2.987 fo} & June 12. | 30.12 ° Q — 15.|29-61 ° h — 16.}29.66 fe} hh Sept. 1. | 30.52 t 3 — 19.}29.25 I h — 2%. 129-49 I © = 23- 129-49 I HHOapRiov 4 ~ Salt 2 wn Aw MN OCOWVWNIADAILADAANHWHWW/ Fh Worwowuwsjol on anagno UaAunnp & wy wn oO oe] o co . Ww ° ra) Bx nN » wm ~ w [e) ~ re) SI CO% wmmyIWIN DHUUNUN|UADA VvKowowvw/OO OM HN AI And LONGITUDE of ABERDEEN. 139 Havine the following obfervations of fixed ftars reduced, I have alfo fent them. Obferved Diftances of Fixed Stars from the Zenith of the Obfervatory. —S ————-s a Error |Mean ; True , Bar.|Th.| Name of Stars. | Zen. dift. |Quad.|Ref. | Ref. [T. Zen. dift. |M. Declina.| Ab. | Nut.| App! Decl.| Latitude. ee --|_—_— -- .}29.82] 55 |Arcturus 30° 50/ 14/|+- 3/0! 43/l0"4 3/136° gil OM \z0° 18% aft 6M — 4/Na0% 18! 1/57 of xP + |29-49] 55 |e Lyra. 32 37 © 19 [9 19 [18 32 57 38 35 45 16 ++ 8/8 36 9 157 9 6 - 130-37 | 44 |Altair. a 48 31 ; I 5 |t 8 48 49 44 19 20 9 On| Se arop nancy 8! 55 26. 130.42 | 44 48 4829] 5 |E 5 |x 8 48 4 42 Saye 9 | oO f8 1911 [57 8 53 e + 2|29.50| 37 |Pole Star. gr "x "0 2 lo 34 Jo 35 gr 1 37 |88 Yo 8 |4+ 17 7 |88 10 32 [57 8 55 ‘© — 74.29.93 | 24 ty Cals. arc Excefs.|87 35 12 j= fo 2]9 2 [87 35 13 59 33 53 17 3 159 3413 |57 9 9 = — | —|é Caffiopeia: 88 1 23 i jo @/O-2 \88 £.a4 [59 “7 12 16 5 soe ga sr 8 $2 B — 27. !28.95| 36 fa Cafliopeia. I 46 47 tlo 2fo 2] 46 48 [55 52 59 16 Sse saexo SF Or 7 Latitude, 57 8 sok Tue declinations of the above ftars were taken from M. DE LA Lanpe’s catalogue of the declinations of 350 ftars, adapted to the beginning of the year 1790. I sHaALL conclude by obferving, that the differences in the above latitudes are to be attributed to the error of obfervation, to the inaccuracy of the divifion of the quadrant, and to the un- certainty of the refraction, efpecially at low altitudes. If the re- fraction at 45° be affumed a little greater than that by Dr BRADLEY, the refults will agree much better. It muft alfo. be obferved, that the fmoke of the town will piercer the refrac-. tion. f if i 7 : és [ am, Dear Sir, Your obedient fervant, ANDREW MAcKaX. kh 2 | Sas ead (ess 140 DETERMINATION of the LATITUDE ™> 2, Cee oa ee Rf ee OE, DEAR SiR, Aberdeen, 20th September 1796. AVING finifhed the comparifon of a confiderable number of obfervations, made in this place, in order to determine its longitude, with correfponding obfervations made at Green- wich, I now fend you the feveral refults. The obfervations ufed for this purpofe are, eclipfes of the fatellites of Jupiter, particu- larly thofe of the firft and fecond fatellites, folar and lunar eclip- fes, occultations, &c. Thefe obfervations were made with one of Dottonnp’s three and a half foot achromatic telefcopes, and powers of about feventy, and one hundred and fifteen, were ap- plied to the telefcope, according to circumftances. The obfer- vations at Greenwich were made with one of DoLLonp’s for- ty-fix inch achromatic telefcopes. As the refults, deduced from a comparifon of the correfpond- ing obfervations of the firft and fecond {fatellites of Jupiter, are much _ * CommunicaTeD 7th November 1796. And LONGITUDE of ABERDEEN. iat much more to be depended on than thofe inferred from. the ob- fervations of the third and fourth fatellites, I have therefore re- , jected the obferyations of the two laft. This I was mclined to, do, partly from» the difagreement of the refults of the corre-. {ponding obfervations of thefe two {fatellites, and partly upon account of the fmallnefs of the number of correfponding obfer- vations. Indeed, as thefe two fateilites take a confiderable time to immerge into, and emerge out of the fhadow of Jupiter, and as the ftate of the atmofphere, at the times of obfervation at Greenwich and Aberdeen, may be very different, and as powers will be applied to the telefcopes according to the ftate of the, atmofphere, it is not wonderful, that there fhould be a con- fiderable difference between the refults of the actual obfer- vations ; and hence the propriety of rejecting the obfervations. * of the third and fourth fatellite will be obvious ; efpecially in the cafe when the corref{ponding obfervations are very few, and the number of immerfions unequal to that of the emerfions. The longitude of this place, as.-deduced from the comparifon of the actual obfervations of the firft and fecond {fatellites of Jupiter, made here and at Greenwich, feems to be lefs than the truth, or, at leaft, lefs than what | had been accuftomed to ftate it; but the near agreement of the final refults of each of thefe fatellites _is really furprifing. OF all the other obfervations which [ have compared, I have fent you only two, as being the moft to be relied on, namely, a folar eclipfe, and an occultation, befides a lunar eclipfe, which I . had publifhed formerly in my Treatife on the Longitude, and which is not far from being a mean between.the refults of the other obfervations. I had, indeed,-only one other occultation, of which the obfervations at Greenwich and Aberdeen were complete, namely, that of (vw of 15th October 1790; my other obfervations of that kind, being either incomplete, or ha- ving no correfponding obfervations at Greenwich. J 142. DETERMINATION of the LATITUDE I HAVE made the calculations for the longitude from the folar eclipfe and occultation, firft, on the fuppofition that the figure of the earth rs a perfect {phere ; and, fecondly, upon Sir Isaac NewrTon’s fpheroidal hypothefis, in which the equatorial dia- meter is to the axis of the earth as 230: 229; between which limits, it is probable, is the real figure of the earth. In the rules which I gave, in my Treatife on the Longitude, for making the calculations by means of the nonagefimal, I followed the method of calculating the parallaxes in latitude and longitude, which had been given by M. pe EA Lanog, in the firft and fecond editions of his 4/fronomie: But, in the prefent calculations, I have ufed the method which was given for the firft time by M. Mayer, in the fecond volume of the Memoirs of Gottingen, publifhed in the year 1753; and, again, in his Solar and Lunar ables, printed at London, by order of the Board of Longitude, in the year 1770. This fame method has alfo been employed. by Meffrs LexeLtt, DE ta Grance, and De Lamsre: And it has been adopted by M. DE ta Lanne, in the fecond volume of the third edition of his A/ronomie, printed at Paris in the year 1792*. It may alfo be proper to mention, that I have. followed M. pu Seyour, and M. pe La Lawpe, in wing an ir- ~ radiation of 33 for the fun’s femidiameter, and an inflexion of the fame quantity for the moon’s. See Seyour’s Traité Ana- iytique, &c. vol. I. p. 253 and 264; and De ta Lanpe’s Affro- nomic, third edition, vol. Il. p. 445. As fome perhaps will be inclined ‘to repeat the calcu- lations for the longitude, from the obfervations of the fo- lar eclipfe and occultation, it will therefore be neceflary to inform * In making thefe calculations, I was led to difcover an error in the method I had given in my Treatife on the Longitude, for finding the longitude of a place by an occultation. That error, and feveral others, will be corrected in a new edition of that work. And’ LONGITUDE of ABERDEEN. 143 - inform them what tables I ufed for that purpofé. The loga- rithmic tables were TAYLor’s, CALLET’s, and SHERWIN’s. From Taytor’s Zadles were taken the logarithm fines and tan- gents of arches, and converfely. The logarithm fines, and converfely of the parallaxes, were taken from CaLet’s Tables : and the logarithms of numbers from SHERWIN’s. By this means much time was faved in thefe extenfive calculations. The natural verfed fines were taken from my TZreatife on the Longitude ; and the augmentation of the moon’s femidiameter was taken from M. pe Lamsre’s Taéles, for finding it by means of the altitude and longitude of the nonagefimal, which, therefore, faved the trouble of calculating the altitude of the moon. The fun’s parallax was taken from the Connoiffance des Temps; and, as I had not the Nautical Almanac for the year 1788, the elements for the folar eclipfe were taken from the Connoiffance des Temps for that year ; but the elements for the occultation were taken from the Nautical Almanac for 1787. DETER- 144 DETERMINATION of the LATITUDE DETERMINATION of the Longitude of the Obfervatory at Aberdeen, by the Eclipfes of the Firft and Second Sa- tellites of Jupiter. ed FIRST SA TELLITLE. SS —————— SS Apparent Time of Obfervation at Longitude in Year, Month, Este Alii ra at ise ei tal aa see Immer. Emer. Immer. Emer. {| Immer. | Emer. Toe i U ‘s h. / 4 h. / " h. ‘ " ‘ pee ae & Jan. 03.3986. | 8 15 54 8 7 39 ee )Sept.18.——_ |16 7 37 15 58 57 8 40 3 30. 10 36 48 10 27 40 8 58 » Dec. 30. 9 45 20 9 37 43 Mex ¥ Jan. 31. 1787. 6 55 32 657 8 8 24 3 Feb. 23. —— 6 31 57 6 23 46 8 11 © Dec.14. 1788.| 8 34 55 S 24 12 7.43 g Mar.:1.1791-} 9 14 8 9 5 23 8 45 » Apr. 9.—— io 4 48 9 56 49 7 59 126| 26 Longitude, 8 315/38 5.2% : ak Mean, . 8 18.3 SECOND SATELLITE. | h. ee Brat .f a LA / " Fo yl / 4 7 $ Nov. 7.1786.| 9 10 27 § , 1.23 9 4 4 Mar. 8. 1787. ly 48 3 7 49 14 7 49 9 Dec. 21. |5 14 30 5 6 24 3.3 py Nov. 9. 1789.'14 23 42; EA ES 24) 8 18 17 22115 52 Longitude, 8 411 7 56 8 41 16 37 Mean, 8 18.5 Mean by 1ft Sat. 8 18.3 Mean Longitude, 8 18.4 DETER- And LONGITUDE of ABERDEEN. 145 DETERMINATION of the Longitude of the Obfervatory at Aber-. ~ deen, from the Apparent Times of Obfervation of the Begin- ning and End of the Solar Eclipfe of 3d June 1788 : Obferved at Greenwich and Aberdeen. h. e " Apparent time of begin. at Greenwich, 19 24 463 at Aberdeen, of end. - 21 F 24 : z 1 36 372 Interval, h. y ia | 19 33 19 20 57 37 124 18 CompuTaTION of the Apparent Time of Conjunction at Green- wich, on the Spherical Hypothefis. Sate it ened Moon’s true longitude at beginning, 2 13 19 37 at ending, Computed parallax in longitude, - M30 TE Moon’s apparent longitude nearly, - 2 13 49 48 Moon’s equat. hor. parallax, - 60 33.0 Sun’s horizontal parallax, - - 8.7 ~ Difference of parallax of fun and moon, 60 24.3. 5 a ee a App. time beg. 19 24 46% Sun’s R. A. 4 §t 302 R. A. meridian, o 16 17 6 Arch, 6 16 17 v. fine, 0.0297853 co-fecant, Latitude, 51 28 4o co-fine, 9-7943612 fecant, Ob. ecliptic, Pie ime fine, 9-6001327 Sum, 714 56 43 co. V.s. 034322 265631 9.4242792 Alt, nonag. 45 34 9 Vv. fine, 299953 fine, Vou. IV.. 5. oe 2 14 41 31 ° / re 2 14 18 59 22 32 Q.001097T 02056388 98537566 eR ee eee Long. 146 DETERMINATION of the LATITUDE . Q , “ Long. nonag. 29 32 39 fecant, 0.0604925 Moon’s app. long. 73 49 48 Diff. = 44 17 9 fine, 9:8440037 ) Alt. nonag. 45 34g fine, 9-85 37566 co-fine, 9-8451277 Diff. hor. par. 60 24.3 fine, 8.2447766 fine, 8.2447756 Par..in long. go. 7.0 fine, 79425369 P.inlat. 42’17."1, 8.0899043 h. , uw App. time end, 24° “E 24 Sun’s R. A. 4 5147 R. A. mer. E59).15 6 Arch, - 5 ee ew v. fine, 0.1685046 co-fecant, 0.0552648 Latitude and obl. 74 56 43 co. v.s. 034322 9-3944939 ' 0.2056388 365593 9.5629985 Alt. nonag. 53 7 26v.fine, 399915 fine, 99030547 Long. nonag. 46 43 15 fecant, 0.1639583 Moon’sapp.long. 74 41 35 / Dift.) 4 Non. 27 58 16 fine, 9.6711972 — Alt. nonag. 46 43 15 fine, 9-9030547 co-fine, 9.7782140 Diff. hor. par. 60 26.2 fine, 8.2450042 fine, 8.24 50042 | _ Par. in long. 22 34.2 fine, 48172561 P. in lat. 36’16."0, $.0232182 t “ if wu Moon’s true mot. in long. in ob. int. - 59 22.0 ‘True mot. in lat. §.,.3%3° 2 Sun’s true mot. in long. - tie 3.51.0 Par. in lat.atend. 36 16.0 | Moon’s true rel. mot. in long. - 55 31.0 Sum, 41 46.3 Par. in long. at beginning, - - 30 7.0 Par. in lat.at begin. 42 17.5 “am at ending, - - + 22 34.2 App. mot..in lat. 30.8 App. rel. mot. in longitude, - 47 58.2 4 Apparent And LONGITUDE of ABERDEEN. 147 4 Apparent mot. in lat. 30.8 1.4885 507 Apparent mot. in long. 47 58.2 3-4591210 3-4591210 Apparent inclination 36'47”, tang. 8.0294297 co-fine, 9-9999751 Moon’s apparent mot, in relative orbit, 2878./3 - 3-4591459 2 , / , W y ty Moon’s femidiameter at begin. 16 30 at.end. 16530 Sun’s femid. 15 48-5 Augmentation, - + 9.0 + 12.5 Irradiation, 3°5 Inflexion, 2 — 3.5 — 3.5 Cor. femid. 15 45.0 Corrected femidiameter, 16, 35+5 16. 39.0 Sun’s femidiameter; - 15 45.0 15 45.0 Sum, - : 32 20.5 32% 24.0 vv Sum of femid. at end. 1944.0 - - ar. co. log. 6.7113037 at begin. 1940.5 ar.co.log. 6.7120864 3.2879136 App. mot. in rel. orbit, 2878.3 ar.co.log. 6.5408639 Sum, Wine 6762.8 Half, - 3381.4 log. 3-5290965 Remainder, - ~ 1437-4 log. 3.1575776 19.9396244 21 6 59 _~ co-fine, 9.9698122 Central angle at begin. 42 13 58 - - fine, 9-8274625 ’ a ° a a“ Central angle at end. 42 8 21 fine, 9:3266798 ° ean fe ° fh Central angle at begin. 42 13 58 atend. 42 8 a1 App. inclination, 36 47 App.in. 36 47 Arch, - 42 50.45 co-s. 9.8652142 Arch, 41 31 34 cO-S.. 9.8742810 Sum of femidiameters, Pino reas 32879136 fumfem. 32 24 3.2886963 23, 42.8 3+1531278 24 15.4 3:1629773 Par 148 ° ‘ 4 Par. in long. at begin. 30 0 . —— Sum, - 53 49.8 Rel. mot. in long. = 2h (yd or Obferved interval, 1) 36) 37% egy er? Int, bet. beg. andconj. 7 33 414 App. time of beg. 19 24 46.5 App. time of conj. 20 58 27.9 DETERMINATION of the LATITUDE atend. 22 34.2 : —_ *» 3-5091756 Diff. I 41.2 _2.0051805 ar. CO. 6.477425 4 6.474254 3-7632408 3-7632408 3-7498418 bet.end & con. Apparent time of ending, 21 2 56.1 2.2458467 ae 20 58 27.9 CompPuTATion of the Apparent Time of Conjunction at Aberdeen. h. , ” h. Par App. time of begin. - 19 33 19 App. time of end. 20 49 29 Eftimated longitude, + 8 36 + 8 36 Reduced time, - 19 41 55 20 §8 5 Moon’s true long. - 2.13 30 8 at end. 214 16 57 Par. in long. nearly, - + 24 49 + 19 4§ Moon's app. long. nearly, 2-13°54 57 2 14 36 42 Moon’s hor, parallax, ES" 23.35 60 34.8 Sun’s 8.7 8.7 Diff, hor. par. . 60 24.6 60 2641 App. time of begin. - 19 35). 19 App. time of end. 20 44 29 _Sun’s right afcenfion, 4, Fees 4 51 47 Right afcen. meridian, © 247-53 I 4% 16 Now, with the right afcenfion of the meridian at the begin- ning, increafed by fix hours, or 64 24’ 53’, the latitude of the place of obfervation 57° 9° 0”, and the obliquity of the ecliptic 23° 28° 3”, the altitude of the nonagefimal is 41° 39° 6”, and its longitude 35° 46° 6”; hence the moon’s apparent diftance from the nonagefimal is 38° 8’ 51”, with which the altitude of the And LONGITUDE of ABERDEEN. 149 the nonagefimal, and difference of the horizontal oa axes of the fun and moon, the parallax in longitude 1 is 24'-47".9, and in latitude 45'8”.2. AGAIN, with 75 41’ 16", the fum of the right afcenfion of the iit uate and fe hours, the latitude and obliquity of the _ ecliptic, the altitude of the nonagefimal, is 47° 17’ 40”, and lon~ gitude 48° 8’ 35”; the apparent diftance of the moon from the nonagefimal is, therefore, 26° 28’ 7; from whence, the altitude of the nonagefimal, and the difference of the horizontal paper: laxes of the fun and moon, the x gore in i aie is 19° 47°.0, and parallax in latitude 40’ 59”.3. THE true motion of the moon in longitude is 46’ 48”.2, and that of the fun 3’ 2”.1; hence the moon’s relative motion in longitude is 43° 46’.1; from which, fubtracting the difference of the parallaxes in longitude 5’ 0.3, the remainder 38’ 45.8 is the apparent relative motion of the moon in longitude. THE true motion of the moon in latitude, in the obferved in- terval, is 4’20".4; from which, fubtracting 4’ 8.9, the diffe- rence of the parallaxes in latitude, the remainder is the moon’s apparent motion in latitude. Now, with the apparent motions of the moon in longitude and latitude, the apparent inclination is found to be 17’ 0”, and the apparent motion of the moon in its relative orbit is 2325”.8. Wirs the altitude and longitude of the moon at the begin- ning and end of the eclipfe, the augmentation of the moon’s fe- midiameter at the beginning is g’.o, and at the end 11.4; hence the moon’s femidiameter, corrected by the augmentation and inflexion, is 16’ 35”.5 at the beginning of the eclipfe, and 16 37.9 at the end; and the fum of the femidiameters of the fun and moon, at thofe times, are’ 32’ 20".5, and 32 22”.9 re- {pectively ; with which, and the moon’s apparent motion in re-~ lative orbit, the central angle at the beginning of the eclipfe is a3 iso DETERMINATION of the LATITUDE 53° 15’ 20", and at the end 53° 9-39’; hence arch firft is 53°32 20°; and: arch! fecomd' 52? +52'13.9. With thefe arches, and the fum of the femidiameters of the fun and moon at the beginning and end of the eclipfe, arches third and fourth will be found equal to 19' 13’.2 and 19/ 327.6 refpectively. Now, the fum of arch third, and the parallax in longitude at the beginning is 44'1’.1, and the difference be- tween arch fourth, and the parallax in longitude at the end, is. 15’.0. Now, with this fum and difference, the moon’s true re- lative motion in longitude, and the obferved interval, the diffe- rence between the beginning of the eclipfe and the conjunétion is 1h 16’ 36%.1, and between the end and the conjunétion 26’.1. Hence the apparent time of conjundtion, inferred from the be- ginning, is 20) 49’ 55’.1, and from the end it is alfo 20) 49' 55-1, But the apparent time of conjunction at Greenwich is 20" 58'27’.9; hence the longitude of Aberdeen in time is 8’ 327.8 weit. CompuTATION of the Apparent Time of Conjun¢tion, on the Spheroidal Hypothefis, at Greenwich. h. , bf / k. , a” Appt. time of beginning, 19 24 464 Appt.time of ending, 21 I 24 Sun’s right afcenfion, A, 5 1.GOx 4 51 47 Right afcen. meridian, © 16 17 r 59 00 _ Moon's true long. 2) 13" 8934 2 14 18 59 _ Eft. par. in long. + 3010 22 52 ere app. long. 2 13 49 47 2 14 41 50 Toon’s hor. par. 69 33.0 60 34.9 Reduction, — 96 9.6 Reduced hor. par. 60 23.4 60 25.3 Sun’s — ——_s And LONGITUDE of ABERDEEN. ret . ° ’ “ re) f ” Sun’s hor. par. 8.7 8.9 Difference, - 60 14.7 60 16.6 Altitude nonag. - 45 46 19 53 29 35 Long. nonag. - 29 21 19 46 35 16 Par. in long. - 30 14.6 22 46.9 Par. in lat. - 42 12 35 19.8 Moon’s true rel. mot.inlon. | 5§ 31.0 Moon's trie mot. in lat. 5142-3 Diff. par. in longitude, 4 24.4 Diff. par. in latitude, 6 2.1 )’s app. rel. mot. in long. 48 3.3 App. mot. in lat. 31-8 App. inclination, - 27 55 App, mot. in rel. orbit, 48 3.5 Moon’s femidiameter, 16 30.0 16 30.0 Augmentation, = + 9.0 + 12.5 Inflexion, a — 3.5 aes Corrected femidiameter, 16 35.5 16 39.0 Sun’s femid. — Irrad. 15 45.0 £5 45-0 Sum, wget: 32 20.5 32 24.0 Central angle, - 42 "6 42 I 30 App. inclination, a2 5 37 55 Arch firft, - 42 45 1 Arch fecond, 4l 23 35 Arch third, 23 44.9 Arch fourth, 24. 18.4 Par. in long. at beginning, 30 14.6 Atend. 22 46.9 Sum, = §3. 50-5. _Ditlerence, * -s L 31.5 Hence interval between h. ’ “” Interval between the end and p, ” ” the beg. and conj. I 33 58.3 conjun¢tion, Oo 2 39.2 App. time of begin. 19 24 46.5 App. time of ending, @r Er 24,0 App. time of conj, 20 58 44.8 20 58 44.8 At Aberdeen. ‘ 5 ‘ h. ‘ ” h: , “a App. time of beginning, 19 33 19 App. time of end, 20 49 29 Sun’s right afcenfion, . 4 51-34 4 51 47 Right afcen. of meridian, © 24 53 I 4r 16 Moon’s ‘1y2 DETERMINATION of the LATITUDE Sue ae ee a Moon’s true longitude, 2 43 30 -8 2.14 26: 54 Eftimate par. in longitude, + 24 55 + * 19 54 Eftimated apparent long. 2 ES RG 08 2 14 36 51 Moon’s hor. parallax, 60 33-3 ~ 60 348 Reduction, - — It — Il Reduced parallax, - 60 22.2 60 23.7 Sun’s hor, par. - — 84 8.7 Difference, - 60 13.5 60 15.0 Altitude nonag. - 41 50 6 47 29°32 Longitude nonag, - 35) ga..53 47 59 26 Par. in longitude, ~ 24 55.4 j; 19 54.2 Par. in latitude, - 44 5202 4O 42.6 Moon’s true rel. mot. in long. 43 46.1 Moon’s true mot. in lat. 4 20.4 Diff. par. in longitude, - 5 1.2 Djiff. par. in latitude, 4. 9.6 App. mot. in longitude, = - 38 44.9 App. mot, in latitude, 10.8 App. inclination, - 15 58 App. mot. in rel. orbit, 38 44.9 Moon’s femidiameter, 16 30.0 16 3¢.0 Augmentation, - + 9.2 + 11.6 Inflexion, — = - — 3.5 — 3:5 Correéted femidiameter, Be 16 38.4 Sun’s femid, — Irrad. 15 45.0 E5 45-0 Sum, - - 32 20.7 y wy re Oana Central angle, - 53 16 36 53 10 55 App. inclination, : 15 58 15 58 Arch firft, - 53 32 34 Arch fecond, 52 54 57 Arch third, > Ig 13.2. Arch fourth, 19 31.7 Par. in longitude, - 24 $5.4 IQ 54.2 Sum, - - 44 8.6 Difference, 22.5, Hense 3 And LONGITUDE of ABERDEEN. 153 \ h. 7 ” h, ’ W Hence the interval between Interval between the end the beg. and conj. is - 1 16 49.2 and conjunction is on 3908 App. time of beginning, 19 33 19. 53 8 50. Longitude nonag. 65 29 36 Par. in longitude, 20 29.3 Par. in latitude, 37 24.9 Moon’s true mot. in long. 40 44.8 Moon’s-true met. in latitude, Diff. of par. in longitude, 7 42.9 Diff. of par. in latitude,. Moon’s appt. mot.inlong. 33 1.9 Appt. mot, in latitude, Appt. inclination, 3 28 56 Appt. mot..in orbit, Moon’s femidiameter, 16 40.1 Augmentation, - + 12.9 Inflexion, - — 3-5 Moon’s corrected femid. 16 49-5 Central angle, . = 1035 40 Appt. inclination, - 3/28 56 Arch firft, - 9.6 44 Arch fecond, Arch thitd, © - 1641.7) Arch fourth, Par. in longitude, - 20 apa Sum, - - 37 10:8, Difference, Hence the interval be- h. ’ ” Interval between the emer. and tween im, andconj. 0 $9 223 conjunétion, Appt: time of immer.. 1118 8 App* timeof emerfion, App*. time of conj. 12: 14 39-3. At Greenwich, 1a 26° 2.5. Longitude in.time, 8 32.2. Ea 155 4 1? ° + 12 38.4 3 0 46 12, 7 ” 24 2.0 35 18.0 59 20-0 §. 61 10.6 a5. 5% 2 76 3 32 12 46.2 35 40.4 3 45-4 I 44.5 2 0.6 oa 5-5 16. 39.9 14.1 3-5 16 50.5, 16 35° 2 3 28 56 14 358 16 20.7. I2 46.0 3 34.0 os “ 5.41.7 12 23 12 12.1 7 3°03 : h. oO Com= 156 DETERMINATION of the LATITUDE ComPuTaTIon of the Apparent Times of Conjunétion in the Spheroidal Hypothefis, at Greenwich. Ss. ° , Mt Moon’s true long. atim. 2 29 50 23 Eft. parallax in longitude, + 22 57 Appt. longitude nearly, 3 0 13 20 Moon’s true latitude, 20 35 Eft. parallax in latitude, gales sy Appt. latitude nearly, 52 9. Horizontal parallax, 61 11.3 Reduétion, : 9.8 Reduced parallax, 61. 1.5 Latitude of Greenwich, 51 28 4o Reduction, - 14 37 Reduced latitude, -* ae 3 Alt. nonagefimal, - 59 3 56 Longitude nonagefimal, 6414 2 Par. in longitude, - 22 56.2 Par. in latitude, - 32 4.8 Moon’s true mot. in long. 43 8.4 Diff. of par. in long. 9 36.9 Appt. mot, in longitude, 33. 31-5 Appt. inclination, = 3.23.8 Central angle at immer. 4 44 16 Arch firft, - 8 47 24 Arch third, . 16 40.2 Parallax in longitude, 22 56.2 Sum, - 39 36.4 Hence the interval between h, ’ ” the immer. and con}, I 3 14.8 Appt. time of immer, IL 22 51.7 Appt. time of conj, 12 26 6.5 4.9 8 Ww: 3 9° 33 32 : 13°19) |. At emerfion, 3. 0 40 e 24.1.3 30 §o%o) 54° «7: 61 10.6 9.8 6r 08 61 19 24 76 22 55 13 19.3 SO> e5aS 3 583 ES Dag . —— I 59.0 3313529 44 AB 'SH . I 20 46 16 51.3 13 19.3 - Moon’s true mot. in latitude, Diff. par. in latitude, Appt. mot. in latitude, Appt. mot. in orbit, At emerfion, Arch fecond, Arch fourth, Difference, Interval between the emer. and conjunction, Appt. time of emer. 3 32.0. 5 38.5 12 31 45. 12°26 6.5 AT “And LONGITUDE of ABERDEEN. 157 ‘At Aberdeen. ‘ 5. ° ‘ at Moon’s true long. at immer. 2 29 52 49 Eft. par, in long. = + 20 45 Appt. longitude nearly, 3 0 13 34 Moon’s true latitude, 20 17 Eftimated par. in latitude, 37 6 Appt. latitude nearly, - 57 23° Moon’s horizontal parallax, -61-92.3 Reduction, - — 113 Reduced parallax, ee 61 0.8 Latitude Aberdeen, - 57 9 0 Reduttion, - 13 4% Reduced latitude, * 56 55 19 Altitude nonag. - $3 21 52 Lo» gitude nonag. - 65 24 42 Par. in longitude, - 20 32.8 Par. in latitude, - BY If )’s true mot. in long. - 4° 44.8 Diff. of par. in longitude, 7 44.5 Appt. mot, in longitude, 33 0.3 Appt, inclination, - 3.28 4 Central angle at immer. 10 51 14 Arch firft - 7 23 10 Avch third, - 16 41.1 Par. in longitude, - 20 32.8 Sum, - - 37 139 Interval between theimmer. h. ° / and conj, - © 59 24.2 Appt. time of immer, rr 18 8 Appt, time of conj. 12 17 352 App‘. time of conj.at Gr, 12 26 6.5 gy 8 ee 3 0 33 34 12 34 At emer. 3-046 8 24 2 35 18 ” §9 20 61 10.6 — 113 Se 60 59+3 a g ff 5p er ae 76 o 36 12 48.3 35> 22.1 3 45-5 I 45.8 2 0,0 33 439 10 50 35 14 18 39 16 19.2 12 48.3 True mot. in latitude, Diff. parallax in latitude, App*. mot. in latitude, Mot, in appt. orbit, At emer. Arch fecond, Arch fourth, 3 39:9 / Mt Difference, Interval between the emer. h. and conj. o 5 36.8 Appt. time of emer, 12 23 12 12 17 35.2 Longitude 158 DETERMINATION of the LATITUDE tae as Longitude in time, - 8 31.3 Long. on fpherical hyp. by occult. 8 32.2 Long. by folareclipfe, - 8 36.6 byeclipfe, 8 32.8 Mean, - - 8 33.9 Mean, 8 32.5 Ir we fuppofe, with Mefirs pu Szyour and La LAnpbs, that the difference between the equatorial and polar diameters is zoz Of the equatorial diameter, in that cafe the longitude will be 8’ 337.6. . ka ‘DETER- es ee And LONGITUDE of ABERDEEN. 15g DETERMINATION of the Longitude of the Obfervatory at Aberdeen, by Obfervations of the Lunar Eclipfe of roth September 1783, made at Aberdeen and at Chiflehurft in Kent, 19’ in Time Eaft of the Royal Obfervatory at Greenwich. | Apparent Time of Obfervation at Names of Spots. | CIF of Mer. : Aberdeen. | Chiflehurft. h. mY aa haw 2 i , “ Ariftarchus, _ 9 42°42-5|-9 50.55 $: B 12-5 Kepler, 9 44 Bs 9 52°20 8 10.4 Copernicus, 9 54 8.7} t0 2 24 8 15.3 Manilius covered, 10 7 35-8] 10 15 30 7 54.2 a Tycho covered, 10. 8 37.8} 1d017 5 8 19.2 Ss Menelaus covered, 10 10 §1.9| 16 Ig 10 8 18.0 $ Dionyfius covered, 10 13 46.9| 10 21 38 % ist Rat Plinius covered, 10 14 55-9| 10 22 4o 7 44. Mare Crifium E, end, | 10 25 51-0] 10 34 34 | 8. 43,0 W.end,} 10 30 53-0] 19 39 45 8. 52.0 | Total darknefs, 10 36 39.0] 10 46 34 9 55-0 Sum, - 254.9 Mean, - §& 23.17 = he es 4/ h. , Mh ? a : Ariftarchus, 12 24 4.3} 42 33 52 9 47-7 - Kepler, 12 27 5-3}.12 37 2 10 20.7 Copernicus, 12 38 34-4 | 12 45 52 10 18.6 Plato E. end, 12. 38 32.4 | 13 47 22 & 49.6 Tycho E. end, 12 40 4.4) 12 48 30 | 8 25.6 ‘ ————W, end, 12 4% 5-4] 12 49 58 8 53.6 4 Menelaus, 12 §3 0.6) 13 5 40 8 39.4 a | Dionyfius, 12 $4 45-6] 13 3 38 8 32.4 i | Plinius, 12 56 48.6] 13 5 40 8 51.4 Mare Crifium E. end, | 13 7 10.7] 13 16 35 Q 24.3 W.end, | 13 12, 20.8 {| 13 20 53 8 32.2- Sum, i 2 95-5 Mean per egrefs, - 9 5.68 Mean per ingrefs, _ = fe 8 23.17 17 31.85 Diff, mer. Aber. and Chiflehurft in time nearly, 8 45.92 Longitude of Chiflehurft in time E. 19, Longitude of Aberdeen nearly, = 8 26.92 Change of equation of time in 8’ 26”.9 12 Longitude of Aberdeen, - 8 26.8 W. DETER- 160 DETERMINATION of the LATITUDE DETERMINATION of the Longitude of the Obfervatory at Aber- deen by a Chronometer, conftructed by Mr Arnozp of Lon- don*. THE chronometer was fet to mean folar time at Greenwich, 16th June 1788, antl loft 7’.5 in eleven days. It was fent to Aberdeen by fea; and being compared with the Obfervatory clock, 15th July, it was found to be 7’ 267.6 faft, and was lofing 644. daily: It is hence probable that the motion of the {hip had altered its rate. Now, fuppofing this alteration to have com- menced when the fhip left London, which was on the 8th of July, its error at that time, for the meridian of Greenwich, would therefore be 15”.0; from this time, till 15th July, it loft 44’.8, (=6’. 4 X 7,) its rate being fuppofed uniform. | Hence its error, for the meridian of Greenwich, 15th July at noon, was — 59’.8.-- But its error, for the meridian of the Obfervatory at Aberdeen, at the fame time, was + 7’ 267.6. Hence the longi- tude of Aberdeen, in time, is 8’ 26.4 weft. Turs laft method of afcertaining the longitude of Aberdeen, although it agrees very well with the former, yet it is not to be fo much depended on, as there are fome fuppofitions intro- duced which may be objected to. From a comparifon of the preceding relclen it may be prefu- med, that the longitude of this place, in time, is probably not lefs than 8’ 18’, as deduced from the obfervations of the eclipfes: of the firft and fecond fatellites of Jupiter, nor greater than 8' 367, as inferred from the folar eclipfe of 3d June 1788. The diffe- rence between thefe limits is only 18” in time; which in this latitude does not amount to two miles and an half. Upon ac- count of the near agreement of the refults of the folar eclipfe and occultation, as well. as from other obfervations, I am led to ' believe * SEE Theory-and Prattice, of finding the Longitude, &c. vol, I- p. 208. _ And LONGITUDE of ABERDEEN. 161 believe that 8’ 32" or 2° 8’ is not far from the exact longitude of this place. Hence the latitude of the Girdlenefs is 57° 8’, and longitude 2° 6’ W. and the latitude of Greigfnefs 57° 7' 20’, and longitude 2° 6' W. alfo. Tue latitude and longitude of Aberdeen, as determined above, differ confiderably from the fame as given in moft books of. geography and navigation, where indeed they are ufually ftated with great inaccuracy. Mr Downie, to whom, at his requett, I communicated the refult of my obfervations, has, in his Nezw Pilot, placed Aberdeen nearly as above, and of courfe has laid down the adjacent coaft, with much more precifion than had been formerly done. This was in 1793; I then fuppofed the longitude 2° g’ W. which is 1’ greater than the above determi-. nation. WEL TVe 2 U 3 LWT. van eae : ovate {llasitee site vod sate ney: nes bin edge Ryd. cose Aeirperaithss sitios oy sda Cae Soria se ol lg aR ae eal amonnriido itt to sinter ody Bose Lo oS bial aad Siuios Bo bigiks, seed ae ‘finan deshasdA heoaly ie bald oad aodiong? ser donar aaiw. dlsos urd ot eae | ob RogguY reds To POV” AE enw oitt* ~igtt yoroh ovods otty ‘aod Totapty F Avid & * \ : , _ . 54 \ é ‘ ; ‘ a 4 is is 1 nd ‘ ; - e bal ‘ a .- ' Cy i é c . ‘ . } 5 tw 1% eo ay / ps ‘ . . ; ~ A 4 4 t 2 . f a } é a ¥ f , ne 6 bes . ~ x : . ha ¢ : 4 F Stee NS ot } eety cS \ . ° yes isi Ps j Yee" s ‘ 3 R 4 t 14 ims = a ~, $ t “4 » ‘ x ! % # ‘ VI. dn Account of certain Motions which Small Lighted Wicks acquire, when fwimming in a Bason of O1L; together with OBSERVATIONS upon the PHENOMENA tending to explain the PRINCIPLES upon which fuch Mo- TIONS depend: Communicated in a Letter from PATRICK WILsON, F. R. S. Evin. and Profeffor of Practical Aftro- nomy in the Univerfity of Glafgow, to foHN PLAYFAIR, F. R. S. Epin. and Profeffor of Mathematics in the Uni- wee ity of Edinburgh. [Read May 5. 1795: ] Dear Sir, Glafgow College, April 28. 1795. Now fit down to give you fome account of the little hydro- {tatical lamp, which | fo briefly mentioned to you in a for-. mer letter. As I am far from being fure whether what I have -to offer upon this fubjeé&t may be entitled to the notice of the Edinburgh Royal Society, fo I will refer this point to your determination, after you have had leifure to. confider the con- tents. / THE phenomena, treated of in the fequel, were quite new to: me a few months ago, and, fo far as I know, have not hitherto: been attended to, or defcribed by any body elfe. What I have called the Hydroflatical Lamp, confifts of a. fmall circular patch of common writing paper, about three eighths of an inch in dia-. meter, having about a quarter of an inch.of foft cotton thread: U2 ftanding 164. MOTION of Small Lighted WICKS {tanding up through a puncture in the middle to ferve as a wick ; and the phenomena, in queftion, are certain motions which fuch minikin lamps acquire, when lighted and made to {wim in very pure falad oil. A sHALLow glafs bafon, with fides rifing nearly perpendicu- lar, of a common glafs falver, will conveniently contain the oil for thefe experiments. As foon as the lamp is lighted, it will immediately fail brifkly forward, in fome direction, till it meets the fide of the veffel, and afterwards will take a circular courfe, always bearing up to the fides, and fo will perform many revo- lutions. SoMETIMES the circulation is from right to left, and fome- times in the contrary direction, according as that point of the paper bafe, which in the direc failing kept always foremoft, turns away from the fide of the glafs a little to the right or to the left hand of that which comes to be the point of contact. This turning away, of what may be called the LEADING PoINT of the bafe, is diftinétly obfervable by a partial rotation of the lamp round the wick as an axis, as foon as it arrives at the fide of the veffel. Sometimes, though rarely, the leading point itfelf attaches to the fide, and forms the vinculum, in confequence of the well known corpufcular attraction between the elevation of oil around the bafe, and that belonging to the fides of the glafs; and when the vinculum fo correfponds to the leading point, the lamp will be found to ftand ftill, without any tendency to cir- culate. | WHEN the little wick has any fenfible excentricity upon the circular paper bafe, the lamp will fail fo as to make that part of the bafe which lies neareft to the wick the fern ; and if the bafe of the lamp be clipped of an oval form, and the wick placed in the longer axis excentrical, that end of the bafe, neareft the wick, will alfo keep hindmoft, when the lamp fails acrofs the falver. In the fame manner, if the bafe be ~ an wl When fwimming in a BASON of OIL, &c. 165 an equilateral triangle, having its wick in the perpendicular which bifects any of the fides, either the vertex or fide will be- come the /ern, and keep hindmoft, according as the wick is placed neareft the one or the other. Lamps, fo conftructed, are found alfo to circulate upon their arrival at the fide of the veflel, when the leading point turns away from the glafs, as it commonly happens. WHATEVER be the caufe of the failing of the lamp directly foreward, the perpetual circulation, after it arrives at the fide, feems to proceed from the force, which formerly impelled it, {till acting in the fame manner, but in a dire¢tion inclined to that of the corpufcular attraction, which forms the vinculum ; and it is evident, that this inclination will be greater or lefs, ac- cording as the leading point is more or lefs averted from the glafs. “When it fo happens that the leading point and vinculum coincide, it fhould feem that both forces, juft now mentioned, mutt urge the lamp in a direction perpendicular to the fide of the glafs; in which cafe it muft ftand ftill, agreeable to obfer- vation. : 3 Tue next thing which I had occafion to take notice of, when the lamp failed in a direct courfe, was, a feemingly very active -repulfion between its ftern and the oil at the furface contiguous toit. This became manifeft, when very fine charcoal duft was lightly fcattered around the lamp. As it then proceeded in its courfe, it marked out a fpreading or diverging wake behind it, entirely clear of all duft, in confequence of the particles being -chaced backwards, and laterally with a motion much more than merely relative. Desrrous of learning how this difperfion of the duft would take place when the lamp was ftationary, I conftructed one of a fine wafer, and with an excentric wick, confifting of a foft cot- ton thread doubled; and to prevent the wafer or bafe from catching fire, 1 coated its upper furface with gold leaf. When thig 166 MOTION of Small Lighted WICKS this was made to reft immoveably upon the oil, the duft retired in all diretions, fo as to leave the fpace, adjacent to the wafer quite free from every particle. But here it was obfervable, that this difperfion of the duft, by the feeming repulfion of the bafe of the lamp, was much more rapid at that fide which lay neareft to the wick than at any other part, and leaft of all fen- fible at the fide diametrically oppofite. THE circumftances laft mentioned, feem fufficiently to account both for the progreffive motion of the lamp, and for the general law of this motion, formerly defcribed. For, regarding this dif- perfion of the duft, as yet, only in a general way, and as the ef- feét of fome repulfion between the bafe and the oil contiguous to it, the facts above mentioned plainly indicate, that, in all cafes, this repulfion is ftrongeft at that part of the areft the wick or flame : and as ation and reaétion are equal and con- trary, the lamp muft therefore be impelled, in the direction of a - line drawn through the wick, towards that part of the bafe moft remote from it, and where the reaction is the leaft. Bor in order to obtain a {till more competent knowledge of the phyfical caufe of thefe motions, it feemed now neceflary to inquire more particularly into this apparent repulfion between the bafe of the lamp and the furrounding oil, as indicated bY de the difperfion of the duft, in the manner above defcribed: and here the following confiderations prefented themfelves.. “t THB oi in the bafon, when of an uniform temperature, has all its parts in a ftate of equilibrium and of reft. When the lamp is hghted, ‘It is evident we have a very active caufe intro- duced, tending to deftroy that equilibrium. This caufe is the flame, which broods over a fmall portion of the oil, and is fepa- rated from it only by the intervention of a piece of paper or a waffer. The oil, in fuch circumftances, in confequence of be- ing violently heated, muft fuddenly increafe im: volume, and. _ mutt now, on account of the decreafe of its fpecific gravity, be prefled. ay - a * ee When Swimming in a BASON of OIL, &. 16% _preiied upwards by a force fufficient to raife part of it above the general level. But this heated portion of oil, in its endeavour thus to rife up, will meet with a refiftance equal to the weight of the incumbent lamp, which will determine it, in feeking a vent, to flide out from under the bafe in a thin fuperficial fiream ; and it feems to follow, with equal certainty, that this conftant ftream will flow moft readily and moft copioufly towards that fide of the bafe of the lamp where the refiftance is leaft, or where it has the fhorteft way to prefs forward; that is, from under the wick or flame, to the edge of the bafe which is the neareft, according to what we have feen to be agreeable to the pheno- - mena. But, from the laws of motion, it is certain, that the re» action of this ftream of rarified oil, thus iffuing moft rapidly and moft copioufly from a particular fide of the bafe, muft im- pel the lamp in the cofitrary direction, and make it fail in the manner we have feen. It may further be remarked, that the heated oil, fo retreating from the flame, and endeavouring to rife fomewhat above the general level, in confequence of its dimi- nifhed fpecific gravity, may more or lefs lift up that fide of the bafe neareft the wick, and aid the reaction of the recoiling ftream, by making the lamp {fail in the oppofite direGtion, as it were down-bill. ' Tuat the rarified oil under the bafe has really a conftant tendency to rife above the general level, feems undeniable, from the following facts, namely, that after any of the lamps has burned a little while, and has got its, bafe foaked with the oil, as foon as the flame is blown out the lamp finks to the bottom ; and even a lamp, with its bafe made of a thin lamina of talck, fails very well till the flame is extinguifhed, and then it imme- diately finks. | | AGREEABLE to thé explanation which.has now been attempt- ed, I found, that when a topical beat was applied to the furface of the oil, by bringing the point of a poker, dully red hot, near- 3 ly 168 MOTION of Small Lighted WICKS ly into contad, there was foon produced a fuperficial ftream or efflux from the iron in all directions, which cleared the face of the oil from the charcoal duft, in a wider and a wider circle, till - at laft the whole particles were crowded os at the confines of the bafon. WueEn the oil in this experiment was fhallow, having gold leaf beat into very minute parts mixed with it, an oppofite ftream was obferved below, fetting in towards the poker in all directions, and then rifing upwards. But this general tendency of all the parts of the fluid of moving in queft of an equili- brium, is iluftrated in a very entertaining manner as follows : Into a tea-cup or punch-glafs, nearly filled with pure water, pour a defert fpoonful of very clean falad oil, with minute particles of gold leaf in it. If the water be cold, the oil, when poured on at the centre, leifurely and continuedly, will reft upon the furface in the form of a lens, and remain infulated or equidi- ‘ftant from the fides of the veffel. A little lamp, when put up- on this lens of oil, and lighted, will fail and circulate as larger ones do in the bafon. If it be now made to ftand ftill, it is very amufing to obferve the minute particles of the gold per- petually thrown out brifkly at the ftern in the fuperficial cur- rent, whilft the particles in the fund of the lens creep in all di- rections towards the lamp, and at laft rife up under the bafe towards the flame, as the great centre of attraction, till they are caught by the retreating fuperficial ftream, in which they ra- pidly trend off to fome diftance, when again they fink to renew. the circulation. WHEN a patch of paper, or a wafer, or fuch light body, fwims upon the oilin the bafon, the point of a hot iron held near to it makes it flit its place, and move away by a feeming repulfion ; but, in reality, by the heat generating a fuperficial ftream, flowing from the iron in, all direétions. AGAIN, eee ee ee ne When fwimming ina BASON of OIL, &c. 169 -Acatn, if upon oil of turpentine, ether, alcohol, or any of the inflammable fluids poffeffing much tenuity, you throw a wafer much heated, it will immediately glide away, and con- tinue in motion till it cools; when the ftream, which iffued ~ from fome part of it moft copioufly, ceafes. Double rum, melt- ed tallow, bees wax, and rofin, alfo afford the fame continued efflux at the furface, upon a topical application of heat, and the fame phenomena as the oil does, when little lamps are made to fwim in them. It is fomewhat remarkable, however, that though the inflammable fluids all agree in this, yet the topical application of heat, at the furface of water, does not produce fi- milar effects. . . For if the point of a poker nearly red hot be held very clofe to the furface of water in a bafon, the particles of the charcoal duft do not at all glide away as they do in the cafe of oil, but feem to acquire only a flow irregular circular motion, _ which in time fpreads wider, whilft the floating motes or particles of duft keep nearly their relative places ; and the fame thing hap-« pens, though the point of the iron touches the water, fo as to make it fimmer. _ I Do not well know how to account for this, unlefs it may be a confequence of the known much lefs expanfibility of water _ by heat, compared to that of the inflammable fluids, and which may be fo inconfiderable as not to deftroy the equilibrium, fo far as to produce an efflux from the lighter and expanded fluid immediately under the heated body. Poflibly, too, the parts of the water, as foon as heated, may tranfmit the furplus tempe- rature to the contiguous colder water much more rapidly than the inflammable fluids do in like circumftances, and thereby re- fift the high temperature, neceffary to that degree of expan- fion, which would difturb the equilibrium, and produce an ef- flux ; not to mention that the maximum of this temperature can never, at any rate, exceed 212°, the boiling point of water. VoL. IV. g x THAT % 170 MOTION of Small Lighted WICKS Tuar the equilibrium, however, amongft the parts of water, is difturbed by the local application of heat, though in a much fmaller degree that what obtains among the inflammable fluids, appears from an experiment I was led to make with a {mall thin cup fwimming on water, and fo contrived as to carry and feed with oil a wick, placed a little way down from the lip in the infide, fo as to be on a level with the water. ‘The confe- quence of this conftruction was, that the cup moved upon the water very flowly, but always with the flame evidently ftern- moft. The fame cup, when taken from the water, and put in- to a bafon of {trong rum, failed a great deal fafter, and accord- ing to the fame ufual law. I am much afraid, that by this time I have wearied you by fuch a detail of minute facts and circumftances, and by thofe frequent repetitions which every new fubje€&t more or lefs re- quires. And | ever remain, Dear Sir, Your moft obedient faithful fervant, PaT. WILson.., P. S. SHouLD you be inclined to repeat any of the experi- ments, the following directions and mifcellaneous obfervations may be attended to: The thread I made ufe of for the wicks was of that foft kind commonly employed in the flowering of muflin. After making the pundiure in the bafe, you put through a bit of the thread, which clip fhort off below, and with a pin force in the burr gently round the thread, to give the bafe a proper hold of it. Then clip away the fuperfluous thread above, leaving the wick about a quarter of an inch long; and fo the lamp is completed. Set it then upon the oil, by taking hold of the wick, that the paper bafe may not be bent or diftorted by handling —— eee eee a | - Whea fwimming in a BASON of OIL, &c. 171 handling it; and, after the wick is touched with a drop of oil, it is ready for being lighted. For this purpofe, a bit of pack thread, which has been fteeped in oil, is a cleanly and conve- nient match, and fheds no impurities on the oil, as a candle or wax taper would do. WHEN you want the lamps to circulate, the oil muft be very pure, and brought into full contact with the fides of the glafs. The oil, and the bafon or falver, fhould all be allowed to come to the fame temperature, between 55° and 60° of Fahrenheit. For if any part of the brim be much hotter than the reft, the lamp, on arriving there, will leave the fide, by the current iffu- ing from the heated part forcing it away. SOMETIMES the lamp, when failing, veers a little into a diffe- rent direction, by the bafe altering or warping by the fcorching "heat of the flame, which determines the {tream to flow out moft copioufly at a different part of the bafe.. In the melted greafe which lies round the wick of a common candle when lighted, there are fometimes obferved atoms, which have been left by the fnuffers, moving to and from the flame continually. Thefe motions have been conceived by fome as occafioned by attractions and’ repulfions, in confequence of an electrical quality imputed to the flame. It fhould feem, howe . ever, that they depend merely upon oppofite currents at the fur- face, and immediately below the furface of the melted greafe, according to the principle above explained. xX 2 VIL. pee + ’ ~~ . if : Ng ri t ve Stare 4? aaa" i 4 sabia & axe The: Seas eu) Tri Kea eet } tay % OD 4 4 a Ane bag 24 fy yA Li om Lae act soe er Tan yen Wir gee. ar od id “$ybtt gal dagvy Regio lit oder guard ‘bee ho) Cees Yo" baygall 5 ath He: buod, pHa “o rated: oily. Brita PEs oe nc ae Poulet a0. “oduhite £29 noah eda otumencnas Sorel. Seam Rec Se. ala gf han adi ox nd sent doar od “saiatd gity. Io.swaiyanyi ing i, sae sg prea od- ihe safyit ods, axael ieee. dt. Brivivind f eA os Wee aes EM Ws Y goivnt Iq Bot oh ong a q.OuaE slag. & Arseny. eariL uit: cre, amahecty. i eiioyot oeda-wed eT igrare 39 ails ded ade. ad A ae HG. Won OF mootth. alk, eiuigrgsiaberls ide -oore he ink 4 eae Bae, | cea CaN ae “alec ots to s1aqf 299781 ay Me . noseato 2 to-do w bagon ¢ evil idoisker: sheerg baits ; Motd yer aciors how ride apenitseaion ou oro cboastgd phi “be Re raid oct praia ba TH et Revo: versal Seta: vt sted ‘sorb : as onck yd. fevisotwo asid sved ettotss aro tot Tis ok ‘nga La eete ) coxa pstnoy (si eso #3 fing 200 vtck Ra hee oie ae “wort imgst blued: it. oran8 dt gr baieqent ytiles bh er 5b ° . “Unt sit, seer iw: na eoucys 10 the nggas-y beta: bawageb: “polls: . om é . yalgoae. bevdorn wilt Ag, yom baidt colts aye bhond “eka, those ef wie az ell oi batdittiqa’ 2 svod Ie aici nti \ = <<“ { ; 4 VII. dn Account of a SincuLar HALo of the Moon. Com- municated in a Letter from WILLLAM HALL, E/q; of White- Hall, F.R.S, Evin. to Sir FAMES HALL, Bart. F. R. Se Ep1n. [Read May 2. 1796.] DEARSIR JAMEs, Whitehall, near Berwick, April 2. 1796. SEND under cover the reprefentation of a very fingular Halo. of the Moon, (See Pl. V.), feen here on the night of the 18th of February laft, about 10 o’clock, and this I have hitherto delay- ed, in order, if pofhble, to gain farther information in the neigh- bourhood concerning it. Durine the fhort continuance of the fall halo, which did not exceed 10 minutes after I got notice of it, I could not lay my hands on any other inftrument to take the angles, but a S1s- son’s theodolite, which, unluckily, having been conftructed fo as not to admit of a vertical angle fo great as the moon’s alti- tude then was, I laid it afide, not recollecting that it might have meafured feveral of the fmaller angles. But I obferved fundry marks, from which I took the angles as exactly as I could next. day. ; THE moon was about S. W. and her altitude nearly 54°, which of confequence was alfo the altitude of the limb of the greater halo, where it was a i and where it pafled through. the 174 ACCOUNT of a SINGULAR the moon ; the altitude of its oppofite limb was 14°; fo that its diameter fubtended an angle of no lefs than a hundred and twelve degrees. | Tue diameter of the fmall halo, which appeared to be a per- fect circle, with the moon in its centre, I found, after repeated trials, was under 12°, and more than 8°; but as the different diameters of the large halo were not meafured, it cannot pofi- tively be affirmed that it was an exact circle; on the contrary, its limb did not feem to interfect the {mall circle quite fo much at right angles, as the circular arch delineated in the plan. It may therefore have been fomewhat eliptical. Tue fmall circle was remarkably bright, particularly at We Refion, about five miles to the northward, the only other place where the halo was obferved, and where it was thought to fend forth flame. The fmall halo alfo continued there much long- er than here, where fome thin fleecy clouds foon put an end to it, but the large halo continued with us near an hour. THE weather about this time was, for the feafon, remark- ably mild, particularly on the day of the halo. The fky was pretty clear all that day, and alfo in the evening; but at the time of the halo there was a {mall degree of hazinefs, particu- larly towards the north, which did not however prevent the moon from fhining with brightnefs ; and the ftars were even vifible within the circle of the fmall halo: there was little or no wind. Tue circles or belts of both halos are reprefented in the plan, nearly of their apparent breadth, or perhaps a little broader ; the light of both was whitifh, and confiderably bright, without co- Jour; that of the large circle was the paler of the two, particu- larly where it pafled through the {mall circle: to the northward it was fomewhat obfcure. By means of the angles taken as above, after having afcer- tained, on a vertical circle of the heavens, the fituations of the moon, HALO of the MOON. 175 moon, of the fmall halo, and of the north-eaftern limb of the large halo, whofe fouth-weftern limb pafled through the moon, the whole was projected on the horizontal plane, as in the figure already referred to. ‘The moon, a little more than half, is pla- ced in the centre of the fmaller halo; and both halos are repre- fented in their true fituations, relatively to the horizon, and in the circular fhape which they appeared to have, though they ought perhaps to have been fomewhat-forefhortened, and thrown into an elliptic form. Tuts halo, as you will fee by the above defcription, appears to be of the kind called by the learned a Corona sand as it fomewhat refembles the famous one of the fun, obferved at Rome in the year 1629, and defcribed by ScHEINER™, it deferves the more attention, efpecially as the great halo, on the prefent occafion, having its fouth-weftern limb elevated to the height of 54°, and its north-eaftern deprefled to within 14° of the ho- rizon, was in an oblique pofition, not eafily reconciled with the theory of Huycens, which feems to require that fuch circles fhould be equally elevated above the horizon all round. It alfo fhews, that SCHEINER’s original plan of the halo at Rome, which reprefented it as oblique, may have been right, and that HuyGEns’s correction, which makes it parallel to the horizon,, _ was probably an erroneous conjecture. eam, Dear Sir JAMEs, Your humble fervant,. Wiut.. HALE. * Smirn’s Optics, vol. I. § 534,. VIL ies Bee: ay nae ig ae We ‘ i ys ae Be ud aes io kl 3 1% 7 , ate i ee - - ‘ I Se | = AM 4 oats { E 2 - ’ x / Tar ola 5 4 , Z 4 gel ph bill ph pa Ainhur A, "Ass. 7 Phil 7: ys. Papers Ey Wy ' \ UW NY ANY ) \ ZZ iY cS aE. ss eae Zi . = GSI Zz OZ, SDE ASS ty Vp WAS SS S WAS AY \ S Ry NS SANS A Sy 2G: WL. FZ. NN N WS SX N . WA \ AY RMN AAAY \\ AN AA VARA AAS AR SN SIN WN SESS 8 SS SN SS WY AN SS ANAS \\ \\ WY NS \\ ANN AY NASA NS AN \\ SN SS SY SSS NY \\ SANS MAY RAN NR \\ OVW PCORADM Me about the 2 ve Berwick shire on the 18 of Feb D Bie en Of C Q6. 7 vy DLizars Seulp oy" = % ae ae ee ad ie VIII. 4 New SeriEs for the RECTIFICATION of the ELLipsis ; together with fome OBsERVATIONS on the EVOLUTION of the Formuta (a* + b* — 2a) cofo)”. By AMES Ivory, A.M. Communicated by FOHN PLAYFAIR, Pro- Selfor of Mathematics in the Univerfity of Edinburgh. [Read Nov. 7. 1796. ] Dear Sir, AVING, as you know, beftowed a good deal of time and | attention on the ftudy of that part of phyfical aftronomy which relates to the mutual difturbances of the planets, I have, naturally, been led to confider the various methods of refolving the formula (a*-+4* — 2ab cofg)* into infinite feries of the form A+ Bcofe+Ccof29+ &c. In the courfe of thefe in- veftigations, a feries for the rectification of the ellipfis occurred to me, remarkable for its fimplicity, as well as its rapid conver- gency. As I believe it to be new, I fend it you, inclofed, to- gether with fome remarks on the evolution of the formula juft mentioned, which, if you think proper, you may fubmit to the confideration of the Royal Society. I am, Dear Sir, Your’s, &c. DovcLastowN, near origci) JAMEs Ivory ~ 2oth O&ober 1796. Io Mr Fohn Playfair, Pro- feffor of Mathematics, Sc. Vou Iv: ey ee 178 RECTIFICATION of th ELLIPSIS, &c. Let ¢ denote the excentricity of an ellipfe, of which the femi- tranfverfe axis is unity, and a the length of the femicircle, ra- dius being unity: Then, I—Yr— Ef pase half the Pek of the ellipfis will be if we put ¢ = “ wh ae ra: sey. —t Se AS ee ST AE |. OS PR hE =45 (+5 e+ = e + Mi OE 2”. 42. 6? ‘ +z 42. 67. ue + &c.), the coefficients ys ee fquares of the coefficients of the radi- cal 7 a THE common feries 1s, ° . . I. i. I. aw X (x anes: ¢ aE | -" babe hah 0 “° — &c.). 2.0 a 2.4 24 2.4.0 2.4.6 TuE firft of thefe feries converges fafter than the other on two accounts : firft, becaufe the coefficients decreafe more rapidly ; and, next, becaufe ¢ is very {mall in comparifon of ¢, even when ¢ is great: Thus, if ¢ be e will be 3 and ¢ = = | In order to point out the way in which the preceding feries was difcovered, let us fuppofe (a + 7 — 2ab cof 9)* =A +. Bcofg+Ccof2a + &c.; and to determine the’ coefficients, A, B, C, &c. let us, with M. DE LA GRANGE, confider the quantity (a*-+ 4? — 2ab cof¢) as the produ@ of the two imaginary expreffions (a SA ‘)s and - (a ieee *\, where ¢ denotes the number ‘whofe hy- perbolic logarithm is unity. Then, by expanding the powers. (a be °¥ Se e and (2 —be ~? Sales into the fe- ries a” ( I — wePV —F4 Be oY es ye HY} aaa &c.) and | RECTIFICATION of the ELLIPSIS, &c. -179 and a” ( I— ad. OV TE eras ee ST ik dat a —_ ee he a, a——tL me MO Te A 2 é > Y — a ee &c. 1.2 1.258 we havea =n, 6 = THEN multiplying thefe two feries together, and putting + mof—t eee yt ° +¢ - 3 2cofm@ for its imaginary value ¢ we fhall find, on equating the terms, A=a"x(rt+a.5+B.5+y. at &e.), ; b 53 bs B= — 24” .X C S hie Pads AY sas &e. }, and fo on. ay Or the feveral feries for A, B, C, &c. the firft deferves parti- cular attention, on account of the fimplicity of the law of its terms. It deferves the more attention, too, that the whole fluent fc 9 (a+ — 2ab cof¢)”, generated while @ from o becomes = a, half the circumference of the circle, is = A+ qa: all the other terms of the fluent then vanifhing. SuPPosE now, in an ellipfis, the femi-tranfverfe = 1, the ex- centricity = «, and ¢ an arch of the circumfcribing circle, rec- koned from the extremity of the tranfverfe: then the fluxion of the correfpondent arch of the ellipfis, cut off by the fame ordinate, will be = ov 1—=* cole. , In this expreffion, I write < 45 cof 2, for cof.7@: and put the refult, 9 ¥ 1 — 7 — 7 colf29 = 9 Va? + F* — 246 cof 29, a and b being indeterminate quantities. To determine @ and 4, we have a? + 4*= 1 — a and-24) = ay 2 2 whence a+ 4= 1,anda—b=Y 1 —¢*fothata =ttvise I— I —e? znd Osea v2 j I 180 RECTIFICATION of the ELLIPSIS, ae ‘| ruus obtain 9 ¥1— @ cof7@ = oV a? + 4 — 2ab cof29: and, taking the whole fluent, while 9 from o becomes = a, it is manifeft, from what has been pees that the femiperiphery of the ellipfis is = Pe EF. 125. B* 4) ae? wXaX(r-+bS-a + oh: a thas oT oe Ads os = oe + Be.) b 1—fi—e Sig ee I I utting —=e= 2anda=—{ = ee or putting — l+Yi—e até at i oe the ee of the ellipfis = Some x (1+ Fe “a tS e e* + &c.) In this Coke as was before obferved, ¢ is a fmall fraction even when « is very confiderable, and. the. coefficients are more fimple in the law of progreffion, and converge fafter, (ef- pecially in the firft terms), than in the common feries. Ir we fuppofe the ellipfis to be infinitely flattened, in which cafe ¢ = 1, and.¢ = 1) mind) the’ ee = 2, this feries gives. 2 = = x(it+ oto oe 7+ &c:), and fo p> wi. - 2 athe ee and Wich xanga oa ee But, we may remark, that as we have here obtained the fum: of the fquares of the coefficients of the binomial when the ex- ponent is =; fo, from the fame fource, we may determine the fum of the fquares of the coefficients correfponding to any other exponent, at leaft by a fluent. For taking the whole fluent when @ = w, we have: fw + 3 — 2ab cof) @ =a" a (x fat. +. ae y*. zt &c.) and fo when a4 = 1, andd= 1). f (GB 2ab cole)’ g =1+.2a7-+ TH saat Koy Now,, Sea) ae A OE le RECTIFICATION of the ELLIPSIS, &c. 38: Now, when a4 = 1, and d= 1,f@ (a*-- ie —2abcofe) ae 4 | f 9 (fin®),” becaufe 2 (nt) = 1 — cof: we thus obtain at mfng(int) si epg 4 ara yh ae! ? the whole fluent to be taken when ¢ = a, or > =>- Ir we put x = fin f. we fhall have urn x eee ee fiseaite]t+h+y+&, 7a the whole fluent to be taken when « = 1; and. in this formula m is any number fractional or integral, pofitive or negative; and a, 2, y,; &c. the coefficients of the binomial raifed to a power of which the exponent is 7. _ WHEN 2 is a whole pofitive number, x27 x T.3.5....(27—1)@.. : {-— = iF Se ae a in the cafe when x = 1: Ly — x? DAO aie ace 27 2 And fo, yg GS OEE ee rt at + 62+ + &e. 2n the middle term of a BaabiMial, raifed to the power expreffed by an. Hence we have a very curious property of thofe numbers: viz. that the fum of the fquares of the coeffictents of a binomial, the exponent being n, 1s equal to the coefficient of the middle term of a binomial, of which the exponent is 2n. ANOTHER remark, which I have to offer on this fubject, may be confidered not only as curious, in an analytical point of view, but as, in fome meafure, accomplifhing an.object that has much engaged the attention of mathematicians. _ In the computation of the planetary difturbances, it becomes 9 0 4.6 Now, 227 re tase Te) dae Oe is no other than the coefficient of ——s neceflary to evolve the fraction (a* + 4 — 2abcofp) into.a , feries 182 RECTIFICATION of the ELLIPSIS, &e. feries of this form, A+ B cof? + C cof2e + &c. The quan- tities a and b reprefent the diftances of the difturbing planets from the fun; and when thefe bear fo great a proportion to one another, (as in the cafe of Jupiter and Saturn, or Venus and the Earth), that the fraction : is large, it becomes extremely difficult ‘to compute the coefficients A, B, &c. by feries, on account of the great number of terms that muft be taken in. This matter not a little perplexed the firft geometers who confidered this fubject, and they were obliged to approximate to the quantities fought by the method of quadratures, and by other artifices. Two things are to be attended to with regard to the quanti- ties A, B,C, &c. The firft_is, That it is not neceflary to com- pute all of them feparately by feries, or by other methods: They form a recurring feries; and the two firft being fo computed, all the reft may be derived from them. The fecond thing is, That the quantities A and B having been computed for any exponent n, the corref{pondent quantities are thence derived, by eafy for- mulz, for the exponents n+1, n+2; n—1, n—2; andin general for the exponent 2+ m, m being any integer number, pofitive or negative. From thefe remarks, it follows, that the whole difficulty lies in the computation of the two firft quantities, A and B; and that we are not confined to a given exponent 7, but may choofe any one in the feries, +1, n +2, &c.; n—1,u—2, &e.; that will render the computation moft eafy and expeditious. THus, in order to compute the quantities A and B, for the exponent — 3, M. DE LA GRANGE makes choice of the expo- I ° 5} . nent M5 ae which, in the whole feries of exponents -+ 3, ae » —-, ae 3, &c. is the moft favourable for computation, on ac- count of the convergency of the coefficients of the feries for A and B. In Ee RECTIFICATION of the ELLIPSIS, &c. 183 _ In confidering thefe fubjects, however, I have fallen upon a method of computing the quantities A and B for the exponent —< by feries that converge fo faft, that, even taking the moft Se at ie cafe that occurs in the theory of the planets, two or three terms give the values required with a fufficient degree of .exaCtnefs. “This is what I am now to communicate. ‘WE are then to confider the expreffion ,(a*7+-6?—240 cof¢) rir : : for the fake of fimplicity in calculation, OS ~~ fa* + 6* —2ab cof? 5 Iwrite2 = c, throwing out a altogether; and I f write- = c, throwing out @ altogether ; an uppofe Pr cate —A+Bcofe+Ccof29+ &c. Ler ¥ be an angle, fo related to ¢, that fin (~— 9) = fin p: | It is obvious, from this formula, that ) = 9% when fin ny = Ou that is, when »¥ is equal to 0, or to w, 2a, &e. We have then, cof ( — 9?) =W1—c? fin’: and taking j A ccof xy ae cool Xp. the fluxions, ) —9:= wy) — 7¥a=e fin*)* of §—c* fin 24, — ccof yp whence 9 =~ X PF = eee ~Bur(¥i— ¢? fin *p —c cofp) =1—-0 fin? + ct cof?) — 2¢ cofy ¥i— 6 fin *y = I +c? — 2c* fin *p,— 2¢ cof} Vie fin ay (becauk ce? cof 2p =c?—c --fin 7x) = easy | a c? —2¢X (c fin) X fine + cof 71 —c? fn’). Now, if we write for -cfin d its equal, fin () — ¢), and for Yt — ¢? fin*p its equal, cof ( —'¢), we fhall have ofiny X fin} + cof x ¥7—<¢ find = fin() —¢),x find + cof x cof(p — 9) = cofg: which being fubftituted, there comes out ; Chara, —c¢ cof)? mite? — 2 cofe Our 184 RECTIFICATION of the ELLIPSIS, &. Our fetus formula thus becomes ¢= T+c*—2ccolp ' yt Pet = Be col Dyes beet oe te v Ui eS ee eS = ——— ee ny Yi—e* fin *y Y¥ t+c* —2ccoig Y (2c? fin DP I NEXT transform the quantity V1 — c* fin 74 as in the in- ° . . . . ° I —j/i — cx veftigation for the elliptic feries, and putting re yr nes airy 4 2 — Vie eae ee! and fo 03 podp sts ay — find v1 Cc fin v= Ite Y7i+c? —2cco19g qE. G+te)y Wi +¢* + 2c cof aw Now, taking the fluents when ¢ = a, and y = a, we fhall have Jot = apediel 277 AXa: And according to the me- 4 er r eee thod of M. pE ta GRANGE, / : ear id x (1 + Lo + = 30+ + Bec.)-: Hence A = (1 + c’) X (x af = pith re cl4 &c.). And in this value of A, ¢c’ will be a {mall fraGion, even though c be large; and the feries will therefore converge very faft. But, taking the value of A direétly m a feries, we have Azithe? +325 ct+ &c. Andfor+ 5 ct psi 2.43 Mewes (re) x (1+ +c? +2 3 c!* + &e.). Now, SF the two feries being exactly alike, it is evident that we may transform the one, as we have transformed the other, and that, if bos, FSV Se . = ihe eee. ‘ CS } ==. 42 cated SEES. * aa we put ¢! = 7 = we fhall have 1 ++ = c!? + oe (1 +c”) x (1 +- =o" +- <3 ee cle kc.) whenceA =(1-+¢’) Ree) Ct ah x c@4 + &c.). ‘ Ly ee a a oe belie le ee tli RECTIFICATION of the ELLIPSIS, &c. 185 Ir is manifeft.we may proceed in this manner as far as we fe PO LS, — e* 1+ fi—el? ” ~~ p+ fr—e"? and fo on, we fhall have the value of A in an infinite product, =\(1 +c) X.(r + 0’) & yt) fr $e) x &c, the quantities c’, ¢”,-c", ce”, &c. converging very rapidly. NotuHinG more feems to be wifhed for, with regard to the ‘computation of the quantity A: fince we can, by methods fuf- ficiently fimple, exhibit the value of it in feries that {hall con- verge as faft as we pleafe. By a fimilar mode of reafoning, I pleafe, and that, if we pute” = i Vd to3 EE a" Minbar E tn Sor 6 find the feries 1 x¥ rae y ae ee, 4 &e, (which occurs in determining the time of a body’s defcent in tie atch of a tirclé), = 5 & TL _ ea eAgLt Wyble ce Dag 17.3%. 5 ere pe VETYESD, ene a4? eo + &e. / where ¢ = Sees fo that the fumma- tion of this feries alfo is accomplifhed by the method above. I HAVE now only to explain the method of computing B. For: this purpofe I refume, : =At Boole +C eofae ke. /t+c*—2ccoig Multiply by 2 cof ¢, and there refults 2 cof @ Vite recog — B+ (2A + C) cofo + &c.. eheuce:i it is manifeft that the Soke fluent {eee 2colexo ees whe ¢ — 2, 19 He ee 0g I+c* —2ccolo From the preceding eee we have ee = J + c— 2¢ col @ a = a cof @ Sgr Sy yr fin 74, Vou. IV. Fis whence 186 RECTIFICATION of the ELLIPSIS, &e. : | @ cof 2c) fin *L: os j . Vi+c* —2ecolo YWi—c* tin?) 24 cof ¥. ; Again, afin?) = 1;— eee ee: ne B Bee ‘ cof 24, and Jie fn td ~~ /1 +e? +2¢ cole ? 4 22 tLQY : - ; A being = pore sero thefe fubftitutions being made, we get apletb At ELT ye'08 PORE IY 23 BNI 310 ee ep om 714 ¢7 —2cc019 VY i+c* + 20 cole Vite +26 cal ag + 2 cofy. I SUPPOSE now, Vite? + 2¢ cong =A'—B'cof2b-fe' cof 4y— &e. it is evident, from what goes before, that, taking the fluents of the above fluxions, when ¢ and} = a, we fhall have B X a =cx(r+c)x (A+) Xz, and fo B =¢ X (I+¢) X aN PR’ (A +). Tue values of A’ and B’, in feries according to the method of M. DE LA GRANGE, are Aarti? + Diet +k oo + &e Eloy V2 Asp gE ge ped I. 3, 1-3-5 ws 7 B= Ce +e 20h ESE, + &e.) 1* 7 ° which feries converge very faft, on account of the {mallnefs of ec’ in ref{pect of c. Ir, however, it be required to find the value of B by feries {t)] more converging, we may eafily do fo: For it is manifeft ‘that B and B’ are fimilar functions of c and c’: and that if we aay Pee 1 fi — ETN Bs 7 Et ———,, and fo on, and put make c’? = ————>== = . b+Yi—e? I+ fi— ee RECTIFICATION of the ELLIPSIS, &c. 187 ADA, Sc. }-B, BY) &e. to denote the correfponding values of A’ and B’, we fhall have Boc.(1t+c)(AX += Bae. (1+e)(Av + =) BY = c.. (ee! (A” + =} &e..: Now, remarking that A’ = (1 +e") A"; AVS (te) A", &c. we have the following values of B: Baex (+4). (rte) (rte art LEC EG +e") B’, Baex(r +o +2 +)G+e V+ BW ike o ce cl lt —(1-6'} (1 +c”) (1 + cl’) B“. And we may proceed in this manner to find the value Ny B in feries that fhall converge as faft-as we pleafe. As the quantities ¢’, c”, c’’’, &c. diminifh very faft, the feries A’, A”, A” will approach rapidly to unity, and B’, BY, B” will _decreafe rapidly to oe enc : Hence we have ultimately, Boex (1 eis 6.5 st oy tke. ) x (ae')(t-he’) (be) &e. oats te) +c’) atc") &e.: : nt al (at a Se SA ep &e.) xX A. We fhall beft fee the degree of convergency of the quantities e, c', c”, &c. if we take the infinite feries by which red are de- rived one from another. Now,.if y = — ieee 2 then alfoy = Sawa ep 4 4 7 4 &e.: whence it is obvious, that in th de cys 64 = whenee it 1s obvious, that in the feries of quantities c, ¢’, c’, &c. the fourth part of the fquare of Z.2. any~ 188 RECTIFICATION of the ELLIPSIS, &c. any term is nearly equal to the following term, and the rapidity ; with which the feries decreafes is therefore very great. THE method, then, that refults from the preceding inveftiga- tions for computing A and B, is fhortly this: IT— /i — ¢* 1+ Yrt—c* qt pga? oh I*. 27, 2 bet bere ge) ee = Put ¢ = : and compute nit PEs (3 1303-5 vs hs and >c' += | cise + &c. = N. ike 8 = (1 +c’) X M, and Bo=exXx (+c) x (M+N). Tue feries M and N will converge fo faft, even in the moft unfavourable cafe that occurs in the theory of. the planets, that the firft three terms will give the fums fufficiently exact ; and it will therefore not be neceflary to have recourfe to hs more converging feries A” and B”. . Sucu is the method that I had firft imagined, for facilitating thefe fort of computations. I have fince found, however, that by means of the common tables of fines and tangents, the quan- tities A and B may be computed in a ftill eafier way from the expreflions, Aztec) (+e) (a +e") &e. Bo=cx(1+¢ ESTE SS + bee) XA I — cof m 2 a oer FR ME ROM ee Ys ee For if ¢ == fin m, then 1, —-.¢?.= cof.m,and ¢o=1 > ical = tan? =: confequently 1 +c’ = fec? 7. In like manner, if 2 4 Y 2 = ; _m e = fina’, c’ = fin m’, &c. we fhall have fin m' = tan? >; . ‘ Se — ee oe — RECTIFICATION of the ELLIPSIS! &c. 189 | ‘ 2 a fin m’ = tan? =, and folon: And x -bic! = fec? fy asec - fec* —, and fo on. Thus: Av fee? = x fec » a x feo? me! x &c. To find the as of A, we have ve Be to add toge- ther the jogarithin fecants of the angles ~ = ai se od to dimi- ; ; : 2 nith the fum by as many times the radius as there are fecants, and to take twice the remainder. As the angles. m,-m', m’, &c. decreafe very faft, it will feldom be neceflary to compute more than two or three of them. Tue feries (1 + g + Re Ge —+% eo et 4c +- &c.) is alfo readily com- 2 2 y puted from the tables; oe a logarithms of ¢';c’, c", &c. be- ing the fines of the angles m',m”, &c. are all ma in the ta- bles. As an example, let ¢ = 0.72333: which is the fraction that arifes from dividing the mean diftance of Venus from the fun, by the mean diftance of the Earth; and this is the moft unfa- ‘vourable cafe that occurs in the theory of the planets: Then to gompute A, I find, in the table of natural fines, that 0.72333 cor- 3 Res to 46° 19 484”: we have therefore = 46° I9' 483” | LL. tan = = 1. tan 23° 9! 54%” = 9.6313206 |L. fec = = 10.0365070 | 2 L. finm’= —_g.2626412 T=” 32" 57 _ L. tan = = 1, tan 5° 16' 283” = 8.9652949 |L. fec = = 10.0018429 2 L.finm’ = - 7.9305898 En mi! =. 0° 29° 18” L, tan 1909 RECTIFICATION of the ELLIPSIS, &c. : L. tan m= 1, tan 0° 14’ 39” = 7.6295664 IL. fec = = 10,0000039 2 —_- 0.0383538 L.finm” = 5.2591328 2 As m" will only be a few feconds,it may| L. A = 0.0767076 be neglected. . Hence A = 1.19318 ‘To compute B,letS = 1 + o4 ~ g + &ce. I = 1.000000 Lee slfina’ = 9-2626412 ; c .= 0.091540 L.¢ = 1, finm’ = 7.9305898 ce = 0.000390 - Lc¢’. ¢*.ce Felgg23210 S = 1.091830 B=cxSXA. Lore! = 1.8593365 L. S = 0.0381948 L. A = 0.0767076 . L. B = 1.9742389, and B = 0.942408 IX, ot ij stati ees, IX. 4 Snort MINERALOGICAL DEscriPTIon of the Moun- TAIN Of GIBRALTAR. By Major IMRIE. Communicated by the Reverend JOHN WALKER, D. D. Profeffor of Na- tural Hiftory in the Univerfity of Edinburgh. [Read Fuly 3. 1797-] HE mountain of Gibraltar is fituated in 36°. 9’ north lati- tude, and in 5°. 17’ eaft longitude from Greenwich. It is the promontory which, with that of Ceuta upon the oppofite coaft of Barbary, forms the entrance of the Straits of Gibraltar from the Mediterranean ; and Europa Point, which is the part of the mountain that advances moft towards Africa, is generally ‘regarded as the moft fouthern promontory in Europe. The form of this mountain is oblong; its fummit a {harp craggy ridge; its direction is nearly from north to fouth; and its greateft length, in that direCtion, falls very little fhort of three miles. Its breadth varies with the indentations of the fhore, but it no where exceeds three quarters of a mile, Thre line of its-ridge is undulated, and the two extremes are fomewhat high- er than its centre. ‘Tue fummit of the Sugar Loaf, which is the point of its greate{t elevation towards the fouth, is 1439 feet; the Rock Mortar, which is the higheft point to the north, is 1350; and the Signal Houfe, which is nearly the central point between thefe two, is 1276 feet above the level of the fea, The weftern 7 fide 492 MINERALOGICAL DESCRIPTION fide of the mountain is a feries of. rugged flopes, interfperfed with abrupt precipices. Its northern extremity is perfectly — perpendicular, except towards the north-weft, where what are called the Lines intervene, and a narrow paflage of flat ground that leads to the ifthmus, and is entirely covered with fortifi- cation. The eaftern fide of the mountain moftly confifts of a range of precipices; but a bank of fand, rifing from the Medi- terranean in a rapid acclivity, covers a third of its. perpendicu- lar height. Its fouthern extremity falls, in a rapid flope, from. the fummit of the Sugar Loaf, into a rocky flat, of contiderable extent, called Windmill Hill. This flat forms half an ov al, and. is bounded by a range of precipices, at the fouthern bafe of which a fecond rocky flat takes place, -fimilar in form and ex. tent to Windmill Hill; and alfo, like it, furrounded by a pre- cipice, the fouthern extremity of which is wafhed by the fea, and forms Europa Point. Upon the weftern fide, this penin- fular mountain is bounded by the bay of Gibraltar, which is in length nearly eight miles and-a half, and in breadth upwards -of five miles. In this bay the tide frequently rifes four feet. Upon the north the mountain is attached to Spain by a low fandy ifthmus, the greateft elevation of which, above the level of the fea, does not exceed 10 feet, and its breadth, at.the bafe of the rock, is not more than three quarters of a mile. This ifthmus feparates the Mediterranean, on the eatt, from the bay of Gibraltar on the weit. THIS mountain is much more curious in its botanical, than in its mineralogical productions. In refpect to the firft, it con- neéts, in fome degree, the Flora of Africa with that of Europe. In refpect to the latter, it produces little variety ; perhaps a few fubftances and phenomena that are ris but none that are pecu- liar. THE principal mafs of the mountain rock confifts of a grey, denfe (what is generally called primary) marble; the different beds Of -GIBRALTAR. 193 o beds of which are to be examined in a face of 1350 feet of per- -pendicular height, which it prefents to Spain in a conical form. Thefe beds, or ftrata, are of various thicknefs, from 20 to up- wards of 4o feet, dipping in a direction from eaft to weft, near- ly at an angle of 35 degrees. In fome parts of the folid mafs of this rock, I have found teftaceous bodies entirely tranf{muted into the conftituent matter of the rock, and their interior hollows filled up with calcareous fpar ; but thefe do not occur often in its compofition, and its beds are not feparated by any interme- diate ftrata. In all parts of the globe, where this fpecies of rock conftitutes large diftri€ts, it is found to be cavernous. The caves of Gi- braltar are many, and fome of them of great extent. That which moft deferves attention and examination is called St Mi- chael’s Cave, which is fituated upon the fouthern part of the mountain, almoft equally diftant from the Signal Tower and the Sugar Loaf. Its entrance is 1000 feet above the level of the fea: This entrance is formed by a rapid flope of earth, which has fallen into it at various periods, and which leads to a fpa- cious hall, incrufted with {par, and apparently fupported in the centre by a large maffy ftala@titical pillar. ‘To this fucceeds a long feries of caves of difficult accefs. The paflages from the one to the other of thefe are over precipices, which can only be paffed by the affiftance of ropes and fcaling ladders. I have, myfelf, paffed over many of thefe to the depth of 300 feet from the upper cave ; but at that depth the fmoke of our torches be- came fo difagreeable, that we were obliged to give up our pur- fuit, and leave caves ftill under us unexamined. In thefe ca- vernous receffes, the formation and procefs of ftaladtites is to be traced, from the flimfy quilt-like cone, fufpended from the roof, to the robuft trunk of a pillar, three feet in diameter, which rifes from the floor, and feems intended by nature to fupport the roof from which it originated. Vou, IV. | Aa THE 194 MINERALOGICAL DESCRIPTION -. THE variety of form, which this matter takes. in its different fituations and dire¢tions, renders this fubterraneous fcenery ftrikingly grotefque, and in fome places beautifully picturefque. The ftalactites of thefe caves, when near the furface of the mountain, are of a brownifh,yellow colour ; but, as we defcend- ed towards, the lower caves, we found them begin to lofe their — darknefs of colour, which by degrees fhaded off to a whitfh yellow. . ix tod: oon oles diiw. qu bak TuE only inhabitants of thefe caves are bats, fome of which are of a large’ fize. The foil, in general, upon the moun- tain of Gibraltar, is but thinly fown ;.and 11 many parts that thin covering has been wafhed joff by the heavy autumnal rains, which have left the fuperficies of the rock, for a confider- able’ extent). bare sand open:to! infpection,: ; In thofe: fituations, an obferving eye!may trace the effects:of the flow,-but conftant, decompofition of. the rock, caufed. by its expofure to’ the air, and: the corrofion of fea-falts, which, -in the heavy gales of eafterly windsy are depofited with the fprayoon:every part of the moun- tain! “Thofé uncovered. parts of the mountain-rockalfo expofe to the eye a phenomenon.worthy of fomé\attention;'as 1titends \clear=» ly tédemontftrate, that; howéver high thei furfaceof this orock may now be elevated’ above .the -levéliof ‘thes fea, it -has:'once: beénthe bed of! agitated »waterseycThis - phenomenon is to be: obfenved inemahy! partssof the: reckyiaiid is.conflantly fobndiny the bedssofdorrents.> [It €onfifts. of ipotelike choles;> of: ivarious: fizes, hollowed: otto of the folidirock,:and formed apparently by the attrition of grawel/or pebbles, fetansmotion: bythe rapidity of:vivers; or! currentsan: the fea. «One of ‘fhofe; which had:been- recently laid open;id sexamnnedswith attention Ll found. atritor be fivefeet-deep) and thteenfeet in diameters! the edgé dfats: mouth rounded ‘off as:if iby-art, and ats fides and-bottonmretdam=: ing a confiderable: degree! of spolifhs.! From tsofnouth, «for ithree: | and a half feet down, it was filledswitha sed! argillaceotscearth)) bg s A V1 .thiily- . ’ —--... — -eee y ‘ = - OT a Of - GaloB RA VoBARAVAM — 295 thinly mixed with minute parts.of tranfparent quartz cryfals; the remaining foot and a half, to the bottom, contained an ag+ gregate of water-worn ftones, which were from, the lize of a goofe’s egg to that of a fmall walnut, and confifted of red’ jaf pers, yellowifh white, flints,, white quartz, and, bluifh, white agates, firmly combined by a yellowifh brown. ftalactitical:cal- careous {par. In this. breccia.I could not.difcover any fragment of thesmountain rock, or any other calcareous matter, except the cement with which it was combined... This pot is g4o feet above the level of the fea. ) Upon the weft fide of the mountain, sehen its bafe, tina’ {trata. occur, which are heterogenial to the mountain rock : the firft, or highett, forms the fegment ofa circle; its convex fide is towards the mountain, and it flopes ‘alfo in that direction.” This ‘ftratum confifts, of, a. number: of thin, beds; the outward one, being, the thineft, is in.a ftate of decompofition; and is moulder- ing down into a blackifh brown or ferruginous coloured earth. The beds, inferior to this, progreflively increafe in breadth to 17 inches, where the {tratification refts upon:a rock of an argil- laceous nature. Tuis laft bed, which is 17 inches shiek oni Gin Se oe a blackifh blue colour, in the fepta or cracks: of which are found fine quartz cryftals, colourlefs, and perfectly tranfparent. Thefe cryftals are compofed. of eighteen planes, difpofed in hex- angular columns, terminated .at both extremities by hexangular pyramids... The largeft of thofé that I have feen does not ex- ceed two-eights of an inch in length: They, in general, adhere to the rock by the fides of the,column, but are detached with- out difficulty... Their, great degree of tranfparency has obtain- ed them the name of Gibraltar, diamonds. » At no. great diftance from-where théfe cryftals are found, upon | the fame flope of the mountain, but-rather nearer to the level of the fea, a ftratum of argillaceous matter has been laid ~- 2 open. 196 MINERALOGICAL DESCRIPTION open, divided into many thin beds, the broadeft of which does not exceed a foot in thicknefs. Its general colour is of a whitifh grey, with a {mall mixture of yellow, and it is divided tranfverfely by ftraight fepta or cracks, both fides of which are covered with dendritical figures, of a yellowifh brown colour, — beautifully reprefenting the objeéts of landf{cape. At the weft- ern bafe of the mountain, on a level with the fea by which it is wafhed, a very extenfive {tratum occurs, of the fame nature as the laft defcribed, bearing from north to fouth, parallel with, . and dipping towards, the mountain, nearly at an angle of 40 degrees. In fome parts of the weftern flope of the mountain, towards the fouth, are found nefts of a dark red fhivery clay, in which are embedded flints of a dirty fap green colour: Of thofe no regular ftratum is to be perceived ; many of them are un- fhapely maffes ; but they, in general, tend to the rhomboidal form, and are from three to four inches long, by two or three broad, and an inch and a half thick. They are not incrufted as the flints found in chalk, nor have they the appearance of ha- ving been worn by attrition. | . . Upon different parts of the mountain, towards its bafe, are found large quantities of fand, compofed of different materials, and affuming various appearances as to colour. The largeft bank of this arenaceous matter is upon the weftern fide of the mountain, and confifts of fmall particles of cryftallized quartz, colourlefs, and perfe¢tly tranfparent per/e, but of an ochreous colour in the mafs, on account of a red argillaceous earth which adheres to them. ‘The fand of this bank is perfectly loofe and uncombined: one half of it has been levelled into an extenfive parade, its furface having been combined by the lime and rub- bifh from the ruins of the town. The fouthern extremity of the bank is ftill to be feen in its natural ftate, and forms the bu- rying-ground of the garrifon. Uron = se ea Of 2G 2 BRA BTA R.A 3 197 Uron the eaft fide of the mountain is found another of thefe banks, of confiderable extent, and, as I mentioned before, rifing from the Mediterranean in a rapid acclivity, and reaching to one-third of its entire elevation. This bank is compofed of {mall particles of cryftallized quartz, of teftaceous bodies rounded by attrition, and of a few minute particles of the calcareous rock; the whole has a whitifh grey colour. The rain-water, which falls from the bare mountain rock above the fand, brings along with it calcareous matter, which is depofited upon the bank, and combines its furface into a cruft, which in fome places is fo much indurated as to bear the prefflure of the foot. In other parts of the mountain, where this fand is furround- - ed by the calcareous rock, and covered in and. protected from the action of the air, and corrofion of the fea-falts, it is found in a perfect indurated ftate, combined by ftalaétitical par, and forming’ a minute breccia. A quarry of this arenaceous ftone has been: opened upon the fouth-eaft quarter of the mountain, and is made ufe of, with great propriety, to line the embrafures of fome of the new works belonging to the garrifon. Its. inap-. titude to fly off in fplinters, when ftruck by a ball, gives, in fuch fituations, additional fafety to the defenders of the place. THE weftern fide of the mountain’s bafe, around Rofia Bay, and the new Mole, is a rock compofed of an aggregate of {mall. fragments of every foffil that has been here defcribed, with the _ addition of two different {pecies of marble that are probably ad- ventitious, as their native beds have not been found in the mountain. The one of thofe is black, and the other of an olive green colour. The whole of this mixture produces a. moft beau- tiful breccia, and is firmly combined by a calcareous.cement of a yellow, verging towards an orange colour. It is fufceptible of a high polifh, except where fragments of the argillaceous ftrata occur: Thefe can be eafily {moothed down, but cannot be brought to a perfect polifh.. The fragments in this breccia are | angular,. 198 MINERALOGICAL. DESCRIPTION aneular, and none of them have the appearance of — water- worn. | Ir only now remains for me to mention what are pen called the foflil bones, found in the rock of Gibraltar. Thefe have been much talked of, and by fome looked upon as.a phe- nomenon beyond the power of explanation. The general idea, which exifts concerning them, is, that they are found in a pe-> trified ftate, and inclofed in the folid calcareous rock; but thefe are miftakes, which could only arife from inaccurate obfervation and falfe defcription. In the perpendicular fiffures of the rock, and in fimnie of ih caverns of the mountain, (all of which afford evident proofs ‘of their former communication with the furface), a calcareous concretion is found, of a reddifh brown ferruginous colour, with an earthy fracture, and confiderable induration, inclofing the bones of various animals, fome of which have the appearance of being human. Thefe bones are of various fizes, and lie in all direétions, intermixed with fhells of {nails, fragments of the » calcareous rock, and particles of {par ; all of which materials are ftill to be feen in their natural uncombined ftates, partially feat tered over the furface of the mountain. Thefe having been f{wept, by heavy rains at different periods, from the furface into the fituations above defcribed, and having remained for.a long feries of years in thofe places of reft, expofed to the permeating action of water, have become enveloped in, and cemented by, the calcareous matter which it depofits. THE bones, in this compofition, have not the fnalleft appear- ance of being petrified; and if they have undergone any change, it’ is more like that of calcination than that of petrifaction, as the moft folid parts of them generally admit of teins cut and fcraped down with the fame eafe as chalk. ‘Bones combined in fuch concretions are not peculiar to Gi- braltar: They are found in fuch large quantities in the country of Of). DG MOB Ry) Le Ay 199 of Dalmatia, and upon its coafts in the iflands of Cherfo and Ofero, that fome naturalifts have been induced to go fo far as to affert, that there has been a regular ftratum of fuch matter in that country, and that its prefent broken and interrupted appearance has. been caufed by earthquakes, or other convul- fions, experienced in that part of the globe. But, of late years, a traveller, (Abbé Atzerto Forris), has given a. minute de- fcription of the concretion in which the bones are found in that country: And by his account it appears, that with regard to. fituation, compofition and colour, it 1s. perfe@tly fimilar to that found at Gibraltar.» By his defcription, it alfo appears, ;that the two mountain rocks of Gibraltar and Dalmatia confit of the fame {pecies' of calcareous {tone ; from which it: is. to be prefu- med, that the concretions in both have! been formed:in the fame manner ‘andyabout: the, fame periods. . “PerHars if the fiflures. and caves of the rock of \Dalmatia. ~ were ftill) more minutely examined, their former communica- tions with the furface might yet be traced, as in thofe defcribed aboves and; in that cafe, there would be at leaft a.ftrong proba-. bility)that the materials: of the: concretions of that country have: been ‘brought together by the fame accidental caufe, which, in. my opinion, has collected thofe: found in the caverns of Gibraltar. I have traced, in:Gibraltar, this concretion, from the loweft part of acdeep perpendicular fiflure, upto: the furface of the moun- tains)» Asritiapproached) to. the furface;» the concretion became lefs firmly combined, and,'whem it had:no covering of the calca- reous'rock, ai{mall degree !of adhefion only remained, which was. evidently produced by thecargillacedus earth, in-its compofition,, having. been:moiftenedsby rain and: baked: by the fun. ~) PuEtdepthysat: which thefe: materials had: been: penetrated. by that! proportion: of» ftalactitical matter;.capableyof ‘giving. to the concretion |its:preateft: adhefion:and:folidity, I fowndsto. vary ac-. aang tovits fituation, and to:the quantity! ofimattér to. be com-- hinedé: 200 MINERALOGICAL DESCRIPTION’ - bined. In fiffures, narrow and contracted, I found the concretion poflefling a great degree of hardnefs at fix feet from the furface; but in other fituations more extended, and where a larger quan- tity of the materials had been accumulated, I found it had not gained its greateft degree of adhefion at double that depth. In one of the caves, where the mafs of concretion is of confiderable fize, I perceived it to be divided into different beds, each bed being co- vered with a cruft of the ftaladtitical fpar, from one inch to an inch and a half in thicknefs, which feems to indicate, that the materials have been carried in at various periods, and that thofe- periods have been very remote from each other. At Rofia Bay, upon the weft fide of Gibraltar, this concre- tion is found in what has evidently been a cavern, originally formed by huge unfhapely maffes of the rock, which have tum- bled in together. The fiflure, or cavern, formed by the difrup- tion and fubfidence of thofe maffes, has been entirely filled up with the concretion, and is now expofed to full view by the outward mafs having dropped down, in confequence of the en- croachments of the fea. It is to this {pot that ftrangers are ge- nerally led to examine the phenomenon ; and the compofition, having here attained to its greateft degree of hardnefs and foli- dity, the hafty obferver, feeing the bones inclofed in what has fo little the appearance of having been a vacuity, examines no further, but immediately adopts the idea of their being incafed in the folid rock. The communication from this former chafm, to the furface from which it has received the materials of the concretion, is {till to be traced in the face of the rock, but its opening is at prefent covered by the bafe of the line wall of the garrifon. Here bones are found that are apparently human ; and thofe of them that appear to be of the legs, arms, and ver- tebre of the back, are fcattered among others of various kinds and fizes, even down to the fimalleft bones of {mall birds. I found here the complete jaw-bone of a fheep; it contained its full of GIBRALTAR. 201 full complement of teeth, the enamel of which was perfect, and ~ its whitenefs and luftre in no degree impaired. In the hollow parts of fome of the large bones was contained a minute cryt{tal- - lization of pure and colourlefs calcareous fpar; but, in moft, the interior part confifted of a fparry cruft of a reddith colour, fcarcely in any degree tranfparent. Ar the northern extremity of the mountain, the concretion is generally found in perpendicular fiffures. ‘The miners there, employed upon the fortifications, in excavating one of thofe fif- fures, found, at a great depth from the furface, two fkulls, which were fuppofed to be human; but, to me, one of them, if not both, appeared to be too {mall for the human fpecies. The bone of each was perfectly firm and folid ; from which it is to be prefumed, that they were in a ftate of maturity before they ‘were inclofed in the concretion. Had they appertained to very young children, perhaps the bone would have been more porous, and of a lefs firm texture. The probability is, that they belong- ed to a f{pecies of monkey, which ftill continues to inhabit, in confiderable numbers, thofe parts of the rock which are to us inaccefiible. THIS concretion varies, in its compofition, according to the fituation im which it is found. At the extremity of Princes Lines, high in the rock which looks towards Spain, it is found to confift only of a reddifh calcareous earth, and the bones of fmall birds cemented thereby. The rock around this {pot is in- habited by a number of hawks, that, in the breeding feafon, neftle here, and rear their young; the bones in this concretion are probably the remains of the food of thofe birds. At the bafe of the rock, below King’s Lines, the concretion confifts of pebbles of the prevailing calcareous rock. In this concretion, at a very confiderable depth under the furface, was found the un- der parts of a glafs bottle, uncommonly fhaped, and of great - thicknefs ; the colour of the glafs. was of a dark green. Vor, IV. | B.b. Ess 202 MINERALOGICAL DESCRIPTION in many parts of the rock I have found concretions, in which there are no bones of any kind; and on the elevated parts of the mountain, where the flopes are rapid, I have found a breccia, (if 1 may fo call it), entirely confifting of fnail-fhells, combined in a mafs of opaque ftalactitical {par of a yellowith brown co- lour. The various progreflive augmentations of this matter were to be traced in various fhades of the fame colour, which, like the zones of the antique alabafter, curve round, and fol- low the form of the fhell. The purer matter of this {par has penetrated the fhells, and in their interior hollows has formed a lining of {mall cryftals, generally colourlefs and perfectly tranf- parent. | 1 nave beftowed more time in endeavouring to defcribe the compofition, and the real fituation, of this concretion of bones, than the fubject, in the eftimation of many, will feem to de- ferve, and indeed more than it deferves in my own opinion; but where an erroneous opinion has obtained a footing, in confe- quence of inaccurate obfervations and partial defcription, it is the duty of every new obferver to endeavour to correct it.) X. Description of a THERMOMETER, which marks the great- ef Decree of Heat and Coup, from one Time of Os- SERVATION. to another, and may alfo regifier its own “Hetent at every Instant. © By ALEXANDER KEITH, Efg; F. R. S. & F. A. S. Evin. | [Read Auguft 3. 1795.) HERMOMETERS have hitherto been defective for meteo- rological purpofes, in fo far as they only point out the de- gree of heat at the moment of infpecting them, but do. not fhow what the difference of temperature has been, from the time of ‘one obfervation to that of another: Nor has any inftrument Been yet con{tructed, fo far as I have been able to learn, which will record the intermediate degrees of heat. : THE ingenious Ropert Hook, in the end of the laft century, mentions his intention of making a thermometer for the. above purpofe ; but it does not appear that it was ever executed: Nei- ther does he explain how it was to have been done. Tue thermometer, invented by M. James Srx, as defcribed in the 72d volume of the Philofophical Tranfactions of the Royal Society of London, is made to fhow its. greateft rife or fall from ‘one period of obfervation to another. This is done by means of two fmall pieces of black glafs, which float on two different B bez furfaces 204 DES C RAP TRON, of a furfaces of mercury, within two glafs tubes hermetically fealed. Thefe floats, when raifed to their greateft height, adhere to the fide of the tube, by means of a fpring of glafs, and become fta- tionary, although the mercury falls. After the obferver has taken a note of the temperature, he, by a magnet held in jis hand, draws down the float to the furface of the mercury, in con- fequence of a {mall bit of fteel wire inclofed in the float, and the inftrument is prepared for another obfervation. This is an in- genious invention, but requires too delicate workmanfhip to be fit for common ufe ; befides, it cannot be made~to record the degrees of heat at intermediate periods. The thermometer, lately invented by Dr RuTHERFORD of Balilifh, and defcribed in the 3d volume of the Tran/actions of this Society, is alfo an | ingenious contrivance, but has the fame defect of marking on- ly the extreme points, to which the liquor has rifen or fallen, in two feparate glafs tubes. SEVERAL years ago it occurred to me, that an air thermo- meter might be ufed for the purpofes required, providing the weight of the atmofphere could be excluded, or a counter-ba- lance formed to it; and as the whole inftrument could be made to rife and fall by the temperature of the atmofphere alone, it might ‘be adapted to a piece of clock-work, which would record the degrees of heat at every inftant through the year: And accord- ingly I read to this Society a defcription of the inftrument. But having formed another inftrument, of a more fimple con- ftru€tion, to anfwer the fame purpofe, I beg leave to give a de- ‘{cription of it. AB is a tube about 14 inches long, (Pl. VI.) and three-fourths of an inch caliber, of thin glafs, fealed or clofe at top. To the bot- tom, which is bent upwards, there is joined a glafs tube 7 inches — ‘ong, and four-tenths of an inch caliber, open at top. The tube . AB FTHERMQMET ER. 205 AB is filled with the ftrongeft fpirit of wine or alcohol, and from B to E is filled with mercury. Ir will be evident, from infpection, that if the fpirit of wine is expanded by heat, the mercury in the fmaller tube will rife, and, if the fpirit of wine is contracted by cold, the mercury will fall: And although they are both fubjected to the preflure of the atmofphere, yet, as liquids are incompreflible by weight in _ any perceptible degree, neither the fpirit of wine nor mercury will be altered in bulk by the different weight of the atmo- {phere. ED is a feale of brafs or ivory, about 6+ inches long, divided in the ufual way. E is a {mall conical piece of ivory or glafs, of a proper weight, made to float on the furface of the mercury in the {maller tube: to which float is joined a wire, reaching to H, having a knee bent at a right angle, which raifes one index, and. depreffes ano- ther index, according as the mercury rifes or falls, which wire fhall be termed the float-wire. II is,a glafs tube, 7 inches and a half long, clofed at top and open at bottom, fo wide as to flide eafily over the fcale, and, by means of a brafs rim cemented to it, is made to fit exactly to the circular bafe of the fcale, fo that, when this tube is put on, it covers the whole fcale and indexes, and defends them from wind or rain. This cover need not be taken off, except when _the inftrument is to be prepared for an obfervation. _ Tue operation of the float and indexes will be better under- - ftood from fig. 2. which reprefents them of the full fize. FG is the fcale fixed to a circular piece of wood or brafs, through which the top of the {mall tube is made to pafs. From G to K is a piece of the fmalleft harpfichord wire, or _ rather of the fmalleft gold wire, ftretched along the fcale, fixed at the ends by two brafs pins. LL 206 | DESCRIPTION of a LI. are two indexes, formed of thin black oiled filk, pierced by the {mall wire in fuch a manner as to flide upwards and downwards with a very {mall force, not more than two grains. H, the knee of the float-wire before defcribed, is made to en- compafs the fmall wire between the two indexes, fo that, when the float rifes, the upper index is moved upwards, and, when it defcends, it leaves the upper index ftationary, and pufhes down the lower index, which is alfo left ftationary, when the float rifes. WueEn the inftrument is to be prepared for an obfervation, the one index is to be pulled down, and the other raifed, by means of a bit of wire bent for the purpofe, until both indexes touch the knee of the float-wire: And, when it is again obferved, the upper index will point out the greateft degree of heat, and the lower the greateft degree of cold, fince the time they were fet. Secvhiie 1a te iE Ir this thermometer is to be adapted to a piece of clock-work, in order to record the degrees of heat at each hour and minute of time, it ought to be made of larger dimenfions. The large ‘tube may be 4o inches long, and not increafed in diameter, but the fmall tube ought to be enlarged in diameter, and notin ‘length. By enlarging the tube, which contains the fpirit of wine, in length only, it will be affeéted by heat and cold in as fhort a time as that before defcribed. Ir is unneceflary at prefent to explain the clock-work. It is fufficient to fay, that a hollow cylinder of ‘any light ‘fubftance, 7 inches long, and 5 inches diameter, is made to revolve upon a vertical axis once in thirty-one days or a month; a piece of fmooth or vellum paper is put round this cylinder, pafted only at the joining, but fo as to make it adhere clofe to the cylinder; on this paper are drawn thirty-one equal perpendicular divi- ~ fions, numbered at the top 1, 2, 3, &c. to correfpond to the thirty-one days of the month, each of which 1s fubdivided into ‘fix parts, to anfwer to four hours. The length of this-cylinder _ is. : THERMOMETER. — %09 is divided by lines furrounding it, or zones, in fuch number as correfpond to the feale of FAHRENHEIT’s thermometer, viz. from to 100 degrees. "Thefe divifions ought to be engraved on cop- _ perplate, and a great number of impreflions thrown off on fmooth or vellum paper, in one that one may be ready to put on each month. Fre. 3, ‘MN reprefents the cylinder covered with one of © thefe impreflions. PP is the fcale fixed to the frame on which the cylinder turns. ‘This fcale is divided into 100 of FAnREN- HEIT’sS degrees, exaCtly correfponding to the divifions of the cy- linder. is. a hats RG black-lead pencil, joined to the end of the flot-wire in the place of the knee before mentioned. This pen- cil is made to prefs lightly on the cylinder, by means of the fmall weight R. And as the pencil rifes or falls by heat and cold, it will mark the degrees on the fcale of the cylinder ; and the cylinder being conftantly revolving, the divifion for each day and parts of a day will fucceflively be marked by the pen- cil, which will leave a trace, defcribing an undulated line, di- - ftin@tly delineating the temperature of each day through the month. Thefe papers, when taken off and bound together, will make a complete regifter of the temperature for the year ; or, if they are pafted to one another, they will form a thermometrical chart, by which the variations of heat and cold, during the year, may all be feen and compared by one glance of the eye. By infpecting fig. 3. the effect of the inftrument may be feen. It appears that the paper had been put on the cylinder the firft day of the month, at midday, when the thermometer {ftood at 45°; that it fell gradually till midnight to 25°; thereafter it rofe till the 2d at 1 P. M. when it ftood at 42°; then it de- fcended at midnight to 35, &c.; that on the 4th, at midday, it rofe to 50; and at noon, the 1oth of the month, it ftands at noe, IF 208 - DESCRIPTION, €&e. - Ir three inches be added to the length of the cylinder, it may be made to delineate the variations of the barometer as well as the thermometer, and thereby to form a complete chart or view of the progrefs of both of them. And if inftruments of this kind were kept in different parts of the country, and their charts compared together, it would afford much information with re- gard to meteorology. XI. Phil Thin Vil 2% Put HP 208 XI. Description of a BAROMETER, which marks the RisE and Fauu of the MERcuRY from two different Times of OBsERVATION. By ALEXANDER KEITH, E/g; F.R.S. & F. A. S. Epin. | Read Fan. 5. 1796. ] N Augutft laft, I read to this Society the Defcription of an Air Thermometer, intended to record the various degrees of heat at every inftant; and mentioned my intention of conftruct- ing a barometer, which would, in the fame manner, record the variations of the weight of the atmofphere: Both which I pro- pofed to adapt to one piece of clock-work. THIs piece of machinery appearing too complicated and ex- penfive for general ufe, I contrived a thermometer, which marks the extreme points of heat and cold from any two times of ob- fervation. Of which inftrument I alfo lately read an account, and produced the machine itfelf. _ I now intend further to lay before this Society the defcrip- tion of a barometer upon fimilar principles, of a very fimple con- ftru€tion, which alfo marks the variation of the atmofphere . from one time of obfervation to another. Von, IV. C Gus Pies. BIO. ve DESCRIPTION ¢f .a Fic. 4. ABCD is a glafs tube, bent in the manner repre- fented, open at D, and hermetically fealed at A. From A to B is 8 inches long, and about ? of an inch caliber. From B to GC 31% inches long, and about § of an inch caliber. And from C to D 4+ inches long, and + inch caliber. THE tube is filled with mercury, the length from B to E be- ing 293 inches. When the tube is hung perpendicular, the - mercury will fall from B to E, leaving a vacuum in the upper half of the tube from B to A. When the atmofphere becomes. heavier, the mercury falls in the tube DC, and when lighter it _ rifes. The range of the fcale is about 3 inches, being equal to that of a common barometer of the beft conftrudtion, which has a bafon with a very broad furface. This inftrument moves in a direétion contrary. to the common barometer, the one rifing while the other falls. Fic. 5. reprefents the tube DC, with the fcale placed above it, of half the real dimenfions. F is a piece of ivory or glafs, of a co- nical fhape, of a proper weight, made to float on the furface of the mercury, having a wire fixed to it reaching toG. From H to H is a piece of fmall harpfichord-wire, or rather gold-wire, ftretched along the ivory or brafs plate on which the fcale is en- graved. IJ are two indexes formed of the thinneft black oiled filk, pierced in fuch a manner by the fmall wire as to move up- wards and downwards upon it with a very fmall force, not more than two grain weight ; and thefe indexes, being not the weight of half a grain, they do not defcend the wire by their own weight, but remain where they are placed. THE wire fixed to the float, (which we fhall call the float-wire), has a knee bent at a right angle, and made to encompafs the {mall wire between the two indexes, fo that, when the float/rifes, the upper index is carried up, and, when it falls, it leaves the upper index, and pufhes down the under index. In — ee | 4 , ‘ : ; ' BARO ME FER: ari in order to ‘prepare this barometer for an obfervation, the -one index is to be brought down, and the other raifed, until both touch ‘the knee of the float-wire. THE next time the inftrument is obferved, the upper index will point out the greateft depreflion of the mercury, or light- nefs of the atmofphere, and the lower index the greate(t rife of the mercury or weight of the atmofphere, from the time the {cale was prepared. qan | By this means the variations of the atmofphere are much more truly pointed out than by the common barometer. For it often happens, that, during tempeftuous weather, or be- fore it, the mercury both rifes and falls within the fpace of a few hours, or during the night time, which variations cannot be difcovered by any of the barometers prefently in ufe. Durinc the late very high winds, in November and Decem- ber laft 1795, I have frequently obferved the mercury to rife and fall within the {pace of two or three hours before the wind begins ; and, during tempeftuous weather, it will fall very confi- derably, and foon after rife higher than before, and ofcillate, or rather undulate, upwards and downwards, the undulations be- coming gradually lefs, until the atmofphere is more {fettled ; which fhows, that, like other fluids, when put in agitation, it undulates till it come near an equilibrium ; for it appears {fel- dom to be in a ftate of perfect tranquillity. THE fudden fall and rife, or even the rife and fall of the mer- cury, always denote an extraordinary agitation in the atmo- {phere. And therefore, to foretell tempeftuous weather, it be- comes of importance to obferve how many degrees the one in- dex is removed from the other; for example, at night, I take note of the common barometer as ftanding at 29% inches, and when I examine it in the morning find it at the fame height ; from which I naturally conclude, that, as there has been no agitation of the mercury, there will be calm or fettled wea- GCe2 ther. 212 D BS'C REPT LO Ny of st. ther. But, if I ufe the barometer before defcribed, and examine it in the morning, I find the common barometer has deceived me ; for although the furface of the mercury ftands at 29; in- ches, yet I obferve, that one of the indexes has been raifed +, and the other lowered 345 during the night. Hence, inftead of denoting calm weather, it fhows that, the mercury having been agitated, tempeftuous weather is to be expected. THE regifter of the weather, kept from an inftrument of this kind, will be much more fatisfactory. than thofe hitherto ufed, and regifters kept at different places can be more accurately com- pared with one another. THE levity of the atmofphere, at great heights, might alfo be difcovered, by fufpending this inftrument to an air-balloon. XIL. aa meaner ET =~ XII. Mereorotocicar Asstract for the YEARS 1794, 1795; and 1796. Communicated by FoHN PLArrAIR, F. R. S. Eprn. and Profeffor of Mathematics in the Univerfity of Edinburgh. . [ Read at the Meetings in Feb. 1795, 1796, & 1797. | HE Journal of the Weather, of which an abftradt is: here communicated, has been kept in a houfe in Windmill Street, on the fouth fide of Edinburgh. The latitude of Edinburgh College, as deduced from a feries of aftronomical obfervations made at Hawkhill, is 55°. 57’. 5” nearly. Wind- mill Street 1s about 500 yards farther to the fouth. Tue barometer ufed in thefe obfervations is a portable one, of the conf{trution invented by Dr Linn, phyfician at Windfor ; the mercury was boiled in the tube, and the fcale is divided in-- to the five-hundredth parts of an inch. The place where it ftands is 265 feet above the level of the fea, or of the mean high-water mark at Leith. The height of it is marked every morning at ro o'clock, as well as that of a thermometer, in the. fame room, which gives the temperature of the mercury. THE thermometer, which gives the temperature of the air, is. placed on the outfide of a window that looks towards the N. W.. | about 214 METEOROLOG ICAL ABSTRACT. about 18 feet above the furface of the ground; and though, in a town, it is impoflible to prevent local caufes from affecting the thermometer, yet the current of air is generally fo confiderable as to prevent thefe irregularities from rifing to. any great a- mount. ; THE regifter contains the ftate of the thermometer for three different hours of the day, viz. 8 A. M. to P. M and alfo about 2 o'clock, when the thermometer is higheft. The hour of this laft obfervation is not however fixed ; it is fuch as to give near- ly the greateft heat of the day, and varies from 1 to half paft 2, or even 3 o'clock. The abftract contains the greateft and leaft heights of the thermometer, that have been obferved at any of thefe hours in the courfe of each month: It contains alfo the mean of the morning, mid-day, and evening obfervations ; and likewife the mean of all thefe means, as being nearly the me- dium temperature of the whole month. THE rain is put down for 1794 and 1795 from a rain-gage kept in Edinburgh, and for 1796 from one kept in the Botanic Garden with great accuracy, under Dr RUTHERFORD’Ss particu- lar infpection. The Botanic Garden is half-a-mile north of Edinburgh, and about roo feet above the level of the fea. In the remarks, reference is fometimes made to the Meteoro- logical Journal kept fome years ago at Hawkhill, near Edin- burgh, of which an account is given in the Phi/ofophical Tranj- actions of London 1775, p. 462. METEO- \ — Ss METEOROLOGICAL ABSTRACT. 215 METEOROLOGICAL TABLE ror 1794. : ee = é x L = oe 4 as 4 ob See le ily sa ee Se eS be ee E S= [68 | ge] 8 S28.) S28 |e. | 52] 3 = mo [5S fees | £ | ao |e] ze | so | 2 oe | eS ecto Se wae pre | Heese rain) cg Sat Se rom a8 5 iS Bidve Beh sel Shae Lo) January, 29.661 | 49.30 | 51-5 | 21-0 | 39.32| 41.43 | 41 20} 40.65 | 1-40 |February, | 29.397] 59-0 | 54-25135-5 | 43-5 | 46.00 | 44.30}-44.10 | 2-145 March, 29.631 | 51.00 153-0 | 38-5 | 44-43 | 48.09] 45.93] 46.15 | 0-995 April, 29-595 | 55-25 | 64-5 | 39-25] 49-50] 52.98 | 48.30] 50.26 | 2.150] May, - 29-752 | 56.32 |62.0 | 42.0 | 50.22] 56.16] 47.22 | 51.20] 1.910 June, 29.884 | 64.50 | 73-0 | 48.5 | 60.4 | 62.30! 57.40 | 60.70 | 1.07 July, 29.768 | 66.70} 75.0 | 52.0 |61.7 | 66.42} 58.61 | 62.24 | 2.12 Augutt, 29.720 | 64.32 | 72.0 | 49.0 | 59.98 | 63.03 | 55.40] 59.47 | 1-84 September, | 29.662 | 58-71 | 64.0 | 41.0 |-54.99] 57.45 | 52.06 | 54.08 | 3.14 O&tober, | 29.516] 54.85 | 62.0 | 36.5 | 50.26] 52.43 | 47.29 | 49.66 | 3.53 November, | 29.416 | 48.90 / 53-5 132-5 | 43-581 45-54 | 43.47] 44-19] 4.51 December, | 29.691 | 48.58:| 50.5 | 26.25 | 41-33] 42.50] 40.10 | 41.31 | 3-92 “Means, 29.641 | 55.72 ; 49-79 | 52.84 | 48.34 | 50.32 Total Rain, 28.73 1d OS CRIS) a ie < Aerag R Tue weather in January and February 1794-was very mild and open. The prevailing winds were from S. W. and S. 5. W.; ufually 2 brifk fteady gale, but fometimes more violent, particularly in. February. The thermometer was as high as 50% ih January, and 54 in February ; and once in January: fo low as 21, only for a fhort time, however, during a N. W. wind; the froft lafted fome days. Very little fnow fell. The temperature of thefé months was 6° or 7° above the mean. of the Hawkhill obfervations. There was a great deal of clear weather, and, though ‘the atmofphere was moift, there fell but little rain. : Marcu and April continued to maintain a fuperiority of 3 or-4 degrees in tem- perature above the fame months in ordinary feafons. March was very dry, and the wind frequently in the eaft. In the end of April, the weather was fqually, with the wind varying from 8. W. to S.E. Is ai6 METEOROLOGICAL ABSTRACT. In May the heat fell down nearly to the common average of that month, viz. — 505, fo that it feemed cold, compared with the reft of the feafon, The wind was often in the eaft, and the nights cold. ‘ June and July were very favourable: warmer than the mean by 1 or 2 de- grees. In June, the temperature was remarkably uniform; and the wind was moftly in the weft. The weather in July was alfo fine; the wind moderate, and generally weft. Tue Harveft began with Auguft; the iiiince tolerable, though more rainy than ufual, and colder. The tem perature of this month is almoft 2° below the mean. THE wind was generally weft; but a furface wind was to be obferved at the fame time blowing from the eaft. This is often obferved with us in the fineft weather : it feldom fails to happen at the time of the great changes of the wind from the eaft to the weft. SEPTEMBER was rainy; its temperature rather below the mean, with braid winds about the middle and end of the month. OcToBER rainy ; the wind variable, though moftly 5. W.; the barometer low ; and the mean temperature 49°. 66, a very little under the mean. NoveEmMBER was warm for the feafon, though rainy, with the wind variable, and often very high from 5. W. ; DEcEMBER was alfo warmer than ufual, by nearly two degrees: The wind was eafterly till near the end of the month, when it changed to the N. E: A good deal of {now fell on the 25th ; and, on the laft day of the year, the thermometer, in the evening, was at 26: The weather clear, with little wind. On the whole, the mean temperature of this year exceeded that of ordinary fea- fons by almoft 2°. This excefs of heat is very confiderable ; but, as it fell chiefly in the winter months, it was not attended with any particular advantage. The rain that fell was 28.73 inches. METEO- METEOROLOGICAL ABSTRACT. 217 METEOROLOGICAL TABLE ror 1795. saa a a al e [2 12 18 ee os <= os oO Ct hes S ol a » bee a] = Nears fe es ate Hee Pe Mie ai gnc thee es ghd nb = aL a ge ae a se be 2 8 2 phe a | @ & |Ho| Bo | By Eee sm |e |e |Se] & (21s Go fee | Re le siesie<| ga lrsiaseise] 2 is |s Oa | Ae | Sos efoelis|se jse|se|se) 0 la ja Inches, | Inches. t 5 5 Aline +; 3 > |\Lnches. Jan.. -|30.306 28.88 5]29.89 114 2.01146.0]16, 513 1.11|32-80|32-20131.7C] 2.732) 14) 17 Feb. |30.450|28.636|29.484141.8}]40.6|27,0]30.14]30.89|28.46|29.83] 3.875) 16] 12 March, 30-125|28.992|29-5 73146-5115 1-5126.0139.92)42.96]37-80|40.23]] 1-372] 23) 8 April, {30.1 46|28.948]29.503]5 2.0115 6.513.014 7.09/49. 5 2|44-73147-11]] 2-11¢] 16) 14 May, |30.320/29.275|29.91 315 5-116 5-5|39.5|50.98]5 3-83/47-03| 50-34]| 1-200] 18] 13 June, |30.272|29.128]29-74 3157-5116 7-0142.5154.40]57-17|50-54|54-COl| 3-920] xcl 20 July, |30.238/29.286]29.806|60.2)172.0]5.0.0|60.42162.85/54-97/59+41]| 2-520| 15] 16 Aug. |30 48 29.210|29.674|64.21173.5}52.0161.11]64.21/59-59|51.3C]] 3-620] 24] 7 Sept. |30.282]29.31.4]29.8 5 3162.01173.c/5 3.2159.89153-4815 7-63]60.00] 1.120] 21] 9 O&. |29.94.4]28.340]29.28015 7.516 3.5144.5/5 3-615 5.5 5152-48]5 3-56] 4.87] 231 8 Nov. |30.49028.4 7 5|29.570147-51l5 1-5|25+2140.60]41-61/39.27/40.49| 4.58cl 26] 4 Dec. {30.220129.080)29.56015.0.5115.5-7136-014 5-43146-23142-961 44.87] 3.81c] 25] 6 Means, ; 47-9C150.04]45.44/47-7 ea Totals, | | : §-72.9|23 034 | THE mean temperature of the whole year is 47.75. BR i Ae Re. Tue winter of 1795 was remarkable for the feverity and: continuance of the cold. The year began with a fharp froft, which had fet in on the 26th of the pre- ceding month, but which lafted only till the 3d of January, when the wind came round to the S. W. and was followed by a thaw. On the roth the froft returned, the wind varying’ from N.. W. to N. E. with heavy falls of fhow between the rsth and 20th. On the 2oth the cold became very fevere; and on the 22d the thermometer, about 8 in the evening, ftood at 144°, the loweft that I obferved it du- ring the whole feafon. - This intenfity of the cold lafted, however, but a fhort time, for by 10-0’clock the thermometer had rifen to 162°. On the fame night, in the Bo- Vou. IV. ; Dd tanical i f 218 METEOROLOGICAL ABSTRACT. tanical Garden, which lies clio Edinburgh and the F rith, and is about 1 150 feet lower than the place where I obferved, a thermometer, siliich marks its loweft point, according to the conftruétion deferibed in the 3d volume of thefe Tran/aéions, fell as low as 5°. The cold at Glafgow, on this night, was ftill more intenfe. Mr -Profeffor Wilfon, who watched the motions of the thermometer, with his ufual dili- — gence and accuracy, found it ftand at wero, from 11 at night till 3 in the morning, when it began to rife, and about break of day was at 10°. Tue night preceding this was alfo obferved, in fome places, to be remarkably — cold. At White Hall, in Berwickthire, 7 miles W. N. W. of Berwick upon Tweed, and about 38 E. S. E of Edinburgh, Mr Hatt obferved the thermometer, in the open air, about ro that evening, at 6° below zero. This was the greateft cold that I have heard of being obferved in Scotland ; and is, at the fame time, an exam- ple of the locality of thefe great colds. The weather at this time was clear ; the wind very gentle, between N, N. W. and N.N. E.; a great deal of fnow had fallen from the xrs5th to the goth, and lay at this time more than a yard thick on the ground, From about the 22d the intenfity of the cold relaxed gradually for Gena days; the thermometer was a degree above freezing on the 24th. From that time the cold increafed ; on the 29th the thermometer was at 16° in the evening ; in the Botanic - Garden at 4°; and at Glafgow, on the afternoon of the 30th, it was between 4° and 4 g 3 4 zero for feveral hours together. This was again followed by a relaxation of the cold, though not fo confiderable as before. On the §th and 6th of February it was again very cold, the thermometer here was at 19°, at Glafgow it defcended to zero. AYTER another remiffion the cold became very fevere on the 13th, both here and at Glafgow. This was fucceeded by a fimilar change, only the remiffion was longer and more confiderable, fo that a good deal of fnow was melted on the 24th and 26th; but on the 27th and 28th the cold once more became fevere, the ther- mometer ftanding at 19 and 20 degrees. It continued much in this fate till the 3d of March, when the wind came about to the S. W.; the thermometer rofe in the evening to 403°; and a very moderate thaw fucceeded, which carried off the fnow, without any of thofe great inundations which did fo much mifchief in the fouthern part of the Ifland. Tue whole duration of the froft was 52 or 53 days; and the medium tempera- ture, during that time, 29°.6. The alternate intenfions and remiffions of the cold, all the while were very remarkable; our climate feemed to lofe nothing of its ufual in- conftuncy, and its viciflitudes were only lower down in the fcale cf heat. By this means, however, many of the bad confequences ef a long and fevere winter were prevented. The infides of houfes were never fo much cooled, that {pirits or beer, or even water, was frozen in them. The room where my barometer is kept, though without fire, was never colder than 37°, and this only for a few days in the end of January. From the fame caufe, the mills in the country were rarely {topped ; and, except from the blocking up of the roads by the fnow, almoft no inconvenience was experienced. The METEOROLOGICAL ABSTRACT. °° 219 The roads were rendered impaffable, both from the depth of the fnow, and the degree of thaw which now and then took. place, by which they became flippery, and uneven inthe extreme. The whole {now that fell, reduced to water, mea- fured 6.607 inches, which, had it fallen at once, would have covered the ground to the depth of about 7 feet. Tue feverity of this winter extended over all Europe; and, on the Continent, the freezing over of the Rhine and the Meufe was accompanied with circumflances that will be long remembered. _~ - THE barometer was above 30.3 at the beginning of the froft, and continued high till the end of January, notwithftanding the heavy falls of fnow, which came almoft all from eaft and N. E. On the 31ft of January it fell greatly, with fnow; and, during the firft 12 days of February, it was generally below 29 inches. It ftood at 30.4 on the 17th, from which it fell gradually till the thaw, when it was un- der 29.5. No-conneétion could be traced between the ofcillations of the barome- ter, and the intenfions and remiffions of the cold. From the breaking up of the froft on the 3d, till about the 20th of March, the {now did not difappear entirely, even in the plains; it ufually froze a little in the night, and the medium temperature was under 38°. On the difappearance of the {now, the thermometer rofe fuddenly about 10°, which muft be afctibed to the cea- fing, at that time, of the abforption of the latent heat, that had taken place during the - melting of the fnow. Tue {pring which fucceeded was tolerable; and the temperature of the latter part of March, the whole of April, and the beginning of May, rather above the mean. About the roth of May the wind, which had for fome time been in the 5. W. came to the eaft and N. E.; the weather, of courfe, was cold, and continued fo, with the wind generally N. E. all the month of June, and till the 24th of July. June and July were alfo very rainy months, The wefterly winds prevailed in Au- guit, and the weather was good, though a confiderable quantity of rain fell. Sep- tember was uncommonly favourable; and the crop, which was extremely late, owed much of its maturity to this month. It proved, however, very fcanty, and was got in but indifferently, O&ober being a very rainy month. NoveEMBER was cold, and very wet: On the 18th the rain was remarkably heavy, and was followed by the greateft floods that had been known for feveral years. In December the weather became much milder, and fomewhat lefs rainy ; but, on the whole, the rain of this year very much exceeded the average, and amount- ed to 35.729 inches. N.B. In the two laft columns of the table for this year, it is marked whether the wind blew from the weftern or eaftern femicircle. The fouth wind is fuppofed to belong to the firft of thefe; the north wind to the fecond. METEO- 220 METEOROLOGICAL ABSTRACT. -METEOROLOGICAL TABLE ror 1706. . | Inches. ° Jan. |29.792128.175]29.19 4150.0 Feb, |30.380}28.682|29.5 56/49.0 March,|30.408]2g.375|28.886148. 5 April, |30.208}29.040|29-373|56.0 | May, |29-995|28.53¢}29-585156.75} June, |30.100}29.315]29-662159.0 {173.0 147.0 July, }30.021129.054]29-445]61.2 5166.5 147-0 |55- a? Aug. 130.240]29.316|29-828164.7 51:74.2'5]50.0 |58.86/68. Sept. |30.166]29.362|29.739|61.62|'70.5 [45-5 O&. — }30.492129.114]29.339154.0 |62.0 134.0 Nov. [30.322}29.026/29.638|47.75 48.5 26.0 Dec. | 30.262]28.978)29.66c140.35] 51.5 |29.0 Loal 3 fe} oF ao n eo” yu s Ss eo v e vo 2 2 Bee AB Heke Scie Atal eal ake afeh aa hes ° Ss aed - o = . te i= Ge oD o res he Gis SS = © 93 Saflee[e. | S2] og ue ee J) x - a a i o @. 12. |S. | sees ebladlaeleois Pa ft ices 88 os | Bowe] es jco ]s Ca Pere Ps ~ G2 pre) BE lei geiae |e pes tme ioe | aa fs 2& £ «af ao 2s g loud a: ee «U sy = Eas) eo a o an Sy el So oe tao £ is fs | oe | 3 (So) 2) 82 |24188 22 [82 ] sz le: om fa] aa |S oe Se Se ZR IESE =e | % A ———=ee | 1 o i) roy i) 43-94/47-1214 5.9414 5-66 34-0 |39-85143-77|40.79/41-47 38.3 5143-88]38.67140.30 Means, 48.1 | Totals, 47-38|51-71147.10 THE mean temperature of the whole year is 48°. 1. | RAE! “MM eCA Ree KierS! TuHE winter of this year was remarkable for its mildnefs, and, compared with that of the former year, may give an idea of the two extremes between which the win- ters of this part of the Ifland will generally be confined. About the middle of January, the thermometer ftood for 10 days conftantly above 50°, day and night; and the mean temperature of the month, viz. 45°. 6, is at leaft 11° above the medium, and nearly the fame with that of the ordinary January of Marfeilles. This extraordi-. nary . , METEOROLOGICAL ABSTRACT. 4x mary depree of warmth was maintained by a high wind, that blew conftantly from S. W. and S. S. W. bringing with it the air and temperature of the foutbern parts of the Atlantic. This wind prevailed over fuch en extent of the ocean, and blew with fuch violence, that it forced back a fleet of Britifh men of war, afier it had endeavoured, in vain, for fix weeks, to make its paflage to the Welt Indies. Ir muit be remembered, that the great cold of the preceding winter was with. a wind N.N. E. and fometimes N. N. W which blew very moderately. | Own the 23d of January there was a hurricane from S. 5. W. that blew down. trees and unroofed houfes: The barometer fell very low, and did not rife to its ordinary height for more than ten days. In March the weather was cold, 5° below the middle temperature of February ; eaft winds prevailed, and the premature appearances of vegetation, produced by the mildnefs of the preceding feafon, fuffered. a fevere check. April was more fa- vourable ; but in May the weather again became cold, with eaft winds, remarkably dry and parching. The grafs every where fuffered extremely from this month. ~ On the 30th there was a hurricane at London, and at Portfmouth on the 3rft. On both thefe days the barometer here was very low, 28.53, though the wind was no more than-a brifk gale at S. W. In June the mean temperature was not fo high by 2° as in ordinary fea- fons. The wind, though welt, was ufually from the northern points of the femi- circle. Jury was worfe than June, and its mean temperature 3° under that of a tole-. rable feafon. Great apprehenfions were entertained for the crops, which, without the fine weather that fucceeded in Auguft, muft have been ruined. The heat of this _ month, which was at a medium about 614°, was not fo remarkable for being great.as for being uniform ; the thermometer, for a great part of the month, was not below 63°, even in the night. There was.a great deal of funfhine, and the wind almoft con--. ftlantly W.S. W. He Tue firft half of September was little inferior to Auguft. On the 21ft, the wind, from the 5. W. came round to the N. E.; aconfiderable fall of rain follow- ed, and the weather became colder, and continued to be fo in O&ober: the medium temperature of which was 3 degrees lower than the average. A smaxT froft fet in on the 29th of November, and next morning the thermo- meter ftood at 26°. This froft continued till the 1eth of December, with an intenfity very unufual fo early in the winter. On the evening of the 5th the ther- mometer was at 21°. Between the roth and 13th the froft had almoft difappeared; but it returned on the 14th with confiderable feverity, and continued till the 28th, when it broke up entirely. The thermometer was at 19° on the 26th, and in many places lower. The fame froft was felt in England, where there were local colds of much greater intenfity, the thermometer, in fome places, having been as low, it was faid, as —10. A tract of very mild and open weather began on the 31{ft of December. Vou. IV. Ee. THE » 222 METEOROLOGICAL ABSTRACT. ~ ; THE mean temperature of the whole year is 48°,1, about + of a degree greater than the common average. E Tue greateft fingularity in this year is its drynefs. The whole rain amounted to no more than 19.395 inches, not much above the half of what fell in 1795. This quantity of rain was, however, perfeétly fufficient for the purpofes of Vegetation, as the crop of corn was very plentiful. END OF PAPERS OF THE PHYSICAL CLASS II. PAPERS OF THE LITERARY CLASS. 4. On the On1tcin and PRinciPLeEs of GoTHIc ARCHITECTURE. By Sir FAMES HALL, Bart. ¥. R. & A. SS. Evin. [Read April 6. 1797.} IN TROD UC T T.G.N. ONG after the arts of ancient Greece and Rome had been 4 loft, and before any effeCtual attempt was made to revive them, a ftyle of building, known among us by the name of Gothic Architefture, began to appear in. Europe. Av firft, a few only of its peculiar forms were employed, which, in fome old buildings, are to be met with, intermixed with the remains of a ftill more ancient ftyle. Afterwards, ri- fing by degrees into favour, it fupplanted, in all the depart- ments of architecture, every other fpecies of defign, and main- tained an unrivalled dominion during three hundred years. a 2 in 4 On GOTHIG ARCHITECTURE. In the early part of the fixteenth century it underwent a fud- den reverfe of fortune; not, however, (I am inclined to think), from any difcovery of its defects, or any inquiry into its me-. rits, but entirely from the general temper of the times. A paf- fionate admiration of the works of antiquity, which had then recently attracted the attention of the moderns, produced a con- tempt for whatever was not profefledly formed upon the models of Greece and Rome. At the fame time, an indifcriminate ha- tred again{t every production of the middle ages, f{trongly felt by men juft emerging from the gloom of that period, led them to overlook the merit of this very brilliant exception to its gene- ral barbarifm. _ But the excefs of thefe impreflions has of late very much abated ; authors of the greateft eminence have teftified a refpe& for Gothic architecture, by advancing various fyftems to ac- count for its forms ; and, whilft they acknowledge the fuperior excellence of the works of the ancient Greeks, they allow that, in airy lightnefs, and in bold grandeur of effect, thofe of the Gothic {tyle have not been furpafled, if ever equalled, by the moft ce- lebrated of our modern produétions. The period, too, in which | it prevailed, being at a diftance from our times, and that di- ftance being magnified in our imagination by the obfcurity of its hiftory, we are inclined to rank its monuments with the works of remote antiquity, which feldom fail to excite even a greater intereft than thofe poffefling the charm of novelty. In concurrence with thefe favourable fentiments, my object, in the following Effay, is to reftore to Gothic architecture its due fhare of public efteem, chiefly by fhewing, that all its forms may be traced to the imitation of one very fimple original ; and, confequently, that they are connected together by a regular fyf tem: thus proving, that its authors have been guided by prin- ciple, and not, as many have alleged, by mere fancy and ca- price. HAVING On GOTHIC ARCHITECTURE. —— ¢ .,Havine endeavoured to inveftigate the theory of Gothic ar- -chite@ture, I fhall prefent a view of what I have been able to colle& concerning its hiftory; and, without pretending to dif- pel the very deep obfcurity which {till furrounds this curious fubject, I fhall venture to fuggeft fome hints, which may be of fervice in guiding the refearches of antiquaries. By this hifto- rical view, I hope, likewife, to refute an opinion, which has contributed greatly to difcredit the Gothic ftyle, namely, that it prevailed only in barbarous times ; fince I fhall fhow, that, al- though it made its firft appearance in a period of that defcrip- tion, it continued to flourifh, while the arts of defign were ad- vancing in excellence, and ftill maintained its pre-eminence, when they had attained to the higheft degree of modern {plen- dour. Last ty, by inftituting, between the Gothic and other ftyles, a comparifon, founded upon the general and fundamental prin-= ciples of architecture, I {hall endeavour fairly to appreciate its merits, and to fhow the high eftimation to which it is entitled, in point both of beauty and of utility *. BEFORE * Turs plan is now nearly completed, the whole Effay being written out, and ac- ‘companied with a fet of drawings fufficient to render it intelligible, but by no means in a ftate for publication. To bring them to fuch a ftate muft be a work of much fabour and time, efpecially fince the nature of the fubjeét has hitherto compelled me , to execute all of them with my own hands. I HAVE judged it advifeable, therefore, to lay before the Society a part of the Ef- fay, which requires but few drawings, while it announces the fundamental and ef- fential views of the theory ; referving the full illuftration of it to another occafion, when I hope to produce the whole in a feparate work. In the mean time, it may not be improper to obferve, further, with refpect tomy general plan, that the firft part, comprehending the theory of Gothic architecture, has been arranged under three fubdivifions; the firft of thefe contains a view of its elements, all its forms being reduced to their fimpleft ftate ; the fecond treats of the deviations from thofe elements, which, in the courfe of pradlice, have been occafioned by various circumftances ; and, the laft, combining the other two, contains an exa- mination - 6. On GOTHIC ARCHITECTURE. BEFORE we enter upon this inquiry, which is chiefly direéted towards the inveftigation of a principle of Imitation, it will be proper to premife a few obfervations, on the mode in which the forms of nature have been introduced into: works of art; a fubjeét which hitherto feems not to have met with the atten- tion it deferves. ALTHOUGH the connexion between beauty and. utility be ftll involved in fuch obfcurity, that we are unable to decide con- cerning the univerfality of that connexion, of one thing we are certain, that, in a work mtended to anfwer fome ufeful purpofe, whatever vifibly counteracts that purpofe always occafions de- formity. Hence it is, that, even where ornament is principally intended, the oftenfibly ufeful object of the work, if it have — any fuch, muft be provided for, im the firft posed in preference to every other confideration. But, in moft ufeful works, fome parts. occur, the fhape of which is quite indifferent with refpect to the propofed utility, and which, therefore, the artift is at liberty to execute as he plea-. fess .a liberty, which has opened a wide field to the tafte and invention of ingenious men of every age and country, who: have turned their attention to the compofition of ornaments ; and whofe exertions have been more or lefs influenced by the ftate of civilization in which they lived. It would feem, however, if we may judge by thofe various efforts, that little has been effect- ed by mere human ingenuity ; fince we fee, that recourfe has. been had, almoft univerfally, to Nature, the great and legitimate: fource of beauty; and that ornament has been attained, by the iniitation. mination of the monuments of the art now in exiftence, and an application of our principles to every part of them. Tue prefent publication confitts of the introduétion to the whole Effay, together: with the elementary part, illuftrated by fix plates. On GOTHIC ARCHITECTURE. ; imitation of objects, to which fhe has ret a determinate and characteriftic’ form. Tuus, among the Pt oe in the period of their higheft re- finement, we find the handles of vafes in the fhape of vine branches, or of ferpents twifted round each other. Some urns of ancient Egyptian workmanfhip: terminate in the head of an owl. The heads of our fhips are decorated with figures of men and of animals; and the hatchets and canoes of Nootka Sound are covered with rude 1 images of various natural objects. . THE bbhitiatty however, in fuch cafes, differs from that in a ftatue or in a picture. In the one, the fole object is to reprefent ~ fome natural object ;: whereas, in the other, the forms of -nature have been partially adopted, and modified in various ways, in order to fuit the ufeful deftination of the work. In this man- ner, artifts of every age have been led to felect, among the forms of a natural object, fuch as anfwered their purpofe, to the exclufion of the reft; and have exhibited modified imitations of nature, which, being juftified by the circumftances of the cafe, do not fuggeft the idea of mutilation. Thus we meet with the foot of a table executed like that of a lion, or the hilt of a fword like the head of an eagle, without afking what has become of the body of the animal, and without being ftruck with any impropriety in the omiffion. FREQUENTLY, where the materials employed are themfelves pofleffed of variety and elegance, the object of ornament has been fufficiently attained, by allowing the natural: forms, in whole or in part, to remain in the finifhed work. For inftance, cups are made of fhells, of cocoa nuts, or of oftrich eggs, the character and beauty of which depend upon the natural form of the materials. And in the cafe of the bottles, ufed by the Roman Catholic pilgrims, an example occurs of an utenfil, in which the 8 On. GOTHIC ARCHITECTURE: the natural form has undergone little or no variation, fince it confifts of the hard outward {kin of a gourd, of the fame fhape in which it grew upon the plant*. Turs laft clafs of forms has been introduced, by Imitation, into works compofed of fhapelefs materials. Thus we have fil- ver cups in the form of thofe made of fhells, and fruit-difhes. of {toneware in the form of bafkets. The ancient Peruvian va- fes of pottery are executed in exact imitation of gourds; a prac- tice which had probably fucceeded the ufe of gourds as bottles. In fuch cafes, the defect of real character in the object is fup- plied by a fi€titious one, which, in the hands of a man of genius, is often productive of the moft happy effects ; fince it enables him to confer upon his. work the merit of confiftency, and truth of charaéter; qualities, which influence the mind of the fpec- tator as powerfully, when founded on fiction as on: reality. For we judge of fuch a work, as we do of a romance, in which, we are {carcely lefs interefted than if we believed it to be: true. | lize WE may now confider the application of thefe principles to every kind of ornamental archite@ture.. As ftone is not natu- rally poffeffed. of any peculiar fhape, and as the ufeful obje& : propofed, by ftructures formed: of it, may be accomplifhed in — various ways, very great latitude is left to the invention ‘of the artift. We fee, accordingly; that, in every country where much, refinement has. been. introduced, great pains have been beftowed, in ornamenting ftone buildings, with. figures repre- fenting various natural objects. It, would feem, that the la- uitude has even been too great; for experience fhews, that’ the ) ) artift * Even. in this cafe, however, the. natural form undergoes a-certain degree of modification, by the device employed to produce the neck of the bottle. The. fruit, while {mall- and tender, is furrounded with a ftring, which-remaining during. — its growth, prevents the part, thus bound, from {welling with the reft. , On GOTHIC ARCHITECTURE. 9 artift has fucceeded beft, where his imagination has been cir- cum{cribed, and forced into a regular channel. For this purpofe, recourfe has frequently been had to the de- vice laft mentioned ; the building being executed in imitation of a f{tructure, compofed of materials, which naturally poflefs a determinate and characteriftic form. Such was the method fol- lowed by the architects of ancient Greece, who conftructed tem- ples, and other public edifices, in imitation of a ruftic fabric, compofed of {quare beams, fupported upon round pofts or ftems of trees; and who derived the numerous ornaments of that beautiful ftyle, from circumftances which would naturally take place in fuch a ftructure *. Vou. IV. b A * Tuart they really did imitate a building of wood, is ftated, in the cleareft man- ner, in the work of Vitruvius, particularly in-his chapter, ‘‘ De Ornamentis Co- lumnarum.” He there fpeaks of archite@tural work in ftone or marble, as a re- prefentation, (zmago ), and of the timber fabric asa reality, (7 verztate ), as will appear by the following quotation. _ Traque, in Grecis operibus, nemo fub mutulo denticulos conftituit, non enim poflunt fubtus cantherios afferes efle. Quod ergo fupra cantherios et templa in ve- ritate debét efle collocatum, id in zmaginibus, fi infra con{titutum fuerit, mendofam habebit operis rationem. Etiamque antiqui non probaverunt neque inftituerunt in faftigiis mutulos, ‘aut denticulos fieri, fed puras coronas; ideo quod nec cantherti nee afferes contra faftigiorum frontes diftribuuntur, nec poffunt prominere, fed ad ftillicidia proclinati collocantur.. ‘¢ Ira quod non poteft in veritate fieri, id non putaverunt in imaginibus factum, poffe certam rationem habere. Omnia, enim, certa proprietate, et a veris nature deduis moribus, traduxerunt in operum perfectiones. Et ea probaverunt, quorum explicationes, in difputationibus, rationem poffunt habere veritatis.” In one refpeét, this paflage is extremely obfcure, but, in another view, it is fuffi- ciently clear to anfwer the prefent purpofe. The obfcurity arifes from the difficul- ty, or rather impoffibility, of difcovering the meaning of feveral of the technical terms employed, thefe being very rarely ufed by authors, and relating to a mode of building different from any now prattifed. But, whilft commentators differ as to the precife meaning of the words cantherius, affer, and templum, as ufed in this paflage,, they all agree in confidering them as denoting parts of the timber frame of a roof. At the fame time, mutu/us and denticulus are well known terms of architeture, and appropriated ’ \ « ~ 10 On GOTHIG ARCHITECTURE. A FAINT and diftant refemblance, however, of the original, has generally been found to anfwer all the end propofed by the imitation ; a refemblance, which may fometimes be traced in the general diftribution of the edifice, fometimes in its minute parts, and not unfrequently in both. But the forms of nature, thus introduced, have been greatly modified by thofe of mafonry. For though ftone is by nature fhapelefs, yet, in the courfe of pratice, many peculiar forms have been long eftablifhed, and currently employed, in working it; fuch as ftraight lines, plain furfaces, {quare angles, and va- rious mouldings ufed to foften the effeé& of abrupt termina- tions; all of which, originating in motives of mechanical con- venience, and of fimple ornament, had, in very early times, been appropriated to mafonry, and confidered as effential in every finifhed work of {tone ; fo that, when the imitation of na- ture was introduced, thefe mafonic forms ftill maintained their ground, and, being blended with the forms of nature, the two clafles reciprocally modified each other. Tu1s combination of art with nature, of which we fee the moft perfe€t example in the Corinthian capital, produces what are appropriated to buildings of ftone. The latter part, which relates to the principle of imitation in general, is fufficiently clear. The paflage, in Englith, is nearly as fol- lows : “ Tuus, inthe works of the Greeks, denticles were never placed under a modil- lion, becaufe it is impoffible that the afleres can be under the cantherii. If, then, what is fituated over the cantherii and templa 7” reality, be exhibited as under them in the cmztation, the principle on which the work proceeds is belied. * In the fame manner, the ancients never approved of, or direéted, the introduc- tion of modillions or denticles in the frontifpiece, but preferred a plain cornice; for this reafon, that neither the cantherii nor afferes lie towards the gable, nor can they proje&t beyond it, but are placed with an inclination to the guttur. “ Tuus, they efteemed it a departure from principle to exhibit, in dn imitation, what could not occur in reality. For in finifhing their works, they introduced every ornament in an appropriated manner, and according to a real analogy borrowed from nature ; and they approved of nothing, which could not be theoretically ac- counted for, on the principle of its refemblance to truth.” —— OnGSGOLHICVARCHITFECTURE. it are called architectonic forms, in which the variety of nature, being fubjected to the regularity of art, the work acquires that peculiar character, which, in a natural object, we confider as of- fenfive, under the name of FORMALITY ; but which, in archi- tecture, we admire as a beauty, under the name of syMMETRY: thus, we reprobate the formality of an avenue, and praife the fymmetry of a colonnade. ’ Sucu is the nature of architectonic imitation; a device, which probably originated in accident, but to which architeture is in- debted for its higheft attainments. I was firft led by Mr Byres, a very refpectable member of this Society, to obferve, among the remains of antiquity at Rome, many beautiful examples of the application of thefe principles by the ancients; and though my view of the fubjet was then very obfcure, the theoretical folution of the queftion not having occurred till long after, I was fully aware of the very great practical advantages which they had derived from the em- ployment of the principle of imitation. OccuPpi£ED with this view of ancient art, as I was travelling through the weftern provinces of France, in my return from Italy, in the end of 1785, I was ftruck with the beauty of many Gothic edifices, which, far from appearing contemptible, after the mafterpieces of art I had feen in Italy and Sicily, now pleafed. me more than ever. I was thus induced to believe, that thofe extenfive works, poffeffed throughout of fo peculiar a character, and fo eminent for unity of f{tyle, could not have been carried on, —unlefs the architeéts who built them, like thofe of ancient Greece, had been guided, in their execution, by fome peculiar principle; and being diffatisfied with all the theories of the art which I had heard of, I undertook the inveftigation, which has given rife to the Pen Effay *. b2 CoNcEIVING | * AFTER ftating my own views at full length, 1 fhall enumerate and examine the various opinions of others on the fubject of Gothic architecture, no lefs than five in 42 On GOTHIC ARCHITECTURE. | Conceivine that fome ruftic building, differing widely from the Grecian original, might have fuggefted the Gothic forms, I had made it my bufinefs to fearch for fuch a one, when the following accidental circumftance greatly aflifted my fpecula- tions. vit ort . Ir happened that the peafants of the country through which I was travelling were then employed in collecting and carrying home the long rods or poles which they make ufe of to fupport their vines, or to fplit into ‘hoops; and thefe were to be feen, in every village, ftanding in bundles, or waving, partly loofe, upon carts. It occurred to me, that a ruftic dwelling might be | conftructed of fuch rods, bearing a refemblance to works of Gothic architeCture, and from which the peculiar forms of that {tyle might have been derived +. This conjecture was at firft employed to account for the main parts of the ftructure, and for its general appearance only; but after an inveftigation carried on, at different intervals, during the courfe of thefe eleven years, with the affiftance of fome friends, both in the colletion of ma- terials, and in the folution of difficulties, I have been enabled to in number. At the time here alluded te, I was acquainted with an opinion, which I have fince found to have originated with Dr Warzurton, that the Gothic ftyle was copied from an alley of trees, I was aware of the advantages of this theory in fome effential points, yet it always appeared to me unfatisfactory in many others ; and I conceive it to be at beft far too vague to ferve as a guide ‘to the artift. + Tuts refemblance, though very obvious in many cafes, has not, tomy know- ledge, been obiefved by any one but the late Mr Grose; to whom it feems to have occurred in a tranfient way. He makes ufe of the fhape of a bower to afflift his de- {cription of a Gothic roof, (Antiquities of England and Wales, p. 75.) ; but he does not go fo far as to afcribe the architeétonic forms to this origin ; a view, which pro- bably, would not have efcaped him, had he not been preoccupied with a different one; for he confiders the rudiments of a Gothic arch as formed ‘“ of two flat ftones with their tops inclined to each other, and touching.” I did not meet with this paf- fage till feveral years after I had undertaken the prefent inquiry, and had carried it a confiderable length. On GOTHIC ARCHITECTURE. 13 to reduce even the moft intricate forms of this elaborate ftyle to the fame fimple origin. In the prefent ftate of the queftion, the following inquiry _muft be confidered as falling under the denomination of, what is called by Mr Stewart *, “ Theoretical Hifory,” and by fome French authors, “ Hi/foire raifonnée ; being an attempt to trace, _ by conjecture, the fteps through which an art has pafled, in attaining the ftate in which we obferve it. Indeed it is probable, that few inveftigations have been undertaken, which more com- pletely correfpond to that definition, fince, in ‘moft fubjects of this kind, many fteps of the progrefs are known, and nothing is required but to fill up, by theory, the interval between them ; whereas, in the prefent cafe, as all direct teftimony is wanting, and as_no fteps of the actual progrefs of the art have come to our knowledge, our opinions on the fubject, hitherto, can only amount to prefumptions, founded upon the correfpon- dence of the theory with the monuments of the art now in ex- iftence; and, the more numerous and complicated the cafes are, in which this coincidence takes place, the greater probability there is in favour of the fyf{tem. But, though fuch be the adiual fituation of the inquiry, we may hope to fee it, hereafter, affume a different form; for, fhould the conjecture, brought forward in the following Effay, carry with it fufficient plaufibility to excite a fpirit of refearch among perfons beft qualified to purfue the fubject, there is rea- fon to expect, that difcoveries may be made, of a literary or ar- chitectural nature, by which its truth or falfehood will be efta- blifhed beyond difpute. Wuar has juft been faid will, it is hoped, ferve as my apo- _ logy for having advanced a fyftem, which, ftrictly fpeaking, is founded on conjecture alone; and, on the other hand, for having enumerated a multitude of particulars, many of which might * BloGRAPHICAL Account of Mr SmitH. 14 On GOTHIC ARCHITECTURE. might juftly be confidered as fuperfluous, were the theory fup- ported by direct teftimony. OF THE ELEMENTS OF GOTHIC ARCHITECTURE. Wuen we enter a Gothic church, our attention is firft at- tracted by a double row of cluftered pillars, compofed of an af- femblage of, long and flender fhafts, which, reaching from the ground nearly to the fummit, there feparate and fpread in all di- rections, forming the ribs or groins (as they are called) of a vaulted roof. In the meeting of thefe groins, and in the win- dows of the fides and ends, we fee the form of the pointed arch, the principal characteriftic of Gothic architecture. Sucu buildings have, I conceive, been executed in imitation of a ruftic dwelling, conftructed in the following manner: Suppose a fet of round pofts, (PI.I. fig. 1. & 5.), driven firmly into the ground in two oppofite rows, the interval between the neighbouring pofts in the fame row being equal to that between ‘the rows, and each poft being raifed above the ground to a height equal to three of thofe intervals. THEN a fet of long and flexible rods of willow, being ap- plied to each poft, (fig. 2. & 6.), let them be thruft into the ground at its bafe, and bound to it by two tyings, one near the ground, and another at two-thirds of its height; the rods being left loofe, from this laft point upwards, and free to be moved in any direction. Let three rods be connected with each outfide corner poit,(as A or H of the ground-plan fig. 6.), and five with each On. GOTHIC ARCHITECTURE. ey each of the others, (as B or G), and let their pofition be fuch as to cover the infide of the poft, (as marked by little circles in : fig. 6.), fo that, when feen from between the rows, the lower part of each poft fhall be concealed from the view, and prefent the appearance of a bundle of rods, (fig. 2.). Tunes being thus difpofed, the fkeleton of a thatched roof may be formed, by means of the loofe ends of the rods. This is reprefented complete in Plate II. figure 15. & 6.; but the ftru€ture being rendered intricate, by the mixture of different fets of forms, I have, for the fake of diftin¢ctnefs, defcribed each of them feparately, and have reprefented them by feparate draw- ings, with each of which a ground-plan is connected. A rod from one of the pofts, being fo bent as to meet a fimi- lar one from the poft immediately oppofite to it, in the middle of the {pace between them, let the two rods be made to crofs each other, and iet them be bound together at their crofling, (Pl. I. fig. 3.). Thus-will be produced the exact form of the. Gothic arch. The fame being done with each pair of op- pofite pofts, and a fet of pointed arches being formed, let them be connected together by means of a ftraight pole, laid upon the forks of the crofling-rods, and bound to each of them, Gig. 7. 8 15}. THEN let a loofe rod be brought from each of any two con- tiguous pofts in the fame row, fo as to form a pointed arch, fi- milar to that juft defcribed, and nearly of the fame height. This being done with every two contiguous pofts, (fig. 8. & 12.), and a new fet of pointed arches being thus produced, ftanding op- pofite to each other in pairs, let each pair be bound by a hori- zontal pole lying on the oppofite forks, and crofling the lon- gitudinal pole, defcribed above. : Two of the reds of each corner poft, and three of thofe of each of the others, being thus difpofed of, we have one of each corner poft, and two of each middle. poft ftill to em- ploy ; 16 On GOTHIC ARCHITECTURE, ploy; which is done as follows: 1A pair of thefe unoccupied rods being brought from any two pofts which: ftand diagonally to each-other, (A and F, fig. 6.), and made to meet in the middle, not as in the firft cafe, crofling in an angle, but fide by fide, forming a femicircle, and joined together after the manner of a hoop, (fig. 4.) ; and the fame being done’ with every pair of dia- gonal potts, (fig. 9. & 13.), the whole rods will have been employ- ed. nthe . Eacu of the three fets of arches having thus been {eparately defcribed, (fig. 7, 8, & g,), the complete ftructure, in which they are all combined, may eafily be underftood, (Pl. I. fig. 10. and 14., and. Pl. IL. fig. 1558.16.) In this manner a frame would be conftr po fit to fupport thatch or other covering, and fuch a one has probably been often ufed. It would feem, however, that, for the fake of {trength, the number of rods- has been increafed in each clufter, by the introduction, between every two of them, of an additional rod, which, rifing with them to the roof, {till continues its middle pofi- tion, as they {pread afunder, and meets the horizontal pole at . an intermediate point. This is fhown in Plate III. figure 19g, which is drawn with its covering of thatch; and the fame is ex-. prefled in the correfponding ground-plan, figure 20. From the imitation of a dwelling, fo conftructed, we may - now trace the three leading chara¢teriftics of Gothic Architec-— ture, the pointed arch, the cluftered column, and the branching roof, (Pl. Il. fig. 17, & 18., and Pl. III. fig. 21, & 22.) *. THE * Iw buildings of ftone, the arch or groin, which joins the diagonal piers, is very generally a real femicircle, fike that in the willow ftru@ture juft defcribed; as I have found to be accurately the cafe at Beverley and Melrofe. This rule of execu-_ tion, with the deviations from it, which we meet with occafionally, will be fully. confidered 1 in a fubfequent part of the Effay; in which it will be fhown, that in thé ufaal roof, where the diagonal groin is a femicircle, it becomes the regulator of all the reft, determining their height and form in every refpect, 7 i On GOTHIC ARCHITECTURE. oe TueE ruftic fabric might thus be covered completely, but would not be habitable, unlefs the openings of the fides and ends were clofed, fo as to refift the weather. This might eafily be accomplifhed, by means of bafket-work, covered, as is {till practifed in many countries, with a mixture of clay and ftraw. In order to furnifh ribs for the bafket-work, a fet of upright rods would be thruft into the ground below, and bound to the arch above, dividing the opening into fpaces reach- ing from top to bottom, (Pl. IV. fig. 23.), which, being filled up with twigs wattled through them, would be entirely clofed, (fig. 24.), and the work would be tolerably ftrong. It might however be thought advifeable, for the fake of greater ftrength, to fplit all the upright rods, down to the level of the points at. which the main rods of the opening feparate from their refpec-. tive pofts ; or, to borrow a term from architecture, down to the level of the impofts of the arch; and then to carry the half rods, fo fplit, acrofs the reft, in fuch a manner as to afford the opportunity of repeatedly binding them to each other, (fig. 25). Bur were the fpaces all fhut in this manner, the houfe would be rendered abfolutely dark. It would therefore be neceflary to provide for the admiffion of light, which might be done, without materially weakening the ftructure, by omitting fome of the wattled work in the middle, fo as to leave part of the ribs open and bare, (fig. 25.). THESE naked ribs feem to have fuggefted the forms of the flender bars of ftone, called Mullions, which conftitute the frame- work of the glafs, in all Gothic windows; the moft common example of which may be feen in (fig. 27.). THE window, in the fabric of ftone, as well as in that of wil- low, being very confpicuous, would naturally become an objec of attention in point of beauty. Accordingly we find, that, in the compofition of Gothic edifices, much pains have been beftowed in ornamenting the windows, by the introduction Vou. IV. C of 18 (On GOTHIC ARCHITECTURE. | of a number of figures, which are often extremely elegant, and fometimes furprifingly complicated, though without confufion; for they can all be traced to fome variety or modification of the fimple elements juft laid down; as will be fhown, when we treat of the more complicated works of Gothic ar- chiteCture ; at prefent, it is neceflary to mention only one other defign. hehe In this window, (fig. 26.), the halves of the neighbouring rods are brought to meet, but not to crofs, and are bound together fo as to touch each other, back to back ; next, the halves of each rod being brought together again, they are bound face to face; then again feparated, and bound a fecond time back to back, with the halves of the neighbouring rods ; and fo on, till the whole fpace is filled with a fet of regular and equal compartments, bounded by waving lines, (fig. 26. & 29.). Tue form of the Gothic door may be traced to an origin fi- milar to that of the laft mentioned window. One pair of rods, (fig. 31.), being brought from the pofts which form the upright fides of the door, are made to meet in a pointed arch, in the manner defcribed above; then, another pair of rods, longer than the firft, and connected with the fame pofts, are brought to meet above them, and are bound together face to face, like the half rods in the laft mentioned window; the {pace between the two pairs of rods being occupied by a circu- lar hoop. Tue reprefentation of the upper pair of rods, when drefled with fome fimall ornaments, as in many Gothic buildings, pro- duces a moft elegant effect. Figure 33. is a door of St Mary’s, Beverley, reduced from a drawing taken on the fpot, at my defire, by Mr J. HALFPENNY. THE form of the fteeple, however various and apparently dif- ferent from what has hitherto been mentioned, can eafily be ree ; duced On GOTHIC ARCHITECTURE 1g duced to the fame principles. The common fteeple, or fharp pointed fpire, feems to have for its origin fimply eight long and ftraight poles thruft into the ground, one in each of the angles of an oétagon ; and fo inclined, that they all meet in a point, directly over the centre of the bafe, and raifed above it four or five of its diameters, the rods, thus placed, forming together a very acute octagonal pyramid, (fig. 34.). The original object of a ftructure of this kind would probably be mere ornament, as it is not calculated to anfwer any purpofe we know of, un- lefs it were to fupport a bell. Perhaps the firft works of this kind, even thofe executed in {tone, were placed upon the ground; but as a fpire is feen to beft advantage from a diftance, an ar- chiteét would naturally think of raifing it in the air, by placing it on the fummit of a tower; which is the cafe with all the {pires of this kind Ihave feen. Figure 35. is a view of the {pire of Tuxford in Nottinghamfhire. _ Besipes the rectilineal {pire, we fometimes meet with others of a curved form, which may be accounted for in a manner no lefs fatisfactory, as fhall be fhewn in a fubfequent part of this pueyt Havine now taken a view of all thofe parts of Gothic ar- chite@ure, which conftitute its folid mafs, it remains, in order to complete the elements of the art, that we confider two fets of fmall, ornaments, which very often occur, and which, though not neceflary in theory, nor univerfally obferved in practice, arife naturally from) the principles already Jaid down, and contri- bute very much. to,give to Gothic archite¢ture that peculiar appearance by, which. it is diftinguifhed. Both thefe orna- “ments; maybe traced to the effe&ts of time upon the mate- rials employed i in the conftruction of our. ruftic fabric ; one fet being connected with the vegetation of the rods, and the other with their death and confequent decay. C 2, As os: On GOTHIC ARCHITECTURE. As it would frequently happen, that the willow rods, thruft into the ground, would ftrike root and grow, the architect feems to have taken advantage of this circumftance, by reprefenting them as decorated with buds and tufts of leaves, whenever he _ thought that fuch ornaments could be introduced with good ef- fect. Tuis practice has been very generally followed in the execu- tion of the door, as in that exhibited in figure 33. the upper part of which is a reprefentation of living rods, covered with tufts of leaves, like thofe in actual vegetation, (fig. 32.). Upon the fpire, . - too, a fet of {mall projections, placed at regular intervals, often occur, as in that of Bunny, in Nottinghamfhire, (fig. 37.), which feem to be the reprefentation of buds fpringing from the poles of the original, (fig. 36.). : THESE ornaments, known by the name of Crockets, when placed on the floping part of doors, fteeples, pinnacles, &c. and of Finials, where they form a tuft on their fummit, univerfally and unequivocally reprefent foliage. The leaves, it muft be owned, however, feldom refemble thofe of trees, but more com- monly fome plant of the cabbage kind. On this occafion, the artift has ufed the freedom to deviate from the ftrictnefs of the imitation, and has contented himfelf with adhering to the gene- ral idea of foliage. But, in fo doing, he has been in a great. meafure juftified by the circumftances of the cafe; for the fo- liage of a tree, efpecially that of the willow, being compofed of a multitude of fmall and detached parts, could not, without much difficulty, be executed in ftone, and would produce a very frail and perifhable work, which could only be placed with ad- vantage in very protected fituations. He has thus been indu- ced, in moft cafes, to choofe fome plant having a mafly and compact form, better adapted to fculpture. This however is _mot without exception, as we do meet fometimes with croc- kets On GOTHIC ARCHITECTURE. ae _kets formed of the leaves of various trees, efpecially of thofe of the vine ; as may be feen in York-Minfter in feveral places; par- ticularly in that very interefting collection of pediments and pinnacles, furrounding the infide of the nave and its aifles. Thefe are executed with amazing delicacy and elegance, and with fuch fertility of invention, that, though eighty-eight in number, not only every two of the pediments, but every two crockets on the fame pediment, differ from each other *. . ‘Upon * One of thefe pediments, with its pinnacles, crockets, and finials, executed on a large fcale, may be feen in that beautiful collection of the ornaments of York-Minfter, now publifhing in numbers by Mr Hatrrenny: in which work, likewife, are many other things applicable to the prefent fubjeét. I am happy to have it in my power to bear teftimony to the faithful accuracy with which the objects are there reprefented, from having examined feveral of the originals in that view, in the courfe of laft fum- mer, (1796), particularly that of Plate XLI, of which I made a drawing myfelf, in company with Mr Hatrrenny; fo that I can vouch for its exactnefs in every tefpe&t. Ihave been induced thus particularly to mention the fubjeét, by a fufpi- _cion mentioned in Mr Hatrrenny’s feventh number, concerning the accuracy of his drawings ; fome gentlemen having imagined, that he had placed the {culpture in too advantageous a light. To this he anfwered, that “in truth he has not been able, “ jin many inftances, to come up to the fpirit and elegance of the originals.” A de- claration no lefs true than it is modeft. Iam well convinced that the gentlemen, with whom this fufpicion has originated, have not been much accuftomed to exa- mine our Gothic buildings of eminence, fince, in any of thefe, they would have met with numberlefs works, executed in too high a ftyle of defign to admit of embellifh- ment in the prefent ftate of the arts. Nor is it wonderful that fuch fhould be the ‘eafe, when we reflect, that they belong to the 14th and r5th centuries; during which, a feries of artifts flourifhed in Italy, who, in point of chafte defign, and care- ful imitation of nature, have never fince been equalled, though they had not attain- ed to many of the refinements which were introduced in the fubfequent age. Thefe artifts travelling over Europe, contributed greatly to the ornament of the Gothic edi- fices which were then building, as we learn from many curious fatts colleGted by Lord OrrorD, in his Anecdotes of Painters. I sHALL enter more fully into this fubje€t, when I {peak of the Hiftory of Gothic Architecture ; and I am led to touch upon it now, though out of place, in order “to call the attention of men of tafte to the fate of numberlefs beautiful ornaments of the 42 On GOTHIC ARCHITECTURE. Upon the monument of King Joun I. and Queen Parrrepa, in the church of Batalha, are two canopies of frittered-work, conftructed in a manner which I fhall endeavour to explain in a fubfequent part of this Effay. The lower part of each of them confifts of an arch of contrary flexure, like that of the door _ of St Mary’s, Beverley, (fig. 33.), but ornamented in a manner fomewhat different, having, in place of the crockets, a fet of leaves, in form and arrangement, greatly refembling thofe of. the willow *. , WHOEVER the Gothic ftyle, which are daily perifhing by the exertions of a miftaken zeal in their favour. Every year, great fums are beftowed in dreffing up the old charthes: 3 in many ~ parts of England, much to the detriment of thefe noble edifices. In fome cafes, this is done by befmearing the building with white or yellow paint, which chokes and confounds all the delicacy and elegance of the fculpture. This evil, however, is not of the deepeft kind; fince, here, the original forms of the work remain entire, and may be again reftored to their purity, when a better tafte prevails. But an in- jury of a much more ferious nature is occafioned by the operation of chipping, in which the mafon, with a barbarous hand, aétually goes over the whole work, and chifels off the furface to a certain depth, leaving but a poor fhadow of the original form. By both operations, the building acquires the harfh and glaring appearance of new work; which, however, is removed in a few years, by ‘the influence of the weather, and the edifice recovers its former grandeur, as far as colour i is concerned, © But the havock committed by chipping is quite irreparable; for the fculpture, when. once removed, canreturn no more. ES I save been told, in vindication of this prattice, that the forms of the old es were reftored exa¢tly as they originally ftood. An idea, worthy | of the fimplicity, of Mummtvs the Roman general, who demolifhed Corinth. As if it were in the power of every ftone-cutter to replace a mafter-piece of the 15th century ! - I was happy to find, at York, that a different fpirit prevailed in the operations. carrying on in the Minfter. In all thefe repairs, the ancient feulpture has been moft_ fcrupuloufly refpe&ted ; and, in many places, the ftone has been carefully freed from, its load of paint, fo as to reftore it to its original purity. For thefe attentions, the, public is greatly indebted to the good tafte. and judgment of . the Rey. Mr Bre, one of the refidentiaries. ) : * Sex Mr Murpny’s admirable *publication ; 2 work to which I thall have very often occafion to refer, when I fpeak of the more complicated forms of Gothic architecture. On GOTHIC ARCHITECTURE. — 23 WHOEVER pays any attention to Gothic architecture, muft obferve, in the upper part of moft windows, an ornament pro- jeCting from the bars, formed by two curved lines meeting in a point. It would be difficult to defcribe this form in words, but it may be underftood eafily by figures 27, & 28. of Plate IV. which reprefent two contiguous windows of St Mary’s, Bever- ley ; in one of which the bars have been executed plain, and in_ the other they have been ornamented in this manner. Figure 30. is the window that lately ftood in the chapel of Holyroodhoufe at Edinburgh, and figure 29. the fame general form executed quite plain, as it fometimes occurs. As this ornament has not, that I know of, been characterifed by any peculiar name, I fhall apply to it that of cu/p, by which mathematicians denote a fi- gure of the fame kind *. , Ir was long before any fatisfactory explanation of this form occurred, though the frequency of its appearance, and the uni- form manner in which it is introduced in all Gothic works, Jeft little room to doubt that it had an origin, in common with the more fubftantial forms of the ftyle. At laft a friend fug- gefted to me, that it may have been borrowed from the appear- ance affumed by the bark of the rods, when about to fall off, | in confequence of decay. ‘With this view, having attended particularly to branches in a fimilar fituation, I have met with feveral facts, which tend to confirm this conjecture. The dead branches of every kind of ‘tree, after being expofed to the weather during three or four years, throw off their bark, which, immediately before it drops, curls into various fhapes, ‘ owing _ * AssemBiaces of thefe cufps are fpoken of in the defcriptions of Gothic works, by the names of trefoil, quadrefoil, femi-trefoil, &c. but no proper word has been ufed to defcribe the form, wherever it occurs, or however combined. This, I trutft, will fufficiently apologife for the liberty I have taken, of introducing a new term into architecture. An application of the word cufp, as ufed by mathematicians, may be feen in Dr Smitu’s Optics, Voi. I. p. 172. where he ufes it in defcribing the cauttics formed by reflection. © 24 On GOTHIC ARCHITECTURE, owing to the unequal contraction of its different layers. This takes place varioufly in different woods; in fome, the bark bends inwards, in fome outwards, in fome acrofs the branch, and in fome lengthways. I have had occafion to obferve, that, univer- fally, the bark of the willow bends concave outwards, and length- ways with refpect to the branch. One of the firft diftin@ ex- amples I met with, of this kind, was on a rail at St Mary’s Ifle in Galloway, in the fummer of 1792, (Pl. V. fig. 38.). The rail had been made entirely of frefh willow, and the pofts had all ftruck root, having then the third year’s growth upon them; the hori- zontal bars had died of courfe, and were in the aé of lofing their bark. This, in fome places, was feen feparated from the wood at one end, and adhering to it at the other, forming a gentle and continued curve with the mafs of bark, which ftill remained at- tached to the wood; fome pieces of bark, a few inches im length, had feparated at both ends, and remained adhering only by the middle ; in fome places two contiguous pieces of rifing bark met, and exhibited a fhape very much refembling that of the . _ cufped ornament which I have juft defcribed. In the fummer of 1795, I faw, at the fame place, a ftill more ftriking example of this, upon an upright poft of willow, (fig. 40.), in which - the two pieces of curling bark formed, together, a cufp from nine inches to a foot in length. In a few days,’the under » piece of bark fell off; but the upper one remained for) more than a month, lying clofe to the wood during rain, and rifing from it when the weather was dry. © Figure 39. reprefents a large branch, which I cut from an old willow, having the curled bark -upon it, and which, being kept dry, ftill retains its Shape, THERE is great reafon to fuppofe, that this accident has fug- gefted the cufped ornament : For if we fuppofe a window of the willow houfe, (fig. 41.), in the fame ftate of decay with the rails juft mentioned, to have come under the obfervation of an archi- tect -On GOTHIC ARCHITECTURE. 25 > © tect, of. genius, in the habit of borrowing all his ideas 'from a houfe. of this kind, and eager to feize upon whatever con- tributed to add beauty or novelty to his work, it is natural to believe, that he would take advantage of the circumftance, by imitating, in ftone, the curling bark; and this being executed with that regular fymmetry, which architeture beftows up- on the natural objects.it reprefents, (fig. 42.), would produce a light and elegant effe@, and the ornament. would foon become general. We, know that to fuch accidents, ry architecture of the Greeks was indebted for many of its principal embellishments ; of which the origin of the Corinthian apical is a ftriking andl authentic example. Rear: that all the effential parts of Gothic architeCure could thus be explained, by tracing its origin to the imitation of a very, fimple ruftic edifice, I was defirous of fubmitting the theory to a kind of experimental teft, by endeavouring actually oto conftrugét a’ building fuch.as has been defcribed. With the help of a very ingemious country workman*, I began this in fpring 1792, and completed it, in the courfe of the winter fol- lowing, in a manner which far furpafled my expedtation, and which has already met with the approbation of feveral Mem- bers of this Society. -The method of conftruCtion anfwered fo. _ well in practice, that I doubt if a better could be followed, with -fuch fimple materials ; and fo primitive is the mode of execu- tion, that I believe, with a little ingenuity, the whole might be executed without the help of a fharp inf{trument, or of any ma- terials but fuch as the woods afford. A seET of pofts of afh, about three inches in diameter, were pla- ced in two rows, four feet afunder, and at the interval of four Vou. IV. a hiss feet. * Joun WHITE, cooper, in the village of Cockburnfpath, in Berwickhhire.. 26 On GOTHIC ARCHITECTURE. feet in the rows. Then a number of flender and tapering wil- low rods, ten feet in length, were applied to the pofts, and form- ed in the manner already defcribed, into a frame, which being covered with thatch, produced a very fubftantial roof, under which a perfon can walk with eafe * Tuts little ftructure exhibits, in aiatneane, all the characte- riftic features of the Gothic ftyle. It is in the form of a Crofs, with a Nave, a Choir, and a north and fouth Tranfept. The thatch, being fo difpofed on the frame, as not to hide the rods of which it is compofed, they reprefent accurately the pointed and — femicircular arclies, and all the other peculiarities of a groined roof. The door is copied from that of Beverley. The windows are occupied by a number of defigns, executed, (by means of {fplit rods), in exact refemblance of thofe which actually occur in vari- ous Gothic edifices. Round each window is a border of compact wicker-work, which, by deepening the fhade, adds greatly to the general effect. At a little diftance ftands the {pire, formed of eight ftraight poles of willow planted in the earth, and ri- fing in an o¢tagonal ‘pyramid to the height nearly of twenty feet. Various other Gothic forms are likewife introduced, which being of the more complicated kind, will be explained in a fub- fequent part of this Effay. TuE appearance of the whole, whether feen from within or from without, bears, I flatter myfelf, no {mall refemblance to a cathedral. In the courfe of {pring and fummer 1793, a great number of the rods ftruck root, and throve well. Thofe of the door, in ; particular, * Tue roof, being proteéted from the weather, is ftill in perfeé& prefervation, though it has now ftood about five years; but the windows and other parts, which are more expofed, are going faft to decay, though they have been often repaired. Soon after the work was finifhed, a very accurate drawing of it was made by an ingenious young artift, Mr A. Carsx, which it is propofed to engrave for the il- luftration of this Effay, when publifhed at full length. Oh GOTHIC. ARCHITECTURE ©. 27 particular, produced tufts of leaves along the bent part, exactly -where they occur in ftone-work; the vegetation did not however reach, as had been wifhed, to the very fummit, but was. more than fufficient to juftify an artift in the execution of doors like that of Beverley, (fig. 33.). Three of the rods of the fteeple, alfo, fent out buds, at {mall intervals, to the height of eight . or ten feet from the ground, fo as, at one ftage of their growth, to refemble the budded {pire already defcribed. I HAVE likewife had the fatisfaction, in the courfe of laft au- tumn, (1796), of finding one entire cufp formed by the bark in a ftate of decay, in a place correfponding exactly to thofe we fee executed in Gothic works. In this manner, all the original forms of Gothic architecture may be accounted for. But they feldom occur in the ftate of fimplicity, which, in order to facilitate their defcription, I have hitherto fuppofed ; for, in a Gothic edifice, they are for the moft part complicated by varieties in execution, and by inter- mixture with each other. They have been modified, likewife, and fometimes difguifed, by the circumftances attending the tranfition from wicker-work to mafonry, which have occafioned changes, both in the general defign of thefe works and in the execution of their minute details. I fhall endeavour to fhow, however, (in the work I have already announced), by an exa- mination of the actual monuments of the art, that the moft - ‘intricate of thefe forms may be traced to the fame fimple ori- ginal. But to accomplifh this, it will be neceflary previoufly to inveftigate the tranfition to Mafonry; an inquiry too exten- five to be comprifed within the limits of an academical memoir. : ae ae _ aq it si ; ; le Ee dtine ayes ee eo a as hae S| he few 9 tech sae d si aes ; debs . ‘ * <5 * : : ity Tiesto ote ; seit ae i bi Bi sigs ab Y aan aig ; oy bets i; a a es ms wc , = iy P fis f v3 : oto. 2077 tat §saigtae, oils Me ihe Be: . ne-Alsg00° imobish = fen aa 36 Ay init: sibectuoaan ¥ ; oe Py et: Oy SRI IGA Oo “bite "ni e " beta nike 4 th = : b sinyads: po nitt: aitbsot.s. gi frotey A ais ostoraiaky ol br eee Die OR ngeies eo shtarieck Daaegilg mies tee ag, ive ie : ras <4 cee y es a Se ones A Sp gE enone? srain) avait voit aol id: eee abi oi - nh : grit 1619 : pe: PS args) o 9 at, perere: a1tei2di oh - py pre, 9) ove Aaidw si nchento} diowsrdoh nee ents “ode ni bae: « ow gis Af Qnty ghabLerdid3 oi: ‘ dscithci P Sate of et Ore f: QO petites ties been ahh, OF WwOesshA’ Bagh, { paelt tsbian ica 4 Seema cs eel £ (baonpeing y bse us | wil. Rial bine, a, * Rom ea Bats bie wit for emer wont Jeno: m8 Hyd Shep e it oem ad of bap acl yaeg ia Bo “tts an : ‘ a Oe Fe 4 . ., Enaiiiesqs ‘fTeke oat od Aiwa di. vib isla Riviere 0208/50) et i: . meee ood Vuib py tg: os: Rariiass orks sie giftern ‘2 4 ae | Looieers ae rin te iF Ave “ Ei ceptil > ¢ ais sty Ok iigiog, oda: rich bj ” POP 1 dig eoh 8 t pa v/s Wis $6 a s yi ; eA ¥. 9 4% i ag: "dei ate, eats Qe Res é Bers 5 J ?, te fie ee ee Be che be A — ao . 3 , aw als 2 Vino. - « : mS As oo ta te “i SS X ‘ees 3: “ om | an ae eG Sat cree 4 M4 rie . } ‘ oe C = r ‘ - ’ - ‘J + bo aN ; . » _- ' ae ae r Ee ’ s ~ dante 3 “* : z ne Be! C ; ay ¥ tm oe 5 | : ra ere Pow’ : ime sys = a bears i - ek —. 7 < \- So ee a = x ‘ i - i 1 v N Tike ok 4 tie See ee a ee ~ pms Cail ILLUSTRATED aud CONFIRMED. 35 him than I.am, the acute and ingenious Mr WaKkEFIELp *, and a learned anonymous reviewer in the Briti/h Critic +. Mr Liston being to return from his embafly at the Porte, towards the conclufion of the year 1795, | was glad to find, by a fhort letter, that he himfelf had made an excurfion to the Troad ; and underftanding that a new edition of M. CHEva- LIER’s Effay was projected, he defired it might be deferred till he fhould come. home, as he had fome obfervations to commu- nicate which would render the work more perfect. When I met with him at Edinburgh he was yery much hurried, owing to his being under the neceflity of fetting off foon for America, as his Majefty’s Plenipotentiary to the United States. He never- thelefs devoted a few hours to the revifal of M. CHEVALIER’s Effay, whilft I fat by him and took notes of his remarks. As a great many of thefe confifted of fmall alterations of various parts of M, CHEvatiger’s defcriptions, with a view to condenfe them where they feemed too diffufe, and to correct them where they feemed inaccurate, it would be tedious at prefent to enter into a particular detail. But, in the cafe of a new edition of the Effay, I am perfuaded that they would be extremely ufeful. It may be fufficient, here in this Introduction, to fay in gene- ral, that Mr Liston confirmed, from his own infpedction, all the great points of M. CHEvALIER’s refearches and difcoveries, af- ter {pending many hours in walking oyer the ground. He faw the fuppofed fite of Ancient Troy, the fources of the Scamander, and the place where that river is now diverted into its new channel. In fhort, I found that Mr Liston, along with a great defire to render every thing as exaét and accurate as poflible, had alfo caught that fort of intereft in the fubject, which is fo €2 | natural _ ™ See “ A Letter to Jacoz Bryant, Efgq; concerning his Differtation on the “War of Troy: by GinpertT WaKEFIELD, B. A. Lond. 1797. 26 pp. 4to. + For May and June 179%, vol. ix. 36 TABLEAU de la PLAINE de TROYE natural to a claffical mind, when engaged in furveying or de- _fcribing fuch pleafing fcenes. In fome parts of M. CHEvALIER’s map, alfo, he found fome inaccuracies, which he was enabled to rectify, both from his own obfervation, and from another map with which he had been furnifhed. This laft he expected to be fent after him from Conftantinople, and intended it fhould contribute to the improvement of M. CHEVALIER’s in the new edition of the Eflay*. Of all this I apprized M. Cueva ier, in a letter direct- ed to him in London, which found him about to fet off for the Continent. Previous to his departure, I received from him two letters in anfwer ; extracts from which will be found in the Ap- pendix f. But one of the chief inducements for bringing the fubject before the Society at this time, is the recent publication of a very ingenious work, entitled, Con/fantinople, Ancient and Mo- dern, with Excurfions to the Shores and Iflands of the Archipelago, and to the Troad. By James Dautaway, M.B. F.S. A. late Chaplain and Phyfician of the Britifo Embaffy to the Porte... This: learned author has been at great pains in afcertaining the: topo- graphy of the Troad; and the refult of his inveftigations there has produced the fulleft confirmation of all the material parts of " M. Cuevatier’s Effay, and a total but refpectful diffent on the part of the author from Mr Bryanvt’s fcepticifm on this fub- ject. To this book, therefore, I fhall, in the rg 2 paper, have frequent occafion to appeal. ABSTRACT * Tus map I have never received, owing to fome omiffion which I cannot ex- plain. In the mean time, this paper is accompanied with a fmall one, fomewhat amended, chiefly from that given by Dr Datiaway, the author of the book pre- fently to be mentioned. + No. VI. + . : re ) 5 1 = y a, . ‘ oa “4 - ‘ ; ct wy —! ;. . . 2 - ~ ‘ = - ~ , ; f 9 . . ‘ = j ‘ 2 \s mu 4 Trans. R-S. Edin. to face page G7 470. Cl. Meuntains of Ida T Obympir stadia 10 —ae Geog. miles, Gotoa deg- ; 7 2 a a TOPOGRAPHICAL SKETCH ofthe PLAIN of TROY. ILLUSTRATED and CONFIRMED. 37 ABSTRACF of the moft material Parts of M. CHEVALIER’S Effay, with the Confirmation of Jubfequent Travellers. “In giving a fhort Abftradt of M. Cueva ier’s inveftigations, I fhall not follow the order in which he himfelf proceeded, but that which feems to convey the cleareft idea of his difcoveries and obfervations, now that they have been made. For the cafe is quite different with a perfon, who gives a detail of the man- ner in which he himfelf advanced in the courfe of inveftigating objects, of which he had at firft but an imperfect notion, where the direct path leading to them was yet obfcure and unknown, and where he had to form conjectures that were fometimes er- roneous ; and with one who points out or elucidates fuch ob- jects after they have been difcovered, and their relative fituations afcertained. AFTER M, CHEVALIER had formed the refolution as explo- ring the Afiatic coaft, where the Hellefpont unites with the figean Sea, with a view to afcertain the true topography of the ad, he happened to land firft at Cape Baba, the ancient pro- montory of Lectos. ‘Thence he proceeded to Alexandria 'Troas, the ruins of which he examined, and has given an account of; and this account Mr Liston in converfation, and Dr DaLLaway in his book, (p. 326.), have agreed in confirming ; but of which a particular detail would be here unneceflary*. The * Tur Turkith name Efe: Stamboul; the warm baths called Lidga Hamam ; the hill on whofe declivi ity thefe are fituated, and which is covered with tombs, whofe farcophagi of white marble the Turks break down and make bullets of, for fupply- ing: 38 TABLEAU de la PLAINE de TROYE The Plain. In advancing from Alexandria Troas, along the coaft, M. CHEVALIER’S attention was particularly attracted by a tumulus, or barrow of immenfe fize, at a confiderable diftance*. This is now called Udjek Tepe, from Udjek, the name of the adjacent village. From the top of this at noon, (Ch, III.), he took a re- trofpect of the ruins of Alexandria, now at the diftance of more than four leagues ; towards the north he faw a large plain, en- compaffled with delightful hills; to the eaft the foot of the moun- tains of Ida; and to the weft the Agean Sea, the iflands of Te- nedos, Imbros, Samothrace, Lemnos, and all the way to the fummit of Mount Athos. Dr Dautaway remarks, that “ from the high ground near “* Alexandria Troas, the view of Tenedos, and of the fea, with “ Udjek Tepee, a vat tumulus above the plain of Troy, on the “right under the horizontal line, is particularly pleafing.” (p. 326.). And that “in the progrefs the country foon be- “* comes lefs woody, and fpreads into a wide heath, from whence “ the whole plain of Troy is feen,” WHEN M. CueEvatier, in the courfe of his mveftigation, ar- rived at the eaftern extremity of this extenfive plain, on the emi- nence above the modern Turkifh village called Bounar-ba/in, and where he at laft concluded the citadel of ancient Troy to have been placed, he obtained a view of the whole extent of it; and it feemed to him of a femicircular fhape}. “ Of the two chains - ce of ing the Caftles of the Dardanelles ; the aquedué& of Heropes Arricus; the circuit of the wall ftill almoft entire ; the thickets of Valonea trees; are all likewife re- marked by Dr DaLLaway, or were mentioned to me by Mr Liston. The for- mer obferves, that “ the whole fite is now a thick foreft of Valonea, or dwarf oak, “* peculiar to the Levant.” Of this fhrub the latter brought away fome feeds. * See the Map. + Mr LisTown adds, ‘ on each fide.” ILLUSTRATED and CONFIRMED. 39 “of hills which embrace it, one appeared to run in a direction “towards the promontory of Yeni-cheybr,” (or Sigeum), “ and “the other towards the point of J-Tepé-Gheulu,” (or Rhoe- teum). The part of the hills to the right, reaching between the villages of Atché and Ichiblac, appeared more cheerful than the reft, and which he had no doubt compofed the Callicoloné of Homer. From this ftation he defcried “ the iflands of Te- “ nedos and Imbros, Samothrace and Lemnos, the high top of “ Mount Athos, and the Thracian Cherfonefus beyond the Hel- “ lefpont.” (Ch. 1V.). As to the foil of the plain, he obferved itto be “ of a rich and blackifh colour, and of great fertility.” The village of Bounar-ba/bi he reckoned to be “ at the diftance “ of four leagues from the fea.” (Ch. XVITL). Mr Hawkins and Dr SisruorPe took horfes at Koum-kaleh on the coaft, and croffed the plain to the village of Bounar-ba/bi, in three hours, “ an extent,” fays Dr SistHorre, “‘ of nine “ miles*.” Mr Hawkins, in his fecond letter to Mr Liston, affures him that Tenedos is to be feen from the hill of Troy, aad that even “ the whole coaft af the ifland 3 is vifible, from the * northern to the fouthern point.” Dr DaLtLaway remarks, that “ the whole plain of Troy, _ “ from the height faid to have been the citadel, is of uninter- “ rupted extent.” (p. 346.).. From the promontory alfo of Ye- ni-cheyhr, or Sigeum, at its lower extremity, the fame intelligent traveller looked over the plain, the whole {cope of which he commanded. “ Its broadeft diameter,” fays he “ may be five “or fix, and its longeft twelve miles to Aiché-keuy. Itis natu- “rally verdant and fertile, and now very generally CoE ae “ excepting near the marfh, which occupies a fifth part.” (p. 347.). This 1 take to be the marth at the mouth of the ‘i- mois, of which afterwards. ce The * See their Letters, Appendix, No.V.. 40 TABLEAU de la PLAINE de TROYE The Site of Ancient Troy. NEAR the eaftern extremity of the plain, upon a gentle accli- vity, is fituated, as has been faid, the Turkith village of Bounar- bafbi. While M. Curvatrer advanced upwards to this vil- lage, by a pleafant and eafy afcent, rifing gradually from the plain, he paffed through a fpacious cemetery, where each of the tombs is adorned with a fragment of marble or of granite. Pafs- » ing the village he continued to afcend for near a mile, till he arrived at the borders of a precipice of great height. (Ch. I'V.). Beneath this precipice a torrent, coming down from the moun- tains above the plain, (but whofe bed in the fummer is com- monly dry), runs in a curve direction toward the north; and, bending its courfe along the northern fide of the plain, flows down through the whole length of it, and difcharges itfelf into the Hellefpont, betwixt the modern Turkifh fort called Koum- kaleh on the fouth, and a fort of haven called Karanlik-limani on the north, near Rhceteum. This river is undoubtedly the Si- mois. And upon the rifing ground extending upwards from the village of Bounar-ba/fbi to the abrupt precipice encompafied by rocks above and the river below, on every fide, except that which opens upon the village, and where the Scean Gate may © be fuppofed to have been, M. Cueva iEr concludes, that the ancient city of Troy was placed. From the fummit of this high ground, where he fuppofes the citadel to have been, and which the Turks now call Ballidahi, mountain of honey, he had a view, as has been faid, of the whole extent of the plain. This being an airy fituation, juftifies, in his opinion, HomeEr’s epithet of | jvemoecoe, {0 often applied to Troy. (Ch. XVII.). The precipices which fkirt this eminence, and the Simois which runs at the foot of them, render the place impracticable to be affailed from any other quarter than from the fide towards the village. (did. ). Mr | ILLUSTRATED and CONFIRMED. 43 M. CuEvacieEr further remarked, on this high fituation, four barrows or tumuli, three of which are fimilar to thofe on the fhore of the Hellefpont, (which fhall be afterwards mentioned), and the fourth confifts of an enormous mafs of ftones. This he conjectured to be the monument of Hecror ; and thought it the remains of a demolifhed ftructure. (Ch. XVIL.). Mr Hawkins and Dr Sistuorre “ fpent a day in vifiting the “hill fuppofed by M. Curvatrer to have been the fite of “Troy; and the fprings of water, which he confiders as the “ fountains of the Scamander*.” Mr Hawkins thought, that “ the place pitched upon for the fite of the city has much natu- “ ral ftrength to recommend it, particularly the eaftermoft angle “of the hill, which, from its height above the Simois, and its. “ perpendicular form, muft have been confidered as a very “ {trong natural faftnefs in thofe times of warfare, and could “ have been eafily rendered an impregnable citadel; for it is not “ large enough for the fite of the whole city.”-—“ Some tumuli,” adds he, “ near the fpot, are certainly ftrong indices.” Dr S1z- THORPE obferved, that “ the fituation, where the citadel is fup- “ pofed to have been, is particularly fteep and rocky:” and that “it 1s covered with prickly barnet, and a few thorny fhrubs. * The almond tree,” adds he, “ which grows wild, is not with- “out its thorns. It has even more pleafing plants, the yellow. ** jafmine and the wild olive.” Mr Liston took particular notice of a contiguous place, where the ftones of what is called the tomb of Hector feemed to have been dug; and he remarked a fort of hollow all around the city, except fome part, which is rocky. Dr Datuaway, who advanced towards the village from the | northern fide, thus defcribes his approach: “ As the fetting fun “was more brilliant than for many days paft, the village of Vou. IV. eo _ Bounar- * See their Letters, Appendix, No. V. 42 TABLEAU de la PLAINE de TROYE “ Bounar-bafbt opened upon us very pleafantly from the ford of “ the Simois, which we pafled within a furlong of the chiftlik “ of Havci Meumer Agha, the prefent proprietor of a do- “ main producing near L. 5000 Sterling per annum, and inclu- “ ding little lefs {pace, and the identical ground of the kingdom “ of old Priam*. His houfe is mean, but many columns were difperfed about it, which had been colleéted from the fites of “ adjacent cities. From the village,’ adds he, “ the hill rifes “ rapidly, and foon becomes an infulated mountain. The lofty “ wall of Troy, and the Sczan Gate, interfected the modern “ village of Bounar-bafmi. Afcending the hill, thickly ftrewn “ with loofe ftones for the {pace of a mile, the firft object on the “ brow is a ftony hillock, which CHEVALIER, with no apparent “ reafon, calls the tomb of Hector. It has been opened and “ examined, but we could not learn the refult. There are others “ covered with grafs, appropriated likewife to Trojan heroes.” Dr Datiaway has given a beautiful defign and engraving of — the tumulus faid to be Hectror’s. ‘This learned traveller is of opinion, that “ upon the area and the intermediate ground “ from the village of Bounar-ba/bi, there is undoubtedly fpace “enough for fuch a city as Troy is defcribed to have been.” (p. 345.) And he obferves, that “ the level falls abruptly on “ the fouth, with a precipitate cliff, into a-deep ravine, forming “a mural rock, now almoft covered at its bafe by the ftream *“ and fands of the Simois, for the length of forty or fifty yards, “ and completing a fortification rendered impregnable by na- ture ; vn ¢ ra 2 *M. Cuevauier had faid, (Ch. XVII.) that “ near the hill were fituate the “ gardens of Priam, where Lycaon, when cutting wood, was, furprifed by AcHIL- “tes; and on that fpot are ftill fituate the gardens of the Agha of Bounar-bafhi, “ who, after forty centuries, fucceeds to the king of the Trojans, &c. (Forty, among the Errata, is corrected thirty: which Dr Datiaway, not obferving, has fuppofed the author guilty of a miftake), Mr Liston told me that he ate grapes in this very place. : ILLUSTRATED and CONFIRMED. 43 “ ture ; and that the face of the ground exhibits nothing worthy * of remark ; bufhes and huge unhewn {tones only being to be fiteen.?’ The Sources of the Scamander. But the chief circumftance which afcertains the pofition of the city is the fources of the Scamander. Thefe M. CuEva- LIER was fo fortunate as to difcover, and defcribes as ftill to be feen, a little below the village to the fouth, and as confifting : 1. Of a folitary copious {pring, rifing from the bottom of a ba- fon, bordered with pillars of marble and granite; of which fpring, in the month of September, he felt the water to be tepid; but was affured that it is much warmer about the middle of winter ; 2dly, Several {mall fprings of cold and limpid water gufhing forth from crevices in the rock, at the bottom of the low hills at the head of the plain, and which uniting into one ftream, a little below, receive alfo the firft mentioned fountain, and thus form the Scamander*. (Ch. IV. xix.). “ We flept,” fays Dr SintHorPE, “ at Bounar-ba/bi, a little be- * low which rifes the Scamander, fed by numerous {prings of a “* pure cryftalline water. One of thefe is faid to be warm in “ winter ; it communicated to us no fenfation of heat.” This was about the middle of September. Dr Dati away, who was there in November 1795, {peaking of the hot {pring, exprefsly fays: “ It “is at leaft tepid ; and the Agha (in the front of whofe houfe * it is to be feen, at a little diftance) told us, that, in the winter “ months, efpecially during froft, it is hot and {mokes.”—“ Ho- “ meER, adds he, “‘ muft be allowed the privilege of a hot “« fpring, and a river full to the brink, if they happen once with- f2 at * Compare Iliad, xxii. 147. 44 TABLEAU de la PLAINE de TROYE “in the year.” (p. 344.). M. Curvanrer found the Turkifh women of the village of Bounar-ba/bi wathing their garments at the fources of the Scamander, as the wives and daughters of the Trojans were wont to do when they enjoyed the {weets of peace, before the arrival of the Greeks *. I repeat this circum- ftance, becaufe Mr Liston affured me that, when he was there, he made the very fame remark. The Courfe of the Scamander. M. CHEVALIER examined the two rivers, the Simois and the Scamander, by tracing them upwards; the latter, from the place where it now difcharges itfelf into the Archipelago, by a new canal; and the former from its mouth upon the Hellefpont, a little to the north of Koum-kalebh, The new canal of the Sca- mander had been firft obferved by him, on his.way from Alex- andria Troas, as he came down from 'Udjék-Tepé, or monument of AsyeTEs. About a mile to the northward of this monument, as you pafs the village of Erke/fighi, and near an elegant Kiofk, | or repofing place, conftru@ted by Hassan, the Turkifh Captain Pafcha, a confiderable {tream flowing down upon the fouth fide of the plain, and then bending towards the Simois, takes a fud- den dire¢tion to the fouth, being plainly diverted into an artifi- cial canal, which carries it a confiderable way, m a floping courfe through a valley, and conveys its waters into'the Ai- gean Sea. (Ch. IIL). This mew ‘canal made a ftrong impreffion on M. CHEVALIER’s mind; .and induced him afterwards to fearch for the ancient bed of this beautiful ftream, which he at length found, and traced, as marked on his map. (Ch. IV.). This was a moft important difcovery; and when, in the invefti- gation, * See Iliad, xxii. 154. si = eT ~~ ILLUSTRATED and CONFIRMED. 45 gation, he came again to the f{tream, where it turns into the new canal, and traced it up to its fources already mentioned, near Bounar-ba/bi, no doubt any longer remained on his mind, that this was the true Scamander, which had formerly united its water with the Simois. SUCCEEDING travellers have, in the moft liberal and decided manner, confirmed the genuinenefs of thefe inveftigations, and acceded to M. CHEvarier’s conclufions. “We faw the place,” fays Mr Hawkins, in his firft letter to Mr Liston, ‘‘ where the courfe of this river was diverted by “ an artificial canal to the Archipelago.” And he adds, more explicitly in his fecond letter: “‘ The moft effential point in fubftantiating the evidence of CHEVALIER is that of the canal, made to divert the waters of the Scamander from their origi- nal courfe towards the Simois. This canal we can bear tefti- mony to. The errors of Woop feem to arife from the over- looking this circumftance. As for Straxso, he had never vifited the fpot in all probability, and relied on the authority * of Demetrius of Scepfis*.” Mr Liston himfelf afterwards. examined the river with the greateft care, and particularly the: new canal, and the old bed. This laft he croffed on bridges in different places, and was convinced, that when, occafionally, the ftream of the Scamander is more copious, part of it {till flows into ‘the Simois by this ancient channel. For he differed in opinion from M. CHEVALIER in ‘the idea, that the Scamander is never fubjeét to any increafe or diminution; (Ch. IV. xi.) ; and faw no reafon why it fhould not occafionally fwell in the cafe of long continued and heavy rains; though by no means to fuch a degree as the Simois, which is fometimes dried up, and fometimes comes down with the utmoft magnitude and impetuofity.. * See Appendix, No. V. ~ va 46 TABLEAU de la PLAINE de TROYE impetuofity *. Moreover, Mr Liston affured me, that from M. CHEVALIER’S defcription, the Scamander feems to be a more diminutive water than it really is Tf. “ For feveral hours,” fays Dr DaLuaway, “ we traced, with “ the utmoft attention the courfe of the Scamander from the * cold or fecond fource, which is a colle€tion of {mall fprings, “‘ through the morafs, where for fome miles it is pofitively hid, *“ till we reached the new canal, and faw plainly the ancient bed. “‘ The banks of this river, where expofed, are verdant and beau- “ tiful, and watered to the brink. M. CHEVALIER’s topography “and general idea, after a fair inveftigation, we acknowledged “to be ingenious and plaufible.” (p. 347.). In chara¢terifing the Scamander, M. CHEVALIER mentions particularly “‘ the tranfparency of the water, which runs upon ‘a bottom of fand and round pebbles, betwixt two verdant ‘( Panksil? | | Dr Datraway fays of the two rivers: “ Simois has broad “ fands, with a fudden and rapid current ; Scamander is tran- “‘ {parent and regularly full, within a narrow channel, and fo “‘ they continue to be till their junction, before they reach the “fofeas’?ts Gai gq.82). M. Cuevacier further defcribes his having pafled the Sca- mander upon an old willow ftretched acrofs, near a mill. Mr Liston alfo mentioned to me this mill, and his having crofled. the current in a fimilar manner. The * Ir this hypothefis of Mr Liston be well founded, perhaps it may be inferred © that the Scamander remains in the fame ftate in which it was in the days of Ho- MER, occafionally flowing into the Simois, but commonly, by what is thought a new canal, into the /Egean Sea. And if this is admitted, it may affift Mr Heyne in ob- viating a difficulty which occurs to him in his Effay on the Topography of the Iliad. See Appendix, No, III. + Peruars I may be partly to blame for this, by calling it, in the tranflation, @ rivulet, (p. 13. 15.), and once a rill, (p.25.). The original is ruzfeau, which might have been rendered a /fream. ILLUSTRATED‘ and CONFIRMED. 47 The Courfe of the Simois. From Yeni-cheyr, which is the Sigean promontory, and which commands:an extenfive view of the plain, M. CHEVALIER particularly obferved the Simois, which interfects the plain along the north fide. “ Its waters were then dried up; but the width “and irregularity of its channel, fuficiently demonftrated the “ nature of its devaftations, and its rapidity.” (Ch. II.). The Turks call it Menderé. An.extenfive marfh occupies the ground at the place of its difcharge on both fides, and reaches almoft to the fortrefs called Koum-kaleh. This marfh is taken notice of by Strazso by the name of Yrowwriuyy, the mouth lake. On his way from this place, M. CHEVALIER pafled the Simois near its mouth, and found it to be more than 300 feet broad. In the marfh, on its banks, he obferved certain {mall lakes of frefh and of falt water, and was ftruck with the prodigious quantity of reeds and tamarifks he met with, as he proceeded along the coaft. (Ch. IV.).. He travelled onwards for half an hour, and faw a large barrow, the monument of Ajax, which he examin- ed, as we fhall by and by mention. Having then proceeded as far as It-Guelmes or Erin-keu, he returned, and refolved to af- cend towards the fource of the Simois; and had not proceeded far, when he was fo fortunate as to difcover, to the right, the bed of a fmaller river, at that time dry, and covered with plants and turf. ‘This proved, on a nearer inveftigation, to be the old bed of the Scamander. If Mr Woop had adverted to this, in- ftead of ftill fearching higher up for the confluence of the two rivers, he probably would have given a more rational account than he has done of the prefent ftate of the fcene of the Iliad. AFTERWARDS, when M. CHEVALIER had examined the Sca- mander, its fources, and the fituation of ancient Troy, as already mentioned, he refumed the defign of tracing the Simois ftill higher ; 48 TABLEAU de la PLAINE de TROYE higher ; and went down to its banks, from the village of Arabler, about half a mile to the fouth-eaft of Bounar-ba/bi. The tor- rent being then dried up, he refolved to afcend within its chan- nel, {crambling over trunks of trees and rocks borne down by the impetuofity of the current. (Ch. IV.). He walked for five hours between two chains of abrupt rocks, which border the valley, and came into a plain, with a village at its entry, called Iné or Ené. Here he found that a river difcharges itfelf into the Simois, and that it takes its rife near a village called Bahar- lar, to which he proceeded in five hours journey to the fouth-_ ward, through a rugged and mountainous country. This {tream he found to be the fuppofed Scamander of Mr Woop. Returning to Evé he continued to trace the Simois, now the Men- deré, up to the high mountain, whence he was affured it iffued. This proved to be Mount Cotylus, now called Cas-dabi, the moun- tain of the goofe, from which, mifled by DemeETRius of Scepfis, STRABO makes the Scamander to flow down, confounding it with the Simois. M. CHEVALIER refolved to afcend to the fum- mit of the mountain, which, after being hindered from doing for fome days, in confequence of a great fall of rain, he at laft effe¢ted ; of which expedition he gives an interefting defcrip- tion, particularly of the fublime profpedts he obtained. Ir does not appear that any of the fubfequent travellers I have mentioned, went to the fource of the Simois, or the fum- mit of Mount Cotylus, as M. Cuevaxier did: but Dr SiB- THORPE remarks, that the fituation, where they fuppofed the citadel of Troy to have been, is particularly fteep and rocky, and is girt by the Simois, “ which is now,” fays he, “ entirely “dry: but perhaps the winter torrents may raife it into a con- “ fiderable river. Its banks are fringed with plants, agnus ca- “ ftus, and tamarifk *.”’ Dr * See-his Letter, Appendix, No, V. ; : d ‘ | TLLUSTRATED and. CONFIRMED. AQ Dr Dattaway crofled the Simois three times: 1. On his way from Udyjek-tepé, or the monument of /EsyeTEs; and’ after he had refted during a tempeftuous night at the Chifiliz, built by the famous HassAwn Pafha, formerly mentioned, on the 5th of November he croffed both the Scamander and the Simois, the latter of which the rains had increafed to a confiderable river ; the bed being from forty to fifty yards wide ; though it is fre~ _ quently almott dry, efpecially in the midft of fummer. This was on his way to the village of Thimbrek-keuy, and the temple of A- POLLO Thymbrzus ; which he paffed and defcended to the fhore, and proceeded as far as Cape Berdier ; and after exploring the fhores of the Hellefpont, he returned by fea to Koum-kaleh. Here haying landed, he again crofled the Simois over a wooden bridge, near its embouchure ; (p. 338.); and advancing upwards on the northern fide of that river, he repafled it within a furlong of the Chiftlik of Hapc1 Meumer Agha, at Bounar-ba/bi. (p. 343.). In viewing the fituation of the citadel, where the Simois runs under the rock, he fays, ‘‘ That the divifion of the rifted rock “from the groupe of foreft mountains, does not exceed 150 “yards, and is fcarcely farther afunder at the top, finking as * perpendicularly as an artificial channel.”’ The Monument of AisvEveEs. M. Cuev Avier, as has been faid, began his refearches in Afia at Cape Bada, the ancient promontory of Le€tos. From thence he proceeded to the ruins of Alexandria Troas; his account of which has been minutely confirmed by Dr Dattaway. But though the narrative of both travellers be very agreeable and interefting, we did not before, nor do we now, think it necef- fary to detail the particulars. On advancing, his notice was particularly attracted by Udjek-tepé, a barrow of an extraordi- Vordv. g nary” 50 TABLEAU dela PLAINE de TROYE nary fize, which already has been mentioned *. He had no no- tion at firft that this was the fame with the monument of Asy- ETES. He contented himfelf with meafuring its dimenfions, and enjoying the magnificent profpect from the top of it. Its height he found to be not lefs than roo feet, and its outline to be 400 paces. He remarked it to be of a conic fhape, and quite regular. After his third journey to the Troad, he had no hefi- tation in concluding it to be the monument of As¥ETEs, (Chi TH XIL) Dr Dacraway fays, that “ the tomb of AsvETEs, according “ to PococKE, or, as it is now called, from the adjacent village, “ Udjek-Tepee, is a barrow of extraordinary height and {fmooth * furface, and was the fituation from whence PotirEs, the fon of “ PrrAM, reconnoitred the Grecian camp, and the oppofite ifland “of Tenedos, with its harbour and promontory +.” Five other Tumuli. Arter M. CHEVALIER had examined the new canal of the Scamander, he proceeded, from the place of its difcharge inta - the A’gean Sea, along the coaft, towards the village of Yeni-cheyr, in order to have a nearer view of feveral high mounds of earth, which had attraéted his attention from the top of Udjek-tepé, or monument of AisyeTEs. The firft he arrived at, called Be- fotk-tepe, is not by any means fo high as that laft mentioned. He next came to that, which, upon the map, he has called 4a- tilocht tumulus, not finding any Turkifh name for it, and which feemed to be of the fame dimenfion with Be/bik-tepé. He then proceeded to the village called /eni-cheyr, fill inhabited by: Greeks, and fituate upon the extremity of the famous Sigean promontory, * See above. p. 38, + Mliad, II. 792, feq. TLLUSTRATED and CONFIRMED. 51 promontory, where, juft as he was entering the Church, he faw the Sigean infcription, fo well known to the learned ; and op- pofite to it the bas relief of marble, of the fineft workmanthip, of which Dr CHANDLER has given an exa¢t account ; and there is an elegant engraving of it in lonian Antiquities. Dr Datxiaway, too, faw this bas relief, as well as the Sigean infcription ; which laft, he obferves, is now placed at the door ef a low hut, confecrated as a chapel: and the letters are nearly worn out, the marble having been fo long ufed as a bench to fiton. Mr Liston told me, that the effacing feems to be pre- moted by a drop which falls from the eaves of the chapel. From the top of the promontory M. CHeva.ier had ano- ther extenfive view of the plain of Troy, and faw particularly the mouth of the Simois, as already mentioned ; alfo the Turk- ifh caftle of Koum-kaleh, mentioned by all the fubfequent travel- lers. At the foot of the promontory he remarked two other tu- mult, of which the neareft is underftood to be the monument of ACHILLEs; and the more diftant one M. CHEVALIER fuppofed to be that of Parroctus. Others take it for thatof PENELEUS; the afhes of Parroc ius having been depofited in the fame mo- nument with thofe of ACHILLEs. “ ADVANCING fome furlongs ever the promontory,” fays Dr Datuaway, “we faw the barrow (be/hik-tepe) called the “tomb of AnTILocuus by Straso. On the other fide of the “ village, under the brow of the hill, crowned by half a dozen “* windmills, near the fea, are two {maller tumuli, generally fup- “ pofed to be thofe, one of which is attributed, by the ancient ‘‘ seographers, to the illuftrious friends ACHILLESs and PaTRo- “* cius, and the other to PENELEus the Boeotian.”’ (p. 350.). AFTER remaining fome days near Keum-kaleb, M. CHEVALIER pafled the Simois; and, travelling for half an hour, came to a fifth zumulus of the fame kind with the reft, having a large aper- ture in its fide, which he entered. ‘The monument being de- £2 molifhed yo TABLEAU de la PLAINE de TROYE molifhed from top to bottom, its whole interior ftructure was to be difcerned. This is fuppofed to be the monument of Ajax, and is called by the Turks In-tepée-Gheuleu, the monument of the marfo. tis fituated at Rheeteum, a promontory or tongue’ of land advancing into the plain oppofite to the Sigean promon- tory. (Ch. TV. XTV~). AN Dr Datiaway, after crofling the Simois the fecond time, pafled over an extenfive level of ploughed fields, and Goulu-/ui, a brook, which empties itfelf into the fea near Fn-tepe, or the tomb of Ayax Telamonius. “ This tumulus,” fays he, “ is now irre- “‘ gularly fhaped. Near the top is a fmall arched way almoft * choked up with earth, which was the entrance into the vault, “and over it a broken wall, where was once a {mall fepulchral “ fane called Atantéum.’’ He thinks the whole to be of a much more modern date than the death of Ajax. Dr SisTHORPE, in his letter to Mr Liston, writes thus: “ I “write to your Excellency in hafte, our veflel tofling about op- “ pofite the tomb of Ajax, where it has been juft drove by a “hard gale of wind *.’’ THESE monuments, with the others formerly mentioned up- on the hill of Troy, appear to have made a ftrong impreffion on M. CHEVALIER’s mind ; and many of the Members of this So- - ciety will recolleét, that, in converfation, he ufed to lay great {trefs on them. They are objects very confpicuous and ftriking to thofe who fail along the coaft, near the entrance to the Helle- fpont, as Mr Liston particularly informed me. They feem to have made a ftrong impreffion hkewife on Dr DaLLaway, who, on viewing them from Ha/lile/i, near the village of Thimbrek-keuy, ({p. 340.), remarks, that the fucceflion of the five tumuli, under the diftant horizon, tend more than any other proof to afcer- tain the Trojan war. He fays afterwards, (p. 349.) : “ Of all the ‘* proofs advanced by M. Cuevatier, the tumuli, fo connected “ with * See Appendix, No. V. ILLUSTRATED and CONFIRMED. Fie! ** with the Sigean and Rheetean promontories, and the outpofts “ of the Grecian camp, are the moft fatisfactory. The fite is “ likewife confirmed by four others, which, to whatever heroes “ they may be conjecturally attributed, with no additional “ weight to the argument, give a certain degree of internal evi- *“ dence, and afcertain the fcene of great military tranfactions, “ or vicinity to a large city.” The Valley of Thymbra. Own quitting the monument of Ajax at the Rhcetean promon- tory, and after taking a view of a {mall adjacent harbour called Karantik-limani, the fbut haven, M. CHEV ALieR continued his journey to the village of Jt-Guelmes or Erin-keuy. It appeared to be of no confequence to the end in view to proceed in that direGtion any farther, and he returned, in order to trace the cir- cumference of the great plain. On his way back, he foon de- fcended into a delightful valley, called Thimbrek-deré, the valley of Thimbrek, or Thymbra. On beginning to afcend towards the fource of a rivulet, which runs through it, he was {topped on its left bank, oppofite to the village of Halileli, by a heap of ruins, among which were fome bas reliefs, columns, capitals, entablatures, and infcriptions. He took them for the ruins of the temple of APpotLo Thymbrzus, and:copied fome of the in- fcriptions, which are now publifhed in the third volume of our TranfaGions. : Mr Luston faw thefe ruins, and told me that they are very confiderable; fome fragments of marble ones’ ftill remaining. - Every year the inhabitants carry pieces of thefe to place over the dead in the adjoming cemetery, near the ruins of an old mofque ; fo that foon nothing will remain but the large pieces. M. CHEV ALTER, in his map, has, in Mr Liston’s opinion, pla- ced 54 TABLEAU de la PLAINE de TROVE ced them too far up, They are at leaft half a mile from the village of Hali/eli, on the oppofite fide of the rivulet. Dr Dat- LAWAY has piven an elegant engraving of them, and fays, that he “ paffed the village of Lhimbrek-keuy, and a dilapidated mofque, “with a cemetery full of parts of fluted columns and cornices, “ fet up as memorials, the probable fite of the temple and city “facred to APoLLO Thymbrezus.” (p. 331.) The Promontories. M, CuEvatier agrees with all preceding travellers, in holdifig the promontory of Sigeum to be at the modern village of Yenr- cheyr, That of Rhoeteum he has no doubt in fixing at Jn-tepée- Gheuleu, near the harbour called Karanlik-limani, where the barrow, fuppofed to be the monument of Ajax, is {till to be feen. He concludes, with the greateft reafon, that M. d’ANVILLE and Mr Woop are miftaken in placing the Rhcetean promontory at Cape Berbier, which, according to the latter, lies about 12 miles from the Cape of JYemni-cheyr or Sigean~ promontory. (Ch. XUI.). He was at the pains to meafure the diftance be- twixt what he thinks the two promontories, and found it to be 3000 fathoms, which agrees with PLiny’s account, who fays it is 30 ftadia. M. Cuevarier thinks Strrazso miftaken when he reckons it at 60 ftadia. Dr Datiaway obferves, that “ the entrance into the great “plain is formed by the Sigean promontory, and that called “ Rhoeteum, about four Englifh miles afunder, through which “ the two rivers Simois and Scamander at length took an united “‘courfe. Between thefe promontories the Grecian fleet was “drawn up on dry ground, and probably remained fo during “ the whole war.” (p. 336, note.). ‘ Woop,” adds he, “ mi- “takes Cape Berbier. for the Rhoetean promontory, which “ STRABO ILLUSTRATED: and .CONFIRME D. 55 * STRABO makes to be Go ftadia, SoLINus, 26, and PLINY, 30, “ from the Sigean; the latter is the true diftance. (p. 337. note.). “ The city of Sigeum covered the fhore between the tumulus and “a bay, in which I anchored for a week, (Nov. 1795), and. re- “ furveyed the whole with attention.” Some Miftakes admitted, and corrected. AFTER what has been ftated, and thus confirmed by fuch re- {pectable authorities as have been adduced, no reafonable perfon can now doubt that M. Cuevarier has given a true and di- ftinct account of the prefent ftate of the Troad. But as he has had occafion to offer various hypothefes, and to make various obfervations and inferences, during the courfe of his Effay, it is not to be wondered at that a few miftakes fhould have been committed, and fome unneceflary animadverfions introduced. The author was himfelf fenfible of this, as appears from the late letters I received from him*. In the notes, too, which accom- pany the Englifh verfion, I now perceive there are fome errors,, which I wifh to take the firft opportunity of corre¢ting. The Map. M. CHEVALIER, upon information being communicated to: him that Mr Liston, as: well as Mr Hawkins *, had found fome inaccuracies in his map, anfwered as follows: “ There is “ nothing I defire fo much as to have any miftakes, that have “been committed in my map, rectified ; and I moft cordially “ give my aid to every improvement of which that performance cee 1S; * See his firft Letter, Appendix, No. VI. 9 \ s6 TABLEAU de laPLAINE de TROYE “is fufceptible. But I will venture to affure you before hand, “ that the alterations which may be made will not extend to the ‘“* monuments effential to the underftanding of the Iliad; fuch “as the fite of ancient Troy, the fources of the Scamander, “the tombs of the warriors, the promontories, &c. All thefe ‘“‘ points are fixed relatively to one another, with a degree of “ precifion fufficient to prevent any change that may be made “upon them from materially affecting my work. As to mo- “‘ dern monuments, fuch as Alexandria Troas, &c. I own that I “did not think it neceffary to pay fuch a fcrupulous attention “to them. ‘The line of the coaft was done with the greateft “ exacimefs, as well as the mouth of the Hellefpont and the “ifland of Tenedos ; and therefore I fufpect that upon this the “new map will make no alteration*.”’ Dr DaLtaway obferves, that M. CHEVALIER has defcribed the artifical canal in his map of the Troad as having much too {traight a direction. — It is conducted round the hill upon which the Chiftlik of Hassan Pafha is built. (p. 347.). The Monument of ius. AsouTt an hundred paces up the Simois, from the place where it is joined by the old bed of the Scamander, and near the place where the city called New Ilium is fuppofed to have been fitua- ted, M. Cuevatter had obferved the ruins of a bridge, which - had been built of hewn ftone, and of exquifite workmantfhip. Fronting thefe remains, on the right of the river, he faw a fort of rifing ground, which he took to be a demolifhed barrow. This he afterwards fancied to be the monument of ILus, and probably the fame with HomER’s Sewopos wediow. In thefe con- jectures, * See Appendix, No. VI. ILLUSTRATED and CONFIRMED. 57 jectures, however, he was, after a converfation with Profeffor HEyYNE, convinced he was miftaken; and readily admitted, that his whole XVIth chapter, which is upon this fubjeA, is good for nothing™. After that converfation, alfo, he was difpofed to think that this barrow might probably be that mentioned by Homer, (Iliad, VII. 337.), which was to be deftined as a com- mon one for the warriors who had fallen in battle ; c#eirov éy Té0in. Situation of the Grecian Camp. Cuarrer XIII, where the author treats of the fituation of the Grecian camp, now appears to me to require much amend- ment. That the camp was fituated fomewhere betwixt the Si- gean and Rhcetean promontories is generally agreed ; but that it occupied the whole fpace or line of coaft in that interval, as M. CuHevatier has fuppofed, cannot be admitted. This would have made it neceffary for the camp, which confifted of the tents, with the fhips drawn out upon the dry land, as was the ancient cuftom, to occupy the place on both fides of the mouth of the Simois, which M. CHEVALIER, and the other travellers, as well as StrRABO, defcribe as being an extenfive marfh. M. CHEVALIER was evidently aware of this inconvenience ; and therefore fuppofes that the Greeks, in the courfe of the war, frequently fhifted their ftation ; and that, at laft, in the tenth year, during the fummer feafon, they encamped, in full force, at the mouth of the Scamander, or Simois, for, at the mouth, they were united. | I REGRET that, in the note, I have endeavoured to fupport this idea, by fuppofing, that “ the Scamander, even in the fum- VoL. IV. ) * mer, * See his Letters, Appendix, No. VI. 58 TABLEAU de la PLAINE de TROYE “ mer, when the Simois was dry, continued to convey its pure “ and perennial, though lefs copious, ftream through the midft “ of the camp, in the fame channel through which the Simois, “ after having joined it, difcharged its winter torrents.” (p. 104.). Ever fince I read Mr Heyne’s Effay, I have given up this hy- pothefis, and willingly accede to his idea, which fuppofes, that the camp only ftretched on both fides towards the promontories Rhoeteum and Sigeum ; and that on the north-eaft it extended no farther than the Simois*. In this way the whole is rendered clear, and free from every objeCtion. This, however, makes nothing againft M. Cuevaxter, but that he was not fo fortu- nate in his hypothefis as Mr Hreyne, on this-occafion, which I am fure he himfelf would have been the firft to admit. Mr Heywne’s notion of the fituation of the camp is confirm- ed by Dr DaLiaway ; and the more ftrongly, as the latter does not appear to have feen the former’s Effay on the Topography of the Iliad, or to have known any thing of the coincidence of Mr Heyne’s opinion with his own. In a very diftinct note on this fubjeét, (p. 336.), he obferves, that “ between thefe pro- ““montories the Grecian fleet was drawn up on dry ground, “and probably remained fo during the whole war.” And he concludes the note thus: “ The purfuit of the Trojans by | ““ AcHILLES, fixes the fituation of the Grecian camp between “the confluence of the rivers and Sigeum, for they retreated “‘ over the Scamander to gain Troy, and he kills many of them <* (One Piven. Of Jome other Miftakes, and erroneous Critici/ms. THE author, in fpeaking of the two tumuli near the Sigean promontory, (Ch. IV. XXI.), fays, that “ he was informed by _ “a Greek inhabitant of the place, that the name given to the ce more * See Appendix, No. III. Se ee ee ee ye - ¢ a. ILLUSTRATED and CONFIRMED. 59 *“ more confiderable of the two was Dios-tapé, which he inter- “ prets the divine Tomb.” Mr Liston obferved, that the inhabi- tants {poke of both monuments by the appellation of dtheo tepé, which, in their language, has no other meaning than the two tombs. He therefore concluded, that M. CHEVALIER had been deceived by the fimilarity of the found. This is alfo noted in Dr Dattaway’s book, with an affertion, (but not of Dr DAL- LAWAY himfelf), that the miftake proceeded from M. CHEva- LIER’s ignorance of modern Greek ; which I have the greateft teafon to believe to be without foundation. In examining carefully the furface of the rock of Ba/li-dahi, M. CuHeva.ier thought he “ diftinguifhed foundations of an * cient buildings, the mafonry of which had affumed the con- “ fiftence of the rock itfelf.” Mr Liston, on a narrow infpec- tion, was convinced that nothing could be difcerned but the real fubftance of the rock, which is indeed rough, of a chalky ap- pearance, and, at firft fight, feems as if there was mortar adhe- ring to it. He brought away a fragment of it, which I have here in my cuftody ; and the gentlemen prefent may judge. ~ Tr feems furprifing that there fhould be a total difappearance of every ruin or veftige of a building, to mark the fite of fo fa- mous acity. STRasBo, however, gives a good reafon for this, as follows: ‘Ore yao txrerogSyuivev trav nvtrw worEwv, ov rertws OF nureorocmevar, rovrys 0’ ex Badeuy CVT ET CCE LEVIS, ob AiJos wevrEs Gig Ty enciveay avrg mereveydnony. Aeyosavanra yovy Qaot cov Mirv- Anvoiov ex rav excirev Aidov ro Yivyeioy exrevyioos. (L. XIII. p. 8g5.). For when all the cities around were laid wafte, but not entirely de- _ molifbed ; and while this one was totally overturned, all the ftones were carried off from it to rebuild thofe others. Accordingly, they Jay, that ARCH EAN ax of Mitylene with the flones taken from thence fortified Sigeum. Dr Dautaway, fpeaking of the city of Ilium, once fituated near the junction of the Scamander and Simois, and which owed its origin to ALEXANDER and Lysimacuus, fays, h 2 (p. 388.)s 60 TABLEAU de la PLAINE de TROYE (p. 338.), “ It excites no wonder, that, after fo long pofleffion of “it by the Turks, not a ftone fhould remain ; yet fome con- *“‘ tend againft the exiftence of Troy, becaufe no veftiges were “ difcoverable when ALEXANDER founded the fecond city, “ whilft they admit the latter fact equally unauthorifed by pre- “ fent appearances *.” | In a paflage quoted from HERopotus, in which an account is given of the march of XERxEs’s army from Sardes to Aby- dos, the expreflion—77) ldnv dé rAaBayv &g aoiseeny eects is tranflated advancing towards the left branch. of Mount Ida, different from the common way of rendering it, having Ida on the left. As this interpretation is difapproved of both by Mr Heyne and Mr Bryant, I have no inclination to difpute the point with fuch learned antagonifts, provided they can make it appear, that Xerxes could and did proceed, with Ida on his left. ‘“‘ Ida,” fays Mr Heyne, “ has many branches and ridges. ‘The army “ may have gone round one of thefe outfkirts of the mountain *“‘ approaching towards the fea, in fuch a manner as to leave it “ on the left T.” ; From M. CHEVALIER’S letters, it appears that he was fen- fible that he had at times introduced unneceflary or inaccurate reflections ; of which kind are thofe in Chap. VI. refpecting : travellers * See, in Mr WaKEFIELD’s letter to Mr Bryant, (p. 11, 12.), a remarkable fact refpe€ting the total difappearance of Flaxford Church, about five miles from Nottingham. + I oBSERVE, too, that this notion is fupported in a paper in the fixth volume of Commenit. Soc. Reg. Scient. Gotting. Ann. 1783, 1784; entitled, Heroporti ac . Tuucypipis Thracia, Jos, CuristopH. GATTERERI: with a map, where XER- XEs’s march is traced accordingly. Mr Bryant enters into a long difcuflion upon the fubject, through which I have -no inclination to follow him now, nor fhall I afterwards, I fuppofe, when I come to take more particular notice of his Ob/erva- tions; but will freely confefs myfelf refponfible for the whole blame of this miftake, having fuggefted the culpable interpretation to M. CHEVALIER, on my firft reading his paper; and I am anxious that he fhould here be cenfured only for paying fo much deference to my judgment as to introduce an equivalent expreffion into the French original. ILLUSTRATED and CONFIRMED. 61 travellers of high diftinCtion, and the priefts in the early ages of Chriftianity : both of which he defires may be ftruck out in a new edition. The former, I obferve, has already been omitted ' in the German tranflation ; and the latter, which begins thus : * But why did not the priefts of the lower empire demolifh “ thofe monuments ?”’—has given great offence to, and has been cenfured and reprobated with uncommon afperity by, Mr BrYANT, in his Obfervations. (p. 42. 43.). Of the Notice that has been taken of STRABO. In giving a defcription of the Troad, it was neceflary to ad- vert particularly to what a geographer fo refpectable as SrRABO has faid upon that fubje@t. This M. Cuevaxier has done in his VIIth and VIUIth chapters. Srraso derived the greateft part of his information, relating to the Troad, from DEME- TRIUS of Scepfis, who, though he had his refidence in thofe parts, was evidently deceived refpecting the true fource of the Scamander, and has led StrRaso into the fame error. They fuppofe that this river takes its rife in Mount Cotylus, far be- yond the place where ancient Troy was fituated. M. CHEva- LIER has fhewn this to be a grofs miftake ; and it is evident that it was likewife the chief caufe of Mr Woon’s errors. STRABO faw and frankly admitted the difficulty of reconciling this with HomeEr’s account in the XXIId book of the Iliad, where the: two fources are explicitly mentioned, the one a hot and the other a cold f{pring, and both as being in the vicinity of the, Scean Gate; but StrAzo has not been fuccefsful in his attempt to obviate this difficulty *. | * Mr Heyne, in a note on the German verfion, (p. 85.), as well as in the pre- face to the fame work, (See App. No. I1.), thinks it evident that Demetrius fet out on a wrong hypothelis, in confequence of mifunderftanding a paflage of the Iliad, (XII, 19.). This paffage I had quoted and explained in a note. (p. 59. of the Eng- hih Tranflation.). 6. TABLEAU de la PLAINE de TROVE M. CHEVALIER being clearly convinced of this error of De- METRIUS and STRABO, and {truck with the confufion to which it has given rife, has perhaps fhewn too great a degree of fufpi-- cion of the latter, in refpect to fome other paflages of his ac- count of the Troad ; and may have cenfured him fomewhat too keenly. Wherever this feems to be the cafe, Mr Hrywe, in his notes on the German verfion, has taken the part of the ancient geographer, to whom fcholars have been fo long accuftomed to look up with the greateft refpect: and if I were to publifh a fe- cond edition of the Englifh, I fhould certainly, in confequence of carte blanche given by the author *, avail myfelf of Mr Hryne’s affiftance to obviate, as far as poffible, every objection . made to STRABO, except upon the great and fundamental error ref{pecting the fource of the Scamander. For this I take to be altogether untenable. “In general,” fays Mr Hryne, in one of his notes, “ nothing can be objected again{t Srraso, but in “the fingle cafe where he has allowed himfelf to be feduced by “ DemeETRIvS, and changed the fources of the Simois and the “ Scamander.” M.'CHEevaLiEr perhaps fhould have been fatis- fied with gaining this point. But though it fhould appear, that the author or his editer had, in one or two inftances, mifconceived or mifinterpreted STRABO, where the text is acknowledged to be obfcure, not yet having been properly elucidated by any able editor or commen- tator, this furely would furnifh no argument for fetting afide M. CuEvaALiEr’s account of the Troad, founded on the author’s actual obfervation, fupported by fo many fubfequent refpectable travellers. In the VIlIth chapter he has, with due refpect, ta~ ken occafion to quote and comment upon fome paflages of. STRABO ; from which it is clear, that the plain of Troy has not changed its appearance fince the days of that learned writer. The * See his Letters, Appendix, No. VI. ILLUSTRATED and CONFIRMED. 63 The opening of ACHILLES’s Monument. Tue XXIft chapter contains a number of pleafing remarks on the fubject of the ¢wmuli to be feen on the fhores of the Hel- lefpont ; and any perfon of fenfibility muft, on the perufal, feel his mind affected with a foothing, though folemn, fenfation ; and be ready to confefs, that M. CuEvazier has there exprefled himfelf in a moft elegant and interefting manner, Inaccuracies, however, and redundancies, may now and then be perceived, fome of which were pointed out to me by Mr Liston, and they ought to be corrected in-a new edition. df Ir appears, in particular, that M. CHEvaLiER had not recei- ved very accurate information refpeGting what was found in the tomb of AcHILLES, in confequence of the operation of digging into it, which had been performed after his departure from Con- | ftantinople, by the direCtion of Count pz Cuorszut Gourrier, the French Ambaflador. He had been told, that towards the centre of the pile were found “ two large ftones leaning at an “angle the one againft the other, and forming a fort of tent, ** under which was difcovered a {mall ftatue of M1inERvA, feat- “ed in a chariot with four horfes ; and an urn of metal filled “ with afhes, charcoal, and human bones; which urn was encir- “cled in fculpture, with a vine branch, from which were fuf- “ pended bunches of grapes done with exquifite art.” THERE does not appear to -have been any foundation for the figure of a chariot. ‘There were however fome curious reliques found there. Mr Liston faw at Conftantinople the very per- fon who had been employed to conduct the operation of dig- ging ; and who had retained fome of the fragments in his own euftody, which he offered to difpofe of. It appears from a let- ter, publifhed in a note by Dr DaLiaway, and giving a very particular account of this affair, that this perfon was the Signiar SOLOMON 64 TABLEAU de la PLAINE de TROYE Sotomon GHorMEZANO, fon of the late French Conful. After immenfe labour, he at laft difcovered the place where the re- liques were depofited. When collected, they filled a large cheft. He delivered them to his employer M. Cuorstu1, who repaid his trouble with thanks only: but he referved feveral fpeci- mens, which he afterwards fhewed and explained, when the Count was no longer formidable. Of thefe a lift is given in the letter ; fuch as, pieces of burnt bones; pieces of a metal vafe ; charcoal of vine branches ; a piece of mortar and ftone ; a piece of metal of a triangular fhape; pieces of very fine pottery, well painted with wreaths of flowers of a dark olive colour, &c. ‘An account is then given of the ftrata of earth dug through. Dr Datuaway, in the text, fays, that “ extreme age, and the “ preffure of the ground, had crumbled into atoms of ruft all “the metallic fubftances. The urn or vafe, M. Fauvat, an “ ingenious artift, now refiding at Athens, received from M. “ CHOISEUL in its decayed form, and made a model from it, “ which has been exhibited to feveral conoiffeurs, as much to “ their furprife as fatisfaction.” Dr DatLaway adds: “ And “* the godde/s, with her chariot and four horfes, feems to prove that “‘ the Troad continues to be the land of invention.” Yet it is very remarkable that Mr Hawkins, who faw M. Fauvat at Athens, exprefsly fays, that this laft mentioned gentleman de- nied the exiftence of an urn, but {poke of a {mall bronze image of MINERVA, of which he fhewed them a caft. ‘ At Athens,” fays Mr Hawkxuns in his fecond letter to Mr Liston, “ we fell “in with M. Fauvat, a very ingenious artift, long in the fer- ** vice of M. DE CuHoisEuL, who affured us, that M. CuEva- * LIER’s account of the goblet, difcovered in the tomb of AcuIL- “« LES, is perfectly fabulous. It originated, it feems, from the “ fragment of a-{mall bronze figure, which, when he had clean- “fed, and put together, proved to be a very curious image of “MINERVA. He fhewed us a caft which he had made of it in * platter, ILLUSTRATED and CONFIRMED. 65 ** plafter of Paris *.” According to M. Cueva ier, then, there were both an urn:and a figure of Minerva; according to Dr DALLAWaAy an urn, but no figure or ftatue; and according to Mr Hawkins a fmall ftatue, but no goblet or urn. It fhould feem, therefore, that this affair ftill ftands in need of further elucidation f. But whatever may be thought of thefe barrows; “ fuppo- “ fing,” fays Mr Heyne, “ that M. CHEVALIER was miftaken, “‘ and that the eminences were not at all tombs, the main point * yemains what it was. The fources of the Scamander are near “ Bounar-ba/bi, and in that neighbourhood is the fite of Troy +.” Of the Objections made by Mr Bry ant. Mr BryAnt, whofe name has been long fo well known in the learned world, has, in the warfare he has thought fit to wage with M. CHEvALieEr, been, no doubt, pretty fuccefsful in feve+ ral affaults, where the latter has laid himfelf fomewhat open ; (as we have admitted to be fometimes the cafe) ; but he has to- tally failed in obtaining any thing like a decifive victory. Tuis learned gentleman having, thirty years ago, embraced an opinion, not a new one indeed, but, I believe, almoft general- ly efteemed very extravagant and paradoxical, that no Trojan war, fuch as forms the foundation of the poems of Homer, was Voz. IV. mh i . ever * Appendix, No, V. +In the above-mentioned letter, quoted by Dr Datzaway, an inftance of a - very ftrange pitch of arrogance is recorded. It is there faid, that ‘‘ when the bar- “ rows were clofed up, Count Cuotsgut canfed a fheet of lead to be placed on the “ bottom, infcribed, Oxurage fait par le Comte DE Cuo1sEuL GourFIER, /’an 1787. $ Conciusion of his preface to the German verfion. See Appendix, No. I, 66 TABLEAU de la PLAINE de TROYE ever carried on *, and that even no fuch city as Troy ever exifted, had employed himfelf occafionally, during that long period, in an attempt to eftablifh the truth of this odd opinion. The fub- jet had grown a favourite one ; and the author feemed to him- felf to be upon the point of achieving his great undertaking ; when M. CHEvALier’s performance appeared. This obliged him to ftop fhort for a little, and to paufe. He took his refolu- tion. Encouraged, by obferving fome flips committed by an author, as yet raw in the art of fyftematizing, it feemed more eligible to him to endeavour to reduce the obftructing fabric toa heap of ruins, than to demolifh and fupprefs his own occafional labour of thirty years. ‘The avowed object, then, of Mr Bry- ANT’s pamphlet, is to fet afide M. CHEVALIER’s De/cription, as unfound and fanciful. I once indeed heard, that, after the Ob- Jervations had come out, the author met with fome travellers, who affured him, that M. CHEVALIER’s account of the prefent ftate of the Troad was a fair and true one; in confequence of which, it was reported, that he had renounced his heretical opi- nion upon the fubject, and was to fupprefs his Differtation. This I was very glad to hear, as I thought the fo doing would have redounded very much to Mr Bryant’s honour. But I was foon convinced that this information was premature, by my re- ceiving a printed copy of the Di/értation, in a prefent, from the learned author himfelf ; in the perufal of which, one, every now and then, regrets (at leaft this was the cafe with me) that Mr BryAnrT had ever undertaken fuch a toilfome inveftigation, em- ployed fo much learning, and wafted fo much ingenuity, which the appearance of M. CHEVALIER’s work, thirty years fooner, might have prevented ; and perhaps ‘might have engaged thofe very talents to affift in fupporting and illuminating a fyftem, which * See Mr Mactaurin’s Differtation, to prove that Troy was not taken by the Greeks. Vol. I. p. 43, &c. Lit. Cl, of Tranfaétions of this Society. “ILLUSTRATED and CONFIRMED. +67 which they have now been employed to puzzle, perplex, and obfcure. After all, if the learned veteran had feen Mr Heyne’s _Effay on the Topography of the Iliad*, and Dr Da1nLaway’s late publication, in both of which M, Cueva ter is fo ably fupported, I imagine he would have been deterred from publifh- ing his grand {ceptical work, notwithftanding the great labour it’ had coft him. ; Mr Bryant, in the introduction to his Ob/ervations, charges the author and his editor with indulging in fevere critical cen- fure again{ft Dr Pocockr, Mr Woop, Dr CHANDLER, and StrRaA- Bo. But I can’t help thinking that the accufation is too ftrong- ly ftated. I hope it was not with an intention to create an early prejudice in the mind of the reader againft the perfons animad- verted upon, and in favour of what was to follow. WitH refpect to the firft of the above-mentioned authors, M. - Guevatter had faid, that “ his account of Troas, though full “ of errors, and in every refpect obfcure, yet. proved to him a “ very ufeful guide in his refearches.’’ (Ch. VI.). He, no doubt, found confiderable obf{curity, and a number of errors, in Dr PococKe’s account ; and where was the harm in faying fo? But Mr Bryant, in his complaint that Dr PococKe has been un- juftly accufed, does not fubjoin the qualifying claufe of the fen- tence, viz. that “‘ notwithf{tanding thefe defects, the work pro- * ved a very ufeful guide ;” but he referves this latter part of the expreflion, till he find an opportunity of introducing it with more effect, and more fitly for his own purpofe afterwards. I am not fure if this way of difmembering expreffions, and expo- fing them in disjointed morfels, fhould be confidered as a very fair ‘mode of attack. If'M. CHEvaALier was convinced that Dr Pococke was mifled by Strano, and regrets that he did not rather “ truft to his own obfervation, which probably would 42 ** have * See Appendix, No. III. 6$ TABLEAU de la PLAINE de TROYE *‘ have brought him to agree with Homer,” I cannot perceive any very fevere cenfure in this: On the contrary, M. CHEva- LIER finds out, and adds a very good excufe for PococKkE, which is, that he could not, at that time, have the afliftance of a geo- metrical apparatus in his obfervations, as it was then hazardous to produce any fuch to the view of the Turks. On other occa- fions, M. CHEVALIER pays compliments to Dr PocockE, calling him, in one place, “ that excellent traveller,” infomuch, that he appeared to me to have even over-rated his merit. In a note, therefore, (p. 100.), I have ventured to fay as much, in as far as related to the art of compofition. For, on reading Po- cockE’s travels, I certainly thought him very deficient in point of arrangement, and very confufed in the communication of his ideas. This, however, was exprefled with all due defe-. rence to his veracity, which I believed to be quite unim- peachable. But, if it will give any fatisfaction to Mr Bry- ANT, I am ready to admit, that I may have been miftaken in thinking Dr Pococke a confufed and inelegant writer. And yet the late Mr Gipson, whofe acutenefs nobody will deny, when he pays a compliment to Dr Pococke’s plan of the feven hills of Conftantinople, adds, “‘ that this traveller is feldom fo fatisfactory.”” As to the manner in which Mr Woop is treated, it will no doubt feem very difrefpectful in the eyes of thofe who are dif- pofed to believe in his doétrine concerning the fource of the Scamander; but to M. CHEva.ier this appeared fo palpably untenable and abfurd, and he was fo confcious of his victory, that he has, no doubt, purfued his triumph with a great deal of vivacity and pleafantry. Where Mr Woop appeared to have merit, it has been allowed him; but becaufe he viewed the ' Troad erroneoufly, Mr Bryant thinks it inconfiftent to admit that his defcription of the coaft is exact; and fmartly fays, (with what ILLUSTRATED and CONFIRMED. 6g what reafon I leave others to judge), “ a mah fo erroneous, and “* fo exact, was never before feen.” Dr CHanD_eR, in one paflage, is blamed for giving his rea- ders too much credit; but a good feafon for this is affigned in. the note. In another place, he is noted as having once inadver- tently {poken of the rivers, repugnantly to his own right notion of them. I have not had time to examine what foundation M. CHEVALIER had for this remark. Perhaps it might as well have been fpared. I find it is omitted in the German edition: very probably at the author’s own defire. Of Dr Cuawp er, M. CHEVALIER {peaks elfewhere with the greateft deference and re- fped&t ; and I queftion, if Dr CHANDLER will thank Mr Bryant for coming forward as his champion, where he had not himfelf obferved any antagonift on the field. Ir is furprifing that Mr Bryant, in his zeal for the reputa- tion of Srrazo, did not perceive that he himfelf is as guilty of rejecting the teftimony of that admired geographer as M. CHE- VALIER, when it happens to difagree with his own ideas. An inftance of which we find in his Differtation. (p. 44.). “ Of “Troy,” fays he, “there is no fign: no remainder: nor was “ there ever any upon record.”—“ Srraso endeavours to give a ** reafon for this: but I believe that it will not be deemed {atis- “ factory.” And fo he produces the paflage which we had occa- fion to quote above. (p. 59.). Mr Bryant employs the firft three pages immediately fuc- ceeding his introduction, in endeavouring to prove that the city of Troy, as defcribed by Homer, muft have been much nearer the fea than the fituation affigned to'it by M. CHEVALIER, which is afferted to be contrary to the very evidence of the poet him- felf. I am glad I have it in my power to give a very fhort, and, I think, a very fatisfatory anfwer to this objection ; and I feel tke more fo, becaufe Mr Bryant’s arguments have, in this par- | ticular, 70 TABLEAU ‘dela, PLAINE 2eOTROYE ticular, brought over to his fide a very learned and intelligent Reviewer in the Briti/b Critic, (May and June 1797); infomuch that, after combating Mr Bryant fuccefsfully in the other — parts of the Obfervations, he at laft feels himfelf under the ne- ceflity of feeking for the fite of Troy farther down the plain, in which I am forry I cannot go along with him. The anfwer al- luded to is furnifhed in a few-words by Dr DaLLAway; and coming from one who has been upon the ground, muft have more weight than any thing which could be faid on the fubje& by a perfon who has not had that advantage. ‘‘ The diftance “‘ from the Grecian camp to the fite of Troy,” fays this accurate obferver, ‘‘ has fupplied thofe who contend againft its exiftence “ with many plaufible objections. It is, however, certain, that “the prefent village of Koum-kaleh is fituate on a fand-bank “ more than a mile in extent, which will reduce the diftance, ‘*‘ fuppofing it to be an accretion from, the Hellefpont, to lefs “ than eight Englith miles from Bounar-bafli, where the Sczan * Gate once ftood. The advanced works, both of the Greeks “and Trojans, leffened the intermediate fpace.. The diftance of “ the moft advanced rank of fhips from the fea is not mention- ‘ed ; perhaps we might not be far from the truth in fuppofing “it half a mile, anda quarterof a mile farther from thence to “the fea. Allowing the firft circumftance of the accretion at “ Koum-kaleb, and the Grecian camp having been advanced in- “ to the plain, the diftance. of Troy as, perfectly reconcileable “‘ with every incident mentioned’ by Homer., It is likewife evi- “ dent from the circumftances of. the wat. Had the city, been, “ very near, the firft work,of) the Grecians.muft have been a “ {trong fortification to prevent. fudden, attacks; without it, “ their deftru€tion muft be inevitable. Befides, there had not “been a, theatre, large’ enough for. the actions) of the war.” (p. 336,.337+)s | Mr ILLUSTRATED and CONFIRMED. 71 Mr Bryant afterwards, (p. 14.), argues from a paflage of Ho- MER, (Iliad, XX. 216.),—érel aw Tasos ion Ey wedia wewoAsso,—that Troy muft have been fituated in the plain, much nearer the fhips than M. CHEvALigeR imagines. To this Dr DALLAWAY alfo gives the following fatisfactory anfwer: “ The moft eleva- ““ ted ground on the edge of a precipice was the Acropolis, other- *“ wife called Pergamus, (Iliad, IV. 507. V. 460. and XXIV. “ 4o00.). Ilion was lofty enough to be called windy, (paffim), yet “ it was lower than Pergamus, (XXIV. 700.) ; fo that it is once -* faid to be in the plain, & wediw, (XX. 216.), as ftanding at the “ head of the plain on an eafier acclivity, and being lower than “ the mountains of Ida. It is, notwithftanding, incontrovertible, “ that Troy ftood on the afcent, (VI. 74. XXIV. 390.); and the “ éeiveoe, which was without the town, has the fame epithet wr- “ dy, (XXII. 145.), from its unfheltered fituation. The wall ex- “ tended only in the front of the plain, the natural fortification “of cliffs above the Simois rendering its continuance unnecef- “fary. Mr Bryant lays much ftrefs on the expreflion & wedia, “ which might have been ufed comparatively, and in contradi- “ ftinétion to higher acclivities, and not pofitively.”’ (p. 349.)- Wuat Mr Bryant fays of the diftance between the promon- tories, the fituation of the Grecian camp, and of the Sewouds re- ‘Bio; (p. 4. to p. 13.); alfo his criticifms relating to SrRaso, and upon a paflage of HzeRopotus, (p. 15.—28.), do not here require a particular anfwer or difcuffion, after the conceflions already made, and the amendments which have been propofed. In the cafe of a new edition of M. CHEVALIER’s Treati/e, it is admitted that feveral of Mr Bryant’s remarks might furnifh affiftance in the corre€tion of fome errors and inaccuracies, and would merit a tribute of praife to the learned author’s acute- nefs ; but they can have no effect in fubverting the great and effential articles of M. CHEVALIER’s inveftigations and difcove- ries, ar Nor 72 TABLEAU de la PLAINE de TROYE Nor will I enter any further into what is objected to the ac- count of the Scamander, taken from the diminutive fize of the river; enough having been already faid upon that fubje& to convince any unprejudiced perfon that the ftream, which has its fources at Bounar-ba/bi, and which has, been explored and defcribed by other refpectable travellers, as well as M. CHEvaA- LIER, anfwers perfeétly to all the defcriptions and hints to be found in the Iliad ; allowance being always to be made for the poetic way of reprefenting fuch things*. Enough too has been already faid concerning the tombs. THE pafflage in the defcription, where M. Cnevniene has expofed himfelf moft to the power of Mr Bryant, is contain- ed in two paragraphs in the Vith chapter, where CLEMENS Alexandrinus is referred to, and where the priefts of the low- er empire are mentioned. The obfervations there made are evi- dently ill digefted, and rafhly thrown out. This the author has frankly admitted, by dire@ting them to be totally rejected in the cafe of his book’s being reprinted +. But ftill this does not in the leaft affect the material parts of the Treati/e; and fuch diminutive or partial victories as this will fcarcely entitle Mr Bryant to the honour of an ovation, far lefs to the glory of a triumph. Mr Bryant, I find, willingly allows the Jie and the edi tor fome praife for exploding the idle notion of Hector’s flight three times round the city of Troy ; and fupports them in their endeavour to fhow the abfurdity of fuch a fuppofition. At firft I was afraid there might be fome fort of decoy in this, fome contrivance, like that of the wooden horfe, for deftroying us ; efpecially as this was a quarter (—i9« PLAN Ap Bares est KOAGS, HOb émbOgopnoy earaero resyos—) where I never had felt very bold, having {till had my doubts about the poet’s acceptation of zegi. But * See Mr Heyne’s Preface, Appendix, No. I. See Appendix, No. VI. “ILLUSTRATED and CONFIRMED. 73 But I was foon convinced that Mr Bryant had no treacherous ' defign in making this conceflion; and the hypothefis having al- fo the {trong fupport of Mr Heyne*, there is now good reafon to be confident that it is well founded. M. CHEVALIER, in the beginning of his XIIth chapter, had remarked, that Mr Bryant has endeavoured to prove “ that “ the Greeks were miftaken in fuppofing thofe to be the tombs “ of heroes, which were in reality confecrated mounds.” This obfervation, it feems, was of too general a nature. Mr Bryant meant what he faid:to be taken in a limited, not a general, -fenfe ; and thinks himfelf much injured by this mifreprefenta- tion. He wifhes, therefore, that M. CHEVALIER had paffed him by unregarded ; and in this. with I heartily concur: for I am fure M. Cuevatier will fincerely regret that he fhould have written any thing that could be conftrued into a defign to in- jure Mr Bryawt’s reputation; which I am as much convinced he never intended, as I am confcious that I never meant, by the long unfortunate note fubjoined on the fubject of barrows, to fupport him in any fuch defign. Bort in following Mr Bryant any further, I am afraid | fhould trefpafs on the indulgence of the Society. I did former- ly, and do now, entertain a high refpeé for that gentleman’s talents, learning, and character: at the fame time, I cannot help lamenting, that he fhould ever have mifemployed thofe talents, and that learning, in a laborious attempt which can never en- lighten the mind with any cheerful rays of conviction ; nor ever reach beyond a dreary and difguftful {tate of obfcurity and doubt, tending to blunt or extinguifh thofe pleafing fenfations which the poems of Homer excite in every breaft qualified to © feel their genuine fpirit; and for a diminution of which, the efforts of a frigid and phlegmatic erudition, even if fuccefsful in proving them to have been derived entirely from fiction, would {carcely be able to compenfate. But that “ the war on which Vor. IV. k “* HomMER * See his Note, Appendix, No. II. 74 TABLEAU de la PLAINE de TROVE. “ Homer founded his famous poems was never carried on, and. “ that, if. the city called Troy ever exifted, it muft have been in “‘ Egypt, and not in Phrygia ;—nay, that Homer himfelf, un- “ der the name of ULyssEs, was the hero of his own Odyfley,” are paradoxes, I fhould think, too whimfical, too violent, and too repugnant to the beft authorities of hitting ever to admit of any thing like a proof. On the other hand, that the fcene of the Iliad has, derived great light from the laudable refearches and fortunate difco- veries of M. CHEVALIER mutt be allowed; and therefore he de- ferves the thanks of every admirer of the works of the great poet. This is the decided opinion of many ; and particularly of one, whom the world allows to be qualified in an eminent degree to judge of this fubject, the learned and fagacious Pro- feffor HEyNE ; to whofe Effay on the Topography of the Iliad, which is annexed in the Appendix*, I beg leave to direct your attention. | f APPEN- * No. ITF. APPENDI x, containing Papers and Letters referred to in the foregoing Detail. No. IL (p. 3i.)e From Profefor HEYNE’s Preface to the German T; ranfiation of. M. CHEVALIER’S Treatife*. O penetrate, at leaft with the mind’s eye, beyond the nar- row circle to which life is bounded, and to ftudy na- ture on a large feale, is a propenfity in the conftitution of man. From this principle arifes the pleafure which we receive from the defcription of foreign lands, and in the reprefentation of na- tural fcenes and profpects. In the cafe of celebrated places, this pleafure is enhanced, when, in countries well known to fame, the remembrance of illuftrious actions is before us. ‘The inte- reft rifes ftill higher, if the {pot be what is termed claffic ground, the mention of which in ancient authors is connected with im- portant events; or where the topography is doubtful, and has become a fubject of controverfy. Tus is the cafe with the Troad. Homer furnifhes us with fo much accurate obfervation, that we are ready to imagine our- k2 felves * I am indebted for the tranflation of the following Extracts, from the German of Mr Heyne’s Preface and Notes, and of the Effay on the Topography of the Iliad, to a very ingenious young gentleman, now the Reverend ALEXANDER Bronton, minifter of Bolton in Eaft Lothian ; formerly educated at this Univerfity, and who refided fome time at Berlin, as private fecretary to the late Josrrn Ewart, Efq Britifh minifter at that court. My learned friend, Mr James Bonar of the Excife, took the trouble of revifing and preparing it for the prefs. D. 46 TABLEAU de la PLAINE de TROYE. felves able to make a vifible reprefentation of the.country. But if we try to complete the picture in all its parts, we fhall meet with gaps and with places which do not coincide with the reft of the defign. Accurate defcriptions of this diftri€t have not been obtained. StrAgo is the only author who has furnifhed us with a mi- nute account of the Troad, compofed not from the perfonal ob- fervations of this great geographer, but borrowed from DEME- TRivs of Scepfis. DEMETRIUs feems indeed to have a juft title to belief and refpedt, as he was born in the neighbourhood of the Troad, and had in all probability furveyed it himfelf. Our good opinion of him is confirmed by the accuracy with which particular places are laid down, and by their coincidence with the defcriptions of the ancient poets. Tu1s author, however, gives rife to a ftill greater embarrafl- ment, not fo much refpecting the fituation of Troy, for it is af- figned to what, in all probability, is its exact place, as in regard to the river Scamander and its fources, which are thrown far back in the mountainous region behind Troy. SUCCEEDING travellers have thrown little light on the Troad, Woop, alone, made it a ferious object to explore this claflic ground, and to form an accurate idea of it. He was prepared for the inveftigation by claflical erudition. He travelled, he fays, with his Homer in his hand, but he feems to have had STRAEO alone in his eye. Without attending to fo many other circumftances, which might have directed his view, the fources of the Scamander were his only point, from which he furveyed every thing elfe; and as he was miftaken in the fituation of thefe, every thing elfe muft have received from him a falfe po- fition and appearance *. To * AN ingenious criticifm on Woop's Effay on Homer, which appears in the ori- ginal of this preface, is here omitted, as not immediately connected with the prefent fubje&. D. \ t a ee ke et ABR END DX Newt: 79 To the edition in.1775 of Woop’s Effay on the Original Genius and Writings of Homer, was added his Comparative View of the ancient and prefent State of the Tread. Some years afterwards, I read in the Society a paper attempting to explain the military tranfactions in the Iliad, according to the topography of the country *.. Had,I kept. by Homer | fhould have fallen into fewer miftakes: but, unfortunately, from confidence in fuch a man as Woop, who had vifited the country with his Homer, in his hand, I took him and his chart of the Troad for my guides, and thus allowed myfelf to be entangled in fuch a labyrinth of errors, that I {trove in vain to extricate -myfelf. - THE main blunder in Woon is the alteration of the fources of the Scamander, and the confequent placing of ancient Troy deep in the mountainous region of Ida. Every thing elfe was now confounded. Woop did not perceive that DemEeTRIvs of Scepfis, whom Srraso- follows, builds, in. this inftance, on a mere hypothefis. DEMETRIUS, I imagine, founded it on an er- roneous interpretation of Iliad, XII. 18, &c..+, which he under- {tood geographically, without confidering that he had before him a poet, not a geographer. Woop, indeed, traced the courfe of a ftream, till at laft he found another that flowed into it: he then fought the fources of this new ftream, and difcovered them. Thus far, all is accurately obferved, and coincides with DeEmeETRiIvs’s affertion. But was this ftream of courfe the Scamander ? ‘and, was. Troy to be immediately transferred to that fpot? Had not Straso preceded him with a multitude of doubts? Woop helped himfelf out with changes of nature, which muft have taken place here, and have altered of confe- quence the face of the country. But fuch changes hiftory knows of only upon the coaft, or when occafioned by the overflow of rivers ; * Tuis paper is publifhed in Coszmentat. Soc. Reg. Scientiarum Gottingenjis, tom. VI. under the title of De acie Homerica, et de oppugnatione caftrorum a Tra- Jans facta. + See above, p. 61. 78 TABLEAU de la PLAINE de TROYE. rivers: and fuch Homer himfelf defcribes, Iliad, VII. 459, &c. XI. 13-33, THE transference of Rhceteum to Cape Berbier is an error not peculiar to Woop: but the Grecian camp derives from thence an extent which again does not accord with Homer’s defcrip- ~ tion. ‘The poet is not indeed to be a geographer; but he muft not feign any thing which contradiéts the firft glance at nature, or clafhes with the known accounts of the topography of the country. The epic poet muft reprefent nature as certain leading circumi{tances require. ‘The main circumftance here is the ge- neral chart of the face of the country, and an eftablifhment of certain principal fpots. As to the reft of the fcene, fancy muft have full play in fuggefting its greatnefs and extent. The epic poet’s chief engine is the marvellous. By an accurate determina- tion of every particular, the illufion would quickly vanifh. Much mutt appear only in great mafles: Some things muft be and muft remain in obfcurity, that the fancy of the hearers or readers may have room to work, to form to itfelf an idea of greatnefs and power. Homer therefore does not give an accurate determination of the Grecian camp, or of the field of battle. Here the fancy of the reader has room to operate, as that of the poet himfelf has been engaged in working up every thing into the great and wonder- ful. Every thing appears to him many degrees higher than it is in real nature. Muft he not raife the reader to the fame pitch? “ I fee gods arifing” is the language of the poet; and when he is read as a poet ought to be, it will be the language of the reader alfo. If we are at any time to figure to ourfelves the Scamander as a tremendous torrent, which, as a god, fights with AcniLLeEs, and threatens to bury him in its waves, Ho- MER muft not inform us how diminutive its real fize is. He muft leave us, by affociation with the greatnefs of the effect, to give it all the bulk our fancy can grafp. He in no place gives the exact dimenfions of the town and fortrefs of Troy. This is quite APPENDIX, No 1 79 quite natural; for fuch accuracy could in no refpect have had an advantageous effect. The combat of AcHILLEs and Hector is filled with the wonderful. The race of both heroes is traced by means of points, which the fancy of the reader may extend as far as it can; the walls, the wild fig tree, the watch-tower, the fources of the Scamander. But it may be premifed, that to _a perfon who knew the topography of the country in the days of Homer, nothing would be reprefented, which he would have recognifed and declared to be falfe and erroneous, elfe the effect of the poem would have been loft, ‘ “WueEn we fpeak of the Troad, it may be viewed in various lights. “What is the prefent appearance of that country ? What was it formerly, at different times, particularly in the days of Homer? and how can its prefent appearance be reconciled with the defcriptions of that poet? Or, again; in Hower there is a certain appearance of the country defcribed. How far does this actually accord with nature? Each of thefe views and queftions it is rather the province of the geographer and hiftorical critic to anfwer. There is {till another view of the fubje@t. As the poet cannot be read with pleafure, without a fenfible reprefenta- tion, what is the reprefentation he gives of the face of the coun- try? To what extent does he give it? and how much of this kind of knowledge muft accompany or precede the reading of the Iliad? q . Tue explainer of Homer is properly bound to difcharge on- dy the laft cafk.. With this view I had entirely new modelled the above mentioned. Memoir, according to Homer, and had. taken no further affiftance from Srraso than coincided with and illuftrated Homer’s account. So much the more lively was my pleafure, when I perceived, in the paper of M.Cueva- LIER, a greater coincidence with my ideas than I had found,in Woop, or in any other work. This induced me to annex to this 8. TABLEAU dela PLAINE de TROYE. this publication my Memoir in a new drefs, in order, at leaft, to remedy the errors it may have formerly occafioned. . TuatT the fources of the Scamander are {till found near Bou- nar-ba/bi ;—that of its junction with the Simois the ancient channel ftill remains, as the ftream is now diverted into a canal, which falls into the fea below Sigeum ;—that the ftream which comes down from the hills is the Simois, and not the Scaman- der ;—and, alfo, that the other ftream, which the former re- ceives, is no Scamander ;—that Bounar-ba/bi exhibits the fite and veftiges of ancient Troy ;—that even the citadel is ftill diftin- guifhed by its abrupt precipice :—all thefe are leading remarks and obfervations which we owe to M. CHEVALIER. The coatt, the promontories, the tombs, the temple of APOLLO at Thymbra, Callicoloné, and other places, receive from him all the diftin@- nefs that readers of Homer can with. M. Cuevarier vifited the country about the year 1787. He was at that time attached to the embafly of M. DE CHoIsEUL Gourrier at Conftantinople. The occafion both of his draw- ing up the paper, of its being read before the Royal Society of Edinburgh, and afterwards publifhed by Mr Dauzet, are de- tailed in the preface of this laft gentleman *. I waD the pleafure of M. CHEVALIER’s acquaintance during his fhort refidence at Gottingen. The perufal of parts of his tra- velling journals made me defirous to communicate to my coun- trymen the whole work. ‘This propofal, however, was attended with feveral difficulties, particularly, that the paper was the pro- perty of the Royal Society of Edinburgh, and that it was affign- ed to a place in the third Volume of their Zran/actions, which ~ was not to be publifhed for a twelvemonth. In the mean time, upon fignifying my wifhes, I experienced a complaifance and readinefs to oblige, which calls for the warmett * See the Preface to the Englifh Tranflation. Ac PRE IN AD! 15S NBT “tata warmeft and moft grateful acknowledgment on my part. Not only M. CHEVALIER gave me every afliftance, but, on the part of the Royal Society of Edinburgh, I was anticipated with aflu- rances which fhew the liberal fentiments of thofe Literati, who are far fuperior to any little felfifh vanity. I had even imme- diate accefs' to a tranflation of the Paper before it had ‘ap- peared in the Society’s Tran/actions. A copy of this tranflation was fent to me before its publication, and the earlieft impref- fions of the'!maps were communicated to me. If ever the occu- pations of learned men merited the title of the ftudies of huma- nity, it was m the prefent'inftance. To the exertions of Pro- feflor Datzex;"I am particularly indebted.» He ‘preferved, on this occafion, his character, already high in my eftimation, by fhewing himfelf in no ways actuated by envy, omby any little jealoufy, towards a profeffor in his own line. : - | commitrep the German tranflation to ‘a young pisoaciht {cholar, Mr Coarues FREDERIC DoRNEDDEN. According to the permiffion which I received from Edinburgh, and from the au- thor, I have added fome remarks, which are chiefly critical, or: relate to the interpretation, particularly of StRaBo, or refer to a comparifon of ‘paflages in Homer. On different points I have received from the author written explanations, and have, by his permiflion, made fome changes and additions. The particular {tate of literature in Germany would perhaps have required other changes, omiflions, and abbreviations ; but the work was not my property. THE author fets out always from tombs, and feems to lay the greateft ftrefs on the obfervations he has made refpecting thefe. There may have been particular reafons for this. For us they! decide little. Suppofing’ that M. Coev ater was miftaken, and that the eminences ‘were not at all tombs, the main point re-. mains what it was; the fources of the Scamander are near Bou- nar-bafbi 5 and in that neighbourhood is the fite of Troy. Vor. IV. l No. II. é . 82 TABLEAU de la PLAINE de TROYE. No. IE. (p. 73-)» Mr Heywne’s Note, additional to Mr Datzeu’s, on ACHILLES’S Purfuit of Hector. (Thad, XXH. 165.). LONG as this note has been*, I find it neceflary ftill to fub- join another. We ought, | think, to take-up the fubjec& im this way. Here, as frequently happens in regard to Homer, two diftinct queftions occur: 1. How the Ancients underftood Ho- MER? 2. How he may and /hould be underftood ? UNQUESTIONABLY the ancients often underftood their Ho- mer furprifingly ill; and in the inftance before us it may very well have happened that they miftook his. meaning. His com- mentators have conftantly been deficient in pomt of acquaint- ance with the topography of the Troad. Seldom was this rug- ged coaft vifited by travellers, as no great road either led to or run through it. Over the precipices of Mount Ida it was hardly. poffible that there fhould lie- any much frequented path. To the prefent hour this coaft continues to be but rarely vifited. Thofe traéts only are known to us through which caravans tra- vel. Even where an accurate acquaintance with the topography of the country might have been moft confidently looked: for, in STRABo for inftance, we find nothing more than an abridg- ment of the accounts of DEMETRIUS of Scepfis ; and, that this laft mentioned) author, in his examination of the ground). car- ried throughout in his mind a preconceived hypethefis, is, evi- dent in what relates to the fountains of the Simois and Scaman- der. This may perhaps have been the cafe too, whem he affert- * See the Englifh: Tranflation of M. CuevaciEr’s Effay, p. 135, &c.; and the German, p. 206, &c. D. APPENDIX, No. Ut. 83 ed, as follows, of the place which he had rightly marked ont as the fite of ancient Troy, “‘ Hxcror could not poflibly have “ been purfued round about New Ilium, but he might very “‘ well have been fo round ancient Troy,” —7 d¢ rurase eyes regideoumy. (STRABO, p. 8g5. A.). _In Quintus of Smyrna, who, as well as DEMETRIUS, refided juft upon the weftern coaft of Afia, we find a fimilar deficiency in point of local knowledge. No wonder, then, that even he makes HEcror be dragged around the walls, awgi xorno. (1. 111. XIV. 132.) ViRGIL’s imitation of this incident, in the combat between #inEas and Turnus before Laurentum, (quoted and referred to in the Effay), can prove nothing more than that VirGit ei-- ther adopted in his narrative a different plan from Homer, or endeavoured to give fomewhat more probability to his ftory; jut as in another paflage we find him fubftituting, for the tri- ple chace of the combatants, the more probable incident of dragging the dead body of Hecror round the city ; Ter circum Ihacos raptaverat HeEcTORA muros. He obferved, in this, the fame rule by which he conduéted him- felf on other occafions, not always to be anxious to tread in the very fteps of Homer, but, where a different delineation fhould of- fer more poetical beauties, to carry his imitation at large through the whole circle of poets, epic or dramatic. In this particular, of the dragging of Hectror’s body, he followed fome other poet, probably Euripipes. (See Excurf. XVIII. ad An. 1). IF it is to be maintained, that the paflage in Homer, refpect- ing this purfuit of the combatants, cannot mean that it was ac- tually round about the city, and that fuch a purfuit could not poflibly have taken place, the main proof muft be drawn from the topographical fituation of the country. Ancient Troy was acceflible only on the fide next the fea. On the quarter of the 12 Acropolis, 84 TABLEAU de la PLAINE de TROYE. Acropolis it was furrounded by abrupt precipices, and deep ra- vines ; and at the bottom lay the rocky bed of the Simois, as M. CHEVALIER, an eye witnefs, aflures us. His teftimony, by the by, affords a folution why the Greeks, numerous as they were, never completely invefted the city, though this would have been a natural and effectual plan of operation. It explains, too, why they did not cut off all approach to the place; for we find frefh fupplies and provifions received without interruption from Phrygia; allies and auxiliaries arriving conftantly at Troy. On the fide next the mountains there muft therefore have been a free accefs to the town. Hence, too, it is no lefs evident, that Homer, intimately acquainted as’ he was with the ground, ne- ver could have faid what has been afcribed to him, that Acutr- LES chafed Hector thrice round the walls. Still lefs can this be fuppofed, when what the poet is thus made to fay is palpa- bly abfurd in itfelf, that two combatants fhould run three ‘times round the walls of a city. For either, if we fhould reckon the thing poflible, our idea of the city muft be diminutive and con-_ temptible ; or, fhould we fuppofe the city to be large, the im- probability becomes obvious, and we are ftruck with the abfur- dity of the army’s ftanding idle, waiting for the re-appearance of the runners from the oppofite fide of the walls. Add to this, that fuch an abfurdity is by no means neceflarily imphed in the words ; nor would it at all occur, were the paflage read without prejudice, and with proper attention to its meaning. All the combats take place before the Sc#an Gate. Thus far had Pa- TROCLUS, the preceding day, driven back the flying Trojans. (XVIUI. 453. XVI. 712.). No battle, no tranfadion, is men- tioned, as happening in any other quarter, or on the oppofite fide of the town. It is on the Scean Gate that Priam and his Trojans ftand, to be fpectators of the fight. (Iliad, II. 145—154. XXIL 25. 462.). Even during the flight of Hector, we do not find Priam running from one gate to another, from one fide - ai SS EEE 4PPENDIX, No. Ul. gs fide of the walls to the other; he continues ftanding on the Sczan ‘Gate.—The whole narrative of the tranfaCtion i in queftion — is as follows :— Hecror at firft takes his ftation before the Scean Gate, waiting on foot the approach of Acurturs, (XXII. 96.); but as ACHILLEs draws near, he is feized with a panic. ‘To efcape from him, he takes his flight along the foot of the wall, (ré-yos' ixd Tedoy. XXIL. 144.), partly with the view of being protected from the walls, partly, perhaps, in order to get away towards the mountains. © ACHILLES gets between him and the wall, and drives him to the oppofite fide againft the Grecian army. This track brings HecTor to the watch-tower, the wild fig-tree, and the fources of the Scamander. Here he finds an opportunity to wheel round, and again approach the walls. AcHILLEs, once more, interpofes betwixt him and the city, and drives him back towards the fources of the Scamander; and this is repeated four times, (v. 157. 165. 188. 194. ‘Ocodas—). On this fpot, at a di- {tance from the walls, near the fources of the Scamander, HrEc- ToR at:length me a ftand, and the laft combat, with his death, enfues. ! Wuewn the fubject is taken up in this aes tot view, the word TEoh, in the phrafes regs oid, meek SDs meek TEV OS, can be under- ftood: inno other fenfe, than: about—before the city,’ without any idea of its meaning “ round about the city itfelf.” Even the. 165th line, “Q¢ ca sreig Meremoto morw regidivnbgrm, (or rather meet dunbarnr); proceeds exprefsly upon the notion, that the flight was) directed’ away from the city towards the fources of the Sca- mander:; fo that no idea of a round about.can be admitted. The matter:is completely cleared up by verfes:194—+208.: The circle of the flight ‘is there accurately marked! out, as extending mere- ly from! the walls towards the fources of the Scamander ; confe- quently verfes 2 3° and 251, cannot be underftood in any other fenfe, isi | As. 86 TABLEAU de la PLAINE de TROYE. As Acuitues flew Hector before the Sczan Gate, fo it was decreed that he himfelf fhould one day fall before the fame gate, (Iliad, XXII. 359. and 360.), evi Zxaimor rvAnor. This is ex- prefled by Quintus, III. 82. Sxaiye aug avrnos. Arrer Hecror is killed, AcHILLEs exprefles the idea,—wor- thy of a warrior; but which would haye embarrafled the poet in the execution, by giving the Iliad at omce an inconvenient termination,—the idea of hazarding immediately, while the pa- nic of the Trojans was frefh, an aflault upon the city ; v. 381. Eid” ayer, compl rorw oy revyecs resenbaprer. Here, alfo, it ig net ne- ceflary to fuppofe, that the troops were to advamce towards the wall round about on every fide. The expreflion' implies only fomething indeterminate in regard to the place, provided other circumftances do not more accurately mark it out. In Quin- Tus, (IV. 86. and 87.), DiomEeDE fays, "AAN aye, ov revyeos 5 cpuoow, nde 4 ixrois Tomer audi roAna. Let us affault the city itfelf,—On one fide, is underftood,—in one place, where an aflault is practicable. On the contrary, when AcHILLEs drags the body of Hector round the tomb of ACHILLES, Teig Dégurus ati oxua,—(Lliad, XXIV. 16.), it feems clear, from the nature of the thing, that, in this paflage, the ex-- preffion may fignify round about. Upon the whole, one muft here call to mind the remark, which I have elfewhere introduced,— What other poets do by art, in throwing into the fhade certain parts of their ftory, that the effect of the whole may be more forcible, HOMER does here, certainly not from theoretical notions, but by the guidance of true feeling, and in the glow of imagination. The poet was now arrived at the great, the decifive moment, when his hero ought to appear with the higheft luftre. The combat itfelf is rai- fed to the marvellous ; even deities muft take a part in it, and contribute APPENDIX, No. I. 87 contribute to the wonders of the feene. So terrible is the look of AcHiLies, that Hector, prepared as he was to ftand the conflict, lofes courage at his approach. The race of the two he- roes goes far beyond human force; but how far,—over that the poet throws a vail. Fancy has now room to work, and may reprefent every thing as far beyond what is common and natu- ral as fhe will or can. They run three times round at the city, —the fpace, the diftance, may be conceived as great as we choofe; but the poet neither does nor ought to determine them. Such determination would fall either into the gigantic or the diminutive. The cafe is different, when, by means of a com- parifon, an idea and image can be enlarged or extended. The poet then makes ufe of what is defined, to render the undefined. object more diftin@, and to throw light on what is obfcure. That however 1s not the’ cafe here. No. HI. (p. 34. 67. 74.). ESSAY on the Topography of the Hiad*. By Profeffor HryNe of Gottingen, Aulic Counfellor to His Britannic Maje/ty, ec. FOR nine years had the war between the Greeks and Trojans been carried on. The former now lay encamped in the neigh- bourhood of Troy, when the quarrel between AcHILLEs and AGAMEMNON, occafioned a divifion in the army. AGAMEMNON,, *. THE tahense Effay follows out the train of ideas, fuggefted ina Paper read be- - fore the Royal Society of Sciences at Gottirigen, De acie: Homerica, et oppugmatione a-Trojanis fata, in the yearn 1783, publifhed in: the fixth volume of. their Tranfae- tions. All the difquifitions, there introduced, refpeting the origin of military tac- tics, the manner of drawing up an army, and giving battle, and the art of fortifying and. attacking. a poft, as deferibed in) the Iliad, are here’ omitted); many topics, of the other hand, are now correéted and enlarged. That Effay was my firft on the Topography of the Iliad ; a fubjeét involved in fo much difficulty. I allowed my- felf $8 TABLEAU de la PLAINE de TROVE. AGAMEMNON, to convince ACHILLEs'that, even without his afliftance, victory might be, obtained, caufes the army to march out of the camp,-and advance towards the city.. Hitherto the Trojans had kept clofe within their walls, following the advice of their.old men*, who faw plainly, that, if a fiege fhould ac- tually take place, the Greeks could, make Jittle impreflion on, the town: -for. the firft. rudiments of the arts of. attack were.then hardly known.. Encouraged, however, it fhould feem, by intel- ligence of the divifion in the Grecian army, the Trojans quitted the city, and ‘met the Greeks, in the field ;—a, new, gratification _ to the. proud fpirit of AcHiLs£eEs, that now, for the firft time, when it was known he was not, withthe ary the paren fhould venture out into the plain fF. THE two armies met. Four principal baialaass are dedanilvedis in the Iliad. The firft, (the fubject of our prefent inveftigation), on the felf then to be mifled by refpeét for Por= and Woop, fo far as to renounce my own ideas, and to mould, according to the reprefentations of thefe gentlemen, the views I had drawn from Homer himfelf. I foor found, however, that I had trufted to bad guides, and at once refolved, laying afide all fecondary aids, to attempt, from the defcriptions given in the poem itfelf,'a fketch of the Topography of the Iliad, fuch as Homer exhibits it. This Effay I now prefent to the public, I had for a long time thrown it afide, when its coincidence with the information colle&ted by M. CHEVALIER on the fubjeét, induced me to revife it, and now inclines me to fubmit it, for further inveftigation, to the friends of the poet. Amendment after this will be an eafy tak. H. . dl Lea nt d * InraD, XV. 721, &c. ‘The fage Porypamas, afterwards, likewife, when the defign of an attack upon the camp feemed likely to mifgive, gave his advice ra- ther to retire again within the city, and take refuge, as formerly, behind the walls, But the rafh Hector would not confent, (X VIII. 266. &c.).. Unqueftionably the long fiege muft have proved extremely harraffing. ‘The provifions, as well as the treafure, of PR1AM were exhaufted, as Hector himfelf urges. (Ibid. 288.), H. + OncE only HecrTor had ventured beyond the Scan Gate, as far as the beech tree; but on that occafion he with difficulty efcaped from ACHILLES. oe IX. 352, &c.). > H. AP PIE ND, 1:X, Nox Uk 89 the plain between the camp and the city, (ILIV. 422. VI. 306.); —the fecond, when the Greeks were driven back to their camp, (Iliad, VIL. 55-—213.) ;—the third, which extends not only to | the flight of the Grecians into their camp, but likewife to the ftorming of the camp itfelf by the Trojans, who break in and fet fire to a fhip, till at length they are repulfed, and purfued al- moft to the city by Parroctus. Here Patroctus falls; and the Greeks, put to flight, are once more driven back to their camp. (Iliad, XI—XVIIL). In the fourth battle, AcHILLEs beats back the Trojans again to the city, and crowns his vic- tory by the fall of HEcTor. | ; No lively idea can be formed, either of thefe battles or of the ftorming of the camp, without fome general conception of the environs of Troy. From Mount Ida, run two hilly ridges from the eaft down to the fea, where two promontories bound a jutting beach. The promontory on the north is Rhoeteum ; that on the fouth Si- geum. Within thefe two ridges lies a plain, floping down to the fhore, and inclofed within their femicircular compafs. (STR A- BO, X VAIL. p- 892, B.), In this plain run two rivers: on the ~ north (fide the Simois; on the fouth the Scamander, called alfo the Xanthus. The latter now difcharges itfelf into the fea to thefouth, below Sigeum, but formerly, before approaching the fhore, it muft have united with the Simois, fo that both rivers had ‘a common outlet into the fea, above or to the north of Si-. geum. This embouchure was furrounded with many marthes, and hence was called Stomalimné ; a name which occurs but once in Homer, in an interpolated paffage. (Iliad, VI. 4.). The exact fituation is laid down. by StRaBo, (XIII. p. 890. A. PLiny, V. 20. 33%). | VobeiN:. mm THE * Or all thefe places, the charts of Pore and Woop give very different views ;, that of M.-CQuEVABIER, however, accords exactly with what is faid by StRazBo.and. PLiny, 90 TABLEAU de la PLAINE de TROYE. Tue Grecian fleet was drawn on fhore at'a place between the two promontories. The diftance betwixt the two, according to STRABO, (p. 8go. B. 891. A.), was 60 ftadia, (about two Ger- man or nine Englifh miles), in a direét courfe by fea. The cur- vature of the land, however, would increafe the diftance in keep- ing along the fhore *. It is generally fuppofed, that the Grecian camp éavitidiea from cape to cape. This notion involves very confiderable difficulty. Had it done fo, the camp muft have reached beyond the Simois, and the marfhes on both fides of it; a cireumftance by no means probable, particularly as the ftream is fo apt to overflow; and not the fmalleft trace occurs in Homer, either of the river running through the camp, or of the left wing being ftationed beyond the river. When Homer, therefore, fays; that the fhips occupied the whole fhore | between the two promontories, he probably fpeaks in a poetical ftyle, to convey a magnificent idea; and it is more likely that the camp only ftretched on both fides towards the promontories Rhceteum and Sigeum, and that on the north-eaft it extended to the Simois f. WITHIN this fpace were the fhips of the Greeks hawled up on the land, at a confiderable diftance from the fhore, with their fterns towards the land, and arranged in feveral rows ||. The rows, * D’ANVILLE, in his defcription of the Hellefpont, (Memoires de l Academie des Infcriptions, tom. XXIV. p. 329.), allows only half the diftance ; M. CuEva- LIER does the fame, (Ch. VIII.), on the authority of the paflage in Piiny, (V. Be) where the diftance is reckoned from AZanteum. Still, however, it is a contefted point, what part of the coaft muft properly be regarded as Rheeteum. + Iniap, XIV. 35 ee nek TART AY amaons . Hiovos orone peneov, oooy ouveceyebay & AK Eh» He does not exprefsly name either Sigeum or Rheteum; on the contrary, he al- ways places the camp on the Hellefpont, in the more extenfive fignification of that term, as meaning the northern part of the Aigean Sea. { See above, p. 57, 58. D. || Tue fhips are therefore faid to have ftood xpéxgoorar, (XIV. 35.), parallel and behind one another, like the fteps of a ladder. That this is the meaning we learn from Heropotus, (VII. 188.). APPENDIX, No. Ill. QI rows, however, muft have been drawn backwards, according to the oblique direétion of the whole camp, from the north towards Sigeum. Behind the foremoft row of the fhips the troops were encamped, fo that the fhips themfelves muft have ferved for a kind of rampart, as is plain from a comparifon of different paf- fages*. In the rear of the left wing muft have been the marfhes called Stomalimné. StTRasBo afligns particular names to feveral parts of the coaft, though he has not put them down in geogra- phical order f. As only one part of the coaft bears the name of Station of the fleet, it may perhaps be inferred from this, that the Grecian camp occupied only a part of the beach. Tue fhips ftood in the order in which they had been drawn afhore. The veflels of PRoTESILAUs, accordingly, occupied the foremoft place ; and next to them were the fhips of Ajax, the fon of TELamon. (Iliad, XIII. 681. XV. 706, &c.). Ajax was ftationed towards Rhceteum, confequently on the left wing of the camp; ACHILLEs, with his Myrmidons, on the right to- wards Sigeumt. In regard to the two extremities there is no doubt; but the arrangement in the intermediate {pace cannot be fo exactly afcertained ; unlefs, perhaps, thus far: Near to AJ Ax, and farther to the right, lay IpomENnevs, with the Cretans, m 2 | (Iliad, *Ix1ap, XV. 653, &c. 408. 426. XIV. 34. } Strapo, (XIII. 890. A.). “ After Rheeteum follows. Sigeum, a town in * ruins, then the ftation of the flect, (ro Neveraéasy), and the harbour of the Greeks, “ (6 Ayaidy amen), and the Grecian camp, (ro Ayaixdy areaténedoy), and Stomalzmné, * and the mouth of the Scamander, (viz. of the Scamander united with the Simois), “ then the promontory of Sigeum.” Compare MEra, I. 19. Puiny, V. 30. 33- t Intap, XI. ad init. It is true that in XVII. 432. it is faid, that the hor- fes of AcuILLEs would not return without Parrocius to the Hellefpont, a) én yas txt mAatdy “EAAnowovrey, But this whole northern arm of -the fEgean Sea, before the entrance of the ftrait, is more than once called the Hellefpont: (Iliad, XVIII. ESQ. 92 TABLEAU delaPLAINE de TROYE. (liad, X. 112.); befide him Nestor, with his Pylians; then followed MENESTHEUS, with the Athenians; next to him was Utysses; near to whom were ftationed the Argives, Myce- neans, and Lacedemonians; after thefe came feveral other corps ; and, laftly, on the right wing were the Myrmidons, - with whom, it fhould feem, the other Theffalian tribes (the troops of PROTESILAUS excepted) were united. By this arrangement, the following paffages appear both to be cleared up themfelves, and to throw light on others in their turn. The poft of Ajax is all along the moft important. To- wards this wing the main aflault upon the camp’ takes place. To that fide alfo the battles tend. When Nestor conduéts the wounded MacHaon into his. own tent, ACHILLEs is at fiich a diftance that he fees only his back, and cannot diftinétly recog- nife his perfon, (XI. 596. 610. et feq.)s PatTroctus, difpatch- ed by ACHILLEs to make inquiry, in returning from NEsTOR paffes the place where the fhips of Utysszs are lying. (XI. 805.). Juft at this fpot he finds Eurypyius, who was coming back from the engagement at the left wing wounded, and was going, it would appear, to the right wing, where probably his Thefla- lians were ftationed. Macuaon, though a Theffalian, was con= ducted by NeEsTor into 4is tent, probably becaufe he was too much exhaufted to be able to reach the right wing. The fhips of Utysses lay in the centre, fo that, from thénce, the fhout, which called the troops to arms, could be heard on both wings *. To this the form of the camp, which, from its pofition, extend- ed more in depth than in length, probably contributed. Hard | by t50. XXIV. 346. Odyff. XXEV. 82. alfo Iliad, VII. 86. XII. 30. XV. 233. XXUI. 2.). And hence muft be derived the explanation of the epithets xausd; and dz:¢gav, which do not feem well applied to the proper Hellefpont; though, in- deed, broad and marrow are relative terms: *Turap, XI. 5. Thefe verfes are likewife inferted, though rather awkwardly 3 ib. VIII. 222. et feq. , AP PON DT Xj Noth 93 by thefe fhips of Unysses, and confequently behind the fore- moft row, was the place for holding the public affemblies, and for the altars for the facrifices. (Iliad, XI. 806-7.), One of thefe, it fhould feem, was the altar of JurITER Panomphzus*. Tue order of the fhips in the catalogue, (Iliad, IJ.), appears to have fome connection with this arrangement in the camp, fo that the Boeotians, and: thofe after them, ‘as far on as the Sala- minians, under Ayax, belonged to the left wing. The Argives, and thofe next in order, as far as the Cretans, Rhodians, and other Iflanders, compofed the centre. The Theffalians, with the Myrmidons, formed the right wing. Tue fucceflion and order of the troops, when afterwards drawn up in the field of battle, is fomewhat different. -Aca- MEMNON runs through the midft of the battle ; and after paff- ing fome, who are not named, he comes to IDoMENEUS. with the Cretans, to Ajax and the Salaminians, to NEsTor with his Pylians, to the Athenians under MENESTHEUsS, to ULyssxs, and laftly to DiomeEDE f: AGAMEMNON, it appears, went from the left to the right wing. ULyssEs was at fuch a diftance from the {pot where the Trojans were prefling on to the affault, that he as yet knew no- thing of their approach, (IV. 331.). In the battle itfelf all or- der *TItrap, VIII. 249, 250: Ovip. Met. XI. 197. Arottxo ftands on the Trojan fhore, Dextera Sige’, Rhetet leva profundi ' Ara Panompheo vetus eft facrata Tonanti. What notion the editors have had of this paflage, it is not eafy to divine. At all events, a point muft be put after. ath and that line muft be underftood as a com- plete fentence: tInrap, IV. 231, &c. The leaders and the corps are by no means all particu- larifed by name. Thus, it appears from lib. XI, 808. IJ. 736, that the Thefla- lians, commanded by EuryryLus, were there: 04 TABLEAU de la PLAINE de TROVE. der is loft; and the combatants, individuals as well ah f{qua- drons, are confufedly mixed with one another. (IV. 457, &c.). Tue ground in this neighbourhood muft have experienced — alterations by the overflowing of the rivers, as well as by the operation of the Simois at its mouth. Homer himfelf inti- mates this, when he takes notice, that not a trace of the wall of the Grecian camp was remaining. (Iliad, XIL ad init.). Hero- potus alfo quotes the fhore of Troy as an inftance of fuch changes. (lib. II. 10.). And fhould we even incline to rejeé the teftimony of StTRaBo, (lib. XIII. p. 890. A.), the fat may - be regarded as certain. Whether the alterations of the ground, however, have been fo great as Woop fuppofes, is a different queftion *. , BEFORE the camp, as already mentioned, a plain, gradually rifing, ftretched towards Troy, diverfified, it fhould feem, with feveral little eminences t. That the two rivers Simois and Sca- mander inclofed this plain, and that farther down they united with each other, Homer exprefsly teftifies{; but he furnifhes us with no further or more accurate information|]. The field of battle lies in the neighbourhood of the Scamander §, and is called likewife the Scamandrian Plain 4], though it alfo re- celves, * M. CHEVALIER anf{wers this queftion. + Or this kind was one immediately in front of the camp, the Sgacuds redo. (Iliad, X. 160. XI. 56.). It lay juft before the place for croffing the Scamander, in going from the camp, on the road towards Troy ; for in the laft battle the Trojans had taken poft tx} Sgacua wediow, (XX. 3.), and from thence they came, in the courfe of their flight, to the paflage of the Xanthus, wigov Sévfov. (XXI.2.). In fo far the delineation, on M. GuevaLier’s map, is erroneous. H. See above, p. 56, 57. D. jt In1ap, V. 713- et feq. Vid. StRaBo, XIII. p. 890. A. 892. C. |] Straso fays: “ A little way before New Ilium the ftreams unite.” It is. doubtful, however, whether by this expreffion he means between Ilium and the fea,- or on the inland fide of the town. § Inrap V. 36. VII. 329. XI. 498-9. q Tliad, IL. 465. 467. : a ee : AP: PiBO ND LX, Noy HI. “O05 ceives, at leaft in the more immediate vicinity of the city, the epithet of Trojan*. More precifely ftill it is faid, (Iliad, VI..1, 8zc.), “the battle raged between Simois and Xanthus.” The lat- ter muft have been neareft the Grecian camp; for when the Tro- jans had advanced very nigh the rampart, and lay a night in the ‘field before it, they are faid to be between the camp and the Sca- mander. (Iliad; VIII. 556.). At the Scamander + Hecror holds a council of war; and when the Trojans; are compelled to re- tire from before’the camp, ‘the wounded Hecror is laid down at the fide of the Scamander. (Iliad, XIV. 433.)..: When, again, PatTRoctius drives the Trojans finally from the camp, he cuts off the retreat of a part of the fugitives to the city, forces them back towards the camp, and falls on them betwixt the ftation of the fhips, the river and the city {. AcHILLEs, in advancing from the camp to the Xanthus, drives a part of the flying enemy into the:river; thereft efcape to the town. (Iliad, XXI. 1. et feq.). Here it feems to be plainly intimated, that, on the way between the camp and the city, the river muft be paffed. And this is confirmed by feveral paffages in the laft book, where Priam, in going from ‘the city to the Grecian camp, after pafling the _tomb of ILus, arrives at the river,—undoubtedly the Scaman- der. Here he waters his horfes. (Iliad, XXIV. 349.). In re- murning, be comes again to the fame {pot, (vy. 692.) ; and here P | there * Inrap, X. 11. XXIII. 464. “STRABO,’p. 892. C. Tt For this muft be the woraué ter! Duverns of iad, VIII. 490. f fand ote Tae RE Méonyo | Najy mei eorayd no Tei NgE0s tnpnrcio. Iliad, XVI. 397: fees it is 5 difficult to form a diftin&: idea of the DW oSt(pibical fituation, unlefs we underftand it thus: Firft, between the fhips and the river ; and farther on, between the river and the town. 96 TABLEAU de la PLAINE de TROYE. there was a place for crofling the river *.. Homer guides us no farther. f I FORMERLY thought it probable that Homer meant only a near approach of the two rivers, not.an entire confluence of their ftreams ; but this opinion I have long fince abandoned. The Scholiafts, and even EvsTaTHius, ogive us no:aid here; they rather miflead; they themfelves had probably \no. ocular knowledge of the place. The Scholia, however, on Iliad, LI.. 465. fay, “ the Scamander comes from Ida, divides. inthe ~“ midft the plain that ftretchés to the fhore, and difcharges it- “felf, on the left hand, into ‘the fea.” ‘But show. is this to be underftood ? If the left hand from Troy is fpoken of, the prefent mouth, to the fouthward of Sigeum, muft)be antended; and on that fuppofition this mouth would ‘be of confiderable antiquity. If the commentator, however, means onthe left hand:going from the foore.to.Mount Ida, it isthen the united f{tream of the Scaman- der and Simois, that is s faid to fall i into the fea at this i: ibe onEVEN % AAW ore on, magoy nites t Saat oral a It-is here’ that- Mi CHEVALIER’ 's obfervations on the fpot, and ie teat ‘ypon the map, give us fo. much light. The Scamander,. as it came near. the fhore, direct ing its courfe-obliquely over the plain, approached the Simois, and run into it, exe actly as defcribedin StraBo. At ‘préfent the’ Scamander is conduéted into a/canal, and: difcharges itfelf into the fea below Sigeum. This is one important obfervation made by M. Cneva.ier. There is another, alfo, relating to the fources of the Sca- mander. Still it is a perplexing circumftance, that, neither in the advancing, nor in the retreat, of the armies, is any exprefs mention made of fo important a circum- ftance as croffing the river. *Almoftyall the paffages, except perhaps the laft, rather imply that the rivers run on each fide. H. See above, p. 46. Note*. D. + 1 DovsT whether-any of, the poets, , QuINTUS of Smyrna, TayPuroporus, or Coturtnus, had an accurate knowledge of this neighbourhood. ‘Tayrmioponvs, for sinitance, lays, (lin. B65 ed3 30.2 : > y ' "Nes nah Eaybe worams xuxdovuevoy vowe Kal cropace nexrnyes Disozioiore “oud APPENDIX, No. lll. 67 Even in Srrazo’s time the fite of Old Ilium was unknown, and was a fubject of difpute; but he marks out diftinétly a new flium. Alexandria Troas was a different place from both, and lay more to the fouthward. New Ilium was twelve ftadia (three- eights of a German mile, fomewhat lefs than two Englifh miles) from the Grecian harbour. Thirty ftadia (almoft a German mile, or about four Englifh miles and an half) higher up, eaft- ward from New Ilium, and nearer Mount Ida, was fituate Old Ilium, on a {pot where then ftood a village named Ilium *. TuE road from the city of Troy to the fea fhore ran from the Scean Gate, paft a beech tree, to the tomb of ILus, on which ftood a pillar +. Another monument was called Ba- tiela, or the tomb of the Amazon Myrinna, an infulated hil- lock, where the Trojans took poft in the firft battle. (Iliad, II. 811—15.). Upon another tomb; that of AisyETEs, fat PoLITEs, as a {cout on behalf of the Trojans. (Iliad, I. 793.).. The Sca-_ Vou. IV. n mander “ Lond roar’d the Xanthus, and the mouth of the Simois ;” fo they were not then uni- ted at the mouth. A little after, (lin. 319.), ‘‘ They were dragging the wooden * horfe, but were retarded, the way being interfected by rivers, and very uneven.” “Odds 9’ teagdiero paxpn, a ~ 0) Ws = — J « 4 LxComsrn worapuoior, Kool ¥ wedscrcwy onary. * StrRago, XIII. p- 889. Ov yee Ci) tvradde ideuce chy modu cu voy oti (New Ilium), arrw oxedoy Ts j rpicbxovree cevarepa %EO5 fu nocd ie THY Iduy, xah thy Axedavicey, (as this old habitation of Darpanus lay ftill deeper in the mountains I], XX. 216, 217. northward from Old Ilium, Straso, XIII. p. 891. D.) card viv dy neervpeivay Tris HOBHYe Compare p- 81. A. 892. D. When Homer fays of Ilium é 20 ita TET OATTOy this is faid in refpe& to Dardania, which lay among the mountains. Troy, however, actually ftood at the foot of the Azl/, at the entrance of the valley or the plain. + Intap XI, 166. 371.. Here Hector. had his poft, on the night when he en- camped before the Grecian camp. (X. 415.). Here Paris ftood behind the pillar, when he wounded DioMEDE with an arrow. (XI. 372.). Juft by the beech APoLto ftood near the city, and the place muft likewife have commanded a view of the coune try. (XXI. 549.)- | : 98 TABLEAU de la PLAINE de TROYFE. mander could not be far from the hillock where the tomb of ILus was. (XXIV. 349. 350. Compare 692, 693.). Nearer the city, on the fouth-weft fide, and juft under the walls, the Watch-tower mutt have {tood, where the deities reforted*. Next to it was the wild fig-tree +, and the fources of the Scamander ; and then the place where clothes were commonly wafhed ft. Be- fore the city, on the north fide, was Callicoloné (zaay zorwrn), a pleafant hill upon the Simois, five ftadia in circumference, and ten ftadia from the village llium |. Tuart it fhould ftill be poffible, after fuch a lapfe of time, to recognife all thefe places, is not to be expected; but there is one of them which we fhould think could even yet be traced, and which, if difcovered, would furnifh at once the moft certain di- rection for all the reft, and even for the fite of ancient Troy it- felf;—that is, the fources of the Scamander, fo accurately and circumftantially defcribed by Homer, (XXII. 147. et feq.), the one of them a warm and {moking fountain, the other, even in * Sxomide (XX. 136.). + Ess. (XXII. 146. XI. 167.), Quite clofe upon the walls, and at the place where they were fo low that the Greeks had once attempted ta force their way into. the city from that quarter. (VI. 433—9.). t See above, p. 44. D. |) AccorDine to StRaBo, (p. 802. D.), who borrowed this information from Demetrius of Scepfis. The Venetian Scholiaft A, upon Iliad, XX. 3, quotes the paffige refpecting Callicoloné, as if taken from the latter; but he miftakes this hillock for the 9,aeud; wsdioo on the Scamander. He adds alfo, “ Here it was that “Paris faw the three goddeffes.” At v. 53. the obfervation is repeated, more juftly indeed, but in a mutilated form. In all other refpeéts, the places hitherto mentioned are determined by M. CnevaLier with great plaufibility and diftiné- nefs. I find upon the map, which I had not an opportunity of feeing till too late, the hill Callicoloné more rightly laid down, than, from the words of the Memoir, I had fuppofed ; (fee p. 94.); and 1 retra&t what I there advanced. The paflages refpecting Callicoloné (XX. 53. 151.) are not, as I imagined, contradictory. APPENDIX, No. Ik 99 in the middle of fummer, of an icy coldnefs. Yet even here there is a very great chafm in our topographical knowledge. At the place, where (according to DemEtRuivs of Scepfis, whom StR4- BO follows), the Scamander had its rife, one {pring only was to be met with ; and Woop, with Srraso in his hand, fought and found this fpring, and this alone*, Arter this preliminary fketch of the Topography of the Troad, let us now try whether it be poffible to get a clear idea of the battles of the Greeks and Trojans. Tue firft battle took place on the plain between Troy and the Grecian camp. The Greeks were drawn out in the Scaman- drian plain. (Iliad, II. 467.). The Trojans, on the other hand, had taken poft on the hill Batieia. (Iliad, II. 811. The engage- ment commences. Paris and Menexaus foon defcry each other. HercrTor negociates a combat between them, which is not attended with any decifive confequences. The armies muft have been pofted at no great diftance from the city, for PR1AM, with his old men, fees from the walls the Grecian-chiefs, and learns their names from HEexLen }. The treacherous PANDARUS, * STRABO, p. 898.9: Woob, p. 323-4. (98. of the German tranflation). And yet Mr Woop did meet with a hot {pring, but in a place where he was not looking for the Scamander. (p. 329.). »M. CHEVALIER was more fortunate in this refpect. He fearched for and difcovered the fources of the Scamander ‘precifely at the hot {pring ; and thus cleared up the whole matter in doubt. + Tue diftance, formerly ftated, of the city from the fhore, or more accurately from the harbour of the Greeks, making in all forty-two ftadia, (one and one-fourth German, nearly five and’ one-half Englifh miles), and the high commanding fituation of the town, render this circumftance by no means improbable, 100 TABLEAU de la PLAINE de TROYE. by difcharging an arrow, brings on a general action. The Tro- jans attack the Greeks, (IV. 221.), and at length the armies clofe. (446.).. The poet defcribes, as a poet muft, individual - combats only. (457, &c.). Thefe however muft have taken place in the neighbourhood of the city; for ApoLto furveys the combatants from Pergamos, and animates them by his fhout. (IV. 507. V. 460. VII. 20.). For a long time the two armies alternately advance and retreat between the Simois and Scamander, (VI. 2, 3.), till Ayax at laft makes the Trojans give way. When near the gate of the city, and not till then, they are rallied by the exertions of /ENEAs and HecTor, and again make a ftand. (VI. 73, &c.). Hector, by the navies of HE- LENUs, and on account of the impending danger, as may be con- jectured, has recourfe to religious rites. He goes into the city, and gives directions for a female proceflion to the temple of M1- NERVA. Inthe mean time, a fingle combat between Giaucus and DIOMEDE terminates in a friendly parley. Upon the return of Hector, the battle is renewed. At length a fingle combat between Hector and Ajax is propofed. With this the narrative of the day clofes. (VII. 1—306.). Both parties retire, the one into the city, the other to their camp. (VII. 310, &c.). Tue following day an armiftice is agreed upon for burying the dead. The Greeks avail themfelves of this interval, and rear in hafte a rampart round their camp. (VII. 325, &c.). Of this more will be faid by and by. NEXT morning, by break of day, a new battle enfues ; the fecond, on the plain between the city and the camp. (VIII. 60, &c.). Towards noon a panic fpreads among the Greeks. They flee, and retreat in diforder to the very camp. (VIII. 68. &c. 139, &c. 213, &c.). At one time, indeed, they again advance to the charge ; but ftill they are forced to give way ; and at laft fhut themfelves up in their camp. (336—34 3° .)» Fortunately for them night intervenes. (485, &c.). HEcToR, APPENDIX, No. Ul. tah Hector, on this occafion, does not draw off his troops into the city, but makes them pafs the night at the river, in the open air, at fome diftance from the camp*, and orders them to kindle watch-fires. By the advice of Nestor, the Greeks likewife fet a watch}. The fame night a deputation is fent by the Greeks to AcHILLES, and Utysses and DiomeEpE fet out on a fcouting party. The fitwation of the Trojan encampment, at this junc- ture, is accurately delineated. (X. 415. 428.). Hector had af- fembled the chiefs at the tomb of Itus. ‘The watch-fires, like the foldiers, were {cattered over the field without any order. The troops extended themfelves down to the fea, (probably the right wing of the Trojans pointed on the north towards Rhee- teum, beyond the Simois), and fome of their pofts reached. as. far as Thymbra. At the outermoft extremity lay the new ar- rived Thracians and RueEsus. (434.).. This muft have been to- wards the fea or the mouth of the Simois, and farther out be- fore the Trojan army towards the Grecian camp; for ULysszs and DiomeEpeg, who furprifed them, went along the ftream of the Simois {. The diftance cannot have been great, for they fet off a good while after midnight, and had returned to the camp by day-break. NEXT * NocQs sav ayayav moraye emt dwnv7. (VIII. 490.). What river now could this be? The Scamander is termed diets, eddying. ‘The Si- mois, however, was ftill more fo, Yet ifthe Scamander had its courfe obliquely thro’ the plain, it muft be the river here intended. + TX, 67. Out at the tomb, azzodas wupa reiQpov epuxtay reixto5 éxtos.. It is more diftin@tly faid afterwards, (v. 87.), between the tomb and the wall, 22d}. pécor rolpeor: xy ttixzos.. Compare 180. 194. 198; + HENcE we find mention made of the heron, (Iliad, X. 274.); of the tamarifks, Cuveixn), and of the fedges, (466-7.). Homer does not take notice of their pafling the river. This, however, they muft.have done.. ron TABLEAU de la PLAINE de TROVE. Next day the Trojans affault the Grecian camp. And here it becomes neceflary to have fome idea of the newly conftructed fortification of the camp. THE fituation has been generally defcribed already. The camp, according to my fuppofition, did not occupy the whole in- termediate fpace, but only a part of the ground, between the two promontories Sigeum on the fouth, and Rheeteum to the north. Perhaps on this fide it went no farther than to the Simois. By all appearances the camp muft have had an oblique front, the right wing receding towards Sigeum, the left bending forwards, and hence more expofed to the enemy’s attacks *. As the Greeks in the firft battle had not been fuccefsful, NE- STOR propofes, during the truce agreed upon for burying the dead, to fortify the open camp. Such a precaution was before. unneceflary; the Trojans having till now kept themfelves fhut up, within their walls. Nestor muft now have been terrified at the fu- periority of the Trojans, and the valour of HEcTor particularly, when there was no ACHILLEs to oppofe him}. The idea of for- / tifying * Tus reprefentation feems to be corroborated by M. CHEVALIER’s map. + To give a hiftorical probability to the circumflance of the Greeks having now, for the firft time, thought of fortifying the.camp, we muft fuppofe, with Tuucyp1- Des, (I. 11.), that immediately upon their firft landing they had beat back the Trojans, or, at leaft, that the latter fought their fafety by remaining within their walls, while the Greeks were unacquainted with any means for catrying on a fiege. In the above quoted paflage of THucypipEs, I may obferve, in paffing, there is fomething which feems to contradi& this explanation, imsd) 02 d@ixcusvoy moyen expernowr, (dmrov dt +o yee true TH otgaromtoy ex Gy iruxicavre), Sc. One fhould think the *«x muft be erafed. Should it be faid, THucyp1DEs may have underftood the matter in a different light; the Greeks would not have been able to fortify their camp, had they not remained mafters of the field. This is contradi¢ted, firft, by the time of their. fortifying the camp, which took place in the tenth year; and, next, by the occafion of its being done: for it was when they were defeated that they firft thought of fortification. The Scholiaft fays: This is to be underftood of a former flight forti- fication. But that is a creature of his own fancy, which only ferves to prove, that, even then, when he wrote, the ’sx was to be found in the MS. APPENDIX, No. Ill. 103 tifying the camp was then entirely new, and the plan for-accom- plifhing it was fingular enough. Nestor advifes to rear, for burning the dead, a common pile on the outfide of the fhips, and upon and round this pile to throw up a hillock, from which a wall and ditch fhould be drawn in front of the camp. The propofal is agreed to, (Iliad, VII. 327343. 434, &c.), the pile is erected, the mound thrown up, and befide it a rampart con- {tructed, (Iliad, XII. 29. 255, &c.), which the poet terms a wall, (refyos and cvgyes). (VII. 338. 436. et al.). It had battlements and breaftworks, and was provided with gates, baftions, and tur- rets*, That all this was a very flight piece of work, may be fup- pofed from the fhortnefs of the time in which it was conftruct- ed. No wonder, then, if, in a fhort time, no trace of it remain- ed. Homer, by an ingenious and highly epic turn, afcribes its annihilation to Neptune and Apotxo. (XII. 1, &c. 459, &c.). It was, however, the firft attempt we know of to fortify a camp; and, in fo far, is fufficiently remarkable to merit fome attzntion. A Few elucidations refpecting the work of this fortification may be added. That the mound was raifed to the north-eaft, in front of the camp, can fcarcely be doubted. Its pofition muft therefore have been on the left wing, to which it muft have ferved for a protection ; and it may be fuppofed, that Ne- STOR, in propofing it, had this very end in view. But, as the river Simois ran on the fame fide, it is not clear what was the po- fition of the mound in relation to the river, and what was the fi- tuation of the left wing, and particularly what was the pofition of the fhips and of the poft of Ajax with refpect to both. In the affault on the camp, which took place on this wing, no mention is made either of the river or the mound. We on- ly fee that the rampart muft have been conftructed at a confi- derable diftance before the fhips; for here, between the fhips and * Lhaes Henares! (XII. 259.). Compare Lycoruron, 291. and the Scho-- hiaft. 1044 TABLEAU dela PLAINE de TROYE. -and the rampart, a fevere engagement enfued. (XIII. 136, &c. ATW ssg09 Bec.) *; THE mound terminated in the rampart, properly a fence of earth, upon which turrets were erected, compofed of beams and {tones. (XII. 29.). That the rampaft was low is clear, from the circumftance of SARPEDON’s being able to catch hold, with his hand, of the battlements of the breaft-work. The fide on which the fhips of Ayax were placed, is defcribed as the loweft. (XIII. 682-3.).. What Quintus sila (VII. 474.), has a.refe- rence to this circumftance. TurovucsH the rampart gates led into the plain}. Among thefe, it fhould feem, there was one principal gate, at the extre- mity of the left wing of the camp. Through it the Greeks marched out to battle. (XII. 118. Compare XIII. 326.). On the outfide of the rampart, towards the plain, a ditch was drawn (VII. 341.) to break the firft onfet of the Trojans. In the ditch palifades were fixed {. Tue fortification feems not to have extended along the whole front of the camp. We do not find, at leaft, that it reached to the * THE poet indeed fays, The mound was thrown up in the field, not far before the fhips. (VII. 334- 433> &e.), turQav mare meo vey yratuuGoy aut HUCNYy—er mediig mort Vdvrav y—veyes tbnrgs eiAce WNDY TE Ky LUT. THE mound muft have been thrown up upon and round the {pot where the burn- ing took place. Compare XXIII. 255, &c. and VirGiL, /epulchrum imponit, VI. 292. in like manner upon the {pot where the funeral pile had been erected ; which is precifely what HomMER means by éugi rognv. In Quintus of Smyrna we find, in like manner, mvexciny x TaPgov, (read taov). XII. 163, 164. + daa (VII. 339, 340. 438-). The Scholiaft on v. 339- feems to be in the right, when he fays, “On the left hand of the fhip-ftation (vatera0uos) was a large ‘« gate, befides which feveral other gates were conftructed.” t VII. 441. XII. 54. 63, &c. Between the ditch and the wall no intermediate {pace was left, as may be inferred from VIII. 2, 3.3; ages wégyé mutt be united. APPEND JX, No. Ul tos the quarter where AcHiLLEs was ftationed. The oblique pofition of the camp muft have been the caufe of this. To the fame circumftance we muft have recourfe to explain how, from the fpot where the Trojans made a breach in the rampart, and at length fet fire to a fhip, the diftance could be fo great to the tents of AGAMEMNoN, and the quarter where the remaining vefléls were hauled up on the land *. - We now come back to the aflault of the camp. At day break the Greeks, leaving their chariots behind them, (XI. 48.), marched out from the camp. The Trojans had taken poft on the field: of battle) which had an acclivity towards Troy j.. Till about noon the fate of the day was equivocal; but then the Greeks made the Trojans give way. The Trojans fled, paft the tomb of Irus,; (XI. 166, &c.), through the midft of the plain, towards the wild fig-tree, (XI. 167.), and never ftopped their flight till they had reached the beech tree and the Scean Gate. (XI..170:).. Here the battle is renewed. (211, &c.). » During all this day AGAMEMNON diftinguifhes himfelf, till he is wound- ed. On this the Trojans take frefh courage, repulfe the Greeks, drive them back again paft the tomb of ILus, where Parts lies in ambuth, and wounds DioMEDE: with an arrow. (XI. 369, &c.). . The combat fpreads to a great diftance over the plain, for Hector fought on the left wing, towards the Scamander, (XI. 498, &c.), againft Nestor and IpomeENeEus, and knew nothing of the defeat which DromEpE, Uryssrs and Ayax had given the Trojans towards the Simois.° Hecror flies ‘to that quarter, and Ayax himfelf is now forced to fall back. (521, &c.): The Greeks flee to their camp, and fhut themfelves up in it. Hector ‘purfues, and refolves to attack them in the camp, to (AVog.. Viens off? ‘3 0 break * Ser Iliad, XIV. 30, &c.; a paflage which I know not how to explain. T Emi Searua mate. (XI. 56.); of which we have fpoken already. 306 TABLEAU dela PLAINE de TROYE. break in, fet the fhips on fire, and annihilate the whole Grecian army. TuIs operation was fo new to the Trojans, that they did not know how to conduct the attack, fo as to make themfelves ma-~ fters of the camp. At length, by the advice of Porypamas, (Iliad, XII. 75.), the chiefs difmount from their chariots, and bring the infantry in five columns over the ditch. Astus alone remains in his chariot. He obferves, upon the left wing of the {hips *, the gate open, through which the Greeks had pafled to and from the field. He makes am attack here, but with an un- fortunate iffue. (XII. 110, &c.). The other divifions affault at different points the rampart and the entrances. (175, &c.). As there were five columns of the Trojans, it is commonly fuppofed that the gates of the fortification muft have alfo been five in number. HeEcTor’s divifion exert themfelves to the utmoft to demolifh the rampart, (251.), particularly around and near one of the gates. (291.). SARPEDON aflaults the rampart at the quarter defended by MEnEstTHEUs, leader of the Athenians. (331.). Mernestueus finds himfelf worfted, and calls for af- fiftance to AyaAx and TEUCER, who were engaged with Hector. By the abfence of thefe two, Hecror is left at liberty to.act. He burfts the gate with a piece of rock, and forces his way into the camp. (437. et feq.). Tue terrified Greeks retreat towards their fhips.. Here the two Ajyaxes had joined. They rally the fugitives, and lead them on again againft the enemy. This column of the Greeks appears to have fome refemblance to a phalanx, the firft outlines of which it is believed may be found here; for the braveft troops, we are told, drew up in thick clofed ranks, and waited for the approaching foe. (XIII. 126, &c.). The enemy, by this manceuvre, is quickly repulfed. WHILE ¥ Naar do dpirrigds (XI. 11Q.). ALP PAE NSD. PX Now TH. 107 Wuite the battle rages here among the fhips *, IpDomenrus, accompanied by MERION, repairs to the left wing }, and there, with the veffels in his rear, makes head againft the troops of Asius. The divifion commanded by HNEAs muft have join- ed the column of Asius, and the troops of PARts united with thefe two. At leaft, all the three detachments, as well as feveral others after them, muft have formed a junction to oppofe Ipo- MENEUs, in the place mentioned above. (XIII. 490.). Tue Trojans, in the mean time, began to crowd in on all fides round the place where Hector was engaged. By the ad- vice of PoLyDAmaAS, (Ib. 726. et feq.), HECTOR calls the chiefs together to a council. He himfelf goes off, (Ib. 674. et feq. f. 754. et feq.), colleéts the braveft_of the chiefs, with their batta- _ lions, and advances with them againft Ayax. (789.). 02 MATTERS * STi: 312. Ey wiornos vyvots + IBID. 326. Ex’ dgireed orgars. Ajax, as afterwards appears, fought in front of his own fhips. The left wing of the camp, therefore, muft have extended beyond the ftation of Ayax.. Compare 679, &c. At that quarter, too, there were fhips lying ; for IDomENEus fought én! medyonzs vecos. (Ibid. 333.). { A rassace of confiderable difficulty, in refpeét of the topography, occurs here. It is faid, (XII. 675.) : “ Hector knew not yet that, on the deft hand of the hips, “ vaav ex’ aesoreg, his Trojans were fuffering fo much; but he ftill kept the place “* where he had firft penetrated into the camp, befide the quarter where the fhips ‘of “* Ajax and ProTesiLaus were hauled up.” (679—682.) The rampart, in front of the fhips, was loweft at this fpot. Here the aftion was fliarpeft. (v. 684.). ” - ev Ooe ariocra ~ = ’ ? ‘ NRE Layencss yiverro aay Ail) GUTOL TE XOb trot. This laft expreffion embarrafles me. How could chariots be of any ufe in the nar- row {pace between the fhips and the rampart? Homer fays further: “ Here fought ‘** the Beeotians, the Ionians, (Athenians), the Locrians, the Phthians,” not thofe fubject to ACHILLES, but thofe who had come with ProTEsILaus, out of Phylace in Theffaly, (II. 695.), but at this time fought under the command of PoDaRcEs, (XIII. 693.), “the Epeans.” I hardly think the fhips of thefe people lay there, . but 108 FABLEAU dela PLAINE de.TROYFeE. Matters had now advanced fo far, that Hecror thought the completion of his wifhes at hand, when the Grecian chiefs, after getting their wounds dreffed, return to the combat. (XIV. 128. 365-——387.).. Hector is wounded, and the Trojans driven from the rampart to the outfide,of the ditch. (XVI. ‘1.). HEeTor recovers again, rallies the Trojans, aflaults the ram- part once more, fills up the ditch, (Ibid. 355. et feq.), and re- news the battle between the fhips and the tents. (367: 384. et feq.). The Greeks beaten back take fhelter behind and between the foremoft row of the {hips on the beach, and with their fhip- poles ward off the Trojans as they prefs on. (Ib. 653. et feq.). Ajax boldly encounters Hector. At length Hecror catches hold of the ftern of a fhip, belonging to the {quadron of ProtE- sILAus, and fets it on fire. (Ibs: 704. et feq. XVI. 124. et feq:). Hers the fuccefs of the Trojans ftopped. PatTrocLus came forward to the combat. The Myrmidons, to the number of 2500, advanced in five divifions, drawn up in clofe columns *. The Trojans are defeated, and forced to retreat to the outfide of the ditch. (XVI. 366. et feq.), There a complete flight en- fues. PaTRoctus cuts off one part from the city, and deftroys them betwixt the fhips, the river, and the town t. Intoxicated with fuccefs, he purfues the fugitives, contrary to the orders of ACHILLES, to the very walls, and even attempts an aflault upon the but that the troops happened to come together in that place. Befides, fo far as I can find, throughout this whole paflage, even where Hecror is fpoken of, the 4 fide muft be underftood as referring to the Grecian camp. It is fo, where mention is made of Paris, (v. 765.), as well as, in apreceding paflage (v. 326.), of IDoME- NEUS. * XVI. 212. Acnitzes and his foldiers, we find, evidently excelled the reft of the Greeks in military fkill. Writers on the art of war, Puysxcur for example, difcover, in this arrangement of the troops Jed on by PatRoc.us, the firft rudiments of cohorts. _ + HERE occurs the remarkable expreffion formerly adverted to, Serbs inti 1 0 ‘vay Ky TEX 05 “bapnroio. (XVI. 396. et feq.). a es -° BYOA VA PVE WD. OX, SNS 109 the city. (698—710.). Hxcror, having halted at the Sczan Gate, rufhes again upon the Greeks and flays Parrocius. He purfues the flying Greeks to their camp; they bring off with them, however, the body of Parrocxus. (XVII. 736.). The fight of AcuILLEs, though unarmed, deters the Trojans from advancing farther. | Tus time too the Trojans pafs the night in the open plain before the camp. (XVIII. 243. et feq.). Hrcror oppofes the fage advice of PoLyDAMAS, to retire into the city, and defend themfelves behind the walls. (Ib. 274. et feq.). At day-break AcHILLES, clothed in new armour, comes out from the camp. (XX. 1, et feq.). The Trojans draw up on the rifing ground* before the camp. This is the fourth and laft battle. At firft both armies difplay equal valour; but at length the Trojans give way, and fall back upon the Scamander. (Ib. 494. et feq.). Here AcHILuLEs feparates the flying army. (XXI. I. et feq.). One part are fortunate enough to effect their efcape acrofs the plain to the city. The remaining part he drives into the river, which, being choked in its courfe, {wells and overflows its banks. . ACHILLES now comes clofe up to the city, (Ib. 520.), which the flying Trojans had already entered by the Scean Gate. (Ib. 526.). . Hecror alone remains before the town; and then enfues the fingle combat, in which HecTor is flain by ACHILLES. ; No. IV. W Emi Seurue medio 5 before the camp. (XX. 2.)e ‘gio TABLEAU de la PLAINE de TROYE. No, IV. (p. 32.). The Reverend Dr Jackson, Dean of Chrifi Church, Oxford, ta Mr Dayzeu*. I caNNOT permit myfelf to leave Oxford for the fummer, without paying you my very fincere thanks for the obliging manner in which you tranfmitted to me the prefent of M. CuE- VALIER’S Effay; and I beg you, when you have an opportunity, to prefent my acknowledgments to M. Cuevarier himfelf: accompanied, however, with a little reproach, for his having for- gotten the promife he made me, of calling at Oxford whenever he came to the fouth of England. I HAVE had a very particular pleafure from the perufal of the work itfelf. No reader of Homer could poflibly be fatisfied with the accounts we had before of the Troad; and Mr Woop’s book, in particular, was idle and childifh in the extreme. Ir was impoflible, alfo, for the reader of Homer to doubt of the fituation of Troy, and the adjacent country, as defcribed in the Iliad ; and I had always, therefore, heard, from the few men who underftood Homer, one and the fame language ;—a lan- guage which I thoroughly adopted, that we were mifinformed and miftaken as to the Scamander: And when I had the pleafure of meeting a fet of friends, a few weeks ago, at Lord Srormont’s in London, I was not furprifed to find that we all agreed in the. fame * At M. Cuevatier’s defire, Mr Daze fent a copy of the Effay to the learned and refpectable Dean of Chrift Church, (to whom M. CHEVALIER was known), and received the above anfwer. Ay PPE NID. TeX, \N6piy. III “ fame opinion, that M. Cuevatrer had cleared up our difficul- ties, and brought every thing into its right place, by difcover- ing the true Scamander.—I have the honour to be, with perfect efteem and regard, &c. Cyr. JACKSON. Curist “ieee Jaly 7. 1792. The late Earl. of MANSFIELD, (formerly Lord Stormont), to Mr DALZEL. I mMUsT not omit repeating my thanks for the Differtation you were fo good as to fend me, which is upon a fubject that has always interefted my curiofity, and which I read twice in the courfe of laft fummer. [After a compliment to the Tran- flation and Notes, his Lordfhip adds] :—I underftand that you may foon expect an anfwer from a very ingenious gentleman*, but one who doubts even of the exiftence of the Trojan war. I can venture to foretel that he will not fhake my faith, which is, and Jong has been, that Homer refted upon hiftorical tradition, not only for the principal faéts, but alfo for the leading diffe- rences in the characters of his heroes ; and that they know little of his real excellence, who afcribe to him that fort of invention,. which is the paltry merit of a modern writer of romance.—L. am, with great efteem, &c.. MANSFIELD.. PoRTLAND-PLACE, 3 June 17. 1793- No. V.- * Tus proved to be the learned Mr Bryant. 112 TABLEAU Ue la PLAINE de TROYE. 1 Now V. (p. 33. 39: 41» 45. 48. 52. 65.). Rosert Liston, E/q; His Britannic Majefty’s -Ambaffador at Conftantinople, to Mr DauzeEu, Greek Profeffor in the eis ity of pa aahins My pear Friend, — Conftantinople, Sept. 25. 1794. To day I have not time to fay a fingle word with regard to myfelf: but I cannot avoid the temptation of fending you co- pies of letters from gentlemen who lately left me, and at my re- queft promifed to infpect the Troad with attention. They are both ingenious men. Dr SisruHorre is Profeflor of Botany in Oxford: The other, noted for his knowledge in mineralogy, and his geographical refearches, a brother of Sir CHRISTOPHER Hawk:Ns. | You will be glad to fee their obfervations tend to confirm M. CHEVALIER’s fyftem. I ever am moft cordially yours, RoBeErT LisTon. i. Hawkins, E/gs to his Excellency ROBERT Liston, His Bri» tannic Majefty’s Ambaffador at Conftantinople. At Anchor, oppofite Karanlik-limani, Sept. 15.1794. Monday Eve. I seize the firft oportunity of giving your Excellency fome account of our expedition to the Troad, but the time will not permit to enter into particulars, WE ¢ APPENDIX, No. V. 11g We caft anchor at Koum-kaleh; about mid-day, on Saturday, engaged horfes; and croffed the plain in three hours to the vil- lage of Bounar-ba/bi, where we flept. We fpent the whole of). the next day in vifiting the hill, which M. Cuevaxibr fappofes to have been the fite of Troy, aid the fprings of gwater, which: he confideérs as the fountains of the Scamander. A day, I think, is fully fufficient for this purpofe, unlefs the traveller means to make topographical obfervations, which was thé cafe with me. We were well lodged and entertained in a Chiftlik at Bounar= bajbi, belonging to Hapcrt MEHEMET Bey, a perfon of forme confequence; who actually refides at the Dardanelles, but is now on a pilgrimage to Mecca. His fubftitute ‘or fteward received us in a manner which left us nothing to wifh for; and our arri- val there feemed to caufe no furprife, as they were accuftomed to frank vifitors. ~We returned by a different rout this day, vi- fiting the tomb of AisvErTEs, (fee CHEVALIER’s map), and thofe néar Cape “Fenitchert, fappofed to be of ‘AcHiuLESs and ‘PaTRo- CLUS. Your Excellency naturally wifhes ‘to hear ‘our prefent fenti-. ments refpecting the hypothefis of M. Cuevanier. We ftill thik ‘it a very platifible one; and although his ‘map 4s incor- rect'in'the detail, it-gives a pretty good idea of the Troad.in general. He ‘has certainly pitched upon a place for the fite ef old Troy,’ which has»much natural ftrength to recommend it,-particularly the eafternmoft angle of the hill, which, from its height above the Simois, and its peninfular form, muft have been confidered:as'a very ftrong:natural faftnefs in. thofe times. of warfare,'and could have been eafily rendered an impreg-. nable citadel; for it is not large enough for the fite of the whole city. Some tvmu/i near this {pot ;are certainly. ftrong in- dices. THERE are two places diftant from each other about two hun- dred yards, in which the fuppofed Scamander iflues out of the Vou. IV. p ‘ earth ; 114: TABLEAU de la PLAINE de ‘TROYIE. earth ; in each, however, by many mouths. The water proved equally cold in them all: neverthelefs in winter one is faid to be warm. We faw the place where the courfe of this river is diverted by an artificial canal to the Archipelago. We are now about to. fhape our courfe for Samothraki. The bearer, our janiffary, fets out alfo on his return to the Dardanelles, where he will confign this to the care of our Conful, to whofe great attention and civi- lities, as well as to thofe of his uncle Mr Kaim, we are much indebted. I szG leave to add, how much I am flattered by the civilities paid me at Conftantinople, and with what truth I have the ho- nour to be, &c. J. HawkIns. Dr Joun S1pTHORPE, Profeffor of Botany in the Univerfity of Ox- ford, to bis Excellency RoBERT Liston, His Britannic Majefty's Ambaffador at Gonftantinople. DEAR SIR, Troy, Sept. 15. 1794. I am juft returned from Troy, as perfuaded as a faithful Muffulman who has made his pilgrimage to Mecca, or as a pious crufader who has been at Jerufalem, that my eyes have beheld the tombs of thofe mighty heroes Homer has fung near two thoufand years fince. It was the “ Campus ubi Troja fuit.” The piety of former ages raifed tombs more lafting than marble or brafs, which time has not deftroyed. Troy and its temples have been fo completely rafed, that not a column, or even a {tone that has been ufed in archite€ture, remains to tell its fite ; and it is from the ¢umuli only, with their relative fituation to the Simois and Scamander, that we are to learn where it once ftood: APSR EYNSD. BX>> NooV. 115 ftood. The fituation where we fuppofe the citadel to be, is par- ticularly fteep and rocky. It is girt by the Simois, the bed of which is now entirely dry. Perhaps the winter torrents might raife it into a confiderable river. Its banks are fringed with planes, agnus caftus, and tamarifk. We flept at Bounar-ba/hi, a little below which rifes the Scamander, fed by numerous {prings of a pure cryftalline water. One of thofe is faid to be warm in winter. At prefent it communicated to us no fenfation of heat. The courfe of the Scamander is often interrupted and choked up. It had overflowed the adjacent lands, which were become reedy, and offered a favourable fituation to wild ducks, fnipes, and coots. The plain of Troy is rich and fertile. We traverfed it from Koum-kaleh to Bounar-bafbi, an extent of nine miles, and flept at the houfe of the Aga. He was himfelf gone to Mecca, but his bomme-d'affaires, or fteward, received us with much hofpitality. Your Excellency will find it the beft fitua- tion to fleep at, when you vifit the Troad. Troy feems to have been built on a moft rocky fpot. We could not find on it even a {pring of water. It 1s covered with prickly barnet, and a few thorny fhrubs. The almond tree, which grows wild, is not without its thorns. It has even more pleafing plants, the yellow jafmine and the wild olive. . I wrITE to your Excellency in hafte, our veffel toffing about at anchor oppofite the tomb of Ajax, where it has been juft drove by a hard gale of wind. The janiflary, who accompanied us from the Dardanelles, is waiting for my letter. He was re- commended to us by our Conful, and has done credit to the re- commendation. In appointing Signior TARAGANO,. your Ex- cellency has nominated a Conful very defirous to oblige and render every fervice to his countrymen. &c. 2 JoHN SIBTHORPE, BP 2: Pt 16 TABLEAU de la PLAINE de TROYE. A fecond Letter on the Subject of the Tread, from his Exee(leney Roserr Liston, Li. D. F. R. S. Epiy, Ais Britannic Ma- Jefy’s tir. at Conftantinople, t@ Mr Dauzen, Profeffor of Greek in the Univerfity of Edinburgh, My DEAR FRIEND, 7 Conftantinople, April 25+ 1799: Your letter of the 28th of December reached me after a long delay, occafioned by the interruption of the communication through Holland. It gives me pleafure to obferve, that the cireumftances I tranfcribed for you, on the fubject of the Troad, appeared inte- refting. I have fince had another letter from Mr Hawks, which confirms {till more perfectly the topography of CHEVA- LER, by removing the only difficulty that could poflibly. caufe HERE SIE a difficulty which had been propofed to mein fo pofitive a manner, as to make an impreflion on my mind, deep- er (it feems) than it ought to have done, As I have not as yet any near-profpe& of vifiting the {pot myfelf, I will once more copy from Mr Hawkins. “T am extremely happy” (fays he) “ that our communications * refpecting the Troad pr oved fo fatisfactory ; and I am happy “that it is in my power to remove the only remaining doubt “ expreffed in your letter, by affuring your Excellency, that Te- ** nedos is really to be feen from the hill of Troy; even the whole “ coaft of the rfland is vifible from the northern to the, fouthern * point. “ Tue mott effential oe in fubftantiating the evidence of ‘ GHEVALIER, is that of the canal made to divert the waters of *{ the ee from their original courfe t towards the Simois. “ This t APPENDIX, No. V. ri * This canal we can bear teftimony to. The errors of Woop * feem to arife from the overlooking this circumftance. As for “ §rrazo, he had never vifited the fpot-in all probability, and “ relied on the authority of Demetrius of Scepfis. “At Athens we fell in with Mr Fauvat, a very ingenious — “ artift, long in the fervice of M. pE CuorsEut, who affured us, * that M. CHEVALIER’s account of the goblet, difcovered in the “tomb of AcHILLES, is perfectly fabulous. It originated, it “ feems, from the fragments of a fmall bronze figure, which, * when he had cleaned, and put together, proved to be a very “curious image of Minerva. He fhewed us a caft which he * had made of it in plafter of Paris. : “ Tuis gentleman fhewed us fome genuine Etrufcan vafes, _ “ difcovered in tumuli he had opened in Attica. This will throw “ new light on the hiftory of art. For my own part, I confider *‘ the Etrufcan as nothing elfe than the early Greek ftyle.” I HAVE copied more than I intended when I took Mr Haw- KINS’S letter into my hand; but you will think probably that the whole is interefting. Ever moft truly and cordially yours, RoBERT LISTON: Ie. -V 1.030. 65, cases 7. 02. 72: )2 M. CHevALieErR to Mr DALZEL: MonsiguR ET CHERAmI, Londres, ce 11. Avril 1796. J’at regu votre reponfe du 2, et j’ai été enchanté d’apprendre que M. l’Ambafladeur Liston avoit prit la peine d’aller verifier lui- 48: TABLEAU Alb sla RL AT Eee eR OTE. lui-méme mes obfervations fur la plaine de Troye. Son temoi- gnage fera du plus grand poids dans la difpute qui s’éleve entre le Dr BRYANT et nous. Quant aux fautes qu’il a trouvées dans © la Carte, je ne demande pas mieux qu’on les corrige, et je préte de tout mon cceur les mains 4 toutes les ameliorations dont cet ouvrage eft fufceptible; mais je ne crains pas de vous aflurer d’avance, que les changemens qu’on pourra faire ne fauroient tomber fur des monumens effentiels a l’intelligence de I’Iliade, tels que la fituation de l’ancienne Troye, les fources du Scamandre, les tombeaux des guerriers, les caps, &c. Tous ces points font fixés relativement les uns aux autres, avec aflez de precifion pour que les changemens qu’on y fera ne puiffent pas affecter fenfible- ment mon ouvrage. Quant aux monumens modernes, tels qu’Alexandria Troas, &c. j’avoue que je n’ai pas cru qu il fut neceffaire de les traiter avec une aufli {crupuleufe attention. La ligne de la cOte a été faite avec la plus grande exactitude; ainfi que l’embouchure de l’Hellefpont et Vile de Tenédos. Je doute, en confequence, que la nouvelle carte y faffe aucun alteration. Au refte: encore une fois je vous donne carte blanche, et de tout mon cceur. Vous pouvez couper, tailler, rogner a votre fantaifie. LorsQue vous publiez la feconde edition, mon ami, vous m’obligerez beaucoup de vous fouvenir du petit nombre d’ob- fervations que je vais vous faire; ou plut6t, que je crois deja vous avoir faites. Je defire, d’abord, que vous fupprimiez ma tirade contre les princes et les femmes voyageurs. Je defire, en feconde lieu, que: Yautre tirade contre les prétres des premiers Chretiens foit aufli fupprimée ; et Mr Bryant vous en adit la raifon. 3°, Tout le chapitre du thro/mos,.et du tombeau d’ILus, ne vaut rien. Mr HeyNeE m’a fuggeré autrefois une trés excellent idée fur ce barrow qu’on voit fur les bords du Simois, en avant le camp : ; : : y ’ 4 ANP POE. N Del X,° Nov Vi, 11g camp des Grecs. Ce monument eft: certainement le tombeau commun que les Grecs éleverent a leur foldats tués dans le com- bat. Vous voudrez bien profiter de cette idée, et arranger a votre facon. Un tombeau fi voifin du camp des Grecs ne pou- voit pas étre un tombeau ‘T'royen. ADIEU, mon ami, vous aurez encore une fois des mes nou- velles avant mon depart. LE CHEVALIER. M. CHEVALIER to Mr DALZEL. MONSIEUR ET CHER AMI, Londres, ce 5 Mai 1790. * * * * * Tr joins ici les corrections que vous m’avez deman- -dées, et qui font beaucoup trop longues pour étre écrites a la marge d’un de nos livres, comme vous aviez paru le defirer. Mo, Jinfifte furtout fur la fuppreffion totale du Chapitre 16. page 112. de la traduction Angloife, qui traite du tombeau dIzus. Il eft évident que je me fuis grofliérement trompé ; pre- miérement, en confondant le Sewcpos| avec le tombeau d’ILus ; et fecondement, le tombeau d’Inus avec. le monument que j’ai decouvert prés des ruines du pont, a peu de diftance de l’em- bouchure du Simois. Mr Hryne, qui fait beaucoup mieux P’Mliade que moi, avoit foupconné que ce monument pouvoit bien étre le tombeau qu’on éleva en commun aux foldats Grecs aprés le premier combat, et dont il eft queftion dans le 7¢ livre, verf. 334, &c. Il me fit part de fes idées, que j’adoptai fur le champ, et c’eft ce qui lui a fait dire, page 168. de fa tradu@tion Allemande, dans une des notes, que M. Lu CHEVALIER, n’étoit pas éloigné de crore que ce tombeau, au lieu d’étre celui d’Iius, éoit vraifem- blablement 120 TABLEAU de ta PLAINE de TROYE. Risin: le tombeau commun. En effet ¢ ce tombeau commun n’étoit pas loin des vaifleaux, puifqu’ Homene le place, TorSov oro ot iene VIL A. : £103 19 ‘ase YEE et que le retranchement fut_bati deletes ma lui. _Ces circor- {tances s’accordent fort bien avec la fituation du monument de- couvert prés des ruines du pont. Do, Je defirerois aufli que vous fupprimafliez tout-a-fait le paflage qui a rapport aux princes voyageurs; vous n’imagineriez jamais qu'il y a eu des perfonnes affez malveillants pour m/’ac- cufer d’avoir voulu faire des applications auxquelles vous favez “que je n’ai jamais fonge. gto, J’ai dit, ala page 12, que du fommet d’Udjek-tepe j’avois appercu a l’oueft la mer Egée, les iles de Tenédos, d’Imbros, de Samothrace, et de Lemnos ; j’ai dit, de piss, a la page 30. qu’en arrivant 4 Kowm-kalé avec M. Casas, j’avois encore remarqué ‘les mémes pics d’Imbros et de Samothrace, &c. Lorfque je fai- fois cette obfervation, j’ignoroit entiérement qu’HomerE lavoit juftifier dans le 13¢ livre de I’lliade, verf. 11, &c. ow il reprefente Neptune obfervant les combats du haut du’pic de Samothrace;, Car de la, dit il, on li ee toute la chaine de l*Ida': ~ Kab yoe o Seopitn§ 150. sivinath TE MOY NY TE "Ls ex’ auporarns noeuP7s Lewes vAgecons a yoe acigias THEO a TOn,— obai Pa, de NEPTung, ON le quitte ‘Samothrace pour fe ,sendre au camp des Grecs, s’accorde aufhi trés bien avec mon sohicat ait ; car il laifle fes chevaux a moitié chemin, entre Imbros et Tenédos : Meconyds Tevédoro xe} "IuBex romerotcons Ibid, 22. 47°, To ) : 7 E A PRPRE LINED AUK ANG. VI. 121 47°, Du moment ou nous fupprimons enti€rement le chapitre qui traite du tombeau d’ILus, je n’ai pas befoin de vous avertir qu'il faut fupprimer le méme tombeau, encore mentionné a la page 63. comme faifant encore aujourd’hui partie des monu- mens cités par STRABON. VoILA, mon ami, tout ce que je puis vous dire en pofte pour le moment. Recevez, pour la derniére fois, mes finceres re- mercimens pour toutes les marques d’amitié que vous m’avez données ; et comptez fur la mienne a la vie ala mort. J’at- tends de jour en jour mon pafleport ; auflit6t qu’il arrive je me mets en route. Mes complimens a tous nos amis. Adieu. Le CHEVALIER.. END OF THE FOURTH VOLUME. q ‘ is a ; ; at i rr ” \ . ! ae ! F ; ‘ i : . 3 é abies. waa OLS SOs: ' eee RS eg Bes vg hee 4 pba } ates i be ‘ey AQnEa Te 18 5 Sie Tan shor. de ab. po uaint sia ee FHNe dein ph, 03 one patie 29 th ii aint; mn migb, sh tneg.rg SOT WET 4 seater gl i. Vir Gh OHO 9F 1. RTT RD aur ah ‘eounf08. Teo att coyote: 2 y “stst-% att COsSt BLS SF ahd ' pak OE al Bue : NaI Thy f ui ty c " - 2 COE OL 4 vives it 1p sOchiets,.4 yrogd sg, Gish: 1505 fo ae "Ope ee a 22 See ie : wew* ph BBP ~djetee rats ABO, &. eqncsiiqnioa ing: in ne amas site fe Sicexieris samngueling- f ee 3 ¥e , - a 2 r wie ~ y ; ved ro 4% ; ' ; x cy , > ‘i ! . ba Ba % Bah Bo AST As HISTORY. Page 14. line 32, for flots, read floats. 30. line laft, for laft Article, Part II. read laft Art. Phyf. Cl, Part I. PART Il. PHYS, PAPERS, Page 111. line 4. from the bottom, for M, read N. 12. from the bottom, for Join AH, read Join EH. 11g. 4. from the bottom, for ArrpoLLonius read APOLLONIUS. 120.. ‘11. from the bottom, for hence the quadrilateral, read hence, if AG, GK be joined, the quadrilateral, &c. 132. 6. from the top, for fig. 20. PI. IV. read fig. 13. Pl. I. N. B. In Pl. IV. fig. 18. the points B and K mutft be joined by a ftraight line. 135. This Paper is by miftake numbered V- inftead of VI. and the fame error is continued in numbering the seimalnints Papers of the Phyf. Cl. age line laft. for the latitude here given, viz. 57°. 9’. 1/’, read 57°. 8’ 59%”, the fun’s femidiameter, ufed in the reduction of the obfervations, , having been 13’ too great. i 178. 6. inftead of the term = e, read >: e". 193: 4. from the bottom, for quilt-like read quill-like PART III. LIT. PAPERS. © Page 86. line 21. for ACHILLES, read PATROCLUS, 10or. . §. from the bottom; Notes, for tomb read trench + ose se = DIRECTIONS FOR THE BINDER. Tue Binder is defired to obferve, that this Vou. confifts of Four Sets of Pages, to be arranged, after the TaBLe oF Contents, in the following Order, viz.: Part I. containing the History oF THE SociETY, with the Pages regularly numbered as far as 40; and afterwards going on with the numbers included between parenthefis, thus (1), &c. to the end of PartI. Then follows Part II. confifting, 1ft, Of Parers OF THE Puysicat Crass, with the Pages numbered in one Series; and, 2dly, PAPERS OF THE LITERARY CLAss, with the Pages numbered in another Series. The Binder will alfo obferve, that there are in all 13 Puates, 6 for the Puystcat Cxass, and 7 for the Literary, which are to be placed exactly according to the references marked on the margin of each. i “> od «Vee 8. Ay Pie OY ne-« oyp xiv stig sed ot aaah 8 | Gssacreibiensd - 2 st ass a Ss per e “pe tao | ‘ad¥-bne" We Yo benne We ae —— ep yas - LD Ad od seetigrekie ads” eo: sae ri oda oi bp : we ; ay : gsi, So oy a oe on 8 : ohana! ' se 5, Salil worn “ea ert Sp Bot ite. i Wompiaher ding: wy, goto! j sient ods moit-.7 ~ A ’ ; 7 a on ? 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