-TRANSACTIONS OF THE ROYAL SOCIETY OF EDINBURGH. VOL. VI ‘EDINBURGH, PRINTED FOR CADELL AND DAVIES, LONDON, : AND ' ARCHIBALD CONSTABLE & CO. AND BELL & BRADFUTE, © : EDINBURGH. . 1812 Wy : St oe ee aS “= PSY essa’ 10. ak f1908 . . * J ~ ; * . * \» = _-* ; ’ wl} ‘ . = 2 ‘ “* . ad > - ? 3, ‘ : ’ . ’ + 2 ee ie ‘ o* 5 owt * x See . 4 ‘ oweasc 1% : PY Raat go 4 rp Oty “Lad * 3 ae ; | eelyad Ur eS | date oe Sea os. oh ieees Saran “Od 4OT phe Behe 3s - > Pres wen > ey mn 46 1 : : oe) ab ‘naa ceevoo Grhai ys te ESS UT DIGL A ig aN OMe : ere ; ; Bie | a : weave nye: * i fs . ' is ; en : ' : ey ; " - XM, Reais sya 2 ea a Pe er *4 * Ng Ba et te aie CONTENTS SIXTH VOLUME. Sr HISTORY of the SOCIETY. Carta Nova Erectionis Societatis Regalis- Edinburgi, - rn 1808, hs Ne & - . Page lit Laws of the Royal Society of Edinburgh, enacted 23d May 1811, = z ! Y Presents made to the Royal Society of Edinburgh since the Year 1809, Ss m ra = I. A Description of the Strata which vc ur in ascending Srom the Plains of Kincardineshire to the summit of Mount Battoc, one of the most elevated points in the Eastern District of the Grampian Mountains. By Lieutenant-Colonel Imrie. - - I. A Geometrical Investigation of some curious and inte- resting Properties of the Circle, &c. By James Glenie, Esq. - ene - XV Vi CONTENTS. III. Account of a Series of Experiments, shewing the Ef- fects of Compression in modifying the Action a Heat. By Sir James Hall, Bart. = qk IV. Of the Solids of Greatest Attraction, or those which, among all the Solids that have certain Properties, Attract with the; greatest: Force ina given Direc- tion. By Mr Playfair. = - Page 187 V. An Account of a very extraordinary Effect of Rare- faction, observed at Ramsgate, by the Reverend S. Vince. Communicated by Patrick Wilson, Esq. 245 VI. Some Account of the large Snake Alea-azagur, (Boa Constrictor of Linnzus), found in the Province of Tipperah. Communicated by Mr James Russell. 249 VII. Chemical Analysis of a Black Sand, from the River Dee in Aberdeenshire; and of a Copper Ore, from ‘Arthrey in blaness 2D By Thomas Thomson, oe a Deane =o . - 253 VIII. New Series for the Quadrature of the Conic Sections, and the Computation, of Logarithms... By Mr Wal- lace. ~ - - 06 & i099 1269 IX. Remarks on a Mineral from Greenland, supposed to be Cr ystallised Gadolinite. By Thomas, Allan, “Esq: = = ‘ a = ne org 345 3 X. On the Progkbsa a Heut when \comiinunicated to Spherical Bodies anon their acai se y “Mr Play- fair. = Hoe HO MOLISE 3 ‘3 353. XI. CONTENTS. vib “XI. Experiments. on Allanite, a new Mineral from Greenland. By Thomas Thomson, M. D. 371 XIE. A Chemical Analysis of Sadalite, a new Mineral from Greenland. By Thomas Thomson, M.D. 387 XII. Demonstration of the Fundamental Property of the Lever. By David Brewster, LL. D. - 397 XIV. On the Rocks in the vicinity of Edinburgh. By Tho- mas Allan, Esq. - - - 405 HISTORY OF THE SOCIET Y.. ee Sn ——_——" N the original charter of the Royal Society, it was provided that the collections of the Society should be deposited, if belonging to Natural History, in the Museum of the Univer- sity, and if to Antiquities, in the Library of the Faculty of Ad- . vocates. Much inconvenience, however, could hardly fail to result from this arrangement, especially wh€n the researches of the Society, having, as of late, been much turned to Geolo- gy, it became an object to collect together the specimens which served to illustrate the subjects under discussion, and to have them at hand when reference should be necessary. ‘Iw a Museum arranged with .a view to public lectures, (like that of the University), such an order as was required for this purpose could not easily be preserved; the Professor of Natural History must feel himself interrupted by the exami- nations which the Mentbers of the Royal Society might wish Vou. VI.—P. II. a to 2 HISTORY of the SOCIETY. to make ; and it would often be a point of delicacy, not to give him the trouble that such examinations would require. TuEse considerations induced the Society to apply for a new charter, under which its collections should remain in its own possession, so as to be at all times accessible to its Mem- bers. As the interest of the two bodies just mentioned, might be somewhat affected by these alterations, the first step taken was to give them information of the intentions of the Society, and to request their concurrence in a measure of such mani- fest justice and utility, The Faculty of Advocates readily as- sented to this proposal; and the University, though at first in doubt whether it were not bound in duty to resist the al- teration, on more mature deliberation, resolved to withdraw all opposition. As it was not meant that the new charter should have any retrospect, the Huttonian Collection, with a great number of other articles, the property of the Society, still remain in the University Museum. The foundation of a new collection, in the Society’s apartments, has been laid, by a cabinet presented by Mr Array, containing specimens of the rocks round Edin- © burgh ; a collection by Colonel Imr1z, illustrating the section of the Grampians which he has given in the 5th volume of the Transactions of the Society; and a collection of specimens from Sir Greorce Mackenzir, illustrating the Mineralogy of Iceland. Tur New Charter, which follows, hardly differs in any thing from that contained in the first volume of the Transactions of the Society, except in what respects the two restrictions that have just been mentioned. ‘CARTA CARTA NOV ERECTIONIS. SOCIETATIS REGALIS EDINBURGI,. 1808... GerorGIus TERTIUS, Der gratia; Britanniarum Rez; Fidei. Defensor ; omnibus probis hominibus ad quos presentes l- tere nostre. pervenerint, salutem: Quandoquidem Nos conside- _rantes, quod petitio. humilis nobis -oblata fuerit a Regali: Socie- tate Edinburgi, et prefideli nostro et» predilecto: consanguineo Henrico Duce de Buccleuch, ejusdem preside, in nomine et vice Societatis, et omnium ejusdem Sociorum ; in qua petitione enar- ratur, quod per regiam nostram cartam, dutam vigesimo nono die mensis Martti anno Domini millestmo septingentesimo et oc- togesimo tertio, Nobis benigné placuisset constituere, erigere et imcorporare quosdam ibi nominatos in corpus politicum et corpo- a2 ratum, 4 HISTORY of the SOCIETY. ratum, nomine titulogue Recauis Socirratis Eptnpurey, ad promovendas literas et scientiam utilem, cum facultatibus et privilegiis ibidem concessis, et speciatim, ut potens et capaw sit tenendi proprietatem realem et personalem, causasque agendi et defendendi, Presidem et Socios eligendi, canones ordinandi, et perpetuam successionem sub tali nomine habendi: quod, virtute predicte carta, Regalis Societas Edinburgi, ita creata, substi- tuerit, suisque officiis a prima institutione, rite functa sit : quod carta predictd ordinatum fuerit, cunctas res antiquas, tabulas publicas, librosque manuscriptos, quos acquiswerit Societas, in Bibliotheca Facultatis Juridice deponi ; atque universas res ad historian naturalem pertinentes, quasque Societas acquisiverit, in Museo Academia Edinensis deponi: quod, ab hac constitu- tione incommodum haud parvum ortum fuerit ; cim Regalis Societas, nullum jus in Bibliothecarios Facultatis Juridica, nec | in Custodes Musei Academia Edinensis, habeat, nec horas eorum ministerii regulasve admussionis ad ea repositoria pra- scribere possit, nec Societati licitum sit congressus suos in eo- rum alterutro tenere ; que citm ita sint, hactenus Societati non licuit suas collectiones ita disponere, ut Sociorum aliorumve studio et disquisitioni apté subjiciantur, undé et alia dona ex- pectanda essent : Quod predicta Societas, causd hee incommo- da amovendi, nostrague bona proposita in hac institutione ad effectum perducendi, sapientia nostre regié humiliter subjiciat, ut detur Societati jus collectiones suas cujuscunque generis uno in loco deponendi, quo sibi ordine placuerit, sub custodibus a Societate eligendis qusque potestati subjectis; itaque ut car- tam, cwn privilegiis idoneis hwmilibus nostris petitoribus conce- dere dignemner sas ut et in hac petitione oratum sit, ut Nobis benignée placeret de novo Cartam Nostram Regiam concedere dicta Regali Societati Edinburgi, ejusque CH qua iterum darentur jura, facultates, et privilegia, im carta regia per quam HISTORY of the SOCIETY. 8 quam corpus istud creatum fuerat concessa, et qua insuper provideretur, uti nobis in regia nostra sapientia zdoneum vi- deatur, ut Societati potestas daretur -collectiones suas anted memoratas in uno edificio deponendi, eis legibus, et eis mini- stris, qui Societati placerent, hosque subi subjectos haberet : Et nos certiores facti hanc petitionem justam esse rationique consentaneam, et.certis conditionibus et modis,'in prasentibus eapressis, concedi debere: Icitur, constituimus, erigimus et incorporavimus, sicuta Nos regid nostra prerogativd, et gratid speciali, pro Nobis notrisque regis successoribus, per has pre- sentes, constituimus, erigimus, et incorporamus, predictum Hen- ricum Ducem de Buccleuch, Sociosque dicte Regalis Societa- tis, atque alios qui postea eligentur Soci, in unum corpus po- liticum et corporatum, vel legalem incorporationem, nomine et titulo Recatis Socretatis Epinpuroi, ad promovendas literas et scientiam utilem, utque talis existens, et tali nomine, perpetuitatem habeat et successionem ; DECLARANTES, Quod dicta Societas capax sit capere, tenere, et frui proprietate reali. seu personali, et petere, causas agere, defendere et re- spondere, et conveniri, in jus trahi, defendi et responderi, in omnibus seu ullis nostris Curtis Judicature ; et declarantes quod dicte Societati fas sit, sigillo, tanquam Societatis sigillo, uti; dantes potestatem dicte Societati, per majorem’ suffragio- rum numerum eorum qui aderunt, eligendi Presidem aliosque officiartos pro negotiorum administratione ; necnon ordinandi canones, ad quos Soci sint eligendi et res Societatis sint admi- nistrande, conditionibus hujus carte sive donationis haud in- congruentes, nec legibus et praxi nostri regni Scotie contra- rios ; et declarantes, quod hujusmodi canones sanciri nequeant,+ nisi rité propositi fuerint in congressu habito saltem uno men- st ante illum congressum quo sanciendi sint : dantes etiam po- testatem Societati ordinandi et administrandi collectiones re- rum 6 HISTORY of the SOCIETY. z rum antiquarum, tabularum publicarum, librorum manuscrip- torum, et rerum ad historiam naturalem pertinentium, quas Societas posted acquisiverit, easque in Museo et Bibliotheca, tali ordine et modo ut Societati placuerit, deponendi: sauvis tamen conditionibus, in hac nostra carta provisis ; declarantes insuper hanc cartam nostram concessam esse sub his conditioni- bus sequentibus, videlicet, Quod jura, facultates, et privilegia, per praesentes in dictam Societatem collata, nulle, modo detra- hent de ullo jure dominii quod competit Academia Edinensi: in collectiones antehac depositas in Museo Academia, virtute car- te nostre Societati Regali data, predicto vigesimo nono die mensis Martii millesimo septingentesimo et octogesimo tertio ; antedicta Societate quantum in se est astricta, omne jus, ad collectiones antehac factas et in Museo. pradicto depositas, in dictam Academiam transferre ; et quod Historie Naturalis Pro- fessori copia introitis in Museum et Bibliothecam Societatis Regalis detur aqué ac Sociis ipsius Societatis ; et quod dicte Societati non sit licitum constituere Professorem, pralectorem seu Doctorem Mineralogie, Geologie, aut Historie Naturalis, nec suis collectionibus uti ad talem institutionem promovendam, nisi que vel nunc sit, vel posthac fuerit, in Academia Edinensi. —In cuyus REI TESTIMONIUM, sigillum nostrum per Unionis Tractatum. custodiend., et in Scotia vice et loco Magni Sigilli ejusdem utend., ordinat., praesentibus appendi mandavimus ; Apud Aulam nostram apud St Jamvs’s, vigesimo septimo die mensis Decembris anno Domini millesimo octingentesimo et octa- 00,, regnique nostri anno guadragesimo nono. Per HISTORY of the SOCIETY. 7 Per signaturam mantis D. N. Regis supra script. Written to the Seal, and registered the thirtieth day of August 1811. James Dunpas, Dep". Sealed at Edinburgh, the thirtieth of August, One thousand eight hundred and eleven years. James RoBERTSON, Subs. £80 Scots. Tuts charter, as well as the former, having left the Society in possession of the power of making By-laws for the regula- tion of its affairs, it was proposed to revise the whole of those ‘laws, and to make such alterations as, after the experience of thirty years, might appear to be necessary. Tue Society, therefore, having at several General Meet- ings taken this subject into consideration, after mature deli- beration, 8 HISTORY of the SOCIETY. beration, and with due attention to the clause in the charter that respects the enactment of such laws, did, at a General Meeting, on the 23d of December 1811, sanction the Laws that follow, and declare them to be the rules by which the Society is to be governed, till all, or any of them are regularly repeal- ed. LAWS ee LAWS ROYAL SOCIETY OF EDINBURGH, Enactep 23d May 1811. I. HE Royat Society oF Epinsurcx shall be composed of Ordi- nary and Honorary Members. , i. Every Ordinary Member, within three months after his election, shall pay as fees of admission Three Guineas, and shall further be bound. to pay annually the sum of Two Guineas, into the hands of the Trea- surer. IH. Members shall be at liberty to compound for their annual subscrip- tion, each paying according to the value of an annuity on his life, deter- . mined as in the ordinary insurance on. lives. The power of raising the annual subscription shall remain with the Society. ; IV. Ordinary Members, not residing in Edinburgh, and not compound- ing for annual subscription, shall appoint some person residing in Edin- burgh, by whom the payment of the said subscription is to be. made. and shall signify the same to the Treasurer. b Vv. 5 de) HISTORY of the SOCIETY. V. Members failing to pay their subscriptions for three successive years, due application having been niade to them by the Treasurer, shall cease to be Members of the Society, and the legal means for recovering such arrears shall be employed. VI. None but Ordinary Members are to bear any office in the Society, or to vote in the choice of Members or Office-bearers, nor to interfere in the patrimonial interest of the Society. vil. The number of Ordinary Members shall be unlimited. Vill. The Ordinary Members shall receive the volumes or parts of the So- ciety’s Transactions, when published, at the booksellers price, or the price at which they are sold to the trade. This regulation to continue in force for five years from the date of its enactment ; and it is left to the Society then to consider, whether the volumes cannot be afforded gratis to the Members. : IX. The Society having formerly admitted as Non-resident Members, gentlemen residing at such a distance from Edinburgh as to be unable regularly to attend the Meetings of the Society, with power to such Non-resident Members, when occasionally in Edinburgh, to be present at the Society Meetings, and to take a part in all their inquiries and proceedings, without being subjected to any contribution for defraying the expences of the Society ; it is hereby provided, that the privileges of such Non-resident Members already elected shall remain as before ; but no Ordinary Members shall be chosen in future under the title and with the privileges of Non-resident Members. The Members at present called Non-resident shall have an option of becoming Ordinary Members; if they decline this, they shall continue Non-resident as for- merly. KG HISTORYS of the SOCIETY. II Xx. The Honorary Members of the Society shall not be subject to the annual contributions. They shall be limited to Twenty-one, and shall consist of men distinguished for literature and science, not residing in Scotland. XI. The election of Members, whether Ordinary or Honorary, shall be by ballot; it shall require the presence of Twenty-four Members at least to make a quorum, and the election shall be determined by the majority of votes. XII. The election of Members shall be made at one General Meeting an- nually, on the fourth Monday of January. XIII. No person shall be proposed as an Ordinary Member, without a re- commendation presented by a Member of the Society, and subscribed by Three, to the purport mentioned below * ; which recommendation shall be hung up in the Rooms of the Society, at least during Three Ordinary Meetings (of the Classes) previdus to the day of election. XIV. In order to carry on with facility and success those improvements in science and literature, which. are the objects of the institution, the So- ciety shall:be divided into two Classes, the Physical and the Literary Class ; the former having for its department the sciences of Mathematics, Natural Philosophy, Chemistry, Medicine, Natural History, and what relates to the improvement of Arts and Manufactures ; the latter having b2 for * « A,B, a gentleman well skilled in many branches of Philosophy and Polite Learning, (Mathematics, Chemistry, Natural History, &c.) being to our knowledge desirous of be- coming a Member of the Royal Society of Edinburgh, we whose names are subscribed, do recommend him as deserving of that honour, and as likely to prove an useful and valu- able Member.” Election of Mem~ bers. 12 HISTORY of the SOCIETY. for its department the inquiries relative to Speculative Philosophy, An- tiquities, Literature and Philology. : XV. The Classes shall meet alternately on the first and third Mondays of every month, from November to June inclusive. It shall be competent, however, to bring matters of a Physical or Literary kind, before either Class of the Society indiscriminately. To facilitate this, one Minute- book shall be kept for both Classes; the Secretaries of the respective Classes either doing the duty alternately, or according to such agreement as they may find it convenient to make. XVI. The Society shall from time to time make a publication of its Trans- actions and Proceedings. For this purpose, the Council shall select and arrange the papers which they shall deem worthy of publication in the Transactions of the Society, and shall’ superintend the printing of the same. The Transactions shall be published in Parts or Fascicuh, and the ex- pence shall be defrayed by the Society. XVII. There shall be elected annually for conducting the publications and regulating the private business of the Society, a Council, consisting of a President ; Two Vice-Presidents ; a President for each Class of the So- ciety ; Six Counsellors for each Class; one Secretary for each; a Trea- surer; a General Secretary; and a Keeper of the Museum and Li- brary. XVIII. The election of the Office-bearers shall be on the fourth Monday of November. XIX. Four Counsellors, Two from each Class, shall go out annually. They ate to be taken according to the order in which they presently stand on the list of the Council. ; XX. HISTORY of the SOCIETY. 13 KX, The Treasurer shall receive and disburse the money belonging to the Society, granting the necessary receipts, and collecting the money when due. : He shall keep regular accounts of all the cash received and expended, which shall be made up and balanced annually ; and at the General Meeting in January, he shall present the accounts for the preceding year to be audited. At this Meeting the Treasurer shall also lay before the Society a list of all arrears due above twelve months, and the Socie- ty shall thereupon give such directions as they may find necessary for recovery thereof. ; XXI. At the General Meeting in November, a, Committee of Three Mem- bers shall be chosen to audite the Treasurer’s accounts, and give the necessary discharge of his intromissions. - The report of the examination and discharge shall be laid before the Society at the General Meeting in January, and inserted in the records. XXil. -The General Secretary shall take down minutes of the proceedings of the General Meetings of the Society and of the Council, and shall enter them in two separate books. He shall keep a list of the Donations made to the Society, and take care that an account of such Donations be pu- blished in the Transactions of the Society. He shall, as directed by the Council, and with the assistance of the other Secretaries, superintend the publications of the Society. XXIII. A Register shall be kept by the Secretary, in which copies shall be jnserted of all the Papers read in the Society, or abstracts of those Pa- pers, as the Authors shall prefer; no abstract or paper, however, to be published without the consent of the Author. It shall be understood, nevertheless, that a person choosing to read a paper, but not wishing to put Treasurer. Secretary. 14 HISTORY of the SOCIETY: put it into the hands of the Secretary, shall be at liberty to withdraw it, if he has beforehand signified his intention of doing so. For the above purpose, the Secretary shall be empowered to employ a Clerk, to be paid by the Society. XXIV. Another register shall be kept, in which the names of the Members shall be enrolled at their admission, with the date. XXV. A Seal shall be prepared and used, as the Seal of the Society. XXVI. The Librarian shall have the custody and charge of all the Books, Manuscripts, objects of Natural History, Scientific Productions, and other articles of a similar description belonging to the Society ; he shall take an account of these when received, and keep a regular catalogue of the whole, which shall lie in the Hall, for the inspection of the Mem- bers, XXVII. All articles of the above description shall be open to the inspection of the Members, at the Hall of the Society, at such times, and under such regulations, as the Council from time to time shall appoint, PRESENTS PRESENTS made to the Royat Society or Evinsurcu since the Year 1809. The Sixth Volume of the Scriptores Logarithmici—From Mr Baron Maseres. Treatise on the Gout, by the late Dr Hamitron of Lynn-Regis——From the Au- thor. Traité de Mineralogie, par M. rz Compre ve Bournon, 3 vols. 4to.—From the Au- thor. An Engraving, representing all the Mountains of the World, by R. Riddel, Esq; together with the History of Mountains, by Joseph Wilson, Esq; vols. 1st and 2d.—From Messrs Rippex and Witson. Recueil de Quelques Antiquités trouvées sur les Bords de la Mer Noire, par M. Leon pe Wexer.—From the Author. ‘Nova Acta Petropolitana, tom. 14.—From the Imprrran Acapemy of St Pe- tersburgh. - Philosophical Essays, by Tuomas Gorpon, Esq; 2 vols. 4to.—From the Author. Transactions of the Linnean Society, vol. 8th and 9th.—From the Linnean So- CIETY. : Asiatic Researches, vol. 10th and 11th.—From the BEneax Socrex¥s Philosophical Transactions, for 1809, 1810, 1811.—From the Rovat Society or Lonpon. Memoirs of the American Academy, vols. Ist, 2d, and 3d.—From the Ame- RicaAN ACADEMY. Transactions of the American Philosophical Society, vol. 6th, part 2d.—From the American Puitosoruican Society. “Observations on the Hydrargyria, by Gzonce AttEy, M. D.—From the Author. ‘Transactions of the Geological Society of London, vol. ist.—From the Grouo- GICAL SoclETy. Travels 16 HISTORY of the SOCIETY. Travels in Iceland, by Sir George Mackenzie, Baronet. Annals of Iceland, from 1796 to 1804. Manuscript copy of the Sturlinga Saga. History of Iceland during the 18th century. A compendium of Anatomy, translated into Ice- landic, from the Works of Martinet. Pope’s Essay on Man, in Icelandic verse.—From Sir Georce Mackenzie. Essay on the Natural History of the Salt District in Cheshire, by Dr Hortanp.— From the Author. Collection of Specimens, illustrating the Mineralogy of the Country round Edin- burgh.—From Tuomas Atay, Esq; Collection of Specimens, illustrating the Section of the Grampians, at the begin- ning of this volume, with a descriptive Catalogue. —From Lieutenant-Colonel Imrie. Model in Relief, representing the Granite Veins at the Windy Shoulder in Gal- loway.—From Sir James Hatx, Baronet. Collection of Specimens, illustrating the Mineralogy of Iceland.—From Siv Grorce Macgenzire, Baronet. ey I, 4 Description of the StRavTA which occur in afcending from the PLains of KINCARDINESHIRE (0 the SUMMIT of Mount Batroc, one of the moft elevated points in the Eaftern Diftrict of the GRAMPIAN MounTAins. By Lieutenant-Colonel Imrie, F.R.S. EpIn.. [Read 5th March 1804.] HE moft mountainous parts of Scotland are fituated in its _ weftern and north-weft diftricts. From thofe parts of the country, feveral chains of mountains branch off, and continue their courfes in various directions, and to various extent. The moft extended of thofe chains is that of the Grampians. This chain takes its rife from nearly about the centre of the above al- pine diftrict, and continues its courfe in a dire@tion almoft due: eaft, or perhaps a little to the fouth of that point, until it difap- pears in the German Ocean, betwixt the towns of Aberdeen and Stonehaven. Tuis chain, in its eaftern diftri, confifts of three ranges, run- ning nearly parallel to each other ; the two lateral ranges being. confiderably lower than the central one. To the lateral moun- tains are attached a range of lower hills, that flope down into undulated grounds, which fkirt the adjacent plains. THE general fhape of the individual mountains compofing thofe three ranges, is oblong, rounded, and fometimes flattifh on the tops; their length is always in the direction of the A 2. chain, 4 DESCRIPTION of the chain, that is to fay, from weft to eaft: and I have obferved, not unfrequently, that the weftern ends of thofe oblong moun- tains are more bulky than their eaftern extremities, and that they flope and taper in fome degree towards this quarter. Their ge- neral covering is that of a coarfe gravelly foil, produced by their own decompofition ; and the produce of this foil is heath. But upon fome of the heights in the central range, I have found beds or layers of that fpecies of turf called Peat, from fifteen to twen- ty feet in thicknefs, which repofe upon the gravelly foil that there covers the native rock. Art this eaftern part of the Grampians, where I am now about to endeavour to give a defcription of the ftratification, the moun- tains feldom thow any confiderable extent of naked rock. In their courfe to the eaftward, as they approach the fea, they begin to contract in breadth, and cover much lefs {pace of coun- try; and where they finifh their courfe at the fea, their height will fcarcely entitle them to the appellation of hills : but although - they become fo diminutive in height and in breadth, yet the ma- terials of which they are formed continue the fame as thofe which compofe the ranges where they are in their greateft alti- tude, and their exterior characters, as to form and figure, alfo continue the fame. AmonG the rivers which have their fource in the Grampians, that of the North Efe is not the firft in rank as to fize, nor is it the moft diminutive. At a confiderable diftance from the plains in the interior of the mountains, a {mall lake called Loch Lee is formed, in a rocky bafon, by a rivulet, and fome fprings and rills flowing from marfhy grounds. From this lake the North Efk iffues, not in a very confiderable flow, but, being foon joined by other ftreams and alpine torrents, it {wells to a confiderable fize, and continues a courfe from this lake almoft due eaft, betwixt the central and fouth lateral ranges of the mountains, for an ex- tent of about feven miles: it then {kirts Mount-Battoc, and be- ing STRATA of the GRAM PIANS. _ ing there impeded, in its eaftern direction, by fome of the hills forming the bafis of that mountain, it then changes its courfe, almoft at a right angle, and from thence flows in a due fouth di- rection. In this laft direction, it opens a way for itfelf through the fouth lateral range, and enters the plains of Kincardine, and - Forfar fhires, where it immediately becomes the line of divifion of thofe two counties. It leaves thofe plains by a hollow betwixt the two low hills of Garvoke and Pert, and after a courfe of near- ly thirty miles from its fource, it joins the fea fomewhat to the eaftward of the town of Montrofe. It is in the bed of this river that I have examined the ftrata of the Grampians of which I am now to give a defcription. The feGtion extends about fix miles, from the horizontal grit or fand{tone in the plain, to the granite of Mount Battoc, which is one of the mountains in the central range, and one of the higheft of the chain in that part of the country. My direction, in this examination, is about due north, piercing through, almoft at right angles, the {trata of the moun- tains, which are here nearly in a vertical pofition. In this fhort ftretch of fix miles, a great deal of matter highly interefting to geology prefents itfelf. In it, we pafs from the fe- condary horizontal {trata of the neweft formation, to the verti- cal, contorted, primary ftrata of the oldeft date, and terminate with granite, the primitive rock in the conception of many geo- logifts. Thus, it embraces a complete range of the foflil objects, which in this part of Scotland intervene between that which is deemed the oldeft and what is accounted the moft recent in point of formation. From the various {trata ftanding in a pofition vertical, or nearly fo, and the river North Efk, cutting acrofs thefe ftrata, at right angles, the fucceffion is uncommonly well exhibited to view, and a fair difplay of the ftru@ure of this country, and of the materials compofing it to a great . depth, is open to the attentive obferver. In addition to this fine difplay of the fucceflion of ftrata, the arrangement of them will be 6 DESCRIPTION of the be found to offer fome very curious and important faéts, parti- cularly the gradual elevation, and the final perfect vertical pofi- tion of the fand{tone and puddingftone, as well as the rather un- ufual manner in which the fecondary and the older ftrata meet each other. In the feries here to be defcribed, the repeated occurrence of rocks of the whm and of the porphyry formation, refpecting the origin of which opinions are fo much divided, adds confiderable intereft ; efpecially when the form and fituation in which they occur, and the condition of the contiguous rocks, are taken into confideration. In the account which I am now about to give, I fhall endea- vour to lay down a fair reprefentation of the facts as Nature pre-~ fents them, unbiafled by any of the prevailing theories of cof- mogony. I fhall avoid every geological difcuflion whatever, leaving it to others to draw thofe conclufions, in relation to their own fpeculations, which they fhall imagine the fats to warrant. In that part of the plains of Kincardinefhire from which I take my departure, the native rock confifts of Siliceous Grit or Sandftone, which is here divided into an immenfe number of beds or layers, of various thickneffes, from one inch to four feet, folid ftone. In many places, gravel of various fizes is found im- bedded in this grit ; which gravel confifts moftly of water-worn quartz, and fimall-grained granites. The colour of the general mafs of this grit is a dark-reddifh brown, and in fome few pla- ces it fhows narrow lines and dots of a pearl-grey colour. The component parts of this grit confift of fmall particles of quartz, and {till more minute particles of filvery-luftred mica: thefe owe their cohefion in mafs to a martial argillaceous cement, to which this rock alfo owes its colour. Thofe lines and dots of pearl- grey colour, generally occur in the moft folid and thickeft beds of. STRATA of the CRAMPIANS. > of the rock: they are formed of the fame materials with the other parts of the ftone; but into them the ferruginous ftaining matter has not apparently been able to penetrate, and they de- rive their prefent greyifh appearance from the natural -colour of its particles of quartz, which are here per /e of a bluifh-white tint. This rock, in the plain, is perfectly horizontal in its pofi- tion; but upon its approach towards the undulated grounds, which here form the loweft bafis of the Grampians, it begins to rife from its horizontal bed, and, gradually increafing in its ac- clivity towards the mountains, it at laft arrives at a pofition per- fectly vertical. For the firft quarter of a mile from where this grit begins to leave its horizontal pofition, the rife is very gradual; but after that diftance, it becomes more rapid, and in a mile it gains its vertical pofition. WHERE this grit or fandftone rock is in its moft folid ftate, and where its pofition is perfectly vertical, betwixt two beds or layers of it, there occurs a bed of Whinftone forty feet broad. THE main body of this bed of whin interfeéts none of the layers of grit, but ftands upright betwixt two of them, to both of which it is clofely joined. The river, at this place, has, in its paflage, worn down this bed of whin equally with that of the adjoining grit, and a perpendicular face of it can be examined upon each fide of the river, from fifty to fixty feet in height. Uron examining the fection of this bed, I found upon the eaft fide of the river two branches, which fprung from the main body of the whin, nearly where the water of the river at prefent wafhes the bafe of its perpendicular furface. One of thofe branches {prings from the right fide of the trunk, and the other {prings from the left fide; they at firft diverge from the trunk as they ‘afcend, and where they pufh out laterally, they interfect the con- tiguous ftrata, and penetrate them in a zig-zag manner; but at laft, in a pofition betwixt two of the layers of the grit, they con- & tmue 8 DESCRIPTION of the tinue their direction upwards, decreafing in their diameters as they afcend, until they finifh their courfe near to the fuperficial foil which here covers the rock. The grit contiguous upon both fides to the bed of whin, is confiderably harder and more com- pact than it is in any other part of the ftratification; and that angle of the grit which lies between the body of the whin and its branches, is more indurated than the ftrata of the grit upon each fide. Vari Soil. Grit in Grit in Aan ! vertical rata. ftrata. The river. Tus {pecies of whin is not very compact in its texture. Its fracture is fomewhat earthy, and is of a brownifh-black colour ; but it has a confiderable degree of induration, and has fome f{pecks of luftre in it. Having paffed this bed of whin, the grit continues in the fame pofition as immediately before the whin occurred ; but, foon after, the gravel, which I have mentioned to be in fome places imbedded in the grit, increafes in quantity, and at laft the ftrata are formed of a rock compofed entirely of that fpecies of gravel, and which may be called Gravel-{tone or Plum-pudding-rock. This aggregate conftitutes a ftratum four hundred yards thick. Its ftretch is nearly from weft to eaft, and it is vertical-in its pofition. Its compofition confilts of quartz, porphyries, and fome fmall-grained granites, all of which have evidently been rounded by attrition in water: they are STRATA of the GRAMPIANS. “9 dre of a vaft variety of fize, from that of a pea to the bulk of an oftrich egg. Thefe are all firmly combined by an argillaceous ferruginous cement. In fome parts of this gravel rock, are to be feen thin lines of a fine-grained grit, ftretching through-it from weft to eaft; it is by thofe lines alone that the vertica- lity and the ftretch of this mafs is difcoverable. Its general co- lour, in mafs, is that of a ferruginous red. Tus plum-pudding rock is immediately followed by a las ceffion of ftrata of fine-grained grit, in thin layers: it has a very confiderable degree of induration, and is of a dark ferruginous brown colour. This deviates alittle from the vertical pofition, and inclines to the fouth: the ftretch is from weft to eaft, and its ex- tent-towards the north is two hundred and fixty yards. To this rock immediately fucceeds a {pecies of Porphyry, the principal mais of which confifts of an-indurated argil. Its colour is of a purple or lilac brown: its induration is very confiderable, and its fracture is rough and earthy. The materials which are im- bedded in its mafs, confift of fmall particles of quartz, felfpar, blackifh-brown mica, and fpecks of iron ochre ; all of thefe are but thinly fcattered. The fpace in the courfe of the river occu- pied by this porphyry is two hundred and twenty yards: its ftretch is nearly-from weft to eaft, and it inclines in a {mall de- gree to the fouth. The rock which fucceeds to this porphyry, and which is in contact with it, is difficult to defcribe ; and this difficulty arifes from the great diforder of the ftratification, and the variety of materials compofing it. The ftrata of this bed do not fucceed each other in a regular manner. Portions of them of various dimenfions lie together, but very varioufly difpofed : fome are vertical, fome horizontal, fome dip to the fouth, one only to the north, affording a folitary inftance of a northern in- - clination of the ftrata in this field of examination. Tue materials of this mafs of confufed ftratification, are of very different defcriptions. In one place, a quartzofe ftone Voi. VI.—P. I. B abounds, 10 DESCRIPTION of the abounds, of a granular texture: it here, in general, refembles a fine-grained, highly indurated, and compact quartz fandftone : fometimes, however, it approaches to horn{tone, and even fome- times to quartz in mafs. Much of it has a white colour: the reft is tinted of an ochery brown, of different fades. In other places, the ftratified matter confifts of a {tone of a-laminated tex- ture, with undulating lamelle of a ferruginous tint, looking like an indurated fhale ; and various gradations of both kinds prefent themfelves. This jumble is in thicknefs three hundred yards ; and to it immediately fucceeds a very narrow ftratum of Argil= lite, which is of a greenifh-grey colour, and very thinly lamel- lated. Tuis argillite is fucceeded by a bed of Whin, thirty-three feet broad. This whin is of a dark blackifh-brown colour, and is of a more compact texture, than the whin which I have defcribed occurring in the grit, and is pofleffed of more induration: the materials of compofition are nearly the fame in both. Irs general ftretch is nearly from weft to eaft; but in this ftretch, where it has been expofed to the eye by the river, it is fomewhat curved, and’prefents its convex fide to the mountains. To this bed of whin fucceeds a narrow ftratum of Argillite, per- fe@tly fimilar to that which I have juft now. defcribed upon its fouthern fide. To this fucceeds a feam of Limeftone, fix feet broad: This limeftone is ofa pale blue colour, and is much in- terfected by {mall veins of quartz trending through it in all db rections: In this limeftone, I’ was unable to trace the remains of any animal or vegetable production. Its pofition is vertical, and it is immediately fucceeded by another-narrow ftratum of argillite, thinly lamellated. To this narrow ftratum of argillite fucceeds-a bed of Whin, feventy-five feet broad. This whin is, in its texture, more com- pact ; and. its fracture. difplays a fmoother furface than either of STRATA of the GRAMPIANS. ei of the two former whins which I have had occafion to mention. Its colour is of a dark-bluifh black. In tracing, with my eye, its vertical cracks-and fiffures, I thought I could perceive a rude tendency to prifmatic forms. It is vertical in its pofition; and its ftretch is from weft to eatt. Tuts bed of whin is fucceeded by an Argillite of fhivery tex- ture, and confufed ftratification ; ‘but as it recedes from the whin, and approaches the mountains, it becomes regularly ftra- tified. This ftratum of flate is of great extended thicknefs ; and it contains a vaft variety of colour and of tint. The colours are, pale greyifh-blue, yellowifh-green, reddifh-brown, purple and black, with a great variety of tints of all thofe colours ; but the predominant colours are the greyifh-blue and the yellowith- green; of which two there are two forts; the one foft, and the other much indurated. The foft is thinly laminated, and fre- quently pafles over into the highly indurated fort, in which the appearance of the laminated texture is almoft loft. In this long fucceflion of argillite ftrata, fome fubftances oc- cur that are heterogeneous to its rock, fuch as jafpers, limeftone, &c. Tue jafpers are in general of a blood-red colour, and are much veined with white quartz: they occur in large amorphous maffles, and in nefts, of eliptic forms, of great variety of fize. One of thofe bodies of jafper, in the eliptic form, has been cut through by the river, and is now to be feen in the face of the perpendicular rock, upon each fide of the ftream. Its fize is thir- ty feet long, by ten broad: the points of its tran{verfe axis are fharp ; and it ftands upright in the argillite. The mafles-of this matter which occur amorphous in the argillite, are of great mag- nitude. I have traced one of thofe for thirty yards in extent. All of thofe jafpers are of great induration, and take a high po- lith. Both the amorphous and the eliptical formed maffes are found imbedded, where the argillite is of a greenifh-grey colour, B2 thinly 12 DESCRIPTION of the thinly lamellated, of a filky, luftre, and faponaceous to the feel : it clings round thofe maffes in all their variety of direction, and of courfe its texture is there much twifted- When the argillite {tratification has extended its thicknefs to near three quarters of a mile, the limeftone which I have mentioned above then occurs, in a bed of twelve feet thick. Its colour is bluifh-black ; and it is much pervaded by veins of quartz, and of calcareous fpar ; the laft of thofe are, in many places, of confiderable breadth, and are of a pale flefh colour. Where this limeftone has been wrought, I obferved it forked ; that is to fay, the bed is there fplit or divided into two, by the intervention of an argillaceous ~ body. Upon each fide of this bed of limeftone the argillite oc- curs of two colours. That which is next to, and in contact with the limeftone, is black, of a fhaly texture, foils the hand, and has veins of ferruginous-coloured quartz trending through it. The argillite which is more remote from the limeftone is of a dark purple colour. IMMEDIATELY after this narrow bed of fhale, the ar gillite re- affumes its greenifh-blue colour, and flaty texture, and becomes highly indurated : here fome fpecks of granulated quartz begin to appear, thinly fcattered in its mafs, and, foon after, it is feen to pafs over into an aggregate rock, chiefly compofed of grains ef quartz, felfpar, and minute particles of mica. The particles of quartz and of felfpar feldom. occur in this aggregate larger than the eight of an inch: thefe have very little the appearance of having fuffered attrition: they are much mixed, and are fre- quently feen to take lineal direCtions ; and in thofe lines the par- ticles of felfpar have frequently a comprefled appearance, and an eye-like form. This rock; in mafs, has a greyifh-blue colour: it is of great induration, and although lamellous or flaty in its texture, a crofs fracture is often more eafily obtained than one with the lamella. Its crofs fracture is pretty even, but appears more granular than foliaceous. This rock occurs frequently in the STRATA of the GRAMPIANS. 13 the diftrict of blue:clay flate, and may almoft be faid to alternate with it. I have been perhaps:more minute in the defcription of this rock than it‘deferved; but I have been fo, becaufe doubts have arifen relative to what name ought to be given to this aggre- gate. In all my geological refearches, I have found this rock only twice ; once, where I have here defcribed it; and, again, near to Banff, on the Moray Frith. In both of thofe fituations, the ag- gregates are of the fame compofition, and fimilar in pofition they both lie among blue clay flate. In this long alternation, two fubftances occur which are he- terogeneous to the rocks among which they lie. The firft of thofe, is a bed of compact Felfpar, of great induration. This bed is ten feet broad: its ftretch is nearly from weft to eaft: its pofition is vertical; and it ftands between two of the layers of the blue clay flate. Its colour is of a reddifh-brown, with a fmall admixture of purple ; and its general fracture is conchoi- dal, fomewhat rough, but not earthy. Nor far diftant from this bed, an appearance occurs wor- thy of fome notice. Where the aggregate and the blue clay flate are alternating, a furface of confiderable extent of the aggregate rock is expofed to view, parallel to its ftratifica- tion. This furface is regularly undulated in {mall undula- tions, bearing a very fltrong refemblance to thofe that may be feen upon the fand of the fea-beach, when recently left by the tide. After paffing the bed of compact felfpar, the blue clay flate and aggregate rock again alternate ; but here the blue clay _ flate predominates. Near to this, the fecond fubftance hetero- geneous to thofe alternating rocks occurs. It is a bed of Whin, the form of which is fomewhat fingular. It confifts of a prin- cipal trunk, which the river, here cuts nearly at right angles. Upon the eaft fide of the river, this principal trunk is feen to fplit into three branches ; and thofe three take an eaftern direc- tion, between the ftrata of the aggregate rock and the blue clay flate, where thofe two rocks are of great induration. The breadth: 14 DESCRIPTION of the ~ breadth of this bed of whin is thirteen feet ; and where it fplits, its three branches are, fix, four, and three feet in diameter. The trend or ftretch of this bed is from weft to eaft; but upon the weit fide of the river, it curves fomewhat to the fouth-weft. Its compofition is nearly the fame with the three other beds of whin which I have before mentioned. It is of a brownifh-black co- - lour, and, when placed in certain directions, it fhows fpecks of luftre. It is vertical in its pofition, has a great degree of indu- ration, and its general fracture is roughly conchoidal. Aggregate Blue rock, Clay flate. The river. ~ Uron palling this bed of whin, the river ceafes to be deeply imbedded in the rocks ; but the aggregate rock and the clay flate ftill continue to be feen for a fhort diftance, in a fhelvy acclivi- ty, where they are loft to view in a long narrow plain, deeply covered with a bed of gravel, compofed of the debris of the in- terior mountains. The river here flows over this bed of gra- vel for a confiderable {pace ; and upon this narrow flat, we pafs through between two of the moft elevated points in the fouth la- teral range of this part of the Grampians. Although the obtru- fion of this mafs of gravel cuts off from infpection the continui- ty of the laft-mentioned rocks, yet the broken and abrupt fides of the mountains, clofe upon each hand, clearly points out, that this part of the fouth lateral range is entirely compofed of mica- ceous fhiftus. Here, we are deprived of the junction of the mi- caceous fhiftus with the two former rocks; and the lofs of all fuch STRATA of the GRAMPIANS. 15 fuch junctions are always to be much Bartee in mineralogical refearch. Havine paffed over this narrow plain, I advanced towards a fecond range of hills, which here form the bafis of the central and higheft chain. It is at this place where the river fo fud- denly changes its courfe from eaft to fouth, and where I was un- der the neceflity of leaving its bed, to continue my northern di- rection towards Mount-Battoc. This, however, I was enabled to do to great advantage, by following up the deep cut bed of a winter torrent, which led me into the direction which I withed to follow. Upon entering the bed of this torrent, I found that the bafis~ of the hills here entirely confifted of micaceous fhiftus, much veined with quartz, and much twifted in its texture. The ftretch of this rock is here nearly from welt to ealt; and it has a foutherly dip of 45 degrees. In pafling through among thofe hills towards the central range, I found in feveral of the beds of the torrents large blocks of reddifh-brown porphyry, with {cattered maffes of micaceous fhiftus and granite. In tracing up one of thofe torrents, I faw the micaceous-fhif- ‘tus rock and the porphyry both expofed to view,’near to each other ; and, foon after, in the bed of the fame torrent, I came to a cafcade which had laid bare both thofe rocks at a point where they are in contact ; and near thofe a fecond bed of porphyry " made its appearance, in the front of a near hill. From my firft view of thofe, and from their relative pofitions, I was led to ima- gine, that they might here alternate in vertical pofition ; but up- on more minute infpection, I found that the porphyry conftituted vertical dikes, ftretching nearly from fouth to north ; which courfe cuts the line of direction of the Grampians here almoft: at right angles : and, on the contrary, I found that the micaceous fhiftus which. flanked thofe dikes of porphyry, had a regular ftretch: from.: 16 DESCRIPTION of the from weft to eaft, and a foutherly dip. To endeavour to have thefe appearances more fully explained to me, I directed my fteps to the brow of that hill, where I had obferved the rock laid bare; and in pafling along the fronts of the hills from eaft to weit, I foon came to a dike of porphyry fimilar to thofe which I had immediately left. This dike is fixty feet broad, ftretching nearly from fouth to north, and flanked upon both fides by mi- caceous fhiftus, ftretching and dipping as before defcribed. In proceeding farther along the faces of thofe hills, I found feveral other dikes of porphyry, of various breadths, and at various di- {tances from each other ; but all of them fimilar in their lines of direGtion, and the micaceous fhiftus always interpofing between them, through which they feemed to rife. The porphyries of thofe dikes are generally of a ferruginous colour, tending fome- times to an orange-red, and of various tints of thofe colours. They have great induration, are coarfe-grained, and produce a rough fracture. The particles of quartz which are fcattered in their principal mafles, are fmall, amorphous, and are of a ferru- ginous colour. The particles of felfpar are of a light tint of the fame colour, and are moftly cryftallized. The furface of thofe dikes are in many places bare, and expofed to the eye for long extents, in their lines of direCtion; and in all thofe lines of di- yeCtion which I have traced, I have never found any of them al- ter in their breadths, in their verticality, nor in their direions. Their furfaces, in general, confift of oblong fquare blocks, now loofe and unconnected with each other; and, in many places, the lines of fraéture of thofe blocks are fo ftraight, that one might almoft fuppofe that they-had been disjoined by the hand of art. I nave often obferved, in this diftria, and in other parts of the Grampians, that the loofe and outlying blocks of both gra- nite and of porphyry, (which have not been worn down by at- M trition), STRATA of th GRAMPIANS. 17 trition), confift, in general, of oblong fquare fhapes. This ob- fervation, when I firft made it, led me to imagine, that thofe rocks here were perhaps ftratified. I have, however, as yet, not been able to trace real ftratification of thofe rocks in this diftri@ of the Grampians. Upon fome of the fummits of thofe hills which here form the bafis of the central range, I firft difcovered the granite in folid rock. In thofe fituations, the granite is only feen in patches, where the fuperincumbent rocks have worn off it. 'Thefe fu- perincumbent rocks, which I here found in contaét with the granite, are of two different compofitions, and occur on the fum- mits of different hills. The one of thofe rocks, and the moft prevalent one, is the micaceous fhiftus ; the other is the granitelle,. or a mixture of quartz and fhorl. In fome parts of this laft- mentioned rock, I perceived a {mall admixture of hornblende: where this appears in the compofition, it perhaps ought to receive the appellation of granitine. In thofe elevated fituations, I found both of thofe rocks, (efpecially the micaceous fhiftus), in a {tate of decompofition, and faft leaving the granite expofed to the eye.. | . From thofe appearances, it is to be inferred, that the interior of thofe hills is compofed of granite, which is but thinly coated by the fuperincumbent rocks. Upon leaving thefe hills, which, I have already faid, form the bafis of the central chain of the Grampians, I regretted very much, that all my endeavours proved abortive to trace out the whole extent, in line, of any one of thofe dikes of porphyry which interfeé their fides. I conftantly loft them wider peat or other foils, before I could trace them to their contac with the granite. It was my anxious wih to fee how thofe two rocks of porphyry and granite connected with each other at their junc- tion. Vou. VL—P.1L C In 18 DESCRIPTION of the In purfuing my refearches towards the fummit of Mount Ba- toc, I proceeded up the bed of a torrent, which, after heavy rains, dafhes down the immediate fide of that mountain. In this bed, the blocks of micaceous f{chiftus and of porphyry, (which I had feen fo abundantly fcattered among the hills that I had juft left), totally difappeared, and no outlyers of any kind were to be feen, excepting fome granites, which were fcattered in large maffes; and in every part, where the torrent had carried off the fuperincumbent foil, the granite was to be feen in folid rock. In my progrefs towards the fummit of this mountain, I fell in with a large face of the native granite rock expofed to the eye. By the cracks in this face being in long-extended horizontal lines, it had at firft the appearance of being ftratified ; but upon a nearer and more minute examination, I found that it was not {tratified, and that the cracks which gave it that appearance were only fuperficial. ArounD this face were fcattered large blocks of granite, which were moftly in oblong fquare fhapes. Soon after pafling this precipice, I gained the fummit of the mountain, which, though not very highly elevated, is in this part of the chain the higheft of the central range. It is about 3465 feet above the level of the fea; and is entirely compofed of a coarfe-grained granite, in which fhorl fometimes occurs; and its felfpar is very generally cryftallized. HavinG here finifhed the extent of my intended inveftiga- tion, I beggto be permitted to add, that the line which I have here given the defcription of, has been traced with much atten- tion, and the true pofition of each foflil has been moft fcrupu- loufly attended to, and is correctly placed in the annexed plate. I — fe panes Sup smondsousp” avdsoy- iil it ~ bunwuuyp yor yibrbibo = pun yuyysanyy puyotribbo ng ypn~ Cummins anys tify Ty 10 poy [r pans yotaibnoys AMY ALOHA fo ung UaySig JMUODIOY PUNOLY PYNPUPY] wrap Diusre p49 2) arth. Fes kk = & IN yy sya wep ya YN) SAL, Degen 1 saad 7 PY SUBKIIS Mf dSnpsaniyy f WM MOT ty L! PT STRATA of the GRAMPIANS. 19 I wis that fome, more able pen than mine, would take up the further defcription of this extended field of geology, fo worthy of inveftigation ; but if none will come forward for that purpofe, I may at fome future period prefume to give to this Society more extended, and more general lines of defcription of the Grampians, than that which I have now had the honour of fubmitting to their examination. II. fs ‘ ‘ aa 5 ee aie tee _— Wf, 4 GEoMETRICAL INVESTIGATION of fome curious and intereft- ing Properties of the Circe, Sc. By FAMES GLENIE, Efgs A.M. F.R.S. Lonp. & Epin. [Read April 1. 1805.] DEAR Sir, Edinburgh, 22d March 18035. S the following paper refers in a great meafure to the gene- ral theorems publifhed by your father, I now commit it to your care, and that of my friend Mr PLavrair, Profeffor of Na- tural Philofophy. I wifh it to be communicated to the Royal So- ciety of Edinburgh, and, if approved of, to be inferted in their Tranfa@tions as foon as poffible. Indeed, I truft, that even fimple as it is, it will not be altogether unacceptable to that learned body. I am, Dear Sir, Mott fincerely your, &c. Ja’ GLENIE, Dugald Stewart, E/q; } Profeffor of Moral Philofophy. bo 2 INVESTIGATION of fom Tuar truly elegant and inventive geometer the late Dr Marttuew Srewarm, publifhed at Edinburgh, in 1746, without demonftrations, a number of general theorems, of great ufe in the higher parts of mathematics, and much calculated for impro- ving and extending geometry. Such of them as refer to the circle, and to regular figures infcribed in, and circumfcribed about it, have not, as far as I can underftand, been yet demon- (trated. Thefe, with an endlefs variety of other theorems, are derivable, as corollaries, from the following general though fimple geometrical imyeftigation, that otcurred. to me fifteen years ago, and which, I fuppofe, has remained fo long unknown and unattended to chiefly on account of its fimplicity. Let A,B,C, &c. (Pl. IL. Fig. 1.) be any number of points in the circumference of a circle, and let that number be denoted by 2. Let RA, RS, ST, &c. be tangents to the circle, in the points A, B, C, &c.; and let POQ be any diameter. Let Qe, Qd, QS, &c. be perpendiculars from the point Q to the diameters paf- fing through the points A, B, C, &c., and Pa, P b, Pe, &c. per- pendiculars from the point P to the fame diameters. Tuen it is evident, that PQ. = AP +AQ =BP +BQ = CP. + cQ, = &c. Wherefore PO. x C= AP + BP + ce +, &e. + AQ’ + BQ + cQ'+, &c. But AP?=AGXAa= PQ. x Aa, BP =PQx Be, cP =PQ*« Cd, &c. ; and AQ’ + BQ+ oe &e. = PQX Ac+Bf+Cd4, &. Now Aa, Be, Cb, &c. are refpeCtively equal to perpendiculars drawn from P to the tangents RA, RS, ST, &c., as are Ac, Bf, Cd, &c. equal to perpendiculars drawn from Q to the fame tangents. Con- fequently the fum of all the perpendiculars drawn from the points P and Q to lines touching the circle in the points, A, B; C, &c. is equal to PQ. X%, or a multiple of the diameter by 2. Tue fame may be proved othewife ; for fince Oa = Oc, Aa — Gc, Aa+Ac=the diameter. In like manner, Be+Bf= the diameter, and C4-+Cd= diameter, &c. In PROPERTIES of the CIRCLE. 23 In the fame way, it is demonftrated, that if from any two points Pp, 7, in the diameter PQ, equally diftant from the centre O, perpendiculars be drawn to the lines touching the circle in the points A, B, C, &c. their fum is equal to a multiple of the diameter by 7. Bur if from any two points V, W, in PQ_ produced, equally diftant from the centre O, lines drawn perpendicular to any dia- meter Br, pafling through any point of contact B, fall beyond its extremities B, 7, the difference of the perpendiculars drawn from W, V, to the line touching the circle in B, is equal to the diameter, and fo on. ; So alfo, when perpendiculars from the points V, W in PQ, produced to the diameters pafling through the points of contact A, B, C, &c. do not fall beyond the extremities of any of thefe diameters, perpendiculars from V and W to right lines touching the circle in the points A, B, C, &c. are taken together equal to a multiple of the diameter by the number of the faid points. Cor. 1. Perpendiculars drawn from P and Q, or f and g, to lines touching the circle in the points A, B, C, &c. are toge- ther equal to a multiple of the radius by 22. Cor. 2. The fum of perpendiculars drawn from P, Q, or Ps 9 to the fides of any regular figure circumfcribed about the circle, is equal to twice the fum of perpendiculars drawn to the fides of a regular figure of the fame number of fides circum{cribing the circle from any point within the fame regular figure. Cor. 3. (2 = fum of the perpendiculars drawn from P to right lines touching the circle in the points A, B, C, &c. d denoting the diameter. Or athird proportional to the diameter and the chord AP, to- gether with a third proportional to the diameter and the chord BP, together with a third proportional to the diameter and the chord 24 INVESTIGATION of fome chord CP, &c. is equal to the fum of the perpendiculars drawn from the point P to right lines touching the circle in the points A, 'ByiG, &c. AQ. BQ’ CQ’ , &e, - AND af = se = fum of perpendiculars drawn from Q to the fame lines. AGAIN, fince by a well known property of the circle, AP* + AQ’ =BP + BO ee + co’'= &e = 2r7+20p, r denoting radius, the fum of the fquares of lines drawn from the points A, B, C, &c. to any two points f, 7, in the diameter equally diftant from the centre, is =2”72?-+ 2X OP = amul- tiple of 7*, by twice the number of the points A, B, C, &c. to-. gether with the fame multiple of the {quare of Op or O g. In like manner, AV +AW+BV'+BW’-+-CV +CW7+, &c. —o2nrt-+2n2XOV = amultiple of 7* by twice the number of the points A, B, C, &c., together with the fame multiple of OV* or OW: Anp fince the fquares of the chords AP, BP, CP, &c. are to- gether equal to the fum of the fquares of the perpendiculars. drawn from P to the right lines touching the circle in the points A, B, C, &c. together with the fum of the fquares of the per- pendicular diftances of P from. the diameters pafling through thefe points, the fum of the fquares of Ap, Bp, CP, &c. is in like manner equal to the fum of the fquares of perpendiculars from p to thefe lines, together with the fum of the fquares of the perpendicular diftances from p to the faid diameters. In like manner, Ag t By atk OT fine: &c. = fum of fquares of perpendiculars from. to the lines touching the circle in A, B, C, &c. together with the fum of the fquares of the perpendi- cular diftances of 7 from the diameters pafling through A, B, C, &c. WHEREFORE PROPERTIES of the CIRCLE. 25 Wuererore the fquares of the perpendicular diftances of ei- ther P or Q, from diameters paffing through the points of con- tact A, B, C, &c., are, taken together, equal to the excefs of the rectangle under half the diameter PQ, and the fum of perpendi- culars- from P and Q to right lines touching the circle in the points A, B, C, &c. above half the fum of the fquares of faid perpendiculars = 72 —7s, (s being equal to the fum of per- pendiculars from O, as, in what follows, to right lines touch- ing the circle, of which OQ. is the diameter, in the points c, d, f, &c.). And the fum of the fquares of thefe perpendicular diftances from both P and Q, is =247?—2rs. This is alfo evident, from all angles in a femicircle being equal to right ones. For AP +AQ + BP +BQ_+CP +cQ + & =27x PQ =4nr;and42r—anr—2rs=2nri—ars ConsEQUENTLY, when the whole circle is divided into equal parts, in the points A, B, C, &c. Ap + Bp +p +&a= Aq + Bq + Gq + cea SS nr nXxOp ; and AV + BV + CV + &. =AW +BW +CW +&c.=27°7+2%0V. For the fum of perpendiculars drawn from f to the fides of any regular figure circum{cribing the circle, is then equal to the fum of the perpendiculars drawn from g to the fides of the fame figure. The fame obfervation holds with regard to perpendicu- Jars drawn from the points V, W. From the foregoing general inveftigation, when the circle is fuppofed to be equally divided in the points A, B, C, &c. Dr Stewart's firft, fecond, third, and Seas theorems can be im- mers derived. F I sHatt, however, proceed regularly with the inveftigation ; and, in the firft place, take the fquares of the perpendiculars from P and Q to the right lines touching the circle in the points A, B, C, &c. which perpendiculars are refpeCtively equal to A 4, Mes BS Bis Cd, Ob; &é Vout. VI.—P. I. D Now 26 INVESTIGATION of fome Now-Ac + Aa =r-+cO +7r—cO =ar4 2x cO Shae = pO AOR ay 1 LO Cd +b = Pa Od 4+7—Od =2r4.2xOd &c. &e. &e. . WuererorE the fum of the fquares of perpendiculars from P, Q to lines touching the circle in the points A, B, C, &c. is —anx rex Oc +Of +Od'4&c. But the points c, d, f, are in the circumference of a circle, of which the diameter is OQ_ or 7, and by Cor. 3. the fum of Oc +Of +Od 4 &c. = OQ x into the fum of perpendiculars drawn from O to lines touch- ing the circle, of which OQ is the diameter, in the points ¢, d, f, &c. Call the fum of thefe perpendiculars s. Then we have the fum of the fquares of perpendiculars drawn from P, Q to lines touching the circle APQ in the points A, B,C, &c, = 2 1.7% ors = (Cor. 3.) AP 4 BP 4OP + &e. + AQ'+BO.+6Q 4&e, de When the circumference is divided into equal parts by the points A, B, C, &c. or the angles at O are equal, s = - x 0Q_ n i or 5 x7 and 2nT Bars one. Ir a regular figure be infcribed in the circle, having its angles at the points A, B, C, &c. or a regular figure be cir- cumfcribed about the circle, having its fides tangents to it in the points A, B, C, &c. we get from the general expreffion —4 —4 —-+ ——~}j —— 4 —_4 Ap + BP +CP + &c. 4, AQ ans 2a r +4rsaqurpanrs 6 nr, or third proportionals to: ra- dius, the chords drawn from either P or Q to the points A, B, C, &c. and the cubes of thefe. chords equal, when taken toge- ther, to fix times a multiple of the cube of radius by the num- ber PROPERTIES of the CIRCLE. 27 ber of the fides of the infcribed or circumfcribed figure; or to {peak algebraically, the fum of the fourth powers of thé chords is equal to fix times a multiple of the fourth power of the femi- diameter of the circle, by the number of the fides of the figure. This is Dr SrEwart’s 23d theorem. s In like manner, Any Ae SP IPOR P= Or Sat 67 xOe By +Be —7+O0f +7—Of =27+6rxOf G2 460 =r Od +7—08 = 2+ 6rxOd &c. &e. &c. And the cubes of perpendiculars from P and Q to right lines touching the circle in the points A, B, C, &c. are taken together —a2nr+6rxOc + Of +0d + &. = (by Corollary 3.) —6- —6 —‘ at ae .C) AP + BP +P + 8c. + 8Q +O +6Q + Be a ; aot of + Od + ke = — when the circumference is equally divided in the points A, B, C, &c. or when a regular figure is circumfcribed about the circle, with its fides touching the fame in faid points. Wherefore the cubes of perpendiculars from P and Q to the fides of a regular figure of a greater num- ber of fides than three circumfcribed about the circle, are taken together = 5293. This is Dr Srewart’s 19th theorem. Anp if a regular figure of a greater number of fides than three be infcribed in the circle, having its angles in the points A, B, C, &c. third proportionals to the cube ef the diameter and the cubes of chords ‘drawn from P and Q to the points A, B, G, &c. will, taken together, be equal to 5 775; or third proportion- als to the cube of the diameter and chords drawn from either P _ 52 — or Q to the faid angular points, will taken together, be ? D2 ‘or, 28 INVESTIGATION of fome or, to fpeak algebraically, the fum of the fixth power of chords drawn Trom either P or Q to the faid points, will be equal to twenty times a multiple of the fixth power of radius, by the number of the fides of the infcribed figure. In like manner, - wf. ae —_—_—_-4 ee Ac i” ee Os uidee Se en oe pices —} al aeons Bee ss, 22 ae a INA aN oS 3 Gd' +b _r+Od +7—Od_, ates x Od" r ; r 7 &e. &c. - &e. And third proportionals to radius, perpendiculars from P and Q_ to right lines touching the circle in the points A, B, C, &c. and the cubes of faid perpendiculars are, taken together equal to anritiarXOc OE 40d + &e. pax FOP LOH 4 Be st AP'4.BP +CP + &. ,, AVHBQ'+6Q + &e. Oe ee hg oe eee Bur Oc + OF +0d + &c. = ”"" when the circumference 2 is equally divided in the points A, B, C, &c. or when a regular figure is circumfcribed about the circle, with its fides touching nr the fame in faid points, and 127 X—-=64%r: Alfo —+} ——4 ——4 “ x OG, FOF Qe ESS ony = we Wherefore thefe te : : ars third proportionals are taken together equal to 8773 + 3 er os 35.2 r3 4 ; and four times their aggregate is equal to 35.273. Or, te PROPERTIES of the CIRCLE. 29 to fpeak algebraically, eight times the fum of the fourth powers of perpendiculars from either P or Q to the fides of a Tegular figure of a greater number of fides than four circumfcribed about the circle, and touching it in the points A, B, C, &c. are equal to thirty-five times the multiple of the fourth power of radius by the number of the fides of the figure. This is Dr STEWART’s 25th theorem. - Anp ifa regular figure of a greater number of fides than four be infcribed in the circle, having its angles in the points A, B, C, &c. the eighth powers of the chords drawn from either P or Q_ to the points A, B, C, &c. (to {peak algebraically) is equal to your =n xX ae 2'.r° = feventy times a multiple of the eighth power of radius by the number of the fides of the fi- gure. - , In like manner, mbOcsr sae a iggy Oe —— =2rs-+a0rxOc +——» Le r Se a a CY ge W7 aan en hon OF + Tone r wa on =a p rtOd ara = 2r3420rxOd + 13x &e. &c. —SS §- ——_ 5 | — 5 WHEREFORE 2 gL e F ease | $s r4+-Od +r—Od ROR T=Or + &c. = 2273410073} sn om — equal (by Cor. 3.) to AP. HBP ohGP 48.4 AQ +BQ. +00. + &e. chen = TT Te as r Sa aa Sa the circle is equally divided in the points A, B, CG, &c. ; AND 30 INVESTIGATION of fome AnD generally when m is any integer whatfoever, we have ae CW; +P =00 FHOf +r—OF r+ Od" 470d" aa ps p53 m—{ mM Seed Hiei: ola '32t 1000 + &c. equal to anrs+— 7TXOc +Of +Od + &u + —+ == ee it eT fee a OF TOROS Gc. Me Eee” ives 3 4 r Soa 3 LAG AG PG m—3 m—4, m—sy, Oc +Of + Od + &e. ai aia aoa (tb x ee a &c. = (Cor. 3.) +BP +CP +&. A iQ p+ bP +¢ 4, AQ0 4 BQ 4 6Q + be, which, when the circle is equally divided in the points A, B, C, &c. by the circumfcription or infcription of a regular figure, coincides with the 36th and 38th of Dr Srewart’s general theorems. Anp ‘univerfally if m have to / any ratio whatfoever, - m m m 7pOc%+47—O0" att Of! +r—Of! 740d! 47r—Od" Se te Se bE ee &e, TRY Tia Be Ta r r r m m—l m m—l m-2l igcanrt x00 +Of + Od + &e. +5: yi =: md ¢ wal Os 4 OF 0 es : m m—l m—2l m—31 m—4l 4l or r EAE at a aka es a5 m—s5! Oc + Of +04 K&L Be, &e. 6/ r3 ; Tuts laft theorem, or expreflion, is more general than any of Dr STEwART’s theorems, and will furnifh an endlefs num- ber of new and curious infinite feries, with their fumma- tions. It may alfo be extended to the chords AP, BP, &c. and expreffed in terms of them. And as to the truth of the bi- nomial PROPERTIES of th CIRCLE. — 31 nomial and refidual theorems, when m has to / the ratio of any two homogeneous magnitudes whatfoever, I muft refer the reader to my general demonftration of both in Baron MASEREs’s Scrip- tores Logarithmici, vol. 5. and to fome of the geometrical formu- le in my Univerfal Comparifon. , In like manner, if pg, p5, pi, &c. be perpendiculars refpec- tively to BO, CO, AO, &c. we have 7 +O i Preroys be gies OF A is 8 4.7405 we FSO 4 ec. 27 bP eR Oi + Or + Ob +&c. = 27r*-+-2. Op ,when the circle is equal- ly divided in the points A, B, C, &c. or when a regular figure is circumfcribed about it, with its fides touching it in thefe points. This is Dr Srewart’s third theorem, of which he gives. a demonftration of confiderable length, In like manner, F401 pr—Or +7408 +r—OF +7406 +7—O8 + &c. are equal to2"r? +67 ~ Oi 4 Og 4. Ob 4 &c. =2ar? +3 rxOP when the circle is equally divided.in the points, A,. B, C, &c. or when a regular figure circumfcribing it touches it in thefe points.. This is Dr Srewart’s 20th theorem. In like manner,. Sarees Nh See OS SS —— 17> r+0i aeaee madi aeas =0F" , 7 HOR +r—04 x r + &c. is equal’ to 2773+ 127x Oi + Og 4.05 4+ &e. + 2x: Pe ag) hea] Tt Ont Casati fe aay r 47° when the circle-is equally divided in the points: A, B, C,; &c. or whena regular figure, circum{cribing it, touches it in thefe points. Anda multiple of this by four, or eight times the aggregate of third: 97 = to22r? 1. 6rxOp x n+ 32 INVESTIGATION of fome third proportionals to 7, the perpendiculars from either p or g to the fides of the regular circumfcribing figure, and the cubes of thefe perpendiculars is equal to 8r? + 24"rx Op +32xX —4 Me ; or, {peaking algebraically, eight times the fum of the fourth ; powers of perpendiculars from either f or g are equal to 8 2 74, together with 24 times a multiple by z of the fourth power of the line whofe {quare is equal to r xO , together with thrice a multiple by 2 of Of. This is Dr SrEwart’s 26th theorem. In like manner, SR ee ree eg heey a eee ae rtOi +7—O1 470g +r—Og 4 7T4+Oh +7—Oh 2 r? r2 = + &e. sa ——z —2 Oi +Or' 402 4.&c. are = 2nr?+-20rxKOz +O +O+ peer te TE A at =2nr*?+102r xOp $78t08 when the circle is equally divided in the points A, B, C, &c. or when a regular figure cir= cumfcribing it touches it in thefe points. Anp generally when m is any integer whatfoever, ry O71 br Oi rFOE +'P Og ~ eee 4+r—Ob r—3 re—3 7-3 drwy Sa om mat ope =e H ets + Oh + &c, += -—. $ Bec ig BES rx Or + Og + Pi —_—_—e —i x54 m—2 y Oi + 08 + Ob ge cea m— 3 BE 7 1 I 3 4 6 st et.) Oi +Og +O0h + &e: , &c. &c.; which, ey aah aera ANT lind paw we aes into when the circle is equally divided in the points A, B, C, &c. or when when a regular figure circumfcribing it touches it in faid points, gives Dr StEwart’s 37th theorem, fince the fame reafoning and mode of demonftration holds good in regard to half the amount of this expreflion, whether the points p and ¢ be in PQ, or in PQ produced. Anp univerfally if m have to / any ratio whatfoever, —_—_—_" m m te . m 740i 4r—Oi? yt tOg Tt + 1-08? tO T+ r—ObT &e a ee ee m m . a o—3 3 xr r r ly, Bl See m m—J m—rl =a2nrs4+7+— -7TXOi + Og +0) 4+&e. + 5-H “ Boy oe eee ¥ m—=3l x Of + Og + OF! + &e. mm m—l m—2l m—3l m—4l 4l r bp RES gs ee aye ee nae eS ule Be Gl +O Ob. Og Oot Been CBee Bee! 6/ fe _ Tuts laft theorem or expreflion is more general than any of Dr Stewarvt’s theorems, and from it may eafily be derived an endlefs number of new and curious infinite feries, with their fummations. Ir is almoft needlefs For me to obferve, that befides thefe theo- rems of Dr MatTTHEew STEWART, an unlimited number of other theorems, refpecting figures both regular and irregular, circum- fcribing and infcribed in the circle, may eafily be derived from the foregoing inveftigation, as well as a great number of geo- metrical infinite feries, with their fummations. And as to theo- rems refpecting given points, right lines and figures either re- gular or irregular, given by pofition, and right lines interfeCting each other either in one point or in different points in angles either equal or unequal, that are deducible from it, they are in- numerable. i Vox. VI.—P. I. E ‘ Now, 4 INVESTIGATION of fome w Now, let a circle (Fig. 2.) be divided into an uneven number of equal parts, by the points A, B, C, D, E, &c. and let PQ be any diameter; from P let Pa, P4, Pc, Pd, Pk, &c. be drawn perpendicular to the diameters pafling through the points A, B, C, &c. and from Q let Qe,Q f, Qs, Q4, Qi, Kc. be perpen- dicular to the fame diameters. THEN it is evident, that Aa, Ae are refpectively equal. to perpendiculars drawn from P, Q; to a tangent to the circle in the point A; and fince Oa = Og, their fum Aa + Ae = 7—Oa+r+Oa, In like manner, the fum of the perpendicu- lars from P, Q to the tangent at Bis = r—Oc +7+ Oc, to the tangent at C is = r—Ok + 7 + Of, to the tangent at D is =r+04+7—O4, and to the tangent at E is = r+Od + r—Od. But r—Oa+7r—Oc 4r—Ohk +r +O0b4+r+Od= r+Oat+rt+Oc+rt+tOk+r—O0b4+r—Od; 2xO0b+0d= 2xOat+Oc+Ok and OF8+O0d =0a+0c+O8, and fince r—Oa + r—Oc +7—-OF +7408 +7tOd =rtO0a 4 x—Oe +7+0k +7—Ob + 7—Od. , we have this equation 4xrxOb+rxOd = 4xrxOatrxOct+rxOQk, or OFF Od=Oa+O0Oc+Ok. ; But if from a point in the circumference of a circle, perpen- diculars be drawn to the alternate fides of a regular figure of an even number of fides circumfcribing the circle, or, which comés to the fame thing, beginning with any one fide, perpendiculars be drawn to the rft, 3d, 5th, 7th, &c. fides, the fum of thefe perpendiculars, the fum of their fquares, the fum of their cubes, n va n—2'h &c. to the fum of their te or powers, is refpectively equal to the fum of the perpendiculars drawn from the fame point PROPERTIES of the CIRCLE. 35 point to the other fides, viz. the 2d, 4th, 6th, 8th, &c. the fum of their {quares, the fum of their cubes, &c. to the fum of their ? thefe added together give gra erxontserx st, ais which, if GA’ = 873, the cube of the perpendicular to the fide touching the circle in the point A, be added, we get 41 pP+1erxOn+367xOn qtr arto’ AAS, 4 Bur the fum of the cubes of perpendiculars, drawn from A and G to the fides of the pentagon is 257‘, as. has been demonftrated, when PQ_ coincides with AG. Wherefore grtarxe Br X07 or agri iar x Ont 247 — xOn = 2575 and 4rxOn + arxOnu=r3, Now, if for . 3 2, Oo —_—?Z this value of 7, there be fubftituted 7° in qi +187 % n-+36rxOn , we PROPERTIES of the CIRCLE, . 3 3 we get are = “5. ~ ; and if r* be fubftituted for its equal in gs ritzoPxOn+ 6orxO7” ve ger 357 HIST? K boi : es 4 ; j AL's 2 Wherefore the fum of the cubes of perpendiculars drawn from the point G to the fides of the pentagon, is equal to the fum of the cubes of perpendiculars drawn from the point A to the fame. SINCE 2x7pOm +2X7r—On =4r43 rx 20m—20n Pan2h +37X 2xOm +2X On +2x0m'—2xOn* = = , and axOm +On=*, we have 37 X 2X Om—2x On + 2xOm _—Or = 47. But a0"—202n=r7 therefore 2X Om —On =73, or Om —On’ = a® = a : Ir P, inftead of bifecting the arc BK, be any point between B and K. the fum of the cubes of perpendiculars drawn from it to the fides of the circum{fctribing pentagon, is equal to the fum of. the cubes of perpendiculars drawn from Q to the fame. For fince Oc + O2 +04 =04+ Od and Oc — O04, Od— Oa and O&, begin together, and become maxima together, Oc—O4 has toOka given ratio. Let that be the ratio of m to 1. Then Oc—Ob= mxOk, and Od—Oa4 = Oc—O5 40/4 = m+1xOk Oc=Ob+mxOk,Oa=Od—m+tixOs —3 ——3. j 2 —_— ‘ i 2 Oc = O06 +3"X0Ob XOk+3m'*xObxOk +m?x Of. Oa = Od = 3xme1 XO | . a= Od —3xm+1XO0d XOk+3xm+1xOdx F 2 a 4 INVESTIGATION of fome of — OF. Wherefore Oc + Oa +08 =O02 +04 43m De Ob x OL — 3x ma x Od X OF + 3m’ x Ob x OF +3.X ati xOdx OF + OF. Now, let this be= OF +04 + V.. Then 3m x Ob —3xm+1X Od + 3m x Obx OL+ as aw > { oe Sy Vv: Cc TH. 2 3x m+1 X¥OdxOk+ OF = + oO» and mx Ob mm+t. > x Od + , when OF = But mx Ob = m+1x Od; therefore V=o. For when O£= 0, O} is the fine of 72°, and Od the fine of 36°... When O é is a maximum, it is the fine of 18°, Oc is =7, O48 is thecofine of 36°, and Oc —O4 the verfed fine: of 36°! © Wherefore,’m + 1:m= OF: 6a) wee fed fine of 36° + fine of 18°: verfed fine.of 36°. Ler BD (Pl. IL.-fig. 3) = BH = fide of an infcribed pentagon ; bifeé BD.in F, and draw OFC, AC, BC and DH. Then, fincé the angle FOB is 36°, CF is the verfed fine of 36°, OG is the fine of _ 18°. But fince the triangles CFB, DGO, are fimilar OG : CF =DG: FB = DH’: DB, and OG + CF:CF=DH+DB:DB=DH ; DB =DG:FB = fquare of the fine of 72°: fquare of the fine of 36°. For when DH i is cut in extreme and’ mean ratio, the greater part is equal to the fide of the pentagon. DH is cut in extreme and mean ratio in the point L, and LH = BD; the triangle CDP is fimilar to the triangle DOB; and the timiek: MDN to the triangle BOC. Tus demonftration, however, was unneceflary._ For if the fum of the cubes of perpendiculars drawn from P to the fides of the) pentagon, be equal to the fum of the cubes of perpendiculars drawn yet ‘ Hog. O- ‘W4pale m+y * PROPERTIES of the CIRCLE. 45; drawn from Q to the fame, both when O é is = 0, and when it is a maximum, this equality muft exift whatever be the magni- tude of O& between thefe limits. AND in a fimilar manner is it demonftrated, that the fum of the cubes of perpendiculars drawn from P to the fides of any other regular figure of an odd number of fides circumfcribing the circle, is equal to the fum of the cubes of perpendiculars drawn from Q to the fame. For if Om, &c. or fuch parts of. perpendiculars drawn from A to the fides of any regular cir- cumfcribing figure of an odd number, 2; of fides as lie between O and G, be denoted by A, B, C, &c.; and Ou, &c. or fuch parts. of perpendiculars drawn from G to the fame as lie between Ovand A, be denoted by 2,4, ¢, &c. A+ B+C+ &e, to” n—tI aie ats, terms, —4 — b — &c. to terms, = 5, if ~—1 be a multiple. of 2 by aneven number. Alfo.A+B-+C+ &c. to ~— terms, ta+h2+c:+ &e.'to aa terms, = FB, and‘ A*-B3? gk CT: 30> z == + C3 ig &c. to eae terms, —a3—b3—c3}— &c. to x 7 ier y ! { w a at, But if n—T be a. multiple of 2. by an odd number; A + B+C+ &c. to- tt “A CATS Deits &c. to 7 Seis, 4 . “3 ny: “y Bt +C 3 Hcl) 96 “Mt terms, Ms “a +e + &e.to == ee Wade A+B + + ea. to terms 46 INVESTIGATION of fome 3 rs ; terms, = >- Thus, in the terms, — a? — 43 — &c. to ae heptagon A+ B—a= , A+B+a= ae and A+ B}— 4 33 _ a= —. In the enneagon A+ B—a—b= a M+B+a oS 4 and A3-+ B’—as— 33 = “ and fo on. But in the enneagon, A is the cofine of 20°, or the fine of 70°, B is the fine of 30° = S a is the fine of 10°, and 3 the fine of 50°. Wherefore the fine of 70° = fine of 10° + the fine of 50°; the {quare of the fine of 70° + fquare of the fine of 10° + fquare of the fine of sor = ; and the cube of the fine of 70° — © - eube of the fine of 10° — cube of the fine of 50° = ns viz. thrice the cube of half the radius. And fo on. r—Oc* = r#— 473 KOc+6r'xOc —4r x Oe + Oc’, - On = r—4rxOa+6rxOa —47XOa +02, eye eR OELET XO — at ROE OL FO) = ri+4r3 xX OF+ 67x OF +4rxO0 +00, 70d = r+4anxOd+ 6x Od +47rxOd +07, Bur PROPERTIES of the CIRCLE. 47 But fince 57 ( = fum of the perpendiculars drawn from P or AP +BP+CP-+DP +EP Q to the fides of the pentagon) = = ay =AQ+EQ+6Q+HQ+EQ, and fince the fum of the PGYI33 {quares of perpendiculars drawn from P to the fides of the pen- tagon, has been demonttrated equal to the fum of the fquares of as SANE We ay eared perpendiculars from Q to the fame, eee ~ ALT + Q'4 1 +EQ =<". And as the cir- cumference of the circle, which has PO for its ea is me vided 1 into five equal parts, in the points a, 4, ¢, d, k, Oc. +. Oa +08 +00 ‘x Od =r x aaeOD 3 ed x” , and Oc. +02 +08 ——d ee ars” + Od ak <= % x OP a a Wherefore, 2 4 es Shah tle FOF BBL Od 2 De 08 +08 +05 + 0d = =a +e < = US xp = XS xr= hae the fum of the fourth powers of perpendiculars drawn from both P and Q to the fides of the pentagon. In the fame way is it demonftrated, that the fum of the fourth powers of perpendiculars drawn from P to the fides of any regu- Jar circumfcribing figure of an odd number, 2, of fides, is equal to the fum of the fourth powers of perpendiculars drawn from eee, 48 INVESTIGATION of fome n 1.2.0. u Q to the fame, = 33" xm=mnax are x rs When P coin- cides with B, Oc is =7, and A++Bt++C+-+ &c. to + herons | terms, (when 2—1 isa terms, + a+ + 4++ c++ &c. to multiple of 2 by an even number) 1s = ab aae xX rt; and At+ 12 > terms, Bi + C++ &c. to - = terms, +a++ 5+-+ &c. to BS (when n—1 is a multiple of 2 by an odd number) is = gn 8 ind 16 aaa In like manner is it demonftrated, that the fum of the fifth powers of perpendiculars drawn from P to the fides of any regu- lar circumfcribing figure of a greater number 2 of fides than 5, is equal to the fum of the fifth powers of perpendiculars drawn n2—T from Q to the fame; and that AS + B>+ Cs+ &c. to a— I ; terms, — 43 — 65 —cs — &c. to terms, (when ~—1 isa 5 multiple of 2 by an even number) is = = and AS-+ Bs+ Cs + &c. to “it terms — a5 — bs — &c. to - 7 3 terms, (when : 5 n—1is a multiple of 2 by an odd number) is = -. PROPERTIES of the CIRCLE. 49 As the cofine of oom , B is the cofine of 3 8 ° cofine of 5 'X — , and fo on; and when 2—T is a multiple of 2 by an even number, the laft of the terms A, B, C, &c. is the ly cofine of “—3 3 DT ; and 4, the firft of the terms a, 4, c, &c. i] is the cofine of sty pBe ; 6, the fecond, is the cofine of a5 x a +; ¢, the third, is the cofine of a x 80 band the laft of the terms a, 5, Cy &e. is the cofine of I x nay 180 or of m—2 X But when #2—1 is a multiple of 2 by an odd number, the laft of the terms A, B, CG &c. is the cofine a2—1.., 180° of x —'s the ‘firft of the terms 4, b, &c. is the cofine of “73 x Jot and the laft of the terms 4, 4, &c. is the co- Bror Univerfally, if m be any odd number fine of n—2 X lefs_ than 2, we have A” + B” + (C” + &c. to out terms, Stat Doe ne ‘terms, = when 7—1I is — a bolle aX to — a + mole of 2 by an even number; and A” -+ B”-+ C"+ &c., 3 terms, = —, when ae ) to terms, — an — 3” — &e.'to 2 Vor, VIL—P. Te er 2—1 Pies INVESTIGATION of fome® nm—t1isa multiple of 2 by anodd number. Thus, in the en- neagon, or figure of nine fides, A is the cofine of 26° or’the fine of 70°, B is the cofine of 60° or the fine of 30°, @ is the cofine of ro0° or the fine of to°, and d is the cofine’of 140° or the PMS ei fine of 50, and A” —4”"—i"= — 2 x2, And. if p be any even number lefs than 2, A? + BY¢+C?+ &e. to on E terms oF os eae tab be ch &e. to se d terms, or “— 3 terms, (according as:7— 1 is a multiple of 2 by an even 4 = he Fees Pa P p er odd number) is s= 7x 13:8 oP ral yg ape Cah 162. 3+4e “a 2 & fequently, A? ao a? + A” —a” Be + be Bu — pz ae &e. to —I A Tas. 50a op o rh ad rn 4 termigy iSpy? ae ee ee a x , iaigigt VE ant an ee peo pr6 PEO... Ah H—_— . ove bd b ON ct ° 1 iS wb and when n—1 is a. multiple of 2 by an odd number A’-+ A” n+tI 4 terms, + 4’—a”"-+ 4. Bey BY + FO" + &e, to ae PROPERTIES of the CIRCLE. 5t ——S—- ——OCr n-— . . bo — 6" 4+. ch —-¢™ + &e. to 4 3 terms, is equal to 7 X ~ 162+3-4 ioe x Pepi er kee when r7=1 pt2 p+6 ptio : 2p—2 . o i 2 2 2 2 I 1S) Sy 0X : x r= nx 4 6 rer 22 2 pH2-pHG...toap—2 : p X 4a. Hence the fummation of _ ani endlefs variety of feries, of which the terms are powers of the fines and.cofines of angles ; and though they do not confift of an infinite number of terms, they may confift of any number of n2—T -terms whatever, fince may be equal to any given number an wellae a aiheOrS pp) expreflion 1 X BRST te OPO tet A Se * £.2.3-4.+.t0% pt+2.p+6...to2p—2 2 2 2 i geree 2 T 4 X ay, sax p X ger » when hia 2 + Bees toe 22 te = is equal to an even number, or / is a multiple of 2 by an even number. But when is an odd number, it is equal to 2 X a 2 ane, se which muft.then be ufed. —2 2,4-. to S=3 2.3 be G2 , THE 52 INVESTIGATION of fome Tue fums of thefe feries, however, vary with the variations. in the magnitude of 7. For when r=2, 3, 4, &e.. — ae + 7” Pp 3 er does not vanifh, and est becomes refpectively 2 70 ewe 2,7 oh 2 P 4 b+2) &e. Ye A® —a™ —— aq” a pe a a fn by Go wo ve Bc. ‘6 r— terms .-= vm . . = when #—1 is a multiple of 2 by an even: number, and-the- fam of the: feries is conftant, orinvariable when ™ is-given; let the number of the terms oenret 3 great or fmall. This. feries, when n is infinitely great, or 7—1 has-to 4 a-ratio greater than . any given or affignable ratio, may be confidered as infinite. . Rea" 4 BY" + C—c"-4+- ee to. terms. te aie. a ; Se See So peg: Tee ai 2 2. A—a +B—é 466 + &c. to terms An —a7+ BY — b+ &c; to omen terms, X A—a+B.—db add +1 5 cles Oceano rey A" + A—a"+a+B" 4 B—l" 48 — yrs dole. iG x terms Pa "a s ewan fa Ti SE ee n—TI A®=—A—*?—at B? —B—b"—b + &e. eras 7"—Pr = 0, when 7 = I: — _— It PROPERTIES of the CIRCLE. 53 Ir may not be unacceptable to geometers to fee the foregoing conclufions in regard to regular figures circumf{cribed about and inferibed in a circle, derived’ by making ufe of one point only, inftead of two, either in or not in. the ‘circumference, which is: eafily effected in the following manner. Lew the fides of any regular figure of an even numberof fides: touch the’circlé BRETCQES (PI. ff. fig. 4s) in the points B, R, E, T, Cc, QL, S, and let DN, DH, DM, DV, be perpendiculars from the point}D to the.diameters joining the points of contact ; and from the points of contact let chords be drawn to any point A in the circumference. Ir GE, or the-radius of the circle, be denoted by 7} and A 4, _ Ab, Ac, Ad, be perpendiculars to the diameters joining the points. of contaé, 4C, 4B, 14,84, Lc, Ec, Qd, dR, are re- fpectively equal to the perpendiculars from the point A to the nay ; é fides of the figure, and are alfo refpectively equal to — 3) at ee. nate ; Py ee Cs ery et) 3 pouty pt 213 to cn AE =a. AL eal AQ, AR But if N-denote the num-. Ba 2%yyar TRF SK. At) : ber’of fides of the figure; the fum of ‘the perpendiculars ae Nx “Wherefore-AG + AB. +JAT. +, &c. =. 2 N-K:7% This is Prop. 4. Dr STEWART’S Theor. yp - “AGAIN, the fim of ‘the fquares of the ‘two! perpendiculars. bas ,2tisq to sedans ose ; Le ee from A, parallel to BC, or Ba +40 = 27° +2 Ga andthe fquares:of» the two-perpendiculars from A: parallel to LE, or Ee STE ES PPE REP ETO 4s SH 2P Ha xT} alfo Rd 4dQ = 2r'+2XxGd. Wherefore the furn of the. fquares of ‘the perpendiculars drawn from the .point A to the fides : 54 INVESTIGATION of fome’ fides of the figure, is — Nxr'+2xGa+Gb +Ge + Gad’. But fince the angles GaA, GSA, Ge A, GdA, are right ones, a circle paffes through the points A, a, 4, G, c, d. having GA for its diameter. And becaufe the angles CGT, QGC, LGQ; are equal, this circle is equally divided by the points a, 4, ¢, d. Confequently the fquares of the chords drawn from thefe points to the point A, are together = N X Ss, that is, Ac (Ga) RO EE pe GR 4+ Aa (Gc) + Ad (Gb) + Ab (Gd) = Nx p= N X : Wherefore the fum of the fquares of the perpendicu- lars drawn from A to the fides of the figure, is = N Xr +2N x : — Nx 3. But the fum of the fquares of thefe perpen- AC’, AB’, AT. AS | AL | AE’ AQ’ 4r° Ar 4r Ate 4r 4r° 4r diculars is = AR’ Therefore AC’ + AB’ +, &c. => NX67r+= N X27% x3r= AG +. AB +, &c. X 37°... Whence this propofition: Ir a circle be divided into any-even number of parts, and from the points of divifion chords be drawn to any point in the circumference, the fum of the fourth powers of thefe chords is equal to the fum of their fquares, multiplied by.thrice the fquare of radius. WHEREFORE PROPERTIES of the CIRCLE. 55 “Wusnstons Aa'+AlyAc+Ad =Aa + Ab + Ac Ad aD Re Sa wea amer tensed ait yes = NX ar , and DM + Dy + DH + DN’ LE EO an eee “DM 4. DV + DA + DN x 2 aN rs ogi met éN,, Des “2 16 Now, it is evident, that perpendiculars drawn from the point D to’the fides of the figures; ate’ refpectively 7 + DM, 7 — DM, r+ DV, r—DV,r+ DH, r— DH, r+ DN, r— DN. bur EDM 4 7 DM = ar + 2xDM, 74+ DV + ASN er sok DNs 74DH +r—DH = 27 + 2x DH, SoD ce r— Dt =2rt+ 2X DN. WHEREFORE the fum of their fquares is equal'to Nxr’ + 2x DM +DV+DH'+DN =NxXr+Nx GD nce the circle which paffes through the points D, M, V, G, H, N, is equally divided by the points M, V,H,N. This is Prop. 5.. of Dr STEWART’s Theorems. 7 DM + 7—DM’ = 2r3 + 67 xX DM, 7+DV + 7—DV =2arnt 6rx DV, 74+ DH cay 9mm) = 2 4 67x DH: 7+ DN +7—DN = 277+ 6rX DN. ay WHEREFORE, 36 INVESTIGATION of fome WHEREFORE, the fum of the cubes of the perpendiculars, drawn from the point D to the fides of the figure, is = Nx 734 6+ x DM + DV + DH’ + DN’ =NXr +67 x DS This is Prop. 23. Srewart’s Theor. When DG =7, the fum of the cubes of the perpendiculars is = N X 5 x nm=N x Sen 73, This is Prop. 22. Dr Srewart’s Theor. Wuen DG =, , or D coincides with A, she fum of he cubes AC’ -of the petpaneiculats is) egiral, tac — a ae am i &c.; and, confequently, we get AG’ 7 AB. ok AT Ae, Be 58 — “.2@Br=NX20 Xr = XN Sr 9ENGEX 20178!= N X lor? X SOT ATE 4, Ir, therefore, the circumference of a circle be divided into an even number of equal parts, and from the points of divifion chords be drawn to any point in the circumference, the fum of the fixth powers of thefe chords is equal to the fum of their fquares, multiplied by ten times the fourth power of radius. 7+DM' 7 i. =artt 1277 DM +2>x DM", FEDV' Fr DV = art+327°x DV + 2x DV, 77 DH hr DA = art-+ yar x DA +2 DA’, 7--DN'+r—DN = oe 127°x DN +2 DN. WHEREFORE PROPERTIES of the CIRCLE. . 57 WHEREFORE, thé fum of the fourth powers of the perpendicu- lars drawn from thé point D to the fides of the figure, is = N Xrt+Nx ay x GD ae NG . x GD: ; and eight times this fum = N X 87+ + 247°. GD + 3°GD.. This is Prop. 29. of Dr SrewarT’s Theorems. Wuen GD = 7, the fum of thefe fourth powers is NX 4ré+ aya) ara Nx Cr a which is Prop. 28. oF Dr SreWARt’ s Theorems AND Gace BC. AB 4 AT aT &c. =Nx aS , we get 2+ 28 2% r* AG + AB 4 AT 4, ec." NX 33, ae = Nx BEEZ 27’. | Awd by proceeding in this-way, (the law of continuation be- ing evident), we get Propofitions 39, 40, 41, &c. of Dr Stewart's Theorems, ‘fince the powers of DM, DV, DH, DN, &c. however high, may always be exprefled by thofe of DG and 7. The fame reafoning ‘holds in all even ‘powers, when the point D is without the figure,” by taking the powers of DH, +7, &c. when 'DH, ‘Secs 18 esha — than 7; inftead of the poeeks of - DH, &c.' >” ‘Let any regular figure of an odd number of fides, (PI. ‘TL. Fig. 5.), circumfcribe the circle, and touch it in the points B, E,. C, QL; and from any point D, let perpendiculars DP, DR, DS, DO, DT, ’be drawn ‘to the ‘fides of the figure; and DF, DM, DN, DH, ‘DV, perpendiculars to the diameters paffing through the points of contact: ‘Vou. VI.—P. I. H _ THEN 58 INVESTIGATION of fome THEN, if radius be denoted by r, it is evident, that DP is — r—GN, DR =r—GF, DS =r+GH, DO =r + GM, and: DT =r-+ GV; and calling N the number of the fides of the figure, the fum of the fquares of thefe lines is N X77 + 27 X GH + GM+GV—GN— GF + GH +GM'+Gv + GN’ + GF. But fince the angles HGN, NGM, MGF, FGV, are equal, and the angles at H, N, M, F, V, right ones, a-circle, ha- ving its diameter = GD, pafles through the points G, H, N, D, M, F, V, and its circumference is divided into equal parts at the points H, N, M, F, V. Wherefore GH +GN +GM + GF GD. 2 x-2-GD + GV = axNx 52 =Nx Gre But DP + DR + 2 —— GD , DS +DO +DT =N xr +N x. (Stewart’s Theor. Prop. 5-). Therefore 2r xX GH + GM + GV — GN — GE — o,or GN + GF = GH + GM. + GV.. Whence this propo- fition: If, from any point, perpendiculars be drawn to the fides: of any regular figure of an odd number of fides, circum{cribing: a circle, the fum of the parts by which thofe perpendiculars,. which are greater than radius, exceed it, is equal.to the fum of, thofe parts by which the perpendiculars, which are lefs than ra- dius, fall {hort of it. And this propofition is alfo.true with re-. gard to any regular figure, of which the number of its fides is a, multiple of any odd number by 2, fince the perpendiculars DF, DM, DN, DH, DV, &c. are the fame both in number and mag= nitude, in any regular figure of an.odd number of fides, and a; regular figure of double the’ number, of fides.. Gonfequently, in a hexagon, one of the three perpendiculars drawn from any point D to the diameters joining the oppofite, points of contact, is. equal PROPERTIES of the CIRCLE. 59 equal to the fum of the other two, and fo on; and if, in the hexagon, the point D be taken in one of the three diameters, the perpendiculars drawn from it to the other two are equal. AGAIN, DP’ + DR 4 DS’ +DO +DP=Nxr+3r x GH + GM + GV — GN — GF + 37x GH +GM +Gv +GN +GF4GH4GM +GV — GN GF =Nxr$Nx3r-24 Gr + GM’ + Gv — GN’ — GF. But finceN X 7?-+N X37 aa = DP + DR’ + DS +DO'+DT GH + GM +GV = GN’ + GF. | Ir D be in a line perpendicular from G the centre, to a dia- meter drawn from any point of contact L, the odd chord GV vanifhes, (V coinciding with G), and GN = GM, GH = GF; and the expreflion for the fum of the cubes of the perpendicu- lars, drawn from D to the fides of the circum{fcribing figure, is ae D fimply NX r3+N x 37x Ir the figure circumfcribing the circle be a pentagon, a line drawn from G, bifecting the angle QG d nearer to G, is perpendi- cular to LG; alfo, if D be in the line G d, the point M coincides ‘with D, GN = GF, GH = GV, and GM coincides with GD, and twice the cube on GF or GN is equal to the three cubes on GD, GH, GV, or to the cube on GD with twice the cube on GH or ‘GY ; and the difference of the cubes on GF, GV, or on GN, GH, H2 P is 60 INVESTIGATION of fome is then equal to half the cube on GD, or 2GF —2Gv = GD. Hence an eafy folution of this problem. HavinG two equal right lines given, it is required to cut one of them into two parts, and the other into three parts; fo that the cubes on the two parts, into which the one of thefe lines is cut, fhall, together, be equal to the cubes on the three parts, in- to which the other is cut, taken together. HENCE, alfo, an eafy conftruction for this problem: On a gi- ven right line, to conftitute a triangle, fuch that twice the dif- ference of the cubes on the other two fides, fhall be equal to the cube on the given line. Ler AC be the given line, (Pl. II. Fig. 6.). With A as radius, defcribe an arc AB. Take the angle ACB = 36°. Draw AG perpendicular to CB, and join AB. From A and C ‘ : .. AB ‘ . as centres, defcribe arcs with the radii ria and CG, interfecting in the point F. Then CFA is the triangle required; and 2-OF —2-AF =CA- DEMONSTRATION. Since the angle ACB is 36°, AB is the fide of a decagon in- {cribed in the circle, which has AC for its radius ; and CG is the perpendiculaf to the fide of an infcribed pentagon. Butitis _ AGH AB and AC = AB + well known, that CG is = ACXAB. Confequently 3AC° = 3AC’x AB + 3ACX AB; add AC’ to both, and we have 4 AG’ = AC’ + 3 AG x AB + 3AC PROPERTIES of the CIRCLE. 6r AC’ + 3AC x AB+3ACx AB _ F: AC x AB’, and AC’ = 4. AC + AB’ — AB’ Df 8 the cube of radius is equal to twice the difference between the cubes on the perpendicular to the fide of the infcribed pentagon, and half the fide of the infcribed decagon. x 2=2XCG—AF. Thus, in any circle, Proposition. Let any. regular figure of an odd number of fides, be circumf{cribed about a circle, and let (7) be any odd number, lefs than the number of the fides of the figure; and from any point within the figure let perpendiculars be drawn to the fides of the circumfcribing figure ; then the fum of the (2) powers of the parts by which thofe pérpendiculars, which are greater than radius, exceed it, is equal to the fum of the () pow- ers of thofe parts by which the perpendiculars, which are lefs than radius, fall fhort of it. _ Hence thefe problems, _Havine two equal given right lines, to cut one of them into two parts, and the other into three, fo that the cubes on the two parts, into which one of them is cut, fhall, together, be equal to the cubes on the three parts, into which the other is cut, taken ~ together. Anp having two equal right lines given, to cut one of them into feven parts, and the other into eight, fo that the cubes, the ‘sth powers, the 7th, gth, 11th and 13th powers, of the feven parts, into which the one is cut, fhall, together, be refpectively_ equal to the cubes, the 5th, the 7th, the gth, the 11th, and the 13th powers, of the eight parts, into which the other is cut. THE firft of thefe two problems is effected by a pentagon, infcribed in a circle; and the fecond, by a quindecagon in{cri- bed. Ir 62 INVESTIGATION Of Jome Ie V be as much on the other fide of the centre G, towards L, as it is towards C, the lines GN, GM, exchange their values or magnitudes, as alfo do the lines GH, GF; and the perpendicu- lars to the fides of the circumfcribing figure then become r— GM, r — GH, 7+ GN, 7+ GF, r— GV; and the fum of their cubes NX73-+NX 37. ae af EN Giaeis Males anys, a3. 1: 7 GD <3 GH — GV"; which added to N X3-4+N xX aitpracott GM Go a Gy 2 EN oe GF yiehe fum of their cubes before found, and the aggregate divided by 2, gives N X7r3-++-N X 3r. _——2 ae the fum of their cubes, when D is in the line drawn from the centre G perpendicular to LG. LET a circle, (Pl. III. Fig. 7.), be defcribed on BC, with the centre G, and let BF be a fquare on the diameter BC ; draw EGD from E, through the centre G, to meet the circle in D, and join DF. THEN, fince BG X CS, or CG X CS = Gs, GC is cut in ex- treme and mean proportion in the point S, and GS is the fide of a regular decagon, infcribed in the circle. And fince the per- pendicular from G to the fide of a regular infcribed pentagon, is S } ass = Bes a G , BS is twice that perpendicular. But et. 3 = 3 li “a an ae —S2 =5. Confequently BS’— GS’, or 7 GS" — -GS’=,4r. Therefore 37° = 31° x GS+ 37 x GS» and r? PROPERTIES of the CIRCLE, — 63 y= xGS+rx GS. But BS is cut in G, in the fame manner as GC is cut in S. Wherefore, if another circle be de- fcribed, with BS as radius, and a line be drawn from one of the angles of a {quare, defcribed on the diameter, through the centre, to meet the circumference in a point, and if this point, and the other oppofite angle of the fquare be joined, 27 -- GS — r° ’ will in like manner be = 4X7-+ GS ,or4XbS , and 773+ 127°. GS + 67. Gs +GS'=4 ri -+1277,GS + 127. es + 4. Gs. . Therefore 373 = 67. Gs ice 3GS*, and r? = 27.GS + GS’ =r. GS-++r. Gs. Therefore 27. GS hi =r+r.GS, and - eit as. GS = 7’, and Gs’ =r. GS—r. Gs. Ir, therefore, from any point in the circumference of the circle. BDC, perpendiculars be drawn to the fides of any regular figure circumfcribed. about it, the fum of their cubes being = N xX 3. r3, (calling N the number of the fides of the figure), is = N X 57. Gs. +N x x GS. ; and twice the fum-of the cubes of thefe perpendiculars is N x oe Gs’ +N xX 107. GS ; that is, equal to five times a multiple by the number of the fides.of the figure of the cube on the fide of -an infcribed regular decagon, and ten times a multiple, by the fame number, of the folid, which has the fquare of the fide of the,infcribed decagon for its bafe, and radius for its altitude; and if the perpendiculars be drawn from any point P, within the circumfcribed figure, that is, not in the circumference of the circle, . 64 INVESTIGATION of fome circle, twice the fum of their cubes will be equal to2NX -~ Gs’ +2r.GS +2Nx 6rx Se, that is, equal to twice a multiple by the number of the fides of the figure of the cube on the fide of the infcribed decagon, together with four times a mul-. tiple, by the fame number of the folid which has the fquare of the fide of the decagon for its bafe, and 7 for its altitude, toge- ther with thrice a multiple by the fame number of the folid, which has the fquare of GP for its bafe, and 7 for its alti- tude. In like manner, may the fixth powers of lines earatiat from the angles of any regular infcribed figure of a greater number of fides than three, to any point either in, or not in the circumfer- ence, be exprefled in terms of the fide of an infcribed decagon, fince their fum is a multiple of the fum of the cubes of the ‘per- pendiculars, to the fides of the circumfcribing figure, by 8 73. Acain, fince r+ GS: 7r::7:GS:: GS:r—GS, we have 2r+GS:r+GS::r+GS:r::r:GS::GS:r—Gs. eee er eae ee WHEREFORE 37 -4+ 2G5 2 pas =4X2r-+Gs, or 26 r3 + 517°. GS + 337. GS +7G6S = 3273+ 487.GS + 247. GS £65", for 37°. GS 97. GS + 3GS = 67°, or r-GS+ 37r-GS + co ego WueEreErorg, fince four times the fum of the cubes of the perpendiculars drawn from any point in the circumference of the circle to the fides of any regular circumfcribing figure, is NX.5 X27; four times the fum of thefe cubes is = N X g7r.GS+ 157. Gs +5GS = SN X77, Go + 37. GS +GS’;; 3 that PROPERTIES of the CIRCLE. «65 that is, equal to five times.a multiple, by the number of the fides of the figure of the cube on the fide of the infcribed decagon, together with fifteen times a multiple, by the fame number, of the folid, which has the fquare on the fide.of the infcribed decagon as its bafe, and 7 for its altitude, together with five times a multiple, by the fame number of the folid, which has = for its bafe, and the fide-of the decagon for its altitude. Let the circumference of a circle-be divided into any number n of equal parts, and from any point in the circumference let chords be drawn to the points of divifion, and let 3m be any number lefs than 2, the fum of the 2 powers of the lines which have refpectively to 27 the diameter, the ratios which the cubes of the chords have refpectively to 87°, the cube of the diameter, is equal to ” X HS: Sr etic Morea Ts : 1+2-3-4i . » 3m 2 Let the chords be denoted by A, B, C, D, &c, to ” terms ; and let 872: A3 =27r:a,873:Bs=27r.b, 87: = arise, " H A3 fa " A™ $73:D? = 27:4, &c. Thenag=—,, and a" =, o"= af 47 Pe ; Bo . A™ cae &c.; and a” -+ 4”-+ &c. to ” terms, is = sare ae vise ae B™ : 3 +o t+ &e. to aterms.. If p=3m, we have a” + ee g A’? BY? ; be + &. = etm Pre + py ne &c, But the fum of p—1 the 2p powers of the chords A, B &c. isa X en y re, Vou. VI.—P. I. I Therefore 66 INVESTIGATION of fome 2m am wee 1.3-5-7- : ght yim a Therefore a” -+- 4" + &c. =X aot x nate ER I ae er - ge 1.2+3-4+ +3” 2 Ir m=1,¢7+0+&.=2X a 4 2 it, and the diameter, (or 27) X @ +5 +c + &c. = fum of the cubes of perpendiculars drawn from any point in the circumference, to the fides of a regular circumfcribing polygon of 7 number of fides, and a’ + 4° + &c. is to the fum of the fquares of thefe perpendiculars as 5 to 6; and if the perpendiculars to the fides of the polygon correfponding to the chords A, B, C, D, &c. and drawn from the fame point in the circumference that thefe chords are drawn from, be denoted by P,Q. R,S, &c. a+ 5+ Loam xP CxR , D = S e+ &e. 27 x or r fr a +P tom 4 &e. = P+ Qa" + R" + &c. = the fum of the 3 m powers of thefe perpendiculars, = 2 X ear . ; = x 73, THEOREM ®. From any pointG, (Pl. III. Fig. 8.), let the chord GA bedrawn ; let GAF bea tangent tothe circleat A; and let AD be perpendicular to the diameter BC, and CF, BG toGF. The right line which has to BC (27), the ratioof AC” to BC’, or the triplicate ratio of the chord of the arc AC, to the diameter, is are or sy =a fourth proportional to the diameter, the chord and the perpendicular drawn from one extremity of the PROPERTIES of the CIRCLE. 67 the chord to the tangent to the circle at the other extremity, or a fourth proportional to the diameter, the chord and verfed fine of the arc AC. For, the angle CAF = the angle ABC = the angle CAD. Therefore CD ='CF, and AD = AF. But CD = Confe- BC | AcscoD:! AC* Ho": a quently = = 8@ which has to BC the ratio of AG’ to BC: Q.E.D. Cor. 1. BD = perpendicular BG ; GF = the chord AE of double the arc AC = twice the fine of the arc AC. ABXBG _ABXBD Cor. 2. Ba or—3q? has to BC, the ratio of AB to BC. 6 Cor. 3 CF = a BG = CF =2 si “ BC = AC aor XE ack BG ah Pte BG = BG BC AB 2 Bi x BC ; and the lines, which have to BC the ratios of Paka dal, Ears 9 ed | AC: BC ; and AB: BG are to each other as ACXGD to AB x BD, or as ACx CF : ABx BG. T2 ‘ SEE 68 INVESTIGATION of fome See Fig. t. and Theorem ®. Since the part of the tangent at the point A, that would be intercepted between perpendicu- lars drawn to it from P and Q; is equal to 2 Pa, or 2 Qe, the part of the tangent at the point B, that would be intercepted be- tween perpendiculars drawn to it from P and Q; is = 2 Pe, or 2Q /; and the part of the tangent at C, that would be inter- cepted between perpendiculars drawn to it from P and Q; is = 2P4, or 2Qd, we have (when AB, BC, &c.. are equal, or when the diameters pafling through A, B, C, &c. make equal angles with one another at the centre O) the fum of the fquares of thefe parts of the tangents, (calling » the number of the I . points of contact), =X =. 2 r’; the fum of their fourth pow- I ers 2x = x 2? 7+; and the fum of the 2 powers of thefe 1 2 Te3.5e eo. 2M—2T parts (7 being any integer lefs than ”) = 2x LG : =“ es cB eit te X 2m7 (r being the radius OP or OQ) = the fum of the 2m powers of the chords drawn from either P or Q, at right angles to the diameters paffing through A, B, C, &c. = the fum of the 2 m powers of chords, drawn to any point in the circumference from the angles of a regular infcribed figure of » number of fides, or from the points where a regular infcribed figure of x number of fides, touches the circle, = the fum of the 2 7 powers of perpendiculars, drawn from P or Q to ” number of right lines pafling through Q_or P,,and interfeéting each other at equal angles. And the fum of the 2™ powers of the halves of thefe parts of the tangents, or of the parts intercepted between the points of conta&t and perpendiculars drawn from either P or Q to the fides of the equal fided figure circumfcribing the circle, or fegment, is 1-3.5.+++ 2M—I = = 1,2.3.+0+ Bie x r™ = the fum of the 2m powers of the PROPERTIES of the CIRCLE. 69 the fines of the angles formed at the centre O, by OP or OQ; and the diameters pafling through the points of conta¢t to the radius OP pe 0Q; con ‘s. Ns ae 4 we a Ps” “% &e. Wu ae” vf OF as Od +, &c. = the fum of the 2m powers of perpen- diculars drawn from any point in the circumference of a circle defcribed from P as a centre, with PO as radius to x number ‘of right lines, interfecting each other in P, and making all the angles equal, = the fum of the m powers of the reCtangles A a X aG, Bexer, Cb x bh, &c.; or of the rectangles Ge x ¢ A, rf Xx fB,4d xX dC, &c. when the regular figure circumfcribing the circle has an odd number of fides; but equal to twice the fum of the 2 ™ powers of faid fines, or to twice the fum of the m powers of faid rectangles, when the regular figure circum{cri- bing the circle has an even number of fides, fince the number of the diameters drawn through the oppofite points of conta¢t, and making equal angles with each other, at their interfection in the centre O, is only half the number of the points of contaét or fides of the figure. But thefe retangles are refpectively equal ' tor—Oa X r+Oa, r—Oe Xr+O084, r—ObXr+O04, &e. iba ies} ein or P—Oa, r—Oce, r°—O4), &c.; and the fum of their m"™ m1 SS ea ee powers is 77?" 7. r"-* x Oa +O¢ +06 +, &c. tom terms, pene et al 5 r+ x Oa" + O2'-+08'+, &e. to m terms +, &c. m ale zi —2m —2mN —2m &e. + Oa + Oc +00 - +, &E. ‘to (2) ‘terms, or to —21m —2m —2N —Oa —Oe —Ob —, &c. to (”) terms, according as m is even or odd. III. a aa 1 AP ciepaetaieeeer ee ; wv if oy satan Bi. ike { HW FONSI SY vibe apo Danio ye hi f ~ ye WER . eae Dura ape Taw 5 wag F was oll igor oD. inks alanis sO Lohson Fah Pas “rechearuant wpe 3 sesnacern pa ‘oloaabarine de. 2ovtod, Cae & oui\ a 46 tadéstria trove tie aatk alain onl ae wos twetb ensompih oz Ro ss Au , ‘eitto ca tee ak it pao ba” TransR.S bE dmVol6.4 P70. PLATE LL. SS ' Dijzars feu.” Le siey rT b, Rah, ee Wie * wae a ‘ ‘e, é a “Al ' za ethene Pa a el Pee eee Dies eis an" ¥ , : Trans RS Edin! Tel P ZO. Puare Il, BLizorsleupt Ill. Account of a SeriEs of EXPERIMENTS, /hewing the Er- FECTS of CoMPRESSION in modifying the ACTION of HEzEatT. By Sir JAMES HALL, Bart. F.R.S, Evin. " [Read Fune 3. 1805.] I. Ancient Revolutions of the Mineral Kingdom.—Vain attempts to explain them.— Dependence of Geology on Chemiftry.—Importance of the Carbo- nate of Lime—Dr Buacx’s difcovery of Garbonic Acid, fubverted the former theories depending on Fire, but gave birth to that of Dr Hor- ron.—Progrefs of the Author’s Ideas with regard to that Theory. —Experiments with Heat and Compreffion, fuggefted to Dr Hurron in 1790.—Undertaken by the Author in 1798.—Speculations on which ~ bis hopes of fuccefs were founded. HOEVER has attended to the ftruéture of Rocks. and Mountains, muft be convinced, that our Globe has. not always exifted in its, prefent ftate ; but that every part, of its mafs, fo far at leaft as our obfervations reach, has been agitated _ and fubverted by. the moft violent reyolutions. Facts. leading to. fuch ftriking conclufions, however i imper= feétly obferved, could hot fail. to, awaken. curiofity, and give rife rit to. a defire of tracing, the, hiftory, and) of inveftigating the made in this way, but with little fuccefs ; for while difcoveries of 42 EFFECTS of HEAT of the utmoft importance and accuracy were made in Aftrono- my and Natural Philofophy, the fyftems produced by the Geo- logifts were fo fanciful and puerile, as fcarcely to deferve a ferious refutation. One principal caufe of this failure, feems to have lain in the very imperfect ftate of Chemiftry, which has only of late years begun to deferve the name of a fcience. While Chemiftry was in its infancy, it was impoflible that Geology fhould make any progrefs ; fince feveral of the moft important circumftances to be accounted for by this latter fcience, are admitted on all hands to depend upon principles of the former. The confoli- dation of loofe fand into ftrata of folid rock; the cryftalline arrangement of fubftances accompanying thofe ftrata, and blended with them in various modes, are circumftances of a chemical nature, which all thofe who have attempted to frame theories of the earth have endeavoured by chemical reafon- ings to reconcile to their hypothefes. Fire and Warer, the only agents in nature by which ftony fubftances are produced, under our obfervation, were employ- ed by contending fects of geologifts, to explain all the phe- nomena of the mineral kingdom. ; Burt the known properties of ‘Water, are quite repugnant to the belief of its univerfal influence, fince a very great propor- tion of the fubftances under confideration are infoluble, or near- ly fo, in that fluid; and fince, if they were all extremely fo- luble, the quantity of water which is known to exift, or that could poffibly exift in our planet, would be far too fmall to ac- complifh the office affigned to it inthe Neptunian theory *. On the other hand, the known properties of Fire are no lefs inade- quate to the purpofe; for, various fubftances which frequently occur in the mineral kingdom, feem, by their prefence, to pre- clude * Tlluftrations of the Huttonian Theory, by Mx Profeflor PLAYFAIR, 430- MODIFIED ty COMPRESSION. 73 clude its fuppofed agency ; fince experiment fhews, that, in our fires, they are totally changed or deftroyed. Unper fuch circumftances, the advocates of either element were enabled, very fuccefsfully, to refute the opinions of their adverfaries, though they, could but feebly defend their own: and, owing perhaps to this mutual power of attack, and for want of any alternative to which the opinions of men could lean, both fyftems maintained a certain degree of credit; and writers on geology indulged themfelves, with a fort of im- punity, in a ftyle of unphilofophical reafoning, which would not have been tolerated in other fciences. Or all mineral fubflances, the Carbonate of Lime is unque-— ftionably the moft important in a general view. As limeftone or marble, it conftitutes a very confiderable part of the folid mafs of many countries ; and, in the form of veins and no- dules of fpar, pervades every fpecies of ftone. Its hiftory is thus interwoven in fuch a manner with that of the mineral kingdom at large, that the fate of any geological theory muft very much depend upon its fuccefsful, application to the va- rious conditions of this fubftance.. But, till Dr Biack, by his difcovery of Carbonic Acid, explained the chemical nature of the carbonate, no rational theory could be formed, of the che- mical revolutions which it has undoubtedly undergone. Tuis difcovery was, in the firft inftance, hoftile to the fup- pofed action of fire ; for the decompofition of limeftone by fire in every common kiln being thus proved, it feemed abfurd to afcribe to that fame agent the formation of limeftone, or of any mafs containing it. ‘Tue contemplation of this difficulty led Dr Hutton to view the aétion of fire in a manner peculiar to himfelf, and thus to. form a geological theory, by which, in my opinion, he has fur- - nifhed the world with the true folution of one of the moft i inte- Vor. VI—P.I. K refting 74 EFFECTS of HEAT refting problems that has ever engaged the attention of men of {cience. He fuppofed, I. Tuar Heat has acted, at fome remote period, on all rocks. , II. Tuar during the action of heat, all thefe rocks (even fuch as now appear at the furface) lay covered by a fuperin- cumbent mafs, of great weight and ftrength. III. Tuar in confequence of the combined action of Heat and Preffure, effects were produced different from thofe of heat on common occafions; in particular, that the carbonate of lime was reduced to a ftate of fufion, more or lefs complete, without any calcination. Tue effential and characteriftic principle of his theory is thus comprifed in the word Compreffion; and by one bold hypothefis, founded on this principle, he undertook to meet all the objec- tions to the action of fire, and to account for thofe’ circum- ftances in which minerals are found to differ from the ufual products of our furnaces. Turs fyftem, however, involves fo many fuppofitions, appa- rently in contradiction to common experience, which meet us on the very threfhold, that moft men have hitherto been deterred from the inveftigation of its principles, and only a few indivi- duals have juftly appreciated its merits. It was long before I belonged to the latter clafs; for I muft own, that, on read- ing Dr Hurron’s firft geological publication, I was induced to reject his fyftem entirely, and fhould probably have continued ftill to do fo, with the great majority of the world, but for my habits of intimacy with the author ; the vivacity and perfpicui- ty of whofe converfation, formed a ftriking contraft to the ob- {curity MODIFIED ly COMPRESSION. "5 fcurity of his writings. I was induced by that charm, and by _ the numerous original facts which his fyftem had led him to - obferve, to liften to his arguments, in favour of opinions which I then looked upon as vifionary. I thus derived from his con- verfation, the fame advantage which the world has lately done from the publication of Mr Prayrair’s Illu/trations ; and, ex- perienced the fame influence which is now exerted by that work, on the minds of our moft eminent men of {cience. Arter three years of almoft daily warfare with Dr Hurt- Ton, on the fubje& of his theory, I began to view his funda- mental principles with lefs and lefs repugnance. There is a period, I believe, in all fcientific inveftigations, when the con- jectures of genius ceafe to appear extravagant; and when we balance the fertility of a principle, in explaining the phe- nomena of nature, againft its improbability as an-hypothefis : The partial view which we then obtain of truth, is perhaps the moft attractive of any, and moft powerfully ftimulates the exertions of an active mind. The mift which obfcured fome objects diflipates by degreee, and allows them to appear in their true colours ; at the fame time, a diftant profpect opens to our view, of fcenes unfufpected before. ENTERING now ferioufly into the train of reafoning fol- lowed by Dr Hutron, I conceived that the chemical effeéts aferibed by him to compreffion, ought, in the firft place, to be inveftigated ; for, unlefs fome good reafon were given us for believing that heat would be modified by preffure, in the man- ner alleged, it would avail us little to know that they had acted together. He refted his belief of this influence on ana- logy; and on the fatisfactory folution of all the phenomena, furnifhed by this fuppofition. It occurred to me, however, that this principle was fufceptible of being eftablithed in a di: rect manner by experiment, and I urged. him to make the at- tempt; but he always rejected this propofal, on account of K2 . the 76 EFFECTS of HEAT™ the immenfity of the natural agents, whofe operations he fup- pofed to lie far beyond the reach of our imitation; and he feemed to imagine, that any fuch attempt muft undoubtedly fail, and thus throw difcredit on opinions already fufficiently eftablifhed, as he conceived, on other principles. I was far, however, from being convinced by thefe arguments ; for, with- out being able to prove that any artificial compreflion to which we could expofe the carbonate, would effectually prevent its calcination in our fires, I maintained, that we had as little proof of the contrary, and that the application of a moderate force might poflibly perform all that was hypothetically, af- fumed in the Huttonian Theory. On the other hand, I con- fidered myfelf as bound, in prattice, to pay deference to his opinion, in a field which he had already fo nobly occupied, and abftained, during the remainder of his life, from the pro- fecution of fome experiments with compreflion, which I had: begun in 1790. Ln 1798, I refumed the fubject with eagernefs, being ftill of opinion, that the chemical law which forms the bafis of the Huttonian Theory, ought, in the firft place, to be inveftigated. experimentally ; all my fubfequent refleftions and obferva-. tions having tended to confirm my idea of the importance of this purfuit, without in any degree rendering me more ap- prehenfive as to the refult. In the arrangement of the following paper, I fhall firft con- fine myfelf to the inveftigation of the chemical effects of Heat and Compreflion, referving to the concluding part, the appli- cation of my refults to Geology. I thall, then, appeal to the volcanoes, and fhall endeavour to vindicate the laws of ac- tion aflumed in the Huttonian Theory, by fhewing, that lavas, previous to their eruptions, are fubjec&t to fimilar laws; and that the volcanoes, by their fubterranean and fubmarine exer- tions, MODIFIED ly COMPRESSION. "7 tions, muft produce, in our times, refults fimilar to thofe afcri- bed, in that Theory; to the former a¢tion of fire. In comparing the Huttonian operations with thofe of the volcanoes, I fhall avail myfelf of fome facts, brought to light in the courfe of the following inveftigations, by which a pre- cife limit is afligned.to the, intenfity of the heat, and to the force of compreilion, required. to fulfil|the conditions ,of | Dr Hutron’s hypothefis :: For, according to him, the power of thofe agents was very great, but quite indefinite ; it was there- fore impoflible to compare their fuppofed effects in any precife “manner with the phenomena of nature. , My attention was.almoft exclufively confined to the Carbo- nate of Lime, about which I reafoned as follows: ‘The carbonic acid, when uncombined with any other fubftance, exifts natural- ly ima gafeous form, atthe common temperature of our atmo- fphere ; but when in union with lime, its yolatility is repreffed,. in that fame temperature, by the chemical, force ofthe earthy. fubftance, which retains it ina folid, form. When the tem- perature is raifed,to a full red-heat, the acid acquires a yola- tility by which that force is overcome, it, efcapes from the. lime, and affumes its gafeous form. It is. evident, that were the attractive force of the lime increafed, or the volatility. of the. _ acid diminifhed by any means, the compound would be enabled. to bear a higher heat without decompofition, than it ¢an in the prefent ftate.of things. Now, preflure muft, produce an effect of this kind; for when,a mechanical force oppofes the expan- fion of the acid, its volatility muft, to a certain degree, be di- minifhed.. Under preflure, then, the carbonate may be expect. ed-to remain, unchanged in a heat, by which, in the open. air, it would have, been calcined. . But experiment alone can teach. us, what comprefling force is requifite to enableit to refift any given elevation of temperature ; and what is to be the refult of fuch an operation... Some of the compounds of lime with acids are “8 EFFECTS of HEAT are fufible, others refra€tory ; the carbonate, when conftrained by preflure to endure a proper heat, may be as fufible as the muriate. . One ‘circumftance, derived from the Huttonian. Theory, induced me to hope, that the carbonate was eafily fufible, and indicated a precife point, under which that fufion ought to be expected. Nothing is more common than to meet with nodules of calcareous fpar inclofed in whinftone ; and we fup- pofe, according to the Huttonian Theory, that the whin and the {par had been liquid together; the two fluids keeping fepa- rate, like oil and water. It is natural, at the junction of thefe two, to look for indications of their relative fufibilities ; and we find, accordingly, that the termination of the fpar is generally globular and {fmooth; which feems to prove, that, when the whin became folid, the fpar was ftill in a liquid ftate ; for had the fpar congealed firft, the'tendency which it fhews, on all oc- cafions of freedom, to fhoot out into prominent cryftals, would have made it dart into the liquid whin, according to the pecu- liar forms of its cryftallization; as has happened with the various fubftances contained in whin, much more refractory than it- felf, namely, augite, felfpar, &c.; all of which having con- gealed in the liquid whin, have affumed their peculiar forms with perfect regularity. From this I concluded, that when the whin congealed, which muft have happened about 28° or 30° of Wepcwoop, the {par was ftill liquid. I therefore expeted, if I could compel the carbonate to bear a heat of 28° without decompofition, that it would enter inte fufion. The fequel will fhew, that this conjecture was not without foundation. I sHALL now enter upon the defcription of thofe experiments, the refult of which I had the honour to lay before this Society on the 30th of Auguft laft (1804) 3 fully aware how difficult it is, in giving an account of above five hundred experiments, all tend- ing to one point, but differing much from each other in vari- ous N MODIFIED ly COMPRESSION. 79 ous particulars, to fteer between the oppofite faults of prolixity and barrennefs. My object fhall be to defcribe, as fhortly as poffible, all the methods followed, fo as to enable any chemift to repeat the experiments ; and to dwell particularly on fuch circuraftances only, as feem to lead to conclufions of eli ance. TueE refult being already known, I confider the account J am about to give of the execution of thefe experiments, as addref- fed to thofe who take a particular intereft in the progrefs of chemical operations: in the eyes of fuch gentlemen, I truft, ’ that none of the details into which I muft enter, will appear fu- s perfluous. Il. Principle of execution upon which the following Experiments were con- dutted.— Experiments with Gun-Barrels filled with baked Clay, and welded at the muzzle. —Method with the Fufible Metal.—Remarkable | effects of its expanfion, Sr Wee ty of introducing Air.—Refults ob- tained. Wuen I firft undertook to make experiments with heat ating under compreflion, I employed myfelf in contriving various devices of fcrews, of bolts, and of lids, fo adjuft- ed, I hoped, as to confine all elaftic fubftances; and per- haps fome of them might have anfwered. But I laid afide all fuch devices, in favour of one which occurred to me in January 1798; which, by its fimplicity, was of eafy appli- cation in all cafes, and accomplifhed all that could be done by any device, fince it fecured perfect firength and tightnefs to the utmoft that the veffels employed could bear, whether form. ed of metallic or earthy fubftance. The device depends upon : the 86 EFFECTS of HEAT the following general view: If, we take a, hollow tube or bar- rel (AD, fig. 1.) clofed at one end, and open at the other, of one foot or more in length; it is evident, that by introducing one end into a furnace, we can apply to it as great heat as art can produce, while the other end is kept cool, or, if necef- fary, expofed to extreme cold. If, then, the fubftance which we mean to fubjec& to the combined action of heat and pref- fure, be introduced into the breech or clofed end of the barrel (CD), and if the middle part be filled with fome refractory fubftance, leaving a {mall empty {pace at the muzzle (AB), we can apply heat to the muzzle, while the breech containing the fubjeét of experiment, is kept cool, and thus clofe the barrel by - any of the numerous modes which heat affords, from the weld- ing of iron to the melting of fealing-wax. Things being then reverfed, and the breech put into the furnace, a heat of any required intenfity may be applied to the fubject of experiment, now in a ftate of conftraint. My firft application of this fcheme was carried on with a common gun-barrel, cut off at the touch-hole, and welded very ftrongly at the breech by means of a plug of iron. Into it I introduced the carbonate, previoufly rammed into a cartridge of paper or pafteboard, in order to protect it from the iron, by which, in fome former trials, the fubjet of experiment . had been contaminated throughout during the action of heat. I then rammed the reft of the barrel full of pounded clay, previoul= ly baked in a ftrong heat, and I had the muzzle clofed like the breech, by a plug of iron welded upon it in a common forge ; the reft of the barrel being kept cold during this operation, by means of wet cloths. The breech of the barrel was then ‘introduced horizontally into a common muffle, heated to about 25° of WepGwoop. To the muzzle a rope was fixed, in fuch a manner, that the barrel could be withdrawn with- out MODIFIED ly COMPRESSION. 81 out danger from an explofion*. I likewife, about this time, clofed the muzzle of the barrel, by means of a plug, fixed by folder only ; which method had this peculiar advantage, that I could fhut and open the barrel, without having recourfe to a workman. In thefe trials, though many barrels yielded to the expanfive force, others refifted it, and afforded fome re- fults that were in the higheft degree encouraging, and even fatisfactory, could they have been obtained with certainty on repetition of the procefs. In many of them, chalk, or com- mon limeftene previoufly pulverifed, was agglutinated into a ftony mafs, which required a fmart blow of a hammer to break it, and felt under the knife like a common limeftone ; at the fame time, the fubftance, when thrown into nitric acid, diffolved entirely with violent effervefcence. In one of thefe experiments, owing to the action of heat on the cartridge of paper, the baked clay, which had been ufed to fill the barrel, was ftained black throughout, to the diftance of two-thirds of the length of the barrel from its breech. This circumftance is of importance, by fhewing, that though all is tight at the muzzle, a protrufion may take place along the barrel, greatly to the detriment of com- plete * On one occafion, the importance of this precaution was ftrongly felt. Having inadvertently introduced a confiderable quantity of moifture into a welded barrel, an explofion took place, before the heat had rifen to rednefs, by which, part of the barrel was fpread out toa flat plate, and the furnace was blown to pieces. Dr Kenneby, who happened to be prefent on this occafion, obferved, that notwith- ftanding this accident, the time might come when we fhould employ water in thefe experiments to affift the force of compreffion. I have fince made great ufe of this valuable fuggeftion: but he fcarcely lived, alas! to fee its application ; fer my firft fuccefs in this way, took place during his laft illnefs.—I have been expofed to no rifk in any other experiment with: iron barrels; matters being fo arranged, that the ftrain againft them has only commenced in a red heat, in which the metal has been fo far foftened, as to yield by laceration like a piece of leather. Vo. VI.—P. I. L 82 EFFECTS of HEAT plete compreflion: and, at the fame time, it illuftrates what has happened occafionally in nature, where the bituminous matter feems to have been driven by fuperior local heat, from one part of a coaly bed, though retained in others, under the fame compreflion. The bitumen fo driven off being found, in other cafes, to pervade and tinge beds of flate and of fandftone. I was employed in this purfuit in {pring 1800, when an event of importance interrupted my experiments for about a year. But I refumed them in March 1801, with many new plans of execution, and with confiderable addition to my ap- paratus. In the courfe of my firft trials, the following mode of execu- tion had occurred to me, which I now began to put in pra¢tice. It is well known to chemifts, that a certain compofition of differ- ent metals *, produces a fubftance fo fufible, as to melt in the heat of boiling-water. I conceived that great advantage, both in point of accuracy and difpatch, might be gained in thefe ex- periments, by fubftituting this metal for the baked clay above mentioned: That after introducing the carbonate into the breech of the barrel, the fufible metal, in a liquid ftate, might be poured in, fo as to fill the barrel to its brim: That when the metal had cooled and become folid, the breech might, as before, be introduced into a muffle, and expofed to any required heat, while the muzzle was carefully kept cold. In this manner, no part of the fufible metal being melted, but what lay at the breech, the reft, continuing im a folid ftate, would effeGtually confine the carbonic acid : That after the ac- tion of ftrong heat had ceafed, and after all had been allowed to cool completely, the fufible metal might be removed entire- ly from the barrel, by means of a heat little above that of boil- ing water, and far too low to occafion any decompofition of the * Eight parts of bifmuth, five of lead, and three of tin. ‘ MODIFIED ty COMPRESSION. 83 the carbonate by calcination, though ating upon it in free- dom ; and then, that the fubje&t of chpeviment might, as be> fore, ‘and taken out of the barrel. . Tuts {cheme, with various modifications and additions, “which: practice has fuggefted, forms the bafis of moft of the following methods. In the firft trial, a ftriking phenomenon occurred, which gave rife to the moft important of thefe modifications. Ha- ’ ying filled a gun-barrel with the fufible metal, without any carbonate ; and having placed the breech in a muffle, I was furprifed to fee, as the heat approached to rednefs, the liquid metal exuding through the iron in innumerable minute drops, difperfed all round the barrel. As the heat advanced, this exudation increafed, till at laft the metal flowed out in continued ftreams, and the barrel was quite deftroyed. On feveral occafions of the fame kind, the fufible metal, being forced through fome very minute aperture in the barrel, fpouted from it to the diftance of feveral yards, depofiting upon any fubftance,oppofed to the ftream, a beautiful af- femblage of fine wire, exactly in the form of wool.’ I imme- diately underftood, that the phenomenon was produced by the fuperior expanfion of the liquid over the folid metal, in con- fequence, of which, the fufible metal was driven through the iron as water was driven through filver * by mechanical per- cuffion in the Florentine experiment. It occurred to me, that this might be prevented by confining along with the fufible metal a fmall quantity of air, which, by yielding a little to the sag of the liquid, would fave the barrel. This re- L2 medy * Effays of Natural Experiments made in the Academie del Cimento, tranfla- ted by WaxteR, London, 1684, page 117. The fame in MusscHENBROEK’s La-- tin tranflation, Lugd. Bat. 1731, p. 63. 84 EFFECTS of HEA medy was found to anfwer completely, and was applied, in all the experiments made at this time *. I now propofed, in order to keep the carbonate clean, ta inclofe it in a fmall veffel ; and to obviate the difficulty of removing the refult at the conclufion of the experiment, I further propofed to connect that veflel with an iron ramrod, longer than the barrel, by which it could be introduced or withdrawn at pleafure. A smALt tube of glafs +, or of Raumur’s porcelain, about a quarter of an inch in diameter, and one or two inches in length, (fig. 2. A) was half filled with pounded carbonate of lime, rammed as hard as poflible; the other half of the tube | being * I found it a matter of much difficulty to afcertain the proper quantity of air which ought to be thus inclofed. When the quantity was too great, the refult was injured by diminution of elafticity,as I {hall have occafion fully to fhew here- after. When too {mall, or when, by any accident, the whole of this included air was allowed to efcape, the barrel was deftroyed. I hoped to afcertain the bulk of air neceffary to give liberty to the ex- panfion of the liquid metal, by meafuring the aétual quantity expelled by known heats from an open barrel filled with it. But I was furprifed to find, that the quantity thus difcharged, exceeded in bulk that of the air which, in the fame heats, I had confined along with the carbonate and fufible metal in many fuccefsful experiments. As the expanfion of the liquid does not feem ca- pable of fenfible diminution by an oppofing force, this fat can only be accounted for by a diftention of the barrel. In thefe experiments, then, the expanfiye force of the carbonic acid, of the included air, and of the fufible metal, aéted in combi- nation againft the barrel, and were yielded to in part by the diftention of the bar- rel, and by the condenfation of the included air. My object was to increafe the force of this mutual action, by diminifhing the quantity of air, and by other de- vices to be mentioned hereafter. Where fo many forces were concerned, the laws of whofe variations were unknown, much precifion could not be expected, nor is it wonderful, that in attempting to carry the comprefling force to the ut- moft, I fhould have deftroyed barrels innumerable. + Lhave fince conftantly ufed tubes of common porcelain, finding glafs much too fufible for this purpofe. MODIFIED ly COMPRESSION. 85 being filled with pounded filex, or with whatever occurred as moft likely to prevent the intrufion of the fufible metal in its liquid and penetrating ftate. This tube fo filled, was: placed in a frame or cradle of iron (df 4, figs. 3, 4, 5, and 6,) fixed to the end (m) of a ram-rod (mm). The cradle was from fix to three inches in length, and: as much in diame- ter as a gun-barrel would admit with eafe. It was compofed of two circular plates of iron, (def g and 4 k /, feen edge- wife in the figures,) placed at right-angles to the ram-rod, one of thefe plates (def 4) being fixed to it by the centre (m). Thefe plates were connected together by four ribs or flattened _ wires of iron.(d 4, ¢ i, f &, and.g /,) which formed the cradle into which the tube (A), containing the carbonate, was intro- duced by thrufting the adjacent ribs afunder. Along with the tube juft mentioned, was introduced another tube (B), of iron or porcelain, filled only: with air. Likewife, in the cradle, a: pyrometer:* piece (C) was placed in _conta& with (A) the tube containing the carbonate. Thefe articles generally occupied. : the Fe Tar, pytometer_pieces rae ans shel experiments were made under my own- eye: Neceflity compelled me to undertake: this laborious and difficult work, in. which Ihave already fo far fucceeded as to obtain a fet of pieces, which, though far from complete, anfwer my purpofe tolerably well. I had lately an oppor- tunity of comparing my. fét-with that of Mr WepcGwoop, ati various tempera~ ‘tures, in-furnaces of great fize and fteadinefs. The refult has proved, that my- pieces: agree as well with.each other as_his; though with my fet each tempera- ture is indicated by a different degree of the fcale. I have thus been enabled to conftru& a table, by which my obfervations have been corre@ed, fo that the temperatures mentioned inthis paper are fuch as would have: been indicated by Mr WeEpnGwoop’s pieces. By Mr WepGwoon’s pieces, I mean thofe of the. only fet. which, has; been fold to the public, and byrwhich the melting heat of pure filver is indicated at the 22d degree. I am well aware, that the late Mr WepcwooD, in his Table of Fufibilities, has ftated that fufion’ as taking place at _ the 28th degree; but I am convinced that his obfervations muft-have been mede. with fome fet different from that which was afterwards fold, 86 EFFECTS of HEAT the whole cradle ; when any fpace remained, it was filled up by a piece of chalk dreffed for the purpofe. (Fig. 4. reprefents the cradle filled, as juft defcribed). Tuincs being thus prepared, the gun-barrel, placed erect with its muzzle upwards, was half filled with the liquid fufible metal. The cradle was then introduced into the barrel, and plunged to the bottom of the liquid, fo that the carbonate was placed very near the breech, (as reprefented in fig. 5, the fu- fible metal ftanding at 0). The air-tube (B) being placed fo as to enter the liquid with its muzzle downwards, retained great part of the air it originally contained, though fome of it might be driven off by the heat, fo as to efcape through the liquid. The metal being now allowed to cool, and to fix round the cradle and ramrod, the air remaining in the air-tube was effectually confined, and all was held faft. The barrel being then filled to the brim with fufible metal, the apparatus was ready for the application of heat to the breech, (as fhewn in fig. 6.) In the experiments made at this time, I ufed a fquare brick furnace (figs. 7 and 8), having a muffle (7 s) traverfing it ho- rizontally and open at both ends. This muffle being fupported in the middle by a very flender prop, was expofed to fire from below, as well as all round. The barrel was placed in the muffle, with its breech in the hotteft part, and the end next the muzzle projecting beyond the furnace, and furrounded with cloths which were drenched with water from time to time. (This arrangement is fhewn in fig. 7). In this fituation, the fufible metal furrounding the cradle being melted, the air contained in the air-tube would of courfe feek the higheft po- fition, and its firft place in the air-tube would be occupied by fufible metal. (In fig. 6., the new pofition of the air is fhewn at pq). AT MODIFIED ly COMPRESSION. 87 ' Arthe conclufion of the experiment, the metal was generally removed by placing the barrel in the tranfverfe muffle, with its muzzle pointing a little downwards, and fo that the heat was applied firft)to the muzzle, and then to the reft of the barrel in fucceflion. (This operation is fhewn in fig. 8). In fome of the firft of thefe experiments, I loofened the cradle, by plunging the barrel into heated brine, ora {trong folution of muriate of lime ; which laft bears a temperature of 250° of Faurenueir before it boils. For this purpofe, I ufed a pan three inches in diameter, and three feet deep, having’ a flat bafon at top to receive the liquid when it boiled over. The method anfwered, but was troublefome, and I laid it afide. I have had occafion, lately, however, to refume it in fome experiments in which it was of confequence to open the barrel with the leaft poflible heat *. By thefe methods I made a great number of experiments, with refults that were highly interefting in that ftage of the bufi- nefs, though their importance is fo: much diminifhed by the fubfequent progrefs of the inveftigation, that I think it proper to mention but very few of them. . Ow the 31ft of March r8or, I rammed forty grains of pound- ed chalk into a tube of green bottle-glafs, and placed it in the cradle as above defcribed.. A pyrometer in the muffle along with the barrel indicated 33°. The barrel was expofed to heat during feventeen or eighteen minutes. On withdrawing the cradle, the carbonate was found in one folid mafs, which had vifibly fhrunk in bulk, the fpace thus left within the tube being pata be ye accurately * In many of the following experiments, lead was ufed in place of the fufible metal, and often with fuccefs ; but I loft many good refults in this way: for the heat required to liquefy the lead, approaches fo near to rednefs, that it is difficult to difengage the cradle without applying a temperature by which the carbonate is injured. I have found it anfwer well, to furround the cradle and a few inches of the rod, with fufjble metal, and to fill the reft of the barrel with lead. 88 EFFECTS of HEA accurately filled with metal, which plated the carbonate. all over without penetrating it in the leaft, fo that the metal was eafily removed. The weight was reduced from forty to thirty- fix grains. The fubftance was very hard, and refifted the knife better than any refult of the kind previoufly obtained ; its frac- ture was cryftalline, bearing a refemblance to white faline marble; and its thin edges had a decided femitranfparency, a circumftance firft obferved in this refult. On the 3d of March of the fame year, I made a fimilar experiment, in which a pyrometer-piece was placed with- in the barrel, and another in the muffle ; they agreed in indi- cating 23°. The inner tube, which was of Reaumur’s porce- lain, contained eighty grains of pounded chalk. The carbo- nate was found, after the experiment, to have loft 34 grains. A thin rim, lefs than the 2oth of an inch in thicknefs, of whitifh matter, appeared on the outfide of the mafs. In other refpects, the carbonate was in a very perfect flate ; it was of a yellowith colour, and had a decided femitranfparency and faline fracture. But what renders this refult of the greateft yalue, is, that on breaking the mafs, a {pace of more than the tenth of an inch fquare, was found to be completely cryftal- lized, having acquired the rhomboidal fraéture of calcareous {par. It was white and opaque, and prefented to the view three fets of parallel plates which are feen under three different angles. This fubftance, owing te partial calcination and fub- fequent abforption of moifture, had loft all appearance of its remarkable properties in fome weeks after its production ; but this appearance has fince been reftored, by a frefh fracture, and the fpecimen is now well preferved by being hermetically inclofed. iil. MODIFIED ly COMPRESSION. 89 Il. Experiments made in Tubes of Porcelain.—Tubes of Wedgwood’s Ware. —Methods ufed to confine the Carbonic Acid, and to clofe the Pores of the Porcelain in a Horizontal Apparatus.—Tubes made with a view to thefe Experiments.—The Vertical Apparatus adopted.—View of Refults obtained, both in Iron and Porcelain.—The Formation of Lime- ftone and Marble.—Inquiry into the Caufe of the partial Calcinations. —Tubes of Porcelain weighed previous to breaking.—Experiments with Porcelain Tubes proved to be limited. Waite I was carrying on the above-mentioned experiments, I was occafionally occupied with another fet, in tubes of por- celain. So much, indeed, was I prepoffeffed in favour of this laft mode, that I laid gun-barrels afide, and adhered to it du- ring more than a year. The methods followed with this fub- ftance, differ widely from thofe already defcribed, though founded on the fame general principles. I procureD from Mr WEpcwoop’s manufactory at Etruria, in Staffordthire, a fet of tubes for this purpofe, formed of the fame fubftance with the white mortars, in common ufe, made there... Thefe tubes were fourteen inches long, with a bore of half an inch diameter, and thicknefs of 0.23 being clofed at one end (figs. 9, 10, II, 12, 13.) I proposeD to ram the reer of lime into the breech (Fig. 9. A); then filling the tube to within a finall diftance of its muzzle with pounded flint (B), to fill that remainder (C) with common borax’of the fhops (borat of foda) previoufly res duced 'to glafs, and then pounded ; to apply heat to the muzzle alone, fo as to convert that borax into folid glafs; then, re- verfing the operation, to keep the muzzle cold, and apply the requifite heat to the cgrbonate lodged in the breech. Vou. VI.—P. I. M Res 90 EFFECTS of HEAT I rnus expected to confine the carbonic acid; but the at- tempt was attended with confiderable difficulty, and has led to the employment of various devices, which I fhall now fhort- ly enumerate, as they occurred in the courfe of practice. The fimple application of the principle was found infufficient, from two caufes: Firft, The carbonic acid being driven from the breech of the tube, towards the muzzle, among the pores of the pounded filex, efcaped from the compreffing force, by lodging itfelf in cavities which were comparatively cold: Secondly, The glafs of borax, on cooling, was always found to crack very much, fo that its tightnefs could not be depended on. To obviate both thefe inconveniences at once, it occurred to me, in addition to the firft arrangement, to place fome borax (fig. 10. C) fo near the breech of the tube, as to undergo heat along with the carbonate (A); but interpofing between this borax and the carbonate, a ftratum of filex (B), in order to prevent contamination. I trufted that the borax in a liquid or vifcid ftate, being thruft outwards by the expanfion of the carbonic acid, would prefs againft the filex beyond it (D), and totally prevent the elaftic fubftances from efcaping out of the tube, or even from wandering into its cold parts. In fome refpects, this plan anfwered to expectation. The glafs of borax, which can never be obtained when cold, with- out innumerable cracks, unites into one continued vifcid mafs in the loweft red-heat ; and as the ftrefs in thefe experiments, begins only with rednefs, the borax being heated at the fame time with the carbonate, becomes united and impervious, as foon as its action is neceflary. Many good refults were accord- ingly obtained in this way. But I found, in practice, that as the heat rofe, the borax began to enter into. too thin fufion, and was often loft among the pores of the filex, the fpace in which it had lain being found empty on breaking the tube. It was therefore. MODIFIED by COMPRESSION. OI therefore found neceflary to oppofe fomething more fubftan- tial and compact, to the thin and penetrating quality of pure borax. In fearching for fome fuch fubftance, a curious property of bottle-glafs occurred accidentally. Some of this glafs, in powder, having been introduced into a muffle at the tempe- rature of about 20° of Wepcwoop ; the powder, in the {pace of about a minute, entered into a ftate of vifcid agglutination, like that of honey, and in about a minute more, (the heat al-’ ways continuing unchanged,) confolidated into a firm and com- pact mafs of Reaumur’s porcelain*. It now appeared, that by placing this fubftance immediately behind the borax, the penetrating quality of this laft might be effectually reftrained ; for, Reaumur’s porcelain has the double advantage of being refractory, and of not cracking by.change of temperature. I found, however, that in the act of confolidation, the pounded bottle-glafs fhrunk, fo as to leave an opening between its mafs and the tube, through which the borax, and, along with it, the carbonic acid, was found to efcape, But the object in view was obtained by means of a mixture of pounded bottle-glafs, and pounded flint, in equal parts. This compound ftill agglutinates, not indeed into a mafs fo hard as Reaumur’s porcelain, but fuf- ficiently fo for the purpofe ; and this being done without any {enfible contraétion, an effectual barrier was oppofed to the bo- rax; (this arrangement is fhewn in fig. 11.) ; and thus the me- thod of clofing the tubes was rendered fo complete, as feldom to fail in practice t. A ftill further refinement upon this me- M2 : thod * In the fame temperature, a mafs of the glafs of equal bulk would undergo the fame change; but it would occupy an hour. + A fubftance equally efficacious in reftraining the penetrating quality of borax, » was difcovered by another accident. It confifts.of a mixture of borax and com- mon fand, by which a fubftance is formed, which, in heat, aflumes the ftate of a very tough pafte, and becomes hard and compact on cooling. ; 92 EFFECTS of HEAT thod was found to be of advantage. A fecond feries of powders, like that already defcribed, was introduced towards the muzzle, (as fhewn in fig. 12.). During the firft period of the experi- ment, this laft-mentioned feries was expofed to heat, with all the outward half of the tube (¢4); by this means, a folid mafs was produced, which remained cold and firm during the fubfequent action of heat upon the carbonate. I soon found, that notwithftanding all the above-mention- ed precautions, the carbonic acid made its efcape, and that it pervaded the fubftance of the Wedgwood tubes, where no flaw could be traced. It occurred to me, that this defeé& might be remedied, were borax, in its thin and penetrating ftate of fu- fion, applied to the infide of the tube ; and that the pores of the porcelain might thus be clofed, as thofe of leather are clofed by oil, in an air-pump. In this view, I rammed the carbonate into a fmall tube, and: furrounded it with pounded glafs of borax, which, as foon as the heat was applied, {pread on the infide of the large tube, and effectually clofed its pores.. In this man- ner, many good experiments were made with barrels lying ho~ rizontally in common muffles, (the arrangement juft deferibed: being reprefented in fig. 13.) I was thus enabled to carry on experiments with this. porcelain, to the utmoft that its ftrength would bear. But I was not fatisfied with the force fo exerted; and, hoping to obtain tubes of a fuperior quality, I {pent much time in expe- riments with various porcelain compofitions. In this, I fo, far fucceeded, as to produce tubes by which the carbonic acid: was in a great meafure retained without any internal glaze. The beft material I found for this purpofe, was the pure por- celain-clay of Cornwall, or a compofition in the proportion of two of this clay to one of what the potters call Corni/b-/tone, which I believe to be a granite in a ftate of decompofition. Thefe tubes were feyen or eight inches long, with a bore. tapering MODIFIED ty COMPRESSION. Pe tapering from 1 inch to 0.6... Their thicknefs was about 0.3 at the breech, and tapered towards the muzzle to the thinnefs of a wafer. _ I now adopted a new mode of operation, placing the tube vertically, and: not horizontally, as before. By obferving the thin-ftate of borax whilft in fufion, I was convinced, that it ought to be treated as a complete liquid, which being fupport- ed in the courfe of the experiment from below, would fecure perfect tightnefs, and obviate the failure which often happen- ed in the horizontal ppition; from the falling of the borax to the lower fide. In this view, (fig: 16.); I filled the breech in the manner defcribed above, and introduced into the muzzle fome: bo- rax (C) fupported at the middle of the tube by a quantity: of filex mixed with bottle-glafs (B). I placed the tube, fo prepared, with its breech plunged into a crucible filled with fand (E), and. its muzzle: pointing upwards. It was now my object to: apply’ sheat to the muzzle-half, whilft the other re- mained cold. In that view, I conftruéted a furnace (fig. 14. and. 1'5.),° ‘having a muffle placed vertically (cd), furround- ed on all fides with fire-(¢¢), and open both above (at c), and ‘below’ (at 'd). » The crucible juft mentioned, with its. tube, being then placed on a fupport directly below the ver-. tical muffle, (as reprefented in fig. 14. at F), it was raifed, fo that the half of the tube next the muzzle was introduced into. the fire. In’ confequence of this, the borax was feen from above to melt, and run down in the tube, the air contained in. the powder efcaping in the form of bubbles, till at laft the. borax ftood with a clear and fteady furface like that of wa- ter. ‘Some of this falt being thrown in from above, by means of a tube of glafs, the liquid furface was raifed nearly tothe muz- _ ale, and, after all had been allowed to become cold, the po-. fition of the tube was reverfed; the muzzle being now plun- ged. 94 EFFECTS of HEAT ged into the fand, (as in fig. 17.), and the breech introduced into the muffle. In feveral experiments, I found it anfwer well, to occupy great part of the fpace next the muzzle, with a rod of fand and clay previoufly baked, (fig. 19. KK), which was either introduced at firft, along with the pounded borax, or, being made red hot, was plunged into it when in a liquid ftate. In many cafes I aflifted the compactnefs of the tube by means of an internal glaze of borax; the carbonate being pla- ced in a {mall tube, (as fhewn in fig. 18.) Turse devices anfwered the end propofed: Three-fourths of the tube next the muzzle was found completely filled with a mafs, having a concave termination at both ends, (f and g figs. 17. 18. 19.), fhewing that it had ftood as a liquid in the two oppofite pofitions in which heat had been applied to it. So great a degree of tightnefs indeed was obtained in this way, that I found myfelf fubjected to an unforefeen fource of failure. A number of the tubes failed, not by explofion, but . by the formation of a minute longitudinal fiffure at the breech, through which the borax and carbonic acid efcaped. I faw that this arofe from the expanfion of the borax when in a li- quid ftate, as happened with the fufible metal in the experi- ments with iron-barrels ; for, the crevice here formed, indi- cated the exertion of fome force acting very powerfully, and to a very fimall diftance. Accordingly, this fource of failure was remedied by the introduction of a very fmall air-tube. This, however, was ufed only in a few experiments. In the courfe of the years 1801, 1802, and 1803, I made a number of experiments, by the various methods above defcrib- ed, amounting, together with thofe made in gun-barrels, to one hundred and fifty-fix. In an operation fo new, and in which the apparatus was ftrained to the utmoft of its power, conftant fuccefs could not be expected, and in fact many expe- riments failed, wholly or partially. The refults, however, upon the MODIFIED ty COMPRESSION. 95 the whole, were fatisfactory, fince they feemed to eftablith fome of the effential points of this inquiry. _ THESE experiments prove, that, by mechanical conftraint, the carbonate of lime can be made to undergo ftrong heat, without-calcination, and to retain almoft the whole of its car- bonic acid, which, in an open fire, at the fame temperature, would have been entirely driven off: and that, in thefe circum- ftances, heat produces fome of the identical effe@s afcribed to it in the Huttonian Theory. By this joint ation of heat and preflure, the carbonate of lime which had been introduced in the ftate of the fineft powder, is agglutinated into a firm mafs, poffefling a degree of - hardnefs, compactnefs, and fpecific gravity *, nearly approach- ing to thefe qualities in a found limeftone; and fome of the refults, by their faline fracture, by their femitranfparency, and their fufceptibility of polith, deferve the name of marble. Tue fame trials have been made with all calcareous fub- ftances ; with, chalk, common limeftone, marble, f{par, and the fhells of fifh. All have fhewn the fame general. property, with fome varieties as to temperature. Thus, I found, that, in the fame circumftances, chalk was more fufceptible of .ag- glutination than {par ; the latter requiring a heat two degrees. higher than the former, to bring) it it to. the fame pitch of ag-- glutination. Tue chalk ufed in my firft experiments, always affumed the- * character of a yellow marble, owing probably to fome flight contamination of iron. When a folid piece of chalk, whofe bulk had been previoufly, meafured in the gage of Wedgwood’s. pyrometer was fubmitted to heat’ under compreffion, its con- traction was remarkable, proving the approach of the particles during their confolidation ; on thefe occafions, it was found. ta: * See’ Appendix, 96 EPPECTS of HEAT to fhrink three times more than the pyrometer-pieces in the fame temperature. It loft, too, almoft entirely, its power of im- bibing water, and acquired a great additional {pecific gravity. ‘On feveral occafions, I obferved, that mafles of chalk, which, before the experiment, had fhewn one uniform character of whitenefs, aflumed a ftratified appearance, indicated by a feries of parallel layers of a brown colour. This circumftance may hereafter throw light on the geological hiftory of this extraor- dinary fubftance. I wave faid, that, by mechanical conftraint, almoft the whole of the carbonic acid was retained. And, in truth, at this period, fome lofs of weight had been experienced in all the experiments, both with iron and porcelain. But even this circumftance is valuable, by exhibiting the infinenee of the carbonic acid, as varied by its quantity. Wuen the lofs exceeded 10 or 15 fer cent *. of the weight of the carbonate, the refult was always of a friable texture, and without any ftony character; when lefs than 2 or 3 per cent. it was confidered as good, and pofleffed the properties of a natural carbonate. In the intermediate cafes, when the lofs amounted, for inftance, to 6 or 8 per cent., the re- fult was fometimes excellent at firft, the fubftance bearing every appearance of foundnefs, and often poflefling a high cha- racter of cryftallization ; but it was unable to refift the ac- tion of the air; and, by attracting carbonic acid or moifture, or both, crumbled to duft more or lefs rapidly, according to circumftances. This feems to prove, that the carbonate of lime, though not fully faturated with carbonic acid, may pof- fefs the properties of limeftone ; and perhaps a difference of this * T have found, that, in open fire, the entire lofs fuftained by the carbonate va- ries in different kinds from 42 to 45.5 per cent. MODIFIED ly COMPRESSION. 97 this kind may exift among natural carbonates, give rife io their different degrees of durability. I nave obferved, in many cafes, that the calcination has reached only to a certain depth into the mafs ; the internal part remaining in a ftate of complete carbonate, and, in ge- neral, of a very fine quality. The partial calcination feems thus to take place in two different modes. By one, a {mall proportion of carbonic acid is taken from each particle of carbonate ; by the other, a portion of the carbonate is quite calcined, while the reft is left entire. Perhaps one refult is the effec of a feeble calcining caufe, acting during a long time, and the other of a ftrong caufe, acting for a fhort time. Some of the tefults which feemed the moft perfect when firft produced, have been fubje& to decay, owing to partial calcination. It happened, in fome degree, to the beautiful fpecimen produced on the 3d of March 1801, though a freih fracture has reftored it. A SPECIMEN, too, of marble, formed from pounded fpar, on 1sth May 1801, was fo complete as to deceive the workman employed to polifh it, who declared, that, were the fubftance a little whiter, the quarry from which it was taken would be of great value, if it lay within reach of amarket. Yet, ina few weeks after its formation, it fell to duft. Numser-ess fpecimens, however, have been obtained, which refit the air, and retain their polifh as well as any marble. Some of them continue in a perfec ftate, though they have been kept without any precaution during four or five years. That fet, in particular, remain perfectly entire, which were fhewn laft year in this Society, though fome of them were made in 1799, fome in 1801 and 1802, and though the firft eleven were long foaked in water, in the trials made of their fpecific gravity. § Vot. VI.—P. I, N A 98 EFFECTS of HEAT A curious circumftance occurred m one of thefe experi- ments, which may hereafter lead to important confequences. Some ruft of iron had accidentally found its way into the © tube : 10 grains of carbonate were ufed, and a heat of 28° was — applied. The tube had no flaw ; but there was a certainty that the carbonic acid had efcaped through its pores. When bro- ken, the place of the carbonate was found occupied, partly by a black flaggy matter, and partly by fphericles of various fizes, from that of a fmall pea downwards, of a white fub- ftance, which proved to be quicklime; the fphericles being interfperfed through the flag, as fpar and agates appear in whinftone. The flag had certainly been produced by a mix- ture of the iron with the fubftance of the tube ; and the fphe- rical form of the quicklime feems to fhew, that the carbonate had been in fufion along with the flag, and that they had feparated on the efcape of the carbonic acid. Tur fubje@ was carried thus far in 1803, when I fhould probably have publifhed my experiments, had I not been in- duced to profecute the inquiry by certain indications, and accidental refults, of amature too irregular and uncertain to meet the public eye, but which convinced me, that it was poflible to eftablifh, by experiment, the truth of all that was hypothetically aflumed in the Huttonian Theory. Tue principal object was now to accomplifh the entire fu- fion of the carbonate, and to obtain fpar as the refult of that fufion, in imitation of what we conceive to have taken place in nature. Ir was likewife important to acquire the power of retaining all the carbonic acid: of the carbonate, both on account of the fact itfelf, and'on account)of its confequences ; the refult be- ing vifibly mproved by every approach’ towards complete fa- turation. . I therefore became anxious to inveftigate the caufe of the partial calcinations which had always. taken place, to a MODIFIED ly COMPRESSION. 99 a greater or a'lef§ degree, in all thefe experiments. The que- ftion naturally fuggefts itfelf, What has become. of the car- bonic acid, feparated in thefe partial calcinations from the earthy ‘bafis? Has it penetrated) the veffel, and efcaped en- tirely, or has it been retained within it in a gafeous, but highly compreffed ftate? It occurred to me, that this que- ftion might ‘be eafily refolved, by weighing the veffel before - and after the action of heat upon the carbonate. Wiru iron, a conftant and ‘inappreciable fource of irregu- larity exifted in the oxidation of the barrel. But with porce- lain the thing was eafy ; and I put it in practice in all my ex« periments with this material, which were made after the que- ftion had occurred to me. The'tube was weighed as foon as its muzzle was clofed, and again, after the breech had been expo- fed to the fire ; taking care, im both cafes, to allow'all to cool. In every cafe, I found fome lofs of weight, proving, that even in the beft experiments, the tubes were penetrated to a certain degree. Inext withed to try if any of the carbonic acid fepara- ted, remained within the tube in a gafeous form; and in that view, I wrapt the tube, which had juft been weighed, in a fheet of paper, and placed it, fo furrounded, on the fcale of the balance. As foon as its weight was afcertained, I broke the tube by a fmart blow, and then replaced upon the fcale the paper containing all the fragments. In thofe experiments, in which entire .calcination had taken place, the weight was found not to be changed, for all the carbonic acid had already efcaped during the action of heat. But in the good refults, I always found that a lofs of weight was the confequence of break- ing the tube. TueEse facts prove, that both caufes of calcination had ope- rated in the porcelain tubes ; that, in the cafes of {mall lof, part of the carbonic acid had efcaped through the veffel, and that part had been retained within it. I had in view methods’ N 2 by 100 EFFECTS of HEAT by which the laft could be counteracted ; but I faw no remedy for the firft. I began, therefore, to defpair of ultimate fuccefs with tubes of porcelain *. ANOTHER circumftance confirmed me in this opinion. I found it impracticable to apply a heat above 27° to thefe tubes, when chargedas above with carbonate, without deftroying them, either by explofion, by the formation of a minute rent, or by the actual fwelling of the tube. Sometimes this fwelling took place to the amount of doubling the internal diameter, and yet the porcelain held tight, the carbonate fuftaining but a very fmall lofs. This ductility of the porcelain in a low heat is a curious fact, and fhews what a range of temperature is embraced by the gradual tranfition of fome fubftances from a folid to a liquid ftate: For the fame porcelain, which is thus fufceptible of being ftretched out without breaking in a heat of 27°, ftands the heat of 152°, without injury, when ex- pofed to no violence, the angles of its fracture remaining fharp and entire. IV. * IT am neverthelefs of opinion, that, in fome fituations, experiments with com- preflion may be carried on with great eafe and advantage in fuch tubes. I allude to the fituation of the geologifts of France and Germany, who may eafily procure, from their own manufaétories, tubes of a quality far fuperior to any thing made for fale in this country. MODIFIED by COMPRESSION. TOI IV. Experiments in Gun-Barrels refumed.—The Vertical Apparatus applied to them.—Barrels bored in folid Bars.—Old Sable Iron.—Fufion of the Carbonate of Lime.—Its action on Porcelain.— Additional appa- ratus required in confequence of that action.—Good re/ults ; in par- ticular, four experiments, illustrating the theory of Internal Calcina- tion, and /hewing the efficacy of the Carbonic Acid us a Flux, Since I found that, with porcelain tubes, I could neither confine the carbonic acid entirely, nor expofe the carbonate in them to ftrong heats; I at laft determined to lay them afide, and return to barrels of iron, with which I had formerly ob- tained fome good refults, favoured, perhaps, by fome acciden- tal circumftances. -On the rath of February ty I began a feries of experi- ments with gun-barrels, ref{uming my former method of working with the fufible metal, and with lead; but altering the pofition of the barrel from horizontal to vertical ; the breech being placed upwards during the action of heat on the carbonate. This very fimple improvement has been productive of advantages no lefs remarkable, than in the cafe of the tubes of porcelain. In this new pofition, the included air, quitting the air-tube on the fu- -fion of the metal, and rifing to the breech, is expofed to the greateft heat of the furnace, and muft therefore reat with its greateft force; whereas, in the horizontal pofition, that air might go.as far back as the fufion of the metal reached, where its elafticity would be much feebler. The fame difpofition enabled me to keep the muzzle of the barrel plunged, du- ring the action of heat, in a veffel filled with water; which contributed 102 EFFECTS of HEAT contributed very much both to the convenience and fafety of thefe experiments. _ In this view, making ufe of the brick-furnace with the vertical muffle, already defcribed in page 93. I ordered a pit (aaa, fig. 20.) to be excavated under it, for the purpofe of receiving a water-veflel. This veflel (reprefented feparately, fig. 21.) was made of caft iron; it was three inches in diame- ter, and three feet deep; and had a pipe (d e) ftriking off from it at right angles, four or five inches below its rim, communi- cating with a cup (ef) at the diftance of about two feet. The main veflel beng placed in the pit (a4) directly below the vertical muffle, and the cup ftanding clear of the furnace, wa- ter poured into the cup flowed into the veffel, and could thus conveniently be made to ftand at any level. “(The whole ar- rangement is reprefented in fig. 20.) The muzzle of the barrel (g) being plunged into the water, and its breech (+) reaching up into the muffle, as far as was found convenient, its pofition was fecured by an iron chain (gf). The heat communi- cated downwards generally kept the furface of the water (at c) in a ftate of ebullition; the wafte thus occafioned being fupplied by means of the cup, into which, if neceflary, a con- ftant ftream could be made to flow. | As formerly, I rammed the carbonate into a tube of porce- lain, and placed it in a cradle of iron, along with an air-tube and a pyrometer; the cradle being fixed to a rod of iron, which rod I now judged proper to make as large as the barrel would admit, in order to exclude as much of the fufible me- tal as poflible ; for the expanfion of the liquid metal being in proportion to the quantity heated, the more that quantity could be reduced, the lefs rifk there was of deftroying the barrels. In the courfe of practice, a fimple mode occurred of remo- ving the metal and withdrawing the cradle- it confifted in pla- - cing _ MODIFIED ly COMPRESSION. 103 cing the barrel with its muzzle downwards, fo as to keep the breech above the furnace and cold, while its muzzle was expofed to ftrong heat in the muffle. In this manner, the metal was difcharged from the muzzle, and the pofition of the barrel being lowered by degrees, the whole metal was removed in fucceflion, till at laft the cradle and its contents became entirely loofe. As the metal was delivered, it was received in a crucible, filled with water, ftanding on a plate of iron placed over the pit, which had been ufed, during the firft ftage of the experiment, to contain the water- veffel. It was found to be of fervice, efpecially where lead was ufed, to give much more heat to the muzzle than fimply what was required to liquefy the metal it contained ; for when this was not done, the muzzle growing cold as the breech was heating, fome of the metal delivered from the breech was congealed at the muzzle, fo as to ftop the paflage. AccorDING to this method, many experiments were made in gun-barrels, by which fome very material fteps were gained. in the inveftigation, Ow the 24th February, I made an experiment with {par and chalk; the fpar being placed neareft to the breech of the bar- rel, and expofed to the greateft heat, fome’ baked clay inter- vening between the carbonates. On opening the barrel, a long-continued hifling noife was heard. The fpar was in a ftate of entire calcination; the chalk, though crumbling at the outfide, was uncommonly hard and firm in the vee The. ‘temperature had rifen to 32°. In this experiment, we have the firft clear example, in iron barrels, of what I call Internal Calcination ; that is to fay, where the carbonic acid feparated from: the earthy ‘bafis, has been. accumulated in cavities within the barrel. For, fubfequently to the action of ftrong heat, the barrel had been'completely cooled; the air therefore introduced by means of the air-tube, muft have . 104 EFFECTS: of HEAT ~ have ref{umed its original bulk, and by itfelf could have no tendency to rufh out; the heat employed to open the barrel being barely fufficient to foften the metal. Since, then, the opening of the barrel was accompanied by the ditcharge of ela- {tic matter in great abundance, it is evident, that this muft have proceeded from fomething fuperadded to the air originally in- cluded, which could be nothing but the carbonic acid of the carbonate. It follows, that the calcination had been, in part at leaft, internal ; the feparation of the acid from the earthy matter being complete where the heat was f{trongeft, and only partial where the intenfity was leis. Tue chemical principles ftated in a former part of this paper, authorifed us to expect a refult of this kind. As heat, by increafing the volatility of the acid, tended to feparate it from the earth, we had reafon to expect, that, under the fame compreflion, but in different temperatures, - one portion of the carbonate might be calcined, and ano- ther not: And that the leaft heated of the two, would be leaft expofed to a change not only from want of heat, but like- wife in confequence of the calcination of the other mafs; for the carbonic acid difengaged by the calcination of the hot- teft of the two, muft have added to the elafticity of the confined elaftic fluid, fo as to produce an increafe of compreffion. By - this means, the calcination of the coldeft of the two might be altogether prevented, and that of the hotteft might be hindered from making any further advancement. This reafoning feemed to explain the partial calcinations which had frequently occur- red where there was no proof of leakage ; and it opened fome new practical views in thefe experiments, of which I availed myfelf without lofs of time. If the internal calcination of one part of an inclofed mafs, promotes the compreflion of other maffes included along with it, I conceived that we might for- _ ward our views very much by placing a {mall quantity of carbo- nate, ” MODIFIED by COMPRESSION. 105 nate, carefully weighed, in the fame barrel with a large quanti- ty of that fubftance ; and by arranging matters fo that the {mall fiducial part fhould undergo a moderate heat, while a ftronger heat, capable of producing internal calcination, fhould be ap- plied to the reft of the carbonate. In this manner, I made _ many experiments, and obtained refults which feemed to con- firm this reafoning, and which were often very fatisfactory, though the heat did not always exert its greateft force where I intended it to do fo. On the 28th of February, I introduced fome carbonate, ac- curately weighed, into a {mall porcelain tube, placed within a larger one, the reft of the large tube being filled with pounded chalk ; thefe carbonates, together with fome pieces of chalk, placed along with the large tube in the cradle, weighing in all 195.7 grains. On opening the barrel, air rufhed out with a long-continued hifling noife. The contents of the little tube were loft by the intrufion of fome borax which had been in- troduced over the filex, in order to exclude the fufible metal. But the reft of the carbonate, contained in the large tube, came out in a fine ftate, being porous and frothy throughout ; fpark- ling every where with facettes, the angular form of which was diftinguifhable in fome of the cavities by help of a lens: in fome parts the fubftance exhibited the rounding of fufion ; in many it was in a high degree tranfparent. It was yellow towards the lower end, and at the other almoft colour- lefs. At the upper end, the carbonate feemed to have united with the tube, and at the places of contact to have {pread up- on it; the union having the appearance of a mutual action. The general mafs of carbonate effervefced in acid violently, -but the thin ftratum immediately contiguous to the tube, fee- bly, if at all. On the 3d of March, | introduced into a very clean tube of porcelain 36.8 of chalk. The tube was placed in the upper VOL. VI.—P. I, O part 106 EFFECTS of HEAT part of the cradle, the remaining fpace being filled with two pieces of chalk, cut for the purpofe; the uppermoft of thefe being excavated, fo as to anfwer the purpofe of an air-tube. The pieces thus added, were computed to weigh about 300 grains. There was no pyrometer ufed ; but the heat was guefled to be about 30°. After the barrel had ftood during a few minutes in its delivering pofition, the whole lead, with the rod and cradle, were thrown out with a {mart report, and with con- fiderable force. The lowermoft piece of chalk had fearcely been acted upon.by heat. The upper part of the other piece was in a ftate of marble, with fome remarkable facettes. | The car- bonate, in the little tube, had fhrunk very much during the firft action of heat, and had begun to fink upon itfelf, by a fur- ther advancement towards liquefaction. The mafs was divi- ded into feveral cylinders, lying confufedly upon each other ; this divifion arifing from the manner in which the pounded chalk was rammed into the tube in fucceflive portions. In feveral places, particularly at the top, the carbonate was very porous, and full of decided air-holes, which could not have been formed but in a foft fubftance; the globular form ‘and fhining furface of all thefe cavities, clearly indicating fu- _ fion. The fubftance was femitranfparent ; in fome places yel- low, and in fome colourlefs.. When broken, the folid parts fhewed a faline fraéture, compofed’ of innumerable facettes. The carbonate adhered, from end to end, to the tube, and in- corporated with it, fo as to render it impoflible to afcertain what lof had been fuftained. In general, the line of conta& was of a brown colour; yet there was no room for fufpecting the prefence of any foreign matter, except, perhaps, from the iron- rod which was ufed in ramming downthe chalk. But, in fubfe- quent experiments, I have obferved the fame brown or black: colour at the union of the carbonate with the porcelain tubes, where the powder had been purpofely rammed with a piece of wood ; MODIFIED by COMPRESSION. 107 wood ; fo that this colour, which has occurred in almoft every fimilar cafe, remains to be accounted for. The carbonate ef- fervefced violently with acid ; the fubftance in contact with the tube, doing fo, however, more feebly than in the heart, lea- ving a copious depofite of white fandy matter, which is doubt- lefs a part of the tube, taken up by the carbonate in fufion. ~ On the 24th of March, I made a fimilar experiment, m-a ftout gun-barrel, and took fome care, after the application of heat, to cool the barrel flowly, with a view to cryftallization. The whole mafs was found in a fine ftate, and untouched by the lead; having a femitranfparent and {aline ftructure, with various facettes. In one part, I found the moft decided cry- ftallization I had obtained, though of a fmall fize: owing to its tranfparency it was not eafily vifible, till the light was made to reflect from the cryftalline furface, which then produced a dazzle, very obfervable by the naked eye : when examined by means of a lens, it was feen to be compofed of feveral plates, bro- ken irregularly in the fra@ture of the fpecimen, all of which are parallel to each other, and reflect under the fame angle, fo as to unite in producing the dazzle. This ftruéture was obfervable equally well in both parts of the broken fpecimen. In a for- mer experiment, as large a facette was obtained in a piece of folid chalk; but this refult was of more confequence, as having been produced from chalk previoufly pounded. Tue foregoing experiments proved the fuperior efficacy of iron veflels over thofe of porcelain, even where the thicknefs was not great; and I perfevered in making a great many experi- ments with gun-barrels, by which I occafionally obtained very fine refults: but I was at laft convinced, that their thicknefs was not fuffiicient to enfure regular and fteady fuccefs: For this purpofe, it appeared ‘proper to employ veffels of fuch ftrength, as to bear a greater expanfive force than was juft ne- repay 3 fince, occafionally, (owing to our ignorance of the re- O2 lation 108 EFFECTS of HEAT lation between the various forces of expanfion, affinity, tena- city, &c.), much more ftrain has been given to the veflels than was requifite. In fuch cafes, barrels have been deftroyed, which, as the refults have proved, had acted with fufficient ftrength during the firft ftages of the experiments, though they had been unable to refift the fubfequent overftrain. Thus, my fuccefs with gun-barrels, depended on the good fortune of ha- ving ufed a force no more than fufficient, to conftrain the car- bonic acid, and enable it. to act as a flux on the lime. I there- fore determined to have recourfe to iron barrels of much greater ftrength, and tried various modes of conftruction. I nap fome barrels executed by wrapping a thick plate of iron round a mandrel, as is practifed in the formation of gun-bar- rels ; and likewife by bringing the two flat fides together, fo as to unite them by welding. Thefe attempts, however, failed. I next thought of procuring bars of iron, and of having a cavi- ty bored out of the folid, fo as to form a barrel. In this man- ner I fucceeded well. The firft barrel I tried in this way was of fmall bore, only half an inch: Its performance was highly fatisfatory, and fuch as to convince me, that the mode now adopted was the beft of any that I had tried. Owing to the fmallnefs of the bore, a pyrometer could not be ufed internal- ly, but was placed upon the breech of the barrel, as it ftood in the vertical muffle. In this pofition, it was evidently expofed to a much lefs heat than the fiducial part of the apparatus, which was always placed, as nearly as could be guefled, at the point of greateft heat. On the 4th of April, an experiment was made in this way with fome {par ; the pyrometer on the breech giving 33°. The fpar came out clean, and free from any contamination, adhering to the infide of the porcelain tube: it was very much fhrunk, ftill re- taining a cylindrical form, though bent by partial adhefions. Its furface bore {carcely any remains of the impreilion taken by the MODIFIED ly COMPRESSION. 109 the powder, on ramming it into the tube: it had, to the naked eye, the roughnefs and femitranfparency of the pith of a ruth - ftripped of its outer fkin. By the lens, this fame furface was feen to be glazed all over, though irregularly, fhewing here and there fome air-holes. In fracture, it was femitranfparent, more vitreous than cryftalline, though having a few facettes : the mafs, was feemingly formed of a congeries of parts, in them- felves quite tranfparent: and,at the thin edges, {mall pieces were vifible of perfect tranfparency. Thefe muft have been produ- ced in the fire ; for the fpar had been ground with water, and paffed through fieves, the fame with the fineft of thofe ufed at Etruria, as: defcribed by Mr Wxpewoop, in his paper on the conftruction of his Pyrometer. Wira the fame barrel I obtained many interefting refults, giving as ftrong proofs of fufion as in any former experiments ; with this remarkable difference, that, in thefe laft, the fub- ftance was compact, with little or no trace of frothing. In the gun-barrels where fufion had taken place, there had al- ways been a lofs of 4 or 5 per cent., connected, probably, with the frothing. In _thefe experiments, for a reafon foon to be ftated, the circumftance of weight could not be obferved; but appearances led me to fuppote, that here the lofs had been fmall, if any. On the 6th of April, I made another nce with the {quare barrel, whofe thicknefs ‘was now much reduced by fuc- ceflive {cales, produced by oxidation, and in which a {mall rent began to appear externally, which did not, however, pe- netrate to the bore. The heat rofe high, a pyrometer on the breech of the barrel giving 37°. On removing the metals,. the cradle was found to be fixed, and was broken in the at- tempts made to withdraw it. The rent was much widened externally : but it was evident, that the barrel had not been -laid open, for. part of the carbonate was in a ftate of faline marble ; 110 EFFECTS of HEAT marble ; another was hard and white, without any faline grains, and fearcely effervefced in acid. It was probably quicklime, formed by internal calcination, but in a ftate that has not oc- curred in any other experiment. Tue workman whom I employed to take out i remains of the cradle, had cut off a piece from the breech of the barrel, three or four inches in length. As I was examining the crack which was feen in this piece, I was furprifed to fee the infide of the barrel lined with a fet of tranfparent and well-defined cry- ftals, of fmall fize, yet vifible by the naked eye. They lay to- gether in fome places, fo as to cover the furface of the iron with a tran{parent coat ; in others they were detached, and fcattered over the furface. Unfortunately, the quantity of this fubftance was too fmall to admit of much chemical examination; but I immediately afcertained, that it did not in the leaft effervefce in acid, nor did it feem to diffolve in it. The cryftals were in general tranfparent and colourlefs, though a few of them were tinged feemingly with iron. Their form was very well defined, being flat, with oblique angles, and bearing a ftrong refemblance to the cryftals of the Lamellated Stylbite of Haiiyv. Though made above two years ago, they ftill retam their form and tranfparency unchanged. Whatever this fubftance may be, its appearance, in this experiment, is in the higheft degree interefting, as it feems to afford an ex- ample of the mode in which Dr Hurron fuppofes many in- ternal cavities to have been lined, by the fublimation of fub- ftances in a ftate of vapour; or, held in folution, by matters in a gafeous form. For, as the cryftals adhered to a part of the barrel, which muft have been occupied by air during the ac- _ tion of heat, it feems next to certain that they were spaishein by fublimation. Tue very powerful effeéts produced by this laft barrel, the — fize of which (reduced, indeed, by repeated oxidation) was not above MODIFIED by COMPRESSION. IfI above an inch fquare, made me very anxious to obtain barrels of the fame fubftance, which being made of greater fize, ought ‘to afford refults of extreme intereft. I found upon inquiry, that this barrel was not made of Swedith iron, as I at firft fup- pofed, but of what is known by the name of O/d Sable, from the figure of a Sable ftamped upon the bars; that being the armorial badge of the place in Siberia where this iron ‘is made *. A worKmaAn explained to me fome of the properties of diffe- rent kinds of irons, moft interefting in my prefent purfuit ; and he illuftrated what he faid by actual trial. All iron, when expo- fed to a certain heat, crufhes and crumbles under the hammer ; ‘but the temperature in which this happens, varies with every different fpecies. Thus, as he fhewed me, caft iron cruthes in a dull-red heat, or perhaps about 15° of WerpGwoop ; fteel, in a heat perhaps of 30°; Swedifh iron, in a bright . white heat, perhaps of 50° or 60°; old fable, itfelf, likewife yields, but in a much higher heat, perhaps of 100°. I merely gueffed at thefe temperatures ; but I'am certain of this, that ina heat fimilar to that in which Swedifh iron crumbled under the _ hammer, the old fable withftood a ftrong blow, and feemed to poffefs confiderable firmnefs. It is from a knowledge of this quality, that the blackfmith, when he firft takes his iron from the forge, and lays it on the anvil, begins by very gentle blows, till the temperature has funk to the degree in which the iron can bear the hammer. I obferved, as the flrong heat of the forge acted on the Swedish iron, that it began to boil at the furface, clearly indicating the difcharge of fome gafeous mat- ter ; whereas, the old fable, in the fame circumftances, acqui- red the fhining furface of a liquid, and melted away without any effervefcence. I procured, at this time, a confiderable ' number ~* T was favoured with this account of it by the late Profeffor Rozison. 112 EFFECTS of HEAT number of bars of that iron, which fully anfwered my expec- tations. By the experiments laft mentioned, a very important point was gained in this inveftigation ; the complete fufibility of the carbonate under preflure being thereby eftablifhed. But from this very circumftance, a neceflity arofe of adding fome new devices to thofe already defcribed: for the carbonate, in fu- fion, fpreading itfelf on the infide of the tube containing it, and the two uniting firmly together, fo'as to be quite infe- parable, it was impoflible, after the experiment, to afcertain the weight of the carbonate by any method previoufly ufed. I therefore determined in future to adopt the following ar- rangement. A sMALL tube of porcelain (74, fig. 23.) was weighed by” means of a counterpoife of fand, or granulated tin ; then the car- bonate was firmly rammed into the tube, and the whole weighed again: thus the weight of the carbonate, previous to the ex- periment, was afcertained. After the experiment, the tube, with its contents, was again weighed ; and the variation of weight obtained, independently of any mutual action that had taken place between the tube and the carbonate. The balance which I ufed, turned, in a conftant and fteady manner, with one hundredth of a grain. When pounded chalk was rammed into this tube, I generally left part of it free, and in that fpace laid a fmall piece of lump-chalk (7), drefled to a cy- linder, with the ends cut flat and fmooth, and I ufually cut a letter on each end, the more effectually to obferve the effects produced by heat upon the chalk.; the weight of this piece of chalk being always eftimated along with that of the powder contained in the tube. In fome experiments, I placed a cover of porcelain on the muzzle of the little tube, (this cover being weighed along with it), in order to provide againft the cafe of ebullition : “MODIFIED by COMPRESSION. 113 ~ ebullition: But as that did not often occur, I feldom took the trouble of this laft precaution. ‘Ir was now of confequence to protect the tube, thus prepa- red, from being touched during the experiment, by any fub- ftance, above all, by the carbonate of lime, which might adhere to it, and thus confound the appreciation by weight. This was provided for as follows : The {mall tube (Fig. 23. 7%), with its pounded carbonate (4), and its cylinder of lump-chalk (7,), - was dropt into a large tube of porcelain (/ #, Fig. 24.). Upon this a fragment of porcelain (/), of fuch a fize as not to fall in between the tubes, was laid. Then a cylinder of chalk (7) was dreffed,fo as nearly to fit and fill up the infide of the large tube, one end of it being rudely cut into the form of acone. This mafs ' bemg then introduced, with its cylindrical end downwards, was made to prefs upon the fragment of porcelain (/). I then dropped into the fpace (7), between the conical part of this mafs and the tube, a fet of fragments of chalk, of a fize beyond what could poffibly fall between the cylindrical part and the tube, and prefied them down with a blunt tool, by which the chalk being at the fame time crufhed and rammed into the angle, was forced into a mafs of fome folidity, which effectually prevented any thing from pafling between the large ma{s of chalk and the tube. In praétice, I have found this method always to anfwer, when done with care. _I covered the chalk, thus rammed, with a ftratum of pounded flint (0), and that again with pounded chalk (f) firmly rammed. In this manner, I filled the whole of the large tube with alternate layers of filex and chalk; the muzzle being always occu- ' pied with chalk, which was eafily prefled into a mafs of to- lerable firmnefs, and, fuffering no change in very low heats, excluded the fufible metal in the firft ftages of the experiment. Tue large tube, thus filled, was placed in the cradle, fome- times with the muzzle upwards, and fometimes the reverfe. I Vou. VI.—P. I. ip have 14 EFFECTS of HEAT have frequently altered my views as to that part of the ar-~- rangement, each mode poffefling peculiar advantages and dif- advantages. With the muzzle upwards, (as {hewn in fig: 24. and — 25.) the beft fecurity is afforded againft the intrufion of the fufi- ble metal ; becaufe the air, quitting the air-tube in the working pofition, occupies the upper part of the barrel; and the fufible metal ftands as a liquid (at g, fig. 25.) below the muzzle of the tube, fo that all communication is cut off, between the liquid me- tal and the infide of the tube. On the other hand, by this arrange- ment, the {mall tube, which is the fiducial part of the appara- tus, is placed at a confiderable diftance from the breech of the barrel, fo as either to undergo lefs heat than the upper part, or to render it neceflary that the barrel be thruft high into the muffle. Wirn the muzzle of the large tube downwards, the inner tube is placed (as fhewn in fig. 22.), fo as ftill to have its muzzle upwards, and in conta¢t with the breech of the large tube. This. has the advantage of placing the {mall tube near | to the breech of the barrel: and though there is here lefs fe- curity againft the intrufion of liquid metal, I have found» that a point of little confequence; fince, when the experiment jis a good one, and that the carbonic acid has been well con- fined, the intrufion feldom takes place in any pofition. In whichever of the two oppofite pofitions the large tube was placed, a pyrometer was always introduced, fo as to lie as near as poilible to the fmall tube. Thus, in the firft-mentioned _ _pofition, the pyrometer was placed immediately below the large tube, and, in the other pofition, above it ; fo that, in both cafes, it was feparated from the carbonate by the thicknefs only of the two tubes. Mucn room was unavoidably occupied by this method, which neceflarily obliged me to ufe fmall quantities of car- bonate, ' MODIFIED by COMPRESSION. - 115 * bonate, the fubject of experiment, feldom weighing more than 10 or’12 grains, and in others far lefs * On the rrth of April 1803, ite a barrel of old fable _ iron having a bore of 0.75 of an inch, I made an experi- ment in which all thefe arrangements were put in prac- -- tice.’ .The large tube contained two finall ones ; one filled with {par, and the other with chalk. I conceived that the heat had’ rifen to 33°, or fomewhat higher. On melting the metals, the cradle was thrown out with confiderable violence. The’ pyrometer, which, in this experiment, had been placed within the barrel, to my aftonifhment, indi- cated 64°. Yet all was found. The two little tubes came out quite clean and uncontaminated. The {par had loft 17.0 per cent.: The chalk 10.7 per cent.: The {par was half funk down, and run againft the fide of the little tube: Its furface was fhining, its texture fpongy, and it was - compofed of a tranfparent and jelly-like fubftance : The chalk was entirely in a ftate of froth. This experiment extends our power of action, by fhewing, that compreffion, to a confider- able degree, can be carried on in fo great a heat as 64°. It feems likewife to prove, that, in fome of the late experiments with the fquare barrel, the heat had been much higher than was fuppofed at the time, from the indication of the pyrometer placed on the breech of the barrel; and that in fome of them, particularly in the laft, it muft have rifen at leaft as high as in the prefent experiment. TSK Pa On * I meafured the capacity of the air-tubes by means of granulated tin, ating as a fine and equal fand.. By comparing the weight of this tin with an equal bulk of water, I found that a cubic inch of it weighed 1330.6 grains, and that ~ each grain of it cerrefponded to 0.00075 of a cubic inch. From thefe data 1 was - able, prin tolerable accuracy, to gage a tube by weighing the tin required to fiil it. 116 EFFECTS of HEAT On the 2rft of April 1805, a fimilar experiment was made with | a new barrel, bored in a fquare bar of old fable, of about two and a half inch in diameter, having its angles merely rounded ; the inner tube being filled with chalk. The heat was main- tained during feveral hours, and the furnace allowed to burn - out during the night. The barrel had the appearance of found- nefs, but the metals came off quietly, and the carbonate ‘was entirely calcined, the pyrometer indicating 63°. On examina- tion, and after beating off the fmooth and even fcale. of oxide peculiar to the old fable, the barrel was found to have yielded in its peculiar manner ; that is, by the opening of the longi- tudinal fibres. This experiment, notwithftanding the failure of the barrel, was one of the moft interefting I had made, fince it afforded proof of complete fufion. The carbonate had boil- ed over the lips of the little tube, ftanding, as juft defcribed, with its mouth upwards, and had run down to within half an inch of its lower end: moft of the fubftance was in a frothy ftate, with large round cavities, and a fhining furface; in other parts, it was interfperfed with angular mafles, which have evidently been furrounded by a liquid in which they floated. It was harder, I thought, than marble; giving no effervefcence, and not turning red like quicklime in nitric acid, which feemed to have no effec upon it in the lump. It was probably a compound of quicklime with the fubftance of the tube. Wiru the fame barrel repaired, and with others like it, many fimilar experiments were made at this time with great fuccefs ; but to mention them in detail, would amount near- ly to a repetition of what has been faid. I fhall take notice of only four of them, which, when compared together, throw much light on the theory of thefe operations, and likewife feem to eftablifh a very important principle in geology. Thefe four MODIFIED ly. COMPRESSION. 117 four experiments ‘differ from each other only in the abe em- ployed, and:in the: ‘quantity of air introduced, Tue firft of thefe experiments was, made on the 27th of A- pril 1893, in oneiof the large barrels, of old fable, with all the ’ above-mentioned arrangements. The heat had rifen, contrary to my imtention, to 78° and 79°. The tubes came out un- * contaminated with fufible metal, and every thing bore the ap- ‘pearance of foundnefs. The contents of the little tube, con- - fifting of pounded chalk, and of a fmall piece of lump-chalk, came out clean, and quite loofe, not having adhered to the infide of the tube in the fmalleft degree. There was a lofs of 41 per cent., and the calcination feemed to be complete ; the fubftance, when thrown into nitric acid, turning red, without effervefcence at firft, though, after lying a few minutes, fome bubbles appeared. _According to the method foltowed in all thefe experiments, and. lately defcribed at length, (and fhewn in fig. 24. & 25.), the large tube was filled. over the fmall one, with various mafles of chalk, fome in lump, and fome rammed into it in powder ; and in the cradle there lay fome pieces of chalk, filling up the fpace, fo that in the cradle there was a continued chain of carbonate of four or five inches in length. The fubftance was found to be lefs and lefs calcined, the more it was remoyed from the breech of the barrel, where the heat was greateft. ~A fmall piece of chalk, placed at the diftance of half an inch from the fmall tube, had fome faline fubftance in the heart, furrounded and intermixed with quicklime, dif- tinguifhed by its dull white. In nitric acid, this fubftance be- came red, but effervefced pretty brifkly; the effervefcence continuing till the whole was diflolved. The next portion of chalk, was in a firm ftate of limeftone ; and a lump of chalk in the cradle, was equal in perfedtion to any marble _ [ have obtained by compreffion: the two laft-mentioned pieces of chalk efferyefcing with violence in the acid, and fhewing no 118 EFFECGTS-of HEAT no rednefs when thrown into it. - Thefe fads clearly prove, that the calcination of the contents of the fmall tube had been internal, owing to the violent heat which had feparated as acid from the moft heated part of the carbonate, according to the theory already ftated. The foundnefs of the barrel’ was ~ proved by the complete ftate of thofe carbonates which lay in lefs heated parts. The air-tube in this experiment had a capacity of 0.29, nearly one-third of a cubic inch. : Tue fecond of thefe experiments was made on the 29th of © April, in the fame barrel with the laft, after it had afford- ed fome good refults. The air-tube was reduced to one- third of its former bulk, that is, to one-tenth of a cubic inch. The heat rofe to 60°. The barrel was covered externally with a black fpongy fubftance, the conftant indication of fai- lure, and a fmall drop of white metal made its appearance. The cradle was removed without any explofion or hifling. The carbonates were entirely calcined. The barrel had yield- ed, but had refifted well at firft; for, the contents of the little tube were found in a complete ftate of froth, and running with the porcelain. Tue third experiment was made on the 30th of pil; in another fimilar barrel. Every circumftance was the fame as in the two laft experiments, only that the air-tube was now reduced to half its laft bulk, that is, to one-twentieth of a cu- bic inch. A pyrometer was placed at each end of the large tube. The uppermoft gave 41°, the other only 15°. The~ contents of the inner tube had loft 16 per cent., and were redu- ced to a moft beautiful ftate of froth, not very much injured by the internal ‘calcination, and indicating a thinner ftate of fufion than had appeared. — Tue fourth experiment was made’on the 2d of May, like the reft in all refpects, with a ftill fmaller air-tube, of 0.0318, being lefs than one-thirtieth of a cubic inch. The upper py- rometer --“ MODIFIED ly COMPRESSION. 119 rometer gave 25°, anditheunder one 169 :. The loweft mafles of carbonate were featcely affected by the heat : The contents of the little tube had loft 2.9 percent. ; both the lump and the pounded chalk were in a fine faline ftate, and, in feveral places had run and fpread upon the infide of the tube, which I had not expected to fee in fuch a low heat. On the upper furface of the chalk rammed into the little tube, which, after its in- ~-trodudion had been wiped fmooth, were a fet of white cryf tals, with fhiming facettes, large enough to be diftinguifhed by the naked eye, and feeming to rife out of the mafs of car-- bonate. I likewife obferved, that the folid mafs on which thefe cryftals ftood, was uncommonly tran{parent. In thefe four experiments, the bulk of the included air was fucceflively diminifhed, and by that means its elafticity in- ‘creafed. The confequence was, that in the firft experiment, ewhere that elafticity was the leaft, the carbonic acid was allowed to feparate from the lime, in an early ftage of the -rifing heat, lower than the fufing point of the carbonate, and complete internal calcination was effefted. In the fecond experiment, the elaftic force being much greater, calcina- tion was prevented, till the heat» rofe fo high as to occa- fion the entire fufion of the carbonate, and its action on the tube, before the carbonic acid was fet at liberty by the failure of the barrel. In the third experiment, with {till greater elaftic force, the carbonate was partly conftrained, and its fufion accomplifhed, in a heat between 41° and 15°. In the laft experiment, where the force was ftrongeft of all, the carbonate was almoft completely protected from) decom- pofition by heat, in confequence of which it cryftallized and acted on the tube, in a temperature between 25° and 16°. On the other hand, the eflicacy of the carbonic acid as a flux on the lime, and in enabling the carbonate to a@ as a. flux on other bodies, was clearly evinced.; fince the firft ex- Ut i periment. ea 120 EFFECTS of HEAT periment proved, that quicklime by itfelf, could neither be melted, nor,act upon porcelain, even in the violent heat of 79° ; whereas, in the laft experiment where the carbonic acid was retained, both of thefe effects took place in a very low tempe- rature. : V. Experiments in which Water was employed to increafe the Elafticity of the included Air.—Cafes of complete Compreffion.—General Obferva- tions. —Some Experiments affording interefting refults ; in particular, Joewing a mutual action between Silex and the Carbonate of Lime. FinpineG that fuch benefit arofe from the increafe of elafti- city given to the included air in the laft-mentioned experi- ments, by the diminution of its quantity ; it now occurred to me, that a fuggeftion formerly made by Dr Kennepy, of ufing water to aflift the comprefling force, might be followed with advantage: That while fufficient room was allowed for the expanfion of the liquid metal, a reacting force of any requi- red amount, might thus be applied to the carbonate. In this view, I adopted the following mode, which, though attended with confiderable difficulty in execution, I have often practi- fed with fuccefs. The weight of water required to be intro- duced into the barrel was added to a {mall piece of chalk or baked clay, previoufly weighed. The piece was then dropped in- to atube of porcelain of about an inch in depth, and covered with pounded chalk, which was firmly rammed upon it. The tube was then placed in the cradle along with the fubject of expe- riment, and the whole was plunged imto the fufible metal, previoufly poured into the barrel, and heated fo as merely to render it liquid. The metal being thus fuddenly cooled, the MODIFIED by COMPRESSION. 121 the tube was encafed in-a folid mafs, before the heat had reached the mcluded moifture. The difficulty was to catch the fufible metal at the proper temperature ; for when it was fo hot as not to fix in a few feconds, by the contact of the cradle and its contents, the water was heard to bubble through the metal and efcape. I overcame this difficulty, however, by firft heating the breech of the barrel, (containing a fufh- cient quantity of fufible metal), almoft to rednefs, and then fetting it imto a veflel full of water, till the temperature had funk to the proper pitch, which I knew to be the cafe when the hifling noife produced in the water by the heated barrel cea- .fed; the cradle, during the laft ftage of this operation, being held clofe to the muzzle of the barrel, and ready to be thruft into it.’ On the 2d of May, I made my firft experiment im this way, ufing the fame air-tube as in the laft experiment, -which was equal in capacity to one-thirtieth of a cubic inch. Half a grain of water was introduced in the manner juft defcribed. The barrel, after an hour of red-heat, was let down by a ‘rope and pulley, which I took care to ufe in all experiments, in which there was any appearance of danger. All was found. The metals rufhed out fmartly, and a flafh of. flame accompa- nied the difcharge. The upper pyrometer gave 24°, and the lower one 14°. The contents of the inner tube had loft lefs ‘than 1 per cent., ftridtly 0.84. The carbonate was im a ftate of good limeftone ; but the heat had been too feeble: The lower part of the chalk in the little tube was not agglutinated: The chalk round the fragment of pipe-ftalk (ufed to introduce the water), which had been more heated than the pyrometer, and the {mall rod, which had moulded itfelf in the boll. of the ftalk, were in a ftate of marble. On the 4th of May, Imade an experiment like the laft, but with _ the addition of 1.05 grains water. After application of heat, the VoL. VI.—P. I. Q fire 122 ; EFFECTS of HEAT fire was allowed to burn out till the barrel was black. The me- tal was difcharged irregularly. Towards the end, the inflam- mable air produced, burnt at the muzzle, with a lambent flame, during fome time, arifing doubtlefs from hydrogen gas, more or lefs pure, produced by the decompofition of the water. The upper pyrometer indicated 36°, and the lower one 19°. The chalk which lay in the outer part of the large tube was in a ftate of marble. The inner tube was united to the outer one, by a ftar of fufed matter, black at the edges, and f{pread- ing all round, furrounding one of the fragments of porcelain which had fallen by accident in between the tubes. The in- ner tube, with the ftarry matter adhering to it, but without the coated fragment, feemed to have fuftained a lofs of 12-per cent., on the original carbonate introduced. But, the fub- ftance furrounding the fragment being inappreciable, it was impoflible to learn what lofs had been really fuftained. Exa- mining the little tube, I found its edges clean, no boiling over having taken place. The top of the fmall lump of chalk had funk much. When the little tube was broken, its contents gave proof of fufion in fome parts, and in others, of the neareft ap- proach to it. A ftrong action of ebullition had taken place all round, at the contact of the tube with the carbonate: in the heart, the fubftance had a tranfparent granular texture, with little or no cryftallization. The {mall piece of lump-chalk was united. and blended with the rammed powder, fo that they could fcarce- ly be diftinguifhed. In the lower part of the carbonate, where the heat muft have been weaker, the rod had acted more feebly on the tube, and was detached from it : here the fubftance was firm, and was highly marked in the fracture with cryftalline facettes. Wherever the carbonate touched the tube, the two fubftances exhibited, in their mixture, much greater proofs of fufion than could be found in the pure carbonate. At one place, a ftream of this compound had penetrated a rent in . the MODIFIED by COMPRESSION. 12 Us the inner tube, which it had filled completely, conftituting a real vein, like thofe of ‘the mineral kingdom: which is {till diftin@lly to be feen in the fpecimen. It had then {pread_ it- felf upon the outfide of the inner tube, to the extent of half an inch in diameter, and had enveloped the fragment of por- celain already mentioned. When pieces of the compound were thrown into nitric acid, fome effervefced, and fome not. I REPEATED this experiment on the fame day, with two grains of water. The furnace being previoufly hot; I conti- nued the fire during one half-hour with the muffle open, and another with a cover upon it. . I then let the barrel down by means of the pulley. The appearance of a large longitudinal rent, made me at firft conceive that the experiment was loft, and the barrel deftroyed: The barrel was vifibly fwelled, and in {welling had burft the cruft of fmooth oxide with which it was furrounded; at the fame time, no exudation of metal had happened, and all was found. The metals were thrown out with more fuddennefs and violence than in any former experiment, but the rod remained in its place, being fecured by a cord. The upper pyrometer gave 27°, the lower 23°.. The contents of the inner tube had loft 1.5 per cent. The upper end of the little lump of chalk, was rounded and glazed by fufions and the letter which I have been in the habit of cutting on thefe fmall pieces, in or- der to trace the degree of action upon them, was thus quite obliterated. On the lower end of the fame. lump, the letter is till vifible. Both the lump and the rammed chalk were ina good femitranfparent ftate, fhining a little in the fra@ture, but with no good facettes, and no where appear ing to have acted on the tube. This laft circumftance is of confequence, fince it feems to fhew, that this very remarkable action of heat, under compreflion, was performed without the affift- . ance of the fubflance of the tube, by which, in many other pl. experiments, 124 EFFECTS of HEAT experiments, a confiderable additional fufibility has been com- municated to the carbonate. : THESE experiments, and many others made about the fame time, with the fame fuccefs, clearly prove the efficacy of wa- ter in aflifting the compreiflion ; and refults approaching to thefe in quality, obtained, in fome cafes, by means of a very {mall air- tube, fhew that the influence of water on this. occafion has been merely mechanical. ; Durinc the following fummer and autumn 1803, I was oc- _ cupied with a different branch of this fubje@, which I fhall foon have occafion to mention. In the early part of laft year, 1804, I again refumed the fort of experiments lately defcribed, having in view principally to accomplifh abfolute compreffion, in complete imitation of the natural procefs. In this purfuit, I did not confine myfelf to water, but made ufe of various other volatile fubftances, in order to aflift compreflion; namely, carbonate of ammo- nia, nitrate of ammonia, gunpowder, and paper impregna- ted with nitre. With thefe I obtained fome good refults, but none fuch as to induce me to prefer any of thefe compreffors to water. Indeed, I am convinced, that water is fuperior to them all. I found, in feveral experiments, made with a fimple air-tube, without any artificial compreflor, in which a very low red-heat had been applied, that the carbonate loft one or one and a half per cent. Now, as this muft have happened in a temperature fcarcely capable of inflaming gunpowder, it is clear, that fuch lofs would not have been prevented by its pre- fence: whereas water, beginning far below rednefs to aflume a gafeous form, will effectually refift any calcination, in low as well as in high heats. And as the quantity of water can very ealily be regulated by weight, its employment for this purpofe feems liable to no objection. On MODIFIED ly COMPRESSION. 125 On the 2d of January 1804, I made an experiment with marble and chalk, with the addition of 1.1 grain of water. I aimed at a low heat, and the pyrometer, though a little bro- ken, feemed clearly to indicate 22°. Unluckily, the muzzle of the large tube, which was clofed as ufual with chalk, was placed uppermoft, and expofed to the ftrongeft heat. I found it rounded by fufion, and ina frothy ftate. The little tube came out very clean, and was fo nearly of the fame weight as when put in, that its contents had loft but 0.074 per cent. of the weight of the original carbonate.’ The marble was but feebly aggluti- nated, but the chalk was in a ftate of firm limeftone, though it muft have undergone a heat under 22°, or that of melting fil- ver. This experiment is certainly a moft remarkable one, fince a heat has been applied, in which the chalk has been chan- ged to hard limeftone, with a lofs lefs than the rooodth par of its weight, (exactly +--+) ; while, under the fame circum- ftances of preflure, though probably with more heat, fome of the fame fubftance had been brought to fufion. What lofs of. weight this fufed part fuftained, cannot be known. On the 4th of January, a fimilar experiment was made, like- | wife with 1.1 grain of water. The difcharge of the metal was accompanied with a flafh of flame. The pyrometer in- dicated 26°. The little tube came out quite clean. Its con- tents had been reduced from 14.53 to 14.46, difference 0.07 grains, being. 0.47 per cent. on the original carbonate, lef. than one two-hundredth part of the original weight, (exactly siz). The chalk was in a ftate of firm faline marble, but with. no unufual qualities. THESE two laft experiments are rendered ftill more intereft-- ing, by another fet which I made foon after, which fhewed, that one effential precaution in a point of fuch nicety had been neglected, in not previoufly drying the carbonate. In feyeral trials made in the latter end of the fame month, I 126 EFFECTS of HEAT I found, that chalk expofed to a heat above that of boiling water, but quite fhort of rednefs, loft 0.34 per cent.; and in another fimilar trial, 0.46 per cent. Now, this lofs of weight equals within o.o1 per cent. the lofs in the laft-mentioned ex- periment, that being 0.47; and far furpafles that of the laft but one, which was but 0.074. There is good reafon, there- fore, to believe, that had the carbonate, in thefe two laft ex- periments, been previoufly dried, it would have been found during compreflion to have undergone no lofs. Tue refult of many of the experiments lately mentioned, feems fully to explain the perplexing difcordance between my experiments with porcelain tubes, and thofe made in barrels of iron. With the procelain tubes, I never could fucceed in a _ heat above 28°, or even quite up toit; yet the refults were often excellent. Whereas, the iron-barrels have currently ftood firm in heats of 41° or 51°, and have reached even to 70° or 80° without injury. At the fame time, the refults, even in thofe high heats, were often inferior, in point of fu- fion, to thofe obtained by low heats in porcelain. The rea- fon of this now plainly appears. In the iron-barrels it has always been confidered as neceffary to ufe an air-tube, in con- fequence of which, fome of the carbonic acid has been fe- parated from the earthy bafis by internal calcination : what carbonic acid remained, has been more forcibly attracted, ac- cording to M. BERTHOLLET’s principle, and, of courfe, more eafily comprefled, than when of quantity fufficient to faturate the lime: but, owing to the diminished quantity of the acid, the compound has become leis fufible than in the natural ftate, and, of courfe, has undergone a higher heat with lets effe@. The introduction of water, by furnifhing a reacting force, has produced a ftate of things fimilar to that in the porcelain tubes ; the carbonate fuftaining little or no lofs of weight, MODIFIED ly COMPRESSION. 127 weight, and the compound retaining its fufibility in low heats *. In the early part of 1804, fome experiments were made with barrels, which I wifhed to try, with a view to another feries of experiments. The refults were too interefting to be pafled over; for, though the carbonic acid in them was far from being completely conftrained, they afforded fome of the fineft examples I had obtained, of the fufion of the carbonate, and of its union with filex. On the 13th of February, an experiment was made with pounded oyfter-fhell, in a heat of 33°, without any water be- ing introduced to aflift compreflion. The lofs was apparently of 12 per cent. The fubftance of the fhell had evidently been in vifcid fufion : it was porous, femitranfparent, fhining in fur- face and fracture; in moft parts with the glofs of fufion, in many others with facettes of cryftallization. The little tube had been fet with its muzzle upwards ; over it, as ufual, lay a fragment of porcelain, and on that a round mafs. of chalk. At the contact of the porcelain and the chalk, they had run together, and the’ chalk had been evidently in a very foft ftate ; for, refting with its weight on the porcelain, this laft had been prefled mto the fubftance of the chalk, deeper than its own breadth, a rim of chalk beimg vifible without the furface of the porcelain ; juft as when the round end of a knife is preffed upon * The retentive power here afcribed to the procelain tubes, feems not to accord with what was formerly mentioned, of the carbonic acid having been driven through the fubftance of the tube. But the lofs by this means has probably been fo fmall, that the native properties of the carbonate have not been fenfibly changed. ' Or, perhaps, this penetrability may not be fo univerfal as I have been induced to think, by having met with it in all the cafes which I tried. In this doubt, I ftrenuoufly recommend a further examination of this fubjec& to gentlemen who have eafy accefs to fuch procelains as that of Drefden or of Seve. i 128 EFFECTS of HEAT upon a piece of foft butter. The carbonate had fpread very much on the infide of the tube, and had rifen round its lip, as fome falts rife from their folution in water. In this manner, a {mall quantity of the carbonate had reached the outer tube, and had adhered to it. The black colour frequently mention- ed as accompanying the union of the carbonates with the porcelain, is here very remarkable. On the 26th of February, I made an experiment, in which the carbonate was not weighed, and no foreign fubftance was introduced to aflift the compreflion. The temperature was 46°. The pyrometer had been affected by the contact of a piece of chalk, with which it had united ; and fome of the carbonate muft have penetrated the fubftance of the py- rometer, fince this laft had vifibly yielded to preflure, as ap- peared by a {welling near the contact. I obferved in thefe ex- periments, that the carbonate had a powerful action on the tubes of Cornifh clay, more than on the pounded filex. Per- haps it has a peculiar affinity for argil, and this may lead to important confequences. The chalk had vifibly firft fhrunk upon itfelf, fo as to be detached from the fides, and had then begun to run -by fucceffive portions, fo as ftill to leave a pil- lar in the middle, very irregularly worn away ; indicating a fucceflive liquefaction, like that of ice, not the nei of a mafs foftening all at once. Ow the 28th of February, I made an medina with oyfter-fhell unweighed, finely ground, and pafled through the clofeft fieves. The pyrometer gave 40°. The piece of chalk below it had been fo foft, as to fink to the depth of half an inch into the mouth of the iron air-tube, taking its impreffion completely. A fimall part of this lump was contaminated with iron, but the reft was ina fme ftate. The tube had a rent in it, through which the carbonate, united with the mat- ter of the tube, had flowed in two or three places. The fhell MODIFIED ty COMPRESSION. 129 fhell had fhrank upon itfelf, fo as to ftand detached from the fides, and bore very ftrong marks of fufion. The exter- nal furface was quite fmooth, and fhining like an enamel. The internal part confifted of a mixture of large bubbles and folid parts: the infide of the bubbles had a luftre much fuperior to that of the outfide, and equal to that of glafs. _ The general mafs was femitranfparent ; but {mall parts were vifible by the lens, which were completely tranfparent and colour- lefs. In feveral places this fmooth furface had cryftallized, fo as to prefent brilliant facettes, fteadily fhining in certain afpects.. | Lobferved one of thefe facettes on the infide of an -air-bubble, in which it interrupted the fpherical form as if the little {phere had been preffed inwards at that fpot, by the contact of a plane furface. In fome chalk near the mouth of the large'tube, which lay upon a ftratum of filex, another very anterefting circumftance occurred. Connected with its lower ‘end, a fubftance'was vifible, which had undoubtedly refulted from the union of the carbonate with the filex. This fubftance was white and femitranfparent, and bore the appearance of chalcedony. ‘The mafs of chalk having attached itfelf to that above it, had fhrunk upwards, leaving an. interval between it and the filex, and carrying fome of the compound up with it. From thence this’ laft had been in the act of dropping in a vifcid ftate of fufion, as evidently appeared when the {peci- ‘men was entire; having a ftalactite and ftalagmite corre- {ponding accurately to each.other.. Unluckily I broke off the ftalactite, but the ftalagmite continues entire, in the form of a little cone. This new fubftance effervefced in acid, but not brifkly..: Dbiwatched its entire folution ; a fet of light clouds aemained! undiffolved, and’ probably fome jeliy was, farmed ; for: 1 obferved, that a feries of air-bubbles. remained «in. the form: of the fragment, and moved together without any vifible connection; thus feeming to indicate a chemical. union be- VVor. VI.—P.L ; R veer 130 EFFECTS of HEAT tween the filex and the carbonate. The fhell, fufed in the ex- periment, diflolved entirely im the acid, with violent effervef- cence. In the three laft experiments, and in feveral others made at the fame time, the carbonate had not been weighed; but no water being introduced to aflift the compreflion, it is probable there was much lofs by internal calcination ; and owing doubt- lefs to this, the carbonates have crumbled almoft entirely co duft, while the compounds which they had formed with filex remain entire. On the 13th of March, I made a fimilar experiment, in which, befides fome pounded oyfter-fhell, I introduced a mixture of chalk, with 10 per cent. of filex mtermixed, and ground to- gether in a mortar with water, in a ftate of cream, and then well dried. The contents of the tube when opened, were difcharged with fuch- violence, that the tube was broken to pieces ; but I found a lump of chalk, then in a ftate of white marble, welded to the compound; which laft, in its fraGure, fhewed that irregular black colour, interfperfed roughly through a cryftalline mafs, that belongs to the al- pine marbles, particularly to the kind called at Rome Cipol- line. It was very hard and firm; I think unufually fo. It effer- veiced conftantly to the laft atom, in diluted nitric acid, but much more fluggifhly than the marble made of pure chalk. A cloudinefs appeared pervading all the liquid. When the effervefcence was. over, a feries of bubbles continued during the whole day in the acid, without any difpofition to burtt, or rife to the furface. After ftanding all next day and night, they maintained their ftation; and the folution being ftirred, was found to be entirely agglutinated into a tranfparent jelly, breaking with fharp angles. This experiment affords a direct and pofitive proof of a chemical union having taken place be- tween the carbonate and filex. VI. MODIFIED by COMPRESSION. 131 VI. Experiments made in Platina,—with Spar,—with Shells, —and with - Carbonate of Lime of undoubted purity. Stnce I had the honour of laying before this Society a fhort fketch of the foregoing experiments, on the 30th of Auguft laft (1804), many chemifts and mineralogifts of eminence have favoured me with fome obfervations on the fubject, and have fuggefted doubts which I am anxious to remove. It has been fuggefted, that the fufibility of the carbonates may have been the confequence of a mixture of other fubftances, either ori- ginally exifting in the natural carbonate, or added to it by the contaét of the porcelain tube. ~Wiru regard to the firft of thefe furmifes, I beg leave ta obferve, that, granting this caufe of fufion to have been the real one, a material point, perhaps all that is ftriétly necefla- ry in order to maintain this part of the Huttonian Theory, was neverthelefS gained. For, granting that our carbonates were _ impure, and that their impurity rendered them fufible, {till the fame is true of almoft every natural carbonate ; fo that our experimenats were, in that refpeét, conformable to nature. And as to the other furmife, it has been fhewn, by com- paring together a varied feries of experiments, that the mu- tual ation between the lime and the porcelain was oc- cafioned entirely by the prefence of the carbonic acid, fince, when it was abfent, no aétion of this kind took place. The fufion of our carbonates cannot, therefore, be afcribed to the porcelain, Beinc convinced, however, by many obfervations, that the fufibility of the carbonate did not id upon impurity, R2 I 132 EFFECTS of HEAT I have exerted myfelf to remove, by frefh experiments, every doubt that has arifen on the fubjeét. In order to guard againft natural impurities, I have applied to fuch of my friends as have - turned their attention to chemical analyfis, (a branch of the fcience to which I have never attended,) to furnith me with carbonate of lime of undoubted purity. ‘To obviate the con- tamination arifing from the contact of the porcelain tubes, I de- termined to confine the fubject of experiment in fome fubftance which had no difpofition to unite with the carbonate. I firft tried charcoal, but found it very troublefome, owing to its irregular abforption of water and air. I THEN turned my thoughts to the conftruGion of tubes or cups of platina for that purpofe. Being unable readily to pro- cure proper folid veflels of this fubftance, I made ufe of thin laminated plates, formed into cups. My firft method was, to fold the plate exactly as we do blotting-paper to form a filter’ (Fig. 26.); this produced a cup capable of holding the thin- neft liquid ; and being covered with a lid, formed of a fimilar thin plate, bent at the edges, fo as to overlap confiderably (Fig. 28.), the carbonate it contained was fecured on all fides aa the contact of the porcelain tube within which it was placed. Another conyenient device likewife occurred: I wrapt a piece of the plate of platina round a cylinder, fo as to form a tube, each end of which was clofed by a cover like that juft deferibed (Fig. 27. and 29). (In figure 26. and 27. thefe cups are reprefented upon a large fcale, and in 28. and 29. nearly of their actual fize). This laft conftruction had the advantage of containing eight or nine grains of car- bonate, whereas the other would only hold about a grain and a half. On the other hand, it was not fit to retain a thin liquid; but, in moft cafes, that circumftance was of no confequence; and I forefaw that the carbonates, could not thus MODIFIED b) COMPRESSION. 133 thus efcape without proving the main — under coriliderae tion, namely, their fufion. Tue reft of the apparatus was ccntcieael in’ all refpects as formerly defcribed, the fame precautions being taken to defend the platina veffel as had ‘been ufed with the inner tubes of porcelain. © In this manner I ord made a number of experiments during this {pring and fummer, the refult of which is highly fatisfactory.. They prove, in the firft place, the propriety of the obfervations which led to this trial, by fhewing, that the pute carbonate, thus defended from any contamination, is decidedly more refractory than chalk; fince, in many ex- periments, the chalk has been reduced to a ftate of marble, while the pure carbonate, confined in the platina veflel, has been but very feebly acted upon, having only acquired the in- duration of a fandftone. In other experiments, however, I have been more fuccefs- ful, having obtained fome refults, worthy, I think, of the at- tention of this Society, and which I fhall now fubmit to their infpection: The fpecimens are all inclofed, for fafety, in glafs tubes, and fupported on little ftands of wax, (fig. 31, 32, 33-). The fpecimens have, in general, been removed from the cup or tube of platina in which they were formed, thefe — devices having the advantage of fecuring both the veflel and its contents, by enabling us to unwrap the folds without vio- lence; whereas, in a folid cup or tube, it would have been dif- ficult, after the experiment, to avoid the deftruction either of the yeflel or its contents, or both. Aprit 16, 1805.—An experiment was made with pure calcareous {par from St Gothard, remarkably tranfparent, and having a ftrong double refraction. A temperature of 40° was applied; but owing to fome accident, the weight was not known. The conical cup came out clean and entire, filled not 134 EFFECTS of HEAT not quite to the brim with a yellowifh-grey fubftance, having a fhining furface, with longitudinal ftreaks, as we fometimes fee on glafs. This furface was here and there interrupted by lit- tle white tufts or protuberances, difpofed irregularly. On the ledge of the cup, formed by the ends of the folded plati- na, were feveral globular drops like minute pearls, vifible to the naked eye, the number of which amounted to fixteen. Thefe feem to have been formed by the entire fufion of what carbonate happened to lie on the ledge, or had been entangled amongft the extremities of the folds, drawing itfelf together, and uniting in drops ; as we fee when any fubftance melts un- der the blowpipe. This refult is preferved entire, without de- ranging the tube. I am forry to find that it has begun to fall to decay, in confequence, no doubt, of too great a lofs of its carbonic acid. But the globules do not feem as yet to have fuf- fered any injury. APRIL 25.—The fame fpar was ufed, with two grains of water, and a heat of 33°. I have reafon to fufpe@, how- ever, that, im this and feveral other experiments made at this time, the metal into which the cradle was plunged, on firft introduction into the barrel, had been too hot, fo as to drive off the water. There was a lofs of 6.4 per cent. The refult lay m the cup without any appearance of frothing or fwelling.. The furface was of a clean white, but rough, having in one corner a fpace fhining like glafs. The cup being unwrapt, the fubftance was obtained found and entire : where it had moulded itfelf on the platina, it had a fmall de- gree of luftre, with the irregular femitranfparency of faline marble: when broken, it preferved that character more com- pletely than in any refult hitherto obtamed; the fracture be- ing very irregular and angular, and fhining with facettes in various directions. I much regret that this beautiful fpecimen no MODIFIED ly COMPRESSION. 135 no longer exifts, having crumbled entirely to pieces, notwith- ftanding all the care I took to inclofe it with glafs and wax. Aprit 26. An experiment was made with fome carbonate of lime, purified by my friend Sir George Mackenzie. Two grains of water were introduced, but were loft, I fufpea, as in the laft cafe. The heat applied was 32°. The lofs of weight was 10.6 per cent. Yet, though made but one day after the laft-mentioned fpecimen, it remains as frefh and entire as at firft, and promifes to continue unchanged. The external furface, as feen on removing the lid of the conical cup, was found to fhine all over like glafs, except round the edges, which were fringed with a feries of white and rough {phericles, one fet of which advanced, at one fpot, near to the centre. The fhining furface was compofed of planes, which formed ob- tufe angles together, and had their furface ftriated’; the ftriz bearing every appearance of a cryftalline arrangement. When freed from the cup, as before, the fubftance moulded on the platina was found to have affumed a fine pearly furface. Some large air-bubbles appeared, which had adhered to the. cup, and were laid open by its removal, whofe internal furface had a beautiful Inftre, and was full of ftrie like the outward fur- face. The mafs is remarkable for femitranfparency, as feen particularly where the air-bubbles diminifh its thicknefs: a fmall part of the mafs being broken at one end, fhews an in- ternal faline ftructure. APRIL 29.—A>cup of platina was filled with feveral large pieces of a periwinkle * fhell, the fharp point of the fpiral being made to ftand upright in the cup, (fig. 30.). A heat of 30° was applied, and no water was introduced. The carbonate loft no lefs than 16 per ceut. The thell, particularly | , _ the .* Turbo terebra, Lry.. 136 EFFECTS of HEAT the fharp end of the periwinkle, retained its original fhape in a great meafure, fo as to be quite difcernible ; but the whole was glazed over with a truly vitreous luftre. This glaze co- vered, at one place, a fragment of the fhell which had been ori- ginally loofe, and had welded the two together. All the angles are rounded by this vitrifaction; the {pace between the en-~ tire fhell and the fragment being filled, and the angles of their meeting rounded, with this fhining fubftance. The colour is a pale blue, contrafted, in the fame little glafs, with a natural piece of periwinkle, which is of a reddifh-yel- low... One of the fragments had adhered to the lid, and had been converted into a complete drop, of the fize of a muftard- feed. It is fixed on the wax (at 4), along with the other {pe- cimens of the experiment (fig. 32.). This refult fhews, as yet, no fign of decay, notwithftanding fo great a lofs of weight. Tne laft experiment was repeated on the fame day, and pre- pared in the fame manner, with large fragments of hell, and the point of the periwinkle ftanding up in the cup. A heat of 34° was applied; a lofs took place of 13° per cent. All the original form had difappeared, the carbonate lying in the cup as a com- plete liquid, with a concave furface, which did not fhine, but was ftudded all over with the white {phericles or tufts, like thofe feen in the former refults, without any fpace between them. When detached from the cup, the furface moulded on the platina, was white and pearly, with a flight glofs. The mafs was quite folid ; no veftige whatever appearing, of the original form of the fragments, (fig. 33.).. A fmall piece, bro- ken off near the apex of the cone, fhewed the internal ftruc- ture to be quite faline. In the act of arranging the {fpecimen on its ftand, another piece came off in a new direction, which pre- fented to view the moft perfect cryftalline arrangement : the fhining plane extended acrofs the whole fpecimen, and was more than the tenth of an inch in all directions. This fraaure, likewife, MODIFIED ty COMPRESSION. 137 Yikewife, fhewed the entire internal folidity of the mafs. Un- fortunately, this fpecimen has fuffered much by the fame de- cay to which all of them are fubjec& which have loft any con- fiderable weight. The part next the outward furface alone remains entire. I have never been able to explain, in a fatis- factory manner, this difference of durability ; the laft-men- tioned refult having loft more in ass an to its weight than this. AxsouT the beginning of June,I nigelved from Mr Hwreii ETT fome pure carbonate of lime, which he was fo good as to pre- pare, witha view to my experiments ; and I have been conftant- ly employed with it till within thefe few days. My firft experiments with this fubftance were peculiarly un- fortunate, and it feemed to be lefs eafily acted upon than any fabftance of the kind I had tried. Its extreme purity, no doubt, contributed much to this, though another circumftance had likewife had fome effet. The powder, owing toa cryftallization which had taken place on its precipitation, was very coarfe, and little fufceptible of clofe ramming ; the particles, therefore, had lefs advantage than whema fine powder is ufed, in acting up- on each other, and I did not choofe to run any rifk of contami- nation, by reducing the fubftance to a finer powder. Whatever be the caufe, it is certain, that in many experiments in which the chalk was changed to marble, this ‘fubftance remained ‘in a loofe and brittle ftate, though confifting generally of clearand . fhining particles. Tat laft, however, fucceeded in obtaining fome very good refults with this carbonate. --In‘an experiment made with it on the 18th of June, in a {trong heat, I ebtained a very firm’ mafs With a Taline fracture, moulded in féveral places on the platina, which was now ufed in the cylindrical form. On the 23d; ina fimilar experiment, the barrel failed, and the fubject of experiment was ‘found in an entire ftate of froth, proving its former fluidity. ‘Wor. VI.—P.I. S On 138 EFFECTS of HEAT On the 25th, in a fimilar experiment, a heat of 64° was ap- plied, without any water within the barrel... The platina. tube; (having been contaminated in a former experiment with fome fufible metal), melted, and the carbonate retaining its cylin- drical fhape, had fallen through it, fo as to touch the piece of porcelain which had been placed next to the platina tube... At the point of contaét, the two had run together, as a hot iron runs when touched by fulphur. The carbonate itfelf was very tranfparent, refembling a piece of {now in the act of melting. . On the 26th of June, I made an experiment with this car- bonate, which afforded a beautiful refult. One grain of wa- ter was introduced with great care; yet there was a lofs, of 6.5 per cent., and the refult has fallen to decay. The pyro- meter cael 43°. On the outfide of the platina cylinder, and on one of the lids, were feen a fet of globules, like pearls, as once before. obtained, denoting perfect fufion. When the upper lid was removed, the fubftance was found to have funk almoft out of fight, and had aflumed a form not eafily defcri- bed. (1 have endeavoured to reprefent it in fig, 31. by anideal fection. of the platina-tube and its contents, made through the axis of the cylinder)... The powder, firft fhrinking upon itfelf in the act of agglutination, had formed a cylindrical rod,.a remnant of which (4c) ftood up in the middle of the tube. By the continued action of heat, the fummit of the rod (at a) had been ,rounded,in fufion, and the mafs being now fof- tened, had funk by its weight, and fpread below, fo as to mould itfelf in the tube, and fill its lower part completely (dfge). At the fame time, the vifcid fluid adhering to the fides (at e atid d), while the middle part was finking, had been in part left behind, and in part drawn gut into, a thin but tapering fhape, united by a curved furface (at 4 and ¢) to, the middle rod. When the platina tube was unwrapt, the thin edges (at e¢ and d) were preferyed all round, and in a ftate MODIFIED ly COMPRESSION. 139 ftate of beautiful femitranfparency. (I have attempted to re- prefent the entire fpecimen, as it ftood.on its cone of wax, in fig. 34.). The carbonate, where moulded on the platina, had a clean pearly whitenefs, with a faline appearance externally, and in the fun, fhone with facettes. Its furface was interrupt- ted by a few fcattered air-bubbles, which had lain againft the tube. The intervening fubftance was unufually compact and hard under the knife. The whole furface (eb aed, fig. 31.), and the infide of the air-bubbles, had a vitreous luftre. Thus; every thing denoted a ftate of ‘vifcid. giver like that: of hos ne pant laft experiments feet: to obviate every ars that re- mained with refpect to the fufibility of the pureft carbonate, without the affiftance of any foreign fubftance. VIL. Meafurement of the Force required to conftrain the Carbonic Acid.—Ap- © paratus with the Muzzle of the Barrel upwards, and the weight acting «by a long Lever.—Apparatus with the. Muxzle downwards. Appa- ratus with Weight acting direétly on the barrel.—Comparifon of various refults. In order to determine, within certain limits at leaft, What force had been exerted in the foregoing experiments, and what was neceffary to enfure their fuccefs, I made a number of ex- periments, in a mode nearly allied to that followed by Count Rumrorp, in meafuring the explofive force of gunpowder. I secan to ufe the following fimple apparatus in ‘June 1803. I took one of the barrels, made as above defcribed, for the purpofe of compreffion, having a bore of 0.75 of an 72 inch, 140 ’ EFFECTS of HEAT inch *, and drefled its muzzle to a fharp edge. To this barrel: was firmly {crewed a collar of iron (aa, fig. 36.) placed at a diftance of about three inches from the muzzle, having two ftrong bars (64) projecting at right angles to the barrel, and dreffed fquare. The barrel, thus prepared, was introduced, with its breech downwards, into the vertical muffle (fig. 35.) 5 its length being fo adjufted, that its breech fhould be placed in the ftrongeft heat ; the two projecting bars above defcribed, refting on two other bars (cc, fig. 35.) laid upon the furnace to receive them ; one upon each fide of the muffle. Into the barrel, fo placed, was introduced a cradle, containing carbo- nate, with all the arrangements formerly mentioned’; the rod connected with it being of fuch length, as_juft to lie within the: muzzle of the barrel. The liquid metal was then poured in till it filled the barrel, and ftood at the muzzle with a convex fur- face; a cylinder of iron, of about ah inch in diameter, and half an inch thick, was laid on the muzzle (fig. 35. and 37.), and to: it a comprefling weight was inftantly applied. This was firft done by the preffure of a bar of iron (de, fig. 35.), three-feet in: length, introduced loofely into a hole (¢), made for the purpafe in the wall againft which the furnace ftood ; the diftance between. this hole and the barrel being one foot. A weight was then fuf- pended at the extremity of the bar (e), and thus a compreffing force was applied, equal to three times that weight. In the courfe of practice, a cylinder of lead. was fubftituted for that of iron, and a piece of leather was placed between it and the muzzle of the barrel, which laft being drefled to a pretty fharp, edge, made an impreflion in the lead: to affift, this: effect, one. fmart blow of a hammer was ftruck upon the bar, direly. over the barrel, as foon as the weight had been hung on. Ir. * This was the fize of barrel ufed in all the following experiments, where the. fa& is not otherwife expreffed. MODIFIED ly COMPRESSION. I4t Ir was effential, in this mode of operation, that the whole. of the metal fhould continue in a liquid ftate during the action: of heat; but when I was fatisfied as to its intenfity and dura- tion, I congealed the metal, either by extinguifhing the furnace entirely, or by pouring water on the barrel. As foon as the heat began to act, drops of metal were feen to force themfelves- between the barrel and the leather, following each other with. more or lefs rapidity, according to. circumftances. In fome. experiments, there was little exudation; but few of them were entirely free from it. LTofave the metal thus extruded, I placed.a black-lead crucible, having its bottom perforated, round the barrel, and. luted clofe to. it, (fig. 37.); fome fand. being laid in this crucible, the metal was. collected on its fur-- face. On fome occafions, a. found of ebullition was heard. during the action of heat; but, this was.a certain fign of. fail-- ure. rt we THE refults. of the moft important of thefe experiments,. have been reduced to a common ftandard in the fecond table: placed in the Appendix ; to which reference is.made by the. following numbers. 7 No. 1.—Own the 16th of June'1803; I made an experiment. with thefe arrangements. I had tried to ufe a weight of 30lb.. producing a preflure of 90 lb., but I found this not fufficient. I then hung on.a weight of 1 cwt., or 112.1b.; by. which a com-. — prefling force was applied of : 3.cwt. or, 3361b. Very little: metal was feen to efcape, and no found of ebullition was heard. ‘Fhe chalk in. the body of the large tube was. reduced to quick- lime ; but what lay in the inner tube was pretty firm, and ef- fervefced to thelaft. One or two facettes, of good appearance, were likewife found. The contents of the {mall tube had loft. but 2.6 per cent.; but there was a fmall vifible intrufion of me- tal, and the refult, by its appearance, indicated a.greater lofs. L.confidered. this, however, as one point gained ; that being the 142 EFFECTS of HEAT firft tolerable compreflion accomplithed by a determinate force. The pyrometer indicated 22°. Tuis experiment wes repeated the tito day, when a ftill fmaller quantity of metal efcaped at the muzzle ; but the bar- rel had given way below, in the manner of thofe that have yielded for want of fufficient air. Even this refult was fatis- factory, by fhewing that a mechanical power, capable of for- cing fome of the barrels, could now be commanded. The car- bonate in the little tube had loft 20 per cent.; but part ont was in a hard and firm ftate, effervefcing to the laft. No. 2.—On the 21ft June, I made an experiment with ano- ther barrel, with the fame circumftances. I had left an empty {pace in the large tube, and had. intended to introduce its muzzle downwards, meaning that {pace to.anfwer as an air- tube ; but it was inverted by miftake, and the tube entering with its muzzle upwards, the empty {pace had of courfe filled with metal, and thus the experiment was made without any included air. There was no pyrometer ufed; but the heat was guefled to be about 25° where the fubject of experiment lay. The barrel, when opened, was found full of metal, and the cradle being laid flat.on the table, a confiderable quantity of metal ran from it, which had undoubtedly been lodged in the vacuity of the large tube. When cold, I found that vacuity {till empty, with a plating of metal. The tube was very clean to appearance, and, when fhaken, jts contents were heard to rattle. Above the littie tube, and the cylinder of chalk, I had put fome borax and fand, with a little pure borax in the middle, and chalk over it. The metal had not penetrated beyond the borax and fand,. by a good fortune peculiar to this experiment; the intrufion of metal in this mode of execution, being extremely troublefome. The button of chalk, was found in a ftate of clean white car- bonate, and pretty hard, but without tranfparency. The little tube | MODIFIED ly COMPRESSION. 143 tube was perfectly clean. Its weight with its contents, feem- ed to have: fuffered no’ change: from what it had been when firft imtroduced. Attending, however, to the balance with ferupulous nicety, a {mall preponderance did appear on the fide of the weight. This was done away by the addition of the hundredth of a grain to the fcale in which the carbo- nate lay, and an addition of another hundredth produced in it a decided preponderance. Perhaps, had the tube, before its in- troduction, been examined with the fame care, as great a diffe- rence might have been detected ; and it feems as if there had. been no lofs, at leaft not more than one hundredth of a grain, which on 10.95 grains, amounts to 0.0912, fay 0.1 per cent. The carbonate was loofe in the little tube, and. fell out by fha- king. It had a yellow colour, and compact appearance, with: a ftony hardnefs under the knife, and a ftony fraGure; but with very flight facettes, and little or no tranfparency.. In fome parts of the {pecimen, a whitifh colour feemed to indicate partial . ‘calcmation. _ On examining the fracture, I perceived, with the - magnifier, a {mall globule of metal, not vifible to the naked. eye, quite infulated and fingle. Poffibly the fubftance may have contained others of the fame fort, which may have compenfated. for a fmall lofs, but there could-not be many fuch, from the general clean appearance of the whole.. In the fracture, I faw here and.there {mall round holes, feeming, though imperfect-. ly, to. dicate a beginning of ebullition. I mabe a number of experiments in the fame manner, that is to fay, with the muzzle of the barrel upwards, in fome of which I obtained- very fatisfatory refults.; but it was. only by chance that the fubftance efcaped. the contamina-- tion of the fufible metal; which induced me to'think of ano-. ther mode of applying the comprefling weight with the muzzle of the barrel downwards, by which I expected to re-. peat with a determinate weight, all gi experiments formerly. made T44 EFFECTS of HEAT ‘made in barrels clofed by congealed metal ; and that, by ma- king ufe of an air-tube, the air, rifing to the breech, would fe- cure the contents of the tube from any contamination. In this view, the barrel. was introduced from below into the muffle with its breech upwards, and retained in that pofition by means of a hook fixed to the furnace, till the collar was made to prefs up againft the grate, by an iron lever, loaded with a weight, and refting on a fupport placed in front. In fome experiments made in this way, the refult was obtained very clean, as had been expected ; but the force had been too feeble, and when it was increafed, the furnace yielded up- wards by the mechanical ftrain. I rounp it therefore neceflary to ufe a frame of iron, (as in fig. 38.3 the frame being reprefented feparately in fig. 39.), by which the brick-work was-relieved from the mechanical ftrain. This frame confifted of two bars (a and fe, figs. 38. and 39.), fixed into the wall, (at aand f,) pafling horizontally under the furnace, one on each fide of the muffle, turning downwards at the front, (in band e), and meeting at the ground, with a flat bar (¢d) uniting the whole. In this manner, a kind of ftirrup (dc de) was formed in front of the furnace, upon the crofs bar (cd) of which a block of wood (4 4, fig. 38.), was placed, fupporting an edge of iron, upon which the lever refted; the working end of the lever (g) ating upwards. A ftrain was exerted, by means of the barrel and its collar, againft the horizontal bars, (@ 4 and f ¢), which was effectually refifted by the wall (at a and f) at one end of thefe bars, and by the upright bars (¢ J and d ¢) at the other end. In this manner the whole ftrain was fuftained, by the frame, and the furnace ftood without injury. Tue iron bar, at its working end, was formed into the fhape of a cup, (at g), and half filled with lead, the fmooth furface of which, was applied to the muzzle of the barrel. The lever, too; svas lengthened, by joining to the bar of iron, a beam of wood; making MODIFIED ly COMPRESSION. 145 making the whole ten feet in length. In this manner, a pref- fure upwards was applied to the barrel, equal to the weight of TO cwt. In the former method, in which the barrel ftood with its muzzle upwards, the weight was applied while the metal was liquid. In this cafe, it was neceflary to let it previoufly con- geal, otherwife the contents would have run out in placing the barrel in the muffle, and to allow the liquefaction eflential to thefe trials, te be produced by the propagation of heat from the muffle downwards. This method required, therefore, in every cafe, the ufe of an air-tube; for without it, the heat acting upon the breech, while the metal at the muzzle was ftill cold, would infallibly have deftroyed the barrel. A great number of thefe. experiments -failed, with very confiderable wafte of the fufible metal, which, on thefe occafions was nearly allioft. But a few of them fucceeded, and afforded very fatis- factory refults, which I fhall now mention. In November 1803, fome good experiments were made in this way, all with a bore of 0.75, and a preffure of 10 cwt. No. 3.—Ow the 19th, a good limeftone was obtained in an experiment made ina a of 21°, with a lofs of only I.I per cent. No. 4.—On the 22d, in a fimilar experiment, there was little exudation by the muzzle. The pyrometer gave 31°. The carbonate was in a porous, and almoft frothy ftate. No. 5.—In a fecond experiment, made the fame day, the heat rofe to 37° or 41°. The fubftance bore ftrong marks of fufion, the upper part having fpread on the little tube: the whole was very much fhrunk, and run againft one fide. The mafs fparkling and white, and.in a very good ftate. No.6.—On the 25th,an experiment was made with chalk,and fome fragments of {nail fhell, with about half a grain of water. ‘The heat had rifen to near 51° or 49°. The barrel had been Voi, VI.—P. I. F. held 146 EFFECTS of HEAT held tight by the beam, but was rent and a little fwelled at the breech. The rent was wide, and fuch as has always appeared in the ftrongeft barrels when they failed. The car- bonate was quite calcined, it had boiled over the little tube, and was entirely in a frothy ftate, with large and diftin@ly rounded air-holes. The fragments of fhell which had occupied the upper part of the little tube, had loft every trace of their original fhape in the act of ebullition and fufion. No. 7.—Own the 26th a fimilar experiment, was made, in which the barrel was thrown open, in fpite of this powerful comprefling force, with a report like that of a gun, (as I was told, not having been prefent), and the bar was found in a ftate of ftrong vibration. The carbonate was calcined, and fomewhat frothy, the heart of one piece of chalk ufed was in a ftate of faline marble. Ir now occurred to me to work with a comprefling force; and no air-tube, trufting, as happened accidentally in one cafe, that the expanfion of the liquid would clear itfelf by gentle exu- dation, without injury to the carbonate. In this mode, it was neceflary, for reafons lately ftated, to place the muzzle upwards. Various trials made thus, at this time, afforded no remarkable refults. But I refumed the method, with the fol- lowing alteration in the application of the weight, on the 27th of April 1804. I concEIvED that fome inconvenience might arife from the mode of employing the weight in the former experiments. In them it had been applied at the end of the bar, and its effect propagated along it, fo as to prefs againft the barrel at its other extremity. It occurred to me, that the propagation of motion in this way, requiring fome fenfible time, a confi- derable quantity of carbonic acid might efcape by a fudden eruption, before that propagation had taken effect. I there- fore thought, that more effectual work might be done, by placing a MODIFIED ly COMPRESSION. 147 placing a heavy mafs, (fig. 40.), fo as to act direfly and fimply upon the muzzle of the barrel; this mafs being guided and commanded by means of a powerful lever, (a4). For this purpofe, I procured an iron roller, weighing 3.cwt. 7 lb., and fufpended it over the furnace, to the end of a beam of wood, refting on a fupport near the furnace, with a long arm guided by a rope (¢¢) and pulley (d), by wach the weight could be raifed or let down at plehfure. Wiru this apparatus I made fome tolerable experiments ; but I found the weight too light to afford certain and fteady refults of the beft quality. I therefore procured at the foundry a large mafs of iron (f), intended, I believe, for driving piles, and which, after allowing for the counterpoife of the beam, gave a direct preflure of 8.1 cwt.; and I could, at pleafure, diminith the comprefling force, by placing a bucket (¢) at the extremity of the lever, into which I introduced weights, whofe effeé& on the ultimate great mafs, was known by trial. Many _bar- rels failed in thefe trials: at laft, I obtained one of {mall bore, inch 0.54, which gaye two good refults on the 22d of June E8O4sihp de No. 8. Dror c to afcertain the leaft comprefling force by which the carbonate could be effectually conftrained in melt- ing heats, I firft obferved every thing ftanding firm in a heat of above 20°; I then gyadually threw weights into the bucket, till the.comprefling force was reduced, to 2 cwt. Till then, things continued fteady ; but, on the preflure being ftill further diminifhed, metal began to ooze out at the muzzle, with in- creafing rapidity. When the preflure was reduced to 14 cwt. air rufhed out with a hifling noife. I then {topped the experi- ment, by pouring water on the barrel. The piece of chalk ‘had loft 12 per cent. It was white and foft on the outfide, but firm and good in the heart. T2 rm § ONO» Os 148 EFFECTS of HEAT No. 9.—AN experiment was made with chalk, in a little tube; to this, one grain ef water was added, I had intended to work with 4 cwt. only ; but the barrel was no fooner placed, than an exudation of metal began at the muzzle, owing, doubt- lefS, to the elafticity of the water. I immediately increafed the preflure to 8.1 cwt. by removing the weight from the bucket, when the exudation inftantly ceafed. I continued the fire for three quarters of an hour, during which time no exu- dation happened; then all came out remarkably clean, with {carcely any contamination of metal. The lofs amounted to 2.58 per cent. The fubftance was tolerably indurated, but had not acquired the character of a complete ftone. In thefe two laft experiments, the bore being fmall, a pyro- meter could not be admitted. On the 5th of July 1804, I made three very fatisfactory ex- periments of this kind, in a barrel with the large bore of 0.75 of.an inch. No. 10.—was made with a comprefling force of only 3 cwt. A fmall eruption at the muzzle being obferved, water was thrown on the barrel : the pyrometer gave 21° : the chalk was in a firm ftate of limeftone. No. 11.—witnH 4 cwt. The barrel ftood without any erup- tion or exudation, till the heat rofe to 25°. There was a lofs of 3.6 per cent.: the refult was fuperior, in hardnefs and tranf- parency, to the laft, having fomewhat of a faline fracture. No. 12.—wira 5 cwt. The refult, with a lofs of 2.4 per cent., was of a quality fuperior to any of thofe lately obtained. THESE experiments appear to anfwer the end propofed, of af- certaining the leaft preflure, and loweft heat, in which lime- ftone can be formed. The refults, with various barrels of different fizes, agree tolerably, and tend to confirmeach other. The table fhews, when we compare numbers 1, 2, 8, Io, 11, 12, That a preffure of 52 atmofpheres, or 1700 feet of fea, is ' capable MODIFIED yy COMPRESSION. 149 capable of forming a limeftone in a proper heat : That under 86 atmofpheres, anfwering nearly to 3000 feet, or about half a mile, a complete marble may be formed: and laftly, That with a preflure of 173 atmofpheres, or 5700 feet, that is, little more than one mile of fea, the carbonate of lime is made to undergo complete fufion, and to act powerfully on other earths. rete Vill. Formation of Coal.— Accidental occurrence which led me to undertake thefe Experiments.—Refults extracted from a former publication. —Explana- tion of fome difficulties that have been fuggefted.—The Fibres of Wood in. Some cafes obliterated, and in fome preferved under comprefion.—Re- Semblance which thefe Refults bear to a feries of Natural Subftances de- Jeribed by Mr Harcuerr.—Thefe refults feem to throw light om the biftory of Surturbrand. As I intend, on: fome future occafion, to refume my ex- periments with inflammable fubftances, which I look upon as. far from complete, I fhall add but a few obfervations to what I have already laid before this Society, in the fketch I had the honour to read. inthis place on the 30th of Auguft laft. Tue following incidental occurrence led me to enter upon this fubject rather prematurely, fince I had determined firft to fatisfy myfelf with regard to the carbonate of lime. (OBSERVING, in many of the laft-mentioned clafs of “experi- ments, that the elaftic matters made their efcape between the muzzle of the barrel and the cylinder of lead, I was in the ha- bit, as mentioned above, of placing a piece of leather between. the lead and the barrel; in which pofition, the heat to which the leather was expofed, was neceflarily below that of melting lead. 150 EFFECTS of HEAT lead. In an experiment, made on the 28th November 1803, in order to afcertain the power of the machinery, and the quantity of metal driven out by the expanfion of the liquid, there being nothing in the barrel but metal, I obferved, as foon as the com- prefling apparatus was removed, (which on this occafion was done while the lower part of the barrel was at its full heat, and the barrel ftanding brim full of liquid metal,) that all the leather which lay on the outfide of the circular muzzle of the barrel, remained, being only a little browned and crumpled by the heat to which it had been expofed. What leather lay within the circle, had difappeared; and, on the furface of the liquid metal, which ftood up to the lip of the barrel, I faw large drops, of a fhining black liquid, which, on cooling, fixed into a crifp black fubftance, with a fhining fracture, exactly like pitch or pure coal. It burned, though not with flame. While hot, it finelt decidedly of volatile alkali. The important circumftance here, is the different manner in which the heat has aed on the leather, without and within the rim of the barrel. The only difference confifted in compreffion, to which, therefore, the dif- ference of effeét muft be afcribed: by its force, the volatile matter of the leather which efcaped from the outward parts, had within the rim, been conftrained to remain united to the reft of the compofition, upon which it had aéted as a flux, and the whole together had entered into a liquid ftate, in a very low heat. -Had the preflure been continued till all was cool, thefe fubftances muft have been retained, pro- ducing a real coal. On the 24th April 1803, a piece of leather ufed in a fimilar manner, (the comprefling force being continued, however, till all was cold,) was changed to a fubftance like glue, owing doubtlefs to compreflion, in a heat under that of melting lead. Turse obfervations led me to make a feries of experi- ments with animal and vegetable fubftances, and with coal; the MODIFIED by COMPRESSION. 151 the refult of which I have already laid before the Society. I fhall now repeat that communication, as printed in Nicnot- son’s Fournal for October laft-(1804). “ I wave likewife made fome experiments with coal, treated in the fame manner as the carbonate of lime: but I have found. it much lefs tractable; for the bitumen, when heat is applied to it, tends to efcape by its fimple elafticity, whereas the car- bonic acid in marble, is in part retained by the chemical force _ of quicklime. I fucceeded, however, in conftraining the bitu- minous matter of the coal, to a certain degree, in red heats, fo. as to bring the fubftance into a complete fufion, and to retain its faculty of burning with flame. But, I could not accomplifh this in heats capable of agglutinating the carbonate; for L have found, where I rammed them {ucceflively into the fame tube, and where the veflel has withftood the expanfive force, that the carbonate has been agglutinated into a good limeftone, but that the coal has loft about half its weight, together with its power of giving flame when burnt, remaining in a very compact ftate, with a fhining fracture. Although this experi- ment’ has not afforded the defired refult, it anfwers another: purpofe admirably well. It is known, that where a bed of coal. is crofled by a dike of whinftone, the coal is found in a pecu- liar ftate in the immediate neighbourhood of the whin: the fubftance in fuch places being incapable of giving flame, it is diftinguithed by the name of blind coal. Dr Hurrow has ex- plained this fact, by fuppofing that the bituminous matter of the coal, has been driven by the local heat of whin, into places. of lefs intenfity, where it would probably be retained by diftil- lation. Yet the whole muft have been carried on under the action of a preffure capable of conftraining the carbonic acid. of the calcareous fpar, which occurs frequently in fuch rocks. In the laft-mentioned experiment, we haye a. perfeét reprefen- tation. 152 EFFECTS of HEAT tation of the natural fact; fince the coal has loft its petroleum, while the chalk in conta& with it has retained its carbonic acid. “ JT HAVE made fonie experiments of the fame kind, with ve- getable and animal fubftances. I found their volatility much greater than that of coal, and I was compelled, with them, to work in heats below rednefs; for, even in the loweft red-heat, they were apt to deftroy the apparatus. The animal fubftance I commonly ufed was horn, and the vegetable, faw-duft of fir. The horn was incomparably the moft fufible and volatile of the two. Ina very flight heat, it was converted into a yellow red fubftance, like oil, which penetrated the clay tubes through and through. In thefe experiments, I therefore made ufe of tubes of glafs. It was only after a confiderable portion of the fubftance had been feparated from the mats, that the remainder aflumed the clear black peculiar to coal. In this way I ob- tained coal, both from faw-duft and from horn, which yielded a bright flame in burning. . “ Tue mixture of the two produced a fubftance having ex- a@tly the fmell of foot or coal-tar. Iam therefore ftrongly in- clined to believe, that animal fubftance, as well as vegetable, has contributed towards the formation of our bituminous ftrata. This feems to confirm an opinion, advanced by Mr Keir, which has been mentioned to me fince I made this ex» periment. I conceive, that the coal which now remains in the world, is but a fmall portion of the organic matter originally depofited : the moft volatile parts have been driven off by the action of heat, before the temperature had rifen high enough to bring the furrounding fubftance into fufion, fo as to confine the elaftic fluids, and fubject them to compreflion. “ Tw feveral of thefe experiments, I found that, when the pref- {ure was not great, when equal, for inftance, only to 80 at- mofpheres, that the horn employed was diffipated entirely, the glafs ee MODIFIED ly COMPRESSION. 153 glafs tube which had contained it being left almoft clean: yet undoubtedly, if expofed to heat without compreflion, and pro- tected from the contact of the atmofphere, the horn would leave a cinder or coak behind it, of matter wholly devoid of volatility. Here, then, it would feem as if the moderate preflure, by keeping the elements of the fubftance together, had promoted the general volatility, without being ftrong enough to refift that expanfive force, and thus, that the whole had efcaped. This refult, which I fhould certainly not have forefeen in theory, may perhaps, account for the abfence of coal in fituations where its prefence might be expected on prin- ciples of general analogy.’” Since this publication, a very natural queftion has been put to me. When the inflammable fubftance has loft weight, or when the whole has been diflipated, in thefe experiments, what has become of the matter thus driven off? I must own, that to anfwer this queftion with perfect con- fidence, more experiments are required. But, in the courfe of practice, two circumftances have occurred as likely, in moft ca- fes, to have occafioned the lofs alluded to. I found in thefe expe- riments, particularly with horn, that the chalk, both in’ powder and in lump, which was ufed to fill vacuities in the tubes, and to fix them in the cradle, was ftrongly impregnated with an oily or bituminous matter, giving to the fubftance the qua- lities of a ftinkftone. I conceive, that the moft volatile part of the horn has been conveyed to the chalk, partly ina ftate of vapour, and partly by boiling over the lips of the glafs tube; the whole having been evidently in a ftate of very thin fluidity. Having, in fome cafes, found the tube, which had been intro- duced full of horn, entirely empty after the experiment, I was induced, as above ftated, to conceive, that, under preflure, it had acquired a greater general volatility than it had in free- Vou. VI.—P. I. U dom ; E54 ; EFFECTS of HEAT . dom; and I find that, in the open fire, horn yields a charcoal equal to 20 per cent. of the original weight. But more expe- ximents muft be made on this fubjeé. Anoruer caufe of the lofs of weight, lay undoubtedly in the excefs of heat employed in moft of them, to remove the cradle from the barrel. With inflammable fubftances, no air-tube was ufed, and the heats being low, the air lodged in inter- ftices had been fufficient to fecure the barrels from deftruction, by the expanfion of the liquid metal. In this view, likewife, I often ufed lead, whofe expanfion in fuch low heats, I expected to be lefs than that of the fufible metal. And the lead requir- ing to melt it, a heat very near to that of rednefs, the fubject of experiment was thus, on removing the cradle, expofed in freedom to a temperature which was comparatively high. But, obferving that a great lofs was thus occafioned, I returned to the ufe of the fufible metal, together with my former method of melting it, by plunging the barrel, when removed from the furnace, into a folution of muriate of lime, by which it could only receive a heat of 250° of FAHRENHEIT. Tue effect was remarkable, in the few experiments tried in this way. The horn did not, as in the other experiments, change to a hard black fubftance, but acquired a femifluid and vifcid confiftency, with a yellow-red colour, and a very offen- five fmell. This fhews, that the fubftances which here occa- fioned both the colour and fmell of the refults, had been dri- ven off in the other experiments, by the too great heat applied to the fubftance, when free from compreffion. I rounp that the’ organization of animal fubftance was en- tirely obliterated by a flight action of heat, but that a ftronger heat was required to perform the entire fufion of vegetable. matter. This, however, was accomplifhed; and in feveral experiments, pieces of wood were changed to a jet-black and inflammable fubftance, generally very porous, in which no trace MODIFIED ty COMPRESSION. 155 trace could be difcovered of the original organization. In others, the vegetable fibres were ftill vifible, and are forced afun- der by large and fhining air-bubbles. » Since the publication of the fketch of my experiments, I have had the pleafure to read Mr Hatcuerr’s very interefting account of various natural fubftances, nearly allied to coal ; and I could not help being ftruck with the refemblance which my refults bear to them, through all their varieties, as brought into view by that able chemift; that refemblance affording a prefumption, that the changes which, with true fcientific mo- defty; he afcribes to an unknown caufe, may have refulted from various heats acting under preflure of various force. The fubftance to which he has given the name of Retina/phaltum, feems to agree very nearly with what I have obtained from animal fubftance, when the barrel was opened by means of low heat. And the fpecimen of wood entering into fufion, but ftill retaining the form of its fibres, feems very fimilar to the in- termediate fubftance of Bovey-coal and Surturbrand, which Mr Hatcuetr has aflimilated to each other. It is well known, that the furturbrand of Iceland, confifts of the ftems of large - trees, flattened to thin plates, by fome operation of nature hi- therto unexplained. But the laft-mentioned experiment feems to afford a plaufible folution of this puzzling phenomenon. In all parts of the globe, we find proofs of flips, and various relative motions, having taken place amongft great mafles of rock, whilft they were foft in a certain degree, and which have left unequivocal traces behind them, both in the derange- ment of the beds of ftrata, and in a fmooth and fhining fur- face, called flickenfide, produced by the direct fri@tion of one - mafs on another. During the action of fubterranean heat, were a fingle ftratum to occur, containing trees intermixed with animal fubftances, fhell- fith, &c. thefe trees would be reduced, to a foft and unctuous ftate, fimilar to that of the piece of wood (ae ies in 156 EFFECTS of HEAT in the laft-mentioned experiment, whilft the fubftance of the contiguous ftrata retained a confiderable degree of firmnefs. In this ftate of things, the ftratum juft mentioned, would very na- turally become the fcene of a flip, occafioned by the unequal preflure of the furrounding maffes. By fuch a fliding motion, accompanied by great compreflion, a tree would be flattened, as any fubftance is ground in a mortar, by the combination of a lateral and direé& force. At the fame time, the fhells along with the trees, would be flattened, like thofe defcribed by BErc- MAN; while thofe of the fame fpecies in the neighbouring limeftone-rock, being protected by its inferior fufibility, would retain their natural fhape. TX. Application of the foregoing refults to Geology.—The fire employed in the: Huttonian Theory is a modification of that of the Volcanoes.—This mo- dification muft take place in a lava previous to its eruption.—An Inter- nal Lava is capable of melting Limeftone.—The effects of Volcanic Fire on fubftances in a fubterranean and fubmarine fituation, are the fame as thofe afcribed to Fire in the Huttonian Theory.—Our Strata were once in a fimilar fituation, and then underwent the action of fire.—All the conditions of the Huttonian Theory being thus combined, the formation of all Rocks may be accounted for in a fatisfactory manner.—Concli- Sion. Havine inveftigated, by means of the foregoing experi- ments, fome of the chemical fuppofitions. involved in the Hut- tonian Theory, and having endeavoured to affign a determi- nate limit to the power of the agents employed ; I fhall now apply thefe refults to Geology, and inquire how far the events fuppofed af MODIFIED ly COMPRESSION. 157- fuppofed anciently to have taken place, accord with the exift- ing ftate of our globe. - Tue moft powerful and effential agent of the Huttonian Theory, is Fire, which I have always looked upon as the fame with that of volcanoes, modified by circumftances which muft, toa certain degree, take place in every lava previous to its eruption. 1 Tue original fource of internal fire is involved in great ob- {curity ; and no fufficient reafon occurs to me for deciding whether it proceeds by emanation from fome vaft central re- -fervoir, or is generated by the local operation of fome chemi- cal procefs. Nor is there any neceflity for fuch a decifion : all we need to know is, that internal fire exifts, which no one can doubt, who believes in the eruptions of Mount Vefuvius. To require that a man fhould account for the generation of internal fire, before he is allowed to employ it in geology, is no lefs abfurd than it would be to prevent him from reafoning about the conftruction of a telefcope, till he could explain the nature of the fun, or account for the generation of light *. But: while we remain in fufpenfe as to the prime caufe of this tremendous agent, many circumftances of importance with regard to it, may fairly become the fubjects of obfervation and difcuffion. ‘ Some authors (I conceive through ignorance of the facts) have alleged, that the fire of Aitna and Vefuvius is merely fu- perficial. But the depth of its ation is fufficiently proved, by the great diftance to which the eruptive percuflions are felt, and ftill more, by the fubftances thrown out uninjured by fome eruptions _ * Tuts topic, however, has of late been much. urged againift us, and an unfair advantage has been taken of what Mr Prayrair has faid upon it. What he gave as mere conjecture on a fubject of collateral importance, has been argued upon as, the bafis and fundamental doétrine of the fyftem. 158 EFFECTS of HEAT eruptions of Mount Vefuvius. Some of thefe, as marble and gyp- fum, are incapable in freedom of refifting the action of fire. We have likewife granite, fchiftus, gneifs, and ftones of every known clafs, befides many which have never, on any other occafion, been found at the furface of our globe. The circumftance of thefe fubftances having been thrown out, unaffected by the fire, proves, that it has proceeded from a fource, not only as deep, but deeper, than their native beds; and as they exhibit {pecimens of every clafs of minerals, the formation of which we pretend to explain, we need inquire no further into the depth of the Vefuvian fire, which has thus been proved to reach below the range of our {peculations. Vorcanice fire is fubject to perpetual and irregular varia- tions of intenfity, and to fudden and violent renewal, after long periods of abfolute ceffation. Thefe variations and inter- miffions, are likewife eflential attributes of fire as employed by Dr Hutton ; for fome geological {cenes prove, that the indura- ting caufe has acted repeatedly on the fame fubftance, and that, during the intervals of that action, it had ceafed entirely. This circumftance affords a complete anfwer to an argument lately urged againft the Huttonian Theory, founded on the wafte of heat which muft have taken place, as it is alleged, through the furface. For if, after abfolute ceflation, a power of renewal exifts in nature, the idea of wafte by continuance is quite inapplicable. Tue external phenomena of volcanoes are fufficiently well known; but our fubject leads us to inquire into their internal actions. This we are enabled to do by means of the foregoing experiments, in fo far as the carbonate of lime is concerned. SomE experiments which I formerly * laid before this So- ciety and the public, combined with thofe mentioned in this paper, * Edinburgh TranfaGions, Vol. V. Part I. p.60—66. MODIFIED ly COMPRESSION. 159) paper, prove, that the feebleft exertions of volcanic fire, are of fufficient intenfity to perform the agglutination, and even the entire fufion, of the carbonate of lime, when its carbonic acid is effectually confined by preflure; for though: lava, after its. fufion, may be made, in our experiments, to congeal into a glafs, in a temperature of 16° or 18° of WEDGwooD, in which temperature the carbonate would fcarcely be affected ; it muft be obferved, that a fimilar. congelation is not to be looked for in nature ; for the mafs, even of the fmalleft ftream of lava, is. too great to admit of fuch rapid cooling. And, in fact, the external part of a lava is not vitreous, but confifts of a fub-- ftance which, as my experiments have proved, muft have been. congealed in a heat of melting filver, that is, in 22° of WEDG- woop ; while its internal parts bear a character indicating that they congealed in 27° or 28° of the fame fcale. It follows, that no part of the lava, while it remained liquid, can have been lefs hot than 22° of WepGwoop. Now, this happens to be a heat, in which I have accomplifhed the entire fufion of the carbonate of lime, under preflure. We muft therefore conclude, that the heat of a running lava is always of fufh-. cient intenfity to perform the fufion of limeftone. In every active volcano, a communication muft exift between. the fummit of the mountain and the unexplored region, far below its bafe, where the lava has been melted, and whence it has been propelled upwards ; the liquid lava rifing through this internal channel, fo-as to fill the crater to the brim, and flow. over it. On this occafion, the fides of the mountain muft un- dergo a violent-hydroftatical preffure outwards; to which they often yield by the formation of a vaft rent, through which the. Java is difcharged in a lateral eruption, and flows in a continued. ftream fometimes during months. On /itna moft of the erup- tions are fo performed; few lavas flowing from the fummit, but generally breaking out laterally, at very elevated ftations.. 2 Ne At. 160 EFFECTS of HEAT At the place. of delivery, a quantity of gafeous matter is pro- pelled violently upwards, and, along with it, fome liquid lava ; which laft, falling back again in a fpongy ftate, produces one of thofe conical hills which we fee in great number on the vaft fides of Mount A®tna, each indicating the difcharge of a parti- cular eruption. At the fame time, a jet of flame and {moke iffues from the main crater, proving the internal communication be- tween it and the lava; this difcharge from the fummit gene- rally continuing, in a greater or a lefs degree, during the in- tervals between eruptions. (Fig. 41. reprefents an ideal fection of Mount tna; ad is the direct channel, and 4c is a lateral branch). Ler us now attend to the ftate of the lava within the moun- tain, during the courfe of the eruption ; and let us fuppofe, that a fragment of limeftone, torn from fome ftratum below, has been included in the fluid lava, and carried up with it. By the laws of hydroftatics, as each portion of this fluid fuftains pref- fure in proportion to its perpendicular diftance below the point of difcharge, that preflure muft increafe with the depth. The {pecific gravity of folid and compact lava is nearly 2.8 ; and its weight, when in a liquid ftate, is probably little different. The table fhews, that the carbonic acid of limeftone cannot be conftrained in heat by a preflure lefs than that of 1708 feet of fea, which correfponds nearly to 600 feet of liquid lava. As foon, then, as our calcareous mafs rofe to within 600 feet of the furface, its carbonic acid would quit the lime, and, afluming a gafeous form, would add to the eruptive effervefcence. And this change would commonly begin in much greater depths, in confequence of the bubbles of carbonic acid, and other fubftan- ces in a gafeous form, which, rifing with the lava, and through it, would greatly diminifh the weight of the column, and would render its preflure on any particular fpot extremely variable. With all thefe irregularities, however, and interruptions, the preflure “* MODIFIED ty COMPRESSION. 16% preflure would in all cafes, efpecially where the depth was confi- derable, far furpafs what it would have been under an equal depth of water. Where the depth of the ftream, below its point of delivery, amounted, then, to 1708 feet, the preflure, if the heat was not of exceflive intenfity, would be more than fuf- ficient to conftrain the carbonic acid, and our limeftone would fuffer no calcination, but would enter into fufion; and if the eruption ceafed at that moment, would cryftallize in cooling along with the lava, and become a nodule of calcareous {par. The mafs of lava, containing this nodule, would then conftitute a real whinftone, and would belong to the ‘kind ‘called amygda- loid. In greater depths ftill, the’ preffure would be propor- tionally increafed, till fulphur, and even water, might be con- ftrained ; and the carbonate of lime would continue undecom- pofed in the higheft heats. Ir, while the lava was in a liquid ftate, during the eruption or previous 'to it, a new rent (de, fig.41.), formed in the folid country below the volcano, was met by our ftream (at d@), it is obvious that the lava would flow into the aperture with great rapidity, and fill it to the minuteft extremity, there being no air to impede the progrefs of the liquid. In this manner, a ftream of lava might be led from below to approach the bot- tom of the fea (ff), and to come in conta@ with a bed of loofe’ fhells (¢¢), lying on that bottom, but covered. with — beds of clay, interftratified, ‘as ufually occurs, with beds of fand, and other beds of fhells. The firft effe&t of heat would be to drive off the moifture of the loweft fhell-bed, in a ftate of va- pour, which, rifing till it got beyond the reach of the heat, would be condenfed into water, producing a flight motion of ebullition, like that of a veffel of water, when it begins’ to boil, and when it is faid to fimmer. The beds of clay and fand might thus undergo fome heaving and partial derangement, but would ftill poflefs the power of ftopping, or of very much im- Vou. VI.—P. I. xX peding, 162 ‘WARD AGT S ofate AT peding, the defcent of water from the fea above; fo that the water which had been driven from the fhells at the bottoni, would not return to them, or would return but flowly ; and they would be expofed dry»to the:action of heat *, In this cafe, one of two things would inevitably happen. Ei- ther the carbonic acid of ‘the fhells) would »be driven off by the heat, producing an incondenfable elaftic fluid, which, heaving up or penetrating the fuperincumbent beds, would force its way to the furface of the fea, and, produce a fubmarine erup- tion, as has happened at Santorini and elfewhere ; or the vo- latility of the carbonic acid would be reprefled by the weight of the fuperincumbent water (4#), and the fthell-bed, being fof- tened or fufed by the action of heat, would be converted into a ftratum of limeftone. mer Tue foregoing experiments enable us to decide! in any parti- cular cafe, which of thefe two events muft take place, when the heat of the lava and: the depth of the fea are known. Tue table fhews, that under,a fea no, deeper than 1708 feet, near one-third of a mile,,a limeftone would be formed by proper heat; and that, in, a depth, of little more than one mile, it would enter into,entire fufion... Now, the .com- mon foundings of mariners extend to 200 fathoms, or 1200 feet. Lord. Muxrcrave + found bottom at 4680 feet, or nearly nine-tenths of a mile; and Captain Exxis let down a fea-gage to the depth of 5346 feet,{. It thus, appears, ; that * Turis fituation of things, is fimilar to what happens when {mall-coal is moi- ftened, in order to make it cake. The duft, drenched with water, is laid upon the fire, and remains long wet, while the heat below fuffers little or no abatement, + Voyage towards the North Pole, p. 142. } Philofophical TranfaGions, 1751, Pp. 212. MODIFIED by COMPRESSION. 163 that at the bottom of a fea, which would be founded by a line much lefs than double of the ufual length, and lefs than half ‘the depth of that founded by Lord Mutcrave, lime- ftone might be:formed by: heat ; and that, at the depth ‘reach- ed by Captain Ex.is, the entire» fufion would be accomplith- ed, if the bed of fhells were touched by a lava: at the extre- mity of its courfe, when its heat was loweft. Were the heat of the lava greater, a greater depth of fea would, of courfe, be requifite to conftrain'the carbonic acid effectually; and future experiments may determine what depth is required to co-ope- rate with any given temperature. It is enough for our prefent purpofe to have fhewn, that the refult is. poffible in any .cafe,’ and to have circumfcribed the neceflary force of thefe agents within moderate limits. - At the fame time it muft be obferved, that we have been far from ftretching the known fats; for when: we compare the fmall :extent of fea in which any foundings can be found, with that of the vaft unfathomed ocean, it is ob- vious, that in afluming a depth of one mile or two, we fall very -fhort' of the medium. M. pz La Prace, reafoning from the phenomena of the tides, ftates it as highly probable that this medium is not lefs than eleven Englifh miles *. Iria great part or the whole of the fuperincumbent mafs confifted, not of water, but of fand or clay, then the depth re- quifite to produce thefe effects would be leffened, in the inverfe ratio of the fpecific gravity. If the above-mentioned oc- currence took place under a mafs compofed of ftone firmly bound’ together by fome previous operation of nature, the power of the fuperincumbent mafs, in oppofing the efcape of X 2 carbonic * “ On peut donc regarder au moins comme trés probable, que Ja profondeur “* moyenne de la mer n’eft pas au-deffous de quatre lienes.” .. Dr 1a PLAcE, Hift, de lAcad. Roy. des Sciences, année 1776, 164, EFFECTS o HEAT carbonic acid} would be very much increafed by that union and by the ftiffnefs or tenacity of the fubftance. We have feen numberlefs examples of this power in the courfe of thefe experiments, in which barrels, both of iron and porcelain, whofe thicknefs did not exceed one-fourth of an inch, have exerted a force fuperior to the mere weight of a mile of fea. Without fuppofing that the fubftance of a rock could in any cafe act with the fame advantage as that of a uniform and con- nected barrel ; it feems obvious that a fimilar power muft, in many cafes, have been exerted to a certain degree. We know of many calcareous mafles which, at this mo- ment, are expofed to a preffure more than fufficient to accom- plith their entire fufion. The mountain of Saleve, near Geneva, is 500 French fathoms, or nearly 3250 Englith feet, in height, from its bafe to its fummit. Its mafs confifts of beds, lying nearly horizontal, of limeftone filled with fhells. Independent- ly, then, of the tenacity of the mafs, and taking into account its mere weight, the loweft bed of this mountain, muft, at this moment, fuftain a preflure of 3250 feet of limeftone, the fpecific gravity of which is about 2.65. This preflure, therefore, is equal to that of 8612 feet of water, being nearly a mile and a half of fea, which is much more than adequate, as we have fhewn, to accomplifh the entire fufion of the carbonate, on the appli- cation of proper heat. Now, were an emanation from a volcano, to rife up under Saleve, and to penetrate upwards to its bafe, and ftop there; the limeftone to which the lava approached, would inevitably be foftened, without being cal- cined, and, as the heat retired, would cryftallize into a faline marble. Some other circumftances, relating to this fubje@, are very deferving of notice, and enable us ftill further to compare the ancient and modern operations of fire. Ir MODIFIED ly COMPRESSION. 165 Ir appears, at firft fight, that a lava having once pene- trated the fide of a mountain, all fubfequent lavas fhould conti- nue, as water would infallibly do, to flow through, the fame aperture. But there is a material difference in the two cafes. As foon as the lava has ceafed to flow, and the heat has begun to abate, the crevice through which the lava had been pafling, remains filled with a fubftance, which foon agglutinates in- to a mafs, far harder and firmer than the mountain itfelf. This mafs, lying in a crooked bed, and being firmly welded to the fides of the crevice, muft oppofe a moft powerful refiftance to any ftream tending to purfue the fame courfe. The injury done to the mountain by the formation of the rent, will thus be much more than repaired; and in a fubfequent eruption, the lava muft force its way through another part of the moun- tain or through fome part of the adjoining country.. The action of heat from below, feems in moft cafes to have kept a channel open through the axis of the mountain, as appears by the fmoke and flame which is habitually difcharged at the fammit during intervals of calm. On many occafions, how- ever, this fpiracle feems to. have been entirely clofed by the confolidation of the lava, fo as to fupprefs all emiffion. This happened to Vefuvius during the middle ages. All appearance of fire had ceafed for five hundred years, and the crater was covered with a foreft of ancient oaks, when the volcano open- ed with frefh vigour in the fixteenth century. Tue eruptive force, capable of overcoming fuch an ob- ftacle, muft be tremendous indeed, and feems in fome cafes to have blown the volcano itfelf almoft to pieces. It is im- poffible to fee the Mountain of Somma, which, in the form of a crefcent, embraces Mount Vefuvius, without being convinced that it is a fragment of a large volcano, nearly concentric with 166 EFFECTS of HEAT with the ‘prefent inner cone, which, in fome great. eruption, had been deftroyed all but this fragment. In our own times, an event of no fmall magnitude has taken: place on the fame fpot ; the inner cone of Vefuvius having undergone fo great a change during the eruption in 1794, that it now bears no re- femblance to what it was when I faw it in 1785. Tue general or partial ftagnation of the internal lavas at the clofe of each eruption feems, then, to render it neceflary, that in every new difcharge, the lava fhould begin by. ma- king a violent laceration. And this is probably the caufe of thofe tremendous earthquakes which precede all great erup- tions, and which ceafe as foon as the lava has found a vent. It feems but reafonable to afcribe like effects to like caufes, and _to believe that the earthquakes which frequently defolate coun- tries not externally volcanic, likewife indicate the protrufion from below of matter in liquid fufion, penetrating the mafs of rock, - THE injection of a whinftone-dike into a frail mafs of hale and fandftone, muft have produced the fame effects upon it that the lava has juft been ftated to produce on the loofe beds of volcanic fcoria. One ftream of liquid whin, having flowed into fuch an aflemblage, muft have given it great additional weight and ftrength : fo that a fecond ftream coming like the firft, would be oppofed by a mafs, the laceration of which would produce an earthquake, if it;were overcome ; or by which, if it refifted, the liquid matter would be compelled to penetrate fome weaker mafs, perhaps at a great diftance from the firft... The internal fire being thus compelled perpetually to change the {cene_ of its action; its influence might be carried to an indefinite extent: So that the intermittance in point of time, as well as the verfa- tility in point of place, already remarked as common to the Huttonian and Volcanic fires, are accounted for on our princi- ples. MODIFIED by COMPRESSION. 167 pless Andcut-thus appears, that whinftone poflefles all the pro- rile which we are led by theory. to afcribe to an imternal lava. bet ni Tuts: conection “is sir aliciitesed by an cieiididie cafe between the refults of external and ifternal-fire, difplayed incan:aGual fection of the ancient part of Vefuvius, which oc- curs in the Mountain of Somma mentioned above. I formerly defcribed. this {cene in my paper on Whinftone and Lava; and I muft beg leave once more to prefs it upon the notice of the public, as affording to future travellers: a) moft interefting field of geological inquiry. Tue fection is feen in the ie ssiibick cliff, feveral hundred feet in: height, which Somma prefents to the view from the little-valley, in form of ‘a crefcent, which lies. between Somma and the interior cone of Vefuvius, called the Atrio del Cavallo. (Figs 42. reprefents ithis :feene, done from the recollection of whatrI: faw in-1785.) abc is the interior cone: of Vefuvius; af g the mountain’ of Somma; and ¢de the Atrio del Cavallo). By means of this cliff. (fd in figure 42. and which is repre- fented ‘feparately in fig.\44:); we fee the internal ftru@ture of the mountain, ‘compofed of :thick beds (#4) of loofe fcoria, which have fallen in fhowers; hetween which thin but firm ftreams: (m m) of lava are interpofed, which have flowed down the outward conicalfides of the mountain. (Fig. 43. is an ideal {éGon of Vefuvius and Somma, through the axis of the cones, fhewing;the:manner in which: the beds. of fcoria and: of lava lie upon each other; the extremities of which beds are feen edgewife inthe, cliff at mm and hk, fig. 42, 43, and’ 44.). Tuts aflemblage-of feoria and lava is traverfed abruptly and vertically by (ftreams: of folid. lava (a2, fig, 44.), reaching from top to bottom of the cliff. Thefe laft I conceive to have flowed in rents of the ancient mountain, which rents had acted as 168 EFFECTS of HEAT as pipes through which the lavas of the lateral eruptions were conveyed to the open air. This fcene prefents to the view of an attentive obferver, a real {fpecimen of thofe internal ftreams which we have juft been confidering in fpeculation, and they may exhibit circumftances decifive of the opinions here ad- vanced. For, if one of thefe ftreams had formerly been con- nected with a lateral eruption, difcharged at more than 600 feet above the Atrio del Cavallo, it might poffibly contain the carbonate of lime. But could we fuppofe that depth to extend to 1708 feet, the interference of air-bubbles, and the action of a ftronger heat than was merely required for the fufion of the carbonate, might have been overcome. Peruaps the height of Vefuvius has never been great enough for this purpofe. But could we fuppofe AZtna to be cleft in two, and its ftructure difplayed, as that of Vefuvius has juft been defcribed, there can be no doubt that internal ftreams of lava would be laid open, in which the preflure muft have far exceeded the force required to conftrain the carbonic acid of limeftone ; fince that mountain occafionally delivers lavas from its fummit, placed 10.954 feet above the level of the Mediterra- nean *, which wafhes its bafe. I recolleé& having feen, in fome parts of Etna, vaft chafms and crags, formed by volcanic re- volutions, in which vertical ftreams of lava, fimilar to thofe of Somma, were apparent. But my attention not having been turned to that obje@ till many years afterwards, I have only now to recommend the inveftigation of this interefting point to future travellers. Wuart lias been faid of the heat conveyed by internal volca- nic ftreams, applies equally to that deeper and more general heat by which the lavas themfelves are melted and propelled upwards, * Phil. Tranf.17474, p. $95- MODIFIED ly COMPRESSION. 169 upwards. That they have been really fo propelled, from a great internal mafs of matter, in liquid fufion, feems to admit of no doubt, to whatever caufe we afcribe the heat of volcanoes. It is no lefs obvious, that the temperature of that liquid mutt be of far greater intenfity than the lavas, flowing from it, can re- tain when they reach the furface. Independently of any actual eruption, the body of heat contained in this vaft mafs of liquid, mutt diffufe itfelf through the furrounding fubftances, the in- tenfity of the heat being diminifhed by flow gradations, in pro- portion to the diftance to which it penetrates. When, by means of this progreffive diffufion, the heat has reached an affemblage of loofe marine depofites, fubject to the preflure of a great fu- perincumbent weight, the whole muft be agglutinated into a mafs, the folidity of which will vary with the chemical com- pofition of the fubftance, and with the degree of heat to which each particular fpot has thus been expofed. At the fame time, analogy leads us to fuppofe, that this deep and extenfive heat muft be fubjec to viciflitudes and intermiflions, like the exter- nal phenomena of volcanoes. We have endeavoured to explain fome of thefe irregularities, and a fimilar reafoning may be ex- tended to the prefent cafe. Having fhewn, that fmall in- ternal {treams of lava tend fucceflively to pervade every weak part of a volcanic mountain, we are led to conceive, that the great mafles of heated matter juft mentioned, will be fucceffive- ly dire&ed to different parts of the earth; fo that every loofe affemblage of matter, lying in a fubmarine and fubterranean fituation, will, in its turn, be affected by the indurating caufe ; and the influence of internal volcanic heat will thus be cir- ‘cumfcribed within no limits but thofe of the globe itfelf. A sERIES of undoubted facts prove, that all our ftrata once Jay ina fituation fimilar in all refpeés to that in which the _ marine depofites juft mentioned have been fuppofed to lie. Tue inhabitant of an unbroken plain, or of a country form: ed of horizontal ftrata, whofe obfervations have been confi- Von, VL—P. I. Y ned 170 EFFECTS of HEAT ned to his native fpot, can form no idea of thofe truths, which at every ftep in an alpine diftri@ force themfelves on the mind of a geological obferver. Unfortunately for the progrefs of geology, both London and Paris, are pla- ced in countries of little intereft; and thofe fcenes by which the principles of this fcience are brought into view in the moft ftriking manner, are unknown to many perfons beft capable of appreciating their value. The moft important, and at the fame time, the moft aftonifhing truth which we learn by any geological obfervations, is, that rocks and moun- tains now placed at an elevation of more than two miles above the level of the fea, muft at one period have lain at its bottom. This is undoubtedly true of thofe ftrata of lime- {tone which contain fhells ; and the fame conclufion muft be ex- tended to the circumjacent ftrata. The imagination ftruggles againft the admiflion of fo violent a pofition ; but muft yield to the force of unqueftionable evidence ; and it is proved by the example of the moft eminent and cautious obfervers, that the conclufion is inevitable *. ANOTHER queftion here occurs, which has been well treat- ed by Mr Pirayrair. Has the fea retreated from the moun- tains? or have they rifen out of the fea? He has fhewn, that the balance of probability is incomparably in favour of the latter fuppofition ; fince, in order to maintain the former, we mutt difpofe of an enormous mafs of fea, whofe depth is feveral miles, and whofe bafe is greater than the furface of the whole fea. Whereas the elevation of a continent out of a fea like ours, would not change its level above a few feet; and even were a great derangement thus occa- fioned, * Saussure, Voyages dans les Alpes,tom. ii. p. 99.—104. a fs MODIFIED by COMPRESSION. ryt fioned, the water would eafily find its level without the af fiftance of any extraordinary fuppofition. The elevation of the land, too, is evinced by what has occafionally happened in volcanic regions, and affords a complete folution of the con- tortion and erection of ftrata, which are almoft univerfally ad- mitted to have once lain in a plane and horizontal pofition. WHATEVER opinion be adopted as to the mode in which the land and the water have been feparatéd, no one doubts of the ancient fubmarine fituation of the ftrata. An important feries of facts proves, that they were likewife fub- terranean. Every thing indicates that a great quantity of matter has been removed from what now conftitutes the furface of our globe, and enormous depofites of loofe fragments, evidently de- tached from mafles fimilar to our common rock, evince the action of fome very powerful agent of deftruction. Analogy too, leads us to believe, that all the primary rocks have once been covered with fecondary ; yet, in vaft diftricts, no fecondary rock ap- pears. In fhort, geologifts feem to agree in admitting the ge- neral pofition, that very great changes of this kind have taken place in the folid furface of the globe, however much they may differ as to their amount, and as to their caufes. Dr Hutton afcribed thefe changes to the adion, during very long time, of thofe agents, which at this day continue flowly to corrode the furface of the earth ; frofts, rains, the or- dinary floods of rivers, &c. which he conceives to have aéted always with the fame force, and no more. But to this opinion I could never fubfcribe, having early adopted that of Saus- SURE, in which he is joined by many of the continental geologifts. My conviction was founded upon the infpedction of thofe facts in the neighbourhood of Geneva, which he has adduced in fupport of his opinion. I was then convinced, Y2 and 172 EFFECTS of HEAT and I ftill believe, that yaft torrents, of depth fufficient to over- top our mountains, have {wept along the furface of the earth, excavating vallies, undermining mountains, and carrying away whatever was unable to refift fuch powerful corrofion. If fuch agents have been at work in the Alps, it is difficult to conceive that our countries fhould have been fpared. I made it therefore my bufinefs to fearch for traces of fimilar operations here. I was. not long in difcovering fuch in great abundance ; and, with the help of feveral of my friends, I have traced the indications of vaft torrents in this neighbourhood, as obvious as thofe I formerly faw on Saleve and Jura. Since I announced my opi- nion on this fubject, in a note fubjoined to my paper on Whin- ftone and Lava, publifhed in the fifth volume of the Tran/~ actions of this Society, I have met with many confirmations. of thefe views. The moft important of thefe are derived from the teftimony of my friend Lord SeLkrrx, who has lately met with a feries of fimilar facts in North America. Ir would be difficult to compute the effects of fuch an agent ; but if, by means of it, or of any other caufe, the whole mafs. of fecondary ftrata, in great tracts of country, has been remo- ved from above the primary, the weight of that mafs alone muft have been fufficient to fulfil all the conditions of the Huttonian Theory, without having recourfe to the preflure of the fea. But when the two preflures were combined, how great muft have been their united ftrength ! We are authorifed to fuppofe, that the materials of our ftrata, in this fituation, underwent the action of fire, For volcanoes have burnt long before the earlieft times recorded in hiftory, as appears by the magnitude of fome volcanic mountains; and it can fcarcely be doubted, that their fire has acted without any. material ceflation ever fince the furface of our globe acquired its prefent. 4 . MODIFIED ly COMPRESSION. 173 prefent form. In extending that fame influence to periods of ftill higher antiquity, when our ftrata lay at the bottom of the fea, we do no more than afcribe permanence to the exifting laws of nature. Tue combination of heat and compreffion refulting from thefe circumftances, carries us to the full extent of the Hutto- nian Theory, and enables us, upon its principles, to account for the igneous formation of all rocks from. loofe marine depo- fites. ; Tue fand would thus be changed to fandftone ; the fhells to: fimeftone ; and the animal and vegetable fubftances to coal. Oruer beds, confifting of a mixture of various fubftances, would be ftill more affected by the fame heat. Such as con- tained iron, carbonate of lime, and alkali, together with a mix- ture of various earths, would enter into thin fufion, and, pe- netrating through every crevice that occurred, would, in fome cafes, reach what was then the furface of the earth, and con- ftitute Java: in other cafes, it would congeal in the internal rents, and conftitute’ porphyry, bafalt, greenftone, or any other of that numerous clafs of fubftances, which we comprehend under the name of whin/jfone. At the fame time, beds of fimi-- lar quality, but of compofition fomewhat lefs fufible, would. enter into: a ftate of vifcidity, fuch as many bodies pafs. through in their progrefs towards fufion. In this ftate, the particles, though far from poffefling the fame freedom as in a. liquid, are fufceptible of cryftalline arrangement *; and the fubftance * Tus ftate of vifcidity, with its numberlefs modifications, is deferving of. great attention, fince it affords a folution of fome of the moft important geologi- cal gueftions. The mechanical power exerted by fome iubftances, in the aé of. afluming a cryfialline form, is well known. I have feema fet of large and broad cryftals 1474 EFFECTS of HEAT fubftance, which, in this fluggifh ftate, would be little difpofed to move, being confined in its original fituation by contiguous beds of more refractory matter, would cryftallize, without undergoing any change of place, and conftitute one of thofe beds of whinftone, which frequently occur interftratified with fandftone and limeftone. In other cafes where the heat was more intenfe, the beds of fand, approaching more nearly to a ftate of fufion, would ac- quire fuch tenacity and toughnefs, as to allow themfelves to be bent and contorted, without laceration or fracture, by the in- fluence of local motions, and might affume the fhape and’ character of primary {chiftus: the limeftone would be highly cryftallized, and would become marble, or, entering into thin fufion, would penetrate the minuteft rents in the form of cal- careous fpar. Laftly, when the heat was higher ftill, the fand itfelf would be entirely melted, and might be converted, by the fubfequent effects of flow cooling, into granite, fienite, &c. ; in fome cafes, retaining traces of its original ftratification, and conftituting gneifs and ftratified granite ; in others, flowing into the crevices, and forming veins of perfect granite. In confequence of the action of heat, upon fo great a quan- tity of matter, thus brought into a fluid or femifluid ftate, and in which, notwithftanding the great preflure, fome fubftances would be volatilized, a powerful heaving of the fuperincumbent mafs muft have taken place; which, by repeated efforts, fuc- ceeding cryftals of ice, like the blade of a knife, formed ina mafs of clay, of fuch ftiffnefs, that it had juft been ufed to make cups for chemical purpofes. In many of my former experiments, I found that a fragment of glafs made from whinftone or lava, when placed in a muffle heated to the melting point of filver, affumed a cryftalline arrangement, and underwent a complete change of character. During this change, it became foft, fo as to yield to the touch of an iron rod; yet retained {uch ftiffnefs, that, lying untouched in the muffle, it preferved its fhape entirely ; the harp angles of its fraéture not being in the leaft blunted. laa MODIFIED by COMPRESSION. 195 ceeding each other from below, would at laft elevate the ftrata into their prefent fituation. Tue Huttonian Theory embraces fo wide a field, and com- prehends the laws of fo many powerful agents, exerting their influence in circumftances and in combinations hitherto un- tried, that many of its branches muft ftill remain in an unfi- nifhed ftate, and may long be expofed to partial and plaufible objections, after we are fatisfied with regard to its fundamen- tal doétrines. In the mean time I truft, that the obje@t of our purfuit has been accomplifhed, in a fatisfactory manner, by the fufion of limeftone under preffure. This fingle refult af- fords, I conceive, a ftrong prefumption in favour of the folu- tion which Dr Hutton has advanced of all the geological phe- nomena; for, the truth of the moft doubtful principle which he has affumed, has thus been eftablifhed by dire& experi- ment. APPEN- * pe sinton al anu vad ed Seas (eer. seal eset ‘sy , a eit Res, PT ° a Aad sites oes ay fe Sapa ee a Bis Dime 2 bile arid ieee ee . iis or a) Seah as ts phe we ey Sas sa se gai | ie Ser PC er. eed 7 pag! ee Sg Naar Yip, ged Sagan “ii , en 5 pila wed eR Wa 3 ‘ad it “Hyt ie eu fa: ems ea o “ y- iy a bie “hi “a 2 ag say q's rs Rotn | oa ~~ SEG ike: 7 ny jak \ ; ae iis pk MC A ie ey Cats SANE . ; get me eat (Nid ll Bw? Be AK gael li i seres 4 i Pues ee aeanvite eo ASM, hei aos ae tot ren eo anh Lai) OS vee APPENDIX. * No. I. SPECIFIC GRAVITY OF SOME OF THE FOREGOING RESULTS. S many of the artificial limeftones and marbles produced in thefe experiments, were poflefled of great hardnefs and com- pactnefs, and as they had vifibly undergone a great diminution of bulk, and felt heavy in the hand, it feemed to me an object of fome confequence to afcertain their fpecific gravity, compared with each other, and with the original fubftances from which they were formed. As the original was commonly a mai{s of - chalk in the lump; which, on being plunged into water, begins to abforb it rapidly, and continues to do fo during a long time, fo as to vary the weight at every inftant, it was impoffible, till the abforption’ was complete, to obtain any certain refult; and to allow for the weight thus gained, required the application of Nol, VI.—P. I. Z a 178 EFFECTS of HEAT [APPENDIX. a method different from that ufually employed in eftimating fpe- cific gravity. ; In the common method, the fubftance is firft weighed in air, and then in water ; the difference indicating the weight of wa- ter difplaced, and being confidered as that of a quantity of wa- ter equal in bulk to the folid body.. But as chalk, when {fatu- rated with water, is heavier, by about one-fourth, than when dry, it is evident, that its apparent weight, in water, muft be in- creafed, and the apparent lofs of weight diminifhed exactly to that amount. To have a juft eftimate, then, of the quantity of wa- ter difplaced by the folid body, the apparent lofs of weight muft be increafed, by adding the abforption to it. Two diftinét methods of taking {pecific gravity thus prefent themfelves, which it is of importance to keep feparate, as each of them is applicable to a particular clafs of fubjects. OnE of thefe methods, confifts in comparing a cubic inch of a fubftance in its dry ftate, allowing its pores to have their fhare in conftituting its bulk, with a cubic inch of water. Tue other depends upon comparing a cubic inch of the fo- lid matter of which the fubftance is compofed, independently of vacuities, and fuppofing the whole reduced to perfec folidity, with a cubic inch of water. Tuus, were an architect to compute the efficacy of a given bulk of earth, intended to load an abutment, which earth was dry, and fhould always remain fo, he would undoubtedly follow the firft of thefe modes: Whereas, were a farmer to compare the fpecific gravity of the fame earth with that of any other foil, in an agricultural point of view, he would ufe the fecond mode, which is involved in that laid down by Mr Davy. As our object is to compare the fpecific denfity of thefe re- fults, and to afcertain to what amount the particles have ap- proached ApPENDIX.] MODIFIED by COMPRESSION. 179 proached each other, it feems quite evident that the firft mode is fuited to our purpofe. This will appear moft diftin@ly, by infpection of the following Table, which has been conftructed fo as to include both. f Z2 TABLE 10 EFFECTS of HEAT [APPENDIX. TABLE OF SPECIFIC GRAVITIES. VI. | VOL. | VI. | 1X. } X. : Difference Specific A Weight i 2 Sra Patohe § Dig rence between | Abforp- smn ek gravity Specific | eight in | Weight in | Weight in] between Calasbas on per Columns com-| gravity air, dry. water, | air, wet. | Columns |ry a ty. or aoe V.. and 1 es by new I. & IIL. ablorption, Vals ods: mode. ————_} | — |] | | | 125.90] 77-35|135-65| 47-35 9-94 6.13] 9.99] 3-81 15-98} 9-70] 16.02] 6.28} 5-47| 3-33] 5-48] 2.14 18.04] 10.14] 18.06] 7.90 ,6.48| 3-74] 7.10] 2.74 10.32] 5-97] 10.36] 4.35 54-57] 31-39) 55-23| 23-27 G22 Ade LO] 7 Oat thes hal 7 37-75| 24-15| 38.30] 16.60 9.75 7.74 , 57-10] 2.604] 2.204 0.05] 9.50] 3.86/2.609] 2.575 0.04] 0.25] 6,32/2.544]2.528 ©.01] 0.18] 2.15/2-55612.544 0.02! O11] 7.92|2.283]2.277 0.62] 9-56) 3.36/2-365] 1.928 0.04] 9-39) 4.39)2-372]2.350 0.66] 1.21] 23.93|2.345|2.280 3-86] 5-34] 35-03]2.318] 2.063 O55] 1-45| 17.15]2.274] 2.207 OO SI ANBwWdnH 21.21] 12.55] 21.26] 8.66] 0.05} 0.24] 8.71/2.449)2.435 | has T 18.59 11.56| 18.61] 7.03] 0.02] 0.18] 7.05]2.644] 2.636 | } 1.571 EXPLANATION. ’ Cotumn I. contains the number affixed to each of the fpecimens, whofe properties are exprefled in the table. THE APPENDIX. ] MODIFIED by COMPRESSION. r8t Tue firft eleven are the fame with thofe ufed in the paper read in this Society on the 30th of Auguft 1804, and pubhfhed in NicuHotson’s Fournal for October following, and which refer to the fame fpecimens. No. 12. Is a fpecimen of yellow marble, bearing a ftrong refemblance to No. 3. No. 13. A fpecimen of chalk. . No. 14. Shews the average of three trials with chalk. No. 15. Some pounded chalk, rammed in the manner followed in thefe experiments. In order to afcertain its {pecific gravity, I rammed the powder into a glafs-tube, previoufly weighed ; then, after weighing the whole, I removed the chalk, and filled the fame tube with water. I thus afcertained, ina dire@ man- ner, the weight of the fubftance, as ftated in Column II., and that of an equal bulk of water, ftated in,Column VIII. Cotumn II. Weight of the fubftance, dry in air, after expo- fure, during feveral hours toa heat of 212° of FAHRENHEIT. Cotumn III. Its weight in water, after lying long in the li- quid, fo as to perform its full abfarption and all air-bubbles being carefully removed. Cotumn IV. Weight in air, wet. The loofe external moitt- ure being removed by the touch of a dry cloth; but no time being allowed for evaporation. _ Cotumn V. Difference between Columns II. and III., or ap- parent weight of water difplaced. Cotumn VI. Difference between Columns II. and IV., or the catia CoLtumn VIL. Abforption reduced to a “tee centage of the dry fubftance. Cotumn VIII. Sum of Columns V. and VI., or the real weight of water difplaced by the body. » CoLtumn IX. Specific gravity, by the common mode, refult- ' ing from the divifion of Column II. by Column V. Cotumn X. Specific gravity, in the new mode, refulting from the divifion of Column II. by Column VIII. THE 182 | EFFECTS of HEAT [APPENDIXx. - Tue fpecific gravities afcertained by the new mode, and ex- prefled in Column X. correfpond very well to the idea which is formed of their comparative denfities, from other circumftances, their hardnefs, compact appearance, fufceptibility of polifh, and weight in the hand. Tue cafe is widely different, when we attend to the refults of the common method contained in Column IX. | Here the fpe- cific gravity of chalk is rated at 2.498, which exceeds confider- ably that of a majority of the refults tried. Thus, it would ap- pear, by this method, that chalk has become lighter by the ex- periment, in defiance of our fenfes, which evince an increafe of denfity. Tuis fingular refult arifes, I conceive, from this, that, in our {pecimens, the faculty of abforption has been much more decrea- fed than the porofity. Thus, if a piece of crude chalk, whofe fpecific gravity had previoufly been afcertained by the common mode, and then well dried in a heat of 212°, were dipped in var- nifh, which would penetrate a little way into its furface; and, the varnifh having hardened, the chalk were weighed in water, it is evident, that the apparent lofs of weight would now be greater by 23.61 per cent. of the dry weight, than it had been when the unvarnifhed chalk was weighed in water ; becaufe the varnifh, clofing the fuperficial pores, would quite prevent the abforption, while it added but little to the weight of the mafs, and made no change on the bulk. In computing, then, the fpe- cific gravity, by means of this laft refult, the chalk would appear very much lighter than at firft, though its denfity had, in fact, been increafed by means of the varnith. A simILAR effeét feems to have been produced in fome of thefe refults, by the agglutination or partial fufion of part of the fubftance, by which fome of the pores have been fhut out from the water. Tuis \ APPENDIX. MODIFIED by COMPRESSION. 183 Tuts view derives fome confirmation from an infpection of Columns VI. and VII.; the firft of which exprefles the abforp- tion ; and the fecond, that refult, reduced to a per centage of the original weight. It there appears, that whereas chalk abforbs 23-97 per cent., fome of our refults abforb only 0.5, or fo low as Q.11 per cent. So that the power of abforption has been re- duced from about one-fourth, to lefs than the five hundredth of the weight. I nave meafured the diminution of bulk in many cafes, par- ticularly in that of No. 11. The chalk, when crude, ran to the 75th degree of WEDGwoop’s gage, and fhrunk fo much during the experiment, that it ran to the 161"-; the difference amount- ting to 86 degrees. Now, I find, that WEDGwoop’s gage tapers- in breadth, from 0.5 at zero of the fcale, to 0.3 at the 240th degree. Hence, we have for one degree 0.000833. Confequently, the width, at the 75th degree, amounts to 0.437525; and at the 161ft, to 0.365887. Thefe numbers, denoting the linear meafure of the crude chalk, and of its refult under heat and compreflion, are as 100 to 83.8; or, in folid bulk, as 100 to 57-5: Computing the denfities from this fource, they are as Ito 1.73, The fpecific gravities inthe Table, of the chalk, and of this refult, are as 1.551: 2.435; that is, as 1 to 1.57. Thefe conclufions do not correfpond very exactly; but the chalk em- ployed in this experiment, was not one of thofe employed in de- termining average fpecific gravity in the Table; and other cir- cumftances may have contributed to produce irregularity. Comparing this chalk with refult fecond, we have 1. 551: 2.575 fo I: 1.6602. TABLE 184 | EFFECTS of HEAT APPENDIX. No. If. TABLE, CONTAINING THE REDUCTION OF THE FORCES MENTIONED IN CHAP. VII. TO A COMMON STANDARD. Is II. III. IV. V. VI VII. Number of | Bore,in de-| Preflurein | Tempera- | Depth of fea | Ditto in miles. | Preffure, ex- experiment | cimals ofan bundred ture by in feet. prefled in at- referred to | inch. weights, Wepc- mofpheres inChap. VII. woop’s pyrometer. I 0.75 3 22 1708 05 | 0.3235 51.87 2 0.75 3 25 1708.05 | 0.3235 51.87 3 0.75 10 20 5693.52 | 1.0783 17202 4 0.75 10 31. | 5603 52 | 1.0783 | 172.92 5 0.75 10 41 5693.52 | 1.0783 172.92 6 0.75 10 isi 5693.52 | 1.0783 172.92 7 0.75 10 — | 5693.52 | 1.0783 172.92 8 0.54 2 — | 2196.57 | 0.4160 66.71 4 — | 4393-14 | 05320. | 133.43 9 O54 334 _ 8896.12 | 1.6848 270.19 10 0.75 sees 21 1708.05 | 0.3235 |° 51.87 II 0.75 4 25 2277-41 | 0.4313 69.70 0-75 5 2846.76 0.5390. 86.46 ms EXPLANATION. APPENDIX. ] MODIFIED by COMPRESSION. 185 EXPLANATION. Cotumn I. contains the number of the experiment, as refer- red to in the text. Column II. The bore of the barrel ufed, in decimals of an inch. Column III. The abfolute force applied to the barrel, in hundred-weights. Column IV. The temperature, in WepcGwoop’s fcale. Column V. The depth of fea at which a force of compreffion would be exerted equal to that fuftained _ by the carbonate in each experiment, expreffed in feet. Co- lumn VI. The fame in miles. Column VII. Comprefling force, exprefled in atmofpheres. Boru Tables were computed feparately, by a friend, Mr J. JARDINE, and myfelf. XN Tue following data were employed. Area of a circle of which the diameter is unity, 0.785398. Weicut of a cubic foot of diftilled water, according to Pro- feffor RoBison, 998.74 ounces avoirdupois. MEAN fpecific gravity of fea-water, according to BLapu, 1.0272. Mean heighth of the barometer at the level of the fea 29-91196 Englifh inches, according to LapLace. SPECIFIC gravity of mercury, according to CAVENDIsH and BRISsON, 13.568. na Oho, coma BBSn. aa eae se ~ ze BS ; P Y. 2s a hi? NEF hy ¢ Ps ae. se , CONTA MAINT af i ut Ox Siege Rh tyeeee Mey shea a8 we RS ee + aad shine PAS * $..: an Sika thay % 5 Soden nds aciianod mia 199). Sisk bred vis Wg sgad oT Ui axiculoD © arxo% ods ai 62 ba a soit sualdide oT JI aimed) dani as toe Sremuneege aff VE asguloD., #lgiow-borbutiil ai lay und | dofdey. 1s ssh to dugah oft VY saute: - lag etaoowad: oa : Weare “dina jails os laps: lasers oud tildes m avibioiqeno9 | to: seats aS { -00" Bonk’ isto 4 9 Asns-ai sscod'e ve > +e ee \ Gale LV -eeeslod olin Mi ors oe T east pe A caer aman xd aoe i ae Dy ee ‘ fi, A Ha 2 * $ 6 + US a cule a: Par ar fh #9 Pi iio leva, ods db Teor ei Sea ‘ols Sana A) i vadont ebtihynd detaes0: bene ban! yecre on Btsilneaon cemarens Spent MELIIIG, 2 ie = Boe-e morrnag % het PLATE I. 2, S. Edin? Vol. 6" P 185. | Simard aude Z Yrans. RS. Edin! Val 6% PISS, Borie. By 77% ain Borax Ser. Carbonate Fig1 0 Re 2 sey rs eee Borax: Silex Siler and bottle glass BORK, Silex Carbonate. Borax. Silex. Silex and bottle glass Borax... Siler and.\ bottle glass \ Silex Silex and bottle glass Borax. Silex. Carbonate... * Borax Siler. Siler and bottle glass | Carbonate. Sitar mn i il Wi “a i CN nL _ I Li I AA th ii i hi ag I IAA HA et a i ACA | HE ATL ot A vl nh TT re IN | : I TT mM | I INU i ITAA a Hh : lh ll a i | ! CI oi i I iin HA wv re Trans. R. 5. Edin? Val 6" P 185 PRR Cee emer, oat. WLS. Lilin” Val. 6° PISS. PLATE IV. Sipoa é eee its —— OG _/ LY -S exsate retelp Trans. RS Edin? Vol. 6° P. 185. ¥ PLATE V. Same ee. nah aS eae ise Bees cz, Lezwis rtd fis all A SS A EO STEREO TET LE LEBEL ID A ETE ED GLE II ETRE Re IV. Of the Sotips of Greatest ATTRACTION, or those which, among all the Souips that have certain Properties, Attract with the greatest Force in a given Direction. By Joun Prayrair, F.R.S. Lond. and Edin. and Professor of Natural Philosophy in the University of Edinburgh. [Read 5th January 1807.] ° a hae inveftigations which I have at prefent the honour of fubmitting to the Royal Society, were fuggefted by the experiments which have been made of late years concerning the gravitation of terreftrial bodies, firft, by Dr Masxutyne, on the Attraction of Mountains, and afterwards by Mr Caven- DIsH, on the Attraction ef Leaden Balls. In reflecting on thefe experiments, a queftion naturally enough occurred, what figure ought a given mafs of matter to have, in order that it may attrac a particle in a given direc- tion, with the greateft force poffible? This feemed an inquiry not of mere curiofity, but one that might be of ufe in the fur. ther profecution of fuch experiments as are now referred to. On confidering the queftion more nearly, I foon found, though - it belongs to a clafs of problems of confiderable difficulty, which the CatcuLus VariaTIonvm is ufually employed to re- folve, that it neverthelefs admits of an eafy folution, and one leading to refults of remarkable fimplicity, fuch as may intereft Vou. VI.—P. II. Aa Mathematicians 188 Of the SOLIDS Mathematicians by that circumftance, as well as by their con- nection with experimental inquiries. In the problem thus propofed, no condition was joined to that of the greateft attraction, but that of the quantity of ho- mogeneous matter being given. This is the moft general ftate of the problem. It is evident, however, that other conditions may be combined with the two preceding ; it may be required that the body fhall have a certain figure, conical, for example, cylindric, &c. and the problem, under fuch reftrictions, may be ftill more readily applicable to experiments than in its moft general form. Tuoucu the queftion, thus limited, belongs to the common method of Maxima and Minima, it leads to inveftigations that are in reality confiderably more difficult than when it is propofed in its utmoft generality. Among the following inveftigations, there are alfo fome that have a particular reference to the experiments On SCHEH ALLIEN. A few years ago, an attempt was made by Lord WEBB SEy- mour and myfelf, toward fuch a furvey of the rocks which compofe that mountain, as might afford a tolerable eftimate of their f{pecific gravity, and thereby ferve to correct the con- clufions, deduced from Dr MasKELYNE’s obfervations, concern- ing the mean denfity of the earth. The account of this furvey, and of the conclufions arifing from it, belongs naturally to the Society under whofe direction the original experiment was made ; what is offered here, is an inveftigation of fome of ‘the theorems employed in obtaining. thofe conclufions. When a new element, the heterogenity of the mafs, or the unequal di- {tribution of denfity in the mountain, was to be introduced into the calculations, the ingenious methods employed by Dr Hurt- ron could not always be purfued. The propofitions that re- late to the attraction of a half, or quarter cylinder, on a par- ticle placed in its axis, are intended to remedy this inconveni- ence, 7 oa — Of GREATEST) ATTRACTION. 189 ence, and will probably be found of ufe im all inquiries con- cerning the difturbance of the direction of the plumb-line by in- equalities, whether in the figure or denfity of the exterior cruft of the globe. Tue firft of the problems here refolved, has been treated of by Boscovien and his folution is mentioned in the catalogue of his works, as’ publifhed im the memoirs of a philofophical fo- ciety at Pifa. I have never, however, been able to procure a fight of thefe memoirs, nor to obtain any account of the folu- tion juft mentioned, and therefore am fenfible of hazarding a good deal, when I treat of a fubjeét that has paffed through the hands of fo able a mathematician, without knowing the conclu- fions which he has come to, or the principles which he has em- ployed in his inveftigation. In fach circumftances, if my re- fult is juft, I cannot reafonably expect it to be new; and I fhould, indeed, be much alarmed to be told, that it has not been anticipated. The other problems contained in this paper, as far as I know, have never been confidered. 8: I. To find the folid into which a mafs of homogeneous matter muft be formed, in order to attract a particle givenjin pofition, with the greateft force poflible, in a given direction, Ler A (Fig. 1. Pl. 6.) be the particle given in pofition; AB the direction in which it is to be attracted; and ACBH a fec- tion of the folid required, by a plane pafling through AB. Since the attraction of the folid is a maximum, by hypothe- fis, any {mall variation in the figure of the folid, provided the quantity of matter remain the fame, will not change the attrac- tion in the direGtion AB. If, therefore, a fmall portion of mat- ter be taken from any point C, in the fuperficies of the folid, ‘and placed at D, another point in the fame fuperficies, there Aa 2 will 190 , Of the SOLIDS will be no variation produced in the force which the folid exerts on the particle A, in the direction AB. Tue curve ACB, therefore, is the locus of all the points in which a body being placed, will attract the particle A in the direction AB, with the fame: force. Tus condition is fufficient to determine the nature of the curve ABC. From.C, any point in that curve, draw CE per- pendicular to AB ; then if a-mafs of matter placed at C be call- 3 ed m', aa will be the attraction of that mafs on A, in the di- m?>X AE rection AC, and AG will be its attraGtion in the direCtion AB. As this is conftant, it will be equal to ao and therefore. AB? -, ora= —— 5 fo that the formula m° r vr = 2m? ‘i aN 2m3_ ri tNnret me above becomes —, ag bs ee 7a Now we may fuppofe m=1, and then the attraction of the posi ie he cylinder = = L(r3+N7° +1). TuHIs Of GREATEST ATTRACTION. 219 Tuts formula vanifhes whether 7 be fuppofed infinitely great or infinitely fmall, and, therefore, there muft be fome magnitude of r in which its value will be the greateft pof- fible. Ir r is very {mall in refpe@ of 1,Vi1+7° = 1 +o and ~6 fo re--va r* = rtn4+5, or fmply = 1+7?. But L (1+73), ifr is very {mall in refpedt of 1, is 735. and there- fore the ultimate value of the formula, when + is infinitely fmall, is 2. x r? = 21, which is alfo infinitely fmall. ’ id AGAIN, let 7 be infinitely great; then V7* +1 = 73}; and fo the formula is = L.2r3, or? ~ 3.27. But the logarithm of an infinitely great quantity 7, is an infinite of ‘an order in- comparably lefs than r, as is known from the nature of logarithms, (Grec. Fontanz Difquifitiones Phyf Math. de Infinito Logarithmico, Theor. 4.)3 fo that 2 Lar is lefs 6 vr? or than : than =. But Cis infinitely fmall, 7 being infinite- ly great, and therefore, when the radius of the cylinder be- comes infinitely great, its folid content remaining the fame, its attraction is lefs even than an infinitefimal of the firft or-’ der. THE determination of the maximum, by the ordinary me- thod, leads to an exponential equation of confiderable difficulty, if an accurate folution is required. -It is, however, eafily found Vou. VI.—P. II. Fe by 220° Of the SOLIDS by trial, that, when the function Su (r3-+NE+47*) is a Therefore, becaufe a = 1 = 25 maximum, r is nearly = : 2, Nir S LoS) 25 ; 6 ; r is nearly to a as F to 30 or as 216 to 1253 and this of con- fequence, is, nearly, the ratio of the radius of the bafe, to the altitude of the half-cylinder, when its attraction, eftimated ac- cording to the ll she of the problem, is the greateft pof- fible. XVII. To determine the oblate fpheroid of a: piven folidity which: fhall attract a particle at its pole with the greateft force.. Let there be an oblate {pheroid generated by the revolution. of the ellipfis ADBE (Pl. 7. Fig. 10.), about the conjugate axis AB, and let F be the focus; then if AF be drawn, and’ the arch CG defcribed from the centre A, the force with. which the fpheroid draws a particle at A, in the direction AC,, 5 At AC .CD* GE: Let this force =F, AC =a, CD=4, the angle CAF=9; Arak a? tan 93 (CF—CG *).. (Macraurin’s Fluxions, § 650).. then CF = a4 tang, and F = (tang—9) a4= 42h tang—o a. tang? — Now if m? be the folidity of the fpheroid, fince that folidity is two-thirds of the cylinder, having CD for the radius of its bafe, * Tue multiplier 27, omitted by Macxuauriy, is reftored as above, 4 X11I. ™ Of GREATEST ATTRACTION. 224 ‘bafe, and AB for its altitude; therefore m3 = 2 xeh X20 3 m3 m?3 ah 3 and2 = 3 =° $a 42a a 47a —4eal; fo tha #= 3 But becaufe AF: AC::1:cofg, or b:4::1:cofg, # = a Sager col g”’ a a cofgo fd 2, Now fince 2? =—“_,, and alfo 3? = age. we have cof @ 47a 2," col @ Sec! and 43 ee Bt oats, or if 3 m3 : = 9; 43 cof? 3 5 7 Arn aoe —me wo aS ? When 9=0, F = react cof 9? 3 3 v ? SSNS, V the folidity m?, as was already fhewn. This laft is the con- clufion we had to expect, the fpheroid, when it ceafes to have any oblatenefs, becoming of neceflity a {phere. Ir is evident alfo, that the variations of g will but little af- fect the magnitude of F, while g and tan 9 are fmall, as the leaft power of tan ¢ that enters into the value of F is the = which is the attraction at the furface of a {phere of {quare. For, inftead of cof. 23, we may, when ¢ is very fmall, write ots eee eee a aen(1+2 tang) (2— — sae tan 9+ a —, &c. ). 7 Ir the oblatenefs of a fpheroid diminifh, while its quantity of matter remains the fame, its attraction will increafe till the oblatenefs vanifh, and the f{pheroid become a fphere, when the attraction at its poles, as we have feen, becomes a maxi- mum. If the polar axis continue to increafe, the {phe- roid Of GREATEST ATTRACTION. 225 roid becomes oblong, and the attraction at the poles again di- minifhes. This we may fafely conclude from the law of con- tinuity, though the oblong f{pheroid has not been immediately confidered. XVIII. To find the force with which a particle of matter is attracted by a parallelepiped, in a direction perpendicular to any of its fides. First, let EM (Fig. 11.), be a parallelepiped, having the thicknefs CE indefinitely fmall, A, a particle fituated anywhere without it, and AB a perpendicular to thé plane CDMN. The attraction in the direction AB is to be determined. Lert the folid EM be divided into columns perpendicular to the plane NE, having indefinitely fmall rectangular bafes, and let CG be one of thofe columns. Ir the angle CAB, the azimuth of this column relatively to AB, be called z, CAD, its angle of elevation from A, e, and m’, the area of the little rectangle CF; then, as has been already cA the attraction of the column CG, in the direction AC, is = AG" - fine; and that fame attraction, reduced to the direction AB, is -. -fine.cofz. This is the element. of the attraction of the folid, and if we call that attraction f, f= a: fine. cof z. Now, if AB =a, becaufe 1: cofz:: AC: AB, AG= =< : fo that f = “. fin ¢ .. cof’. Bur 226 Of the SOLIDS _ Bur BC =a.tanz; and therefore KC, the fluxion of BC, is , eer z ae = 3 if, then, CE =a, m=CExCK =n. =a. and fubftituting this for m’, we get f—n2z. fine. Next, to exprefs fine, in terms of z, if we make E = BAL, the angle fubtended by the vertical columns, when it is great- eft, or the inclination of the plane ADM, to the plane ACN, then we may confider the angle CAD, as meafured by the fide of a right angled fpherical triangle, of which the other fide is go—x, and E the angle, adjacent to that fide, and therefore tane = fin (go — i tanE = cofz.tanE. But tanE = tan. BAL = Bea ? fappofing BL, or CD =. Me fine 2D ‘ THEREFORE tane= = cof z, or =" cof 2. HENCE fine _ 8 cofst, or ants ASD cofz*, and ENC cole a 9 1—fine — a 40 2 , b fne = 2 .cofz? — fine’. 2 cofz?; and therefore fine = Ir this value of fine be fubftituted for it, we have % A bnz col z fanz. fne= ee 2 alr +5 cof z* LE? Of GREATEST ATTRACTION. 234 Der a ee - fin %, then = z cof 2, and cote” =1—x°; where- b nt. avr + 5 av) fore, again, by fabititution, f= bnu fa + F—F u Let a +2, or AL? = i then f o ban bnu fo —F a a oi oo c Ir, therefore, @ be fuch an arch, that : == fin. % a Ss err p SSS eee bnu - Seal Vi—e a = wy ee 7 ———— &- FOG and. VI =) 06 ae A Sa aa Hy es a tou °° | they 8! 23% es ‘Rin Jost isd Janets B being a iJJRUIL Pater quantity... ue adi to aoitssitis axi3 bu 5b $3 ar od " Now, fince fin 9 = rites fin %..@ is nothing when z is nothing ; : and. as f may be fuppofed to begin when z begins, we have likewife B=o03 and a2 ? =». multiplied into an arch, the fine of which i is to the fine of, .%, in.the given ratio of ¢ to = sit — 2 BG. BRA Ba ee is fuch that = find = 2 * AG = AL™ AG: Vor VIP ne 8 pee an -— Muttipry \ 228 Of the SOLIDS Hence this rule, multiply the fine of the greateft elevation, into the fine of the greateft azimuth of the folid ; the arch of which this is the fine, multiplied into the thicknefs of the fo- lid, is equal to its attraction in the direction of the perpen- dicular from the point attracted. Tue heighth and the length of the parallelepiped, are, there- fore, fimilarly involved in the expreflion of the force, as they ought evidently to be from the nature of the thing. XIX. Tus theorem leads directly to the determination of the at- traction of a pyramid, having a rectangular bafe, on a particle at its vertex. For if we confider EM (Fig. 11.) as a flice of a pyramid parallel to its bafe, A being the vertex, then the flice behind EM fubtending the fame angles that it does, will have its. force of attraction = 7 ¢, n' being its thicknefs, and fo of all the reft; and, therefore, the fum of all thefe attractions, if p denote the whole height of the folid, or the perpendicular from A on its bafe, will be pg. But as 7@ is only the attraction of the part HB, it muft be doubled to give the attraction of the whole folid EM, which is, therefore, 2” 9; and this muft again be doubled, to give the attraction of the part which is on the fide of AB, oppofite to EM; thus ‘the element of the attra@tion of the pyramid is 4'7 , and the whole attraction oe to the depth pf, is 4 pig OU Ir the folid is the frudum ofa pytamid Ae depth i is p! ; ane vertex A, the angle ¢ being determined as before, the attraction on A is 479. Ir Of GREATEST ATTRACTION. 229 Ir we fuppofe BC and BL to be equal, and therefore the angle BAL = the angle BAC, calling either of them 2, then fin @ = fin 7, by what has been already fhewn ; and from this equation, as 4 is fuppofed to be given, ¢ is determined. Tus expreflion for the attraction of an ifofceles pyramid, having a rectangular bafe, may be of ufe in many computations concerning the attraction of bodies. Ir the folidity of the pyramid be given, from the equations f=4/ 9, and fin g = fin 7’, we may determine 2, and , that is, the form of the pyramid when f is a maximum. Ler the folidity of the pyramid = m3, then , being the al- titude of the pyramid, and half the angle at the vertex ptany= half the fide of the bafe, (which is a fquare), and _ therefore the area of the bafe = 4 p* tan 7, and the folidity of the pyramid 3 p3tany ; fo that ¢ Pitan, = m3, Now tan 7? = ine, and fin @=fin 7’, alfo 1 — fin o= fin @ 1 —fin 7 = cof’, therefore tan 77 = ———*— é I1—fng 3 fo that m= 4 p3 fin and p3 ia 3, 5 3° ° 1—fn?’ 4 fag? he? fue m/f see, we have, therefore, f, that is 499 = 9/30 Ee AP 0): This lat is; ther amo i/ 5 ra This laft is, therefore, a maximum Ef 2 by 230 Of the SOLIDS by hypothefis ; and, confequently, its cube, or 64 m3 93 x 3 —fing) oy omitting the conftant multipliers, g?. 1 ing 4 fin g fin g muft be a maximum. Ir we take the fluxion of each of thefe multipliers, and di- vide it by the multiplier itfelf, and put the fum equal to no- p cof > cot thing, we fhall have, y “aoe oR aie ce 2 = Oe cof 9 cofp _ cof. fing + cof — cof. fing 1—fing fin 9 fin 9 (1 — fin 9) cof . : 3 in @ GQ — fin ¢)’ set inverting thefe fractions : fin 9 (1 —fin 9) = tane(1— fing), or p= 3tane(1—fing). col ¢ Tue folution of this tranfcendental equation may eafily be obtained, by approximation, from the trigonometric tables, if we confider that 1 —fin¢ is the coyerfed fine of g Thus taking the logarithms, we have Lp =L.3+ L.tane+L.coverf. ¢. From which, by trial, it will foon be difcovered, that ¢ is nearly equal to an arch of 48°. To obtain a more exact va- ine of 9, let ¢= arc (48° +6), B being a number of mi- nutes to be determined. Becaufe arc. 48° = .8377580, and arc (48° + 8) = .8377580 + .0002909 B, therefore log. arc (489 + 8) = 9.9231186 + .0001506 @. In Of GREATEST ATTRACTION. 231 In the fame manner, Ltan (48° +8) = 0.0455626 + .0c002540 £, and L. coverf. (48° + 8) = 9.4096883 — .0003292 B L3-= 0.4771213 Sum = 9.9323722 — .0000752 6B Subtract Log arc (48° +8) = 9.9231186 + .o001506 8 Remainder = .0092536 — .0002258 B=o. — 92536 _ yy Whence, 6 = ce ag 41’ nearly. A SECOND approximation will give a correction = — 20’, fo that ~ = arc . 48°. 40’ os and fince fing = fing’, fing — N fin g, fo that 7 => 76°. 30’, and 2, or the whole angle of the pyramid = 153°. An ifofecles pyramid, therefore, with a fquare bafe, will at- tract a particle at its vertex with greateft force, when the in- clination of the oppofite planes to one another is an angle of 153°. XX. To return to the attraction of the parallelepiped, it may be remarked, that the theorem concerning this attraction already inveftigated, § xvi11. though it applies only to the cafe when the parallelepiped is indefinitely thin, leads, neverthelefs, to fome very general conclufions. It was fhewn, that the attra@tion which the folid EL (Fig. 11.) exerts on the particle A, in the di- rection AB, is 7.9, @ being an arch, fuch that fing = fin BAC x fin BAL = fin z.fin E; and, therefore, if B be the centre of a 232 Of th SOLIDS a rectangle, of which the breadth is 2 BC, and the height 2 BL, the attraction of that plane, or of the thin folid, having that plane for its bafe, and 2, for its thicknefs, is 47.9. Now, 9, which is thus proportional to the attraction of the plane, is al- fo proportional to the fpherical furface, or the angular {pace, fubtended by the plane at the centre A. For fuppofe PSQ_ (Fig. 12.) and OQ_ to be two quadrants of great circles of a fphere, cutting one another at right angles in Q; let QO9=E, and QR=z. Through S, and O the pole of PSQ; draw the great circle OST, and through P and R, the great circle PTR, interfecting OS in T. The fpherical quadri- lateral SQRT, is that which the rectangle CL (Fig. 11.) would fubtend, if the {phere had its centre at A, if the point Q was in the line AB, and the circle PQ; in the vertical plane ABL. Now, in the fpherical triangle PST, right angled at S, cof T = cof PS x fin SPT = fin QS X fin QR = fin EX fin z. ~ But this is alfo the value of fin ¢, and therefore ¢ is the complement of the angle T, or g=90—T. Burt the area of the triangle PQR, in which both Q and R are right angles, is equal to the rectangle under the arch QR, which meafures the angle QPR, and the radius of the fphere. Alfo the area SPT =arc.(S+T+P—180°)73 that is, be- caufe S is a right angle, = arc.(T + P — 90) Xr = arc. (T+QR—go) Xr; and taking this away from the triangle PQR, there remains the area QSTR = arc.(QR —T—QR +90°)Xr=(g0—T)r=9xr. Thearch 9, therefore, mul- tiplied into the radius, is equal to the fpherical quadrilateral QSTR, fubtended by the rectangle BD. Tus propofition is evidently applicable to all rectangles whatfoever. For when the point B, where the perpendicular from A meets the plane of the rectangle, falls anywhere, as in Fig. 15. then it may be fhewn of each of the four rectangles BD, Of GREATEST ATTRACTION. 233 BD, BM, BM’, BD’, which make up the whole rectangle DM’, that its attraction in the direGtion AB is expounded by the area of the fpherical quadrilateral fubtended by it, and, therefore, that the attraction of the whole rectangle MD’, is expounded by the fum of thefe f{pherical quadrilaterals, that is, by the whole quadrilateral fubtended by MD’. In the fame manner, if the perpendicular from the attracted particle, were to meet the plane without the reGtangle MD’, the difference between the {pherical quadrilaterals fubtended by MC and M’C, would give the quadrilateral, fubtended by the rectangle MD’, for the va- lue of the attraction of that rectangle. ‘ THEREFORE, i in general, if a particle’ A, gravitate to a rec- tangular.plane, or to a solid indefinitely thin, contained between. two parallel rectangular planes, its gravitation, in the line per- pendicular to those planes, will be equal to the thickness of the solid, ‘multiplied into the avea of thespherical quadrilateral sub- tended by either of those planes at the centre A. Tue fame’ may be extended. to all planes, by/whatever figure they be bounded, as they may all be refolved into rectangles of indefinitely ‘fimiall breadth,’ and hier vee nae ie ceri i to! a ftraight line givenbin pofition. ' oTHe: gravitation’ ‘ofa point toward any’ yrphslee 2 in'a fine: per- pendicular tovit; is, therefore, equal-to n, a quantity that ex- preffes the-inténfity of ‘the attraction, multiplied into the area of the ‘fpherical! figure, . ory as “it” a be called, the’ angular {pace fubtendedvby: ‘the givensplane: I Tuus, in the cafe of a triangular pli eae Ais angles fubtended at A, by the fides of the triangle, are a, } and c; fince Evter has demonftrated * that the area of the fpherical triangle contained by thefe arches, is equal to the re@tangle un- Pe: der Q -qerzt t i t * Nov. Ada Petrop, 1792, p. 47. 234 Of the SOLIDS 1 der the radius, and an arch A, fuch that’ cof : A pL aah ae ©; if A be computed, the attraction 4colta.cofté. cof + ha DN In the cafe of a circular plane, our general propofition agrees with what SirIs aac NewrTon has demonftrated. IfCFD (Fig. 13.) be a circle, BA a line perpendicular to the plane of it from its centre B; A, a particle anywhere in that line; the force with which A is attracted, in the direction AB, is 29 G-s ane *, in which the multiplier 2 7 is fupplied, being left out in the inveftigation referred to, where a quantity only proportional to the attraction, is required: ‘Now. AD! is the cofine of, the, angle BAD, and, theréfore, 1 01 AEB 29 is its ebb fine § and, AD therefore, if the arch:GEK. be deferibed. FiO the centre. Asi with the radius 1, and if the fine, GH, andthe. chord,-EG: be: drawn, HE is the -verfed fine: off BAD, and the attraction =27EH.. But 2.EH = EG’, becanfe 2 is the diameter of the circle GEK ; therefore the attraction = x. EG? = the area of the circle of which EG is the radius, or the f{pherical furface) included by the’ cone, which hasiA for ‘its Magee and. the circle CFD. for its bafe. to : {3 i lev XXI. * Princip, Lib. i. Prop. go. Of GREATEST ATTRACTION. 235, XXI. From the general propofition, that the attraction of any plane figure, whatever its boundary may be, in a line perpen- dicular to the plane, is at any diftance proportional to the angular f{pace, or to the area of the f{pherical figure which the plane figure fubtends at that diftance, we can eafily deduce a demonftration of this other propofition, that whatever be the figure of any body, its attraction will decreafe in a ratio that approaches continually nearer to the inverfe ratio of the {quares of the diftances, as the diftances themfelves are greater. In other words, the inverfe ratio of the fquares of the diftances, is the limit to which the law by which the attraGtion decreafes, continually approaches as the diftances increafe, and with which it may be faid to coincide when the diftances are infi- nitely great. Tuis propofition, which we ufually take for granted, with- out any other proof, I believe, then, fome indiftin& perception of what is required by the law of continuity, may be ri- goroufly demonftrated from the principle juft eftablithed. Let B (Fig. 14.) be a body of any figure whatfoever, A a particle fituated at a diftance from B vaftly greater than any of the dimenfions of B, fo that B may fubtend a very {mall angle at A; from C, a point in the interior of the bedy, fup- pofe its centre of gravity, let a ftraight line be drawn to A, and let A’ be another point, more remote from B than A is, where a particle of matter is alfo -placed. Tue directions in which A and A’ gravitate to B, as they muft tend to fome point within B, muft either coincide with AG, or make a very {mall angle with it, which will be always the lefs, the greater the diftance. Vou. VI.—P. II. Gg Ler 236 - Of the SOLIDS Let the body B be cut by two planes, at right angles to AC, and indefinitely near to one another, fo as to contain between them a flice or thin fection of the body, to which A and A’ may be confidered as gravitating, nearly in the direction of the line AG perpendicular to that fection. » THE gravitation of A, therefore, to the aforefaid fection, will be to that of A’ to the fame, as the angular fpace fubtended by that feGtion at A, to the angular fpace fubtended by it at A’. But thefe angular fpaces, when the diftances are great, are in- verfely as the fquares of thofe diftances, and therefore, alfo, the eravitation of A toward the fection, will be to that of A’, in- verfely as the {quares of the diftances of A and A’ from the fection. Now thefe diftances may be accounted equal to CA and GA’, from which they can differ very little, wherever the feétion is made. THE Feast of A and A’ toward the faid fection, are, I act “we the gravitation to all the other fections, or laminz, into which the body can be divided by planes perpendicular to AC; there- fore the fums of all thefe gravitations, that is, the whole grayi- tations of A to B, and of A’ to B, will be in that fame ratio, therefore, as — And the fame may be proved of that is, as —~> or inverfely as the fquares of the di- I act RIC? ftances from C. Q.E.D. Ir is evident, that the greater the diftances AC, A'C are, the nearer is this propofition to the truth, as the quantities rejected in the demonftration, become lefs in refpect of the reft, in the fame proportion that AC and A‘C increafe. Ir is here aflumed, that the angular {pace fubtended by the fame plane figure, is inverfely as the fquare of the diftance. This Of GREATEST ATTRACTION. 237 This propofition may be proved to be rigoroufly true, if we confider the inverfe ratio of the fquares of the diftances, as a limit to which the other ratio conftantly converges. Ir is a propofition alfo ufually laid down in optics, where the visible space fubtended by a furface, is the fame with what we have here called the angular space {fubtended. by it, or the portion of a fpherical fuperficies that would be cut off by a line pafling through the centre of the fphere, and revolving round the boundary of the figure. The centre of the {phere is fuppofed to coincide with the eye of the obferver, or with the ree of the particle attracted, and its radius is fuppofed to be nity. Tue propofitions that have been val now demonftrated con- cerning the attraction of a thin plate contained between paral- lel planes, have an immediate application to fuch inquiries concerning the attraction of Me as were lately made by Mr CAVENDISH. In fome of the experiments inftituted by that ingenious and profound philofopher, it became neceflary to determine: the at- traction of the fides of a wooden cafe, of the form of a parallel, epiped, on a body placed anywhere within it. (Philofophical Tranfactions, 1798, p. 523.). The attraction in the direction perpendicular to the fide, was what occafioned the greateft dif- ficulty, and Mr Cavenntsu had recourfe to two infinite feries, in order to determine the quantity of that attraction. The de- termination of ‘it, 45 ae Bea eae is eafier and more accurate.’ Let MD’ (Fig. 15.) seplunene a thin rectangular plate, A, a particle attracted by it, AB a perpendicular on the plane MD’, NBC, LBL’, two lines nce through B parallel to the fides of the rectangle MD’. Let AC, AL, AN, AL’, be drawn. Gg 2 wake THEN, 238 Of the SOLIDS THEN, if we find 9 fuch that fin g = oe x = the attrac- AL" AC tion of the rectangle CL is 7. p, n denoting the thicknefs of the plate. ; _. BL |, BN ‘ vali So alfo, if fing =a * AN’ the attraction of LN is = 2.Q. Ir fing’ = a x oer the attraction of NL’ is = 2. 9’. Lastriy, i ine? = = x ao the attraction of L‘'C = ee ie Tuus the whole effet of the plane MD’, or f = n(ote+eo+ ?”). WE may either fuppofe ¢, ¢ &c. defined as above, or by the following equations, where 7, 7', 1’, &c. denote the angles fub- tended by the fides of the reCtangles that meet in B, beginning with BC, and going round by L, N and L’ to C. fine = fing .finy’ fine’ = fin, .finy’ fin 9? = fin,’ . finn” fin Q” = fin n . fin y. Ir the computation is to be made by the natural fines, it will be better to ufe the following formule : fin = cof (1 —1)—Scof(n +2’) fing = Leof (x — xf) —2 cof Gr! +9”) fin 9” Of GREATEST ATTRACTION. 239 fing’ = = cof ( 1" — n”) — = cof (n'+ 2”) fin oN = = cof ("— 1 ) = - cof ("++ 4 ve By either of thefe antehods: the determination of the attrac-. tion is reduced to a very fimple trigonometrical calculation. XXII. THE preceding theorems will alfo ferve to determine the at- traction of a parallelepiped, of any given dimenfions, in the di- rection perpendicular to its fides. Let BF (Fig. 16.) be a parallelepiped, and A, a point in BK, the interfection of two of its fides, where a particle of matter is. fuppofed to be placed; it is required to find the attraction in the direction AB. . Tuoucu the placing of A in one of the interfections of the. planes, feems to limit the inquiry, it has in reality no fuch ef- fect ; for wherever A be with refpect to the parallelepiped, by drawing from it a perpendicular to the oppofite plane of the fo- lid, and making planes to pafs through this perpendicular, the whole may be divided into four parallelepipeds, each having AB for an interfection of two of its planes; and being, there- fore, related to. the given particle, in the fame way that the: parallelepiped BF is to A. Let GH be any fection of the folid parallel to EC, and Iet it. reprefent a plate of indefinitely fmall thicknefs. Let AB =x, B%é, the thicknefs of the plate =%. Then 9 being fo determined, that fin 9 = fin BAH x fin BAG, the at- graction of the plate GH is 9%, which, therefore, is the ele- ment 240 Of the SOLIDS ment of the attraGtion of the folid. If that attraction =F, then F= (0%. But for=on— fre; and the determi- nation of F depends, therefore, on the integration of x Q. Now ¢cofg= fin Q, and, therefore, x ¢= core eG Taner ica BAG —%, —P-) AGT Ngo x heey sv ey IRA a and fin B'AH = —~ = —~———; fo that fing = —— x AH NB? x? Nag + x" @ a Bp Nepe ? = FE ee Fe) Hence, colo = 1—fing’ =1 0 os 10. iB straint ta Gr) FF) me (e+e+ x) ne as at aNGEe fx’ Grey CRY O= VGaN CP Acain, becaufe ‘a pe at cop eg pee NP Ext NOx (2 ++ x)? x Bliss ag hill x uti att) +e) +e) Gtx fi : HENCE mate or oO '= (ee a) +e x@t+xy C+! xGt+e? " x Of GREATEST ATTRACTION. 241 GEA e+e bak % aN OPER Ex a a) (ct x’)? bps Frere. ate: x Cc x THEREFORE x9 = — i AS me (+ x") (e+ a bBxx . (@° + x") (c* + x)? Now, -——""** __ =Yipa eit 4 C; O+e) C+) Nie (Harmonia Menfurarum, Form. 1x.) ; and ah itll tea (B°-+-x") (c’-+- x*)* DENG x &K Lo J 8 Log Nae +C THEREFORE fe o— eR pte + x" L EB4+Ne*+ x? Cc =e NB + x eae N BE x? “a ,and foe = BENct+ x" b4+NC4 x7 | x — b Log —__— — . Log —+____!—. — C, ? 8 NPEx B 8 N BF x? Ir, then, we determine C, fo that the fluent may begin at K, and end at B; if, alfo, we make » the value of 9, that corre- fponds to AB or 4; and 7’, the value of it that correfponds to AK 242 Of the SOLIDS AK ora’, we have the whole attraétion of the folid, or F = B4+Ne+a y No + a" NG-a B+Ne+a" b4+NC4+a - Vea ( Ve + a" b+Vcipa" 2a—2a —b Log — p Log Ir, in this value of F, we invert the ratios, in order to make the logarithms affirmative, and write like quantities, one under the other, we have F= 7a — 7a’ G+-VE +a" _ Ve+a 6L Ss a = SSS i 0g B+%o4+a x VO +a“ b+No+a*, NB +a b4+NG4a ve pa + @ Log Tue firft two terms of this expreflion deferve particular at- tention, as is an arch, fuch that fin, = fin BAE x fin BAC; therefore, by what has been before demonftrated, 4 is the mea- fure of the angular {pace fubtended at A by the rectangle BD. The firft term in the value of F, therefore, is the product of the diftance AB, into the angular fpace fubtended by the rec- tangle BD. In like manner, the fecond term, or 7a’, is the product of the diftance AK, into the angular {pace fubtended by the rectangle KF. Tue relation of the quantities exprefling the ratios, in the two logarithmic terms, will be beft conceived by fubftitu- — ting for the algebraic quantities the lines that correfpond to them in the diagram. Becaufe ci = J°+ = EB* + BC Of GREATEST ATTRACTION. 243 BC’ — EC’, therefore c= EC or BD. So alfo, c+ a= BD’ + BA* = AD*%, becaufe ABD is a right angle, &c. Thus, (AF+EN)AE | (AD + DE) (AN (AF + FM) AC (AD + DC) AM" Fo>=,a—7a4+BE. Log BC. Log Tuts expreffion for the attraction of a parallelepiped, though confiderably complex, is fymmetrical in fo remarkable a de- gree, that it will probably be found much more manageable, ' in inveftigation, than might at firft be fuppofed. That it fhould be fomewhat complex, was to be expected, as the want of con- tinuity in the furface by which a folid is bounded, cannot but introduce a great variety of relations into the expreflion of its attractive force. The farther fimplification, however, of this _ theorem, and the application of it to other problems, are fubje@s on which the limits of the prefent paper will not permit us to enter. The determinations of certain maxima de- pend on it, fimilar to thofe already inveftigated. It points at the method of finding the figure, which a fluid, whether elaftic or unelaftic, would affume, if it furrounded a cubical or prifma- tic body by which it was attracted. It gives fome hopes of be- ing able to determine generally the attraction of folids bound- ed by any planes whatever ; fo that it may, fome time or other, be of ufe in the Theory of Chryftallization, if, indeed, that theory fhall ever be placed on its true bafis, and founded, not on an hypothefis purely Geometrical, or in fome meafure arbi- trary, but on the known Principles of Dynamicks. Vox. VL—P. IL. Hh Vv. asi Meaaaas ine I ee WORT ONAT Bey seat fo. AS ve x "Se hh 0%, © a : wT 8 clans Bigs cee sod, tae Pie ~ ee iy ee ee ban Bi 14) Pe eabe 15'S 4 Dt gol. Oa ae é digaotis Soqiqstolinasg OEE aul act fvoiBangis) fT ae _, sob “a oldinduseor oh. ot Inotiseniun yt el. ralqatos xldetabagos ms olds gerinan' stom Hourr-bauot sd eldedorg Hiw ‘ti tort ostg bivodt si sed T -bstogqrit ad fir}. 3s idgisn aeds woitegilovai ai -1109 to inew olan. cbosqxs [ad 03" enw .xelqaroa seclwomiot od - ud jonags ;bobauod ei dilok-e doide yd « somtul ods ot inn aii to noille x9 ol} 03 digaia m at Magee nt. aids Yo ava : | -odT voxdt ovilbortse a. sus gurldorg 191 a bilqq: od bas oe : son, Siw saqag testeiq odds od - eam ods atk 10 eRajdat con 9b wnwisan aiezise to ie dittiayob oft roi ‘aeuaniod 21. abpagifioy it, e < Lore: x aa " : aay SIE ; Ah rer % 2 , i i eae aint vit Siti - re ey Latei> te hae: Bingeore, se OP ng H/o Tra RS Ldn’ Fol VW page 220. \ es ra] HH “4 = toa ey net Mb 0% Drans RS Kdin VAT page PLATE VIL V. An Account of a very extraordinary Eject of Rerrac- TION, observed at Ramsgate, by the Reverend S. Vince, . A.M. F.R.S. Phounian Professor of Astronomy and Ex- perimental Philosophy at Cambridge. Communicated by Parrick Witson, Esq; F. RS. Epin. [Read 5th January 1807.| is £ if, HE: phenomenon about to be defcribed, was feen on. Aus guft 6. 1806, about feven in the evening; the air being very ftill, and a little hazy. The tops of the:four turrets: of Dover Caftle ufually appear above the hill, lying. between Ramfgate and Dover; but, :at the above-ftated time, not only the tops were vifible, but the whole of the Cattle, appearing as if it were fituated on the fide of the hill next to peng and. rifing as much above the hill as ufual. , Let, AB (Plate VIII. Fig. 1.), reprefent the termination Be the hills v, x, W,y, the tops of the four turrets of the Caftle, as they ufually appear. - But, at the time above mentioned, befides thus feeing the turrets, the whole Caftle mr s was vifible, and aps peared as if it had been brought over and placed onthe Ramfgaté fide of the hill, as|reprefented inthe figure. This! phenomenon was' fo. very fingular and unexpected, that, at firft fight, I thought i it to be fome illufion ; but, uponicontinuing my obfer- Hh2»: Ot vation, « 38! 246 EXTRAORDINARY EFFECT vation, I was fatisfied that it was a real image of the Caftle. Upon this I gave the telefcope to a perfon. prefent, who,.upan attentive examination, faw alfo a very clear image of the Caftle, exactly as I had defcribed it. He continued to obferve it for about twenty minutes, during which time the appearance re- mained precifely the fame; but rain coming on, we were pre- vented from making any further obfervations. Between us and the land; from which the hill rifes, there was about fix miles, of} feay:and fromthence'to the top of the hill about the fame diftance, and we were about) feventy feet above, the fur- face of the water. Tne hill itfelf did not appear through the image, which, it might have been expected to do. The image of the Caftle ap- peared very ftrong, and well defined; and although the rays from the hill behind it, muft undoubtedly have come to the eye, yet fo it was, that the ftrength of the image of the Caftle fo far obfcured ‘the back-ground, that it made no fenfible im- preffion upon us. Our attention was of courfe principally di- rected to’ the image of the Caftle ;. but if the shill’ behind had been: at all vifible, it could not haveefcaped our obfervations as wei continued to look at it for a confiderable time <7 a. good telefcope. liliv stow atjoa ads (A PHENOMENON asf this kind I do ‘not remember to have feen defcribed; and it muft have been ‘a? very extraordinary’ ftate of the air to have produced it. ‘'Itis manifeft, that! a ray of light coming from the ‘top of the°hill, muft have come to the eye iia curve lying between the 'two curves deferibed by the rays coming from the:top and bottom of the Gaftle; in or- der to produce the effete: 900 Shyu eat BS oe . Ler AB! (Platé VIM. Figs:2.) repretent the Cattle; ‘EG the! Cliff (at Ramfgate), BTD the Hill, ‘DC the Sea, E the place of the {pectator, Tothe top of the hill) AywE? a ray of light coming from the top of the Caftle to the fpectator, Bewk 44 Rt ay ~ of REFRACTION. 247 BawE a ray coming from the bottom, and TxzE a ray coming from the top of the hill, falling upon the eye at E, in a direction between thofe of the other two rays; then it is manifeft, that fuch a difpofition of the rays will produce the obferved appearance. To elect this, there muft have been a very quick variation of the denfity of the air which lay be- tween the two curves y v E, x w E, fo as to increafe the curva- ture of the ray TxzE, after it cuts BwE in x, by which means, the ray T x z E, might fall between the other two rays. The phenomenon cannot be otherwife accounted for. As there are not, that I know of, any records of a phenomenon of this nature, the conftitution of the air muft have been fuch as but very rarely happens, or fuch an appearance would before have been taken notice of. THE phenomena which I faw at the fame place, and which I defcribed in the Philofophical Tranfactions of the Royal So- ciety for the year 1798, I explained upon the fame principle, that of a quick variation of denfity; and this was afterwards confirmed by fome very ingenious experiments made by Dr Wo.t.aston. Perhaps this phenomenon may afterwards be fubjected to an experimental illuftration. VI. ~~ ee f "if A, , tits pe AaPy' , i Oe a z Mt . 4 a | 2 i & Pe ON a AO eae ae ae eA wee 7 2 PAMOVTONNRRAL Bot; i 7RaieRs goqe Qeilish hi ie cast south | ger awd tadag ods 16 ea) he woikoSitiis Wi esabtag Min’ eget oft RocnoisRoepib wdou). 20:19. Siesta pereciade rho ie eG sSanmitegqa baniide sds od gad brerves, : oyiiteeb onda to cowspiaay Lapsed ab St ish in As pean ows ail gps wa - pied ab asits ba (Be suis arks Aosisryh - “eet poi aun ob ta a ‘ neh ies an Hk, Ae Re RE OL ie teary are’ BO! rabies ev igees Shai fet cate thd: BUA! CY ogee iSeest! has aha oA ty - she ote Levies iia its eel ett iw, thine: oR wie wa diene in ‘ “tly: 4 vii the Hid ts Pati derhas “t os nape ian Sheba Meola ips Cadre dir We hie ae a Ho hia aati dagpesce: Hk apt ch aga or sate Ree date! * Ae able ante jas agg: fey peta ar Be “tha. SSP Snag: re Wake Gay - on fA HDs Spee BES rhe Saat as 3 ak Mite (resists. Bee vu ee Ube iii, sav 2IY 2 ay ey? SR powag: Krom si crepe iat, the aie ey int ear Hs Ries ee A al Lraus RS Eda Vol VE pe. 248 Pirare VIL = = Ht Hr IAN UF an : 3 i : AI a ae D.Lizars feulpt VI. Some Account of the Large Snake ALEa-azacur, (Boa Consrrictor of Lannxvs), found in the Province of Tipperah. Communicated by Mz James Russewt. Ex- tracted from the Memorandum Book of Joun Coisz Scort, spin [Read 28th April 1807]. wf een 1. 1787. Lance, OAS of this fpecies, was: brought to Comillah. ‘It meafured 15 feet. 3 inches in.length, and 18 inches in pea stir about the middle. This: meafurement, however, waried confiderably by the, wreathings: and contortions it made, in order to free itfelf from confinement. 9 _ -TueEcefophagus, from. the mouth: to the pylorus, or bottom ae the ftomach, meafured altogether 9 feet'3 inches,and was fo wide as to take in a man’s. head with ‘eafe: The ftomach was eafily, diftinguithed “bythe thicknefs of its coats, or the number of rug on its internal forface.;, But-there was»no contraction, at the, cardia or, entrance of the fomach.»: The outlet or pylo- Tus, however, was fo narrow.as hardly to admit two fingers. hBEb head of the fhake was {mall.in proportion to its body.. And. -I was. curiops, to obferve. the mechaniifm of the j Jaw, by which it; can, {g eafily take into.its mouth ally. pes as oan as the thickeft part of its Pedy. poor THE 250 ACCOUNT of a LARGE SNAKE. Tue lower jaw confifts of two bones, connected anteriorly by 38 the anterior ends can be feparated an 1 inch from each other. The pofterior extremity, or condyle of each lower jaw- bone, is likewife connected, to the head in fuch.a manner, as to “allow! of confiderable fepar ation. The two bones which com- ‘\pol'the! upper jaw) ure capable only of a yery fmall degree of - feparation at the {ymhphifis or’ anterior part. . Durs-fingulan degree oft laxity ‘in the ftru@ure of ‘the arti- culations, permits of a degree of diftenfion which is’ incompa- cible with the firmnefs requifite to perform the function of ma- ftication. July 7. 1790. A sNAKE of the allea {pecies was brought in, of a very un- common thicknefs in proportion to its length, which induced me\to open it. A very large guana was extracted from the gullet.and ftomach:;: for’the "animal was gorged to the throat. ‘The guana, from the nofe to the tip of the tail, meafured 4 feet 3 inches, and in circumference round the belly 1 foot 6 inches and yet the :fnake; after: the guana was taken out; meafured only 8 feet 6 inches im length. ©) ~ > EOF FOES Ee _ Tue circumference of this fnake is not given ; ‘but if it’ bore the fame -proportion to its: length that it did in’ the former fnake, it would be nearly 10 inches. In this inftance, there- fore, the fnake had fwallowed ‘an animal of Sire magnitude than itfelf almoft im the proportion of 9 to 5. ‘On the 16th of the fame month another fnake was brought in, having nearly the {ame appearance as the laft, but ftill more diftended. It was opened while yet alive, and an entire fawn of one year old extracted. The fawn meafured 1 foot 8 inches round the belly ; and the extreme rei ag of the ae was only g fect 3 inches. “April ACGOUNT of a LARGE SNAKE. 250 April 5. 1791. A snake of the fame fpecies was brought to Comillah and opened, from which a fawn was taken ftill larger than the one juft mentioned ; but the fnake was 10 feet 6 inches in length. Ir is the general opinion, that fnakes break the bones of their prey before they {wallow it, if the animal be of any confi- derable fize. This, however, I am difpofed to doubt, as in none of the above inftances had the animal fuffered fuch offifraction, if I may be allowed the expreflion. The mechanifm of the jaws, and the width of the gullet above defcribed, render fuch violence unneceflary. THE animal is fwallowed very gradually, being firft, I fu- fpect, well lubricated with flime, with which this kind of large. fnake appears abundantly provided. THESE circumftances may undoubtedly be deemed rather fa~ bulous by thofe who have never feen nor examined large {nakes. But they are facts not to be denied, and are well authenticated by every one who has had opportunities of feeing and opening fuch {nakes. Durine Mr Lecx1e’s refidence at Comillah, I have learned from undoubted authority, that a fnake of the above mentioned fpecies was found dead, with the horns of a large deer fticking in his throat, fuppofed to be the caufe of his death. The f{nake: and the horns were both brought to Comillah in this fituation ; but in a putrid ftate. The fnake meafured above 17 feet in tength; and the bones of it were afterwards fent to Mr Cuar_es Continson of Banleak. VoL. VI.—P. II. I i VILE.. i a ke Rireybivt fits" ¢ aoctey pais eee ee ‘Si AUT Rey be: eu Fe Arent AOR AS each. pee chips er is ony Ah “Nie - ona) ath bes cs sabainteads aie ‘deseo st 0 aM ati cabs oneal) ogee NTR tose nee Ae TETRA Babe» ‘eeala grea ai Sag aes eee sient 1 zante oth sawed s |) De yeas Se i eet aie lab anananaratee ba" driss bswolial segues F ri y - Bore thera ag ‘pits 16° Habjtevsds: baw wewey ets aor ie he: sth im fs ind fa gaits, as esl oytal toto widls dolubve alsin Sanit diy seein a 2a rs AEA iat it: Beier ¢ Broiagst Niner nti a bits obey ane nat core “ababtivett 18" (A oagigeonbe mata dani Octal tesla WB > Agave > Reel abt AeA Oh EE: pre U an 2 eet ive. 1h Le a ie 4 Sm iit, ste 4.’ VII... Chemical Analysis of a. BuAck, Sanp, from the River » Dee in Aberdeenshire ; and of a CoprEr:Orxe, from Ar- threy in Stirlingshire. By Tuomas Tuomson, M.D. * Lecturer on Chemistry, ‘Edinburgh. [Read 18th May 1807.] HE fpecimen which formed the fubject of the firft of the following analyses, was brought from the banks of the river Dee, about feven years ago, by my friend Mr James Mitt, who at that time refided in Aberdeenfhire. By him I was informed, that confiderable quantities of it are found in different parts of the bed of that river,—that it is called by the inhabitants zron- ‘sand,—and that they ufe it for fanding newly written paper. I tried fome experiments in the year 1800, in order to afcertain its nature} but’was ‘too little fkilled at that time, both in mi- netalogy and praétical chemiftry, to manage an analyfis of any confiderable difficulty. ’ "Tue black’ powder is mixed with a good many fmall whitith, reddifh, and brownifh grains, which, when examined by means of a glafs, prove to be pieces of quartz, felfpar, and mica. From this it would appear, that the fand of the river Dee confifts chiefly of the detritus of granite or gneifs. > ‘WHEN a magnet is pafled over the fand, fome of the black grains adhere to it, and are by this means eafily obtained fepa- Ts2 rate. 254 ANALYSIS of a BLACK SAND rate. But after all that can be attracted by the magnet is re- moved, the greater part of the black powder ftill remains. This refidue is indeed attracted by a powerful magnet, but fo very feebly, that it is not poffible by means of it to feparate it from the grains of fand with which it is mixed. Thus we learn, that the black matter confifts of two diftiné fubftances; one of which is powerfully attracted by the magnet, the other not. As this fecond fubftance was obvioufly f{pecifically heavier-than the grains of fand with which it was mixed, I placed a quanti- ty of the powder on an inclined plane, and by expofing it cau- tioufly, and repeatedly, to a jet of water, I fucceeded in wafhing away moft of the grains of fand, and thus obtained it in a ftate of tolerable purity. Tue firft of thefe minerals we may call iron-sand, and the fecond iserine, as they belong to mineral fpecies which oryc- tognofts have diftinguifhed by thefe names. I, IRON-SAND... st uods 931 THE iron-fand is much fmaller in quantity than the iferine, and does not exceed one-fourth of the mixture at moft. Its co- lour is iron-black. It is in very {mall angular grains, common- ly pretty fharp-edged, and fometimes having the fhape of im- perfect octahedrons. The furface is rough; the luftre is feebly glimmering and metallic; the fracture, from the fmallnefs of the grains, could not be accurately afcertained, but it feemed to be conchoidal. Opake, femihard, brittle, eafily reduced to pow- der. Powder has a greyifh-black colour; powerfully attrac- ted by the magnet ; fpecific gravity 4.765. 1. As acids were not found to aé& upon this mineral, 100 grains of it were reduced to a fine powder, mixed with twice its from the RIVER DEE.. 255 its weight of carbonate of potath, and expofed for two hours to a red heat, in.aporcelain crucible. The mafs, being foftened in water, was. digefted. in, muriatic acid. By repeating this procefs twice, the whole was diffolved in muriatic acid, ex- cept a brownifh-white matter, auhach, being dried in-the open abs owe 193 SFaIDSe wv st bode, THe muriatic acid folution, hick had a deep yellowith- brown colour, was concentrated almoft to drynefs, and then di- luted with water. It affumed a milky appearance; but nothing was precipitated. Being boiled for fome time, and then fet afide, a curdy-like matter fell. It was of a milk-white colour, weighed, when dry, 7 grains, and: ass the properties of oxide of titanium. -' aogy Tue refidual kicgitd being fuperfaturated with ammonia, a dark reddifh-brown matter precipitated, which being feparated bythe filter, dried, drenched in oil, and heated to rednefs, af- fumed the appearance’ of’ a black matter, ftrongly attracted by the magnet. It weighed 93-7 grains, and was oxide of iron. ~l aia Tuk: 19.5 grains of refidual powder, being mixed with we times its'weight of carbonate of foda, and expofed for two hours;to ‘a red ‘heat, in a platinum crucible, and afterwards heated with muriatic acid, was all diffolved, except about a grain of blackifh matter, which was fet afide. 5. THE muriatic folution being concentrated by evaporation, a dittle white:matter was feparated. It weighed ith of a grain; and poflefled the characters of oxide of titanium. 6. WHEN 356 ANALYSIS of a BLACK SAND 6. WHEN evaporated to drynefs, and rediffolved in water, a white powder remained, which proved to be filica, and which, after being heated to rednefs, weighed one grain. 4. THE watery folution being fuperfaturated with potafh, and boiled for a few minutes, was thrown upon a filter, to fe- parate a reddifh-brown matter, which had been precipitated. The clear liquid which paffed through the filter, was mixed with a folution of fal ammoniac. A foft white matter flowly fubfided. It was alumina, and, after being heated to rednefs, weighed half a grain. 8. Tue brown-coloured matter which had been precipitated by the potafh, when dried upon the fteam-bath, weighed 20.2 grains. It diflolved with effervefcence in muriatic acid. The folution had the appearance of the yolk of an egg, When boiled for fome time, and then diluted with water, it became white, and let fall a curdy precipitate, which weighed, when dry, 4.6 grains, and poflefled the properties of oxide of tita- nium. ; g. THE refidual liquor being mixed with an excefs of ammo- nia, let falla brown matter, which, after being dried, drench- ed in oil, and heated to rednefs, weighed 6 grains. It-was flrongly attracted by the magnet, but was of too light a colour to be pure oxide of iron. I therefore: diffolved it in muriatic acid, and placed it on the fand-bath, in a porcelain capfule. When very much concentrated by evaporation, fmall white” needles began to make their appearance in it.) The addition of hot-water made them difappear; but they were again form- ed when the liquor became fufficiently concentrated. Thefe cryftals, when feparated, weighed 1.3 grains, and proved, on examination, to be white oxide of arfenic. During the folution of from the RIVER DEE. 257 of the 6 grains in muriatic acid, a portion of black matter fepa- rated. It weighed 0.2 grains, and was totally diffipated before the blow-pipe in a white fmoke. Hence, it muft have been ar- fenic. Thefe 1.5 gr. are equivalent to rather more than 1 grain of metallic arfenic. Thus, it appears, that the 6 grains contained 1 grain of arfenic, which explains the whitenefs of their colour. The reft was iron. It can fcarcely be doubted, that the proportion of arfenic prefent was originally greater. Some of it muft have been driven off when the iron oxide was heated with oil. 10, THE infoluble refidue, (No. 4.), was with great difficul- ty diffolved in fulphuric acid. When the folution was mixed with ammonia, a white powder fell, which weighed 0.8 grains. It was accidentally loft, before I examined its properties. But I have no doubt, from its appearance, that it was oxide of tita- nium. 11, Tuus, from the roo grains of iron-fand, the following conftituents have been extracted by analyfis : Black oxide of iron, - ' 98.70 White oxide of titanium, 12.65 Arfenic, - - 1.00 Silica. and alumina, - 1.50 Total, 113.85 Here there is an excefs of néarly 14 grains, owing, without _ doubt, to the combination of oxygen with the iron and the titanium during the analyfis. Hap the iron in the ore been in the metallic ftate, the ex- cefs of weight, inftead of 14, could not have been lefs than 30. For the black oxide is known to be a compound of too metal and 258 ANALYSIS of a BLACK SAND and 37 oxygen. Hence, I think, it follows, that the iron in our ore muft have been in the ftate of an oxide, and that it muft have contained lefs oxygen than black oxide of iron. A good many trials, both on iron-fand, and on fome of the other mag- netic ores of iron, induce me to conclude, that the iron in moft of them is combined with between 17 and 18 per cent. of oxy- gen. This compound, hitherto almoft overlooked, by che- raifts, I confider as the real protoxide of iron. THENARD has lately demonftrated, the exiftence of an oxide intermediate be- tween the black and the red; fo that we are now acquainted with four oxides of this metal. But the protoxide, I prefume, does riot combine with acids like the others. Analogy leads us to prefume the exiftence of a fifth oxide, between the green and the red. if a As to the titanium, it is impoffible to know what increafe of weight it has fuftained, becaufe we are neither acquainted with it in the metallic ftate, nor know how much oxygen its differ- ent oxides contain. It is highly improbable, that, in iron-fand, the titanium is in the metallic ftate, if it be made out that the iron is in that of an oxide. The experiments of VAUQUELIN and Hecut, compared with thofe of KLaPprotn, have taught us that there are three oxides of titanium, namely, the blue, the red, and the white. From an experiment of VauQuELIN and Hecurt, and from fome of my own, I am difpofed to con- fider thefe oxides as compofed of the following proportions of metal and oxygen : METAL. OXYGEN. 1. Blue, 100 16 gamed, 4 * 1G0 33 3. White, 100 . 49 I find, that when the white oxide of titanium is reduced to the ftate of red oxide, it lofes one-fourth of its weight ; and that ‘ red from the RIVER DEE. 259 red oxide, when raifed to the ftate of white oxide, increafes ex- aétly one-third of its weight. It was the knowledge of thefe facts, that led me to the preceding numbers. And I think they may be ufed, till fome more direct experiment lead us to pre- cife conclufions. — REpD oxide being the only ftate in which this metal has yet occurred feparate, we may conclude that it combines, in this ftate, with metallic oxides, and that the titanium in iron-fand, is moft probably in this ftate. But white oxide, diminifhed by one-fourth, gives us the equivalent quantity of red oxide. On that fuppofition, the titanium prefent, before the analyfis, in the 100 grains of ore, weighed 9.5 grains. THE appearance of the arfenic furprifed me a good deal, as it was altogether unexpected. I am difpofed to afcribe it to fome particles of arfenic pyrites which might have been acci- dentally prefent. This conjecture will appear the more pro- bable, when we reflect, that arfenic pyrites very frequently ac- companies iron-fand. Before the microfcope, the iron-fand ap- pears to contain fome white fhining particles, which, probably, are arfenic pyrites. Tue fmall quantity of filica and alumina, I afcribe, without hefitation, to grains of quartz and felfpar, which had adhered to the iron-fand, and been analyfed along with it. Some fuch grains were actually obferved and feparated. But others, pro- bably, efcaped detection. 12. Ir thefe fuppofitions be admitted as well founded, the iron-fand was compofed of Protoxide of iron, 85.3 Red oxide of titanium, 9.5 Arfenic, - - I.0 Silica and alumina, - 1.5 Lofs, - - 27 100.0 Vou. VI.—P. II. Kk The 260 ANALYSIS of a BLACK SAND The lofs will not appear exceflive, if we confider, that a por- tion of the arfenic muft have been fublimed, before the pre- fence of that metal was fufpected. Upon the whole, I think we may confider the fpecimen of iron-fand examined, as compofed of g parts protoxide of iron, and 1 of red oxide of titanium. The prefence of titanium in this ore had been already detected by Lampapius, though, as: I have not feen his analyfis, I cannot fay in what proportion. II. ISERINE. TuE colour of this ore is iron-black, with a fhade of brown. It confifts of fmall angular grains, rather larger than thole of the iron-fand, but very fimilar to them in their appearance. Their edges are blunt ; they are fmoother, and have a ftronger glimmering luftre than thofe of the iron-fand. Luftre femi- metallic, inclining to metallic. The fracture could not be di- ftinétly obferved, but it feemed to be conchoidal; at leaft no- thing refembling a foliated fra@ure could be perceived. Opake, femihard, brittle, eafily reduced to powder; colour of the - powder unaltered; fpecific gravity 4.491 *; fcarcely attract- ed by the magnet. B 1. A HUNDRED grains of the powdered ore were mixed with fix times their weight of carbonate of foda, and expofed for two hours to a red heat, in a platinum crucible. The mafs obtain- ed being foftened with water, diffolved completely in muriatic acid. When the folution was concentrated, it aflumed the ap- pearance * Tr, as the following analyfis would lead us to expect, the {pecimen exami- ned was a mixture of four parts iferine, and one part quartz and felfpar, the fpe- cific gravity of pure iferine fhould be 4.964. from the RIVER DEE. 264 pearance of the yolk of an egg. It was boiled, diluted with water, and fet afide for fome time. A white matter gradually depofited, which, when dried on the fteam-bath, weighed 53 grains, and poffefled the properties of oxide of titanium. 2. THE liquid thus freed from titanium, was evaporated to drynefs, and the refidue rediffolved in water, acidulated with muriatic acid. A white powder remained, which, after being heated to rednefs, weighed 16.8 grains, and poffeffed the pro- perties of filica. 3. THE folution was precipitated by ammonia, and the brown matter which had feparated, boiled for fome time in liquid pot- afh. The whole was then thrown on a filter, to feparate the undiffolved part, and the liquid which came through, was mix- ed with a folution of fal ammoniac. A white powder fell, which, after being heated to rednefs, weighed 3.2 grains. It was alumina. ; 4. THE brown fubftance collected on the filter, was dried, drenched in oil, and heated to rednefs. It was ftrongly attract- ed LBy the magnet, and weighed 52 grains. _ gs. Ir was digefted in diluted fulphuric. acid; but not being rapidly acted upon, a quantity of muriatic acid was added, and the digeftion continued. . The whole flowly diflolved, except a blackith matter, which became white when expofed to a red heat, , and, as far as I could judge from its properties, was oxide of titanium, flightly contaminated with iron. It weighed 1.8 grains. 6. Tue acid folution being concentrated by gentle evaporation, a number of fmall yellowifh-coloured needles made their ap- Kk2 . pearance 262 ANALYSIS of a BLACK SAND pearance init. By repeated evaporations, all the cryftals that would form were feparated. They weighed 6 grains. I redif- folved them in water, and added fome ammonia to the folu- tion. A fine yellow powder fell, which I foon recognifed to be oxide of uranium. It weighed 4.2 grains. 7. Tuus it appears, that the 52 grains (No. 4.), attracted by the magnet, contained 46 grains of iron, and 6 grains of ura- nium and titanium. 8. Tue following are the fubftances feparated from 100 grains of iferine, by the preceding analyfis : Oxide of titanium, 54.8 Oxide of iron, - 46.0 Oxide of uranium, 4.2 Silica, - - 16.8 Alumina, - a2 Total, 125.0 Here is an excefs of no lefs than 25 grains, to be accounted for by oxygen, which muft have united to the three metals during the procefs. As to the filica and alumina, there can be little hefitation in afcribing them to grains of fand, which had been mixed with the ore. The pure iferine, in all probability, was compofed of iron, titanium, and uranium. If we fuppofe that each of thefe metals exifted in the ftate of protoxide, we muft diminifh the titanium by one-fourth, the iron by one-feventh nearly, and the uranium, according to BucnoLz’s experiments, by one-fifth. This would give us, Titanium, from the RIVER DEE. 263 Titanium, - 41.1 Iron, - - 39-4 Uranium, - ae Silica and alumina, 20.0 103.9 Here, then, is ftill an excefs of nearly 4 per cent. But this I am difpofed to afcribe to the oxides of titanium and uranium, having been only dried upon the fteam-bath. Upon the whole, it appears, that, in the fpecimens of iferine analyfed, the pro- portions of titanium and iron were nearly equal, and that the uranium did not exceed 4 per cent. The appearance of uranium furprifed me a good deal. I perceive, however, that it has al- ready been detected in this ore, from an analyfis publifhed by Profeffor JamEson, in the fecond volume of his Mineralogy, which, I underftand, was made by Lampapius. The fpeci- men examined by Lampanptus yielded very nearly 60 parts of titanium, 30 of iron, and 10 of uranium. Whereas, in mine, if the foreign matter be removed, there was obtained, very nearly, - - 48 titanium, 48 iron, 4 uranium, a Too But, there can be no doubt, that the iferine which I analyfed was ftill contaminated with a good deal of iron-fand; for it was impoflible to remove the whole. 13th - 264 ANALYSIS of a4 COPPER ORE Eee Analysis of the Grey Coprrer Ore, from Airthrey. THE copper mine of Airthrey, near Stirling, confifts of a thin vein, which runs. through the weft corner of the Ochils. It has been twice wrought, by two different companies. But, in both cafes, was abandoned, after a few years trial. I went to it fome years ago, and examined the ore, at the requeft of one of the proprietors... The fpecimens which were employed for the fubfequent analyfis, were the pureft that I could feled, - out of a confiderable quantity. I was told, however, that from the lower level, which was at that time full of water, much richer ore had been extracted. But, afterwards, when the lower level was freed from its water, I went down to it myfelf, and found the ore precifely of the fame kind:as in the upper, with this difference, that it was more mixed with calcareous fpar, and perhaps, on that account, more eafily {melted. Tue veinftones in the Airthrey mine are fulphate of barytes, and carbonate of lime, and with thefe the ore is almoft always more or lefs mixed. Tue colour is at firft light fteel-grey ; but the furface foon tarnifhes, and becomes of a dark dull leaden-grey, and in fome places aflumes a beautiful tempered fteel tarnifh. ,Maflive and difleminated. In fome {pecimens, it exhibits the appearance of imperfect cryftals. Internal furface fhining and metallic ; but, by expofure, it foon becomes dull. Fracture fmall-grained, inclining to even. Fragments indeterminate, and rather blunt- edged. Semihard, the degree being almoft the fame as that of calcareous fpar; for thefe two minerals reciprocally feratch each “from AIRTHREY. 265 each other. Streak fimilar, opake, brittle, eafily frangible ; fpecific gravity 4.878. 1. To free the ore as completely as poflible from foreign matter, it was reduced to-a coarfe powder, and carefully pick- ed. It was then digefted in diluted muriatic acid, which dif- folved a quantity of carbonate of lime, amounting to 13 per cent. of the original weight of the ore. 2. THus purified, it was dried on the fteam-bath, and 100 ‘grains of it were reduced to a fine powder, and digefted in di- luted nitric acid, till every thing foluble in that menftruum was takenup. The refidue was digefted in the fame manner, in muriatic acid; and when that acid ceafed to act, the refidue was treated with nitro-muriatic acid till no farther folution could be produced. - The infoluble matter was of a white co- lour; it weighed 6.9 grains, and was almoft entirely fulphate of barytes. No traces of fulphate of lead, nor of oxide of anti- mony, could be detected in it by the blow-pipe. 3. Tue three acid folutions being mixed together, no cloudi- nefs appeared, nor was any change produced; a proof that the ore contained no filver. »4. Tue folution being evaporated nearly to drynefs, was di- luted with water, and precipitated by muriate of barytes. By this means, the fulphuric and arfenic acids, which had been, formed during the long-continued action of the nitric acid on the ore, and the prefence of which had been indicated by re- agents, were thrown down ; for nitrate of lead, added to the re- fidual liquid, occafioned no precipitate; a proof that no arfe- nic acid was prefent. 5. THE 266 ANALYSIS of a COPPER ORE §. Tue liquid, thus freed from arfenic acid, was mixed with an excefs of ammonia. It affumed a deep blue colour, while a brown matter precipitated. It was feparated by the filter, and - being dried, drenched in oil, and heated to rednefs, it was to- tally attracted by the magnet. It weighed 45.5 grains, and was iron. 6. THE ammoniacal liquid was neutralifed by fulphuric acid, and the copper thrown down by means of an iron plate. It weighed 17.2 grains. 4. To afcertain the quantity of fulphur and arfenic, 100 grains of the purified ore, in the ftate of a fine powder, were put into the bottom of a coated glafs-tube, and expofed for two hours to a red heat. When the whole was cold, and the bot- tom of the tube cut off, the ore was found ina round folid mafs, having the metallic luftre, a conchoidal fracture, and the colour and appearance of variegated copper-ore. It had loft 16 grains of its weight. 8. The upper part of the tube was coated with a yellowith- brown fubftance, like melted fulphur. It weighed 12.6 grains. Thus, there was a lofs of 3.4 grains. As the tube was long, this lofs can fearcely be afcribed to fulphur driven off. I ra- ther confider it as water. For towards the beginning of the procefs, drops of water were very perceptible in the tube. Whether this water was a conftituent of the ore, or derived from the previous digeftion in muriatic acid, cannot be deter- mined. g- WuEN the 12.6 grains of yellowifh brown matter de- tached from the tube, were digefted in hot potafh-ley, the whole was diffolved, except a fine blackifh powder, which weighed from AIRTHREY. 267 weighed 1 grain, and was arfenic. The diflolved portion I confidered as fulphur. 10. THE potafh folution, being mixed with nitric acid, 4 grains of fulphur fell. The remaining 7.6 grains muft have been converted into fulphuric acid, by the adtion of the nitric acid. Accordingly, muriate of barytes occafioned a copious precipitate. 11. THE 84 grains of roafted ore being reduced to a fine powder, mixed with half their weight of pounded charcoal, and roafted a fecond time in a glafs-tube, one grain of fulphur fu- blimed. But the tube breaking before the roafting had been continued long enough, the procefs was completed in a cru- cible. The roafted ore weighed 70 grains. 12. From the preceding analyfis, we learn that the confti- tuents of the Airthrey ore, are as follows : Iron, :" 45:5 Copper, - 17.2 Arfenic, - 14.0 Sulphur, - 12.6 Water, - 3-4. Foreign bodies, 6. 99.6 Lofs, - 4. 100.0 If we fuppofe the water and the earthy refidue to be only acci- dentally prefent, then the only effential conftituents are the firft four, and the ore would be a compound of Iron, 51.0 Copper, 19.2 Arfenic, 15.9 Sulphur, = 14.1 : 100.6 VoL. VI.—P. II. L 1 If 268 ANALYSIS of 4 COPPER ORE, &e. If we compare this analyfis with feveral analyfes of grey cop- per ore, lately publifhed by Kuarrorn, we fhall find, that the conftituents are the fame in both; but the proportions of the two firft ingredients are very nearly reverfed. KiaPrroTH ob- tained from 0.4 to 0.5 of copper, and from 0,22 to 0.27 of iron, This renders, it obvious, that the two ores were not in the fame ftate. I have little doubt, that the difference, how- ever, is merely apparent, and that it arofe, altogether, from. a quantity of iron pyrites, ‘and perhaps alfo of arfenic pyrites, which I could not feparate from the grey copper ore which I examined. Both of thefe minerals could be diftin@ly feen in many of the fpecimens, intimately mixed with the grey cop- per; and I have no doubt that the fame mixture exifted, even in thofe fpecimens which'were felected as pureft. The differ- ence in the proportions of copper and arfenic, obtained by Kxarroru * in his various analyfes, is fo confiderable, as to lead to a fufpicion, that even his {pecimens, in all probability, contained a mixture of foreign matter. ® GrHLEn’s Jour, vol. v. p. 9. 21.13. VIII. VIII. New Series for the QuapRatTuRE of the Contc SEc- TrIons, and the ComevTation of LoGaRiTHMSs. By Wir11am Watzace, one of the Professors of Ma- _ thematics in the Royal Military College at.Great Mar- low, and F.R.S. Epix. [Read 27th June 1808.]} CHE Quadrature of the Genre coasts and the Compu- tation of Logarithms, . are problems of confiderable importance, not only in the elements of Mathematics, but alfo in the higher branches of that fcience. On this account, every fuccefsful attempt to fimplify their refolution, as well as any new formule which may be found applicable to that purpofe, muft always be interefting, and muft in fome meafure contri- bute to the improvement of mathematical knowledge. ; 2, THE object of this Paper, is to give folutions of thefe problems, which fhall be at once {imple and elementary, with- out employing the fluxional or other equivalent calculus ; and it is prefumed, that thofe which follow, will be found to par- take fo much of both thefe properties,, that they may even ad- /mit of being incorporated with the elements of Geometry and Analyfis. Befides, the formule which refult from the invefti- eon, are, as far as I know, entirely new, while each is appli- Ll 2 cable 270 NEW SERIES for the cable to every poflible cafe of the problem to be refolved. Now this laft circumftance is the more remarkable, as it generally happens, that a feries which applies very well to the quadra- ture of a curve within certain limits, is quite inapplicable be- yond them. 3. ALTHOUGH, in a general way, this Paper may be faid to treat of the quadrature of the Conic Sections, yet there is one of them, namely, the Parabola, which I fhall not at all notice ; becaufe, although its area may be found in a way analogous to that which is here employed in the cafe of the other two, yet the formula which would thence refult, muft, from its nature, be the fame as would be found by any other mode of proceed- ing. As the quadratures of the ellipfe, and any hyperbola may be deduced from thofe of the circle and equilateral hyperbola, I fhall, in the following Paper, treat only of the two laft; and as the quadrature of a fector of a circle, and the rectification of its bounding arch, are reducible the one to the other, it is a matter of indifference which of thefe we confider. I fhall, however, confine myfelf to the latter. 4. IN treating of logarithms, I might, after the example of the earlier writers on this fubjeét, deduce the formule for their computation from thofe which we fhall find for the quadrature of the equilateral hyperbola. I prefer, however, treating this fub- ject in a manner purely analytical, without adverting at all to the hyperbola, being of opinion, that every branch of mathematics. ought, as much as poflible, to be deduced from its own pecu- liar principles; and therefore, that it would be contrary to good method, to haye recourfe to the properties of geometrical figure, when treating of a fubject entirely arithmetical. 5. To QUADRATURE of the CONIC SECTIONS, &c. = 27 5. To proceed now in the inveftigation of the different fe- ries, for the re¢tification of an arch of a circle, let A denote any arch, the radius being fuppofed unity. Then, from the arithmetic of fines, we have I I I I S| ——————-_ tan — A. tanA 2tanzA 2 2 In this formula let each term of the feries of arches I I I I I (which is a geometrical progreflion, having the number of its terms 7, and its common ratio 4,) be fucceffively fubftituted for A, and let the refults be multiplied by the terms of the corre- fponding feries of fractions Bay Ale a I re SMe Dg ONG | Gaceah gaat then we fhall obtain the following feries of equations : I I : = — —- tanya, tana 2tan+4 2 I Gey ie eae t tanta, 2tant+a 4tanta 4 x = z T tanta 4tanta ~ 8tanja Sige oe = : tan +z @ Stan¢a — i6tan;;a Re og ie e ° e e ° ° ° ° ° - I a, I ma a Qn—2 tan 2"—I tan a Qi 2Qn—V? Qi—a Qn. > I mn I a ar—! tan 2" tan — - gn—t1 2% Let 272 NEW SERIES for the Let the fums of the correfponding fides of thefe equations be taken, and obferving that the feries i I I I ia gil gad cagA gail. ig pitane ia tania Stania a 2 4 rs cy ae as is found in each fum, let it be rejected from both; and the re- fult will be ( I oes t= 4 I I Zit cog Ehonl I I tana cee ries ber be oe iv wea: the number of terms of the feries in the parenthefis being x, and hence we have I I I I I I I - = saat ~ tan—- 4-4 - tan = a+, tant a+ pepe tan 2 2 4 4 Qn a Sei aaviaa oe = tan 4, I I an 2" 6. Now, 2tan{a4 is the perimeter of a figure formed by drawing tangents at the ends of the arch z, and. producing them till they meet; and 4 tan +a is the perimeter of a figure formed by bifecting the arch a, and drawing tangents. at its ex- tremities and at the point of bifection, producing each two ad- sear : —- Aa: joining tangents till they meet ; and in general 2" tan = the perimeter of a figure formed in the fame way, by dividing the arch QUADRATURE of the GONIC SECTIONS, &c. 273 arch a into’ 2*+! equal parts, and drawing tangents at the points of divifion, and the extremities of the arch. Therefore, denoting the a ya of the figure thus so by P, we have 2. 35 ook Fe tes aac titap hg. 1 2 tan ie P tang 2 4 8 8 ® I I a tan — a... — tan — ee 3 ype oma and this is true; whatever be the number of terms in the feries ae me 3 PB, I a T tan -a+ -tan-4a....-+ —tan—*, 2 2 4 4 20 Qn 7. Now fuppofing » the numberof terms in the feries, to, in- creafe, then 2"—', the number of equal parts into which the arch is conceived to be divided, will alfo increafe, and may be- come greater than any aflignable number. But it is a principle admitted i in the elements of geometry, that/an ‘arch being divi- ded, and a polygon’ defcribed about’ it in the manner fpecified in. ‘article 6., the perimeter of the polygon will continually ap- proach to the circular arch, and will at laft differ from it by lefs than, any given quantity. Therefore, if we fuppofe » inde- finitely great, fo that the feries may go on ad infinitum, then,!in- ftead of P in the formula of the laft aiticle, we may fubftitute its limit, namely, the arch a, and thus we fhiall have’ mol S07 orpish Hi yt I I I =o -+ ctan-a-+ -tan = a+ >-tan = a a oe el 2 aa 4 13 8 34 ~ poy pe ) Thus > * WE may here obferve, that this formula may be confidered as the analy- tic expreffion of a general theorem (which is not inelegant) relating to regular. figures defcribed about any arch of a circle; and others analogous to it will occur in the following inveftigations. 274 NEW SERIES for the Thus we have the circular arch, or rather its reciprocal (from which the arch itfelf is eafily found), exprefled by a feries of a very fimple form ; and this is the firft formula which I propo- fed to give for the rectification of the circle. 8. WE now proceed to inquire what is the degree of conver- gency of this feries. In the firft place, it appears, that the nu- meral co-efficients of the terms are each one-half of that which goes before it. Again, A being any arch of a circle, we have by a theorem in the elements of geometry, fecA:1::tanA —tantA:tantA; therefore, 1-+fecA:1::tanA:taniA, tac. faa ? and hence tantiA= glee ee But as fec A is greater than 1, therefore 1 + fec A muft be greater than 2, and confequent- tan A tan A rarer ra lefs than muft be lefs than tan A. Thus it appears, that a being any arch lefs than a quadrant, the tangent of any one of the feries of arches + 4,44, 74, &c. is lefs than half the tangent of the arch before it. By combining the rate of convergency of the tangents with that of their numeral co-efhicients, it appears, that each term of the feries, after the fecond, is lefs than one- fourth of the term before it ; and this is one limit to the rate of convergency of the feries. 3 hence it follows, that tant A g. AGAIN, to find another limit, let us refume the formula =f ype tee CATIA CARE: tans A ee ee teen from which it follows, sa Te ine tan Ae. I , and fimilarly, that fa TA Pees But I ™~ r+fecA fince QUADRATURE of the CONIC SECTIONS, &c. 275 ) : ; I I ie fec ; A ~ tanta; Bey pe > Stanta * : ae &e. from which it appears, that in the feries, 1 — ; Pimp l tan Fg a ana! 3 I I I r I rT" age q tan got = tan 7g 4 +, &e. each term after the third (that after + tan 4a), is greater than a third proportional to the two terms immediately before it, taken in their order; and this is, another limit to the rate of. convergency of the feries. 10. Tue, limits which we have found to the rate of conver- gency of the feries, enable us alfo to affign limits to the fum of all the terms after any given term. Let the feries be put. under this form,, Ts vr I I I I == haa gn 7 Oia 4. ue t Tom) + T(m+1) + P(m42) +, &e. Vou. VI.—P. IT. Mm. where: 276 NEW SERIES for the where T(m), T(m+1), T(m+2), &c. denote the terms whofe places in the feries are exprefled by the numbers m, m+1, m+2, &c. Then, becaufe T(m42)< ; Tom4n)s T(m+3) < 7 Ton) Tents < 5 Timgar RCs ri We have T(m+2) + T(mt3) + Tmga) , &e. < i (Tent) + T(m42) + T(m+3) +, &c.) ‘That is, putting S for T(m42) + T(m+3) + T(m44) +, &e. or for the fum of.all the terms after T(m41), I Ss <5 (Tom+1) + S), and hence 3 w= 7 T(m+1),&S aa T(m+1): Thus it appears, that the fum of all the terms of the feries fol.- lowing any term after the firft, is lefs than the third part of that term. 11. AGAIN, from what has been faid in Article 9., we have Tim+2)> Bane T(m+1), and therefore pitee) > Ems) (m1) Tq)’ F Tim ) Tom 2) m T g lay t+? 5 qd = (m+4) zieba), and fimilarly T(m+z) at T(m+ 1) ii T(m43) ‘ Tom42)° and QUADRATURE of the CONIC SECTIONS, &c. 274 and fo on, From which it follows, that T(m T(m42) > coe T(m+t1), Gn i} Tena 3) > py? Tengah Tm T(m+4) > a ram Tom 43)s &e. HENCE, faking the fum of the quantities on each fide of the fign >, and putting S for T(m42) + T(m4 3) + Dente) +, es we get. S> Tony (Toss) +8). pp hei s— caps: S> = and \confequently by ao eqs \' my, 4] } sagt 125109 Byets) omg) of Nay ea ees Tm) — T(m41) (ee ue elit it appears, that the-fum of all the terms following any- afligned | term. after the third, is greater than a third pro- portional to.the difference, of the, two, terms immediately be- fore it and the latter of the two, But fince this limit will not differ much from: thé former, which is = Tet) it may be more conveniently exprefled thus) oj) 6) jy550 om iorr eqing ele Tay AT mer pe) glimpses a Toe pe 2 3 3 , 3(Tim—Tatn) Mm 2 which 278 NEW SERIES for the which formula, by reduction, will be found to be the very fame as the other. 12, Tue refult, then, of the whole inveftigation, may be briefly ftated as follows: Let @ denote any arch of a circle of which the radius is unity, then fhall I I I at: I Meant a+ ltanta+itanta+ td tanta... _ janat Sy rae rok in etna Neagle eae ges I a + T(m) + Tom+ 1) + SIE af Tim) and ‘['”(m+1) denote ‘any two fucceeding terms of the feries : tan : a+ i tan : a+, &c., their places in it being exprefled by the numbers m and m+1; and where S$ is put for the fum of all the remaining terms; and the limits of S are the two Ripe = 5 Tots) and - 2 Peat — (Toy~4 T(m+1)) T(m+x) Sea a ee 3(T (m) — Tin+1)) y is, S is lefs than the former, but greater than the latter. The expreflions tan — 4, tan z a, tan 5% &e, are aes de- 2 4 ducéd from tan a, and from one ‘another, by a wall known for mula in the arithmetic of fines, which may be exprefled ‘thus, : te oatoy ides sedis Mp amit:

- A, which, by ta- q tan A 2tantA.).2 y king the fquare of each fide, is transformed to I ogg I 21 I —— = ——____ + - tan -A— =. tan* A Ee ee 2 2 In this formula, let each term of the feries of arches ee Se a G2 By ss Gye aleve,« 9 : 2 4 8 Piast “sof which the number of terms is 2, be fubftituted fucceflively for a, and let the refults be multiplied by the cc has terms of the feries of fractions, ' of? pease Sey coe ee aA oar van thus there will be formed the feries of equations I I I I =, Slleteee amity tiaqr ~tan'- 4 —i tan’ a 2*tan’ ia 4 2 2? I ey are I I “7 2 = ar] aang ‘ + = = (tan = a eee Pa 2° tan’+a 4 tan’ >a 4 2A : i = ees = ea 8 = tan* = g)°2 Heat 4 tan’ +a tan +4 43 8 2.42 I I re I I I RSIS PEE ae eee 8 ne Stan —* zea) ee ee 3* tan’? +a 16° tan’ =, 4 44 16 2.43” tod } oti I I , @ I _ = : ot jot tan’ a 227—4 tan 22n—2 tan ~ Qn—2 x _Qimt DB af I a > = x + = tan? = 4 ited 4” an 2.4°—1 27—2 tan —~ 22n tan’ 4 gn—I Qn 280 NEW SERIES for the Let the fum of thefe equations be taken, as in the inveftigation of the firft formula, and obferving that the feries I I I I Favte Gare” Stan ta" + 22"—2 tan? —-— n —TI is found on both fides of the refulting equation, let it be reject- ed from both; then we obtain past hee I T tan 4—= + tan*= 2 + —tan® SRE tan Pee Ee ent 4 A ng 2 iy AeA cog UE es Blan 16 . 2 I oa) te I I tan — — GC Bagi ag as e * +). Now it appears, that one part of this expreflion, viz. ee pha oie ela x I 2 © 248) 2.4 2.43 2.42 is a geometrical feries, the firft term of which is =; the laft 4 : ‘ term — et and common ratio = 3 therefore its fum_ is I a (x = et 3 4 Alfo, fince 2” tan = is the expreffion for the perimeter of a polygon, formed by dividing the arch @ into 2"—1 equal parts, by drawing tangents at the points of divifion, and producing the QUADRATURE of the CONIG SECTIONS, &c. 281 the adjacent tangents until they meet, (Art. 6.); therefore 22" tan’ < will be the fquare of that perimeter. Let the pe- rimeter itfelf be denoted by P, then, fubftituting P* in the equation inftead of 2% tan “, and 2 (1— a) inftead of the gs ae feries to which it is equivalent, and bringing pz t0 one fide, we get RD ee a | marat 3 ( z I BE inis & I4 ty Tay OT aX Ev ia'T — = 4 —(- tan’ — 4+ — tan’ — — tan’ = —tan —@... oe { C 3 sue citys an’ ae tat =f | : naa 15. THis is true, whatever be the value of 2, the number of terms of the feries in the parenthefis. Let us now conceive the feries to be continued indefinitely, then, as upon this hypo- thefis, n may be confidered as indefinitely great, + will become 4” lefs than any aflignable quantity, and therefore 2 (x ch 3 4" will become fimply + moreover, P will in this cafe become a, (Art. 7.), and P* will become .a*. Thus, upon the whole, we fhall 282 NEW SERIES for the fhall have I 2 | z += tan’ a 3 B spices I ie | == — (7 tan’ 5 eats fant?= pat pen gars, ~ tan ety FP 7 16 | 4.) and “a may be confidered as a ‘Reond formula for the reétifi- eation of any arch of a circle; for the procefs by which an arch is found from the fquare of its reciprocal is fo fimple, that the latter being known, the former may alo be regarded as known. 16. InstEAD of exprefling the fquare of the reciprocal of the arch in this manner, by the fquares of the tangents of its fub-multiples, we may exprefs it otherwife by the {quares of & their fecants. For fince tan’ Le | | re) fe) ar a a L— (Tet Te ++ + Te) + Tots) + Tin42) +, &e.)s where T(1), T(2), » «+ T(n), &c. now denote merely the terms of the feries taken in their order, then becaufe T(m42) < = T(m41)> I T(m+3) < Rie T(m42)> Tim+4) < = T(m+3)s &c. Therefore, ‘Tm-a) + T (m4 3) F Tm44) Hy Se. < 3 (Tern + T(m42) + Tim+3) +, &c.) That QUADRATURE of the CONIC SECTIONS, &c. 287 That is, putting S for Tom+2) + T(m+3) + T(m+4) +, &ee iy I S< ~ § Ton+1) + Bit and hence S < re T(m+1): Thus it appears, that the fum of all the terms following any : I term, is lefs than = of that term. 20. As to the other limit, it muft be the fame:as the like li- mit of our firft feries, on account of their having the fame li- mit to their correfponding rates of convergency. That is, putting S to denote as above, then ; —_ Tm4+n) T S Pe nL A m 4 T(m) — T(m+1) Weipa Tm) — 16 T(m41) or S > me T m ae 7 + m e 5 6s eae CE (ue) aT (ea) OED 21. Ir yet remains for us to confider how the feries of quan- heh — cof — cof + ! : tities Pareare eet ee &c. are to be found. Now this may be done, either by computing the cofines of the feries of 4 ! T 3% &c. one from another by means of the arches 4, z a, ze a, ark formula cof 7A= NA a and thence computing the fe- I—cofta 1—cofta . ——.2-, ——_-+,, &c. Or we ma 1+cofta’ 1+ cofia’ y compute each fraction at once from that which precedes it, by a formula which may be thus inveftigated.: ries of fractions Put 288 NEW SERIES for the I-+cofA ~~” Top cole Oe CO aes r+ cofA et 0% 2 I+?t ~/1+cofA 2 I a 4, 3 alfo cof = A=i—, now cof 7 A 2 +t he IT » therefore Oia tp 1+¢ Vi-+t » and hence pi Lele a Se ie pe oe 22. Uron the whole, then, the refult of the inveftigation of the fecond feries may be ftated briefly as follows. Let a de- note any arch of a circle, its radius being unity, then ( 1 1+cofa L 41—cola 6 = (1 1—cofta, 11—cof;a, 1 1—cofya & Cc. _ JY rfeolga" Brfeotsa” 44 1Feols a" { 4a? Leaay ee ed where T(m) and T(m+1) denote any two fucceflive terms of the {eries in the parenthefis, and S denotes the fum of all the fol- lowing terms ; and here S will always be between the limits I I __ (Tim) — 16 Tem) Tomer) 13 re ere 15 (T(m) — T(m+1)) that is, it will be lefs than the former, but greater than the lat- ter quantity. Tue feries of cofines are to be deduced one from another by means of the formula fA cof ~ ees ites. Or, QUADRATURE of the CONIC SECTIONS, &c. 289 Or, compute the feries of quantities ¢, 7’, ’, ¢’”, &c., one from another by means of the formulz I—cofa ,_ VI+t—r1 Vrtis1 ba, fe EY SS ce. 1+ cofa’ Vat +a Vl tft Then will f r1+cofa . 4 1—cola te a Po A Posten Fete os E Un(Se+ hese te $¢T im tT 8), where T(m), T(m4x1), and S denote the fame as Before: I consipDER this fecond feries for the redtification of the circle (under either of its forms), as preferable to the other f{e- ries given at Article 12. for two reafons ; firft, becaufe of its greater rate of convergency, and, next, becaufe the quantities Ir a ee cofa, cof= 4, cof- 4, &c., alfo the quantities ¢, z’, 2”, &c. can 2 4 be deduced more eafily one from. another than the feries of I ~a, &c. I I tangents tan 4, tan a 4, ir a, tan F 1023. THatT, we may; inveftigate another’ feries, let us I I I eformiala, ————|== == _-_ tan = A: ¢ refume th m Gan sah S +A; the cubes of both fides of the equation being now taken, the refult. is eae a Oe 6 = 31 ‘tan? A 8tan3tA eee oA. Bene a} =tan 5A To 290 NEW SERIES for the To the fides of this equation let are correfponding fides of the equation I =if I tanA” 2 ‘tantA —tanzA } be added; then we get I iat a tan? At ae hiaa gists Gow We deduce the following feries of equations, the number of which is 7: fec’ a tan3 a —)-§ (tan = A+ tan} =A). QUADRATURE of the CONIC SECTIONS, &c. 298 a ae I fec' a Be aie ns Boy hE ea 2 atest iva, tan? a a%*tantia 8 2 2 fec’+a fec’ ia I Bitee oe a 4 A Ea Saas CL RS = 3 tan —@ 1€ ’ 2? tan’ +a 43 tan? +a 8 4 4 fec*'+ 4 fec* +a I I Cag aE, = Ong nee 8) Tapes ie fec 3” 4? tan’ 74 8 tanga 2 fec” eo fec aa is Tsoi qu | — —he tan 4. fect 4, 23—") tans _* 23(m—1) tan} 8 Qn—2 | 27—tI a fec* aro fecs— é is ia i n n 2 27% tans = 231) tins = 2n—1 Let the fums of the correfponding fides of thefe equations be now taken, and rejecting from both the common feries fec? fec* +4 us fec’+ a vi gn—t 3 3 3 oe eaeer ae d 23tan°*t@ 23tan?+e@ / ate) ean gmk the refult will be 4 Ir I I I I I [ * tan 2 a fec sate gamete feck be ] —< 3 c L J VoL. VI.—P. II. O (6) and 292: NEW SERIES for the and here the number of terms Campane the feries in; the pa- renthefis is 7. ; LET us now conceive the feries to go on ad infinitum, fo that n may be confidered as indefinitely great, then it is manifeft, that fec* < will become equal to, rad’ 5, now 2 tan = will be- Tom aes . come 4, (Art. 6. and 7.) therefore 23"tan3 will become a? 3. t fec’ & hence, fubftituting at for 2". in our equation, and tran- 2 3™han? — a . Qn {pofing, we get at laft fec”a L \~ - \ ih = Ly oF = [eet g BS fec’ = sats z tans a fc" am - I as bak a tang ta fect X aby 8 ails and this is the third feries which I propofed to agi for the rectification ofan arch of a circle. 25. THE feries we have juft now found, is evidently of a very fimple form; it alfo converges pretty faft, each term be- ing lefs. than the 16th of that which precedes it. As, however, to apply it to actual calculation, it will be neceflary to ex- tra@t the cube-root of a number, which is an operation of con- fiderable labour when the root is to be found to feveral figures, . perhaps, confidered as a practical rule, this third formula is in- ferior to the two former. But if, on’ the’ other hand, we re- gard it merely as an elegant analytical theorem, it does not feem lefs. deferying of notice tham either ef them., 26. THE QUADRATURE of the CONIC SECTIONS, Sc. . 293 , 26.’'Txe mode. of reafoning by which we have. found, {eries rioiepme ings the three finft powers of the; reciprocal of an..arch, will-apply, equally to/any higher power, but)the feries will be- ‘come more and more complex as we proceed, befides requiring in their application the extraction of high roots. In the cafe;of the fourth power, however, the feries is fufficiently fimple, and converges fatter than-any we have yet “inveftigated, while, at the fame time, in its application we have only extractions of ‘the fquare root. On thefe accounts, I fhall here give its invef- paestian. i I MoS oy I fit te ae ex effion So i 5 tan = A: ee tanA” 2taniA 2, let the fourth power, and alfo the fquare of each fide of the equation be taken, the refult will be eR set eh al = = 44 tan¢+A 16 tan* +A tera nh3 eke 2A + S tan"+ A, IT “ I * I I Le a ian A — qamgA 314 tan*1+ A. a firtt of thefe equations be multiplied a me and the ‘fecond by, 3, and let the refults be added ; then, reducing the fractions to a common denominator, we get » tan’ A YI 3+4tan’ tA en Crain ordeal ro + go tate sts tan’ A}. LET us, for the fake of brevity, exprefs the couples quanti- tan* A ftood as raed ‘produét of two quantities f and A, but as a ¢harac- ter denoting a particular function of the arch A ;) and, fimilar- ty tater Ay by the mbok 7 A, (which i is not to be under- hy, let Gan 2= be denoted by f $A, and foon. Alfo . / Oo 2 let 204 NEW SERIES for the let the other complex expreffion 4tan’ + A + 3 tan*+/A be de- noted by F + A; and if there were others like it, that is, which only differed by having + A, ; A, &c. inftead of 4 A, they would be denoted by F1 A, F4A, &c.; then our laft equation will ftand thus, ee ifs. pe ed oF ote Loe See ay ee aC iia weet and fimilarly, putting +A, + A, 4A, &c. fucceflively for A, and ees ; 3 I -U@lIegy multiplying the refults by the feries of fractions 76’ 16” 16s &c. 16 16° 16° | 16° i + ep 41. Fs ee 2s af, geieA reid A 16° Fea, &e. By continuing this feries of equations to m terms, and then taking their fum, and rejecting what is common to each fide of the refult, exactly as in the inveftigations of the three preced- ing formule, we fhall get ; fA= ase ~ 4 betietie “+t gia b ange 2 - +QFIA+ BFPAtS FIA. bak S and this equation holds true, iad any whole pofitive num- ber whatever. 276 Lar. oe QUADRATURE of the CONIC SECTIONS, &c. 295 sigh LET us OW; however, fuppofe » name re great, then A oa ta 3+ 4tant 2 the quantity ety Ori ares be- us (2 (wand) A : A caufe tan S, and confequently 4 tan’—, vanifhes, and 2” tan — ", becomes fimply -3 a becomes A, as we have already had occafion to obferve (Art. 6. and 7.).Alfo the geometrical feries I I I 76° 16) 363.1? having the number.of its terms indefinitely great, and their common ratio oi. igi be + rch Therefore, by fubftitution and. eranfpofition we have Ata tAheer frahe A+ Fi A+— FEA t, &e.? or, fubficuting. for fA, and, F4)A, &c.: the: Acorns: ‘which. thefe fymbols exprefs, [3+4tamA , 14 | tan? A 15 cele ent 5 7 ’ ji3 I 8 ‘ . : : ; i= { — 7g (4tan’s A +3 tant 4A) + (4 tans A4-gtan*1A) * | 8 a ABEHAY 3t0"4 A), BP 2 and this j is s one form of eee feries which we Saran to alien tigate. - ya se 28, THis. “296 od NEW SERIES for the\ 28. Tus feries, however, admits of being expreffed _ under another form, better adapted to eaicnlation, and to effect this an transformation, Jet us begin aie the term aut 4, i A In —cof2A this quantity let 2 1+ cof2A be fubflituted for tan’ A; it has i rove *S : Se A ar aA becomes, after proper reduction, S22 taaole AltA aioe gain, in this expreflion let Je be fubftituted for cof’ 2 A, we then get g+4tanvA — 130of 4 A+ 12: cof2 A’ tant AD * 3+ cof4 A—4 cola A ” THE yemaining terms of the feries, which are fimilar to one another, and of the form 4 tan’ — = eee 3 an A, let's of a AA ol Like» transformation ;. for “ ye ‘ fubftituting”’ —e for Ate yep, &) 5 347 i ; 1 r+ cof = A io tan*— A, and again ——*- for cof"! Ai in n the Sor we 2n eet é ber ig tot Ao coll a oa TatsuntZa= s Eeqotta Siidigo dot Zacpoq eat Lia > (998313 By : QUADRATURE of ‘the CONIC SECTIONS, &c. 297 By: epee transformed an in the feries, it becomes: , ie i opunifionai yer. gard wxoK 2 hegre wast coe ee Cola A a Ded _ $e adeacearh cso esvedbe’ 4: 13—sof A — 1a ¢0f SA 16; -3-+col2zA+4colA, far 3+colA+ 4coiZA 4 ty 13 —‘cof* A —tr2cof+ ea) &e. t 16° iia ike A+ 4coitA eee fer = . .3 tans a 3 3—tar ta I bi I _ 8 -tan5a 3tanta gtanga 3° 3—tan’5@’ T niet I 3 8" tan 5@ gtanga™” 27tan3>a@, 33 3—tan’5'@ &e. Now conceive this feries of equations to be continued, till the number of equations be 7, and their fum to be taken, and the quantities common to each fide of the refult rejected, as in the inveftigations of the other formule ; then we fhall have tan @ QUADRATURE of the CONIC SECTIONS, &c. 299 mi Ty) {* tanta "8 ‘tanta tana srtan 33—tan’>a ~ 3° 3—tan'ta + eee ef e 8 era —tan’ 54 a a 3 3 3 — tan’ — And this is true, 2 being any number whatever. Now, if we | confider that 3” tan = exprefles the fum of the fides of a figure formed by dividing the arch into 3” equal parts, and drawing tangents at the points of divifion, whofe orders, reckoned from one end of the arch, are indicated by even numbers, (that end itfelf being reckoned one of them), and producing each to meet thofe adjoining to it, and the laft to meet a radius of the circle produced through the other end of the arch, it will be obvious, that being fuppofed to increafe indefinitely, the expreffion 3r tan =will have for its limit the arch a, and in this cafe the feries will go on ad infinitum. Thus we fhall have Toy E 8 tania ano £ tan< a 8 tan 3. a4 afiga tana 4 3.3—tan’y a7) 3} 3—tan*2a 3 3—tan’ 5a’ and by tranfpofition, 1 ii Ny 8 tanta — tan! a tan = +5 chef er | nite: a tana,’ 3 tan AON: j—tan™ 34 =693° 3—tan’ oa and this is the feries which I propofed to inveftigate. Vou. VI.—P. II. Pp 31. THE a) 1 fima 2 fin +a a2 eon 300 NEW SERIES for the 31. THE feries we have juft now found, may be prefented under various forms. Thus, by confidering that To: .. COA hee SU A eOiAe sn TI 2. A tanA” finA 2finA ~ 1r—cofl2A’ and that fin A tan A’) cote ein A rok A 1, . di 3—tan A tn A ~ 24col-A—1~ 21+ 2¢0i2e cof A it will appear that by due fubftitution the feries may be other- wife exprelffed as follows : +5 fin; 4 2 fns5a £1 3 I-+-2c0f + a I+2c0ka ' 331+2c0f 4 And other forms might be given to it, but they would all con- verge with the fame quicknefs, and each term would be lefs than ;th of the term before it. The feries, however, under whatever form it be given, and all others which like it require for their application the trifection of an arch, are, when com- pared with thofe we formerly inveftigated, of little ufe as prac- tical rules ; becaufe it is well known that to determine the fine, or other fuch function of an arch from a function of its triple, is a problem which produces a cubic equation of'a form which does not admit of being refolved otherwife: than by trials, or by infinite feries, both of which procefles are fufficiently labo- rious, and only to be employed where the objec in view can- not be attained by eafier means. 32. As from the different feries we have found for the redti- fication of an arch of a circle, the {pirit of our method muft be fufficiently obvious, I fhall not inveftigate any others at pre- fent. QUADRATURE of the CONIC SECTIONS, &c. 30% fent. Before leaving this part of our fubject, however, it may be proper to obferve, that the fecond feries may be deduced from the firft, and the third from the fecond, and fo on with refpect to innumerable others of the fame kind, by the fluxional or differential calculus. For refuming the firft feries I ot ead * tan 5 a jean | a tan 5 Ta &ce. Boe re 7 La +; a if we take the fluxion of si term, alain a as a variable quantity, we have —da _ —dafec’a aS hae css Bes a tan 4 a ‘ da fec* > a+ = dafec’* yet pds fec*s a+, &c, and hence, changing the figns, and rejecting da from each : I term, and putting 1-++ tan =a for fec** a, we find n ( ae ETE ) eta a ge pec teaaps cits Bete — OR RE net's . tan & L © 92 tag an oh c) In this expreffion, ar of the numeral feries 7 3 + et gb &c. (which is a geometrical progreffion having its common ratio *) fubftitute its value, viz. > and the refult is Life oii 2 I aI I I i = — Yotan? ca stan’ l a4 tant + . - : "3 F ri » &e ¢ a; tan’ a ait which is cae with the formula found at Art. 15. Pp2 FRom 302 NEW SERIES for the From this feries, by a like mode of proceeding, we may de- duce our third feries, and thence, again, our fourth, and fo on: but this mode of inveftigation, although very fimple, is certain- ly lefs elementary than that which we have followed. And it muft be kept in mind, that one principal object of this paper is to employ only the firft principles of geometry and analyfis in treating of the fubjects announced in its title, 33- By a mode of deduction differing but little from that employed in the laft article, we may even derive our firft feries. from a known formula, the invention of which is attributed to Ever. It is this, ; a = fina fee ~ ee at, &c. * From this expreflion, by the theory of logarithms, we get log a= log fin a + log fec 5 a+ log fec= a + log fee 54-4, &c. we have now only to take the fluxions of all the terms, and re- ject da, which is found in each, and the refult is Am pe tan + a+ 7 tan pot geny a+, &e. a tana which is the feries in queftion. 34. I now proceed to the inveftigation of formule for the quadrature of the hyperbola, and as the principles from which they. * Turs formula, although very elegant as an analytical transformation, does not feem to admit of being applied with advantage to the reétification. of an arch, on account of the great number of faétors of the produé which would be requi- red to give a refult tolerably correct. QUADRATURE of the CONIC SECTIONS, &c. 303 they are to’ be deduced are in effe@ the fame as we have had occafion to employ when treating of the circle, it will be pro- per to ufe the fame form of reafoning, and the fame mode of notation, in the one cafe as in the other. THEREFORE, in the equilateral hyperbola ABB’, of which C is the centre, (Plate IX. Fig. 1.), and CA the femitranfverfe axis ; let CB be drawn to any point B of the curve, and BD perpen- dicular to CA; then, in imitation of the notation commonly ufed in the arithmetic of fines, which we have followed in the former part of this paper, we fhall confider the co-ordinates CD, DB, as functions of the hyperbolic fector ACB, and put- ting S to denote its area, we fhall: denote the abfcifla CD by ab S, and the ordinate BD by ord S. Draw AE touching the curve at its vertex, and meeting CB in E; then, from fimilar triangles, we have AE — DB x CA; CD therefore fuppofing the femitranfverfe axis AC to be unity, ordS © ab S°* AES Now this expreflion for the tangent correfpond- fin A cof A prefflion for the tangent of an angle A, we may fimilarly de-. note AE by the abbreviation tanS. In like manner, if CB’ be drawn to a point B’ of the curve, bifecting the fetor ACB, and meeting AE in E’, and B’D’ be drawn perpendicular to CA; ing to a hyperbolic fector S, being analogous to - , the ex- then, ‘as the feG@or ACB’ will be =S, it follows, that CD’ = ab ; S, B'D’= ord : S, and AE’= tan : S; and fo on. 35. FRoM: 304. NEW SERIES for the 35. From the nature of the hyperbola, we have ab S = ab*2$-+ord’+S, ord S=2ab*Sord2S; 2 2 2 2 therefore, by divifion, ys peace ie) t ord> 3S ordS ~ 20rd+S ' 2 ab+8’ thadisyollbs tales td tans 2tan> Tuis laft formula exprefles a property of the hyperbola per- fe@tly analogous to that of the circle (Art. 5.), from which we have deduced our firft four feries for the rectification of an arch. Therefore fimilarly, putting s, 55 * s, &c. fucceflively 4 inftead of S, and multiplying by the feries of numbers 1, = ; &c. we have as in that article I I I I es —-+-= tan -s, tan s tan 2.§ 2 2 I I I I Sees) Se et i, Pte" tans yp 4 I I I I juts vas pallid eb pal Ze, 4tanis 8 tan 3s 8 8 &e. Tuis feries of equations being fuppofed continued until their number be ”, by proceeding exactly as in Art. 5. when treating of the circle, we obtain I —_— — 2” tan mo QUADRATURE o the CONIC SECTIONS, &c. 305 (1 ee ee t Ls | ae —(Etant rite ptand 5 t tan's ae © tan ds. pM Sa aa : y t +08 m3 36. Ler us now fuppofe the hyperbolic fector ACB to be di- vided into 2” equal parts, by lines drawn from the centre to the points I, 2, 3, 4,-..-7 in the curve, and tangents to be drawn at the extremities of the hyperbolic arch AB, and at the alter- nate intermediate points of divifion 2, 4, 6, &c. fo as to form the polygon AFF’ F’ F’ BC. Then, by a known property of the hyperbola, the triangles ACF, FC 2, 2 CF’, FC4,... F” CB are all equal, and as their number is 2”, the whole polygon bounded by the tangents, and by the ftraight lines AC, CB will be equal to the triangle ACF taken 2"times. But the area of this triangle is > AC xAF= - tan = (becaufe AF = tan ap : & therefore 2” tan— expreffes twice the area of the polygon AFF’ F’ F’ BG. Let Q denote this area, then, fubftituting = Q. for 2” tan = and multiplying all the terms of. the feries by 2, we have TO IT Ir. T I T ae tan —- 5s = tan = “Ss - tan- §s — tan — Sie. aint ne ( 2 x 7 8 mi 8 «16 Q 2: I Ss +70 5) Now oe 306 NEW SERIES for the Now, the rectilineal fpace Q_is evidently lefs than the hy- perbolic fector s ; but x may be conceived fo great that the dif- ference between Q and s fhall be lefs than any aflignable {pace, as it is eafy to demonftrate upon principles ftritly geometrical ; therefore, if we fuppofe » indefinitely great, then Q becomes s; and as, upon this hypothefis, the feries goes on ad infinitum, we have alae I I I I I I a —(tan 55+ rhage wile a tan 5+, &e.) | ~ tans which is our firft feries for the quadrature of an hyperbolic pee I z I : > feGor. And as Gas =20e=s + Zi tan = S, by refolving this equation in refpect of tan ; S, we get the formula by which the feries of quantities tan 7 5, tan ; s, &c. may be od . ord s deduced from tans = SEs? and from one another. 37. Tuis expreflion for an hyperbolic fector is perfeétly fimilar in its form to that given in Art. 7. for an arch of a circle. It may, however, be transformed into another better adapted to calculation, by means of a property of the hyperbo- la to which there is no corref{ponding property of the circle, or at leaft none that can be expreffed without employing the fign Y“—t. The property alluded to may be deduced from the known Pir acd QUADRATURE of the CONIC SECTIONS, &c. 30% known formule I 2ab - = (ab s-+ ords)" + (abs — ord sy", I 2 ord = = (abs + ord ges (ab s — ord sy, by proceeding as follows. Let each fide of the latter of thefe equations be divided by the correfponding fide of the former, the refult is T ai 7 5 on a _ (abs+-ords) —(abs—ords) , ah I £ na (abs-+ord 5)" + (ab s— ord 5)" which expreflion is equivalent to this other one, s ab s + ord 5)" ee ley soe ) aoe Ait ab © i n (PP saoo ab s—ords +1 abs-+ords abs—ords’ then, te- LeT us now put # for the fraction ; a 5 marking that ; = tan -, we have Vo. VI.—P. II. Qq an 308 NEW SERIES for the an equation which exprefles the property we propofed to invef- tigate. > 38. WE have now only to fuppofe z in this formula to have thefe values, 2, 4, 8, &c. epetieey and ‘to fubftitute inftead of the terms of our feries I 2 a = Se es =+t 5 5 ma ; (un ies an 4 Atl an Deel ‘fre / tan's their values as given by the Goal) putting alfo 2°°* inftead ae of tans, and the feries becomes Ste _ sab?“ hblty thems 4 tah 5g, —ord's t= 2 - 4 TFS ee ee and this is the new form under which we propofed to exhibit it. . 39. LET us now inquire what are the limits of the rate of convergency of this feries.; and in doing this, it will be moft convenient to refer to the firft of its two forms. Now, from : tT’ I I ope Be ‘formula ee le = tan > S,* we get the «(formule nS 2tan=S 2 Bigs g pT yk tan 2 S= Ltan$ (1+ tan” = 8). But 1 + tan*® — S> 1, and, 2 2 0) therefore = lian S (1+ tan’ - 7) > ~tan S, hence it follows, that tan £S>2tan$. Thus it appears, that each term of the fe- 2 2 ries QUADRATURE of the CONIC SECTIONS, &c. 309 I ; s, &c. is greater than half the ’ f Cs ele nh ries of quantities PRT 5, tan term before it; and as thefe, multiplied by the fractions *, > &c. refpectively conftitute the terms of the feries, each term of the feries, under either of its:forms, is greater than one-fourth ofthe'term before it. *4o. Acatn, from the formula tan Ss =< tans (a+ tan’ S) tan+S I Sige 697 + we find Pesca Ri = 1+tan* = S, and fimilarly, pens eis tans Is12 tanisS I+ tan’ ‘i S. But from the nature of the hyperbola tanis ub r+ tan? 2S <1 tan’ 2$;-therefore 24029 _2tan 78 ang 4 2 tan;S tan 5 tan*+S hence tan 2S < 2, 4 tan S Therefore, putting = s inftead of S, and multiplying by at we have r b pea 0 erry es 2n n . —tan-— sS< AO ot <= gan Bee, 82 I I 2n - tan—s n n from. which it appears, that each term of the feries, following the fecond, is lefs than a third proportional to the two terms immediately before it. So that, upon the whole, it appears, that the limits of the rate of convergency of our firft feries for an hyperbolic fector, are the fame as thofe of our firft for an arch Qq2 of & 310 NEW SERIES for the of a circle, (fee Art. 8. and g.), only the greater limit in the one cafe correfponds to the leffer limit in the other, and vice VETSAs 41. We might now, from thefe limits to the rate of conver- gency, determine two limits to the fum of all the terms of the feries following any given term, by the mode of inveftigation employed at Art. 10. and Art. rr. in the cafe of the circle; but the refult in both cafes would be found to be the fame, with the difference of the fign < for >, and> for <; that is, we would find the fum of all the terms following any term of the feries, to be greater than one-third of that term, but lefs than a third proportional to the difference between the two terms immediately before it and the latter of the two. 42. Upon the whole, then, our firft formula, for the quadra- ture of an hyperbolic feétor, may be exprefled as follows. abs -+ ords Let s denote the area of the fector, and put f for in age Then, | pea owihe sat adios, Aa 0 ipa pee - 2abs s r I I ord s : 21% ch ie Re Bi oe Pk Xp pa oP rg tg eg Sr T(m) a5 T(m41) + Ri where T(m) and T(m4.1) denote any two fucceeding terms of the feries, and R the fum of all the following terms*. And here * Tur fame feries may alfo be put under another form, which it may not be improper to notice briefly, on account of the facility with which the terms may be QUADRATURE of the CONIC SECTIONS, &c. 311 here . \y . Ree Duet) 3 Hie Ri EGTA) hues Svea ® T(m) — T(m+1) As thefe limits to R differ but little when the terms T(n),. T(m41) are confiderably advanced in the feries, the latter may be exprefled more conveniently for calculation thus I $ Tm ra Ty m)) T m R <3 Tmt) + (lens Fem oe ) oS). 3. 3 (T (m) — Tin+1)) 43- Let us next inveftigate a feries for the quadrature of the hyperbola, which may be analogous to our fecond feries for the rectification of the circle. For this purpofe, proceeding as at Art. 13. we refume the formula ——~ : I I = ——__.. s iL tanS Bran lS Sey 0 Ss and taking the fquare of each fide of the equation, get Eee ee Pa ers fun ss poets Sire Inftead be deduced one from another by the help of the common trigonometrical tables, It is this, — 2abs ™~ “ords ' I , I ur I iv — (fina + age eile Uke lgeai + 3 fin a 26+ Tm) + T41) + R):- The arches a’, a”, al”, al’, &c. are to be deduced one from another as follows. ; 0 = —_ Take a fuch that fina om, then, fina! tan = a, fin. tan-2 fin gi! — 2 rom tan > a’, fin ai’ = tan z*? &c. The fymbols T(m), T(m+1) and R, denote. the fame things as in the other form of the feries. 312 NEW SERIES for the Inftead of S, we now fabftitute i in this expreffion s, - 5; salt ae 4 &c. fucceflively, and multiply the refults by the terms of the feries 1, ia > ? &c. fo as to form the following feries of equations, the number of which is 2. I I I I z ee se tans 2 Can Sst A 2 2 I I I I ———S a es St ole =(s = 2 tan’ +s 4 tan’zs5 3 4° x 2.4 I I 2 ———— Si et 4 tan*= 5 \ 4 tants S*tan’zs 48 8 hog ap 2.4° I I Pn I ae ee tans pleat 8* tan’ > s 16*tan’ sy 5 oe 4* 16 2.4” &e. From thefe, by: proceeding in all refpects as in the atticle above quoted, that is, by adding, and rejecting what is common to each fide of the fum, we get (ees an tan? 2 git I = I 21 I I I = ~ tan — 5 -+—tan? ne = tan’ Eas, a ae I I I I Bice Tt og ie Roaagl yc Now, QUADRATURE of the CONIC SECTIONS, &c. 313 Now, as we have found (Art. 36.) that 2" tan = exprefles twice the area of the polygon AFF’F’F” (Plate IX.), the numerical value of which we have there denoted by Q, it Ay ° follows, that 2 tan’ —= = Q:. Moreover, the geometrical fe- Hae Ty {ANS apy Mi ad aaopabpagheds a * is equivalent to ~ (z —<); 2.4 a daod i therefore, by fubftitution and tranfpofition, we get I I i (= tan’ = s+ tame ae + tan’ss....+-—tan?=), 4 8 4” 2” 4X | 44. LET us now conceive 2 to be indefinitely great, then, as upon this hypothefis, Q becomes s, and : (e+ becomes fimply 2 and the feries whofe terms were 2 in number, now 3 goes on ad infinitum, we have at laft, after multiplying the oes expreffion by 4, fig es tan’ s 3 x, b> Q (tan = s nin tan? 2 ae 1 tan?2s5 ae tan? — - - = A + tan seit &e. ). And this is one am of the feries to be eke 45. Tur 314 NEW SERIES for the 45. Tue fame feries, however, may be given under another form, better adapted to calculation. For fince, by the nature of the hyperbola ab’ S+ ord’S=ab2S, and ab’S —ord’S=1, therefore, taking the fum and difference of the correfponding fides of thefe equations, we get 2ab*S=ab2S8+1, 20rd S=ab25—13 and hence, by dividing the latter of thefe equations by the former, and putting tanS inftead of pubs , we find ab2S—1I ab2S+1 From this formula, by fubftituting s, +5, +5, &c. inftead of S, we obtain expreflions for tan’ s, tan’>s, tan?+s, &c. Thefe being fubftituted in the feries, and afterwards s put inftead of 25, +5 inftead of s, +5 inftead of ts, &c. (fo as to produce a refult involying only the abfciffae correfponding to the fector s, and its fub-multiples) ; and, finally, the whole being divided by 4, we fhall get fabs+1 2 | abs—1r 3 tans = =| = rabis—1_, rabis—1, 1 abis—1 and this expreffion is analogous to our fecond feries for an arch of a circle, as given at Art. 17. 46. Wr may now inveftigate what are the limits to the rate of convergency of this feries, as alfo the limits to the fum of all its terms following any afligned term. With refpect to the firft of QUADRATURE of the CONIC SECTIONS, &c. 315 of thefe inquiries, it appears, that the terms of the feries, un- der its firft form, (Art. 43) are exactly the {quares of the cor- refponding terms of the former feries, under its firft form (Art. 36.), fo that the one being written thus, ==P— (Tey Tee) ++ ee tT (m+ T (mes) + Tinta) ts &es) Ss the other will be SSP (Ta) AT) «FT + Ting 1) FT na) +, &-), and here P and P’ are put for the parts of the two expreffions which do not follow the law of the remaining terms, but T(1), T(2), &c. denote the fame quantities in both. Now, as each term in the former feries has been proved to be greater than one-fourth of the term immediately before it (Art. 39 ), each term of the latter muft be greater than one-fixteenth of the term immediately before it ; and this is one limit to the rate of convergency. _ AGarn, as it has been proved (Art. 40.), that in the , therefore, fquaring, we have ool : T’(n+1) firft feries Ton+2) fe bie a 4 T’(n+2) ot. Now this quantity is a third proportional to Tn) and T*(n41)3; hence it follows, that the greater limit of the rate of convergency in-the two feries is the very fame; _ that is, each term is lefs than a third proportional to the two terms immediately before it. As thefe limits to the rate of convergency differ from thofe of our fecond feries for an arch of a circle (Art. Pos), only by the leffer limit in the one cafe correfponding to the “greater in the other, and the contrary, it is fufficiently evident, Vou. VI.—P. II. sr that 316 NEW SERIES for the that by proceeding, as in the cafe of the circle, to determine limits to the fum of all the terms following any afligned term, we would obtain an analogous refult, namely, that the fum of all the terms following any afligned term is greater than ;'-th of that term, but lefs than a third proportional to the difference of the two terms immediately before it, and the latter of the two. 47. Ir now only remains to be confidered, how the numeri- cal values of the terms of the feries are to be found. Now, this may evidently be done by computing the values of the quanti- ties abis, ab+s, ab4s, &c. from the abfcifla correfponding to the whole fector, and from one another by the known for- mula abS+1 ab 4S =A/ 3 abts—1 abis—I &e and thence the values of the quanties ——2—~—_—, —_4 = q ~ abes+a abis+r Or we may deduce each of thefe from that which precedes it, by a formula analogous to that found at Art. 21. in the cafe of the circle, and which may be inveftigated as follows. Let abS—r ab>S—rI j 3 re == 7, as = 7 = ab SE , and abis Seok , then we have ab § er, and eae ee +3‘ we have alfo ab Six taht and fince by the nature of the hyperbola ab}S= NA Siege therefore QUADRATURE of the CONIC SECTIONS, &c. 317 I / therefore —__—— — ! it and hence 7 = r—z” I—/Y/1—?t Toe ar which is the formula required. 48. Tue refult of the whole inveftigation of this fecond fe- ries, for the area of an hyperbolic fector, may now be collected into one point of view, as follows. Puttinc s for the area of the fector, let its correfponding abf{cifla be denoted by the abbreviated expreflion abs; alfo let the abfciff correfponding to the other fectors which are its fub-multiples be denoted fimilarly. Compute the feries of quantities abs, abis, abys, &c. from abs, and one another, by the formula abig—Vapd+2 ig OS SD 2 Then fhall 6220ab Seb iwin ince — abs —1I 3 i rabas—1, 1 abys—t Yabts—r tas gabis+1° Pabis+i-° 4g abzs+1 ie SER ae a ae J where R denotes the fum of all the terms following the term T(m+x1), and this fum is always contained between the limits T*(m+1) I It, q — Timta) T5 Ee +1) an T(m)— L(m+1)’ Rr 2 é being 318 NEW SERIES for the being greater than the former, but lefs than the latter. This laft limit may alfo be otherwife expreffed thus, (16 Timt1) — T m) Tent1) 15 (T(m) ne = T(m4r1) + Or compute the feries of HARRIS t, t', t’, &c. one from another by thefe formulz Jabra pT? | raver ~ absae dr PNG RE pee Then fhall Ln BS a8 82 Eo ns Poker eae seal! + Bt teh tb Tob Tot TR), the fymbols Tym), T(m+1), and R, being put to denote the fame as before. 49. WE might now inveftigate other feries for the quadra- ture of an hyperbolic feétor, fimilar to the third and fourth fe- ries we have found for the rectification of an arch of a circle; but this inquiry would extend the Paper to too great a length. For this reafon, and alfo becaufe the manner of proceeding in the one cafe is exactly the fame as has been followed in the other, it feems unneceflary, in the cafe of the hyperbola, to ex- tend our inquiries farther. I fhall therefore now proceed to the third and laft object propofed in this Paper, namely, the in- veftigation of formule for the calculation of logarithms, be- ginning with a few remarks that may ferve to connect thefe formule with the common theory. 50. Ir is ufually fhewn by writers on this fubject, that all numbers whatever are confidered as equal, or nearly equal, to one QUADRATURE of the CONIC SECTIONS, &c. 319 one or other of the terms of a geometrical feries whofe firft term is unity and common ratio, a number very nearly equal to unity, but a little greater; and any quantities proportional to the exponents of the terms of the feries, are the logarithms of the numbers to which the terms are equal. Locaritums, then, being not abfolute but relative quanti- ties, we may aflume any number whatever as that whofe loga- rithm is unity ; but a particular number being once chofen, the logarithms of all other numbers are thereby fixed. HeEncE it follows, that there may be different fyftems, ac- cording as unity is made the logarithm of one or another num- ber; the logarithms of two given numbers, however, will al- ways have the fame ratio to each other in every fyftem what- ever ; thefe properties which are commonly known, are men- tioned here only for the fake of what is to follow, as we have already premifed. 51. TAKING this view of the theory of logarithms as the foundation of our inveftigations, LET us put 7 for the common ratio of the geometrical feries, x for any number or term of the {eries, 4 for the number whofe logarithm is unity, y for the exponent of that power of r which is equal to x, m for the exponent of the power of r which is equal to 4. ‘Then we have x =7’, and =r”, and becaufe by the nature of logarithms log x: log 4::y:m, therefore log x =2 x log 4; but by hypothefis log 6 = 1, therefore log « = z 52. Let 320 NEW SERIES for the 52. Ler w denote any number greater than unity, and p and n any two whole pofitive numbers ; then, by a known formula uv ye — IT = —tfutytepor.. te}, fopopopot... tor fs therefore, dividing each fide of the firft of thefe equations by the correfponding fide of the fecond, we get v—r i vtv+tu+u...+ vi v+ut+utu... fu Now, v being by hypothefis greater than unity, the fraction on the right hand fide of this equation is lefs than this other fraction vo + or t+ve+v?...+v? (to pterms) _ pv? aes Cr EE rh. becaufe it has manifeftly a lefs numerator, and at the fame time a greater denominator. The fame fraction is, however, greater than this fraction rti1t+i1+i1.--+1 (topterms) _ Se eer ee Garten voto +o... +0" (tom terms) — ip becaufe it has a greater numerator, and a lefs denominator. Therefore, we—T ye pe , < p = > p ? Peo T n U—TI nv" and hence, dividing the firft of thefe expreflions by v¢, and mul- tiplying the fecond by v", yb —"T vo" (vt — 1) no w(t —t1)’ yeaah (a). 53. PuTTING QUADRATURE of the CONIC SECTIONS, &c. 32%. 53. Purtine v and f to denote, as in laft article, it is mani- feft that the feries is greater than this other feries TFL et t-te ct a, (to pyterms) = A, but lefs than this feries v+u+u+u...+4 (topterms) = pv; but by a known formula, the fum of the firft of thefe three ie- ries is U—— F ——, therefore, p U—tI U1 U—tI 1 > p; I t i Ft = i ? B Gad ok) > a 54. Ler us now recur to the fymbols r, x, b, y and m, whofe values are affigned in Art. 51. and let us aflume y = /, and r= v"; then, from the two expreflions () in Art. 52, we have I> i 322 NEW SERIES for the y x ; ‘r—r y Sat r—tI and hence, multiplying by 2, and dividing by m, 2 } Z =| BN (rr) n(r" —1T) m 2" m(r—t) m S50 Ga cae But 7? =x, and 7"= 4, (Art. §1.), from which it follows, that - T nm ry =x, andr=b" ; moreover, = = log «; therefore, fubftitu- ting, we get n (as) oon (x — 1) , logx —. x” m(b —t1r) and in thefe expreflions » denotes any whole, pofitive number whatever. 55. By fubtracting the leffer of thefe limits to the logarithm of x from the greater, we find their difference tobe n («" —tI) ests x (o" a ae I) 1 (o" =1) Now zyx [4 x m a QUADRATURE of the CONIG SECTIONS, &c. 323 Now we have found, that one factor of this expreffion, viz. I a(x = 1) cannot exceed the logarithm of x; with re- ae m(b a) = -[4 T I fpe&t to the other factor b" «”—1, fince it appears from the firft of the four formule (@), (Art. 53.), and « <1 ee = ot therefore, aoe x < eas ( , and hence Z" eae eee | Se Cae UL Min . _ Now as we may conceive m and 7 to be as great as we pleate, it is evident that this quantity, which exceeds the factor I T 3" Pg 1, may be {maller than any aflignable quantity ; there- fore the product of the two factors, or the difference between the limits to the value of log x, may, by taking m and 2 fuffi- ciently great, be lefs than any affignable quantity. Upon the whole, then, it appears, that the logarithm of w is a limit to which the two quantities n (x” — Ey nay (x" —1I) =. : int m(b" —1) m(b” — Vou VI.—P. II. Ss continually ols 324 NEW SERIES for the continually approach when m and n are conceived to increafe indefinitely, and to which each at laft comes nearer than by any aflignable difference, juft ds a circle is the limit to all the polygons which can be infcribed in it, or defcribed about it. T Tt 56. THE two expreflions (x — 1), m(b"—1), which en- ter into thefe limits to the logarithm of x, and which are evi- dently functions of the fame kind, have each a finite magni- tude even when m or » is confidered as greater than any aflign- able number ; for fince when v is greater than unity, and p any whole pofitive number, we have Ws I ee =e r) Ey pee a * (ot) S 1—*, (Art. 53+) Therefore, fuppofing x and 4 both greater than 1, (which may always be done in the theory of logarithms), the expreffion I nu . . . . . n(x —1) is neceflarily contained between the limits x — 1 I I = ofge m : and 1—-3 and in like manner, m (d"— 1) is between b—1 x I and I— >. b Tt 57. As the expreffion m cu" — 1) depends entirely upon the value of J, the number whofe logarithm is aflumed = 1, (and which is fometimes called the dasis of the fyftem), the li- mit to which it approaches when m increafes indefinitely will be a conftant quantity in a given fyftem; but the limit to which ete QUADRATURE of the CONIC SECTIONS, &c. — 3:25 which 2 re 1) approaches, when z is conceived to be inde- finitely increafed, will be variable, as it depends upon the par- ticular value of the number x. Ler us therefore denote the limit of m (3 a 1), or that of I m 1) ————,, (for they are evidently the fame), by B, and then rp in the fyftem whofe bafis is 4, the logarithm of «x will be the li- mit of either of thefe two expreflions I I I n (x" —1) a(x" — T) ay B : B : n x when z is conceived to increafe indefinitely, or to {peak brief- I ly, log « ad when 2 is indefinitely great. = B logarithms have denominated the modulus of the fyftem. As in TuE conftant multiplier — is what writers on the fubjeé of NapieEr’s fyftem it is unity, we have, ~ being indefinitely great, Nap. logx = 2 fiek 1), and fince in any fyftem whatever B=m oe 1), or Boa (o" —1), for we may put m or x Ss 2 indifcriminately : 326 NEW SERIES for the indifcriminately ; therefore B= Nap. log 4, and confequently Nap. log x og « (to bafis 2) Naples as is commonly known. 58. Stnck, therefore, the logarithms of any propofed fyftem may be deduced from thofe of Naprer’s fyftem, I {hall throughout the reft of this Paper attend only to the formula Nap. log x =2 (x" —1), being indefinitely great. Ler us then, agreeably to the mode of proceeding employ- ed in the former part of this paper, affume the identical equa- tion X+1_ X+1 1X—I X'—1- 2(X—1) 2X+1° aN LF a Wr : In this expreffion let x2, x*, «®, x**, &c. be fubftituted fuc- P ceflively for X, and let the refults be multiplied by the corre- {ponding terms of the feries, I, =, ? &c. Thus hete-will be formed a feries of equations, which, putting » for their num- ber, and m for 2", may ftand as follows: x+tr “x—TI QUADRATURE of the CONIC SECTIONS, &c. x +1 % —TI x—+r I pes + 2 : 2 7 2(x —TI) K --I = = 2 x +1 x’ +o x —T x I 2 re 4 R gee ; 2 (x —1) 4(«* —1) ae oe = Ls os x +r % der x nal, I 3. Me: ¥ fg R 4a(@ +3) 8 (* =) wie = Z = ee fare naan. si I u a a + 16 2 3 6 8 (« +1) 16 («224 wd a z z 2 (x" + 1) x +r ice evar) et I 2 Fr x rte : m (x —1) m (x — 1) x +d 327 Ler the fum of thefe equations be now taken, and the quantities found on both fides of the refult rejected, then, af- ter 328 NEW SERIES for the ter tran{pofing, we get "i x+r x—I Ir I I I 2 4 t To x —I x —tI x —I xX ——I im ' I I I I x +1 a r + - E + 3 1 + 6 ° z = “x +1 x +I x +I x +r m (x — 1) é m | —I I | += —— l x +1 THIs equation, which is identical, holds true whatever be the value of 7. Let us now, however, fuppofe, that # is inde- finitely great, then the feries will go on ad infinitum, and m = 2” will become indefinitely great; but this being the cafe, will I Pas id I become fimply 2; and m (e* — 1) will become Nap. log x, (Art. 57.) ; therefore eee eatia) thefe limits, and cing by 2, we have Ix+I 2X —--1 1 a uf t? — ' wen a I sit ak dtl at a I ~—+37—-+3——-+5 +, x? +1 xt +t we +1 3 wie ty and QUADRATURE of the CONIC SECTIONS, &e. 329 and this is the firft feries which I propofe to inveftigate for the calculation of logarithms. 59. Tue feries juft now found agreeing exactly in its form with our firft feries for an hyperbolic fector, (Art. 40.), as it ought to do, will of courfe have the fame limits to the rate of its convergency, and to the fum of all its terms, following any propofed term. As the latter of thefe have been deduced from the former, in the cafe of the hyperbola, by a procefs purely analytical, and the fame as we have followed in treating of the rectification of the circle, it is not neceflary to repeat their in- veftigation in this place. The limits to the rate of convergen- cy, however, having been made to depend partly upon the na- ture of the curve, it may be proper, in the prefent inquiry, to deduce them entirely from the analytical formula which has been made the bafis of the inveftigation. Ler any three fucceflive terms of the feries of quantities ei —1 wt —1 x? +1 xt +1 evident from the formula, (Art. 58.), that the relation of thefe quantities to one another will be exprefled by the equa- tions » &c. be denoted by ¢, z#’ and?’; then it is ? 2218 Y pp .2 2 Jr é = t Sp emes (AS t t + ? t er From the firft of thefe we get 2/ =¢(1-+ 7"), now each of the quantities 7, t’, &c. being evidently lefs than unity, it fol- lows, that 1-+#2 <2, but > 1, and therefore that 27’ < 21, , I : and 2’ ¢, and t’> 5 ft Hence it appears, in 330 NEW SERIES for the in the firft place, that each term of our feries, taking its co-ef- ficient into account, is greater than one-fourth of the term be- fore it. aT 4 ii AGAIN, becaufe 7=3 (1+2”); and, fimilarly, v= (1+7”), and it having been proved that ¢’ <7, fo that fimilarly, ¢” <7’, abe a T a Seren hi therefore g (i 77), < z (1+7"), and confequently aro and re s ‘ 8 - i < ri Thus it appears, that each of the quantities 7’, &c. is lefs than a third proportional to the two immediately before it, and the fame muft alfo be true of the terms of the feries. 60. Uron the whole, then, our firft feries for the calculation of logarithms may be expreffed as follows : 5 Si getd Mthdy ee pik teetemeah tnobe ail on ogx 2%x%—I arcs ge ue seria 10,5 4 y + Tm) + T(m+1) + R)3 and here, as in the former feries, Tim) and T(m+1) denote any al : : : I two fucceeding terms, andR is a quantity greater than ~ T(m+1), 3 but lefs than a third proportional to T(m) — T(m41) and Tn+1) 3 or it is lefs than Dcsusporis T(m41) — T(m) T (asta) 3 (Lm) — Tomtx) PY Qobe Or. LHAT | QUADRATURE of the CONIC SECTIONS, &c. 351 61. THAT we may inveftigate a fecond feries, we muft take the {quare of the formula, (Art. 58.), which will be ey axe ea From this expreffion, proceeding exactly as in Art. 58. we form the following feries of equations, (a= Ty 4 (x? — 1) un? al I (x? +1)" (w* +1) eh = . +4 (.—) +4, A(wi ty opty 4A Nae Ah (x? + 2)? (x? ++ 1) ig: emt €@%—1) etary + Nb 4d Way 2 : & 4(« +1) (x" + 3)" rst at tae Ee et (ig y+ a mm (x"—1) © m(x"—1) x” va I Here n denotes the number of equations, and m is put for 2”. Let the fum of the correfponding fides of thefe equations be ta- ken, and the quantities common to each rejected, as ufual, and Vou. VI.—P. II. ; Te the 332 NEW SERIES for the the refult, after tranfpofition, will be apie kee 2 ct Se 24 24° 2.45 2.47—* Cee “ft ee ae te socsoudeay r hoa C ae ae oa Bs dae m* (x" —1)° | ‘ : This Soke holds true when 2 is any whole pofitive number whatever. But if we fuppofe it indefinitely great, then the two feries will go on ad infinitum, and the limit of the numerical fe- ries will be 2, alfo the limit of (#"+-') ‘will be'4; and tHeli+ mit of m(x”—1)° will be log, (Art. 57.) ; therefore, fub- ftituting thefe limits, and alfo putting —4* 4+ for @ =a) =a) = , and dividing the whole expreflion by 4, we get i Tt — log’ * ~~ QUADRATURE of the CONIC SECTIONS, &c. 333 (ish I hoa. FS - if a 2 4 2 8 mi 4 te Cai I ea 0 gall a oe Wipe apiosad I are I 44 I ie Z g * 4\ > 4 = =, z x +I x +i Ee ear! and thus we have obtained a fecond feries for the logarithm of a number, which, by putting ¢, 7’, &c. inftead of the fractions ue Ee x7——IT xt—Ff ; , &c. and remarking that the relation which x? aE xt +1 the quantities 7, z’, &c. have to one another is identical with that of the quantities tans, tants, &c. (Art. 35.), it will ap- pear to be the fame as our fecond feries for the area of an hy- perbolic fector, (Art. 43.). Of courfe it will have the fame li- mits to the rate of its convergency, and to the fum of all its terms following any given term. Now thefe have been found without any reference to the geometrical properties of the curve, therefore it is not neceflary to repeat their inveftiga- tion. 62. We muft now transform our feries upon principles pure- ly analytical, fo as to fuit it to calculation. And, in the firft W—To2 wx? —ax+y 1(w+1)—1 place, becaufe ( ) = : 4 i x +1 — ———— = —___—_ if a -anpax 9 +2) +2? pa we 334 NEW SERIES for the we put - («+ =) = X, it follows, that CS == beret; I In like manner, putting * ie +=) = X’, and i(#-) 4 xe 2 ¢ 4 1 a 1 2 w?—I x4—I u" x’ — I xe = X”, we have | — a= _ and 4 begee ee at I eh PP x? ty &c. Again, becaufe X'= : (#44). therefore 2X* = x? I I € +1) ERs (: 4 =) =X, therefore 2X" =X +4, 2 in 2 x and X’ i — In like manner, it will appear, that yy = (eee &c. 63. From the preceding inveftigation it appears, upon the whole, that our fecond feries for the calculation of a logarithm may be expreffed as follows. Purrinc «x for any number, let a feries of quantities X, X’, X’, X”, &c. be found fuch that Xai fet te x NATE ie &e. Then will log’ « QUADRATURE of the CONIC SECTIONS, &c. 335 : pgietans Spe See | (w—1y* wi 12 zy wu ieee ee pe aa et ie i X’+1 4° X’+1 its 4 X"+1 °°" Lo + Twn) + Tein + RE and here T(m), T(m+z1), are put for any two fucceflive terms of the feries,-and R for the fum of all the following terms: And in every cafeR is greater than # T(m+41), but lefs than I 16 T(m+1) — T(m) =" T m <= - PANT el Ae ee m I)}e ue eet Ted) 64. From the analogy of the two formule from which we have deduced the feries for the rectification of an arch of a circle, and for the calculation of logarithms, it is eafy to infer that there will be correfponding feries for the refolution of each of thefe problems. And as the two preceding feries for a logarithm have been inveftigated in the very fame way as the firft two feries for an arch of a circle, fo, by proceeding exact- ly as in the inveftigation of the third and fourth feries for the circle, we may obtain a third and fourth feries for a logarithm. The mode of deduction, then, being the fame in both cafes, and alfo fufficiently evident, I fhall fimply ftate the refult of the inveftigation of a feries for logarithms which is analogous to our fourth feries for an arch of a circle, (Art. 28.). Ler x be any number, and X, X’, X’, X”, &c. a feries of quantities formed from x, and one another, as f{pecified in the beginning of the laft article. Then I logts — 336 NEW SERIES for the m (wt ge ee) es 6 (x — 1)* 8.9.10 I =J+4 I es SF pate i X'+12X’—13 _ log* x | 316 X+- 4X4 3 310° X'+4 X74 3 | ne ee 2 XO TS Loh grote tes ee The terms of this feries approach continually to thofe of a : 5 f Kren/ tad geometrical feries, of which the common ratio is OE and hence it follows, that the fum of all the terms after any aflign- ed term, approaches the nearer to ra of that term, according as it is more advanced in the feries. 65. BesipEs the foregoing, our method furnifhes yet another kind of expreflion for the logarithm of a number, namely, a product confifting of an infinite number of factors, which ap- proach continually to unity. Such an expreflion may be inyef- tigated as follows. From the identical equation X r= (XK? — 1) (KF $0). Let there be formed the feries of equations ho I =2(e? 2th 2@?—1)=4e* ete z -_ m “ (x"—1)=m (x” —tI) pM Bis = a here | QUADRATURE of the CONIC SECTIONS, &c. 337 — here m is put for any integer power of 2. Let the product of the correiponding fides of thefe equations be now taken, and the common factors rejected, and the refult will be I r—I=m(« — 1) Ser we uN and hence ro 2 2 2 2 m (x" — 1) = (% —1) I watir wer xt ty men B This equation holds true, m being any power of 2 whatever. Let us, however, conceive it indefinitely great. Then the number of factors will become infinite, and m ere 1) will become Nap. log x (Art. 57.). Therefore, 2 2 2 2 atay gee ee aie ate b y Nap. log « = (# — 1) » &e. ad infinitum. Tue product of any finite number of thefe factors being al- ways a function of this form m (a”—1) will of courfe be great- I ze er than log 2, (Art. 54.). However, the function — m (vc —r) m x I or m (: — — }, being in like manner expanded into an infi- nite 338 NEW SERIES for the nite product, we get from it -=( 1! log a= G y) ad infinitum. —<—____ 2 I I ; carta we cam oa tata 4 2 +1 I = a? and. the product of any finite number of factors of this expref- fion will always be lefs than log a. TuEseE formule, which are analogous to that given by Ev- LER for an arch of a circle, (fee Art. 33.), are not inelegant, confidered as analytical transformations. It does not feem, however, that without fome analytical artifice, they can be ap- plied with advantage to the actual calculation of logarithms, by reafon of the great labour which would be neceflary to ob- tain a refult tolerably accurate. 66. I sHaLt now conclude this Paper, with fome examples of the application of the formule to the computation of the length of one-fourth the circumference of a circle whofe radius is unity, (which is the extreme and the moft unfavourable cafe), and to the computation of a logarithm; as alfo of the modulus of the common fyftem of logarithms, which is the re- ciprocal of NariEr’s logarithm of Io. EXAMPLE 2UADRATURE of ihe CONIC SECTIONS, &. 339 Exampte I. The length of an arch of 90°, computed to 12 places of decimals, by means of the firft feries, (Art. 12.). Here a= 90°. I ——_ = cota—=o tan > tana ta tanta=TI tan iy tan 4 4 = 0.414213562373r tanzts tan 3 a= 0.1989123673796 tan =+> a= a a= a= 0.024.5486221089 = 0.012272462379. = 0.0061 36000157. = 0.003067971201. tan 7's 4@= 0.0984914033571 = tan -75z @ = 0,001533981094.. tan 3; 4= 0.0491268497694. tan >'75 4 = 0.00076699054.. ae —_——==_e==== 3 tan a= .500 000000 c00 0 4 tan | 4 = .103 553 390 593 3 “y tan ¢ 4 = .024 864 045 9225 ‘jf -tan sa .006 155 712 7098 zz tan zy 4 = 001 §35 214 056 3 S < 0000001248357 S > .cocococor iy q 4 = .000 383 572 2205 = .000 095 878 612 3 = -000 023 968 7506 = -000 005 992 131 3 = -000 001 498 029 3 = +900 000 374 507 1 Hence S = .000 000 124 8365 vf ee a — 036 619 772 367 7 Arch of 90°, OF 4= 1.570 796 326 795. Vou. VI. P. Il. Uu EXAMPLE 340 NEW SERIES for the _ ExaMPLe II, The length of an arch of 90°, computed by- the fecond feries, (Art. 22.). cofa=o ee: a = 0.99518472667.. cof + a= 0.7071067811865 cof ,'5 4 = 0.998795456aI.. cof +4 = 0.9238795325113- cof ;'; 4= 0.9996988187... colt 4 = 0.980785280403. aay Amount of pofitive 1 1+ cofa re 5 = .416 666 666 666 7 terms, 4 —cola ie PISA OS «ne, vey ce yt era we ae = .010 723 304 703 4 hee cofta ) ai sine eats -000 618 220 7796 & t—cofta 4*1+colta t r1—colft.a _ 4°>1+col+.4 = .000 037 892 7990 .000 002 356 882 2 1 100954 — 900 000 147 127 6 4°1-+cof4 & Ecole = .000 000 009 1927 471+ cols,4 i 00 612 8 pees feictels Hence = .000 000 000 612 7 S> .000 g00 000°612 6 Amount of negative terms, .O11 381 932097 2 Difference between the apie of Lacgigasaanes 560% and negative terms, bee ; == 636 619 772 3677 Arch of 90°, or a= 1.570 796 326.795- EXAMPLE QUADRATURE of the CONIG SECTIONS, &c. 34% Exampre III. The length of an arch of 90°, calculated from the fourth feries, (Art. 28.). ’ . cofa=o cof} a= 0.980 785 280.... cof$a= 0.707106 781 1865 coft;a=0.905 1847...... colt a= 0.923 879532 51.-. cof -a=o0.998 80.5... I 13—cofa+12cofta _ “316° 3-4 cola—4colia — -163 053 go2 0108 Cee = .O0I 215 2777778 Amount of pofitive terms, .164 269 179 788 6 a 13 —cof+4a—t12cofta 3.16° 3+cofsa+4colta iene 13—cofita—tz2colita ~ 3.164 3+ colta+4colz,a I 13—cofsa—i200f,4 3-165 3+ colzga+ 4colysa Pika 13 — cof, a— 12 cof 74 3.16 3-4 cols-a+4colz,a Each of the remaining terms, being tn} -000 013 261 796 5 = .000 000 198 794 2 = -000 000 003 074 4 = .000 000 000 047 8 ly z'5th of the term before it, their fum ¢ .002 000 000 000 8 will be nearly #5 of the laft term, or itt Amount of negative terms, /000013 463 7137 Difference between the “ar Ua agi seabed th Slam and negative terms, or gi — *164 255 716 074.9 I = = +405 284 734 569 3 Aj = .636 619 772 3676 Arch of 90°, or 4 =.1.570 796 326 795. Uu2 EXAMPLE aaa 5 NEW SERIES for the Exampie IV. The reciprocal of Naprer’s logarithm of 10, (which is the modulus of the common fyftem), calculated by the fecond feries for logarithms. (See Art. 63.). x ==10, and hence X= 5.05 X*’ = 1.010 373154 20... X' = 1.739 252 713 092 7 X” = 1.002 589 934 6... X’ = 1.170 310 367 614 6 x" = 7.000647 27x cis X" = 1.041 707 820 748. Be. GO, VOT BOR cam, x 7 = .123 456 790123 5 vz = 083 333 333 333 3 Sum of pofitive terms, .206 790 123 456 8 aXe = 16 867 116 4758 ee = .001 226 137 7606 7% I X“oS % to’ 6 8 re se 709 5180 ead ay = .000 005 038 8826 4° t X* —T — \000 00 31 a“ Xv+1 Tr 3 5 745 2 T xXx*'—Tt_ 6 px = .000 000 019 746 9 1 X¥""=1 = .000 000 oor Bee ae 7.34 4 R > .0000000000822,9 2 R <.0000000000823,1 5 i Sum of negative terms, 0018 178 426 445 8° Difference of the a I__ — 388611697 0110 , and negative terms, log* ro y tF log 10 R = .000 000 000 082 3 = -434 294 481 903. EXAMPLE QUADRATURE of the CONIC SECTIONS, &c. 343 Examexe V.. Naprer’s logarithm of 10, calculated by the third feries for logarithms., (See Art..64.). w= 10) XS 5.05 X”"= 't.0417078207.' .”. X’ = 1.739252713093- ee SSP LOST BPS se es = EROOZ HO.” fetes X’= 1.17031036761. . 2. a (a +4e+1) 6 (w—1)* 1 ROOTS 3.167 X+4X +3 3.167 X + 4X’ +3 3-20! XR 4 XY + 3 5.1ps_ Oe + AE + 3 ti R12 M13 310) K+ 4X + 3 gs of laft term = fum of the =} maining terms nearly, -035 817-710 714.8 = .O00O1 121 093 421 4 = .000 024 O4T 1229 = .000 000 409 2394 = .000.000 006 5357 = .000 000 000 102 7 .000 000 000 OO! 6 From fum of pofitive terms, = .036 963 261 138 5 Subtraat ae = .00r 388 888 888 g There remains eeras = 1035 574 3722496 oe a= .188 611 697 OII 3 fons = +434 294 481 903 « EXAMPLE 344 NEW SERIES for the Exampie VI. To thew that the feries inveftigated in this Paper are applicable in every cafe, whether the number whofe logarithm is required be large or fmall, let it be required to calculate the common logarithm of the large prime number 1243 to feven decimal places, by the fecond feries, (Art. 63.). me: X” = 1.42356148 MX = 621.50040225 XY = 1.10080913 X'= 17.64228446 XY = 1.0248925. X’= = 33.05 305457 a =| T:G0G8047 nae = -000 805 Sor vz = +083 333 333. Sum of pofitive terms, -084 139134 X'’—1 = Xp = 1055 794 813 xe X41 Ee : = .007 914 766 Mt aa = .000 682 688 sa pee = .000 046 861 # ar = .000 003 OO oa : = .000 000 189 R > .000000012,6 R = ston e00083 R. < .000000012,7 Sum of negative terms, -004 442 331 Ce. See 68 Nap. log* x on9 ati I at Maes ee i A ed Common log of 1243 = ae = 3.094 471 I. « No. IX. 4 i i Trans RS Edin Wot tlp. 3b : ———————————————— PLATE IX ae : e : ‘ Pras 1 iy cp Reve aft 4 eat he IX. Remarks on a Mtnerat from Greenuanp, supposed to be CrRYSTALLISED GADOLINITE. By Tuomas Autan, Ese. F.R.S. Ep. [Read 21st November 1808]. NON a parcel of minerals which I procured laft fpring, there are fpecimens of two very, rare fofflils ; one of them, the Cryolite, the other I believe a variety of the Gadolinite. _ The former, is accurately defcribed in the different mineralo-- gical works, and I have little to add to the information con- tained inthem. But the Gadolinite appears to be very imper- feétly known, and has never yet been defcribed as a crystallifed. foffil. _ Tue minerals in queftion were found on board a Danith: prize, captured on her paflage from Iceland to Copenhagen, and were fold with the reft of her cargo at Leith. On examination, I was furprifed to find they correfponded fo little with the fof- fils which are ufually: brought from that ifland, and confe- quently endeavoured to trace from the fhip’s papers, any parti- culars that might lead to the knowledge of their geographic ~ origin. All I could learn was, that they were fent. from Davis’ Straits by a Miffionary. _I consipeEr this limited information, however, fufficient to fix on the coaft of Greenland as the place from whence they had- 346 On a2 MINERAL supposed to be had been brought ; the only,Cryolite known in Europe having been fent by a Miflionary from Greenland to-Copenhagen. Tne Gadolinite, from its extreme fcarcity, is a mineral to be found in very few cabinets; and when this collection fell into my hands, was one of ‘thofe I knew only by de- {cription. I was led to fufpeét that fome of the minerals in this parcel belonged to that fpecies, by obferving, im- bedded in a piece of granite, fome fmall fhapelefs mafles, whofe external characters appeared to correfpond entirely with thofe afligned to the gadolinite ; but on reference to the mi- neralogical works which treat of this ftone, I found more diffi- culty than could have been fuppofed in afcertaining whether they did fo or not. The inveftigation, however, furnifhed a ftrong proof of the fuperiority of chemical teft over external character; for although the fhape, luftre, fra@ture, and geogno- ftic relations, left me fcarcely any room to doubt, yet on apply- ing the blow-pipe and acids, it was quite evident, that the ftone I firft tried could not be gadolinite. I examined with great care the reft of the parcel, and picked out feveral, which, though very different, refembled in various refpects the one that originally at- tracted attention; and with a view to fatisfy myfelf, I fent duplicates to a friend in London, from whom I learnt, that one of thofe which I fuppofed to be gadolinite was certain- ly that mineral. Notwithftanding the very refpectable autho- _ rity I had obtained, to which I was inclined to pay the utmoft deference, it was not till after minute and repeated inveftiga- tions that I found myfelf difpofed to fubmit to it; the phyfical characters of the fpecimen in queftion SHEETS, fo very widely from thofe I was taught to expect. Ir is more than twenty years fince the gadolinite was firtt obferved by M. ARRHENIUS, in an old quarry at Roflagie, near Ytterby in Sweden. It was defcribed by Mr Geyer, and by him confidered as a black zeolite. In / CRYSTALLISED GADOLINITE. 347. In 1794, M. Gapotrn analyfed it, and found that it con-» tained 38 per cent. of an unknown earth, whofe properties approached to alumine in fome refpects, and to calcare- 6us earth in others; but that it eflentially differed from both, as well as from every other known earth. In 1797 M. Exeserc repeated the analyfis of M. Gano- Lin, and obtained 474 per cent. of the new earth. This in- creafe of quantity he attributed to the greater purity of the fpecimens he fubmitted to experiment, and in confequence of having confirmed the difcovery of Gapozin, he called the ftone after him, and gave the name of Yttria to the earth. ANALYsES by VauQueL:n and Kiaprortn have fince ap- peared. The quantity of yttria obferved by the former amounted only to 35 per cent.; ‘but the latter ftates 593 per cent. Tue fmall portions of this mineral, which, from its rarity, it is natural to conclude were at the difpofal of thefe celebrated chemifts, may in fome meafure account for the diverfity of their refults ; but it is likewife by no means impoflible, that the mineral itfelf may have varied i in the epeiorcry: of its chemi- cal ingredients. Tue difference which we find in the mineralogical defcrip- tions of this foflil; hitherto only found in one fpot, is much more difficult to account for. If the information I have other- wife obtained be correé, of which I have not the flighteft doubt, we cannot, help attributing a certain degree of careleff- nefs to fome of the authors, particularly the French writers, who have fuch opportunities at command *, of inveftigating - every point relative to natural hiftory. The great veneration’ Vou. VI. P. II. Xx they * Lucas notes the Gadolinite as one of the minerals in the colleftion at the Fardin de Plantes. 348 On a MINERAL supposed to be they entertain for the talents and accuracy of the celebrated Haiiy, may induce them to think his obfervations require no concurring teftimony ; and, on the other hand, the pupils of the German School, confider no mineral deferving a place in their fyftem, till it has been examined and claffed by their illu- ftrious mafter, whofe authority will be handed down by them with equal refpeét to pofterity. Ir is unneceflary to occupy the time of the Society, in gi- ving a comparative view of the different defcriptions of the Gadolinite. I fhall only notice a few prominent features. Ir is defcribed by every one of the authors, as pofleiling a. fpecific gravity of upwards of 4, and as acting powerfully upon the magnet. This laft character is noticed by Profeflor Jame- son, in the firft account he gives of the gadolinite; but in the fecond it is omitted, along with fome others. KLaprotu takes no notice of its magnetic power, but flates the fpecific gravity at 4:237- Tue French writers defcribe the colour as black and-reddith black. The German as raven or greenifh black. Thefe varia- tions, with feveral others which may be obferved on referring to the different authors, fhew that fome incorrectnefs muft ex- ift. But the moft remarkable of all is, that the gadolinite, if ever magnetic, is not always fo; for the fpecimens in the poffef- fion of the Count pE Bournow are not, nor, as he informs me, _ are any that he has ever feen. It is therefore’ reafonable to _ conclude, that magnetifm in the gadolinite.may depend on accidental caufés. F Tue following is the defcription of the foffil, which I fup- pofe to be that fabftance in a cryftallifed ftate; although no- thing fhort of analyfis can afford indifputable teftimony of the identity of any mineral fo little known. SPECIFIC CRYSTALLISED GADOLINITE. 349 sabanbsek Gravity, 3.4802. The {pecimen iat 1136.39 ~ «grains. Its furface is a little decompofed, and it has allo fome minute particles of telfpar intermixed with it; both of which would affect the refult in fome degree ;_ but nei- ther were of fuch amount as to do fo in any confiderable degree. | Harpness: fufficient to refift fteel, and {cratch glafs, but not quartz. Lustre: fhining, approaching to refinous. FRACTURE : uneven, verging to flat conchoidal. Cotour: pitch black which I confider velvet black with a fhade of brown; when pounded, of a greenifh grey co- lour. Ficure: it occurs cryftallifed. The fimpleft figure, and perhaps the primitive form, is a rhomboidal pritm, whofe planes meet under angles of 120° and 60°. In fome of the fpecimens, the acute angle is replaced by one face, in others by two, thereby forming fix and eight fided prifms. All the fpecimens I poffels are only frag- ments of cryftals, none of which retain any part of a ter- mination. They occur imbedded in felfpar, probably gra- nite. CuemicaL CHaracters: before the blow- pipe froths up, and melts but only partially, leaving a brown fcoria ; with borax it melts imto a black glafs. When pounded, and heated in diluted nitric acid, it tinges the liquid of a ftraw colour ; and, fome time after cooling, gélatinates. Tue principal diftinguifhing character of the gadolinite, is its forming a jelly with acid, a chara&er belonging to few other minerals. The Mezotype Lazulite, Apophilite, Adelite, and Oxide of Zine, fo far as I know, alone pofleis the fame qua- lity ; aud it cannot eafily be miftaken for any of them. Bx) 2 Ir 350 On a MINERAL supposed to be Ir has not the fmalleft attraction for the magnet; it does not decrepitate and difperfe when expofed to the blow-pipe ; it is not in any fhape tran{parent. Tue Swedifh foflil occurs in roundifh amorphous mafles, im- bedded and diifeminated in a granitic rock, having the external furfaces covered with a flight whitith coating, perhaps from the attachment of micaceous particles. ‘There is no fuch ap- pearance on the furface of the cryftallifed gadolinite. Tue fituation which this mineral fhould hoid in the fyftem has been a matter of difficulty among mineralagifts. Haiy has placed it in the clafs of Earthy Foflils, immediately after his Anatafe and Dioptafe,—rather an unfortunate fituation, both thefe having been recognifed as ores of known metals, titanium and copper, fince the publication of his admirable treatife. . WERNER, On account of its weight, has claffled it among the metals; and from its natural alliances, and chemical com- pofition, has given it a place among the irons *. If weight en- titled it to be clafled among the metals, feveral other minerals have an equal claim to the fame fituation. Of its natural alli- ances we know very little, farther than that the Swedifh di- ftri& where it is found abounds in iron; and as to its chemi- cal compofition, if 174 per cent. of iron be fufficient to counter- balance 592ths of a new earth, it would be right to arrange it accordingly. The analyfes of fo many chemifts of known ce- lebrity, are certainly fufficient to juftify the conftitution of a new fpecies for its reception. WERNER, however, may feel himfelf licenfed in this arrangement, as he does not confider it neceflary that a mineral compound fhall preferve the charac- ters of its components ; but that any of the components may give to the compofition characters fufficiently marked, to de- termine its relations. It is upon this diftinction that he founds the difference between-the predominant and chara¢teriftic prin- ciples t. | THE * JAMESON, Vol. ii. p. 613. + BrocHantT, vol. i. p. 44. CRYSTALLISED GADOLINITE. — — 35 THE arrangement of BRONGNIART appears much more ju- dicious; he has placed it at the commencement of the Earthy Minerals, and aflighs as a reafon, that it is unique in its com- pofition ; and if placed in any other fituation, it would interrupt the feries, either in refpedt to its compofition or external cha- racters. Or the Cryolite I have very little to obferve, in addition to the defcriptions given in the different mineralogical works. The fpecific gravity I found to be 2.961; Haiiy ftates it at 2.949. Among the various mafles I examined, there was no trace of cryftallization, farther than the cleavage, which is threefold, and nearly at right angles. The mafles broke in two direc- tions, (which may be fuppofed the fides of the prifm), with. great facility, leaving a very fmooth furface ; but the tranfverfe cleavage was more difficult, and by no means fo {mooth. Se- veral of the fpecimens being mixed with galena, pyrites, and. cryftals of {parry iron-ore, it would appear that the cryolite is a vein-ftone ; but I was not fo fortunate as to find any of it at- tached to a rock fpecimen, fo as to throw light on its geo- gnoftic relations. i Besa eee Rat 375 hig ee Sy he 2) is) HAG ict a: igs * “ ve mali ate ai bei eG se a pi wre ave: ae a t sWoaigicn ta cy g ®! tif ines Area hibvaRe sete ve ithe ese ipesecate Bite ehaey at A ee Mae yt OE ie fade ah a2 We. es ain “ag. pest tg ween tga wun My, xX ages. ings uy : Bae A ve ae ae a a aie aa rdea wane ee! ne. see .. ore rs a Bi feta Fee 4 a waa es ai ae aa 2 His bry ae ea k af Rhy | ney ee To ; & ike Sk, s hey! ronan fi m Lit leag ¢ Bete yh, Cee “wigan Pus ‘ SEERA REIN 4a xe ; ‘ he wy she “Al” te AY ik ot Py , - : wie ¢ = Mer 12 he ~ P oe: aT X. On the Progress of Heat when communicated to Spheri- cal Bodies from their Centres. By Joun Prayratr, F.R.S. Lonp. Sect. R.S. Evin. and Professor of Natural Philosophy in the University of Edinburgh. [ Read March 6. 1809.]} N argument againft the hypothefis of central heat has been ftated by an ingenious BENS as carrying with it the evidence of demonftration. “cc “ Tue effential and charadteriftic property of the power producing hear, is its tendency to exift every where in a ftate of equilibrium, and it cannot hence be preferved without lofs or without diffufion, in an accumulated ftate. In the theory of Hutton, the exiftence of an intenfe local heat, acting for a long period of time, is affumed. But it is impoffible to pro- cure caloric in an infulated ftate. Waving every objection to its production, and fuppofing it to be generated to any ex- tent, it cannot be continued, but muft be propagated to the contiguous matter. If a heat, therefore, exifted in the cen- tral region ofthe earth, it muft be diffufed over the whole mafs; nor can any arrangement effectually counteraé this diffufion. It may take place flowly, but it muft always con- tinue progreflive, and muft be utterly fubverfive of that fy- {tem of indefinitely renewed operations which is repre- Wou: WLP, I: Yy “ fented 354 On th PROGRESS of HEAT “-fented as the grand excellence of the Huttonian Theory *.”’ “ Again, he obferves, in giving what he fays appears to him a demonftration of the fallacy of the firft principles of the Hut- - tonian Syftem, “ it will not be difputed, that the tendency of “ caloric is to diffufe itfelf over matter, till a common tempe- “ rature is eftablifhed. Nor will it probably be denied, that a “ power conftantly diffufing itfelf from the centre of any mafs “ of matter, cannot remain for an indefinite time locally accu- “ mulated in that mafs, but muft at length become equal or “ nearly fo over the whole f.”’ 2. 1 muft confefs, notwithftanding the refpe& I entertain for the acutenefs and accuracy of the author of this reafoning, that it does not appear to me to poflefs the force which he afcribes to it; nor to be confiftent with many facts that fall every day un- der our obfervation. . A fire foon heats a room to a certain de- gree, and though kept up ever fo long, if its intenfity, and all other circumftances remain the fame, the heat continues very unequally diftributed through the room ; but the temperature of every part continues invariable. If a bar of iron has one end of it thruft into the fire, the other end will not in any length: of time become red-hot; but the whole bar will quick- ly come into fuch a ftate, that every point will have a fixed temperature, lower as it is farther from the fire, but remain- ing invariable while the condition of the fire, and of the medium that furrounds the bar, continues the fame. The reafon indeed is plain: the equilibrium of heat is not fo much a primary law in the diftribution of that fluid, as the limitation of another law which is general and ultimate, confifting in the tendency of heat to pafs with a greater or a lefs velocity, according to circumftances, from bodies where the temperature is * Murray's Syflem of Chemistry, vol. iii. Appendix, p. 49. + Page 51. in SPHERICAL BODTES. 355 is higher, to thofe where it is lower, or from thofe which con- tain more heat, according to the indication of the thermome- ter, to thofe which contain le‘. It is of this general tendency, that the equilibrium or uniform diftribution of heat is a confe- quence,—but a confequence only contingent, requiring the pre- fence of another condition, which may be wanting, and actually is wanting, in many inttances. This condition is no other, than that the quantity of heat in the fyftem fhould be given, and fhould not admit of continual increafe from one quarter, nor diminution from another. When fuch increafe and diminution take place, what is ufually called “ the equilibrium of heat’’ no longer exifts. Thus, if we expofe a thermometer to the fun’s rays, it immediately rifes, and continues to ftand above the temperature of the furrounding air. The way in which this happens is perfectly underftood: the mercury in the thermometer receives more heat from the folar rays than the air does; it begins therefore to rife as foon as thofe rays fall on it; at the fame time, it gives out a portion of its heat to the air, and always the more, the higher it rifes. It continues to rife, therefore, till the heat which it gives out every inftant to the air, be equal to that which it receives eve- ry inftant from the folar rays. When this happens, its tempe- ature becomes ftationary ; the momentary increment and de- crement of the heat are the fame, and the total, of courfe, con- tinues conftant. The thermometer, therefore, in fuch circum- ftances, never acquires the temperature of the furrounding air ; and the only equilibrium of the heat, is that which fub- fifts between the increments and the decrements juft mention- ed: thefe indeed are, ftrictly fpeaking, zm equilibrio, as they ac- curately balance one another. This fpecies of equilibrium, however, is quite different from what is implied in the uni- form diffufion of heat. J Yy 2 3. In 356 On th PROGRESS of HEAT 3. In order to ftate the argument more generally, let A, B, C, D, &c. be a feries of contiguous bodies ; or let them be parts of the fame body; and let us fuppofe that A receives, from fome caufe, into the nature of which we are not here to inquire, a conftant and uniform fupply of heat. It is plain, that heat will flow continually from A to B, from B to C, &c.; and in order that this may take place, A muft be hotter than B, B than C, and fo on; fo that no uniform diftribution of heat can ever take place. The ftate, however, to which the fyftem will tend, and at which, after a certain time, it muft arrive, is one in which the momentary increafe of the heat of each body is juft equal to its momentary decreafe ;. fo that the temperature of each individual body becomes fixed, all thefe temperatures together forming a feries decreafing from A downwards. To be convinced that this is the ftate which the fyftem muft af- fume, fuppefe any body D, by fome means or other, to get more heat than that which is required to make the portion of heat which it receives every moment from C, juft equal to that which it gives out every moment to E; as its excefs of tempe- rature above E is increafed, it will give out more heat to E, and as the excefs of the temperature of C above that of D is diminifhed, D will receive lefs heat from C3; therefore, for both reafons, D muft become colder, and there will be no ftop to the reduction of its temperature, till the increments and decrements become equal as before. 4. Ir, therefore, heat be communicated to a folid mafs, like the earth, from fome fource or refervoir in its interior, it muft go_off from the centre on all fides, toward the circumfer- ence. On arriving at the circumference, if it were hindered from proceeding farther, and if {pace or vacuity prefented to heat an impenetrable barrier, then an accumulation of it at the furface, and at laft a uniform diftribution of it through the whole mafs, would inevitably be the confequence. But if. heat it SPHERICAL BODTES. 357 heat may be loft and diffipated in the boundlefs fields of va- - cuity, or of ether, which furround the earth, no fuch equili- brium can be eftablifhed. The temperature of the earth will then continue to augment only, till the heat which iffues from it every moment into the furrounding medium, become equal to the increafe which it receives every moment from the fup- pofed central refervoir. When this happens, the temperature at the fuperficies can undergo no farther change, and a fimilar effect muft take place with refpect to every one of the fphe- rical and concentric ftrata into which we may conceive the folid mafs of the globe to be divided. Each of thefe muft in time come to a temperature, at which it will give out as much heat to the contiguous ftratum on the outfide, as it receives from the contiguous ftratum on the infide ; and, when this hap- pens, its temperature will remain invariable. 5. THAT we may trace this progrefs with more accuracy, let us fuppofe a fpherical body to be heated from a fource of heat at its centre ; and iet 4, 4’, hb’, be the temperatures at the furfaces of two contiguous and concentric ftrata, the diftances from the centre being «x, x’, #”; and let it alfo be fuppofed, that the thicknefs of each of the ftrata, to wit, x/—x, and x«”—12’, is very {mall. TueEn fuppofing the body to be homogeneous, the quantity of heat that flows from the inner ftratum into the outward, in a given time, will be proportional to the excefs of its tempera- ture above that of the outward ftratum multiplied into its quan- tity of matter, that is, to (4 — hb’) (#’? —x’). 6. In 358 On th PROGRESS of HEAT 6. In the fame manner, the heat which goes off from the fecond ftratum in the fame time, is proportional to (h'—bh”) (x3 — x’) ; and thefe two quantities, when the temperature of the fecond ftratum becomes conftant, muft be equal to one another, or (b— 4’) («’? —x°) = (b'— b”) («#3 — x”). Bur becaufe 4—d’, and «’—x are indefinitely fmall, b—b =h, and x—x> = 3x°x3 therefore 4x ga'x ma given quantity; which quantity, fince * is given, we may re- an a x prefent by a'4°3 fo that b= 22 = 4 or, becaufe b is tor wre ys negative in refpect of «, being a deccrement, while the latter is an mike 4 » a x a* increment, = — aa and therefore 4 = C-+ ae +. To determine the conftant quantity C, let us fuppofe that the temperature at the furface of the internal nucleus of ignited matter is = H, and y= radius of that nucleus. Then, in the particular cafe, when x =7 and 4=H, the preceding 2 2 equation gives H=C + Gc 3; fo that C= H— ce and confe- 2 quently = H— “+ am or b=H+> CG->) 3 8, Ir is evident, from this formula, that for every value of. y there is a determinate value of 4, or that for every diftance from the centre there is a fixed temperature, which, after a certain time, muft be acquired, and will remain invariable as long it SPHERICAL BODIES. i age long as the intenfity and magnitude of the central fire conti- nue the fame. 9. Ir remains for us to determine the value of a’, which, though conftant, is not yet given, or known from obferva- tion. At the furface of the globe we may fappote the mean tem- perature to be known: let T be that temperature, and let R = the radius of the globe. Then, when x =R, b= tr, and by fubftituting in the general formula, we have T=H+— ae —), 3(T—H) _ ag Rep (Eb T) and a = Tot ae 1 era Kongens a 2 G- *) enh = onan Hence alfo by reduction RT—7H Rr(Ai—T) hie R—r_ a v(R—r) *- Rr(H —T Es gear a lec ua game From this equation, it is evident, that ) — potion or —r the excefs of the temperature at any diftance x from the centre, above a certain given temperature, is inverfely as a. But the conftruction of the hyperbola which is the locus of the preceding 360 On the PROGRESS of HEAT preceding equation, will exhibit the relation between the tem- perature and the diftance, in the way of all others leaft fubje@ to mifapprehenfion. Lert the circle (Plate X. fig. 3.) defcribed with the radius AB, reprefent the globe of the earth ; and the circle defcribed with the radius AH an ignited mafs at the centre. Let HK, perpendicular to AB, be the temperature at H, the furface of the ignited mafs ; and let F D be the temperature at any point whatever, in the interior of the earth, BM reprefenting that at _ the furface. Then AB being =R in the preceding equation, AH =7, HK—H, °BM=T5 ‘AP=<%;and- F DF; thele two laft being variable quantities ; fince G— —— x= a we have, (taking AE = a and drawing E L parallel to AB, meeting HK in N, ahd FD in 0) ODxOE 2 = ARES es which is a given quantity. THEREFORE D isina rectangular hyperbola, of which thecentre is E, the affymptotes E G and E L, and the rectangle of the co- ordinates, equal to BA.AH X Sey or, which amounts to the fame, to KN.NE. Ir is evident from this, that if the fphere were indefinitely extended, the temperature at the point B and all other things remaining the fame, the temperature at its fuperfices would not be lefs than A E, or than the quantity Aro THE Ce wn SPHERICAL BODIES. 361 Tue quantity AE, or obese bee is fuppofed here to be fubtracted ; if RT be lefs than 7 H, it will change its fign, and muft be taken on the other fide of the centre A. _ to. Tue refults of thefe deductions may be eafily reprefent- ed numerically, and reduced into tables, for any particular ~ values that may be affigned to the conftant quantities. Thus, if the radius of the globe, or R = 100, that of the ignited nu- cleus or y= 1; the temperature of the nucleus, or H = 1000, and T the temperature at the furface = 60, the formula be- comes / = 50.505-+ otal Values of x Values of +} 10 145°-454 20 98 .423 3° 82 .599 40 74 .686 5° 69 -938 60 66.330 70 63 -926 80 62 .361 go 61 .055 100 60. Vou. VI. P. II. Zz Iz. OTHER 362 On the PROGRESS. of HEAT 11. OTHER things remaining as before, if we now make ry = 10, then 4 = — 44-444 + 4 x b 20 477°.556 30 303 -556 40 226 .556 50 * 164-556 60 145 +550 7O 104.556 80 85 .056 ‘ go 64.556 100 60.000 12, Ig R=10, r=1, H= 10000, and T = 60, 9 TOMA b= — 1044.44 + ~“ChbA4 Values of x Values of 4 I0000°.00 4477-70 2637 .04 1716.67 1164.44 796 .30 533 +33 346.16 182.72 60.00 O% CONTI AW bw bd ~~ 13. THE in SPHERICAL BODIES. 363 {3- 1. THE general conclufions which refult from all this are, that when we fuppofe an ignited nucleus of a given mag- nitude, and a given intenfity of heat, there is in the {phere to which it communicates heata fixed temperature for each par- ticular ftratum, or for each fpherical fhell, at a given diftance from the centre ; and that a great intenfity of heat in the inte- rior, is compatible with a very moderate temperature at the furface. 2. HowEver great the {phere may be, the heat at its furface cannot be lefs than a given quantity ; R, 7, H and T remain- ing the fame. It muft.be obferved, that though R is put for the radius of the globe ; it fignifies in fact nothing, but the dif tance at which the temperature is T, as r does the diftance at which the temperature is H. THEREFORE were the fphere indefinitely extended, the tem- perature at its fuperficies would not be lefs than the quantity RT—rH R— ceding examples, than — 44.4 in the fecond, or — note 4 in the third. , that is, not lefs than 50.5 in the firft of the~pre- 4 14. In all this the fphere is fuppofed homogeneous ; but if it be otherwife, and vary in denfity, in the capacity of the parts for heat, or in their power to conduct heat, providing it do fo as any function of the diftance from the centre, the calculus may be inftituted as above. For example, let the denfi- ty be fuppofed to vary as rs ~, then we have as before (b—B’) («’3 — x) mn for the momentary increment of heat in a ftratum placed at the diftance x from the centre, LZ 2 or 364. On the PROGRESS of HEAT b b+n or 4X 3K28x xX = to a given quantity, or to a *, and therefore pees x) * 2 ee _ as =: rs = 3a" ox Hence ) = WEE = a - Log x, Suppofe that when x= 7, the radius ef the heated nucleus, 4 =H; then H= 2 a c+ Sut Log 7, and C= FY a. Sage < Log 7; therefore 4 = ar a a ae £ In this expreffion a* will be determined, if the temperature at any other diftance R from the centre is known. Let this be T ; then by fubftitution we have a T—H and a= : : : - Ce en ee T—H bience 2 ae ee Oe BNR 3 Sok °F R I z I r Care or 15. Tris < heen ry i Oe in SPHERICAL BODIES. 365 15. THIs is given merely as an example of the method of condudting the calculus when the variation of the denfity is taken into account, and not becaufe there is reafon to believe that the law which that variation actually follows, is the fame that has now been hypothetically affumed. 16. THE principle on which we have proceeded, applies not only to folids, fuch as we fuppofe the interior of the earth, but it applies alfo to fluids like the atmofphere, provided they are fuppofed to have reached a fteady temperature. The propaga- tion of heat through fluids is indeed carried on by a law very different from that which takes place with refpedt to folids ; it is not by the motion of heat, but by the motion of the parts of the fluid itfelf. Yet, when we are feeking only the mean re- fult, we may fuppofe the heat to be fo diffufed, that it does not accumulate in any particular ftratum, but is limited by the equality of the momentary increments and decrements of tem- perature which that ftratum receives. This is conformable to experience ; for we know that a conftancy, not of temperature, but of difference between the temperature of each point in the ‘atmofphere and on the furface, actually takes place. Thus, near the furface, an elevation of 280 feet produces, in this country, a diminution of one degree. The ftrata of our atmo- fphere, however, differ in their capacity of heat, or in the quantity of heat contained in a given fpace, at a given tempe- rature. Concerning the law which the change of capacity follows, we have no certain information to guide us ; and we have no refource, therefore, but to affume a hypothetical law, agreeing with fuch facts as are known, and, after deducing the refults of this law, to compare them with the obfervations made on the temperature of the air, at different heights above the furface of the earth. 17. LEP 366 On the PROGRESS of HEAT 17. Let us then fuppofe, that the ftrata of the atmofphere have a capacity for heat, which increafes as the air becomes r rarer, fo as to be proportional to mb *,% denoting, as be- fore, the diftance from the centre of the earth, 7 the radius of the earth, m and 6 determinate, but unknown quan- oe vet m1 : : tities, fuch that mé ors, exprefles the capacity of air for heat, when of its ordinary denfity, at the furface of the earth. The formula thus aflumed, agrees with the extreme cafes ; , m ; for, when. x=7, the capacity of heat = za finite 3 : GSR quantity ; when w increafes, ze diminifhes, and fo alfo does r ¥. . : m =. F, b”, if b is greater than unity, and therefore — increafes conti- bF nually. It does not, however, increafe beyond a certain limit, for when x is infinite — becomes +> OF m. bz 18. HENCE, ~~ —_. in SPHERICAL BODIES- 367 18. Hencs, by reafoning as in § 6. the momentary incre- ment of the temperature, or fenfible heat, of any ftratum, is as es directly, and its capacity for heat, or m b inverfely, Tipe a ais Oar ae x b 2 mre ax a ee a and 3mx 3mr LET = =y, then — re = 7, fo that — 2 a by a J therefore = ae ¥,°:. Hence @.= C-- 3mrLogb Bi oe a = C3, 3mrLogb ss 19. To determine C, if T be the temperature of the air at 2 ab the furface, when r=7, T = C+ 3m Loge? dnd» C= a b ae 3mrLogb ne ab a b : Hesce: bt 2 3mr Log b ui 3mrLogb — a (b—b7) eye 3mrLogd Tuis formula, when x =7 gives 5=T, and when »# is in- tee *(b— 5 : finite, it gives k= T— mr In all intermediate cafes, 368 On the PROGRESS of HEAT : cafes, as x is greater than r, 4* is lefs than 4, (b being a 5 ig number greater than 1) and therefore )—4* is pofitive, fo that 4 is lefs than T, as it ought to be. 20. WE may obtain an approximate value of this formula, without exponential quantities, that will apply to all the cafes in which « and r differ but little in refpe@ of 7, that is, in all the cafes to which our obfervations on the atmofphere can pof- fibly extend. fe Ir, in the term 47 we write r-+2z for x, x being the height of any ftratum of air above the furface of the earth, r r = a x = hrt+s we have J : r 21. But, from the nature of exponentials, we know 47 = r* (Log 6)’ r> (Log 6)? 1 + ~ Log b + —— ae are &e. r° (Log 8) tt pag OE airs) ee Now mG — es a = + = —, &c. And if we leave out the higher powers of z, we have nearly 8 bas + R in SPHERICAL BODIES. r ee x Ae = “ged Tr a 22 ee aan r a, 32 G+zyp — i= ig: &ce. ‘ THEREFORE, by fubftitution, we have 4’+* = r+(:) Log 4 + (2-32) SB? 4, & rH Logs 4 GED! WORD ge) z 2 ay. & (Log 5)° | L — ; Logs — = (Log 4) eg a Pea he Now, from the nature of exponentials, b=r1+ Log 5+ “28% eo 4 ree” +, &c. And = Log 5+ = (Log )' + soy &e. a hogs (x4 Legs + S27 ae We = 7b Log 6; theetere when 2 is very fmall, 5 = Vou. VI. P. II. Oe SA. 359 370 On the PROGRESS of HEAT, &e. . (b— bre)” 3mr Log 6 ~ 6— — * Log b, and therefore (§ 19.), 4” bz Log d ome r Jee abe 3 mr Log b = amr? hence when z is very a Whe 3mr° fmall, 4=T — 22. THEREFORE when 2, or the height above the furface is fmall, ) diminifhes in the fame proportion that the height in- creafes, which is conformable to experience. 2 ° In our climate, when. z= 280 feet, BOEVATEE bx 26 =1°; fo 3mr that the co-efficient ame et = a and therefore z Fata PTS ess Te b=T 280° Wuen the conftant quantities are thus determined, the for- mula agrees nearly with obfervation. In the rule for barome- trical meafurements, it is implied, that the heat of the atmo- {phere decreafes uniformly; but the rate for each particular cafe is determined by actual obfervation, or by thermometers obferved at the top and bottom of the height to be meafured. XI. XI. Experiments on Allanite, a new Mineral from Green- land. By Tuomas Tuomson, M.D. F.R.S.E. Fellow of, the Imperial Chirurgo-Medical Academy of Peters- burgh. [Read Nov. 5. 1810.] BOUT three years ago, a Danith veflel * was brought into Leith as a prize. Among other articles, {he contained a fmall collection of minerals, which were purchafed by THomas ALLAN, Efq; and Colonel Imriz, both members of this Society. The country from which thefe minerals had been brought was not known for certain; but as the collection abounded in Cry- olite, it was conjectured, with very confiderable Renee sae that they had been collected in Greenland. Amonc the remarkable minerals in this collection, there was one, which, from its correfpondence with Gadolinite, as defcri- bed in the different mineralogical works, particularly attracted the attention of Mr ALLan. Confirmed in the idea of its being a variety of that mineral, by the opinion of Count Bournon, added to fome experiments made by Dr Wott aston, he was in- duced to give the defcription which has fince been publifhed in a preceding part of the prefent volume. Axout a year ago, Mr ALuan, who has greatly diftinguifhed himfelf by his ardent zeal for the progrefs of mineralogy in all Az2 its * Der Fruuiine, Captain Jacos KETELSON, captured, on her _ Passage from Iceland to Copenhagen, 372 On ALLANITE, a new its branches, favoured me with fome {pecimens of this curious mineral, and requefted me to examine its compofition,—a re- queft which I agreed to with pleafure, becaufe I expected to obtain from it a quantity of yttria, an earth which I had been long anxious to examine, but had not been able to procure a fufficient quantity of the Swedith Gadolinite for my purpofe. The object of this paper, is to communicate the refult of my ; experiments to the Royal Society,—experiments which cannot appear with fuch propriety any where as in their Tranfac- tions, as they already contain a paper by Mr ALLAN on the mi- neral in queftion. I. DeEscRIPTION. { am fortunately enabled to give a fuller and more accurate defcription of this mineral than that which formerly appeared, Mr Atzuan having, fince that time, difcovered an additional quantity of it, among which, he not only found frefher and better characterifed fragments, but alfo fome entire cryftals. In its compofition, it approaches moft nearly to Cerite, but it dif- fers from it fo much in its external characters, that it muft be confidered as a diftiné fpecies. I have therefore taken the li- berty to give it the name of Allanite, in honour of Mr Auuan, to whom we are in reality indebted for the difcovery of its pe- culiar nature. ALLANITE occurs maffive and diffeminated, in irregular maffes, mixed with black mica and felfpar; alfo cryftallifed ; the varieties obferved are, 1. A four-fided oblique piifm, meafuring 117° and 63°. 2. A fix-fided prifm, acuminated with pyramids of four fides, fet on the two adjoining oppofite planes. Thefe laft are fo minute as to be incapable of meafurement. But, as nearly as the eye can determine, the form refembles Fig. 1.3; the prifm of which has two right angles, and four meafuring 135°. Fig... PLAT TE Ss | ‘Transactions 2t.S Lidin VAVI-P 373. ——SS Wiazars fenlp. : pa r J rineneniv a ate Pity Re 3 . 3 ie 45% Sey Fang me = 2 “ ; om : . i ne £ a F . A eee adil fs 2p | ea Yi - me i ; +a , : ; t, - ak Pind gt 4 = i < ' ‘ ; Y 7 ) ‘4 . F 4 7 4 } a p ‘ = oS : * . a 4 . x ? % eo a ae gen f reer tr en rT t 4 ' i ates MINERAL from GREENLAND. “393 3- A flat prifm, with the acute angle of 63° replaced by one plane, and terminated by an acumination, having three principal facettes fet on the larger lateral planes, with which the centre one meafures 125° and 55°. Ofthis °* fpecimen, an engraving is given in the annexed Plate, Fig. 2. SPECIFIC gravity, according to my experiments, 3.533. The fpecimen appears to be nearly, though not abfolutely, pure. This fubftance, however, is fo very much mixed with mica, that no reliance can be placed on any of the trials which have been made. Count Bournon, furprifed at the low fpecific gra- vity noted by Mr Ain, which was 3.480,broke down one of the fpecimens which had been fent him, in order to procure the fubftance in the pureft ftate poffible, and the refult of four experiments was as follows, 4.001 3-797 3-654 SaEL ORS ; ‘In a fubfequent experiment of Mr Atian’s, he found it 3.665. From thefe it appears, that the fubftance is not in a pure ftate. Its colour is fo entirely the fame with the mica, with which it is accompanied, that it is only by mechanical attrition that they can be feparated. Co our, brownifh-black. - External luftre, dull; internal, fhining and refinous, flight- ly inclining to metallic. FractTuRE, {mall conchoidal. FRAGMENTS, indeterminate, fharp-edged. - OPAKE. SEMI-HARD in a high degree. Does not feratch quartz nor felfpar, but {eratches hornblende and crown-glafs, BRITTLE. EAsILy 374 On ALLANITE, a new Eastty frangible. Powper, dark greenifh-grey. Berore the blow-pipe it froths, and melts imperfectly into a brown {coria. , GELATINISEs in nitric acid. In a ftrong red heat it lofes 3-98 per cent. of its weight. Il. ExprRIMENTs TO ASCERTAIN ITS COMPOSITION. My firft experiments were made, on the fuppofition that the mineral was a variety of gadolinite, and were pretty much in the ftyle of thofe previoufly made on that fubftance by Exx- BERG, KLAPROTH, and VAUQUELIN, | I. 100 grains of the mineral, previoufly reduced to a fine powder in an agate mortar, were digefted repeatedly on a fand ' bath in muriatic acid, till the liquid ceafed to have any action onit. The undiffolved refidue was filica, mixed with fome frag- ments of mica. When heated to rednefs, it weighed 33.4 grains. 2. THE muriatic acid folution was evaporatet almoft to dry- nefs, to get rid of the excefs of acid, diflolved in a large quan- tity of water, mixed with a confiderable excefs of carbonate of ammonia, and boiled for a few minutes. By this treatment, the whole contents of the mineral were precipitated in the {tate of a yellowifh powder, which was feparated by the filtre, and boiled, while ftill moift, in potafh-ley. A fmall portion of | it only was diffolved. “The potath-ley was feparated from the undiflolved portion by the filtre, and mixed with a folution of fal ammoniac, by means of which a white powder precipitated from it. This white matter being heated to rednefs, weighed 4.9 grains. It was digefted in fulphuric acid, but 3.76 grains refufed to diffolve. This portion poffeffed the properties of fi- lica. The diffolved portion being mixed with a few drops of fulphate =" MINERAL from GREENLAND. 375 fulphate of potath, fhot into cryftals of alum. It was therefore alumina, and amounted to 4.14 grains. 3. Tue yellow matter which refufed to diffolve in the pot- afh-ley, was mixed with nitric acid. An effervefcence took place, but the liquid remained muddy, till it was expofed to heat, when a clear reddifh-brown folution was effected. This folution was evaporated to drynefs, and kept for a few minutes in the temperature of about 400°, to peroxidize the iron, and render it infoluble. A fufficient quantity of water-was then poured on it, and digefted on it for half-an-hour, on the fand- bath. The whole was then thrown upon a filtre. The dark red matter which remained on the filtre, was drenched in oil, and heated to rednefs, in a covered crucible. It was then black, and attracted by the magnet; but had not exadtly the appearance of oxide of iron. It weighed 42.4 grains. _ 4. THE liquid which paffed through the filtre, had not the fweet tafte which I expected, but a flightly bitter one, fimilar. to a weak folution of nitrate of lime. Hence it was clear, that mo yttria was prefent, as there ought to haye been, had the mineral contained that earth. This liquid being mixed with carbonate of ammonia, a white powder precipitated, which, after being dried in a red heat, weighed 17 grains. It diflolved in acids with effervefcence ;. the folution was precipi- tated white by oxalate of ammonia, but not by pure ammonia. When diffolved in fulphuric acid, and evaporated to drynefs, a light white matter remained, taftelefs, and hardly foluble in. water. Thefe properties indicate carbonate of lime. Now, 17 grains of carbonate of lime are equivalent to about 9.23 grains. of lime. 5. From 4 376 On ALLANITE, a new 5. From the preceding analyfis, fuppofing it accurate, it fol- lowed, that the mineral was compofed of Silica, - - - 37.16 Lime, - - - 9-23 Alumina, ~ - - - 4.14 Oxide of iron, - * - 42.40 Volatile matter, ita - 3-98 96.91 Lofs, - - - 3.09 100.00 But the appearance of the fuppofed oxide of iron, induced me to fufpect, that it did not confift wholly of that metal. I thought it even conceivable, that the yttria which the mineral contained, might have been rendered infoluble by the applica- tion of too much heat,.and might have been concealed by the iron with which: it was mixed. A number of experiments, which it is needlefs to {pecify, foon convinced me, that, befides iron, there was likewife another fubftance prefent, which pof- fefled properties different from any that I had been in the ha- bit of examining. It poffefled one property at leaft in com- mon with yttria ; its folution in acids had a fweet tafte ; but few of its other properties had any refemblance to thofe which the chemifts to whom we are indebted for our knowledge of yttria, have particularifed. But as I had never myfelf made any ex- periments on yttria, I was rather at a lofs what conclufion to drawy. From this uncertainty, I was relieved by Mr ALLAN, who had the goodnefs to give me a finall fragment of gadoli- nite, which had been received dire@ly from Mr Exeserc. From this I extracted about 10 grains of yttria; and upon com- paring its properties with thofe of the fubftance in queftion, I found MINERAL from GREENLAND. -~ 399 found them quite different. . Convinced by thefe experiments, that the mineral contained no yttria, but that one of its confti- tuents was a fubftance with which I was ftill unacquainted, I had recourfe to the following mode of analyfis, in order to ob- tain this fubftance in a pure ftate. Ill. ANaAtysis or ALLANITE. I. 100 grains of the mineral, previoufly reduced to a fine powder, were digefted in hot nitric acid till nothing more could be diffolyed.. The undiffolved refidue, which was filica, mixed with fome {cales of mica, weighed, after being heated to redne(fs, 35.4 grains. 2. Tue nitric acid folution was tranfparent, and of a light- brown colour. When ftrongly concentrated by evaporation, to get rid of the excefs of acid, and fet afide in an open capfule, it concreted into a whitith folid matter, confifting chiefly of foft cryftals, nearly colourlefs, having only a flight tinge of yellow. Thefe cry ftals being left expofed to the air, became gradually moift, but did not {peedily deliquefce. The whole was therefore diffolved in water, and the excefs of acid, which _ was ftill prefent, carefully neutralifed with ammonia. By this treatment, the folution acquired a much deeper brown colour ; but ftill continued tranfparent. Succinate of ammonia was then dropped in with caution. A copious reddith-brown pre- cipitate fell, which being wathed, dried, and heated to rednefs im a covered crucible, weighed 25.4 grains. It poffeffed all the characters of black oxide of iron. For it was attracted by the magnet, completely foluble in muriatic acid, and the folw.- tion was not precipitated by oxalate of ammonia. 3. Tue liquid being ftill of a brown colour, I conceived it not to be completely free from iron. On this account, an ad- Vou. VI. P. II. 3 B ditional 378 On ALLANITE, a new ditional quantity of fuccinate of ammonia was adde. And we precipitate fell ; but inftead of the dark reddifh-brown colour, which characterizes fuccinate of iron, it had a beautiful fleth- red colour, which it retained after being dried in the open air. ‘When heated to rednefs in a covered crucible, it became black, and had fome refemblance to gunpowder. It weighed 7.2 grains. 4. Tuts fubftance attracted my peculiar attention, in confe- quence of its appearance. I found it to poflefs the following characters : a. Ir was taftelefs, and not in the leaft attracted by the mag- net, except a few atoms, which were eafily feparated from the ret. | b. Ir was infoluble in water, and not fenfibly acted on when boiled in fulphuric, nitric, muriatic, oy nitro-muriatic acid. c. Brrore the blow-pipe it melted with borax and microcof- mic falt, and formed with both a colourlefs bead. With car- bonate of foda it formed a dark-red opake bead. d. WHEN heated to rednefs with potafh, and digefted in wa- ter, fnuff-coloured flocks remained undiffolved, which gradual- ly fubfided to the bottom. The liquid being feparated, and exa- mined, was found to contain nothing but potafh. When mu- riatic acid was poured upon the fnuff-coloured flocks, a flight effervefcence took place, and when heat was applied, the whole diflolved. The folution was tranfparent, and of a yellow co- lour, with a flight tint of green. When evaporated to drynefs, to get rid of the excefs of acid, a beautiful yellow matter gra- dually feparated. Water boiled upon this matter diffolved the whole. The tafte of the folution was aftringent, with a flight metallic flavour, by no means unpleafant, and no fweetnefs was perceptible. rae N MINERAL from GREENLAND. 399 was A portion of the black powder being expofed to a red _heat for an hour, in an open crucible, became reddifh-brown, and loft fomewhat of its weight. In this altered ftate, it was foluble by means of heat, though with difficulty, both in nitric and {ulphuric acids. The folutions had a reddifh-brown co- lour, a flight metallic aftringent tafte, but no fweetnefs. f. Tue folution of this matter in nitric and muriatic acid, when examined by re-agents, exhibited the following pheno- mena : (1.) With pruffiate of potath, it threw down a white precipi- tate in flocks. It foon fubfided ; readily diffolved in nitric acid ; the folution was green. (2.) Pruffiate of mercury. A light yellow precipitate, fo- luble im nitric acid. (3-) Infufion of nut galls. No change. (4.) Gallic acid. No change. (5-) Oxalate of ammonia. No change. (6.) Tartrate of potafh. No change. (7.) Phofphate of foda. No change. (8.) Hydro-fulphuret of ammonia. Copious black flocks. Liquor remains tran{parent. (9.) Arfeniate of potath. A white precipitate. (1o.) Potath. - - - Copious yellow-coloured (11.) Carbonate of foda. - - piene 3 readily yee in (12.) Carbonate of ammonia. nitric acid. (13.) Succinate of ammonia. A white precipitate. (14.) Benzoate of potath. . A white precipitate. (15.) A plate of zinc being put into the folution in muriatic acid, became black, and threw down a black powder, which was infoluble in fulphuric, nitric, muriatic, ni- tro-muriatic, acetic, and phofphoric acids, in every 3 B2 - temperature, - + 380. On ALLANITE, a new temperature, whether thefe acids were concentrated or diluted. (16.) A plate of tin put into the nitric folution, occafioned no change. tad (17.) A portion being inclofed in a charcoal crucible, and ex- poted for an hour to the heat of a forge, was not re- duced to a metallic button, nor could any trace of it be detected when the crucible was examined. THESE properties were all that the fmall quantity of the matter in my pofleffion enabled me to afcertain. They une- quivocally point out a metallic oxide. Upon comparing them with the properties of all the metallic oxides known, none will be found with which this matter exactly agrees. Cerium is the metal, the oxides of which approach the neareft. The colour is nearly the fame, and both are precipitated white by pruffiate of potafh, fuccinate of ammonia, and benzoate of © potafh. But, in other refpedts, the two fubftances differ entire- ly. Oxide of cerium is precipitated white by oxalate of am- monia and tartrate of potafh; our oxide is not precipitated at all: Oxide of cerium is precipitated white by hydro-fulphuret of ammonia; while our oxide is precipitated black : Oxide of ce- rium is not precipitated by zinc, while our oxide is thrown down black. There are other différences between the two, but thofe which I have juft mentioned are the moft ftriking. THESE properties induced me to confider the fubftance which I had obtained from the Greenland mineral as the oxide of a metal hitherto unknown ; and I propofed to diftinguith it by the name of Junonium. In the experiments above detailed, I had expended almoft all the oxide of Junonzum which I had in my poffeflion, taking it for granted that I could eafily procure more of it from the Green- land —_—— - —— os - ——-- »~ ‘MINERAL from GREENLAND. 38 Jand mineral. But, foon after, I was informed by Dr Wotia- ston, to whom I had fent a {pecimen of the mineral, that he had not been able to obtain any of my fuppofed Junonium in. his trials. This induced me to repeat the analyfis no lefs than three times, and in neither cafe was I able to procure any more of the fubftance which I have defcribed above. Thus, it has been out of my power, to verify the preceding details, and to * put the exiftence of a new metal in the mineral beyond doubt. At the fame time, I may be allowed to fay, that the above ex- periments were made with every poffible attention on my part, and moft of them were repeated, at leaft a dozen times. I have no doubt my(felf of their accuracy ; but think that the exift- ence of a new metal can hardly be admitted, without ftronger proofs than the folitary analyfis which I have performed. 5. Tue liquid, thus freed from iron and junonium, was fuper- faturated with pure ammonia. A greyifh-white gelatinous mat- ter precipitated. It was feparated by the filtre, and became gradually darker coloured when drying. This matter, after being expofed to a red heat, weighed about 38 grains. When boiled in potafh-ley, 4.1 grains were diflolved, of a fubftance which, feparated in the ufual way, exhibited the properties of alumina. 6. THE remaining 33.9 graims were again diffolved in mu- riatic acid, and precipitated by pure ammonia. The precipi- tate was feparated by the filtre, and allowed to dry fpontane- - oufly in the open air. It aflumed an appearance very much refembling gum-arabic, being femi-tranfparent, and of a brown colour. When dried upon the fand-bath, it became very dark- brown, broke with a vitreous fracture, and ftill retained a {mall degree of tranfparency. It was taftelefs, felt gritty between the teeth, and was eafily reduced to powder. It effervefced in fulphuric, nitric, muriatic, and acetig‘acids, and a folution of it was 382 On ALLANITE, a new was effected in each by means of heat, though not without con- fiderable difficulty. The folutions had an auftere, 2Nd flightly {wectith tafte. When examined by re-agents, they exhibited the following properties : (1.) Pruffiate of potafh. A white precipitate. (2.) Oxalate of ammonia. A white precipitate. (3-) Tartrate of potafh. A white precipitate. (4.) Hydrofulphuret of potafh. A white precipitate. (5-) Phofphate of {.da.. A white precipitate. (6.) Arfeniate of potafh. A white precipitate. (7-) Potafh and its carbonate. A white precipitate. (8.) Carbonate of ammonia. A white precipitate. (9.) Ammonia. A white gelatinous precipitate. (10.) A plate of zinc. No change. THESE properties indicated Oxide of Cerium. I was there- fore difpofed to confider the fubftance which I had obtained as oxide of cerium. But on perufing the accounts of that fub- ftance, given by the celebrated chemifts to whofe labours we are indebted for our knowledge of it, there were feveral cir- cumftances of ambiguity which occurred. My powder was diffolved in acids with much greater difficulty than appeared to be the cafe with oxide of certum. The colour of my oxide, when obtained from oxalate, by expofing it to a red heat, was much lighter, and more inclined to yellow, than the oxide of cerium, In this uncertainty, Dr WotLtaston, to whom I communi- cated my difficulties, offered to fend me down a fpecimen of the mineral called cerife, that I might extract from it real oxide of cerium, and compare my oxide with it. This offer I thank- fully | : : MINERAL from GREENLAND. 333 fully accepted *; and upon comparing the properties of my oxide with thofe of oxide of cerium extracted from cerite, I was fully fatisfied that they were identical. The more dificult folubility of mine, was owing to the method I had employed to procure it, and to the ftrong heat to which I had fubjected it ; whereas the oxide of cerium from cerite had been examined in the ftate of carbonate. 7. In the many experiments made upon this powder, and upon oxide of cerium from cerite, I repeated every thing that had been eftablifhed by Berzerius and Histncer, KLaprotu _ and Vauquezin, and had an opportunity of obferving many -particulars which they have not noticed. It may be worth ~ while, therefore, without repeating the details of thefe chemifts, to mention a few circumftances, which will be found ufeful in examining this hitherto fcarce oxide. a. THE precipitate occafioned by oxalate of ammonia is at firft in white flocks, not unlike that of muriate of filver, but it foon affumes a pulverulent form. It diffolves readily in nitric acid, without the affiftance of heat. The fame remark applies to the precipitate thrown down by tartrate of potafh. But tartrate of cerium is much more foluble in acids than the oxa- late. b. THE * Tur fpecimen of cerite which I analifed, was fo much mixed with aétino- lite, that the flatement of the refults which I obtained cannot be of much im- portance. The fpecific gravity of the fpecimen was 4.149. I found it compo- fed as follows : : A white powder, left by muriatic acid, and prefumed to be filica, 47.3 Red oxide of cerium, - 4 5 44: Tron, 3 ks = -. 2 aa Volatile matter, - Win tue & 3. Lofs, - > - 1. 100.0 384 On ALLANITE, a new ). Tue folution of cerium in acetic acid is precipitated grey by infufion of nut-galls. Cerium is precipitated likewife by the fame re-agent from other acids, provided the folution con- tain no excefs of acid. This fact was firft obférved by Dr Wottasron, who communicated it to me laft fummer. I im- mediately repeated his experiments with fuccefs. c. CERIUM is not precipitated from its folution in acids by © a plate of zinc. In fome cafes, indeed, I have obtained a yel- lowifh-red powder, which was thrown down yery flowly. But it proved, on examination, to confift almoft ‘entirely of red oxide of iron, and of courfe only appeared when the folution of cerium was contaminated with iron. d. Tue folutions of cerium in acids have an aftringent tafte, with a perceptible fweetnefs, which, however, is different from the fweetnefs which fome of the folutions of iron in acids pof- fefs. e. THE muriate and fulphate of cerium readily cryftallife ; but I could not fucceed in obtaining cryftals of nitrate of ce- rium. } f. THE beft way of obtaining pure oxide of cerium, is to precipitate the folution by oxalate of ammonia, wath the preci- pitate well, and expofe it to a red heat. The powder obtained by this procefs is always red; but it varies very much in its fhade, and its beauty, according to circumftances. This pow- der always contains carbonic acid. g. I consiper the following as the effential characters of ce- rium. The folution has a fweet aftringent tafte: It is precipi- tated white by pruffiate of potath, oxalate of ammonia, tartrate of potafh, carbonate of potath, carbonate of ammonia, fuccinate of ammonia, benzoate of potafh, and hydrofulphuret of ammo- nia: The precipitates are re-diflolved by nitric or muriatic . acids : SR os MINERAL: from GREENLAND. 385 acids: Ammonia throws it down in gelatinous flocks: Zinc does not precipitate it at all. h. Tue white oxide of cerium, mentioned by HistnceEr and Berzetius, and defcribed by VaugueEtin, did not prefent itfelf to me in any of my experiments ; unlefs the white flocks preci- pitated by ammonia from the original folution be confidered as white oxide. They became brown on drying, and when heat- ed to rednefs, were certainly converted into red oxide. As cerium, as well as iron, is precipitated by fuccinate of ammonia, the preceding method of feparating the two from each other was not unexceptionable. Accordingly, in fome fubfequent analyfes, I feparated the cerium by means of oxalate of ammonia, before I precipitated the iron. I found that the proportions obtained by the analyfis above defcribed, were fo near accuracy that no material alteration is neceflary. 8. THE liquid, thus freed from iron, alumina, and cerium, was mixed with carbonate of foda. It precipitated a quantity of carbonate of lime, which amounted, as before, to about 17 grains, indicating 9.2 grains of lime. From the preceding analyfis, which was repeated no lefs than three times, a different method being employed in each, the conftituents of allanite are as follows : ; Silica, - - ~ 35-4. Lime, .. = - - 9.2 Alumina, - - 4.1 Oxide of iron, - - 25-4 Oxide of cerium, - - 33-9 - Volatile matter, - - 4e 112.0 Nox. VI. P. II. 3C I 386 On ALLANITE, &e. I omit the 7 grains of junonium, becaufe I only detected it in one fpecimen of allanite. The excefs of weight in the preceding numbers, is to be afcribed chiefly to the carbonic acid combi- ned with the oxide of cerium, from which it was not complete- ly freed by a red heat. I have reafon to believe, too, that the proportion of iron is not quite fo much as 25.5 grains. For, in another analyfis, I obtained only 18 grains, and in a third 20 grains. Some of the cerium was perhaps precipitated along with it in the preceding analyfis, and thus its weight was appa- rently increafed. ; ° XII. A Chemical Analysis of Sodalite, a new Mineral from Greenland.. By Tuomas Tuomson, M.D. F.R.S. E. Fellow of the Imperial Chirurgo-Medical Academy of Pe- tersburgh. [Read Nov. 5. 1810.] HE mineral to which I have given the name of Sodalite, “was alfo put into my hands by Mr Atztan. In the - Greenland collection which he purchafed, there were feveral fpecimens of a rock, obvioufly primitive. In the compofition of thefe, the fubftance of which I am about to treat, formed a conftituent, and, at firft appearance, was taken for felfpar, to which it bears‘a very ftriking refemblance. Tuis rock is compofed of no lefs than five different foffils, namely, garnet, hornblende, augite, and two others, which form the pafte of the mafs. Thefe are evidently different minerals ; but in fome fpecimens, are fo intimately blended, that it requi- red the fkill of Count Bournon to make the difcrimination, and afcertain their real nature. Even this diftinguifhed mine- ralogift was at firft deceived by the external afpect, and confi- dered the pafte as common lamellated felfpar, of a greenith co- ~lour. But a peculiarity which prefented itfelf to Mr Arian, in one of the minerals, induced him to call the attention of Count Bournon more particularly to its conftracion. On. a clofer examination of the mimeral, M. de Bournon found that fome fmall fragments, which he had detached, pre- aCe fented 388 On SODALITE, a new fented rectangular prifms, terminated by planes, meafuring, with the fides of the prifm, 110° and 70° or nearly fo,—a form which belongs to a rare mineral, known by the name of Sahlite, from Sweden. He further obferved, intermixed along with this, another material ; and after fome trouble, fucceeded in detaching a mafs, prefenting a regular rhomboidal dodecahe- dron. It was to this form that Mr ALLan had previoufly re- quefted his attention. SomE time before this inveftigation, M. de Bournon had examined a mineral from Sweden, of a lamellated ftru@ture, and a greenifh colour, which, he found, indicated the fame form. From this circumftance, together with fome external refemblance, which ftruck him, he was induced to conclude, that our mineral was a variety of that fubftance. To that fubftance the name of Swedith natrolite had been gi- yen, in confequence of the inveftigation of Dr WoLLaston, who found that it contained a large proportion of foda. THERE are few minerals, however, that are fo totally diftinc in their external characters as the natrolite of KLAproru, and the fubftance we are now treating of. The mineral examined by KLAPROTH occurs at Roegan*, on the Lake of Conftance, in porphyry-flate, coating the fides of veins and cavities in a ma- mellated form, the texture of which is compaét, fibrous, and ra- diated ; the colour pale yellow, in fome places pafling into white, and marked with brown zones. Hitherto it had never been found in a ftate fufficiently perfect to afford any indi- cations of form. Lately, however, M. de Bournon was fo fortunate as to procure fome of it, prefenting very delicate needleform cryftals, which, by means of a ftrong magnifier, he was able to afcertain, prefented flat re@angular prifms, ter- minated by planes, which, he thought, might form angles of 60° * Ir has been obferved alfo by Profeflor JamEsoy, in the fletz-trap rocks behind Burntifland. atl i a a ~ Be i MINERAL from GREENLAND. 389 60° and 120 with the fides of the prifm. With this, neither our mineral nor the Swedifh can have any connection, farther than fome analogy which may exift in their compofition. ConcERNING the Swedifh mineral, I have not been able to obtain much {fatisfactory information. There is a fpecimen of mt in Mr Atian’s cabinet, which he received directly from Sweden, fent by a gentleman who had juft before been in Lon- don, and was well acquainted with the collections of that city, from which it is inferred, that the {pecimen in queftion is the fame as that examined by Count Bournon and Dr Wotta- STON. WERNER has lately admitted into his fyftem a new mineral {pecies, which he diftinguifhes by the name of Fettstein. Of this I have feen two defcriptions ; one by Haiiy, in his Tableau Comparatif, publifhed laft year ; and another by Count DuniNn Borxkowsk1, publifhed in the 69th volume of the Journal de Physique, and tranflated in Nicholson’s Journal, (vol. 26. p. 384). - The fpecimen, called Swedish Natrolite, in Mr ALLAN’s pot- . feffion, agrees with thefe defcriptions in every particular, ex- cepting that its fpecific gravity is a little higher. Bor- KowsKI ftates the fpecific gravity of fettsten at 2.563; Haiiy at 2.6138 ; while I found the fpecific gravity of Mr ALLAN’s fpecimen to be 2.779, and, when in fmall fragments, to be as high as 2.790. This very near agreement in the properties of the Swedifh natrolite, with the characters of the fettftein, leads me to fuppofe it the fubftance to which WERNER has given that name. This opinion is ftrengthened, by a fact mentioned by Haiiy, that fettftein had been at firft confidered as a varie- ty of Wernerite. For the fpecimen fent to Mr ALLan, under the name of Compact Wernerite, is obvioufly the very fame with the fuppofed natrolite of Sweden. Now, if this identity be ad- mitted, it will follow, that our mineral conftitutes a fpecies apart. It bears, indeed, a confiderable refemblance to it; but neither the cryftalline form, nor the conftituents of fettftein, as 390 On SODALITE, a new as ftated by Havy, are fimilar to thofe of the mineral to which I have given the name of Sodalite. The conftituents of fett- ftein, as afcertained by VauQUELIN, are as follows : % Silica, = - - 44.00 Alumina, - _ 34.00 Oxide of iron, - - 4.00 Lime, “ 5 f 0.12 Potafh and foda, - - 16.50 Lofs, sd - - 1.38 100.00 II. DescrirpTION OF SODALITE. SopALITE, as has been already mentioned, occurs in a pri- mitive rock, mixed with fahlite, augite *, hornblende, and gar- net +. Ir occurs maflive ; and cryftallifed, in rhomboidal dodecahe- - drons, which, in fome cafes, are lengthened, forming fix-fided prifms, terminated by trihedral pyramids. Irs colour is’ intermediate between celandine and mountain ereen, varying in intenfity im different {pecimens. In fome cafes it feems intimately mixed with particles of fahlite, which doubtlefs modify the colour. a ExTernaL luftre glimmering, internal fhining, in one direc- tion vitreous, in another refinous. Fracture foliated, with at leaft a double deuaek 3 crofs fracture conchoidal. FRAGMENTS indeterminate; ufually fharp-edged. : TRANSLUCENT. * Turs fituation of the augite deferves attention. Hitherto it has been, with a few exceptions, found only in fleetz trap rocks. + Tue particular colour and appearance of this garnet, fhews that the rock came from Greenland: For fimilar garnet has never been obferved, except in fpecimens from Greenland. MINERAL from GREENLAND. — 391 . TRANSLUCENT. Harpness equal to that of felfpar. Iron fcratches it with difficulty. : BRITTLE. Easixy frangible. SPECIFIC gravity, at the temperature of 60°, 2.378. The fpecimen was not abfolutely free from fahlite, WHEN heated to rednefs, does not decrepitate, nor fall to powder, but becomes dark-grey, and aflumes very nearly the appearance of the Swedifh natrolite of Mr Arian, which I confider as fettftein. If any particles of fahlite be mixed with it, they become very confpicuous, by acquiring a white colour, and the opacity and appearance of chalk. The lofs of weight was 2.1 per cent. I was not able to melt it before the blow- pipe. II. CHEMICAL ANALYSIS. 1. A HUNDRED grains of the mineral, reduced to a fine pow- der, were mixed with 200 grains of pure foda, and expofed for -an hour to a ftrong red heat, in a platinum crucible. The mix- ture melted, and.aflumed, when cold, a beautiful grafs-ereen colour. When foftened with water, the portion adhering to © the fides of the crucible acquired a fine brownifh-yellow. Ni- tric acid being poured: upon it, a complete folution was ob- tained. _ 2. Suspectinc, from the appearance which the fufed maf affumed, that it might contain chromium, I neutralifed the {o- lution, as nearly as poflible, with ammonia, and then poured into it a recently prepared nitrate of mercury. A white preci- pitate fell, which being dried, and expofed to a heat rather un- der rednefs, was all diffipated, except a fmall portion of grey matter, 392 On SODALITE, a new matter, not weighing quite 0.1 grain. This matter was info- luble in acids; but became white. With potafh it fufed into a colourlefs glafs. Hence I confider it as filica. This experi- ment fhews that no chromium was prefent. I was at a lofs to account for the precipitate thrown down by the nitrate of mer- cury. But Mr Arian having fhown me a letter from Exr- BERG, in which he mentions, that he had detected muriatic acid in fodalite, it was eafy to fee that the whole precipitate was calomel. The white powder weighed 26 grains, indicating, according to the analyfis of CHENEVIXx, about 3 grains of mu- riatic acid. 3. Tue folution, thus freed from muriatic acid, being con- centrated by evaporation, gelatinifed. It was evaporated near- ly to dryneis; the dry mafs, digefted in hot water acidulated with nitric acid, and poured upon the filter. The powder re- tained upon the filter was wafhed, dried, and heated to rednefs. It weighed 37.2 grains, and was filica. 4. Tur liquor which had paffed through the filter, was fu- perfaturated with carbonate of potafh, and the copious white precipitate which fell, collected by the filter, and boiled while yet moift in potafh-ley. The bulk diminifhed greatly, and the undiflolved portion affumed a black colour, owing to fome oxide of mercury with which it was contaminated. 5. Tue potafh-ley being paffed through the filter, to free it from the undiffolved matter, was mixed with a fufficient quan- tity of fal-ammoniac. A copious white precipitate fell, which being collected, wathed, dried, and heated to rednefs, weighed 27.7 grains. This powder being digefted in fulphuric acid, diflolved, except 0.22 grain of filica. Sulphate of potafh being added, and the folution fet afide, it yielded alum cryftals to the very laft drop. Hence the 27.48 grains of diflolved powder were alumina. 6. THE ‘ aap eee MINERAL from GREENLAND. 393 6. Tue black refidue which the potafh-ley had not taken up, was diffolved in diluted fulphuric acid. The folution being evaporated to ‘drynefs, and the refidue digefted in hot water, a white foft powder remained, which, heated to rednefs, weighed 3.6 grains, and was fulphate wf lime, equivalent to about: 2 grains of lime. 7. Tue liquid from which the fulphate of lime was fon rated, being exactly neutralifed by ammonia, fuccinate of am- monia was dropped in; a brownifh-red precipitate fell, which, being heated to rednefs in a covered crucible, weighed 1 grain, and was black oxide of iron. 8. THE refidual liquor being now examined by different re- ‘agents, nothing farther could be precipitated from it. g.. Tue liquid (No. 4.) from which the alumina, lime, and iron had been‘ feparated by carbonate of potafh, being boiled for fome time, let fall a fmall quantity of yellow-coloured mat- ter. This matter being digefted im diluted fulphuric acid, part- ly diffolved with effervefcence ; but a portion remained undif- folved, weighing 1 grain. It was infoluble in acids, and with potafh melted into a colourlefs glafs. It was therefore filica. The fulphuric acid folution being evaporated to drynefs, left a refidue, which poffefled the properties of fulphate of lime, and. which weighed 1.2 grains, equivalent to about 0.7 grains of lime. 10. THE conftituents obtained by the preceding analyfis be-- ing obvioufly defective, it remained to éxamine whether the mineral, according to the conjecture of Bournon, contained an alkali. For this purpofe, 100 grains of it, reduced to a fine: powder, and mixed with 500 grains of nitrate of barytes, were expofed for an hour to a red heat, in a porcelain crucible. The fufed mafs was foftened with water, and treated with muriatic acid. The whole diffolved, except 25 grains of a white pow- Vou. VI..PoIk + < 3D ont &.- dere 394 On SODALITE, a new der, which proved on examination to be filica. The muriatic acid folution was mixed with fulphuric acid, evaporated to dry- nefs ; the refidue, digefted in hot water, and filtered, to fepa- rate the fulphate of barytes. The liquid was now mixed with , an excefs of carbonate of ammonia, boiled for an inftant or two, and then filtered, to feparate the earth and iron precipita- ted by the ammonia. The liquid was evaporated to drynefs, and the dry mafs obtained expofed to a red heat in a filver cru- cible. The refidue was diffolved in water, and expofed in the open air to fpontaneous evaporation. The whole gradually fhot into regular cryftals of fulphate of foda. This falt being expofed to a ftrong red heat, weighed 50 grains, indicating, ac- cording to BERTHOLLET’s late analyfis, 23.5 grains of pure fo- da. It deferves to be mentioned, that during this procefs, the filver crucible was acted on, and a fmall portion of it was af- | terwards found among the fulphate of foda. This portion: was feparated before the fulphate of foda was weighed. Tue preceding analyfis gives us the conftituents of fodalite as follows : Silica, - - - ee Pee Alumina, = - 27.48 Lime, - - - 2.70 Oxide of iron, - - 1.00 Soda, - - - 23.50 Muriatic acid, — - - 3.00 Volatile matter, - - Jette) Lofs, - - - 1.70 100.00 MINERAL from GREENLAND. 395 P) ‘Mr Atxan fent a fpecimen of this mineral to Mr Exe- BERG, who analifed it in the courfe of laft fummer. The con- ftituents which he obtained, as he ftates them in a letter to Mr ALLAN, are as follows : Silica, ~ - ebay igGe Alumina, - - = ele gas ; Soda, - - - Bigs Muriatic acid, = = 6.75 Oxide of iron, - - 0.25 100.00 ‘Tuts refult does not differ much from mine. The quantity of muriatic acid is much greater than mine. The lime and the volatile matter which I obtained, efcaped his notice altogether. If we were to add them to the alumina, it would make the two analyfes almoft the fame. No mineral has hitherto been found containing nearly fo much soda as this. Hence the reafon of the name by which I have diftinguithed it. 3D 2 XUE. 2 ; ¥ Rade | - A ae run my ee ae — " paseieer aati vatilegesab re nk a) “ciapatienabs ai XIII. Demonstration of the Fundamental Property of the Lever. By Davip Brewster, LL. D. F.R.S. Evin. [Read December 3. 1810.} T isa fingular fact in the hiftory of {cience, that, after all the attempts of the moft eminent modern mathematicians, to obtain a fimple and fatisfactory demonftration of the funda- mental property of the leyer, the folution of this problem gi- ven by ArcuimepEs, fhould ftill be confidered as the moft legi- timate and elementary. Gatitro, Huycens, DE LA Hire, . Sir Isaac Newron, Macriaurin, Lanpen, and HAMILTON, have directed their attention to this important part of mecha- nics ; but their demonftrations are in general either tedious and abftrufe, or founded on affumptions too arbitrary to be recog- nifed as a proper bafis for mathematical reafoning. Even the demonftration given by Arcuimepes is not free from objec- tions, and is applicable only to the lever, confidered as a phy- fical body. Gaxteo, though his demonftration is fuperior in point of fimplicity to that of ARcHIMEDEs, reforts to the ine- legant contrivance, of fufpending a folid prifm from a mathe- matical lever, and of dividing the prifm into two unequal parts, which act as the power and the weight. The demonftration given by HuyceEns, aflumes as an axiom, that a given weight removed 398 DEMONSTATION of the removed from the fulcrum, has a greater tendency to turn the lever round its centre of motion, and i is, befides, applicable on- ly toa commenturable proportion of the arms. The founda- ~ tion of Sir Isaac NEwron’s demonftration is ftill more inad- miffible. He affumes, that if a given power ac in any direc- tion upon a lever, and if lines be drawn from the fulcrum te the line of direction, the mechanical effort of the power will be the fame when it is applied to the extremity of any of thefe lines ; but it is obvious, that this axiom is as difficult to be pro- ved as the property of the lever itfelf. M. Dr 1a Hire has given a demonftration which is remarkable for its want of ele- gance. He employs the reductio ad absurdum, and thus deduces the propofition from the cafe where the arms are commenfu- rable. The demonftration given by Macraurin has been highly praifed ; but if it does not involve a petitio principit, it has at leaft the radical defedt, of extending only to a commen- furable proportion of the arms. The folutions of LanpEN and HamittTon are peculiarly long and complicated, and refemble more the demonftration of fome of the abftrufeft points of mechanics, than of one of its fimpleft and moft elementary truths. In attempting to give a new demonftration of the fundamen- tal property of the lever, which fhall be at the fame time fimple and legitimate, we fhall affume only one principle, which has been univerfally admitted as axiomatic, namely, that equal and opposite forces, acting at the extremities of the equal arms of a lever, and at equal angles to these arms, will be in equilibrio. With the aid of this axiom, the fundamental property of the lever may be eftablithed by the three following propofitions. In Prop. FE. the property is deduced in a very fimple manner, when the arms of the lever are commenfurable. In. Fundamental Property of thee LEVER. 399 In Prop. II., which is totally independent of the firft, the de- monftration is general, and extends to any proportion between the arms. ‘In Prop. III. the property is eftablifhed, when the forces act in an oblique direction, and when the lever is either rectilineal, angular, or curvilineal. In the demonftrations which have ge- nerally been given of this laft propofition, the oblique force has been refolved into two, one of which is directed to the fulcrum, while the other is perpendicular to that direction. It is then affumed, that the force directed to the fulcrum has no tendency to di- sturb the equilibrium, even though it acts at the extremity of a bent arm; and hence it is eafy to demonftrate, that the remaining force is proportional to the perpendicular drawn from the ful- crum to the line of direction in which the original force was applied. As the principle thus affumed, however, is totally in- admiffible as an intuitive truth, we have attempted to demon- ftrate the propofition without its affiftance, Prop. 1.—Jf one arm of a straight lever is any multiple of the other, a force acting at the extremity of the one will be in equilibria with a force acting at the extremity of the other, when these forces are reciprocally proportioned to the length of the arms to which they are applied, Let AB (PiaTE XI. fig. 1.) be a lever fupported on the two fulcra F,f, fo that Af=fF =FB. Then, if two equal weights C, D, of 1 pound each, be fufpended from the extremities A, B, they will be in equilibrio, fince they act at the end of equal arms Af, BF ; and each of the fulcra f, F, will fupport an equal part of the whole weight, or r pound. Let the fulcrum f be now remo- ved, and let a weight E, of 1 pound, aé upwards at the point Jf; the equilibrium will ftill continue ; but the weight E, of 1 pound, acting upwards at f, is equivalent to a weight G of 1 pound, acting downwards at B. Remove, therefore, the weight E, 400 DEMONSTRATION of the E, and fufpend the weight G from B; then, fince the equili- brium is ftill preferved after thefe two fubftitutions, we have a weight C, of one pound, acting at the extremity of the arm AF, in equilibrio with the weights D and G, which together make two pounds, acting at the extremity of the arm FB. But FA is to FB as 2 is to 1; therefore an equilibrium takes place, when the weights are reciprocally proportional to the arms, in the particular cafe when the arms are as 2 to 1. By making Ff fucceflively double, triple, &c. of FB, it may in like manner be fhewn, that, in thefe cafes, the propofition holds true. LEMMA. If any weight BC cb, (fig. a. No. 1.), of uniform shape and density, is placed on a lever A 0, whose fulcrum is 9, it has the same ten- dency to turn the lever round 9, as if it were suspended from a point G, so taken that bG =Ge. Ir a weight W, of the fame magnitude with BC, acts upwards at the point G, it will be in equilibrium with the weight BC, and will therefore deftroy the tendency of that weight to turn the lever round g. But the weight W, acting upwards at the point G, has the fame power to turn the lever round 9, as an equal weight w, acting downwards at G. Confequently the tendency of the weight BC to turn the lever round 9, is the fame as the tendency of an equal weight w, acting downwards at G, Prop. II. If two forces applied to a lever, and acting at right angles to it, have the same tendency to turn the lever round its centre of mo- tion, they are reciprocally proportional to the distances of the points at which they are applied from the centre of motion. Ler A od, (fig. 2. No. 2.) be a lever whofe fulcrum is 9, and let it be loaded with a weight BD dé of uniform fhape and den- fity. Fundamental Property of the LEVER. 401 fity. . Then by the lemma, this weight has the fame tendency to turn the lever round, as if it were fufpended from the point n, fo taken that bu =dn. Make gc = od, and let the weight BD dd be divided at the points C and F, by the lines Ce, F 9. The weights CF gc, D F 9d, being in equilibrio, by the axiom, have no tendency to turn the lever round g, confequently the remaining weight BC cd, has the fame tendency to turn the le- ver round ¢ as the whole weight BD dd. Hence if bm=c m, the weight BCcd acting at the point m, will have the fame tendency to turn the lever round 9, as the weight BD dd acing at m. © Now BDdd:BCch=bd:bc=nd:mc; and fince be=bd—cd, we hayveme=ybd—tcod=nd—ycd=n¢, and ad=no+icdazmec+icdumg. Confequently, BDdb:BCcb=m9o: 79. ~ LEMMA. Two equal forces acting at the same point of the arm of a lever, and in directions which form equal angles with a perpendicular drawn through that point of the arm, will have equal tendencies to turn the lever round its centre of motion. Let AB (fig. 3.) be a lever with equal arms AF, FB. Through the points A, B, draw AD, BE, perpendicular to AB, and AP, Ap, BW, Bw, forming equal angles with the lines AD, BE. Produce PA to M. Then, equal forces acting in the direGtions AP, Bw, will be in equilibrio. But a force M equal to P, and acting in the direG@tion AM, will counteract the force P, ating an the direGtion AB, or will have the fame tendency to turn the lever round F; and the force W, acing in the direction BW, will have the fame tendency to turn the lever round F as the 402 DEMONSTRATION of the the force M: Confequently the force W will have the fame ten- dency to turn the lever round F as the force w; and this will hold true, whether the arms AF, FB, are ftraight or curvili- neal, provided that they are both of the fame form. Prop. III.—Jf a force acts in different directions at the same potnt in the arm of a lever, its tendeney to turn the lever round its centre of motion, will be proportional to the perpendiculars let fall from that centre on the lines of direction in which the force is applied. Ler AB, (fig. 4.) be the lever, and let the two equal forces BM, Bm, act upon it at the point B, in the direction of the lines BM, Bm. Draw BN, Bz, refpectively equal to BM, Bm, and forming the fame angles with the line PB » perpendicular to AB. To BM, Bm, BN, Bz, produced, draw the perpendiculars AY, Ay, AX, Ax. Now, the fide AX = AY, and Ax = Ay, on account of the equality of the triangles ABX, ABY; and if M/Z, Ma, be drawn perpendicular to Ba, the triangles ABY, BM/, will be fimilar, and alfo the triangles ABy, Bm: Hence we ob- tain AB: AY = BM: Bd, and AB: Ay= BM: Ba Therefore, ex equ, AY: Ay= BJ: Ba. Complete the parallelograms BM oN, Bmwn, and B/, Ba will be refpectively one-half of the diagonals Bo, Bw, Now let two equal forces BM, BN, act in thefe diredtions upon the lever at B, their joint force will be reprefented by the diagonal Bo, and confequently one of the forces BM will be Transactions B.S Edin? Vol VP 378, XI. PLATE | =a ae RE AE REA IS TO Fig.2. 2772. D A Fundamental Property of the LEV ER. 403; be reprefented by BJ = 4Bo. In the fame manner, if the two equal forces Bm, Bz, act upon the lever at B, their joint force will be reprefented by Bo, and one of them, Bm, will be repre- fented by BA=4+Bo. Confequently the power of the two forces BM, Bm, to turn the lever round its centre of motion, is reprefented by B/, Ba, refpectively ; that is, the force BM. is to the force Bm as B/ is to Ba; that is, as AY is to Ay, the perpendiculars let fall upon the lines of their direction. 3E2 XIV , a set HAN aX wy ‘if oh 3 2 silat aac ) ‘ ion ee Ps - . rtd i WN Ms t¥ o y Vp ¥ { ' ees oe Ow" age: tore fone ortigael: a ey o\a ve bins ai wot smiof isd? fi. 3h yart of SOG we yx OY ew EE. Aon! Lope regan ach L tine om ensdirtoratio bits ea. ve ‘Dbeftidisaqe id Tw ods oils To 1704 ris ‘ybasupsition Dee eck hed ee coidoms, Yo.2151199-2ti bait avs) ada: ces’ OF yw AGE Saat _ ML ayo ack .al sql 2 Uovibsdqiot ee A Bd Bosnstorqin, ar 3 is aes: a VA ab fat edd hE OF VA Rh WH OE ID CP if soffit sete egal vis Heat: sac gSt angle Syaeicn He XIV. On the Rocks in the vicinity of Edinburgh. By Tuomas Attan, Esq; F. R.S. Evin. [Read March 4. 1811.] LTHOUGH {fcience has only within thefe few years ac- knowledged the importance of Geology, the eagernefs with which it has been cultivated, affords fufficient proof of the intereft it is capable of creating. OF this we have a recent ex- ample in the laborious undertaking of Sir Gzornce MacKEn- zig and his friends, who, notwithftanding all the dangers pre- fented by a voyage through the moft tempeftuous ocean, and the deprivations to which they were expofed, in a journey through a country deftitute of the flighteft trace to guide the route of the traveller, were not deterred from exploring the inhofpitable fhores of Iceland. - Thefe, and other travellers, have extended our knowledge of various diftri@s on the furface of the globe; but we have ftill to lament the extreme imper- fection of the {cience, which, as yet, has affumed no decided cha- racter or form. This appears principally owing to the want of - fome fimple method, grounded on clear and intelligible princi- ples : 406 On the ROCKS in the ples; perhaps alfo, to its having always been the object of thofe who have treated the fubject, to accommodate their ob- fervations to a particular theory ; and when this is the cafe, it is obvious, that the mind cannot refufe itfelf the fatisfaction, of dwelling with comparative enthufiafm on facts which appear fa- vourable to the adopted fyftem ; while others of a different ten- dency, are either reluctantly, and therefore fuperficially confi- dered, or what is yet worfe, even ftudioufly avoided. In the prefent ftate of our knowledge, to diveft geology of theory, would be to deprive it of all its intereft. We muft not defpair, however, that by the multiplication of particular facts, and the expofition of others, with which we are ftill unac- quainted, a fyftem of geology may yet be formed, founded ex- clufively on the phenomena of nature, or at leaft on reafoning much lefs hypothetical than is now required. Tue moft obvious means of attaining this object, feems to be a careful, minute, and candid examination of every circum- ftance which appears to convey an explanation of itfelf, with- out reference to any theory ; and from thefe we may ultimate- ly hope to obtain fome data, equally certain and comprehen- five. Ir is with this view, that I have always formed my collec- tions of geological fpecimens ; and although it will appear, that the arguments I have deduced are favourable to one fet of opinions, yet I can aflert with confidence, that the diftric which it is the objeét of the prefent paper to examine, has been faith- fully explored, and, I hope, candidly defcribed.. Tt VICINITY of EDINBURG.’ 407 Ir is generally admitted, that no city in Europe is more favour- ably fituated than the metropolis of Scotland, for the ftudy and purfuit of geology: even the ground which it occupies, when laid open for the erection of buildings, has occafionally prefented fome very interefting phenomena. ‘he hills in the immediate neighbourhood, always at command, afford a neyer-failing fource of refearch; and in the furrounding country, a greater variety of foflils is to be met with, than almoft in any {pace of the fame extent. TuE importance of a complete acquaintance with the pheno- mena which furround this city, cannot therefore, I think, be confidered of a trivial nature. Indeed, by the number of in- genious works already before the public, it may be thought that the fubject is exhaufted. But this is an error I am very defirous to combat, not only becaufe in my own experience I have found it to be one, but becaufe, as fcience advances, our ha- bits of inveftigation improve, phenomena become more fami- liar, we learn to trace and to feize not only the objects we are in purfuit of, but alfo to dete@ others, which our lefs practifed eye had originally paffed over unnoticed. - We all think ourfelves perfectly acquainted with the rock, on which our Caftle ftands. But I fufpect there are many mem- bers of this Society, who will be furprifed to learn, that fand- ftone occurs near its fummit, and alfo at its bate. Sa- or lifbury 408 On the ROCKS in the lifbury Craig and Arthur’s Seat appear perfectly familiar to us ; there are phenomena belonging to both, however, of which, I have no doubt, many are yet ignorant. That any-circumftance of an interefting nature, fhould remain unobferved, can only be accounted for, by its being taken for granted, that thefe confpi- cuous objects, having already undergone much critical examina- tion, nothing farther remains to be noticed. This is an opi- nion, which I fhall prove in the fequel, to be without founda- tion. Artbhur’s Seat and Salisbury Craig, are naturally the objects, which firft attra@ the attention of the geological traveller, on his arrival in Edinburgh ; and to thefe places he is general- ly conducted by fome one of our amateurs, when the favourite theory is introduced, and each corroborative fact dwelt upon, with all the ufual keennefs of theoretic difcuffion. This was the eyound which, in all probability, firft fuggefted the Theory of Hurron ; and it was perhaps here, that his comprehenfive mind originally laid the foundation, of the ftrudture which he afterwards fo fuccefsfully reared. . But that theory, in itfelf fo beautiful, and in many points fo perfect, I am very far from embracing entirely. Iam very far, indeed, from follow- ing him through his formation and confolidation of ftrata, or the tranfportation and arrangement of the materials, of which they are compofed. There are other circumftances alfo, which, though totally irreconcilable with any ether hypothefis, are yet but imperfeatly explained by his. I particularly allude to the fin- gular contortions, exhibited in what are termed Transition ftra- “ta, fo finely exemplified on the coaft of Berwickfhire. I with-to carry my induétions, juft as far as-facts will bear them out. It is therefore, only in the regions of unftratified rocks, or in their immediate vicinity, that I have as yet, been able to difcover VICINITY of EDINBURGH. 409 difcover a language, which, if ftudied with due attention, can- not fail, I think, to become intelligible, and carry conviction to - thofe, who choofe to reafon impartially on the fubject. In the writings of Dr Hutton, we do not meet with defcrip- tions of particular diftridts, his obfe& being rather to eftablith _a general theory, by the particular facts which thefe diftrias afforded. We cannot, therefore, look to him for a mineralogical ac- count of the neighbourhood of Edinburgh; and we have to re- gret, that no other geologift has yet undertaken that tafk. In a (hort notice, i the Appendix of a work on another county, by Profeflor Jameson, this vicinity is mentioned as principally belonging, to what is termed the Coal Formation by WERNER, which, according to the fyftem of that celebrated na- turalift, forms part of the Fletz rocks. To render thefe terms intelligible to the general reader, it is neceflary to give fome explanation, as, without a confiderable knowledge of the fyftem to which they exclufively belong, they muft be totally incomprehenfible. WERNER is the only perfon, who has attempted a regular ar- rangement of rocks ; an arduous undertaking, which I have no doubt he has accomplithed, with all the accuracy the fubje@ was fufceptible of, and fo far as the country he examined allow- ed *, Bur it appears very evident, that the facts he met with were fuch, that, in confequence of the hypothefis he had previoufly thought proper to adopt, it became neceflary to invent a theo- Vor. VI.’P. IL. ele ry * Linxs from other quarters, having been fubfequently added to his forma: tion-fuites, by his pupils. 410 On the ROCKS in the ry capable of embracing all the phenomena, which the con- ftruction of his fyftematic arrangement led him to obferve. A peculiar language was therefore indifpenfable; and as this language has been conftructed with fo much regard to his theo- ry, unlefs that is underftood and adopted, his terms become ufe- lefs. By a formation is meant, any feries or fuite of rocks which ufually occur together ; hence the Coal Formation is compo- fed of 1. Sandftone, - 6. Limeftone, 2. Coarfe Conglomerate, 7. Marl, 3. Slate-clay, 8. Clay-ironftone, 4. Bituminous Shale, = —‘g._-Porphyritic Stone, 5. Indurated Clay, 10. Greenftone *, with which the Coal occurs in numerous beds, varying extreme- ly in thicknefs. Thefe, however, never all occur together, and it is no detriment to the Coal Formation fuite, even if Coal it- felf fhould not be found among them. Acatn, the term Fletz is given to all the formations, contain- ed between the tranfition and alluvial rocks, and implies that they are diftinguifhed by their frequent occurrence in beds, which are much more nearly horizontal, than the primitive and tranfition * Greenftone is a literal tranflation from the German ; it is an extremely im- proper name; but as we have no other by which we can distinguish this variety of trap, we muft ufe it till a more appropriate is found, even at the expence of fuch language as red and blue greenftones, In the mean time, it muft be under- ftood merely as an arbitrary term. VICINITY of EDINBURGH. art tranfition rocks. If directly tranflated, the word fignifies far, and may be correctly deferiptive of the diftri@ts originally exami- ned by WERNER; but as this conftruction will not apply uni- verfally to this clafs of rocks, and as it is particularly at vari- ance with thofe belonging to it in this country, it would be bet- ter to follow the example of Profeflor Davy, and ufe the term parallel rocks, which is much lef liable to objection. Tue Huttonian Theory has no language peculiar to itfelf, having nothing to defcribe, that cannot be done in the ufual phrafeology of any country. This, by the zealous admirers of that dodtrine, may no doubt be lamented, as depriving it of an apparent {y{tematic arrangement, to which the oppofite theory is fo deeply indebted. In forming a collection from the rocks in the neighbour- hood of Edinburgh, the circumftances aboye narrated, indu- ced me to begin with thofe of Salifbury Craig and its vicinity. The colleétion I have now the honour of prefenting to the So- ciety, I began fome years ago: it is only part of a feries, which, as completed, I hope may be found worthy of a place in their cabinet. I confider it of very great importance, that every geological paper, fhould be accompanied with fpecimens, in order that if the former be found deferving of publication in your Transactions, thofe who perufe the defcription may know, that the fpecimens referred to, are to be feen in the re- ~ pofitories of this eftablifhment. 3F2 SALISBURY. 412 On the ROCKS in the . SALISBURY CRAIG is fituated on the north fide of Arthur’s Seat, againft which its fouthern extremity refts: from this it extends, in a northern direction, and rounds towards the eaft, fo as to form the fegment of a circle, about half a mile in length It is furmounted by a magnificent fagade, which .is loweft at the extreme points; towards the mid- dle, the perpendicular rock may be from 80 to go feet high. From the bafe of this precipice, a floping bank, covered with debris, reaches to the valley below, altogether form- ing an elevation of nearly 4oo feet. From the upper edge of it, a regularly inclined plane, flopes gently, on the oppofite fide, at an angle of about 15°, in a north-eaft direction, and forms the left bank of the valley, called the Hunters Bog. On the right of this valley, the rocks again rife rapidly, affording indications of two or three feparate facades. Thefe are not characterized in the diftin@ manner of Salifbury Craig, but are furmounted by a furface, which, though a little rounded, pre- fents an inclination correfponding with that of the Craig, in a very ftriking manner. From the bafe of Salifbury Craig, or rather from the bafe of the debris by which it is encircled, towards the fouthern ex- tremity, the ground again rifes, and prefents an inclined plane, fimilar to its own, but of lefs magnitude. This is known by the name of St Leonard’s Hill. Hence it appears, that there are three fimilarly inclined planes or terraces, of which Salifbury Craig forms the interme- diate one, each of them having a different elevation. From this ftructure we may eafily conceive the origin of the Swedifh word Trap, which has been employed as a generic term, for the VICINITY of EDINBURGH. 413 the clafs of rocks to which this appearance may generally be attributed *. Ir we imagine a vertical plane, to pafs from St Leonard’s Hill in an E.N.E. direction, which fhall cut Salifbury Craig, and continue through the right bank of the Hunters Bog, we fhall find the rocks difpofed in the following manner : St Leonard’s Hill. Sandftone. Porphyritic Greenftone. : Sandftone. : Salisbury Craig. Sanditone. Greenftone. Sandftone. Hunters’ Bog. Greenftone. Sandftone. Porphyritic Greenftone. Trap-Tuff. Bafalt. The * One of the greateft difficulties which geology as well as mineralogy has laboured under, is the multitude of fynonymous terms which have been applied to every individual foffil. Trap has fuffered from this difadvantage, perhaps more than any other variety of rocks; as above noticed, that name is derived from the fimilarity to the fteps of a ftair, which may generally be traced in the outline of a country, in which this rock abounds; and as it has been employed as a generic term by mineralogifts throughout Europe, I think it proper to use it, to the exclufion of whzn/eone, the name it bears in the writings of Dr Hurron ; a 414 On the ROCKS in the The two laft of thefe are not comprehended in the Coal For- mation fuite; they are confidered as members of another for- mation, denominated the Neweft Floetz-Trap. THE upper fandftone of St Leonard’s Hill, and the lower fandfione of Salifbury Craig, are, fo far as we know, continu- ous; but as thefe, fuppofing the lines of the ftrata to be pro- jected, would form a bed of 450 feet thick, it is poflible alternations of greenftone may occur in it. Above, I have on- ly mentioned fuch as are vifible. Tuose on the right of the Hunters’ Bog, are not fo diftin@ly expofed as the reft ; but the foffils are all found in the order I have ftated. Occafionally fmall feams of reddifh-brown co- loured flaty clay, and clay-ironftone occur, principally inter- mixed with the fandf{tone; but they are fo thin, and fo uncon- nected, that they can fcarely be confidered.as ftrata. THE feries of {pecimens I.am now about to defcribe, are thofe of St Leonard’s Hill and Salifbury Craig. No. 1. is a fpecimen of the Sandftone of St Leonard’s Hill ; it is of a reddifh-white colour, and extremely coarfe-grained. It was taken from the middle of the quarry, and pretents a fpe- cies of conglomerate, the fragments of fandftone being agglu- tinated by a dark-red ferruginous patte.. No. 2. from the fame quarry, is more compact, and prefents a ftreaked appearance, correfponding with the direction of the ftratum. There is a confiderable degree of irregularity to be obferved, in tracing the line of junction at St Leonard’s Hill. In fome places, two or three folds of the ftrata are cut off abruptly a name which, though perfeGly underftood in this country, is not received abroad, and ought therefore to be relinquifhed. VICINITY of EDINBURGH. ATS abruptly at each end by the greenftone; in another, that fub- ftance finks fuddenly as it weré into a gap in the ftrata, and be- ing loft in rubbifh, has fomewhat the appearance of a dike. Beyond this a double horizontal wedge of greenftone, with the ends turned downwards, appears among the ftrata; and a little farther, towards the north, a roundish mafs of the fame fubftance alfo occurs ; this has very much the appearance of an included fragment, but the decompofition of the fandftone has juft be- gun to expofe its connection with the rock above. On the fandftone, Porphyritic Greenftone (No. 3.) refts. The colour of this is reddifh-brown; the texture is fine-grained ; and it contains finall {pecks of flefh-coloured calcareous fpar. It is traverfed in various places by veins of Hematitic Iron-ore (No. 4.) accompanied with fulphate of barytes.. Thefe two _ fpecimens have very much the charater of fome varieties of porphyry-flate, and on breaking one mafs, I obferved a tenden- cy to a flaty arrangement. In different places of this quar- ry, the greenftone aflumes a variety of appearances (No. 5. and 6.), fome of which might be attributed to decompofition. I do not conceive, however, that any external caufe has ever had much effect upon this rock, although in fome places it has entirely loft its luftre, (No. 7.), and might be miftaken for © trap-tuff, were it not for the fhape of the cryftals. Asove this, the rock graduates into a highly oryfal- line Porphyritic ftone, (No. 8.) the pafte of which is of a brownifh-grey colour, very clofe-grained, with an uneven fplintery fracture, containing both cryftals of felfpar and horn- _ blende. In this quarry there are feveral inftances of slikensides, _ one of which is rather remarkable, it occurs in’an inclined rent in the fandftone: the traces of the flip, (No. 9.), are horizon- ; tal, 416 On the ROCKS in the tal, and extremely well defined ; but immediately over it, im the erecnftone, the appearance of the flip is not continued. Some indications of a flip appear a little to the right of it. Ina part of the Greenftone which is confiderably decompo- fed, a vein, ftretching horizontally, of a dark-green fibrous fubftance occurs, (No. 10.); it is foft, and has a fhining fatiny luftre, like afbeftus. I have not anywhere in this vicinity met with any fimilar fubftance. WE now proceed to Salifbury Craig, where the circumftances I fhall principally notice, are, 1. The texture of the greenftone rock, with the foffils it con- tains. 2. The vein of greenftone by which the Craig is interfected. 3. The included mafs of fandftone which occurs in the green- {tone ; and, 4. The indurations and interruptions of the ftrata. No. 11. is a fpecimen of the greenftone taken from the lower edge of the bed, at the great quarry, where it touches the fand- ftone; the point of contact being marked by a {mall remaining fragment of the latter, at which the grain of the ftone is much finer than at the other extremity. The colour is iron-grey, with fmall fpecks of calcareous matter interfperfed. Nos. 12, 13, & 14. are different gradations of texture, taken ina vertical line, from the edge towards the centre, where the {tone is always moft perfedtly cryftallifed; from hence it again de- clines in grain towards the upper furface, where we find it in the fame earthy and uncryftallifed ftate (No. 15.) obferved at the bottom. In the laft fpecimen, there is a fmall detached fragment. VICINITY of EDINBURGH. ary fragment of the ftratified matter imbedded in the green- ftone, a circumftance connected with a very important clafs of facts. No. 16. This fpecimen of greenftone is remarkable, as exhi- biting a variety of colours; thefe are not blended, but diftin@- ly divided from each ether. The colours are iron-grey, light- grey, dark-red, and brick-red. No. 17. This fpecimen is a {trong example of the improprie- ty of the name which it bears; it is a greenftone, decidedly of a red colour. The fingular penetration of ferruginous matter, which is exhibited in various parts of this rock, is not eafily ac- counted for; but fuppofing it to have been once in a ftate of fu- fion, it may have obtained this fuperabundance of iron by ab- ! forption, as the adjoining ftrata frequently abound in that mineral. In various parts of the Craig, veins of a peculiar nature may be obferved ; they are compofed precifely of the fame ingre- dients as the rock, and are diftinguifhable only by the red co- lour of the felfpar, (No. 18). Thefe are termed contemporaneous veins, or veins of secretion ; they are deeply wayed, and gene- tally follow the direction of the bed. Some of them prefent a very bright brick-red colour, (No. 19.), mixed with fpecks of calcareous fpar. Nos. 20, 21. in thefe {pecimens, are fmall globules of a black earthy fubftance, which I am at a lofs to name. I fhould have confidered it Amphibole, but for the next fpecimen, (No. 22.), in which the fame fubftance appears-to occur in irregular fragments. No. 33. Analcime with cryftallifed Calcareous Spar. I be- fore noticed, that it was in the heart of the bed where the _fubftance of the greenftone prefented the cryftalline texture in Vou. VI. P. I. 3G the ‘ 418 On the ROCKS in the the higheft perfe@ion. The occurrence of the analcime is connected with the fame fact. I have never been able to find it on Salifbury Craig, excepting at one period, when an entire fection of the bed was quarried off, and about the middle of this the analcime occurred. No. 24.. with aabphate of barytes, with calcareous {parry iron- ore.. No. 25. part of a very irregular vein. Its fides are formed of calcareous {parry iron-ore, which 1s followed by a coating of hematitic iron. Here the regular ftratification, as it is called, of the vein ends, and calcedony, firft femitranfparent, then opake, and common calcareous f{par, occupy the reft. No. 26. calcareous {parry iron-ore cryftallifed, with fome tranfparent cryftals of quartz. No. 27. large cryftals of calcareous {par, fick cryftallifed. and radiated tufts of quartz. No. 28. red oxide of iron, with a vein of calcareous {parry iron-ore. No. 29. green coloured quartz, with a coating of cryftallifed quartz. No. 30. cryftallifed quartz, with amethyft. Sucu are the minerals which occur on Salifbury Craig. Some of them are rare, and others to be found only when the rock is working in particular places. Tur next circumftance I have to notice, is the vein of creenftone *. It occurs a little to the north of the fpot, to which * The term dyke has been very generally applied to veins of this defeription, and-I am not fatisfied that it is the leaft proper of the two; as there certainly is a marked diftin@ion between veins compofed of rocks, and what we general- ly ” VICINITY of EDINBURGH. 419 which the cart-road, along the bafe of the rock extends, a few feet beyond a gap, known by the name of the Cat’s Nick. I po not think this vein attracted the attention of geologifts in any particular manner, prior to 1805. It certainly was ob- ferved long before that period, but was not known to extend through the bed of greenftone, till Sir James Hart and myfelf ‘noticed, that after cutting the fandftone, it continued its courfe uninterrupted to the top. This obfervation contributed very much to increafe our curiofity, and a. man was employed to clear away the foil and rubbifh, which had accumulated on the furface. A confiderable portion of the rock was foon laid open, below the point from which it was at that time vi- fible. Nothing, however, of much intereft, was by this means difcovered. The dike, after bending a little to one fide, conti- nued its courfe downwards. . ‘Tue {pace which this dike occupies, may be from fix to eight feet wide ; its width varies a little in fome parts, and thefe va- riations are apparently increafed, if the feGtion which is obfer- ved be not at right angles with the walls. That portion embraced by the ftrata, which we found principally co- vered with debris, was very much decompofed, prefenting on the furface a certain degree of nodular exfoliation, of a rufty- 3G 2 brown ly underftand by mineral veins. The firit are formed of one uniform rock, compofed in all their parts. of the fame conftituents, and differing only in po- fition, from the beds thefe materials more ufually form; while the latter, though fometimes formed only of one fubftance, fuch as quartz or calcareous . Ipar, are generally compofed of a feries of foffils, arranged in lines parallel to the walls. No fuch appearance ever prevails in rock veins, or conftituting mountain mafles; therefore, in ufing the term vein, when applied to greentftone, granite, or the like, it muft be underftood as a generic term, of which these lat. ter, {pecify the variety. 420 : ‘On the ROCKS in the brown colour. On breaking into the rock, it exhibited (No. 31.) * the concentric lines fo common in decompofing greenftone; and beyond this, the ftone prefented a degree of frefhnefs, with a very coarfe grain of a peculiarly light afh-grey colour, and a very dull earthy texture, (No. 32.) Between this portion of the vein and that embraced by the greenftone, there is a very remarkable difference, the . latter being of the ufual iron-grey colour, and otherwife perfectly characteriftic. Before it leaves the fandftone ftrata, it feems to contain an unufually large proportion of calcareous matter. This may have aided the decompofition, together with the moifture retained by the debris, fo lately removed from its furface, and which has left it in a ftate eafily affected by the weather. Since I commenced writing this paper, I made an excurfion to the fpot, and was greatly furprifed to obferve the devaftation of laft winter. Before the vein rifes above the level of the ftrata, a portion of it, ftill more decompofed than the reft, of a dark-purple co- lour, branches off; and embraces a wedge-fhaped mafs of the fandftone (No. 33. and 34.) indurated in a very high degree. Juft at the top of this indurated mafs, the whole dike changes its colour, and, I may alfo fay, its confiftence. It here prefents a light-greyifh afpect, deeply ftained, with red ferruginous marks, of a dull earthy texture, an even fracture, and a tolera- bly fine grain, (No. 35.) That portion correfponding with, and immediately over the included fandftone, I found much coarfer in the grain, (No. 36.), and in a more decompofed {tate ; * Correfponding numbers will be found in the annexed engraving, which will explain more fully the relative pofition of the fpecimens. oe PLATE Xl. | i ie Hs WN LY \ TiansactionsR.S F:din® lol LIP 420. SSesSsn SSS SSS Fe ee ie eR yj Yi Wi WW PSS a S “SS - Ni a BY wr YY 2 s oy eS \ ] ~ NUR ~ ~ Ay *\ i Y y er < Sis hon Wake ‘" q x ‘ Ny) N SS ¢ ON ~ IS WAS st . \ ‘ \ ts ; ‘ ‘ y ) AN\ vf \\\ pe \) SS "| AS A NARA A AS i\ aw SAN Y ih fone . S \\\\ SS x) S q A \ WN S\N ve 3) hy 4! i ‘\ WY ‘ > yo XG WAS ~ SSS eS . ; mt VICINITY of EDINBURGH. 423: ftate ; while it differed from No..37., the ftone on the fides, which were perfectly fimilar to each other in compofi- tion. Tracinc the friable purple-coloured portion upwards, I found it gradually became harder, and, of a fudden, chan ge to a. fine-grained blue-coloured greenftone ; and the part correfponde ing with the included mafs, alter to a hard coarfe-grained rock, (No. 38.) I foon obferved, that this coarfe-grained mafs, which. is about ten inches thick, continued. upwards, maintaining an uniform dimenfion and-pofition, in refpect to the walls of the. vein, as high as the eye could trace it in the rock, thus divid- ing it into two portions; that on the left fide being about eigh-- teen inches wide, while the other is about five feet. On. comparing the texture of the included ftripe, with that: of the walls on each fide, (No. 39. left fide; No. 40. included. ftripe; No. 41. right fide,) taken in a horizontal line, about fix. feet above the ftrata, I found as clofe a refemblance as it is poflible to conceive ; they are.all coarfe-grained, and highly cryftallifed. This fimilarity is not more remarkable, than the difference be-- tween the fubftance of the vein and the included mafs.. Speci-- mens taken from the junction of thefe, mark this in a ftriking. manner. No..42. is from the left fide of the right portion of the vein, to which the fine-grained part belongs. No..43. is from the middle of this portion; and No. 44. from the fide next the right wall.. Thefe were alfo taken in a: horizontal line, and exhibit the fame gradation of grain’ noticed as exifting in the great bed. Even in the narrow portion of. eighteen inches, on the left fide, this circumftance is quite vi- fible; but the fpecimens taken from the other are highly illu-. ftrative of the fac. Ji 422 On the ROCKS in the I nave had an opportunity of examining many veins of greenftone; but I know of none more interefting in a geolo- gical point of view than this. I THINK it can icarcely be doubted, that the fame effort which feparated the included portion of fandftone, cleft the correfponding ftripe of greenftone from the great bed. This, as well as the gradation of grain, everywhere obfervable in beds and veins of trap, are remarks, in my opinion, of confiderable value to the Huttonian hypothefis. On a former occafion, when I had the honour of fubmitting fome remarks on the north of Ireland to the Society, [ took an opportunity of dwelling particularly on the laft.circumftance. Like the charring of coal, when that fubftance is found in contac with whin, as has been ably remarked by Profeflor Piay- Farr, “ few facts in the hiftory of foffils fo dire@tly af- “ fimilates the operations of the mineral regions with thofe ‘“‘ which take place on the furface of the earth *.”” This gra- dation of texture has a ftrong analogy to many accidental facts obfervable in furnaces, of glafshoufes and the like, and ftill more fo to thofe experiments made exprefsly for the purpofe of af- certaining the effects of flow cooling, by Sir James Hay and others. One additional argument for the igneous origin of thefe veins, has been added by the obfervations of Sir GEorcE Mac- KENZIE and his friends, in Iceland, in perfect correfpondence with the above fact. He there found many veins of this fub- ftance, coated on the fides with a glafly covering, exactly fimi- lar to melted greenftone, when rapidly cooled. I sHouLp expect the fame circumftance would be met with in veins of porphyry and granite; but I have not been able to ex- tend * Iluftrations of the Huttonian Theory, § 68. VICINITY of EDINBURGH. 423 tend my obfervations fo widely, as to embrace the facts refpect- ing thefe rocks. One remark I fhall, however, hazard in this place, refpecting an eflential difference between veins of granite and thofe of greenftone. The former feem to be of fimultaneous formation with the great body of that rock, to which they may generally be traced, and, fo far as I have hither- to obferved, are never found to cut it. Veins of greenftone, on- the other hand, I have never feen connected with the great beds of that fubftance; they traverfe thefe juft as they do every other kind of rock, and confequently are in all inftances of a pofterior formation. I am aware, that thefe ideas are ve- ry much at variance with certain received opinions. I there- fore wifh to be underftood as fpeaking folely upon my own experience.. : I HAVE now to mention the well-known included mafs of . fandftone. Along the edge of the ftrata, a number of inftances occur on Salifbury Craig, affording the moft unequivocal marks of difturbance; but it prefents only one example; of a mafs to- -tally enveloped in the fubftance of the greenftone *. "Turis {pot has been the fcene of much controverfy, between contending geologifts. While the Huttonian confiders it as a moft incontrovertible proof of violence and of heat, the Werne- rian contends, that there is nothing in the leaft extraordinary in the appearance, and afferts, that the fuperficies of the apparently included mafs, is no. more than the fection of fome part of the ftratum, which, if traced, would be found to connect with the reft; that it had been enveloped in the fluid menftruum of the green{tone, when in this elevated pofition ; and that the rock be- ing * Since this paper was fent to prefs, others have been obferved in different parts of the rock. 424 On the. ROCKS in the ing cut in acertain direction, a fection having the appearance of an infulated mafs, would of courfe be expofed to view. There is no doubt that fuch a circumfiance is perfectly poffible ; but, in the prefent inftance, this explanation will not be found at all applicable. In every other cafe, where the ftrata appear difplaced, they are not torn from the reft, nor has the greenftone infinuated itfelf, except as a wedge, fupporting the lifted mafles. The included mafs is of a light greenith-grey colour, in fhape quadran- gular, and, when minutely examined, will be found fhivered in- to numerous diftinct fragments, with veins of greenftone run- ning through it in every direction. It partly retains its ori- ginal ftratified texture (No. 45.) although indurated in a very high degree, and is fo firmly welded to the greenftone, that it is no difficult matter to obtain fpecimens (No. 46.) of the conjoined rocks; one {mall fpecimen (No. 47.) in the collec- tion, is twice interfected by that fubftance. It, therefore, has no refemblance whatever to thofe pieces of ftrata, which are only in part detached, and which, if cut in a tranfverfe diredtion, would, in all probability, exhibit an infulated fection. That fection, however, would not difplay the broken and diftorted . appearance defcribed above, at leaft if we may be allowed to judge by the integrity of the longitudinal fections, of which there are fo many examples in this vicinity. Befides, the colour of the included mafs is totally different from that of any of the {trata near it, which are here of a deep red (No. 48.), and at this particular fpot are remarkable for their apparent derange- ment. I therefore conclude, that there is every reafon to con- fider this, as a fragment detached from fome other part of the fandftone, and left fufpended in its prefent fituation, when the greenftone affumed a folid confiftence, as was originally con- jectured by Dr Hutton. I VICENITY of EDINBURGH. 425° I now come, as propofed, to that divifion of the fubje& which relates to indurations. By induration is meant, a greater degree of compactnefs, obfervable in particular parts of ftratified rocks, than is ufual throughout their mafs. One part of a bed may be harder than another, confequently more indurated. But the in- duration here alluded to, is that which is fuppofed to have been effected, by an alteration in the denfity of the ftone, in confe- _quence of the action of heat. Turse phenomena are of a very ftriking nature, and were firft brought into notice by Dr Hurron ;, in them, he found evidence, to him perfeétly conclufive, of the igneous formation of whin, and, with that ingenuity and perfeverance which cha- tacterife the whole of his works, he did not fail to generalife his obfervations, and to place the facts, firft noticed in this {pot, in fuch a light, as to render them effentially ufeful to his. theory. Tue anxiety which the difciples of the Wernerian fchool have always evinced, to undervalue the merit of this obferva- tion, is a fure mark of the eftimation in which they hold it; and it is, therefore, very properly confidered by the fupporters — of the oppofite doctrine, as one of their ftrongeft holds. In the following lift, are comprehended moft of the varieties, which this indurated fandftone prefents on Salifbury Craig. No. 49. is a junction fpecimen*, taken near the fouthern extremity, of the Craig; here the greenftone is of the deep red tinge noticed at No. 17. Vou. VI. P. Tk.» 3H No. t * By junéfion /pecimen is meant, a {pecimen which exhibits the greenftone and the fandftone conjoined. : 426 On the ROCKS in the No. 50. is another {pecimen of the fame kind ; the greenftone is here of the ufual colour, and the line of junction moft admi- rably defined. This.was taken from the great quarry. The next, (No. s1.), is a fpecimen of the fandftone in its fuppofed unaltered ftate. Nos. 49, and 50. are beth from the lower junction. No. 52. is from the upper edge, taken about half- way between the higheft part of the Craig and Holyroodhoufe. Here the fandftone prefents a facetted appearance, an arrange- ~ ment which may be owing to the fuperabundance of calcareous matter. No. 53. is highly indurated, of a deep red colour, with a conchoidal fraéture, and a facetted texture. No. 54. has the fame facetted appearance. No. 55., extremely clofe-grained, is from one of the contor- tions north of the dike. Nos. 56, & 57. Thefe are the varieties of the fandftone which have been called jasper. This is an improper name, as it con- founds two fubftances totally different. The moft compaé con- tains a large proportion of lime, and in afpect is very fimilar to fome of the limeftones of Gibraltar. Nos. 58, to 61. are varieties of the fandftone, found near the greenftone. j No. 62. Although this fpecimen was taken very near the ereenftone, ftill it does not exhibit the ufual induration, This exception occurs in different places on Salifbury Craig; and it even fometimes happens, that the ftone next the whin is lefs in- durated than the one below it. - No. 63. Containing a large proportion of ferruginous mat- ter. No. 64, to 66. Different fhades.and varieties of the fandftone, in an indurated flate. No. i ee VICINITY of EDINBURGH. 427 No. 67. In this {pecimen there is fomething very like the ap- pearance of an agate ; it, however, is not contained in the fub- ftance of the greenftone, but in the ftratified matter below it. No. 68. Another fpecimen of the fandftone, in its unaltered ftate, taken about thirty feet from the greenftone. Dr Hurron conceives, that the duration, fo very remark- able in the above fpecimens, was occafioned by the heat of the whin, when it was injected between the ftrata of fand{tone, cau- fing it to undergo a certain degree of fufion; and, to this idea, the facetted texture of fome of the fpecimens adds confiderable weight, fuch arrangements being very familiar in ftones which have undergone fufion. Tue Wernerian {chool, to account for the fathe phenomenon, afferts, that as fandftone is generally porous, the fluid folution of the trap being introduced into the fiffure, naturally percola- ted to a greater or lefs extent *. Again, that it is owing to the intermixture of the matter of the vein, with the rock that forms its walls +; and, as a proof of this, it is added, that no indu- ration appears, where the traverfed rock is poffefled of a quart- zy bafe. THEsE arguments occur in different works, but they appear to me very little calculated to fupport the point in difpute, if not in fome refpects contradi@tory. On Salifbury Craig, and generally throughout the neighbourhood of Edinburgh, where- ever we find fandftone coming in contact with greenftone, either in beds or veins, we are almoft certain, that an indura- tion will be exhibited along the edge of the ftrata. ER 2 It “ Comparative View of the Huttonian and Neptunian Theory, p. 13¢.. + System of Mineralogy, vol. iii. p. 365. 428 On the ROCKS in the Ir has already been obferved, that there are {pots on Salif- bury Craig, where this is not fo apparent as in others, and it very often happens, that fmall feams of clay occur, in a per- featly foft ftate. In Ineland, at Scrabo, in the county of Down, and at Fairhead in that. of Antrim, I found fandftone in the former, cut by veins, and in the latter, overlayed by a bed 300 feet thick, where no induration was to be feen. Now, it appears conclutive, that there could not have been a deficiency of induration in any {peck of Salifbury Craig, far lefs a total abfence, as in the cafes quoted in Ireland, had it in any inftance been effected either by percolation, or by the intermixture of the matter of the vein. The fuperincumbent or included mat- ter, if in a fluid ftate, whatever its chemical powers were, would, to a certain extent, act mechanically, and be, in all cir- cumftances, poflefled of the fame power of communicating its moifture to the furrounding mafles. It is therefore impoflible to conceive, how it fhould have withheld it in one inftance, and parted with it fo amply in another, how it fhould have indu- rated the fandftone, and left the thin feams of clay ina foft and friable ftate. It is quite unimportant, of what bafe the fandftone may be formed; it is a fubftance, allowed as above to be generally porous, (and, in the cafes alluded to, it certain-, ly was fo); into that porofity, therefore, the fluid muft have percolated, whatever the bafe may have been. On the contrary, according to the Huttonian hypothefis, it in- duration diftin@ly depends, on the compofition of the ftrata ex- pofed to the influence of heat. Some {trata may either whol- ly, or in part, be capable of refifting much higher temperatures than others. It is confequently to the ingredients of which they are formed, that we muft look either for the caufe of in- duration, or the abfence of it. This remark originated in ob- ferving, ' ; { VICINITY of EDINBURGH. 429 férving, that all the indurated fandftones of this country, con- tained more or le{s calcareous matter, while the unindurated fpecimens from Ireland, did not afford ‘the flighteft indication of that fubftance, when fubjected to the fame feft. Beroke I take leave of Salifbury Craig, I muft notice one more circumftance, which, fo far as I have hitherto feen, is quite peculiar to the fpot. I mean the occurrence, in veins, of a fubftance in all refpe&s familar to the indurated fandftones, I have juft been deferibing. The firft of thefe I obferved, is about thirty paces north of the vein. The ground being cut ’ away, in order to fee its connection with the ftrata, it branched out like the prongs of a fork, and had the interftice filled with a red decompofed fubftance (No. 69.), fimilar to that which occurred at the extremity of the included ftripe of greenftone in the vein. Where the prongs join, it is about three or four.inches wide, and is there, partly compofed of indurated fandftone, and partly of hematitic iron-ore and calcareous fpar. (No. 70.) Higher up, where the vein is narrower, it is whol- ly compofed of fandftone, the fpecimen, No. 71., being the en- tire thicknefs of it. ~ Here the grain is finer than at firft, and, higher up, it becomes ftill more fo, (No. 72.) It ftill conti- wiues to taper upwards, and even when reduced to lefs than half an inch, the fubftance retains the ufual afpect ef indurated fand- ftone, (No. 73-) This vein rifes about twenty to thirty feet into the rock, always diminifhing, and about that height dif- appears. I have remarked other veins, alfo containing fub- ftances fimilar to indurated fandftone (No. 74.), one was of a much larger fize than that above defcribed (No. 75.), but the grain not near fo compact, (No. 76.) Tuese veins all fet off from the lower furface, and fo long as they are of any confiderable thicknefs, the including rock is ftained 430 On the ROCKS in the . ftained with ferruginous matter. This fact feems connetted . with the fingular appearances, which occur in the vein of green- ftone, at the level of the junction of the fandftone ftrata with the incumbent bed. Wirnour offering any remarks on a faci as yet fo infulated, [ content myfelf with merely mentioning it, in hopes that fimi- lar appearances may prefent themfelves to geologifts in other quarters, and perhaps throw fome light on a phenomenon, which by farther elucidation may prove interefting. BeroreE I clofe this paper, I fhall take the opportunity of pre- fenting to the-Society, two fpecimens which were given to me by Sir Grorce Mackenziz, and which I efteem of con- fiderable value; one of theni, a fragment of the rock of Salif- bury Craig; the other, of the Calton Hill, marked im: the handwriting of the late Dr'Kennepy, as the fubftances he ana- lyfed, and of which an account was given in the 5th volume of thefe Zraasactions. The great variety in the rock, both of Salifbury Craig and Calton Hill, makes it of importance to afcertain with precifion the kind employed in’the refearch of that celebrated chemift; and as'the moft proper place for their reception, I depofite them in the cabinet of this Society, along. with my own collection, under the Nos. 77, and. 78. roth VICINITY of EDINBURGH. 43% 19th March. Since I had the honour of reading the foregoing paper to the Society, a {trong cafe in illuftration of what is mentioned in the commencement of it, has prefented itfelf; I mean, with refpect to the conftant occurrence of new and interefting mat- ter, even in the moft frequented ground. A Frew days ago, Profeffor PLayrair mentioned to me, that - by the cutting down of a fection of the Craig, within: thirty paces of the fouthern extremity, feveral maffes of fandftone had made their appearance, imbedded in the greenftone. I loft no time in vifiting the fpot, and was greatly pleafed to find, a confiderable addition to the interefting facts, already exhibit- ed on Salifbury Craig. At this part of the rock, the greenftone becomes very thin, being no more than twenty to twenty-five feet thick ; it has the appearance, however, of having once been of greater extent, the upper part being apparently cut away by fome operation of nature, of which we have now only to obferve the effects. It flopes rapidly towards the fouth, and is covered to a confider- able depth with foil and travelled ftones. It is at the upper furface of this, that the imbedded mafles occur; they appear to be portions of ftrata, which obferve the general inclination of the fandftone of Salifbury Craig, that is, dipping towards the north-eaft, while the expofed fections are parallel to each other, and nearly horizontal; confequently, being near the fur- face, they are cut off, or crop out, on the fouth fide. Their ; appearance, gage FO On the ROCKS in the appearance, however, befpeaks their having been, at fome for— mer period, totally included in the greenftone. One mafs, in- deed, a little towards the north, is unequivocally fo; at leaft we: know with certainty, that a fhort time ago it was inclofed in the greenftone, and not to be feen ; and there is-at prefent, great apparent probability, that the next fection taken from the fame. part of the rock, will carry it away altogether. TLL now, we only knew of one included mafs in the green- ftone of Salifbury Craig; and with this, thefe now difcovered. have confiderable analogy ; they are of the fame colour, and al- though they appear to be only four or five diftiné mafles, thefe maffes are all interfected vertically and diagonally, and axe fplit through the whole length of the horizontal line; fo that in examining a feGtion of about ten feet perpendicular, no. tefs than nine different alternations of fandftone may be reckon- ed. Some of them are no doubt very minute; but {till they were all obfervable when I examined the rock. From the moft northern ma{s of included fandftone, I was enabled to procure a. few fpecim€ns, which I have added: to the above collection. The rock rifes fo rapidly from the fouth, that although this mafs is nearly in the fame hori- zontal line with the others, all'of which crop out to the furface,. and although it is not diftant more than four or five yards, yet it appears to be fituated nearly about the middle, between the fandftone and the upper furface, from which it may natural- ly be inferred, that the mafles which now crop out, were like this, once entirely included in the fubftance of the greenftone. It is highly indurated, and at the extremities, is drawn out into minute veins. The thicknefs. of the principal mafs may be from ten to twelve inches, and in length from fix to eight feet.. This body, as above noticed, is cut in all directions by the . ereenftone.. VICINITY of EDINBURGH. 433 greenftone. The fpecimen No. 79. fhews a portion of the ‘fandftone, with that fubftance traverfing its ftratified lines dia- gonally. No. 80. is a mafs of the fandftone, containing a {mall portion of greenftone, much of the fame fhape as the double wedge of St Leonard’s Hill, and formed, as I conceive, exactly in the fame manner. This wedge, on one fide of the fpecimen, is two inches long, but, on the oppofite, it is not one; and in the counter part of the fame fpecimen, (No. 81.) it is only to be feen on one furface ; it does not penetrate to the other fide, though fearcely an inch thick. ;, T am glad to find, that intereft has been made to prevent this valuable fet of fa@s from being foon deftroyed, as, in a few weeks, the rock in which thefe are contained would have been broken down, and carried off for the repair of the neigh- bouring roads. Ir is on this account, that much activity is requifite to keep thefe perifhable phenomena from being loft, in the neighbour- hood of fuch a town as Edinburgh. Similar things are pre- fenting themfelves conftantly, but they are opened only for a day, and if not feized and recorded on the inftant, will be thut up, and loft for ever. END OF THE SIXTH VOLUME. Tg er, < OFS Oy ig hae De ak! rs p j voN “ee : =e Sod) Tae. a > ore am) aes F een jee so oa J a ee 4 ye RINE gate Wh)? Paes ied RELI oy, tines Mie vat aa RE IeG he ee as ee: Va eg dope HF Shisageh Hits aga? Mere em ita Sheet 38 Yebow sfdiials ; of ear piagh, he Petey ocd vet a ee “amet Salou é ce r . a ae te ] on Wi by on ae ey “re bite Aa, jad. Pa @ BH a} 5 Pats re i “J ig a * 4 a Cw « + ilie eA i a Pres ‘2 sited pixie a be fey alae, tan rea 7 t , bli * - Pea, + a y he lke ote te er Be : ahy areretsih Ni aM eer ont fhe ‘ . . <. m 7 ; ‘ fins ir yy Ste a - ae Hoi pit skies For See Pi: fens Ww Ran er STA pe Searle ’ + om " 7 * : “ ’ Bh F/ if es snd. ign rhs: rlesten welarith oe Cry ug a re ake : sip yn aot + AMOOION HITE HT 40 HE a cranti pee “ ut ; kai POE rie eure eatery th TAR WOE Gy . y - Pas, F re we Pe Fhe f 8 Rye ~ pes na hixD golG ef a PP ek ‘ehtn “a AY ies # . i ba . * . * % 4 ‘ ‘ i‘ RATT? A (20h MR SRM > atten Ca ys x te athe Ga ty 2 a ‘fEe » bd ; } : wl 4 S ‘ ; ae Os aaowe coma a” MRA ONE Bee INE LF wtiting BY Oia nae ™ - 3 Pond i ae fy eace 1 « ’ ‘ es “fa ‘, ‘ “Ca ; ¥ ak dy 4 fixiaee ies t . > . . i % } e . 4 - w! e 4 - _ X \ i 7 ~ by > x DIRECTIONS TO THE BINDER: The sheets marked a and b, containing the History of the Society and the Laws, . to be placed in front of the volume, immediately after the general title-page : and general table of Contents. The temporary title-pages and tables of:Contents for Parts I. and II. to be can- celled, as now unnecessary. The last leaf of signature 3 D; pp. 390, 400, and the first leaf of 3-E, pp. 401, . 402, are to be. cancelled, and two new-leaves substituted.” Plate I. fronting p. 18: II. and III. fronting p. 70. Sir James Hax1’s Plates, marked with small numerals, Pl. 1, 11, 1,-1¥, v. to front:: p- 186. Plates VI, and VII. fronting p. 244. — VIII. - ~- 248. — IX. = - 344. ee - - 376. — XI. : - 402. oom. OME. - - 420. *,* The Binder will take notice that the Plates. must fold out. 1 gotcha e Sa ry Sp %y re ‘ Pe ; ERS Fu ea as 4