HARVARD UNIVERSITY. LIBRARY OF THE MUSEUM OF COMPARATIVE ZOOLOGY. 43 HS Rae December 5) 1916. See ae TRANSACTIONS OF THE PHILOSOPHICAL SOCIETY: sa AMERICAN J) HWELOD AT \ PHILADEBPHIA, TOR PROMOTING PSS USEFUL KNOWLEDGE. Z VOLUME 1, THE SECOND EDITION CORRECTED. Pei AD £2 fF & i A: PRINTED BY &@..AITTAEN & SON, AT POPRE's HEAD IN MARKET STREET, wm M.DCC.LXXXIX, PROTHONOTARY’s OFFICE, Philadelphia county. IDO certify that on this 19th day of April, 1789, a Book entitled “ 'Tranfactions of the American Philofophicel Society, held at Philadelphia, for promoting ufeful Knowledge,” vol. t. the fe cond edition correéled, printed at Philadelphia, by R, Aitken & Son, at Pope's Head, in Markets Street, was entered in my office, by Robert Aitken, JAMES BIDDLE, Pror, ADVERTISEMENT. HE promoting of ufeful Knowledge in general, and fuch branches thereof in particular, as may be more immediately fer- viceable to the Britith Colonies, being the ex- prefs purpofe for which the American Pui- LOSOPHICAL Society was inftituted; the Pub- lication of fuch curious and ufeful Papers, as may, from time to time, be communicated to them, becomes, of courfe, one material part of their defign, As foon therefore as the Socicty judged that they had received a fufficient Number of Communications for a Volume, they appointed a Committee, to affift the Secretaries, in fe- leéting out of them fuch as might be mott pro- per for the public view. And for their direc- tion in the execution of this truft, the twa following rules were given, viz. Firft, “That the grounds of the Commit- tee’s choice of Papers for the Prefs, thould al- ways be, the importance or fingularity of the fubjects, or the advantageous manner of treat- ing them, without pretending to anfwer, or to make iV ADVERTISEMENT. make the Society anfwerable for the certainty of the facts, or propriety of the reafonings, contained in the feveral Papers fo publithed, which muft full reft on the credit or judgment of their refpective Authors. Secondly, ‘That neither the Society, nor the Committee of the Prefs, do ever give their opi- nion as a body, upon any paper they may pub- lith, or upon any fubjec&t, of Art or Nature that comes before them.” Thefe Rules were adopted from the Rules of that illuftrious, Body the Roya Socigry of London, whofe example the American Put- LOSOPHICAL Society think it their honor to follow, in their endeavours for enlarging the Sphere of Knowledge and ufeful Arts. And though, in Countries where the Arts and all ufeful Improvements have arrived almoft at their maturity, the following Work may fcarce be confidered as a mite thrown into the com- mon treafury; yet here, where they are but in their infancy, it may be received as fome ac- ceffion to our fmaller Stock. LAWS a LAWS: wie R DEUL wa PEON S, OF BHE American PHILOSOPHICAL SOCIETY Hetp at PHILADELPHIA, FOR PROMOTING CSEFUL KNOWLEDGE. W O Societies having formesly fubfifted in Philadelphia, whofe views and ends were the fame viz. ‘* the Advancement of ufe- ful Knowledge” —it was judged that their union would be of public advantage; and they were accordingly united January 2d, 1769, by a certain Fundamental Agreement; the chief Articles of which are— Firfl, That the name of the United Society thall be The American Philofephical Society, held at Philadelphia for promoting ufeful Know- ledge. : Secondly, That there fhall be the following Officers of the Society,. viz. one Patron, one Prefident, three Vice Prefidents, one Treafurer, four Secretaries, and three Curators. Thirdly, That all. the above officers fhall be chofen annually by ballot, at the firft meeting of the Society in January; excepting only that inftead of electing a Patron, the Governor of the Province be requefted to be Patron. Other Laws were to be made by the United Society; and accord? ingly the following LAWS, &c. were pafled February 3d, 1769: I. Of the annual Payments to be made by Members. EVERY Member of this Society fhall fubferibe Ten Shillings yearly, to be applied by the Society to fuch purpofes as they thal direét; and no Member fhall be entitled to a vote in the annual elec- tion of officers, unlefs it appears that he has paid into the hands of the Treafurer, the fubfcription of the preceding year, and all former arrears, if any there were. Every Member hereafter to be chofen, agreeable to the Laws‘of this Society, fhall pay Ten Shillings admiflion money, and alfo fub- {cribe for the yearly payment of Ten Shillings, before he is entitled to have any vote in the bufinefs of the Society at their mectings. Hl. Of Il. Of the Eleétion of Members. The election of new Members fhall be by ballot, and that only on the third Friday in the months of January, April, July and Odtober; and in order to fuch election at leaft twenty Members muft be prefent. Any Member may, at any meeting, propofe fuch perfon or per- fons, as he thinks proper to bea Member or Members of this Soci- ety; but no perfon fhall be ballotted for, unlefs his name, together with the name or names of the Member or Members who propofed him, has been fixed up by the Secretaries for the view of the Society, at the two meetings preceding the time of election, Nor fhall any perfon be deemed duly chofen unlefs three-fourths of the votes of the whole Members be in his favour. Ill. Of the Officers, and manner of their eleétion. The election of fuch Officers as are to be chofen in this Society, fhall be on the firft Friday in January every year, by ballot or writ- ten ticket, between the hours of Two and Five in the afternoon, at fuch place in this city as fhall be fixed by the Society at their previ- ous meeting on the third Friday in December every year; of which notice fhall be given in the Gazette, or fuch other public Papers as the Society fhall order, at leaft one week before the day of eleétion. Before opening the eleGtion, the company that thall be met at half an hour after Two, fhall appoint three Members of the Society as judges of the election, and alfo two clerks or fecretaries, for taking down the names of the voters. And in cafe of an equality of votes for any Officer, after cafting up the ballots, the decifion fhall be by lots, to be drawn by one of the judges. IV. Of the Prefident. The Prefident is to prefide at all meetings, to preferve order, to regulate the debates, and to ftate and put queftions, agreeable to the fenfe and intention of the Members. V. Of the Vice-Prefidents. In the abfence of the Prefident, his duty fhall devolve on the Vice-Prefidents, fo that they fhall prefide alternately at meetings. But if the Vice-Prefident, whofe turn it is to prefide at any meeting, fhould be abfent, his place fhall be fupplied by any of the other Vice- Prefidents, who fhall be prefent, according as he may be next in turn, If only one Vice-Prefident be prefent, he fhall of courfe prefide; and if neither the Prefident, nor any Vice-Prefident be prefent, the Mem- bers met, fhall appoint one of their number to take the chair for that meeting. VI. of Look. Way. dee. Vit VI. Of the Treafurer. The Trea/urer fhall receive the fubfcriptions of the Members, and all the other monies that may become due to the Society, and fhall pay the fame agreeable to their orders, certified to him by the Pre- fident, Vice-Prefident or Member, who was in the Chair when the order wasmade, The Treafurer fhall keep a regular account of all monies received and paid by him as aforefaid; and once every year, or oftener if required by the Society, he fhall render an account to them ofthe ftock in his hands, and the difburfements made by their order, and fhall deliver up to his fucceffor the books:and all papers belonging to them, together with the ballance of cafh in his hands, And for the faithful difcharge of his truft, he thall before he enters on his office, give bond and fecurity to the Prefident and Vice-Pre- fidents, in double the fum which they, or any three of them, fhall judge he may probably become entrufted with, during his faid offices VII. Of the Secretaries, The Secretaries fhall fo fettle matters as to take equal fhares of all all bufinefs, and fo as that two of them fhall ferve at every meeting, viz. one to take the minutes, and one to read all letters and papers that may be communicated to the Society. It is alfo the bufinefs of the two Secretaries of each particular meeting, to copyinto the minute book, the proceedings of that meeting in order to produce the fame fair to the next meeting. They are further to copy into the proper books all fuch letters, papers andeflays, as the Society may think fit to pre- ferve on record, and to have the fame ready to be laid before the next meeting. The other two Secretaries are, in the mean while, to give notice to new members of their eletion, and agreeable to the directions of the Society, to write or anfwer letters; and in general, to manage all matters of Corre/pondence. The Secretaries may, for their own eafe, change places; fo that the two who have ferved as corre/ponding Secretaries, for one month or limited time, fhall take their turn to ferve for the like time as fitting or attending Secretaries. VIIL. Of the Curators. The bufinefs of the Curators fhall be to take charge of, and pre- ferve, all Specimens of natural Produétions, whether of the Animal, Vegetable or Fofil kingdom; all models of machines and inftruments, and all other matters and things belonging to the Society, which {hall be committed to them; to clafs and arrange them in their pro- per eer Vili Lode (NO By Be, per order, and keep an exact lift of them, with the names of the refpective donors, in a book provided for that purpofe; which book fhall be laid before the Society, as often as called for. The Curators, on entering upon their office, fhall give fuch a receipt for every thing that is committed to their charge, as the So» ciety fhall think proper; and, at the end of their term, thall deliver up the fame to their fucceffors. For the faithful performance of their duty, and of the truft repofed in them, they fhall give bond to the Prefidents, and Vice Prefidents, in fuch a fum as they, or any three of them, fhall require. IX. Of the Meetings of the Society. The ordinary meetings of the Society fhall be on the firft and third Fridays of every month, from October to May, both inclufive, at fix o’clock in the evening, and on the third Friday in cach of the other four months, at /even o’clock. No meeting fhall be continued after ten o’clock, nor any new mat- ter be introduced by motion or otherwife, after nine o'clock. X. Of the Difpofition of Money, and making new Laws. No part of the Society’s ftock fhall be difpofed of in Premiums, or otherwife, nor fhall any new laws be made, until the fame have been propofed at one mecting, and are agreed to by two-thirds of twenty or more Members prefent at a fubfequent meeting. XI. Of other Proceedings of the Society. No queftion fhall be put on a motion, unlefs the motion be /econd- ed; and the determination of any queftion fhall be by ballot, inftead of open fuffrage, if defired by any four Members. In cafe of an equality of votes on any queftion, the fame fhall be deferred to ano- ther meeting. When any Member fpeaks he fhall ftand up, and addrefs himfelf to the Chair, and the reft fhall remain filent in their feats. When two or more Offer to fpeak at the fame time, the prefiding Member, in that, as in other matters of order, fhall regulate and determine who fhall fpeak firft. XIL Of Committees. The Members of this Society fhall be clafled into one ot more of the following Committees. 1. Geography, Mathematics, Natural Philofophy and Aftronomy. 2. Medicine and Anatomy. 3. Natural Hiftory and Chymiftry 4. Trade ( ie) 4. Trade and Commerce. gs. Mechanics and Architecture. 6. Hufbandry and American Improvements. Thefe Committees fhall meet on their own adjournments, and at fuch other times as the Society fhall appoint, for the confideration of any matters referred to them, and fhall have power to chufe their own Chairman. But no Committee, as fuch, thalltake up any new bufinefs of the Society, but fhall confine themfelves only to the fub+ jects for which they are appointed, and to matters referred to them by the Society. fl true Copy, compared with WILLIAM SMITH, 7 pee the original Laws in the CHARLES THOMSON, § eoretartess Society's Books by = = = = LS LIST or tHe OFFICERS, OF THE AMERICAN PHILOSOPHICAL SOCIETY, Held at Purtapsrpura, for promoting ufeful Knowledge, For the YEAR 1770. PATRON. The Governor of the Province, for the time being. OFFICERS, ele&ed January 5th, 1770. PRESIDENT. Benjamin Franklin, LL.D. F. RS. Gott. & Sen Jofeph Galloway, Efq. Speaker of the Affembly of Pennfylvania. Vick PRESIDENTS: 4 1, Thomas Bond. Samuel Rhoads, Efquire. TREASURER, Mr. Philip Sing. Fs William Smith, D, D. Provoft of the College of Philadelphia. SECRETARIES. Mr, Charles Thomfon, Thomas Mifilin. George Roberts. Began ee M. D. Profeffor of Chymiftry, Cel- nea ege of Philadelphia. ; ae eh Mr. Owen Biddle. Ifaac Bartram. Vou. fi b HONORABLE x Lis T or;| MEMBER'S. A ONORABLE William Allen, Efg. Chief Juftice of Pennfyl- vania. John Allen, Efq. Andrew Allen, Efg. James Allen, Efq. Mr, James Alexander, Francis Alifon, D. D. Vice Provoft of the College of Philadelphia, Dr. James Anderfon of Maryland, Mr.Arbo of Bethlehem, Pennfylvania, Mr, Matthias Afpden.* B Samuel Bard, M. D. Profeflor of the Pra€tice of Phyfic, King’s College, New-York, Thomas Barnfley, Efg. of Bucks county, Pennfylvania, Rev. Thomas Barton, A. M. of Lan- cafter, Pennfylvania. Mr. John Bartram, Botanift to the King; Acad. Reg. Suec. Soc. Mr. Mofes Bartram. Mr. William Bartram. Mr. John Baynton., Paul Bedford, Efq. of Barbadoes. Hon, Jonathan Belcher, Efq. Chief Justice of Nova-Scotia, Mr. Henry Bembridge. - Mr. John Benczet. Dr, Charles Benfall, of Germantown, Philadelphia county. Mr. William Bettle. Mr. Clement Biddle. Edward Biddle, Efq; of Reading in Pennfylvania. James Biddle, Efq; Phineas Bond, M. D. Mr. Thomas Bond. Mr. Thomas Bradford. Mr. Joleph Bringhurft, George Bryan, Efq; Dr. Thomas Cadwalader. Mr. John Cadwalader. Mr. Lambert Cadwalader, Mr. Samuel Caldwell. Lionel Chalmers, M. D. of Charlef- town, South-Carolina, Dr. John Chapman, Benjamin Chew, Efq; Dr. Gerardus Clarkfon. Matthew Clarkfon, Efq ; Mr. Thomas Clifford. Hon, Cadwalader Colden, Efq; Lieut, Governor of New-York, Thomas Coombe, Efq ; Miles Cooper L. L. D. Prefident of King’s Coll, New-York. D Rev. James Davidfon, A. M. Profef- for of Languages in the College of Philadelphia. Mr, Benjamin Davis. Rev. John Davis, A. M. : John Deas, Efq; of Charleftown, South-Carolina. Dr. John De Normandie, of Briftol, in Pennfylvania.~ ~~ Mr. James Dickinfon. John Dickinfon, Efq; Mr. Henry Drinker. Mr. John Drinker, Jacob Duché, Efq; Rev. Jacob Duché, A, M, Mr. Edward Duffield, Samuel Duffield, M. B. Hon, Daniel Dulaney, Efq; of Ma- ryland, E Mr. Samuel Eldrige, Mr. Samuel Elliot, of Bofton, Dr. Cadwalader Evans, Rowland Evans, Efq; Philadelphia County, Capt. Ofwald Eve, Rev. John Ewing, A. M, F Rev. Frederick Farmer, Mr, Samuel Felfted, of Jamaica, Mr. Thomas Fither. Paul Fooks, Efq; Profeflor of the French and Spanifh Languages} Coll. Philad. Jofeph Fox, Efq; ga Foxcroft, Efq; Thomas Foxcroft, Efq; His Excellency William Franklin, Efq; Governor of New-Jerfey, His Excellency General Gage, Com- mander in Chief of his Majefty’s Forces in North-America, Benjamin * All thofe Members whofe places of abode are not {pecified, are of the city of Philadelphia. soe ogee | | | emcee ee eee LVS T or MEMBERS. xi Benjamin Gale, M, D. of Conneticut, Alexander Garden, M. D, of Char- leftown, South-Carolina, Valentine Gardner, Efq; of News York. Sidney George, Efq; of Maryland, Mr, ‘Thomas Gilpin, George Glentworth, M, D. Dr, Archibald Glofter, of Antigua, Thomas Graeme, M, D, H Hon, James Hamilton, Efq; Mr, David Hall, = Rev, Mr, Harding, Dr, Robert Harris. Mr. dgieen Marrifon, | of New-Eng- Mr, Peter Harrifon, J land, Mr, William Henry of Lancatfter, | Pennfylvania, Gilbert Hicks, Efq; Bucks County, Pennfylvania, Mr, Henry Hill, Michael Haligees, Efq; Mr, John Himili of Charleftown, South-Carolina, Richard Hockley, Efq; ay, Holiday, Efq; of Maryland, Mr, Levi Holingfworth, Edward Holyoke, LL, D, of Maffa- chufetts-Bay, Hon, Stephen Hopkins, Efq; of Rhode-Hland, Mr, William Hopkins. Francis Hopkinfon, Efq; Jothua Howell, Efq; Jofeph Hutchins, A. B. of Barbados, I Mr. Benjamin Jacobs, Philadelphia County, Abel James, Efq; Davi Jamel ales M. D. of York, Pennfylvania, Hon, Sir William Johnfon, Bart, of . Mount Johnfon, in the Province of New-York. John Jones, M. D. of New-York, Ifaac pe Efq; Robert Strettell Jones, A. M. — Ralph Izard, Efq; of Charles-Town, S, Carolina. K Dr, John Kearfly, Dr. John Kearfly, Jun. me Rev, Ebenezer Kinnerfley, A, M. Profeffor of Englith and Oratory, Coll, Philadelphia, John Kidd, Efq; ( Bucks Jofeph. Kirkbride, Efq} J County, Adam Kuhn, M.D, “Prof, Bot. & Mater, Med, Coll, Philad, L Lynford Lardner, Efq; Arthur Lee, M. D, 1 Francis Lee, Efq; Thomas Livezcy, Eiq; Philadelphia County. ae Livingfton, Efq; of New- ork, William Logan, Efqs Dr, John Lorimer of Weft-Florida, Dr, James Lloyd, of Botton, John Lukens, Efq; Surveyor-Gene- ral of Pennfylvania. M Mr. }rederic Marfhall, of North-Ca- rolina, Thomas Me, Kean Efq; of Newcaftle on Delaware, Mr. Humphrey Marfhall of Chefter County, Pennfylvania, Dr. Hugh Mercerof Frederickfburgh, Virginia, Sanicel Mifflin, Efay Mr, Samuel Miles, Mr, Peter Miller of Ephrata, in Penn« fylvania, Dr, Mim of York, Pennfylvania, Charles Moore, M, D. Dr. Samuel Prefton Moore, Mr, George Morgan, John Morgan, M, D. F.R.S. Prof, Theor, and Pratt, Phyfic, College Philadelphia, pes Morris, Efq. r. Morton, of Jamaica, Mr, John Murgatroyd. of Virginia, N Mr, Lewis Nicola of Northampton, Pennfylvania, Rev, L. 1-8 -T = or O Rev. Jonathan Odell, A. M. of Bur- lington, New-Jerfey. Mr. John Francis oo, of Beth- ii Mr. John Okely, lehem in Dr. Otto, : Pennfyl, Mr, Jofeph Ottolenge, of Georgia. Hon, Andrew Oliver, Lieut. Gov. Maffachufetts Bay, P William Parr, Ef{q, Mr. Laac Pafchal, . John Pafchal of Derby, Pennfyl, . ea i Pafchal, . stephen Pafchal, _ Mr. James Pearfon, does Pemberton, . Ifrael Pemberton, . Edward Pennington. Richard Peters, D, D, Re€torof Chrift Church and St, Peters, Philadelphia. Edmund Phyfick, Efq. Mr, William Poole of Wilmington, Pennfylvania. Mr. Chriftian Frederick Poft, of the Mofquito Shore, _ Mr. Thomas Potts, of Philadelphia County. Jonathan Potts, M. B, of Philadelphia County, Samuel Powell, Efq. Dr. Thomas Prefton, Ebenezer Prime, M. D. of New-York, Mr. Robert Proud. Mr. Thomas Pryor. Mr, Samuel Purviance, Jun, R Hon, Charles Read, Efq. of Burling- ton, New-Jerfey, John Redman, M. D. Jofeph Reade, Efq. Mr. John Reynell. Mr. John Rhea, Mr. Samuel Rhoads, Jun, Dr, Charles Ridgley of Dover, on Delaware, | . David Rittenhoufe, A, M. Mr. Hugh Roberts, Mr. Samuel Robinfon, ohn Rofs, Efq. Wilham Rumiey, Efq. of Maryland, . Ps, Dr. Sandiford of Barbados, MoE-M Bak R-S. John Morin Scot, Efg. of New-York, Mr. William Scull of Reading, Penn- fylvania. John Sellers, Elq. of Chefler Coun- ty, Pennfylvania. © Edward Shippen, Efq. of Lancafter, Pennfylvania. Edward Shippen, Jun, Efq. Jofeph Shippen, Jun, Efq. Dr. William Shippen, William Shippen, Jun. M. D. Prof, Anat. Coll. Philad. Samuel Shoemaker, Efq. Mr. Pierre Eugene du Simitiere, Williams Smibert, M. D. of Bofton Hon. Samuel Smith, mn | ofthe Pro- Ae Smith, Efq. vince of » Peartree Smith, Efq. uf N, Jerfey, Dr. Ifaac Smith, Hon, William Smith, Efq. of New- York, Jonathan Smith, A. M, Mr, Robert Smith. Mr, Thomas Smith, Dr. Peter Sonmans, Alexander Stedman, Efq. Right Hon, William Earl of Stirling, of Bafkenridge, New- Jerfey, Richard Stockton, Efq. of New- Jerfey Rev. Samuel Stillman, A, M, of Bot. ton. Ezra Styles, D. D. of Conneéticut, Captain Jofeph Styles, r Tr Mr. Richard Thomas, of Chefter county, Pennfylvania, James Tilghman, Efq. Dr, John Tweedy, of Newport, ‘Rhode-Ifland, WwW. Nicholas Waln, Efq. ohn Walker, Eefq. of Virginia, Hon, Afhton Warner, ied Hon, Thomas Warner, Efq. ic oo Samuel Warner, Efq. - sal Stephen Watts, Efq, Mr, James Webb of Lancafter, Penn- fylvania, Mr. Richard Wells, of Burlington, New- Jerfey, Rev, Mr, Samuel Welt, of New- England, Mr, i. Ets 1° ¢9 Mr, William Weft. Mr, Ifaac Wharton. Mr. Samuel Wharton. Rev. Ch. Whittlefey, of Conneéticut. William White, A. M. Alexander Wilcocks, Efq. Hugh Williamfon, M. D, Thomas Willing, Efq. James Wilfon, Efq, of Carlifle, Penn- fylvania. EU-R OPE A ONSIEUR Buffon, of Paris. Peter Bergius, M. D, Prof, Nat. Hitt. Stockholm. John Martin Butt, M. D. of Bath, England. William Cullen, M. D. Prof. Med. Univerfity of Edinburgh. Sir Alexander Dick, M. D. Bart. of Edinburgh. Mr. Jeremiah Dixon, London. Mr, James Fergufon, F.R.S. London. John Fothergill, M.D. F.R.S. London. Signior Famitz, of Naples. Dr. John Gill, of Kinfale, Ireland. Mr. William Hewfon, Preeleétor Anat. London. Richard Huck, M.D. F.R.S. London. John David Hahn, M.D, Prof. Med. and Philof, Univerfity of Utrecht. MEMBERS. xiii John Winthrop, Efq. F. R,S, Hol- lifian Prof. Mathematics, at Cam- bridge, in New-England. John Witherfpoon, D. D. Prefident of the College of New-Jerfey. Mr, James Worral, James Wright, Efq. of Lancafter county, Pennfylvania.. Mr. Benjamin Wynkoop. N«M:E- MBE i Si Hon. Maac Jamineau, Efq. Britifh Conful, Naples. Sir Charles 4 Linné, M. D. Knight of the Polar Star, Firft Phyfician to the: King of Sweden,. Prof. Med. and. Bot. Upfal. William Logan, M.D. London. Nevil Mafkelyne, B.D. F. R. S. and Aftronomer-Royal, Greenwich. Mr. Charles Mafon, London. Chriftian Magee, L. L.D. of Heidelberg. Mr. Edward Nairne, London. Richard. Penn, jun, Efq. London. Sir G. Saville, Bart. York, in England. James Span, M. D. Profeff. Materia Medica, Univerfity of Dublin. Mr. Benjamin Weft, London. Charles Magnus Wrangel, D. D, of Sweden. oe ET a eee ORF LOGE RS for the Year 1773. Presipent and Vicre-Prestwents, the fame as forthe laft Year, Treasurer. Thomas Coombe, Efq, ‘William Smith, D. D. Provoft College Philadelphia. . ) David Rittenhoufe, A.M. gp SECRETARIES. 9 Roy. John Ewing, A. M, Robert Strettel Jones, A.M. J Benjamin Ruth, M, D, Prof. Chym. | Coll CURATORS, | will Kuhn, M. D. Prof. Bot. & Mat.Med. $ 5° i William Shippen, jun, M. D. Prof. Anat. [ Philadel. CONTENTS (. xiv ) COON dy Basket os 0 F VOLUME 1. A DESCRIPTION of an Onnury, executed ona new plan, By D. Rr. “4H venuousez, A. M, Page 4 Calculation of the Tranfit of Venus over the Sun, as itis to happen Fune 3a, 1769, in lat. 40°. N. long. 5h. Weft from Greenwich, By D, Rirrenuouss, A. M. communicated Fune 21 ft, 1768. pe 4 Calculation of the fame for the city of Philadélphia, By Rev. Joun Ewrne, A. M, ~ Communicated Fune 2rft, 1768. pe 5 An account of the Tranfit of Venus over the Sun, June 3d, 1769, as obferved at Norriton, in Pennfyluania, By the Commuttee appointed for that obfervation. Drawn up, and cummunicated, in behalf of the Committee, by. Rev. Wit.iam SmirHy Da D, p. 8 An account of the Transir oy Vusus over the Sun, June gd, 1769, and of the Tranfit. of. Mercury Nov. 9th, both. as obferved in the State- Houfe Square, Philadelphia. By the Committee. appointed for thofe n ecarme Drawn u and communicated, in behalf of the Committee, by Reve Joun Ewrna, A. M, “3 An account of the Transitiof Venus over.the Sun, Fune gd, 1769, as ibd near Cape ip on Delaware. By the Committee apointed for that obfervation. Drawn up and communicated, in behalf of the Comiittee, by Mr, Ownn BippDLe, p 39 An account of the Tranfit of Venus over the Sun, June gd, 1769, as obferved at Pro. vidence, New England. Drawnup by Benjamin Waust, A, M, and tranf- mitted to the Society by Mr. Fofeph Brown, pr gi. Obfervations of the Tranfit of Vunus and Eclipfe of the Sun, June 3d, 1769, made at the Royal Obfervatory, Greenwich. By Rev. Novit Masxeuyne. B.D. F. R.S. and Aftronom r-Royal. Tranfmitted by himfelf, and communi« cated to the American Philofophical Society, by Witu1am Smitu, D.D, p. 100 Some account of the Tranfit of Venus and Echpfe of the Sun, as obferved at the Liz- ard Point, Fune 3d, 1769. By Mr. Joun Braviey, Extraéted from a paper of the Aftronomer- Royal. p. 108 A letter from Rev, Nevirt Masxeryne, B.D. FR. S. Aftronomer- Royal, to Reo, Wiiriam Smirn, D. D. Provoft of the College of Philadelphia, giving Jome account of the Hudfon’s Bay and other Northern obfervations of the Tranjit of Venus, June gd, +769. pe waa An account of the terreftrial meafurcment between the Obfervatories of Norriron and PuitApEeLPHia; with the difference of longitude and latitude thence dea duced. By WittiaAm Smita, D. D, pi iti4 Apparent time of the Contracts of the limbs of the Sun and Venus ; with other circumftances of moft note, in the different European obfervations of the Tranfit, June 3d, 1769. ” p. 120 An improvement in the conflruction of Godfrey's ( commonly called Hadley’s ) Qua- drant, By Rev. Joun Ewing, A. M. acer An -~& @i mM U8 BPS xv An effay on Comers, and an account of their luminous appearance ; together witle Some conjeétures concerning the origin of Hnat. By Hueu Witriamson, M. D, » 133 Obfervations on the Comnt of June and July, 17703 with the Elements of fi Mo- teon, and the Trajeétory of its Path, intwo Letters, from DavipRitTENHOUSE, A, M. to WittiaAm Situ, D. D. Provoft Coll. Philadelphia. pe t44 An Account of the fame Comet, mma letter from the Right Hon, WiL.1am, Earn or StirtinG, fo Wittiam Smitu, D, D. Provoft Coll. Philad. ps 152 An eafy Method of deducing the Time of the Sun’s ane the Meridian per Clock, wilhout the help of the Equation Tables, by equat Altitudes taken on two fucceeding Days. By Daviv Rirtennouse, A. M. Communicated by W1iLL1AMSMITH, D. D. Provoft Coll. Philadelphia, Pi 455 An Account of the Tranfit of Muxcury over the Sun, Nov. oth, as obferved at Norrirton, in Pennfyloania; by the Committee appointed for that Objervation. Drawn up and communicated by darettion and in behalf of the Committee, by W 11.- Liam Smitu. D. D. Provoft Coll. Philadelphia. p. 158 The Sun’s PARALLAX deduced from a Comparifon of the Norrairon Obfervations of the Tranfit of Venus, 17693 with the Greenwich and other European Ob- Jervations of the fame. By WitLiam SMITH. D.D. Provoft Coll. Phila. p. 162: CONTENTS of Sect, JL An Effay on the Cultivation of the Vine, and the making and: preferving of Wine, Juited to the different climates of North- America, By the Hon, *Ep ward ANTILL Efq. Communicated by Mr, Cuan.es THomson, bs 180. The Method of curing Fics 5 and obfervations: on the raising and drefing of Hem, By Hon, Eywarp Antinn, Efq. pr» 266 Obfervations concerning the FPuiy-Wesvit, that deftroys the Wear ; with fome ujeful difcoveries and Conclufions, concerning the Propagation and Progrefs of that pernicious Infect, and the Methods to be u fed. for preventing the Defructon of the Grain by it, By Colonel Lancpon Carrer, of Sabine-Hall, Virginia; com- municated by Colonel Lux, of Virginia. pe 274 Obfervations on the fame fubject + by the Committee of Hufbandry, Ses p. 287 Objervations on. the Narive Sirx Worms, of North-America; by Mr. Moses BARTRAM. p. 204 A Memoir on. the Diflillation of Perstmons. By Mr. Isaac BarrrRam. p. 301 Account of an Orr made from the Seeds of the Sun-Flower. By Dr. Orro, of Bethlehem. Communicated by Dr. Tuomas Bono, p. 904 An Effay on the exprefing of Orn from the SuN-FLoweEr Step. By Joun Morecan, M.D. P 395 A Letter on the exprefing of a fine Oil from Bens Szrp. By-Mr. Joun Moret, of Georgia. Communicated by Mr. Cuarces TPHomson, p» 309 The Method of deftroying wip GARLIC. By Mr. Henry Hourinesworta, of Elh-Ridge. A Method if p. 3tt referving Peafe’. from the Worms. By Mr. Petur Miter, of Ephrata. Communicated by Mr. Cuaries THomson, p. 313 An cafy Method of preferving Sunjects in Spirits. By Mr.L. Nrco.a. p. 314 A Letter from Bethlehem, on making Currant WINE. p» 317 A Letter from Dr. Lorimer, of Weft-Florida, to Hucu Witriamson. M, D. containing fome Remarks on the Climate, vegetable Productions, Ge. p. 320 A catalogue of fuch foreign Plants as are worthy of being encouraged in the American Colonies, for the Purpofes of Medicine, Agriculture and Commerce. Pr 325 Direttions * Mr. Anrin was one of his Majefty’s Council for the Province of New-Jerfey, and a worthy Member of the American Philofopbical Society ; but he died before the publication of the Litt prefixed to this Volume. XVI aU Mw. 2. wD SS Direthions for putting up Seeds and Plants, fo as to preferve them in a fate of Vegem tation, for being tranfported to diftant countries. b. 330 dn Attempt to account for the Change of Climate, which has been obferved in the Middle Colomies in North- America, By HucuWirtiamson, M.D. px 396 CONTENTS of Sect. Ill. An Account of the Eruption of Mount Vefuvius, in 1767 3 in a Letter from an Eng lifh Gentleman refiding at Naples. to Joun Morcan, M. D. Prof. Med, Coll, Philadelphia, ; Pp» 345 A Deferiptron of a Self-moving or Suntinet Rucisters invented by Mr, Wir- ' uiAm Henry, of Lancafler, in Pennfyluania. Pp: 350 An Account af a@ Machine for pumping Veffels at Sea without the Labour of Men. By Mr. Ricuarn Wett1s. p> 353 An Abftradt of fundry ee and Propofals for improving the Inland Navigation of Pennfyloania and Maryland, by opening a Communication between the Tide- Waters af Delaware and Chefapeak-Bay, illuftrated with a Map, 8c. p. 357 A Defcription of a Machine for cutting Files. p- 365 CON TEN TS of Sect. IV. An Analyfis of the Chalybeate Waters of Briftol, in i pe in two Letters from Dr. Joun Dre Normanpte of Briftol, to Dr. Tuomas Bonp of Phila- delphia, V. P. of the American Philofophical Society. ps 368 Remarkable a of a Teranos and Locxyn Jaw cured by amazing Quantities of Opium; by Dr. Arcuiparp GrosteR, of Antigua; communicated by JOUN Morcan, M. D. Prof. Phyfic, Coll, Philadelphia. p. 379 An Account of the Effects of the Strammonium, or Thorn Apple. By Bunjamin Rusu, M. D. Prof. Chym. Coll. Philadelphia, db. 384 An Enquiry into the Nature, Caufe and Cure of the Ancina SurKocativa, or Sore Throat Diftemper, By Samurn Barn, M. D. Prof. Phyfic, King’s Coll. New-York; communicated by Joun Morcan, M.D. Prof. Phyfic, College Philadelpma. p. 388 An Account of an Aurora Borealis, from a Correfpondent at Lancafter, in Penn- fylvamia. : p» 404 An Account of a Horizontal Wind-Mill. by Mr. Tuomas Gixrin.- 405 An Account of a new Species of Grape Vines, by Mr. Joun Jones, at Indian River, Worcefter County, Maryland, pf.» 406 rhe FAC FE. Piss Rs aR low Binet taggers yes NOW LEDGE is of little ufe, when confined to mere fpecu- lation: But when {peculative truths are reduced to practice, when theories, grounded upon experiments, are applied to the come mon purpofes of life; and when, by thefe, agriculture is improved, trade enlarged, the arts of living made more eafy and comfortable, and, of courfe, the increafe and happinefs of mankind promoted; knowledge then becomes really ufeful. ‘That this Society, therefore, may, in fome degree, anfwer the ends of its inftitution, the mem hers propofe to confine their difquifitions, principally, to fuch fubs jects.as tend to, the improvement of their country, and advancement of its intereftand profperity. The tra& of country now poffefied by the Engli/h in North- Amex rica is large and. very extenfive; the foil and climate various; and, ly~ ing between the agth and 5 5th degrees of North latitude, is not only fubje& to the gradations from extreme heat to extreme cold, but feems capable of fupplying almoft all the productions of the earth. Tt is watered with plentiful ftreams, accommodated with crecks, bays. and havens, and interfected by rivers, which run far into the country, and not only open an eafy communication with the ocean, but, by interlocking with each other, afford an inland navigation of fome thoufand miles, that with no. great expence might be ren- dered ftill more extentive, By the induftry. of its inhabitants, the land jn many places is cleared of its wood, reduced to arable and pafture ground, and ren« dered fit to receive thofe fruits, trees, plants and grain, which are proper to every foil.---The Indians who were natives of this coune try, and whofe employments were hunting and fithing, paid little re- gard to hufbandry, or thecultivationof the land. To trade and come merce they were ftrangers. Elegance of living they defpifed, They depended on the bow, and were content if, with the fortune of the chafe, the fpontangous. fruits of the foreft, the fith which they caught, and a little Jndian corn whichthelr women and children raifed, they could fupport life. Hence it was that, upon the firft difcoves ry of America by the Europeans, Indian corn was the only grain found here. The fruits, trees, plants, and grain, introduced by the new in« habitants, are moftly fuch as were cultivated in European countries, c from (2) Bell's Travels into China, Du Halde’s Hiflory of China, Kemplor'e Hiftory of Japan, xvii PURGE Re ACE, fyom whence thefe inhabitants came. But the foil and climate of thefe countries being different from that of Europe, no wonder if many ofthem do not fucceed here as well as in Europe. If we may truft to the report of travellers, (a) this country, in the fame degree of latitude, very nearly refembles China, or the tract of land that forms the eaftern fide of fia, in foil, climate, temperature of the air, winds, weather and many natural productions. And the fame refemblance is remarkable between the weftern fide of the’ old world and the weftern fides of our continent; (4) whereas the eaftern and weftern fides of the fame continent differ greatly. From the lateft and beft accounts, (c) we find that Kamt/chatha, and the coaft to the north of it, are in almoft every refpect, fimi- lar to Labrador in America; but very different from thofe parts of Europe which are comprehended within the fame degrees of latitude. Philadelphia lies in the 4oth degree of north latitude, the very fame as Pekin in China, and nearly the fame with Madrid in Spain, and that part of California, of which Sir Francis Drake took pof- feffion. In Philadelphia and Pekin, which lie on the fame fides of the two continents, namely, the eaftern, the winters are cold, and the fummers are very warm. The fame winds, in both places, pro- duce the fame effects. Thus in both, the north-weft winds are cold and piercing; the fouth-weft warm and dry; the north-eaft cold and wet; the fouth-eaft wet but warm. Befides, the general winds that prevail are the north-weft in winter, and fouth-weft in fummer. But the cafe is different in Madrid and California, though thefe places agree with each other in almoft every circumitance. This refemblance is manifeft not only in the weather and climate,’ but is alfo remarkable in the foil and natural produce. Tobacco, Phytolacca, (or poke) the perfimon tree, the mulberry tree, with fe- yeral others, are natives of China, they are alfo the natives of this part of America. Ginfeng is gathered to the weftward of Pekin, and as far as we know, has not been found in any other part of the world, except within the fame degrees of latitude in America. Thefe ob- fervations give grounds to hope that, if proper enquiries were made, many more of the native plants of Ghina, and very poffibly the Tea, fo much in ufe amongft us, and now become fo neceflary a part of our diet, might be found in America. ‘ Who knows whether the arrack tree, of which we read, may not be the fame as the American cocoa; or as our fugar maple, which, for many years fucceflively, will yield a large quantity of rich, fweet fap, from whence a fine fpirit may be diftilled? It might be worth enquiring (4) Natural and Civil Hiflory of California, (c) Muller’s Voyagesfrom Afia to America. Pr Bos Bs Br Are Gee ix enquiring, whether the cotton of Virginia, which is different from that raifed in our iflands, is not the fame as that of which the Chinefe make their fine callicoes and muflins; whether the /ndian hemp of America, oy more probably, the filk grafs found in Virginia, is not the fame as the Chinefe Herbay and whether the filk, gathered from the trees in Ghinay of which pocts and travellers have told marvel« lous ftories, is any thing more than the cocoons, which, in many places, are to be found in great plenty, on our trees and buthes. The filk of China feems ta be of different forts; that of which their Bandanoes,and coarfe filks are made, is ftrong and harfh; that which they work up into their fine damatks is foft, but of a weaker thread, Hence it is probable, that they have different fpecies of ‘filkeworms.. In this part of America, different kinds of filk-worms are found upon different trees and fhrubs; the cocoons of fome of them, particularly thofe that feed an the faflafras, are larger, and thefilk they produce, though not fo fine, is much flronger than that of the Italian filk-worm that feeds on the mulberry. Is there not reafon then to believe that, if experiments were made with our awn filk-worns, and fuch as are moft ufeful were propagated, this coun try might, in a few years, produce plenty of filks? Such of the plants of China as have been intraduced here, feem to agree with our foil and climate, and to thrive in a degree equal to our warmeft expectations; witnefs the rice, the whifk and the CAze nefe vetch. _Thete may encourage us to try others. From the trials made in our iflands of the fugar cane, coffee, ginger, &c. there is rea~ fon to hope, that the {pices of the Haf-Indies may be propagated and cultivated there, Thus by introducing the produce of thofe countries, which lie on the eaft fide of the old world, and particularly thofe of China, this country may be improved beyond what heretofore might have been expected. And could we he fo fortunate as to introduce the induf- try of the Chinefe, their arts of living and improvements in huf~ bandry, as well as their native plants, America might in time become as populous as China, which is allowed to contain more inhabitants than any other country, of the fame extent, in the world. ‘We have many trees, plants, roots and herbs, to the medical viy« tues and ufes of which weare flrangers. The fruit of our perfimon tree has been ufed, to good purpofe, in brewing beers but it was not known before the experiment was made, by order of this Society, lait winter, that one bushel of this fruit will yield above a gallon of proof fpirit, of an excellent tafte and flavour. To what ufes in pharmacy the KX PvE Ps a the gum, the bark and roots of this tree, which is fo very aftringent, may be applied, is unknown. The virtues of the Magnolia and {pice- wood are not fufficiently afcertained, though they have been ufed, and found to be excellent remedies in fome diforders. ‘There isa tree called the Xantholixum, that grows in Maryland, Virginia and both the Carolinas, the bark of which is of fuch a particular qua- lity, that the fmalleft bit of it, on being chewed, ftimulates the glands of the mouth and tongue, and caufes a flow of faliva equal to that of a flight falivation, while its ation continues. No rational experiments have yet been made to find out its virtues and ufes. A number of other trees might be mentioned, fuch as the faflafrafs, the wild cinnamon, the magnolia altiflima; the fragrant finell and aro-~ matic tafte of which prove that they have medicinal qualities, though their ufes are not fully known, ‘The fumach likewife deferves exa- mination. Its feed or berries, if not the wood itfelf, might be ufed indying. The /ndians mix its leaves with their tobacco, and there- by render it more aromatic and agreeable in fmoking. ‘There isa {pecies of it which yields a gum that nearly if not exactly refembles the Gum Copal. Indeed there is reafon to believe it is the very fame. Our wines and raifins are imported from foreign countries 5 while nature points out, that there cannot be a country more proper than this is for producing the grape. Before our lands were cleared, and fo many of the grape’vines extirpated, foreigners who vifited this country, could not help obferving and admiring the quantity that, like native vineyards, prefented themfelves to their view. And even now our hills, vales and level land abound with them. They grow in every foil, are fuited to every climate, and without cultivation, pour forth their fruits in abundance; many ofthem rich and luf- cious to the tafte. Itis not a little furprifing ‘therefore, ‘that’ the culture of the grape was not among the firft of our improvements. Confidering the great variety of vines we have on this continent, ‘it is not to be doubted that, with a little care and induftry, America might produce wine fufficient, not only for home confumption, but even for exportation; and, confidering the richnefs of many of our grapes, in their prefent wild, uncultivated ftate, and the improve- ment they mult receive from culture, there is reafon to hope that, in time, our wine may be much efteemed. It would be endlefs to recount all our plants, roots and herbs; many of which, though now neglected, might, with a little care and attention, become articles of commerce, and be of great ufe to our country. It is found from experience that flaxfeed, by reafon of the PR OE A BA a SE. XX ‘the drought and fcorching Sun in May and june, does not grow well, and hemp requires fo rich a foil, that few pieces of ground will ‘produce it. here is a plant, a native of this country, which grows in many places, but delights more particularly in light fandy foils, known commonly by the name of Indian hemp; its bark is fo ftrong that the Jndians make ufe of it for bow-ftrings. Could we but find a method of feparating and foftening its fibres, fo as to render it fit to be {pun into fine thread, it might ferve as a fubftitute for flax and hemp. This plant deferves:to ‘be cultivated on another account. The pod it bears contains a fubftance that, from its foftnefs and elaf- ticity, might be ufed inftead of the fineft down. Its culture is eafy, inafmuch as its root, which penetrates deep into the earth, furvives the winter, and fhoots out frefh ftalks every fpring. Five or fix years after being fown, it is in its greateft perfe€lion. With the roots of plants, unknown to white people, the Jndians ftain wood, hair and fkins of a beautiful colour, that preferves its luftre for years, though expofed to the weather. With the juice of herbs they relieve many difeafes, heal wounds, and cure the bite of the moft venomous {nakes. A perfect knowledge of thefe fimples, and of many others, with which our country abounds, might be of great ufe to mankind. The bowels of ovr carth are but little explored, notwithftanding the encouragement received from the experiments that have already been made. There is a great variety of clays, many of them valuable. Of fome, good crucibles have been made, and fire bricks, equal to any in the world. Others have anfwered fo well in burning, as to induce one to hope, that in time, a porcelain, equal to that brought from Ghina, may be made here. Near Newca/file on Delaware, a clay is found, which, ufed as a paint, retains its colour for years, ‘even when expofed to the weather, without any mixture of oil. In many places is found a kind of earth, which has been ufed inftead “of Spani/h brown, and anfwered the end. In other places there is an ochre, which dyes a wainfcot colour. May not fome of thefe clays have medicinal qualities? About eighteen miles frem this city, on the banks of Ne/bameny, is a large bed of black lead. The lands to the fouthward are fo replete with nitre, are fo favourable for pro- ducing it, that, infundry places, itappearslike a hoarfroft, on thefur- face of the ground. We are informed that a gentleman: in Virginia made a large quantity of faltpetre from the fweepings of his tobacco- houfe, for which he received a medal from the Society of Arts: And, to evince the importance of this difcovery, the fame gentleman afferts that, from the floor of a tobacco-houfe, fixty by forty feet, may be collected by a very fimple procefs, fixteen hundred weight of nitre ina year. Nay, it is faid there are, if the expreffion may be allowed, mines of faltpetre in the mountains. Of xxii PR OE AF A XC H, Of ores and minerals 4merica produces variety, as well as plen= ty; iron, copper and lead are found in many places. Some {amples of tin, antimony and bifmuth ores have been lately difcovered, and . other minerals, the nature and properties of which are not fuffici- ently afcertained. It would be worthy of every perfon, therefore, who withes to im~ prove his country, and advance its intereft, to try whether he cane not find at home, or introduce from abroad, new fpecies of plants, trees, fruits, grain, &c. fuitable to our own foil and climate, for the fupport and ornament of life, and for articles of trade and commerce. Each one according to his opportunities and ability, fhould explore the virtues of ournative plants, &c. and fearch out the treafures which nature has concealed in the bowels of the earth. Such difcoveries will not only be a benefit to ourfelves, but they will render us more ufeful to our mother country. ‘They will give full {cope to our induftry, without exciting her jealoufy, or interfere~ ing in the leaft with her manufactories; they will enlarge and give {tability to her commerce. For if by thefe means, the continental co- lonies can fupply her with the rarities of China, and her iflands can furnith the rich fpices of the Eaft-Indies, her merchants will no longer be obliged, in order to obtain thefe, to traverfe three quarters of the globe, encounter the difficulties of fo tedious a voyage, and, after all, fubmit to the infolence, or exorbitant demands of foreigners. Already has Britain experienced the advantage of her colonies furnifhing thofe articles, with which fhe ufed to be fupplied by for- eign nations. In the infancy of the colonies, and before they were fettled, fhe depended on Sweden and Rufia for naval ftores. Thefe nations, imagining that fhe could not procure them elfewhere, and refolving to increafe their gain, entered into a combination to raife the price: And had not her colonies furnithed thefe articles, the muft have given up the empire of the fea, or fubmitted to their ar- bitrary impofitions. But to accomplith thefe deGrable ends, it is efteemed neceflary, and propofed, that men of learning and enquiry fhould turn their thoughts and attention to thefe fubjects. The bulk of mankind fol- low a beaten track. They feldom turn their thoughts to experiments, and fcarcely ever adopt a new meafure, until they are well aflured of fuccefs and advantage from it, or are fet upon it by thofe, who have weight and influence with them. That this Society may, as far in their power, contribute to the carrying fuch a plan into execution, it is propofed to make it a prin- cipal part of their bufinefs to inquire, and try to find out, what our country RE ££ 6 Gf XK. XXlii country is capable of producing; what improvements may be made in agriculture, farming, gardening, &c. The beft methods of manu- ring land, of reftoring foils, that are worn out, and of protecting and guarding our fruits, trees, plants, and grains, from worms, in- fects and blafts; how to improve the breed of ufefulanimals, and introduce other fpecies from foreign countries; how to preferve our timber for fhip-building and other purpofes, and to increafe the mott valuable forts, the beft time for felling and the beft method of fea- foning it; what are the virtues and ufes of the many plants, &c. which this country produces; what exotics or medicinal plants may be introduced, and the beft method of propagating the moft ufeful of them; what new vegetable juices may be difcovered, and the bett way of managing them; what improvements may be made in the art of fermentation, making of wine, cyder, vinegar, &c. the cheap- eft and bett methods of making highways, caufeways and bridges, joining of rivers, and increafing our inland navigation. But it is not propofed to confine the views of the Society, wholly, to thefe things, fo as to exclude other ufeful fubjects, either in phyfics, mechanics, aftronomy, mathematics, &c. The means of conveying. knowledge are now become eafy, Print ing houfes are erected in all the principal towns on the continent, and regular pofts eftablifhed to carry letters and papers from one'to ano~ ther, Philadelphia, (the place where this Society meets) hath, by its central fituation, not only a ready communication by land, with our continental-colonies; but likewife with our Iflands, by. veffels employed in carrying on our trade. Lefides, hints thrown out in our public circulating papers are not loft, as in this country, almoft every manisfond of reading, and feems to have.a thirft for knowledge. The Society are very fenfible how unequal they are to the tafk of carrying into’ execution a plan of fo extenfive a nature. But they hope the ufefulnefs of it will procure them the countenance and affift- ance of every man who wifhes well to his country. There are many gentlemen in different parts of the country, whom Providence hath bleffed with affluence, and whofe underftanding is. improved by a liberal educations From fuch the Society promife themfelves: great afliftance, as their fortunes. enable them to make experiments, which men of narrow circumftances would not dare to attempt. The farmers employed in cultivating the lands are intel- ligent and fenfible, capable of obfervation, and of making many ufe- fulexperiments. From thefe we fhall thankfully receive every hint and practical obfervation, relative to the improvement of their farms, the culture of trees and grain, the raifing of ftock, &c. As among Our XXIV ret. Ff -e -s, our mechanics many are expert and ingenious, the Society hope to be favoured with any new inventions and difcoveries they thall make; . and as many of our young men, who have turned their thoughts to philofophical fubjeéts, have difcovered fuch a degree of judgment and genius, as will enable them to carry their refearches far into nature, their fentiments on fuch fubjects, as they fhall be pleafed to commu- nicate to us, fhall be received with thankfulnefs. For befides the other advantages that may redound from an inftitution of this fort, | it may have a tendency to infpire our youth with a love of know- ledge, to draw them gently from fcenes of diflipation, and to ani- mate them with a laudable defire of diftinguifhing themfelves by im- provements in arts and fciences, and by ufeful difcoveries that may do honour to themfelves, and promote the intereft of their country. Every {pecimen of what is curious or valuable in forming a cabi- net, or collection of foffil, vegetable or animal fubftances, that may enlarge the bounds of natural hiftory in general, and of this part of the world in particular, will be efteemed agreeable prefents, and grateful acknowledgments will be made to the refpective donors. The Society propofe, as foon as their ftock will enable them, to reward with fuitable premiums every perfon who fhall make any va- luable improvement, invention or difcovery, in any of the fubjects before mentioned. They will always be ready to incorporate as members, thofe who deferve well of their country. In fhort, the chief merit the Society mean to claim to themfelves is only 7 that of encouraging and directing enquiries and experiments, of re- ceiving, collecting and digefting difcoveries, inventions and improve- ments, of communicating them to the public, and diftinguifhing the authors; and of thus uniting the labours of many, to attain one end, | namely, the advancement of ufeful knowledge and improvement of our country. i i | | TRANS- TRANSACTIONS OF oT Hck _ American Puitosopnican Sociery, ec. KH Gol! id. bol: MATHEMATICAL and: AsrRONOMICAL Papers. A defeription. of a new ORRERY, planned and now near- ly finifhed by Davip Rittennouss, 4..M. of Nor- triton, in the county,of Philadelphia. Communicated by Dr. SMITH. & . Man aes. © fp YHIS machine is intended to have three faces, te ftanding perpendicular to the horizon: -..“"7. That in the front to be four feet {quare, made of fheet brafs, curioufly polithed, filvered and paint- ed in proper places, and otherwife ornamented. From the center arifes an axis, to fupport a gilded brafs ball, in- tended to reprefent the /u, Round this ball move others, made of brafs or ivory, to reprefent the planets: They are to move in elliptical orbits, having the central ball in one focus; and their motions to be fometimes fwifter, and fometimes: flower, as nearly according to the true law of an equable defcription of areas as is poflible, without too great a complication of wheel-work. The orbit of each planet is likewife to be properly inclined to thofe of the others; and their Aphelia and Nodes juftly placed; and \V.QL. 1. A their EE ADEE AREER ET LE I EE ER SETS SNS ES 2 MATHEMATICAL anp. their velocities fo accurately adjufted, as not to differ fen-. fibly from the tables of aftronomy in fome thoufands of ; * years. sacri | ff b : the balls re- For the greater beauty of the inftrument, the b prefenting the planets, are to be of a confiderable bignefs ;. but fo contrived, that they may be taken off at pleafure, and others, much {maller, and fitter for fome purpofes,. put in their places. ee eee When the machine is put in motion, by the turning of a winch, there are three indexes, which point out the hour. of the day, the day of the month and the year, (according to the Fulian account) anfwering to that fituation of the heavenly bodies which it then reprefented; and fo conti- nually, for a period of 5000 years, either forward or backward. ‘ dace In order to know the true fituation of a planet, ‘at any. particular time, the fmall fett of balls are to be put each. on its refpective axis, thea the winch to be turned round. till each index points to the given time; then a fmall Te-. lefcope, made for the purpofe, is to be applied to the cen- tral ball, and directing it to the planet, its longitude and inclination will be feen on a large brafs circle, filvered, and properly graduated, reprefenting the Zodiac, and having a motion of one degree in 72 yéars, agreeable to the preceflion of the Equinoxes: So likewife by applying the telefcope to the ball reprefenting the Earth, and di- recting it to any planet, then will both the longitude and and latitude of that planet be pointed out (by an index, | and graduated circle) as feen from the earth. Li The two lefler Faces are four feet in heighth, and 2 feet i 3 inches in breadth: One of them reprefents and exhibits all the appearances of Jupiter, and his fatellites, their eclipfes, tranfits and inclinations: Likewife all the appear- ances of Saturn, with his ring and fatellites. And the other reprefents all the phanomina of the Moon, particularly the exact time, quantity, and duration of her eclipfes, and thofe of the Sun, occafioned by her interpofition; with a mott ASTRONOMICAL PAPERS. 3 moft curious contrivance for exhibiting the appearance of a Solar Eclipfe at any particular place on the earth: Like- wife the true place of the Moon in the figns, with her Ja- titude, and:the place of her Apogee and Nodes, the Sun’s declination, equation of time, &c. It muft be underftood that all thefe motions are to correfpond exactly with the celeftial motions, and not to differ fome Degrees from the truth, as is common in orreries, dat The whole may be adjufted to, and kept in motion, by a {trong Pendulum Clock, neverthelefs, at liberty to be turn- ed by the winch, and adjufted to any time, paft or future. N. B. The above machine is to be fupported by a ma- hogany cafe, adorned’ with foilage, and fome of the beft enrichments of fculpture.’. The part containing the me- chanical aftronomy of the Moon, has been fometime finifh- ed, and is found perfeétly’ to an{fwer, by many trials al- ready made of it. The remainder of the work is now al- . Moft completed. The clock part of it May be contrived to play a great variety of Mufic. The 4 MATHEMATICAL ands The following CALCULATIONS | and PROJECTIONS of the Tranfit of Venus were laid before the Society a= agreeable to their Dates, and. claima aks e\here, as it may be of Ufe, in various Refpetlss to compare them sivit the a&tual Obfervations of the Tranfit, afterwards made in this Province; and from thence to collet? the Diffe- rences between Computation and Obfervation, ts. ro with the Caufes of thofe ji aniagineige pene ql30i33 i “at Read me ROJECTION of the enfuing Taansrr of VENUS ¢ core te N, whi bei t June. 1768 ae P ol June 3d, ai iy David AGN A.M. ARN, vie ’ ‘Exements from Halley’s Tables, for Lat. 40° Ny. wo Long. 4§ WwW. from Greenwich, fj. fy yf ey (IOI IgGs if - * ASTRONOMICAL. PAPERS. 5 The following Paper. by the Revd. Mr. Ew1ne, was alo eO0 { ified 3f © ; communicated. ; vy ) GENTLEMEN Sh oil Reed g 2% A S you have taken under confideration, the A propofal which I made to you the 19th of April lat, of obferving the enfuing Tranfit of Venus over; the difk of the Sun, which will be on the 3d of June, 1769; permit me to lay before you a pro- jection of the Tranfit, as feen from Philadelphia, to- gether with the elements of the projection, deduced from as accurate a calculation as 1 could make from Dr. Halley’s Tables. I find from the obfervations made on the laft Tranfit in June, 1761, that the mean mo- tion of Venus, for the year 1769, fhould be 21" more than thefe tables make it, and that the place of the nodes of Venus, as ftated in thefe tables, needs the following cor- _ rection. Atthe time of the ecliptical conjunction of the Sun and Venus in June 1761, their place was 2° 15° 36! 33", and her geocentric latitude was 9’ 44” .g fouth. Then fay, as. 72626.3 the diftance of Venus from the Sun : 28894.9 the diftance of Venus from the earth 3: 584.9 her geocentric latitude : 3/ 52".74 her heliocentric latitude at that time. ‘Then fay, asthe tangent of the inclination of her orbit with the ecliptic, is to rad. fo is the tangent of her heliocentric latitude to the fine of her diftance from the ‘nodes: 2. ¢. :a8: Ty 3°23" 20": radi oT, 93! §2".9n's S, 1° 5’ 14", which dedu& from her place June 6, 1761, at the time of the tranfit, viz. at 5" 57’ 20” at Greenwich; and the remainder viz. 2° 14° 31’ 19" is the place of her afcending node at that time. The motion of her nodes, as ftated by Dr. Halley, is 31” per annum; therefore, for 8 years, add 4!’ 8" to the abovementioned place of her node and the fum, viz. 2° 14° 35’ 27” isthe place of the node in the year 1769, June 3d. With thefe corrected elements, and others, as in the tables, the following cal- culations are made. The Sc Sa tp Se ee 6 MATH E MAP iO AE fan The apparent time of the ecliptical conjunction of the Sun and Venus, as feen from the center of the earth, 1769, June 3d, 5”. 4' 43”, as reckoned at Philadelphia, 5". o/ 32" weft from Greenwich. The place of the’ Sun and Venus, at the time of the tranfit, is 2° 13° 26’ 32”. The place of her defcending node is 8° 14°35' 27” at that time. The geocentric latitudeof Venusatthat timeis to’ 16.295 The Sun’s femidiameter’ is 15/°45".65. The: femi- diameter of Venus o’ 29”.° Their fum 16’ 14.65; Their difference is 15’ 167.65. Venus’s ‘horary motion from the Sun 3° 57.43. The angle made by the axis of the earth and ecliptic, as feen from the Sun, 7° 3/16". ‘The angle made by the axis of Venus’s vifible path and the axis of the ecliptic, is 8° 34’ 17”; the angular point or node being 1° 8’ 55” weft of the Sun. The angle made by the earth’s axis and the axis of Venus’s vifible path is equal to the fum of thefe, 15° 37/ 35”. The horizontal pa- rallax of the Sun on the day of the tranfit is 8.5204, when his diftance from the earth is 101521.2, his paral- jax at his mean diftance 100000 being {uppofed tobe 8.65, as found at the laft tranfit, 1761. The horizontal parallax of Venus on the day of the tranfit 29’.9348, when her diftance from the Sun 72626.3, her mean dif- tance being according to her periodic time 72333. The difference of thefe, viz. 21.4144, is the horizontal pa-~ rallax of Venus from the Sun on the faid day. The tran- fit begins, asfeen from the earth’s center, at 2", 17' 20/.48, and ends at 8". 41' 46".72. The total ingrefs at 2", 36' 31".38; the beginning of egrefs at 8". 22’ 35”.82; fo that the whole duration between the internal contaéts will be 5°, 46’ 4.44. But thefe times will be confiderably al- tered by the parallaxes of Venus in longitude and latitude, as obferved from different parts of the earth. The whole effe&t of the parallaxes of longitude and latitude at the time | of the external contaét to haften it, being 3’ 31", the time of it, as feen from Philadelphia, is at 2", 13’ 49” 28” P.M. And the time of total ingrefs: at Philadelphia i a, ) ASTRONOMICAL PAPERS. 7 2", 32' 27"; the total effedt of thefe parallaxes to accele- rate the internal conta@ being 4! 4". Thefe times depend upon the longitude of Philadelphia, welt of Greenwich, which in this calculation is fuppofed to be 5°; 0" 32", whichisas near as have yet beenable toafcertain it, by comparing a.number of obfervations made on the e- clipfes of the firft fatellite of Jupiter, with Mr. Emmerfon’s. tables, But thefe cannot be depended upon for the longi= tude,.within a minute or two of time, which will by no means anfwer the defign. of afcertaining the diftances of the Sun and planets by the enfuing tranfit. I would there- fore beg leave to propote to the Society, that provifion be made, without lofs of time, for ere@ting a {mall obfervatory in fome convenient place that the occultations of fome Known ftars by the Moon, and the eclipfes of Jupiter’s fa- tellites, may be noted, and compared with the correfpon- ding obfervations made at Greenwich and other places: And that fome proper perfons be appointed to make the ‘obfervations, at the expence of the Society, that our lon- gitude may be afcertained with the precifion that is necef- fary. It would be proper, that at leat two fetts of obfer- vers be appointed to view the tranfit in this city, in order to guard againft the fatal accident of lofing the Sun out of the field of the telefcope, in the critical and important moment; which I. find happened to a good aftronomer in the Eaft-Indies, at the time of the laft tranfit. It is very difficult to’ preferve a celeftial objet in the field of a telef- cope, that magnifies confiderably. _ The expence of making thefe obfervations, with fufficient accuracy, muft be confiderable; but it is hoped that an op- portunity will not be neglected on this account, which, for its importance to the interefts. of aftronomy and navi-~ gation, has juftly drawn the attention of every civilized na- tion in the world, and which will not be prefented again for more than a century to come, Thefe —_ LOA \ rice to the judgment of this refpectab sien a Their very humble: oan ~~ Philadelphia Fune 14, 1768... JOHN EWING. N. B. "The difference betwee Foti of thefé Numbers and thofe printed in the American Magazine, was occafion- ed by negle@ing the-ar” of correétion in’ the place of Venus, as inconfiderable, ‘the’ éffe@’’ of which is here ta~’ ken into the computation, ; and ‘the refult i is fet down above. See the projetion, plate i a 4 bas sage “a . =e Witt1am Smitu;, rts D. Prova of the Colleg' of Phi- ladelphia, Joun Luxens, E/g;, Surveyor-General of Pennfylvania, Davip RirTENHOUSE, A. Me of Norri- ton, and Joun SELLeRs, L/q; Reprefntative in - ~ bly for Chefter County-——; 8 Mean tite MA BCs bos 5 Sabeouale are fubmitted, with all’ 4 Samm fan a. ened patil the Commitee’ appointed for that Obferiatien, by ibe A | AMERICAN PurLtosopurcaL Socrery; held ‘at Phi- ladelphia, for promoting ufeful Knowledge. Communicated to the Society, July 20rb, 1769, by Direc tion, and in Behalf of the Committee; Ly Dr. Roles ‘GENTLEMEN, MON G the various public fpirited: defigns, that A have engaged the attention of this Soczery, fince its firtt Inftitution; none does them more honor than ‘their early seinen to appoint) Commirress, of their own Members, to takeas many obfervations, in’ different places, of that! rare Phenomenon, the’ TRANSIT OF VENUS Over the Sun’s Disk, as they had any probability of being able to defray the expence of, either from their own funds, or the public affliftance they expected. As \J é ' Earths le nei ofthe Ed ifih | ASTRONOMICAL PAPERS. 9 | As the members of the Norriton-Committee live at fome diftance from each other, I am, therefore, at their requeft, now to digeft and lay before you, in one view, the whole of our obfervations in that place; diftinguithing, however, the part of each obferver; and going back to the firft pre- parations. For Iam perfuaded that the dependance, which the learned world may place on any particular Tranfit- Account, will be in proportion to the previous, and fubfe- quent care, which is found to have been taken in a feries of accurate and well conducted obfervations, for afcertaining the going of the time-pieces, and fixing the Latitude and Longitude of the place of obfervations, &c. And I am the more defirous to be particular in thefe points, in order to do juftice to Mr. Rittenhoufe, one of our committee; to whofeextraordinary fkill and diligence is owing whatever advantage may be derived, in thete re- {pects, to our obfervation of the Tranfit itfelf. It is fur- ther prefumed, that aftronomers in diftant countries, will be defirous to have not only the work and refults belong- ing to each particular Zranfit-Obfervation, but the mate- rials alfo, that they may examine and conclude for them- felves. And this may be more particularly requifite, in a . New Obfervatory, fuch as Norriton, the name of which hath perhaps never before been heard of by diftant aftro- nomers; and therefore, its latitude and longitude are to be once fixed, from principles that may be fatisfactory on the prefent, as well as on any future occafion. Our great difcouragement, at our firft appointment, was the want of proper apparatus, efpecially good Tele/copes, with Micrometers. The generofity of our Provincial A/~ JSembly {oon removed a great part of this difcouragement, not only by their vote to purchafe one of the beft reflect- ing Telefcopes, with a Dollona’s Micrometer; but likewife by their fubfequent donation of One Hundred Pounds, for ereting Obfervatories, and defraying other incidental ex- pences. It was forefeen that on the arrival of this telefcope, added to fuch private ones as might be procured in the Vou. L B city 10 MATHEMATICAL awnp city, together with fitting up the inftruments belonging to the Honorable the Proprietaries of the province, viz. the equal Altitude and Tranfit Inftrument, and the large aftro- nomical Sector, nothing would be wanting for the City Obfervatory in the State-Houfe Square, but a good Time Piece, which was eafily to be procured. We remained however ftill at a lofs, how to furnifh the Norriton Obfervatory. But even this difficulty gradually vanifhed. Early in September, 1768, foon after the no- mination of our Committees, I received a letter from that worthy and honorable Gentleman, Thomas Penn, Efq. one of the Proprietaries of this Province, which he wrote at the defire of the Rev. Mr. Mafkelyne, Aftronomer Roy- al, exprefling their defire, “* That we would exert our- « felves in obferving the Tranfit, for which our fituation “ would be fo favourable;” and inclofing fome copies of Mr. Mafkelyne’s printed direétions for that purpofe. This gave me an opportunity, which I immediately em- braced, of acquainting Mr. Penn what preparations we had already made; and what encouragement the Aflem- bly had given in voting One Hundred Pounds Sterling, for the purchafe of one reflecting Telefcope and Micrometer, for the City Obfervatory; but that we fhould be at a great lofs for a telefcope of the like conftruétion for the Norri- ton Obfervatory, and requefting him to order a Reflector of two, or two and an half feet, with Dollond’s Micrometer,. to be got ready as foon as poffible in London. It was not long before I had the pleafure to hear that Mr. Penn had ordered fuch a Telefcope, which came to hand about the middle of May, with a moft obliging letter, exprefling the fatisfa@tion he had in hearing of the fpirit fhewn at Philadelphia, for obferving this curious Phoenomenon when it fhould happen; and concluding as follows « T have fent by Captain Sparks, a reflecting Telefcope « with Dollona’s Micrometer, exact to your requeft, which “I hope will come fafeto hand. After making your ob- “ fervation with it, I defire you will prefent it, in my “ name ASTRONOMICAL PAPERS. 1 * name to the college—Mefirs. Ma/on and Dick/on tell me, “they never ufed a better than that* which I formerly “‘ fent to the Library Company of Philadelphia, with “* which a good obfervation may be made, though it has ‘* no micrometer.” We were now enabled to furnifh the Norriton Obferva- tory, as follows, vz. 1. AGregorian Reflector about 2 f. focal length, with aDollond’s Micrometer. This Telefcope hath four different magnifying powers, viz. 55, 95, 130, and 200 times; by means of two tubes containing eye glafles that magnify differently, and two fmall Speculums of different focal diftances. Made by Nazrne. Ufed by Dr. Smitu. 2. A Refractor of 42 f. its magnifying power about 140. The glafles were fent from London with the large Reflector, and belonged to Harvard College, New-Eng~ land; but as they did not arrive time enough to be fent to that place before the Tranfit, they were fitted up here by Mr. Aittenhoufe; and ufed by Mr. Lukens. 3. Mr. Rittenboufe’s Refractor, with an object glafs of 36 f. focus, anda convex eye glafs of 3 inches, magnify~ ing about 144 times. Ufed by Himsetr. Both thefe RefraCtors, as well as the Refletor, were in moft exquifite order. 4. An Equal Altitude Inftrument, its telefcope three and .an half feet focal length, with two horizontal hairs, and a vertical one, in its focus, firmly fupported on a ftone pedeftal, and eafily adjufted to a plummet wire 4 feet in length, by 2 fcrews; one moving it in a North and South, the other in an Eaft and Weft direGtion. : 5. A Tranjfit Tele/cope, fixed in the Meridian on an axis with fine fteel points; fo that the hair in its focus can move * Mr. Owen Binnie, who was appointed by the Society to conduct the obfervation near Cape Henlopen, had this telefcope; nothing being defired there but the contaé?s and their exad time; which he obtained to great fatisfadtion, as by his report may appear. As he had but a time to prepare, and there was a difficulty in getting the neceffary apparatus for fixing, by his own obfervations, the longitude and latitude of the place chofen for his ftation, it was re- folved to depend on the afcertaining thefe articles, by running a line from the place of his ob- fervation to a known point in the work of Mefits, Adu/en and Dixen, when employed in fet- tling the boundary lines of Penn/ylvania and Maryland; and in meafuring a degree of latitude, along that fine level peninfula, between Delaware and Chefapeak Bays. t Un He F He i 12 MATHEMATICAL awnp move inno other direétion than along the meridian; in which are two marks South and North, about 330 yards — diftance each; to which it can be readily adjuftedin a hori- zontal pofition by one fcrew as it can in a vertical pofition by another {crew. 6. An excellent Time-Piece, having for its pendulum- rod a flat fteel-bar, with a 60h weighing about 121b. and vibrating in a fmall arch. | It. goes eight days; does not ftop when wound up, beats dead feconds, ‘and is kept in motion by a weight of slb. for Sniyiinrgsin Thefe three laft articles were alfo Mr. Rittenhoufe’s pro- perty, and made by himfelf, » Dam yy 7. An Afironomical Quadrant, two and an half f, radius, made by Sifon, the property of the Ea/t Ferfey Proprie- tors; under the care of the Right Hon. William Earl of Stirling, Surveyor-General of that Province; from whom Mr. Lukens procured the ufe.of it, and fent it up to Mr, Rittenboufe for afcertaining the latitude of the Obferva- tory. Thus we were at length completely furnithed with every inftrument proper for our work. | As Mr. Rittenhou/e’s dwelling at Norriton is about 20 miles North-Welt of Philadelphia, our other engagements did not permit Mr. Lukens, or myfelf, to pay much at~ tention to the neceflary preparations; but we knew that we had entrufted them to a gentleman on the fpot, who had joined toa complete fkill in mechanics, fo extenfive an: aftronomical and mathematical knowledge, that the ufe, management, and even the conftru@tion of the neceflary apparatus, were perfectly familiar to him. Mr. Lukens and myfelf could not fet out for his houfe till Thurfday, June 1ft; but, on our arrival there, we found every pre- paration fo forward, that we had little to do, but to exa- mine and adjuft our refpective telefcopes to diftin@ vifion, He had fitted up the different inftruments, and made a great number of obfervations, to afcertain the going of his Time-Piece, and to determine the latitude and longitude of his Obfervatory. The laudable pains he hath taken in thefe ASTRONOMICAL PAPERS. ry thefe material articles, will beft appear from the work it- felf, which he ‘hath committed into my hands, with the fol- lowing modeft introduction ; giving mea liberty, which his own accuracy, care and abilities, leave no room to exercife. Norriton, July 18th, 1769. DEAR SIR, “ "HE inclofed is the beft account I can give of the % Contacts, as I obferved them; and of what I “‘ faw during the interval between them. I fhould be “¢ glad you would contract them, and alfo the other papers, ‘¢ into a fmaller compafs, as I would have done myfelf, if “ Thad known how. L beg you would not copy any thing « merely becaufe I have written it, but leave out what “ you think /uperfluaus. Tam, , With great efteem and affection, Yours, &c. © DAVID RITTENHOUSE.” _To Revd, Dr. SMiTH. Mr. Rittenhoufe’s Ob/erwations at Norriton, before and after the Tranfit of Venus, June 3d, 1769; for fixing the Latitude and Longitude of his obfervatory, and the going of his clock, &c. «“ ARLY in November, 1768, I began to ereé& an “ Obfervatory, agreeable to the refolutions of the “ American Philofophical Society; but, through various _ “ difappointments from workmen and weather, could not “‘ complete it, till the middle of Apri/, 1769. -I had for “ fome time expected the ufe of an Equal Altitude inftru- “ ment from Philadelphia; but finding I could not depend “on having it, I fell to work, and made one of as * fimple a * conftruction * It is defcribed above, No. 4. of the Apparatus, 14 MATHEMATICAL ann. * conftruction as I could. March 20th, this inftrument was finifhed, and put up out of doors, the Obfervatory not being yet ready. “‘ I had, however, for fome weeks before this, with my “¢ 26 f. Refractor, obferved eclipfes of Jupiter’s fatellites, “in fuch a manner that, though my equal-altitude inftru- * ment was not finifhed, and confequently I could not fet “‘ my time-peace to the true noon, I fhould neverthelefs “ be able to tell the time of thofe eclipfes afterwards, when “the inftrument fhould be ready. For this purpofe, I 6 obferved, almoft every fair evening, the time by the clock, when the bright ftar in orion difappeared be- “hind a fixed obftacle, by applying my eye to a fmall “ fight-hole, made through a piece of brafs faftened to a “ ftrong poft. The Obfervations were as follows, viz. 4769. Star difappear- Equal altitudes of © Hence appar. are, 90 7. 17. 16: Feb DD. Wem. fee. | 8. 59: $9: 55 7 ar 28 , 13.21 16 14. 3% 0 | + 45. 44 93 16.150 1 ed, per clock. Immer. ft fate]. per noon, or ©’s Fe. D. hh. m. fec. clock, cent. on Merid. 45 9. 26. 39 |Feb, D. h. m. fec.| Mar. A. M, BP. MM. per clock. 2% 2. 58.9% 16. 14. 24, 58 |D. “h. m. fec. h. m. fec, 44 8. 50. 57 23 16. 17. 41 6. Fo. $2. We SOs 53 Th om, - fee, Hence, from column | 19 Ili $F. 3%: Mar. 3 8. 23. 21 | 3d, the apparent J I I Me 53. 3% 12 7. 48. 26 | times of the two 14 7. 40. 41 | immerfions above, 8. 56. 40. 2 58. 26 iy 7. 2 4 140 Im 57, 28, uh 7 6 \ “‘ From this time, to May 20th, the clock was altered s¢ feveral times; once taken down and cleaned, removed *¢ back to the obfervatory, and regulated anew. Care was, *« however, taken to obferve equal-altitudes of the fun, on “ the days preceding and following any vifible eclipfe of the ft fatellite; when the wheather would permit. “The whole obfervations, during this period, were 6 the following, Equal ASTRONOMICAL PAPERS. rg Equal Altitudes of © Hence appar. | Obferved Immerfi- April 34, 1769. noon; or ©’s ons of rt Satel- cent. on Merid. lite. A.M, Po iM. per clock. April 34. h.. m.. fec h. m. fec 8. 5. 24 4. 1. 56 h. m. fec. h. m. fec. ‘ 8.8. 16. 5 se See oe ee gong I4. 52. 40 4th. 8. 3. 43 4. 3:5 3 The 3-5 8. G38 Av Qe IO : ers : roth, 8 32. 8 16. 46. 20 8.. 35. 6 Cloudy:. Day-Light. 8. 36. or Lith, 8. 30. 23 3. 30. 43 8. 33. 18 3: 27. 47 12, ©, 20 8. 34. 41 3. 26. 22 ag ae Tath. ek: : 3 33. 16 ‘ ie 12. 14. 38 : T4th 8. 25. 4% 3: 33- 56 Cloudy, Sah Of Ik. 59. 38 8-30. om 3. 296 37. May 4th. 8 5: 15 3. 44. 6 S&S. Be 3 Sai 26 Il. 54. 3% 8.9. 23 . 3: 39. 58 : sth. ; 8 agit 344. ST shi. Sths. 8 26) 39 3. Am A II. 54.. 22 Hie dP 8. 8. 19 3 40. 42 6th. 8. 3. 3. 45. 37 8. 5. 54 3.4% 5¥ IX. 54. 14 8. 7. 15 “se & : rith, 8. 34. 51 3 19. 12 Ge 30) 08 3. TS. 49 LT Fh Bu 37s. AC 3. 14.- 92 terse oe rsth, . 9: 1% 59 % 39. 28 . May 14th. Rae a3h -9’ o. 15. 5a a. 36. 3% In 56.7 Emerfion. ‘ SA AEE 8 Radio? 9« 58. 20 “© May 20th, in the morning, the clock was fet up for “ the laft time, pretty near the mean time. It had no “ provifion for preventing the irregularities arifing from “ heat and cold; nor could I find leifure to apply any con- « trivance of this fort. “ This 16 MATHEMATICAL ann “ This day I likewife put wires inftead of hairs in the *« telefcope of the equal-altitude inftrument; and the fol- “lowing are the obfervations, taken both with it, and “with the meridian or Tranfit-Telefcope, in the order ‘* wherein they were made. “The ill ftate of my health would not permit me to fit up “ at nights, totake equal altitudes of the ftars. I was there- “ fore obliged to content myfelf with thofe of the fun on- 6 ly. 1769. : “May 20th. a : Equal Aititudes of ©) Hence ap- | Obferved E- Objervations with the "Hence ap- a i Ps | par. noon; | merfions of | Meridian T elefcope. | par. noon; h. m. fee. h. m. fec. | or ©’s cent. |. 2f’s Satel- or @’s cent. 8. 1. 30* 3.51. 28°} on Merid. | lites. h.m.fec. | on Merid. 8. 2. 52. 3,50. 8 | per clock, © W.limb 11.65.16 | Per clock. Goh 1k 3.48. Ag ct OE, ee. on Merid. 55 «ims f6c. 8. 5. 36 3.47. 24 | IL. 56. 23% Eaft Do. 11.57.31 | 13. 56. 234 May 21h, She ON Bae ie iim. at Sat.” G@)W. limb, 11.55.23 300 SO) yesh sas| hb. mm fen E.Do. — 13.57.37 | 11. 56. 30 Clouds. 3:49 27 Q center : - } 9 4 tl, ot) 40 on Merid. § 178-39 May 13d. BO. 4 3-53. 36 : B, . 24 3.52. 16 It. 56. 4§ OW. limb 11.55.39 Irr. 56, 46 B. 2 47 3.50. §3 : E.Do. 11.5753 8.4. 8 - = = : ‘ , May ath. © E. limb, 11.58. 0 —paff. © femidi. x, 3 | 1 56 5% §. center ditto, wd, May 25th. . T5945 3-54 57 : 8.0.35 3-53 38 Toy go, x. OW. limb, 11.55. 53] 11. 57. 1. BT. 58 3.59. 18 oes E.Do. 11.58. 9 B08 Aro. aA May v6th, 7+ 5854 355+ 38 . & Ots. 3.54: 18 Il. 57. 10 ©w. limb 11.56. 3 [| 11. 59, Io} 8. 2.57 B53 56 le E. ditto, 1.58.18 & 2.57 3st. 35 May 27th. : > W. Limb 13.56. 12 Par. o>, 1 | E.Do. 11.58. 27 a May 30th, ; 2 i. Limb. (ek ieaaers om aan | | on Merid. t geal 31 * {nthe above Equal Altitudes, it may be proper to obferve that thofe in the afte fet down in an inverted order, the 4th P. M. being Lee and correfponding to the ce — The aft fet, according to the order inwhich they ftand, is the fun’s upper limb at 4 debi: the fecond isthe upper limb at lower hair; the 3d the lower limb at upper hair; and the 4th the lower limb at lower hair, as the telefcope inverts, May 31% ASTRONOMICAL PAPERS. “a |. 1769. May 3h. qual Altitudes of @)) Hence ap " Oblerved E- ( Obiervations withthe ; Hence ap- ae 2. par. noon; | merfions of Meridian Telefcope. par. noon; .m. fee, h.m. fee} or ©’s cent.| 2f’s fatellites. or ©’scent. 7+ 57:29 3.58. 49 | on Merid. on Merid. 7- 58.49 3-57 30 | perclock. h. m. fec. | per clock. B. Ott 6.56, & m. fee. @QW. limb 11.56. 58 h. m. fec. eo 9t Seh4. 49 | It 58. Sh +pafl. © femidi. x, 81 rr. 58. 6 fune 2d. ut {maller wires in | the Telefcope ; hence the differs ence of the inter~ © W. limb 11. 57. 26 vals. E. ditto, 11.59.48 | 1%. 58 334 4. 599 a 02.6 | 7. 58.29 3-58.47 | IT. 58. 34 T+ 59°53 357. 2% o LI he. 6 Fune 3d. TRANSIT DAY. Equal ppt ‘were not taken this day ‘ as the inftrument © ae P5749" | ii, 5S. Ag was to be other- ditto, 12.59.57 wife employed in the afternoon. June Ath. ee @ a ly 2 sete J. 58.10 3659- : W. limb rr. 597. 54 + 59:34 id . ay Ih 59.0% OW ditto, a gael ee 7 ee Shah Zot on Fune 5th. vo a A. I. 50 9. $803» Ae O 30) sy 6g, yg 7. 59.27. 3.59. 7| 1 5% 338 8. 0.47. 3.57. 47 : £ Fune 6th. soa On sOe ke Em. ft Sat. He Whe eG ony he 18b. =e e gig8i-gt | tt. $9.26. | hm. fec. |@ W. limb x7. 58. 18 1 9. 11.30 2.47. 26 to 1h 8 E, ditto, 13. ¢. 33. ee oe 225 June 7th. fe GHG bee be BS ‘Em, 2d Sat. |@ W.lunb ai. 58. 27 7. $916 4.0% I] 4, 59. 36 8. 23. 42 ee 12, 0 44 | 11, 59: gst 8. v9 - +s Lee. . lim a on Merid, t 3: 4% 53 Fune 8th. W. 50007 Av 3 de @) W. limb ee ae eer 48 on Merid. 11.5840 | 1, 59, 48h 4. 59.10 4.10, 28 <2) Editto, 12.,0.57 SE care eh aard as Sune Loth, on vn Ae dE ‘7 5 Tod ee ee 03 M912 4. % 19 | ** o 98 8. 0.3% 3.59. 7 Fune 12th, @ W. limb 1.59.2 : | | | E, ditto. 12. rH | hl Tiana Vou. I. Equal 18 MATHEMATICAL awnpb etiieieed 176) “fune 1 3th, Equal Altitudes of ©) Hence ap- | Opferved B- | Obfervations with the Hence ap-| BiMas Po MM | par. noon;| merfions of | Meridian Telefcope. | par. noon; h, m.fec. h. m. fec.| or @’s cent. | 2f’s Satellites. or @)’s cent, q+ 59:13 4. % 30] on Merid, hem. fec, | on Merid. 0.33 4. I. 31] per clock. Em, 1ft Sat. © W. limb 14.59. 42 | per clock, h. m. fec. | bh. m. fec, E. ditto, 12, 1. 59 | h. m. fec. Ty 00 66 12, 5. 59: ‘ 12. 0. 50% oe Fune 14th, : © W.limb 11.59. 57 I | E, ditto, t#: 4/13) "= i ; Fune 16th. 9. 56.52 4. 6. 16 © W. limb 43 0. 26 | 7. 58.14 Ae he 57 1a 1 34 oe ditto, (12%, “| 12 Ts. Bq ©5930 4. 3s 33 cent, : 5 “ast Ay % 1 on Merid. ¢ ea Fune 17th, © W.limb. 12. 0. 36 --pafl. femid. x. 8,8] 12.7. 448 meetin! There 2. center mo- 99° 4 on Mitid. ¢ ig ed ae Sune Toth. : © W.limb. 12. 0. 56 ae 8 paff.femidi x, "8,8 | 12 ae | nik on mer. 8.53, a4, ale tate Sune 21ff, @W.limb 12, 4.17 | 42. a, Usk | E Do. 12. 3. 34 | Therm. 83° Fune 22d. ( i : @W.limb 13. 1. 28 12. a, 305 | | E, Do, 32. 3. 45 _| ‘Therm, 74°% Fune 43d. | ; (©W.limb, 12, 1. 39) 1a, a Ao. (a, Do. 1% 3. §§ (Therm. 73°% ; June tath, © W. limb 12, 1.49] 12. 2. 57 | . | E, ditto, 12. 4. 5 [Therm, 84° Sune ~sth. 3d fat. out of the fhadow, | © W. limb ra. 3. 57 1a. 3, cht : on applying | LE. ditto, 12. 4. 14 Therm. 86° : the eye at | : 8. 54. 39_ Fune 26th. © W.limbia. a, 67 E. ditto, 12. 4. 23 | 12. 3. 14d DE. limb 2 19, 4 | Therm. 85° on Merid. 13-5 oe June 29th, W. limb 12. 2. 14 peat ditto, 12. 4. 31 | 7% 3. 2a D E. limb on Merid, § 19° 4:19 Therm. 88°. Uc.on Mer. 8. 19.58 June 28. ASTRONOMICAL PAPER S. 1g sth D June 28th. Rees Equal Altitudes of @| Hence appar.) Obferved E- { Obfervations with the [Hence appar. 4.M. P. M. | noon; or ©’s| clipfes of 2f’8] Meridian Telefcope. | noon; O's h. m.fec. h.m. fec.} cent. on Mi-| Satellites. cent. on Mi- 9-59. 1X 4. 7.45 | rid. per clock. rid. per clock. 8. On 3h 4018s hs: faw fec. h. mm. foci i om. . foc. 8.0. 55 4. S10} 12 3. 29,4 @W.limb, 12. % ar | 12. 3. 295 8. 3. 15 - - = E. ditto, 12. 4. 38 tune 29th. : 3 = a Ae z 43 Em, ut Sat. | d . 0.48 4. 6.22/12 3. 37. fhavingbeenhid © W.limb 12. 2. 29 i 3. 3). + IT Ae 4 59 by acloud, at, Se ditto, x en te Br 3u 32> Ave gy 88 thedecuy: ee une 30th. 10. 25, I Therm. 85°. Fuly rd. . 8.0. B4 a. 7. 28 Immerfion. | © W. limb 12. % 5% 8. tiag- as 6. 8) 119. 3. 89 3d Satellite. E, ditto, 12. §. 8 | 12. 4: © 8. 3. 8. a we a It. I9. 36 Therm. 82°% 8. 4.29: - = = ~ a Fuly 3d. Ba 40 4. 7. 20 Se dis Fe tds S56 58 +5 6 © W. limb 12. 2.59 | 12. 4. 6% Su 3k 3I 4 4. 37 ss E. ditto, 12. 5.15 | Therm, 87° Side ST 43-16 Fuly 40 Sa Sas by WiLa 3 2 30 Ae Se 5% Ia 4. 14 ‘limb 12. 3. IF 8.23.53. di 4s GL E. ditto, 12. 5. 23 Th $149 8. 5.14 4. 3. 10 Therm. 87° Fuly 5th. B. 5. 90 4s a 57 | TR de 1953 © W. limb 12 3. 11 ae 4. 19} er. ++paffedfemidi. x. 8. 5 | at 3P.M. 94° t Fuly 816. ; Berne a E Al A cb eg 193.30) 1% 4 44 8. 2. 56 4 6. 20 I 4. 4% ditto, 12. 5. 52 |x © 8 43) Ak oT herm. 83°% TABLE of the Eclipfes of Jupiter's tf Satellite, 13h; compared with the calculated times of the Longitude of the Obfervatory. andthe Emerfions with the Gregorian Reflector. t/t. Sat. Zmmerfions. obferved at Norriton, from Febr uary 16th to Fune Jame Eclipfes, for Greenwich, in order to jix the The Immerfions were obferved with Mr. Rittenhoufe’s Re/radior, Calculated apparent time of the Longitude of Norriton W. 1769. Apparent time at Norriton. fame at Greenwich. from Greenwich; thence deduced. D. bh. tm fee. De hie fet. h. mm. fee. Feb. 16 14. 21. 30 Feb. 16 19, 22 29 a tc 1g a3 16. 15. & 23 4 16. 35 Ste Ge April, 3 14. 49. 45 April 3 9 SI. 24 Se te g9 16.160 f00> 0 IO 21. 47. 14 Bi Noda 12 I. 14. 37 13 16, 16. 33 es May IT. 29. -27 May § 16. 31. 20 5. 53 Emerfions. Emerfions. Or A%. 55. 13 at: 16.56. 49 Sot 36 Sune 6 10. II. 3% June 6 15. 1% 59 Ske 27 3 Tay Seed 13.27. 6 35 oi, 50 Difference of Longitude for a mean of the above 9 Eclipfes 34,22 5 which we mutt fix for the Longitude of our Obfervatory, for the prefent. 20 MATHEMATICAL awp But fhould the obferved * times of thofe eclipfes, come out different at Greenwich from their calculated times in the nautical almanac, for the prefent year, a correétion of the difference of longitude muft be made accordingly. OBSERVATIONS for fixing the Latitude of Norriton Obfervatory, with an Aftronomivale Quan drant of two and an half feet radius; made by Siffon. This Quadrant was fent up by Mr. Lusens, and ereéted in the meridian of the Obfervatory, May 20th, by Mr. Rittenhoufe, who took the following obfervations with it, viz. . Zenith diftances of tars, for diftovering whether there might be any error in the inftruments. With the face of the Quadrant ene | With the face se aa we a May 31 20°. 36. d j, . SFune 9006 Bs! 550 Higheft ftar in left oy) Higheh ftar in the , eg of Bootes * ail . = ¢ . left leg of Bootes $ ot ce i ce ar 19; e 18 : Fune 6 19. He 5 )fune X 19. 46. 14 7 19. 46. Ardurus 92 ates Ardurus 8 19. 46. 73 F106 46.80 f Io 19. 46. 4% Bright ftar in the § June & 12. 39. 36 Bright ftar in the § June 6 12. 39. 34 Crown 3 Paes 30. 97 Crown : TO 12. 39. 18 From a mean of the above 18 obfervations, the error of the quadrant is 3,5 to be fubftracted from the Zenith diftance when the face is weftwards and added when it is eaflwards, ' OBSERVATIONS * Since drawing up the above, the Revd. Mr. Mafkelyne, Aftronomer Royal, agreeable to ‘my requeft, hath been pleafed to communicate the following lift of eclipfes o Jupiter’s 1 Sa~ tellite as obferved at the Royal Obfervatory, from Aprilto June, beth inclufive, viz. 1769. gpraret tie Immerfions of tit Sat. at Greenwich. . » Mm. tec, March 29 19. 25. 7 with af. Refle&. made by Shorts Apert. 4,5 inches diameter, April 1% 16. 16. 8 with af. Refle&. made by Bird; Apert. 3,8 inches diameter, 43 14. 3%. 17 with Short’s % f, Reflector. Emerfions. : mM 6 $9 3% 152 with Shorts af, Reflector. es Ee 31. 35§ with 6 f, Newtonian Refledor; Aperture 9 inches diameter. June 8 9. 40. 56 with 6Ff. ditto. 15 11. 35. 33 with Short’sa f. Reflector. July 1 9G. 50. 24 with ditto, Mr. Mafkelyne writes that the 6 f. reflector fhews an immerfion later and an emerfion fooner than Short’s 2 f. Reflector by about 20’; and that the difference of the 9 f. reflectors, owing to the difference of their appertures, may be about 5, There are only three me the above eclipfes obferved at Greenwich, (viz. the 3 immerfions) that could have fea feen here, and but one of them happens to be among thofe actually ob- ferved, viz. April rath, j 16h. 16. 8 at Greenwich, IX. 14.37 at Norriton. Hence 5. 4%. 31% Difference of longitude. : "Till we have an opportunity, the enfuing fpring, to obferve more eclipfes of Jupiter's Sa- tellites, we would rather depend on the difference of fotgitade deduced from the two foregoing correfponding obfervations, than on the mean deduced from the calculated times; which, hew- ever, puts us only 3/ more weft. ‘he immerfion of April rath was taken at Greenwich, with Bird’s telefcope of 3, 8 inches aperture, and the fame immerfion at Norriton with arefrator that, in all trials, as near as can € jodged, ives the fame fecond with the Gregorian refleQor of 4, 4inches aperture ; fo that 2// or 3 might be added to the time of the immerfion at Green- wich to agree with our telefcope, which would make sh. 1 33” or 34” diff, long. the fame as got from the mean of the calculated times. ‘The eclipfes of ad and gd fatellite are not fet down, as they are not fo much to be depended en, as thole of the ft. ASTRONOMICAL PAPERS. 20 OBSERVATIONS of the Zenith Difance of the Sun's upper and lower Limb ; and the latitude of ‘ the Obfervatory deduced from each feparately ©’s upper limb 2 Zenith. Hence Lat. | ©'s lower limb a Zenith. Hence Lat. By, 95 18° 48%. as! 4b°. rol. 19!"| Sune 8. 17%. 20, 33” | 40% 9! 48! 18. 38. 18 40. Io. To On I GAL ag 40. 9. AT Hr». «5815 98.. AE gar x9 #. 90. 171 AOe F4 AOe oO. 49. cloudy, an mm 17. I$. 59 40. 9 Sa Futte Lo TJ» ABe AT S aaakeal, mM Wweob oy ae. ose a. IF. 365 16 Aon Te: ¢% 7 ee ey. Ae Qh doubtful. 6. 17. 8. $3 AQa - Ove 34 Te akT 3. at 40. g. Th, 16,5 gr, to A TO Th E35: 10, oy ay 40, IQ. 78 fi : Mean of the above Meant of the 5 ob : 9 obfervations of ©’s¢ 40°. ro, i, 33!” fervations of the low-f 4o°..9/. 50.48l"t upper limb is: : .er limb, Do. from the 5 ob-") fervations of lower? 40.. 9: 50. 48 limb EES RES te ORR ; Mieanof both, 40°..9.) 56" roll! for the lat. of Norriton Obfervatory. And . 39 56. 54 lat. of Philadelphia Obfervatory. The difference of the above obfervations is greaterthan might be wifhed. All that can be offered to excufe them is the want of better inftruments; though Mr. Rittenhou/e thinks the differences chiefly arofe from the action of the fun on the wooden frame which fupported the quadrant. For he always obferved that when the fhutter in the roof was opened, the plummet-wire would, in a minute or two, leave the point, though it had ftood over it quietly all the forenoon. Yet, not with{tanding thofe differences, a Mean, - from fo many, may be fuppofed very near the truth; fince,. if we leave out that of June 6th, which differs. moft from the others, the mean of the reft will be but 2” great- er than it is fet down above. So far I have given Mr. Rittenhou/e’s obfervations, pre- vious, and fubfequent to the Tranfit, for afcertaining the going of his timepiece and fixing the latitude and lon- gitude of the obfervatory, from February 15th to July 8th;. by which it will appear what laudable diligence he hath ufed in thefe material articles. He hath taken many more obfervations fince; but thofe given above, are judged fully fufficient to thew that both the latitude and longitude of the obfervatory may be* depended on, and alfo the times given on the day of the tranfit. It * Asthe menfuration of the ground between the Od/ervatories of Philadelphia and Norriton,, will give the fame difference both of longitude and latitude, which was got by the different aftronomical ubfervations at each place, they may be therefore taken as aconfirmation of ¢ach ethers. ie mE * aa ey ; ae uf oi it ff | 22, MATHEMATICAL anp It hath been mentioned before, that it was on Thurfday afternoon, June rft, that Mr. Lukens and myfelf arrived at Norriton with a defign to continue with Mr.Rittenhoufe till the tranfit fhould be over. The profpeé before us was very difcouraging. That day, and feveral preceding, had been generally overcaft with clouds, and frequent heavy rains; a thing not very common for fo long a period at that feafon of the year in this part of America. But, by one of thofe fudden tranfitions, which we often experience here, on Thurfday evening, the weather became perfectly clear, and continued the day following, as well as the da “of the Tranfit, in fuch a ftate of ferenity, {plendor of fun- fhine, and purity of atmofphere, that not the leaft ap= pearance of a cloud was to be feen. June 2d, and the forenoon of June 3d, were {pent in making the neceflary preparations, fuch as examining and marking the foci of our feveral telefcopes, particularly the reflector, with and without the micrometer. The reflector wasalfoplaced on a polar axis, and fuch fupports con- trived for refting the ends of the refractors, as might give them a motion as nearly parallel to the equator as fuch hafty preparations would admit. Several diameters of the Sun were taken, and the micrometer examined by fuch other methods as the fhortnefs of the time would allow. The Sun was fo intenfely bright on the Day of the Trarit, that inftead of ufing the coloured glaffes fent from England with the Reflector, I put on a deeply-fmoaked glais prepared by Mr. Lukens, which gave a much more beautiful, natural and well-defined appearance of the Sun’s Ditk. The fmoaked glafs was faftened on the Eye Tube with a little bees~-wax, and there was no occafionto change it during the whole day, as there was not the leaft cloud, or intermiflion of the Sun’s f{plendor. Mr. Rittenhoufe, in his previous projection (fee p. 4) had made the firft external conta to be, June. 2d-g%, yy! for lat. 40” N. and long. 5". W. of Greenwich; on a fuppofition of the Sun’s horizontal parallax being 8”. He happened ASTRONOMICAL PAPERS. 23 happened to be very near the truth. For at 2". 10’ 33° mean time, the rft external contac? was at Norriton, lat. 4.0°- 9’. 56” N. and long. 5". 1’. 31" weft. Other calculations. made it generally from 6’ to 8' later for the latitude and longitude. Though this calulation was not given, to be entirely de- pended on, yet it was fufficient to make us keep what, in the fea phrafe, would be called a good look-out ; and there- fore, at one o'clock, we took off the Micrometer, which had been fitted to the RefleQor with a power of 95,and adjufted it to diftin& vifion, with the * fame power to ob= ferve the Contacts. And during the hour that was to in-: ° tervene from one to two, we refolved to keep an alternate watch through the Reflector, on that half of the Sun’s limb, where Venus was certainly expected to touch; while . the others, not thus employed, were fixing what more re- mained to be done, as follows, viz. Firft, That each of us might the better exercife our own judgment, without being influenced, or thrown into any agitation by the others, it was agreed’ to tranfact every thing by fignals, and that one fhould not know what ano- ther was doing. The Situation of the Telefcopes, the two | Refractors being at fome diftance without the Obfervatory,. and the Reflector within, favoured this defign. Secondly, Two perfons, Mr. Se//ers, one of our Com- mitee, and Mr. Archibald M’Clean; both: well accuftomed to matters’ of this kind, were-placed at one window of the Obfervatory, to count the clock and take the fignal from Mr. Lukens. Two of Mr. Rittenhoufe’s family, whom he hath often employed to count the clock for him. in his obfervations were placed at another window to: take his fignal. * Asthe two Refrading Telefcopes, wled by my affociates, took into their field but a fall part of the Sun’s limb, and were difficult to manage on account of their length and the Sun’s great altitude, it wasthought beft that I fhould not ufe the greateft power of the Reflecor ; pity de ing a larger field, 1 might be able to give notice to them; if the Contact fhould happen at any great diftance from that part of the Sun’s limb where it was expected, and which might not be within their field. But if it fhould happen near that part, we were to tranfact every ~ thing by fignals given to the counters at the clock, without the leaft notice to each other. It was alfo thought beft that there fhould be fome difference in our magnifying powers; and Tam well pleafed that I did not ufe a larger with the Reflector, as the vifion, with the power I uled, was exquifitely diftingt and accurate. | ier th a fignal. My Telefcope was placed clofe by theclock, and I was to count its beats, and fet down my own time. Thefe Preliminaries being fettled, we prepared at two o'clock to fit down to our refpective Telefcopes; or (I - fhould rather fay) lie down to the Refracfors, on account of the Sun’s great height. As there was a large concourfe of the inhabitants of the ~ .. county, and many from the city, we were apprehenfive ‘that our fcheme for filence might be defeated, by fome of them fpeaking, when they fhould fee any of the fignals for the Contacts; and therefore we found it neceflary to tell them that the fuccefs of our obfervation would depend on their keeping a profound filence’till the Contac#s were over. And todo them juftice, during the 12' that enfued, ther could not have been a more folemn paufe of filence and expectation, if each individual had been waiting for the fentence that was to give him life or death. So regular and quiet was the whole, that, far from hearing a whifper, or word fpoken, I did not even hear the feet of the coun- ters, who pafled behind mefrom the windows to the clock; and was fuprifed when I turned from my Telefeope to the clock, to find them all there before me, counting up their feconds to an even number; as I imagined, from the deep filence, that my affociates had yet feen nothing of Venus, As the Contaéts are among the moft effential articles re~ lative to this phenomenon, it is material, before we fet down the times, to give a particular account of the manner in which each obferver judged of them, and the circum- ftances attending them. Mr. RITTENHOUSE’s Account of the Contaéts. ” At 2". 11'. 39” per clock, the Revd. Mr. Barton of Lancafier, who affifted me at the Telefcope, on receiving my fignal,as had been agreed, inftantaneoufly communicated it to the counters at the window, by waving a handker- chief; who walking foftly to the clock, counting feconds as oc, ”~C ASTRONOMICAL PAPERS? | ; 4 : A veg ote anime: te AGE habs “suse: hcanee oe Mee Te Se j ee : ae + on ee Bo eee '$ ea Tg ayn aa a ae, < aa : ; cmon ~ ar ee OM 2a aa placid ise . ‘pai Ny eRe! Gin fi fee Z Sey Qe - 2 pe 2 a 4 TE aoe +— B BERR qr “TheP be ij are hase ly IU! hitenhnsti bis san s WEE cont: Be gecaapen etna see: Eiocuirprtic | 14 13 12 Ie _10 9 18 v6 > & rary Q ° “ © to 0 1) Q © [Sy et in rf 9 || Hh to w © me to | ro) ~ © — or od “I eT i Q Wen = | OK i) hed a iy reese reel Saad LSE TE Soe eS ene Bee a is ed Fy isabel ne sage . i = 3 ie it x : a Be. ‘ “ i x Tire = Va ee i ‘4 nt es = bias x ‘ * : pach 2, ee Af fing, Devine, wi aaa = Sees am fs san nnn han ae einen aitnsimnminennneccen immanent sibitnNOki iN SRRA OSCR edema ASTRONOMICAL PAPERS. 25 _ » ; . as they went along, noted down their times feparately, ‘ agreeing to the /ame fecond. And three feconds fooner than this, to the beft of my judgment, was the time when the leaft impreflion made by Venus on the Sun’s limb, could be feen by my telefcope. “* When the planet had advanced about one third of its diameter on the Sun, as I was fteadily viewing its pro- grefs, my fight was fuddenly attracted by a beam of light, . which broke through on that fide of Venus yet off the Sun. : Its figure was that of a broad-bafed pyramid; fituated at about 40 or 45 degrees on the limb of Venus, from a line pafling through her center and the Sun’s, and to the left hand of that line as feen through my telefcope, which inverted. About the fame time, the Sun’s light began to {fpread round Venus on each fide, from the points where their limbs interfeéted each other.” See a reprefentation of both thefe phanomena, plate 3. fig. 1. ** As Venus advanced, the point of the pyramid {ftill grew lower, its circular bafe wider, until it met the light which crept round from the points of interfection of : the two limbs; fo that when half the planet appeared on the Sun, the other half yet off the Sun was entirely fur- “ rounded by a femicircular light, beft defined on the fide a next to the body of Venus, which continually grew bright- er, till the time of the internal conta&.” See plate 3. fig. 2. “« Imagination cannot form any thing more beautifully ferene and quiet, than was the air during the whole time; nor did I ever fee the Sun’s limb more perfectly defined, or more free from any tremulous motion; to which his great altitude undoubtedly contributed much. “When the internal contact (as it is called) drew nigh, I forefaw that it would be very difficult to fix the time with any certainty, on account of the great breadth and brightnefs of the light which furrounded that part of Venus yet off the Sun. After fome confideration, I refolved to judge as wellasI could of the co-incidence of the limbs; and accordingly gave the fignal for the internal contact NOL. ts D at 26 MATHEMATICAL. AND..4 at 2". 28 4s” by the clock (when the appearance of Venus and the border of light where as in fig. 3. plate 3.) and immediately began tocount feconds, which any one who has been accuftomed to it, may do for a minute or two, pretty near the truth. In this manner I counted no lefs than 1’ 32" * before the effect of the atmofphere of Venus on the Sun’s limb wholly difappeared; leaving that part of the limb as well defined as the reft. From this I concluded that I had giventhe fignal for the internal contact too foon; and the times given by the other obfervers at Norriton confirm me in this opinion.” Mr. LUKENS’s Account of the Contacts. “The telefcope I ufed, being a refractor of 42 fect, giving but a fmall field, and fomething difficult to manage, by reafon of the Sun’s great altitude; I was obliged to move t often, and apprehend that I did not difcover the firit impreffion of the planet on the Sun, which my tele- feope would have fhewn. For, after one of thofemovements, on bringing the glafs to bearagain on that part of the Sun’s limb where Venus was expected, I faw a large tremulous fhadow, already fome what advanced, and feeming to prefs fill inwards on the Sun’s limb. Having contemplated this for a few feconds, and perceiving the appearance erow more dark, and make a better defined impreflion on the limb, I gave the fignal to the perfons who counted time for me, which they noted down feparately at 2”. 12! 3" by the clock. I fuppofe my telefcope might have {hewn the impreffion on the Sun’s limb at leaft 15" fooner, «© When Venus was near one half of her diameter ad~- vanced on the Sun, I faw diflindly a border of light en- compafling that part of her which was yet off the Sun, This was fo bright that it rendered that part of Venus vifible and pretty well defined, although not yet entered on the * Mr. Rittenhoute thinks that aperfon who had feen the Sun nearer the horizon, and could not fo well diftinguith between the body of Venus, and this furrounding atmofphere, would nave been near 1/ Jater than him in pronouncing the contact; and that the other 32” elapfed before the Sun’s limb (through the large refradtor he ufed) appeared totally reftored to its for- mer {plendor. + Vhe obfervers with the refra@tors were obliged to lie on the ground, with their heads bolftered up by the perfons that aififted them. : ies ~owseeorennenen tm enemies ht te aac ASTRONOMICAL PAPERS. 27 the Sun. But towards the internal contact, the circular border of light feemed to grow more dufky towards the points where the luminous fegments of the Sun’s limb were ready to clofe round the planet. This dufkinefs did not feem to part wholly from the Sun’s limb, at the time [apprehended the body of Venus to be wholly entered onthe Sun, and when I gave the fignal for the internal contact, which was noted by both the perfons who coun- ted for meat 2". 28. 58” by the clock. AndI judge at leaft from 16" to 18” more, before I faw the Sun’s limb clear of this dufky fhadow.” — Dr. SMITH’s AccounT oF THE ConTACTS. «“ The power kept on the Gregorian reflector, for obfer- ving the contadis, as hath been already obferved, was the fame which we had been ufing, and were again to ufe, with the micrometer, magnifying g5 times. I had therefore - a large field, taking in about half the Sun’s difk; and the inftrument was fo firmly fupported, with its axis ina po- lar direction, that it could not be fhaken by any motion on the earthen floor of the obfervatory, and required only an eafy movement of one part of the rack-work to manage it. With thefe advantages, any part of the Sun’s limb could be readily kept in the middle of the field, without neglecting, every 4" or 5", to caft my eye on all other parts of the limb on both fides, where there was any pof- {ibility of the contact to happen. « Within half a minute of the time calculated for the rft contact by Mr. Rittenhoufe, I fpoke to the counters at the windows to be very attentive to thofe who were to give them the fignals from the telefcopes out of doors; and turning my eye clofely to the part of the Sun’s limb where Venus was expected, I had viewed it {tedfaftly for feveral feconds, without having occafion to change my field, when I was fuddenly furprized with fomething ftriking into it, like a watery pointed fhadow, appearing to give a tremulous motion to all that part of the limb, although the telefcope flood quite firm, and not the leaft diflurbance or undulation were perceptible about any other part. " ine ee per: our roomr parm et ee MATHEMATICAL anpb «« The idea I had formed of the contact was---That Ve- nus would inftantaneofly make a well defined black and {mall impreffion or dent on the Sun. But this: appearance was fo different, the difturbance on the limb fo ill defined, undulatory, pointed, waterifh, and occupying a. larger fpace than I expeéted, that I was held in a fufpenfe of 5.” or 6” to examine whether it might not be fome fkirt of a watery flying cloud. « Perceiving this fhadow (atmofphere, or, whatever elfe it was) to prefs ftill forward on the limb, with the fame tremulous pointed appearance, the longeft points towards the middle, 1 began to count the beats of the clock for either 15” or 16", when a well-defined black dent, appa- rently occupying a lefs fpace on the Sun’s limb, became diftinétly vifible. I then quitted the telefcope and turning to the clock, noted the time it then fhewed, which was 2". I 2! Le ° Git 22" fooner than this (viz. the 16” I counted, and the 5” or 6” in which I remained in doubt at the be- ginning) was the firft vifible impreflion on the limb which my telefcope would thew; and I alfo marked that time down: viz. 2". 11 go" to 43". If this firftimpreffion is to be taken for the external contadt, | think it may be judged of almoft to a fingle fecond, by perfons having equally good eyes and telefcopes; which cannot be done, as I apprehend, to Jeveral feconds, either with refpec& to the internal contact, or even with refpe& to the moment of the firft diftin& black dent, commonly marked for the external contac?. \n both thefe, fome differences may well happen among the beft obfervers, from their different manner of judging, in refpe&t to acireumflance of fuch exquifite nicety. «“ Whether a telefcope of larger powers than what I made ufe of, might not have fooner fhewn this firft fha- dowy impreffion (that preceded the diftinét black conta) I will not take upon me to determine; though, from the time given by Mr. Rittenbou/é, L think it would, But this I can tng aon nent AN NNR ASTRONOMICAL PAPERS. 29 Tcan be fure of, that I faw the firft ftroke of it perceptible: through my telefcope, having that part of the Sun’s limb in full and fteady view; and I might have noted the time to a fingle fecond, if I had re it in that way. “* As to the zternal contad?, the thread or crefcent of light, coming round from both fides of the Sun’s limb, . did not clofe inflantaneoufly about the dark body of the J planet, but with an uncertainty of feveral feconds; the points. of the threads darting backwards and forwards into’ each other, in a quivering manner, for fome fpace of time, be- fore they finally adhered. The inftant of this adhefion I determined to wait for, with all the attention in my power,. and to note it down for the internal conta; which I did,. at 2", 29' 5” by the clock; a few feconds later than Mr. Lukens, who judged in the fame way. And even then,. though the points of the thread of light feemed to clofe, yet thelightitlelf did not appear perfect on that part of the limb till about 12” afterwards; and I apprehend that a perfon who had waited for the perfe@tion of this {mall thread of light, would have given the contact that number of feconds. later than I did, although I was later than the others. « After the ft conta, having quitted the telefcope, to note down my time, the gentleman who counted for us, and feveral others now in the obfervatory, were impatient to fee Venus before fhe had wholly entered on the Sun; an indulgence not to be denied them, as the refleGtor was moftconvenient for them. For this reafon 1 did not fit down to it again till within 5’ or 6’ of the internal contact, and confequently faw none of thofe curious appearances, on that part of the planet off the Sun, mentioned by my affociates, But their account may be fully depended on, as both of them are well accuftomed to celeftial obfervations, and: are accurate in judgment as well as fight. The fimall dif- ferences in the times of our contacfs, it is prefumed, may be eafily reconciled, from the different powers of our te= le{copes, and other circumftances mentioned in the manner of judging. At any rate, we have fet them down faithfully. 66 As SAG 30 MATHEMATICAL anp « As to the firft difturbance in the Sun’s limb, it may be worthy of confideration, whether it was really from the interpofition of the limb of Venus, or of her atmofphere. One cannot eafily imagine it to be the former, without fuppofing her limb and body much more ragged and une- ven, than they appear when feen on the Sun. An atmof- phere is.a much more probable fuppofition, not only from the faint and waterifh colour at firft, but the undulatory motion above mentioned, which mightarife from the grow- ing denfity of the atmofphere, pufhing forward on the Sun, and varying the refracfion of his rays, as they pafs in fucceflion through it. “If fuch an atmolphere be granted, it will probably ac- count for the tremulous motion, in the thread of light creep- ing round Venus at the: internal contact; which may be thus prevented from clofing and adhering quietly, till this atmo{phere (or at leaft its denfeft part) has entered wholly onthe Sun, and confequently the co-incidence of the limbs be paft. For, though the atmofphere of Venus (as far as we could poflibly judge) be not vifible on the Sun; yet that part of it which is furrounding, or juft entering his limb, may be vifible; having, if I may fo exprefs it, a darker ground behind it. «© But thefe are only hafty conjeCtures, fubmitted to others; although, if they have any foundation, it would make fome difference in the time eftimated between the contacts. And therefore, thofe aftronomers who may happen to be in the world at another tranfit, will perhaps think it beft to fix on fome general mode of pronouncing with re- fpe&t to the contacts ; either by neglecting this atmofphere altogether; or taking their time from the appearance and difappearance of its effects on the Sun’s limb. In either cafe, itis prefumed the times of different obfervers having nearly the fame altitude of the Sun, and equal advantages of weather and inftruments, would not differ fo much as . has been the cafe hitherto, even among eminent aftrono- mers at the fome place,” General i ASTRONOMICAL PAPERS. 3 General TABLE of the CONT ACTS of the Limbs of the SuN and Venus, as obferved at Norriton, Fune 3d, 1769, Reduced to apparent Time, N B. June 3d, (by the preceding tables of the work) the Sun’s center was on the meridian at rth. £8, 4g” by the aes and June 4th, at rrh. 59/. 2, and therefore gained at the rate of| 13/in 2q4hours. Hence, at noon June 3d, the clock being 1’. 11/ {low of apparent time, fhe was only t/. 9/, 48!” flow at the external contact, and 1’,.9". 40” flow at the internal contact. But to avoid fra@ions, we fay, 1/. ro” flow at both contacts. Whence—— External Contact, by Dr. Smirn, Firft vifible impreflion on ©’s limb, in form of a tre- mulous pointed fhadow, at hi mi dec, % I% 50t053 ‘A. well-defined black dent in @)’s limb, at Oe 15.15 The apparent time of the Contadls, by different Obfervers, was-—— External Contact, by Mr. Lukens. Mr, Lukens changing his field. A finall dent in ©’s limb, at «Why ARCs Qe 13. 13 External Contact, by Mr. Rirrenuovuse. Kirt impreflion on ©’s limb, at hime dec, a. Tas 49 Internal Contact, A thread of light, clofing round the dark body of 9 with a tremulous motion, at he me tec, : m, 30. (15 ‘The luminous thread be- ‘come clear and quiet in 12// Roa viz. at 2. 30. 27 Internal Contac. Thread of light beginning to clofe round @ at h, m. fee. ai 730.8 Thread of light feemed, complete, at @. 30. 94 Internal Contact. Appearance as in plate 3, fig. 3, and judged by him for the Contact, at hom. tec m 29 55 When Venus was fully entered on the Sun’s limb, and we had compared the different papers on which our contaéts were written down, and-entered them in our book, we prepared for the micrometer and other obfervations, Thofe of the micrometer reducedito apparent time, are as follow, viz. ‘4 | Apparent | Micrometermeafures | Value of } Parallaxes of 9 from@ adjufted ° time. of leaft diftance of | micromet. to thetimes of the micrometer & | June 3d, neareft limbs. of ©) | meafures; meafures, in order to the pro- ie) 1769. and 9 orleatt ditt. jection; by Mr, Rittenhoufe, = oflimbs, in e| min. and te fee. of ©’s In the | In Path {Perpendi. g : diameter, Vertical. | of ¢ to Path. ” | HAM.See. | Inches. 20ths. sooths. | M. Sec. Seconds. | Seconds. | Seconds. I] 3 F089 O. 4, 5 Te 4554 14,54 13,67 4,94 214) Th 39 oO a 2 I. 37,6 14,74 13,88 4,96 B fy 2% 4a Oe sh 2 2 1355 15,09 | 14,24 5,01 A} 332 3 or G6, 14 a 52,7 5.77 40 Tage 5313 S13 40 4 CG 17> * 3. 8,6 16,17 15,33 5523 614 35. 5 0. IO. 21,5 4. 46,67 18,45 17545 6,01 Pla SF oO IL. 19 5+ 10575 19,02 17595 6,32 845. 7 49 O. IE. 22,75 5. 14,5 19,5 18,36 6,63 9] 5. aI. 40 Oo IT. 23,5 § Lig 19,88 18,64 6,98 TO 1 §.- or 46 Ov TE Biy3 5: 13587 20,12 18,8 9593 T1 | 5. 4% 38 oO II. 17,5 5. 8,93 20,36 18,95 7,48 £2.15) $1, 1Q oO. IT. 13,5 Se 4d, 7 20,52 19,06 9,67 T3 | O29. 14 6. 10. 5,5 4. 2957 21,00 19,21 857 ta | Oa # O; 9. 40 4, 18,58 @1,12 19,22 8,82 15.| G. 4te 24 9 8 3+ 57538 21,22 19,15 9,14 161 6. 48. 12 o. BIg 3. 44,66 21,26 19,12 9531 17 | 6. 53. 30 O28 1,5 3+ 32,47 31,28 19,04 9549 1816. 56. 22 G Fi 33 3. 38,96 41529 19,02 9,56 Diftance: MATHEMATICAL anp 32 7) Dutance of the limbs of () and 9 in Chords pa-| Parallaxes to the times of the a rallel to the Equator. micrometer meafures. 2) o Gy 4 | H.M.See. | In. 2oths. gsooths. M. Sec, Seconds. ' Seconds. | Seconds. 1 | 3. 58. 53 | 17. 143 E.limb] 7. 44557] 17,0 16,1 5,40 a\ 427.18 .% 3 6 Belimbl to. t4,74] 18,16 17,18 5,86 9) 6. 4.27 \%. ©. 20 E. limb} 18." 0,08) 20,75 19,16 8,06 4' 6 9.28 \o 15. 6.5 W.limb 6.3457 20,81 195% 8,2 Diameters of @) June 3, 1769. Diameters ot 9 ong on () June 3d, 1769. 'Timeper clock ; Micrometer Value. Time per Mitiienciet Value. A. Wis meafures, ' clock. meafures, : h. m. fec. |In. 20ths. sooths. m. fec. {h.m. fec. | In. 20ths, sooths. Sec. 8. 35. 9 3. It. 13 aI. 34,16 | 3. 9,0] O% 2 4,6 54575 %. 40; 6 a tty 10 Ot, 37,34 3. 2, GO. os Lyia) 57518 B45. 8 |g 1 %e 3%. 34,16 | 3. 4.0) OF 1%. 5,25 | 57144 P.M, lode T8001] Oy a7 56,91 ba pe eee | otters QI. 3d. 15 [5 S501 2. 4 457 56,91 1%, 40; 0 eG ae 31.°33,1 50. 0'| O. $399) 157553 Mean of the above 5 horizontal “3I, 34,59 oe diameters of @ - - ~ a | Mean of the above 6 for dia- Orleaving out the ad which differs meter of Q = = = = i S7)1% moft from bo reft, and was judged : 8 ina to be taken too large; the mean of 3T. 33999 the other 4 is - - = Which gives @’s femidiameter 15/. 46, 945 that is, oxe/econd and 4 of a fecond larger than the diameter given in the nautical almanack forthe tranfit day. Yet, Venus’s diameter, though taken with the utmoft care by the fame micrometer and at the fame focus (as the Sun’s) comes out about one fecond lefs than it was expected, being 57,12; or about 1-33 of @’s diameter, The vertical diameter of @ on the fame day was gr, 31”,8at 4h. 40. P. MM, Of the micrometer meafures, the 2d, 5th, and 18th diftance of the neareft limbs of the Sun and Venus ; the iftin a chord parallel to the equator, the 1ft and 6th of the diameters of Venus; and the 1ft and 4th of the diame- ters of the Sun, were taken by Mr. Rittenhoule. The 3d and 16th diftance of the neareft limbs, the 3d diameter of Venus and the 2d of the Sun, were taken by Mr. Lukens. All the other micrometer meafures were taken by myfelf, while Mr. Rittenhoufe applied himfelf totake the appulfes of the limbs of the Sum and center of Venus to the crofs hairs of his equal altitude inftrument, Mr. Lukens writing down the obfervations and their exact time. The, micrometer meafures were all feparately reduced to their value in minutes and feconds by Mr. Rittenhoufe, and by myfelf, making the proper allowance for the error of adjuftment of the inftrument. Many more micrometer meafures might have been taken; but had we made the intervals einen concatenate ASTRONOMICAL PAPERS. 33 intervals between them much thorter than 8 or 10 minutes, they would-have: been of little ufe in the projection, and. would have crouded it too much. Nor could we have be- flowed the fame care in fetting the inftrument, reading off the vernier, &c. if a much larger number had been taken. In order to judge of the errorof the micrometer (if any) Jupiter’s diameter was not only taken with it both ways, viz. to the right and to the left, but Mr. Rittenhoufe like. wife took a mean to the right of ro diameters of a white painted circle about 3 30 yards diftant, and alfo a mean of as many to the left. This work was performed early in the morning before fun-rife; when the air was free from all tremulous motion; and the refult gave an error of adjuft- ment of 1”, 12 to be fubftraéted. from all the micrometer meaiures. s 75 It was once intended {till further to confirm the work of the following delineation, by applying the obfervations of the appulfes of the limbs of the Sun and center of Venus, mentioned to have been taken above. But the lines necef- fary for‘this, would have confufed the figure; and the micrometer obfervations being found fo exa&, any further ufe of the others, than to try how well they wouid agree, _ was thought to be needlefs, efpecially as the fra@ions of fe- conds in them could not be eftimated, fo as to come up to the accuracy of the micrometer. For this reafon, they are not fet down. . Delineation of the Tranfit of Venus over the Sun, according to the foregoing Obfervations, with the principles of the work. ‘ By Mr. Rirrennousr. cc FILE Sun’s horizontal parallax is afflumed 8,6 ¢ am at his mean diftance from the earth; from which, and the obferved leaft diftance of the centers of the Sun and Venus, the chord of the tranfit line was laid down. The Sun’s femidiameter and that of Venus are taken as by the above obfervations. One pointin the tranfit line was then fix- ed by the firft micrometer diftance of the limbs at kB ae 3 Vor. I. ah apparent 34¢0C«“ MATHEMATICAL AND! apparent time. | This line was then: divided. carefully ‘nto hours and minutes, fuppoling Venus to move '24.0,"36° ovet the Sun’s Difk in an. hour; according to’a calculation 1 had formerly made from Halley’s tables. ‘The place of Venus’s center in the tranfit line, was then marked to the times of each of the obfervations; and from thence the ap~ parent place of her center found, by fetting off the quantity of her parallax from theSun in its proper direction. About each of the centers fo found, «a circle is defcribed with the radius 28',50. the obferved fernidiameter of Venus. Blank lines were next drawn through the Sun’s center and the apparent place of the center of Venus; and on thefe the black lines were drawn from the Sun’s limb precifely of fuch length as we found they ought to be by the micro= meter; fo that it may be feen at once how far they corre-' {pond with each other, by obferving how much they exceed or fall fhort of reaching the limb of Venus. . Out of the 18 micrometer obfervations, there is fo exact a correfpondence among 14 of them, that lam well con- vinced they may be depended upon. Two of the others, as will appear by the figure, -reach about a./écond over the: limb of Venus; and the other two are {carce a fecond fhort of it. Such {mall differences might eafily have happened for the leaft inaccuracy in reading off the time, or the divi- fions of the vernier, or from. their mot being exactly taken in the direction of the neareft diftance of the limbs; that 1s in a line joining the center of the Sun and Venus. The meafures intended to be taken in chords parallel to the equator, are likewife exceeding near the truth, if it be confidered in fetting’the micrometer to that direction, we had only the truth of the polar axis to depend on, which was contirudted haftily to. anfwer the purpole, ofthe day. Three of thefe meafuresagree well witheach other; and with all the other micrometer obfervations, on fuppofing the chord in which they were taken inclined half a degree to the plane of the equator, The 4th is ftill more nearly pa- rallel, but diverging fomething the other way.) Thefe ) ' chords sonatas ment a — o~ ASTROIMOMIGAL PAPERS. 35 -chords aredelineatedin the projetion, and ferve to confirm the other ‘work, All the parallaxes of Venus from the Sun were taken from. a projection’ on a large fealé of half an inch toa fe- cond, and then reduced ‘to the feale of this delineation. Af- ter calculation fomé of thofe parallaxes, and finding that thofe got by the projeGtion came as near thofe got by cal- culation, as it was poflible to lay them down from the {cale; any further nicety was not thought neceflary. The angle of Venus,s vifible way with the Bictpptic DiGndhtobe vr pa so O.+.28t 09" ’ The angle of the ecliptic with a parallel of _ declination at 3", P.M | é Feu 513" Decreafing 53" per hour. Latitude of the Obfervatory (as above) 49°.9". 56” Hence the parallaxes were fitted to cach of the micrometer obfervations, aslaid dow ‘above! If ‘A computation be made from the firft micrometer obfervation of the diftance of the limbs, we fhall find the time of the leaft diftance of the centers of the Sun and Venus as feen from the Earth’s center to have been - ~ - S.. Cole 16" If'alike computation be made from the . 16th obfervation it will be found ; 20. 21 By comparing fome other obfervations with thefe I con- clude the time of leaft diftance of the centers to have been SG 2Ghs20f 0) -L el. at Then fay, as radius to the tangent of the angle of Venus’s vifible way with the ecliptic; fo isthe leaft diftance of the centers, to that portion of the: path, intercepted between the place of Venus at the time of the leaft diftance of the centers, and her place at the time of ecliptic conjution; thatasenss yoy 0) Rad 3) Ts) 8% 28/..29" 3: 610": go",88, But-go",88 reduced:tostime is .< =. 0%, 29/. ar! ‘Time of leaft diftance of centers is = 5+ 20. 20 Difference of which is thetime of wok ecliptic conjunction : geal yg Again 36 “MATHEMATIOAL awa Again Rad: fec. 8°. 28/ 27": 610":616"5735 the geo- centric latitude of Venus at the time of ecliptic conjunc- tion, . ! From the logarithm of Venus geocent. lat. 2.7900974. Subftra&t the diff. of the logarithms of Venus’s diftance fromy the earth, and ¢ 0.4002370 from the fun, ) ) ——- Remains the log. of the heliocentric lat. 2.3898604=4'.5"539 Then fay, as the tangent of the inclination of the orb of Venus, is to radius, fo is the tangent of her heliocen- tric latitude to the fine of her diftance from the node in the ecliptic; that is T. 3°. 23'. 20": Rad :: T. 4’. 539 : Sine 1°. 9'. 4” the diftance from the node. The Suan’s place by Halley’s tables at the 2. .+ 1,0. 46 45" time ab achatie eruntiant was plginatteu Diftance of the node from the Sun, es 9: 4 Thefum is the place of Venus’s afcendin Pet der ealvending & a, gs 33: 36 But, by Halley’s tables, the place of Venus to the above time is only That. is ten feconds too flow... g 9289.09) Se Thus gentlemen you have a faithful account of our whole work, which we could have wifhed to have reduced to lefs compafs. Had our latitude and longitude been previoufly fixed, as they had been at Philadelphia by able mathematicians, a great part of our work might have been faved, But we thought it neceflary (as hath been before hinted) to fhew that fuch pains were taken in thefe mate- rial articles that they may be depended on. And as we were happily favoured at the tranfit, with advantages of weather, and other circumftances, which cannot have hap- pened to the generality of obfervers in many parts of the world, it was thought we fhould be more readily excufed, by men of feience, for the infertion of things that might be fuperfluous, than the omiffion, of the leaft article mate- rial, ASTRONOMICAL PAPERS, 4 rial, in the account of the pheenomenon, that will never be obferved again, by any of the prefent generation of men. I am, Gentlemen, with great refpect, Your moft obedient humble fervant, Philadelphia. Fuly WILLIAM SMITH, roth, 1769. P. S. As it.is hoped that not only this province in ge- neral, but likewife the fociety who fet on foot, and the honourable Houle of Affembly, who: fo liberally encou- raged, the defign for obferving the tranfit here, may de- rive fome credit from the laudable {pirit fhewn on’ that occafion, I fhall add an extract of a letter from the Revd. Mr. Mafkelyne, the Aftronomer Royal, to fhew how well our labours have been received at home. $1 R; GREENWICH, Auguf 2, 1769. “VT THANK you for the account of the Pennfylyania I obfervations (of the tranfit) which feem excellent and complete, and do honour to the gentlemen who made them, and thofe who promoted the undertaking ; among whom T'reckon yourfelf in the firt place. ‘“ As foon as I can fettle the longitude of their places. of obfervations, with refpe& to this place, I hope to be able, from comparing them with my own, and other Ey. ropean obfervations, which I have already received, to find the Sun’s parallax, ‘nearer than we could depend onit from the tranfit-in 1761. ““T do The reader is defired to make the following correction of the equal altitudes of April rith, and 14th, as that part of the work was printed off before the miftake was difcovered, : - fi MM,» By NM. Hence appar, rs at PLM, Appar. noon; a, | he me fee.” hem. fee, noon; per % | 8. m. fec. oh. m, fec.| per clock, mi} (80) 385 “9530, 43. | clock. ‘a Bo 83.98 4 oF ae, | ee (PR dost 3 $f. t/h. my fee, = 18. 34.53 3:26, 2.1 1a. Cease | WBG., m9 29 37] It. 59, 39 which gives 1” to be fubtraGed from, inttead of being added to, the obferve. merfion of ift fatellite, April rath, and makesit 1th. 14/, 37” (as it flands corrected in the table 8.25. 49 3: 34. 56 printed above for April 11th, compared with thofe ot April 14th. a emerfion of ad fatellite, per clock, June 7th, is alfo to be read, 8h. 49/, 29”, infleadef oh. 23/, 4/, 38 «MATHEMATICAL ayn. «J do not yet know whether the obfervations made by Meffrs. Mafon and Dixon in Pennfylvania will fuflice to fetile the longitude of Philadelphia, to the exaCtnefs here requifite. I with, therefore to receive the obfervations of the eclipfes of Jupiter’s fatellites, made there in the {pring of this year, of which Dr. Smith makes mention. Thofe «which have been made here, I have fet down on the * next page, and requeft you will be pleafed to fend them to him, with my. beft compliments and congratulations on his and his fellow obfervers fuccefsful labours. 1 with al- fo to have an account of the difference of latitude and longitude between the Philadelphia obfervatory, and the two other ob/ervatories at Norriton and the Capes of De- laware; and alfo how much the State Houfe {quare dif- fers from the fouthermoft point of the city of Philadelphia, to which Meffrs. Mafon and Dixon have. referred, their obfervations. , «© When you receive any further account of the Penn- fylvania obfervations, promifed by Dr. Smith, or any other American obfervations, I fhall be obliged to you for a fight of them. « | beg you will accept of the enclofed account of ‘my. obfervations of the tranfit, and of the eclipfe of the Sun, June 3d. You will perceive that feveral phoenomena noted at Norriton agreed with thofe obferved here; but they have further obferved a curious circumftance at the firft entrance of Venus, which the low altitude of the Sun did not permit me to obferve here; as, on the other hand, fome phoenomena were noted here, which they have not taken notice of. “ Ina few days I will do myfelf the pleafure to leavefome of my pamphlets with you, which I beg you would fend to the Pennfylvania obfervers, when you have an oppor~ tunity. Lage Lot, Your very humble Servant NEVIL MASKELYNE.” Tothe hon. Thomas Penn, £/q. * They are inferted above at the bottom of page 20. The Tay | EOE Te a ' u re * ois ¢ ee i NS x | ‘ , : s ‘og 4 ag a 7 y “04 $ ) — pe, | ri) a \ i a iP «aero maser eee! at fe: bie Sa sae oe # “th GF Fe 3 7 ar IR é Bs f: Poe ee “Ee NS Ps on ; he Pe AN i “ FN ie es | UE a eS a. oth ‘ Ve | 2 \ - : Soir | , sat aN i Ea . mi ; : \\ / j ie + 2 re “0 ‘ ase Ay, ee . } ‘ sy é = yp > \ - ——.. * Nes ~— Kae ‘s ; ‘ sapere ‘ : a eo a Z tee "Ops 5 | Sey OU Pe yaaa: Ki ->s Se e % : : “a | \ tf vee eeeceteree eter ste aoe ip eg ee AT Tt 9 ——e Io It IZ {4 LS Ne A : f g 3 : i ot ; 3 rie a &, ey ae © 5 a M St ae + 8 sey SES mR =) \ Seer | i Tak Bet ee oe com is WS 4 ti 4 ‘* ' or oe eae , io a . i ARs = B i ott us ig im 2e ic. ‘aa re Hig oti 4 hy, ap ee ae 4s \ { } | TTT yd | : 1 fi Pz fF 2 Ste eheee eee a we a || @ EEE t}- es Ean Fis 1 | | ae h i! o 4 oo al ; A OEP ET Fy HSA ee avescavaie:) (14 fale i‘ SH tr L . oe 1 t A " J Wen { ¥ } / } ef hk ; é : wie + sat Bint Rigs ee: < i oe Se eS tiem nde oes a : sa = - . ae ~ 7. i } 4 a) task es eal = rs 4 iv 4 : oa aie ata ter ‘ 1 4 ‘ Teo, OES TR a Sa as ale sly nese ASTRONOMICAL PAPERS, “39 - The above letter was occafioned by a fhort account I had fent to Mr. Penn four days after the tranfit, informing him of the fuccefs of our obfervations, the times of the con-. tacts, and afew other circumftances attending them ; which he communicated to Mr. Mafkelyne. Since that, Mr. Mafkelyne has received full fatisfa@ion on all the points: mentioned in his letter, as complete copies of our different obfervations have been tranfmitted to Dr. Franklin, to com- municate to him, and fuch other aftronomers as he may think proper among his correfpondents in Europe. The — particular circumftances which I mentioned relative to the firft entrance of Venus, was the dufky tremulous fhadow or atmofphere that feemed to precede her body, and the hight that furrounded that part of her limb not entered on the Sun, which was alfo obferved by the gentleman at Philadelphia, and by Mr. Biddle at the Capes. Which of thefe, or whether both, may bethe curious cireumftance, or ¢ircumftances, obferved here, which Mr, Mafkelyne fays the low altitude of the Sun did not permit him to ob- ferve, we cannot tell; as his account of the Greenwich obfervations has not yet come to hand, We 8. An Account of the Obfervationson the Tranfit of Venus over the Sun, on the 3d of Fune, 1769, by the Committee ap~ pointed to obferve it at Philadelphia; drawn up, and prefented to the American Philofophical Society, held at Philadelphia, for promoting ufeful Knowledge, By Joun Ewine. GENTLEMEN, T doubtlefs mutt appear ftrange to many, that the pa- rallax of the Sun, which is fo important and fundamen-= tal an article in aftronomy, has not been fettled’ by aftro- nomers long ago, as fo many things in that ufeful {cience depend upon it. But this furprife is leflened by confidering, that the {mallnefs of the parallaGtic angle has eluded their moft cateful refearches in all ages, as it is but about 8 or g feconds 40 MATHEMATICAL awnpb g feconds of a minute; fo that the fubtenfe of it, were it much larger than it is, muft be invifible to the naked eye at the diftance of 6 inches, and it is hardly poflible to dif- —tinguifh to feconds by inftruments, let them be ever fo {kilfully made. Many methods have been devifed by aftronomers, which fhew the ingenuity of the inventors; but the difadvantage of them all was, that they depended upon obfervations to be made with a precifion, which no inftruments hitherto conftrudted could poflibly accomplith. The tranfits of Venus alone afford an opportunity of de- termining this problem with fufficient certainty, and thefe, from the {trict laws of her motion, happen {fo feldom, that there cannot be more of them than.two in one century, and in fome centuries none at all. Three only have been ob- ferved fince the creation, and the firft of them by two perfons only. The peculiar advantage of this phoeno- menon for determining the parallax of the Sun with a precifion which is not to be expected from any other me- thod, confifts in its being deduced from the abfolute time that elapfes between the inftants of the contacts with the Sun’s limb, as feen from different parts of the earth; or from the difference of total durations as noted by diftant obfervers, properly ftationed for that purpofe. A fecond of time being eafily diftinguifhed bya well regulated clock, if the aforefaid abfolute difference of time be carefully no- ted, in places where it will amount to 24 minutes, it will give the parallax, {mall as it is, within the hundreth part of a fecond of a degree, and confequently the diftance of the Sun and planets within the feven hundredth part of the whole. In fome tranfits this difference of time will be greater, and in others lefs, in certain places on the earth, which renders thofe that happen on the northern part of the Sun’s difc, in general, more favourable to our purpofe, than thofe that happen onthe fouthern hemifphere, Hence it is, that although much was done in this matter by the fe- dulity and care of aftronomers at the tranfit in the year 1761, when Venus pafled fouth of the Sun’s center, yet our i ASTRONOMICAL PAPERS. 4i our expectations could not be fully anfwered by the obfer- vations that were then made; as it was eafily forefeen that much greater precifion might be attained, from the advan- tageous circumftances that would attend the tranfit in 1769. The great proficience, which the aftronomers made in fettling this fundamental element, beyond what was ever known before, has only raifed their expectations and engaged their attention to improve every advantage, that can be derived from a careful obfervation of this tran- fit. If they have not been difappointed by unfavourable weather, we hope for the utmoft certainty that can be gain- ed in this matter, from the obfervations they have made, when they fhall be compared together. But after all, we muft fit down with thedifagreeable affurance that the dif- tance of the Sun cannot be determined by them, let them be made with ever fo great accuracy, within many thoufand miles; which will not appear ftrange, when we confider that his diftance is upwards of 94 millions of miles, and that an error of a fingle fecond in his parallax will give an uncertainty of ro or 11 millions of miles in his diftance. This approximation, however, is fo much greater than could be expected, from any other method, that has ever been propofed, that it has defervedly engaged the attention of every civilized nation in the world; and it muft redound to the honor of our fociety, that they have taken fuch ef- fe€tual care to have proper obfervatories erected, to furnith them with the neceflary inftruments, and to appoint pro- per perfons, to ufe them on that occafion. As the credit of our obfervations, and the ftrefs that will be laid upon them, in determining the parallax of the Sun, will greatly depend not onlyon the care and fkill of the perfons that made them, but alfo on the goodnefs of the inftruments, with which we were furnifhed; it has been judged proper to give the public the following ac- count of our apparatus, and of the pains we have taken to have it in the beft order. OL. is F As oo 42 MATHEMATICAL anv As the Society were pleafed to appoint Fofeph Shippen, Efq. Dr. Hugh Williamfon, Mr. Charles Thomfon, Mr. Tho- mas Prior, and myfelf, as a committee to obferve the tran~ fit at the obfervatory, which they had erected in this city, we fpared neither time nor labour to have every thing ne- ceflary for the obfervation in readinefs. We were provided with an excellent fector of 6 feet radius, made by the ac- curate Mr. Bird, and an equal altitude and tranfit inftru- ment, both belonging to the honourable Proprictaries of this province, which the Governor very generoufly lent to the fociety on this occafion. Our telefcopes were, a large reflector of 4. feet focus and 7 inches aperture, which mag- nified from 100 to 400 times with an excellent mi- — crometer of Mr. Dollond’s conftrudtion fitted to it, which the aflembly of the province had ordered over at the re- queft of the fociety ; arefraCting telefcope of 24 feet focus, belonging to Mifs Norris; two reflecting telefcopes of 18 inches focus, one the property of Mr. Hamilton, the late Governor of this province, and the other of Mr, Prior, to- gether with another refleCtor of 12 inches focus. With thefe, and a good time-piece, we promifed ourfelves the pleafure of making accurate obfervations, if the weather fhould prove favourable. For this purpofe we met fre- quently before the day of the tranfit, to adjuft our inftru- ments, and to remove every local obftruction that might hinder our obfervations. ; Some of us gave particular attention to the regulation of the time-piece, and therefore took the paflage of the Sun’s limbs over the crofs hairs of the tranfit inftrument, both forenoon and afternoon for many days before and after the tranfit, and particularly on that day. As it had three horizontal hairs fixed in the focus, it afforded us fix fets of correfponding altitudes, which generally agreed in giving the time of apparent noon within 2 feconds of each other; fo that by comparing them together daily, and ap-. plying the proper equations for correfponding altitudes, on account of the Sun’s change of declination between the forenoon ASTRONOMICAL PAPERS. 43 forenoon and afternoon obfervations,. we were aflured of the rate of our clock’s going and the time of. apparent noon to a fingle fecond. We did not think it neceflary to burden our minutes, with the great number of obfer- vations of this kind, that we made. Let us fuffice to fay, that they were made with the utmoft care, and that our time-piece was fixed to a large poft funk into the round four or five feet, fecured from fhaking by a brick wall at the bottom, and no ways communicating with the _ fides of the building. The long expected day of the tranfit came, fo favour- able to our wifhes, that there was not the leaft appearance of acloud in the whole horizon from morning ’till night, and the fky was uncommonly ferene. The committee af- fembled in the morning at the obfervatory, examined the adjuftment of their teleicopes anew, and appointed two afliftants to obferve the clock, one to count the feconds with an audible voice, and the other to write down the mi- nutes as they were compleated, to prevent a miftake in that article. : ee Every obferver being fixed at his telefcope, at leaft half an. hour before the beginning of the tranfit; we obferved the contacts of the limbs of Venus and the Sun at the times mentioned in the following accounts, as they were drawn up feparately by the obfervers themfelves, and are here inferted in their own words. Account of the Contacts, by JOSEPH SHIPPEN, Ese. «| obferved this very uncommon and curious phoeno- menon with a new refleCting telefcope, made by Mr. George Adams, whofe tube is two feet and half an inch long, its aperture 4,15 inches diameter, and its magnify- ing power about go times. After having well adjufted its focal diftance, the Sun’s limb appeared fo well defined, that the leaft obf{curation of it might be clearly difcerned by a good eye. ce In a i ] I : 44 MATHEMATICAL awn “ Tn order to difcover the firft external contact, as near the precife time of its happening as poflible, I kept con- ftantly in the field of the telefcope, but a {mall arch of the Sun’s limb, and only that part of it, where it was expected the planet would enter; by which means I believe I faw the obfcuration on. the limb of the Sun as near the exact time of its beginning as the power of the telefcope would admit of, . “* The firft alteration which I perceived in the Sun’s difk, was a jagged lke appearance ona {mall arch of the limb ; as if a fhadow had been caft on it with an irregular notched edge, which at every fecond, feemed to increafe with a kind of waving and tremulous motion. I firft perceived this change at 2". 13’. 47" apparent time, though I was not then convinced that that appearance was, either the phoenomenon we looked for, or caufed by the planet’s near approach to the Sun’s limb; but imputed it rather to fome duft that might accidentally have fallen on the large mirror of the telefcope, as 1 expected the conta would have fhewn itfelf by one {mall arched zndent on the Sun’s limb. And it was not ’till after twelve feconds more had paffed, that I was certain the contact had happened; for then, viz. at 2.13’. 59" apparent time, I could plainly diftinguith a fingle impreflion, or indent, in the Sun’s limb; yet it was exceedingly fmall, and without any of the yayyed appearance before mentioned. “ [cannot well account for thefe different appearances in fo {mall a fpace of time, but by fuppofing that the firft was occafioned by an atmofphere around the body of Ve- nus, which might have obfcured in a fmall degree, part of the Sun’s limb, a few feconds before the contact; and that after Venus herfelf had a@ually entered on the Sun’s limb, the brilliancy of the folar rays might have fo far il- Juminated the atmofphere of Venus, as to caufe the obfcu- ration at firft perceived to difappear, and leave only the well defined form of the planet on the Sun’s difk. 66 On ASTRONOMICAL PAPERS. 45 ‘‘ On confidering the matter in this view, I am inclined to think that the firft external contact did not really hap- pen till at leaft three feconds after I firft perceived the jagged obfeuration’on the Sun’s limb; and then it would be at 2". 13/. so” apparent time. “ But of aftronomers agree to fix the time of the firtt contact at the beginning of that obfcuration, I think it is probable the contact may have happened two or three fe~ conds before I difcerned ‘that obfeuration: In which cafe, the contact may be faid to take place at 2". 13!, 44" ap- parent time. ; “¢ In determining on the manner in which I fhould judge of the znternal contact, I confidered that after Venus fhould move on the Sun’s difk with half her diameter, the horned points occafioned thereby in the Sun’s limb would appear more acute, and approach nearer to each other as the planet proceeded till the points fhould a@tually unite. From this: refletion I was induced. to think, that the inftant of the: clofing of thofe points ought tobe fixed on as the precife time of the internal contact; becaufe Venus muft then have. paffed the Sun’s limb with her whole diameter, and both their circumferences, or limbs, might be faid to coincide. “ T therefore carefully obferved the progrefs of the plan- et, and faw very diftin@ly, as fhe moved onwards, that the illuminated: points of the Sun’s limb became better de- fined; and when they approached. fo near each other as to be within about 8 feconds of touching, which was at 2". 31". 26" ap. time, | heard one of the obfervers call out, contact; but as his obfervation did not feem to agree with the manner which I had fixed for judging of the conta®, { continued viewing with the clofeft attention, in order to fix the time of contact according to the idea’ I had formed of it; andat 2°.31/ 34. ap.timel could fcarcely diftinguith the illuminated points of the Sun’s limb to be any longer feparate; for in two feconds more they appeared to be fo far clofed as to form a fingle thread of light on that part of the Sun’s limb, which a few feconds before had been eclipfed. [therefore 46 MATHEMATICAL awnp I therefore conclude that the apparent firft internal conta& of Venus happened at 2". 31’. 34" ap. time. Yet it is not improbable that her real conta&t may have happened _a few feconds fooner, if it be certain that the has an atmo/~ phere; becaufe that might have obfcured the Sun’s limb a few feconds after Venus was entirely immerfed within the difk; in the fame manner as I judged with refpeét to the external contact, that the beginning of the obfcuration of the Sun’s limb was occafioned by the intervention of the atmofphere of Venusa few feconds before her body a@tually came in contact with the Sun.” Account of the Contacts, by Dr. WILLIAMSON. “I made ufe of a refraGing telefcope 24 feet long, which magnifies ninety times. The glafles were in very good order, and the air uncommonly ferene, fo that the Sun’s limb appeared very diftinét and well defined, whence I promifed myfelf the pleafure of fixing the external con- tact to a fecond, but the event convinced me that I had promifed too much. A dufky appearence once and again drew my attention to a particular part of the Sun’s limb, but I could fee no fuch dark {pot there as I thought Venus muft produce, and it was not till 2". 11’. 31” mean time, or 2". 13’. 46” apparent time, that I determined to ftop a watch which I had in my hand, to afcertain the time of my obfervation, leaft fome accident fhould prevent my hearin the afliftant, who ftood at § or 6 yards diftance by the clock counting feconds. At that very time I was doubtful, whether the appearance on the limb of the Sun was cer- tainly occafioned by the interpofition of the body of Venus; for though the darknefs was of fome extent along the Sun’s limb, yet the impreflion was not proportionably deep, fuppofing that it was made by a circle fo {mall as Venus compared with the diameter of the Sun, nor was the dark- nefs equally perfect; yet the fubfequent progrefs of the darknefs foon convinced me that I had not been much too hafty in noting the time of the external contac. “« When ASTRONOMICAL PAPERS. 47 ‘When Venus had advanced with a little more than half her body on the Sun, her whole eaftern limb appeared faintly illuminated: This light feemed to encreafe as fhe advanced farther on the Sun, till near the time of the in- ternal contact. By this time I was convinced that Venus is furrounded by adenfe atmofphere ofa confiderable height, which doubtlefs had prevented my fixing the external con- tat, with that accuracy I had expected, and had occafion- ed that inequality in the darknefs, which I had obferved. on the Sun’s limb,. “In determining the internal conta, which I appre= hend. was done with great exactnefs, I attended to the in- ftant, when there was a prefe&t coincidence of the limb of Venus with the limb of the Sun, as when two circles touch internally. .'This appeared at 2°. 31‘. 24” apparent time. I expected by the time the affiftant had counted another _fecond, to have feen light diftin@ly round the eaftern limb: of Venus; not fuch a radiance as had for 7 or 8 minutes rendered that part of the planet vifible; but a certain nar- row. portion of the Sun’s limb which had a very diftin- guifhable appearance from the light I have mentioneds. The edge of the Sun did not appear fo foon; neverthelefs.I fixed upon 2"..31/. 25” for the precife time of the internal contact, being certain, that no part of Venus was then off the Sun. One or two feconds more were counted before the Sun appeared diftinGly without the limb of Venus. But then. it was obvious that Venus did notthen.touch the Sun’s limb in. any part, fo that the contact was certainly over.”’ Mr. Prior made his obfervations with his. own reflect-. ing telefcope, whofe magnifying power he does not cer- tainly know, but fuppofes it tobe at leaft an hundred times. . He gave. the following account of his obfervation. of the contacts, viz. “ The uncertainty where Venus would touch the Sun’s limb made me take the following method. From 8 or 9. minutes paft two o’clock I made it a rule to pafs my eye from the lower edge of the field of my telefcope to the up- pers 48 MATHEMATICAL anp per, many times in a minute, and examine the limb of the Sun ftrictly, in hopes of difcovering the atmofphere of Venus approach, fo as to give an opportunity of taking the _ contacts of the limbs to a great certainty, In pafling my eye along the limb of the Sun, I difcovered a {mall imper- fection, which I thought mutt be the ftroke of the atrnof- phere, but in four feconds I difcovered it to be the limb of Venus, the atmofphere not being vifible on the Sun. The time therefore that I note for my external conta@ is, when I firft difcovered that imperfection on the Sun’s limb, which was at 2". 13’. 42” apparent time. When the bo- dy of Venus was fomething more than one third on the Sun, | faw her eaftern atmofphere very diftin@lly reflecting the light of the Sun fo ftrongly on the limb of Venus, as to fhew it well defined; but as it came on the Sun, it was entirely loft. The time, I note for my internal contaé, was, when the thread of light was diftin@ly feen all round the body of Venus, which was at 2", 31’. 28” apparent time.” Mr. James Pearfon, having obferved the external con- tact at 2". 13". 50" apparent time, with a {mall telefcope, belonging to the honorable proprietaries of this province, whofe magnifying power is about 60 times; Mr. Charles Thompfon obferved the internal contact with the fame te- lefcope, of which he gavé the following account, viz. “ At 2", 29'. 11” mean time, or 2°. 31’. 26". apparent time, I faw fome tremulous rays of light pafs from the up- per or eaftern limb of the Sun to the eye, acrofs, and fo as juft to touch the upper limb of Venus. Marking that down therefore as the time of contact, I counted four fe- conds, at which time I faw acontinued thread of light, like a filver lace, but ftill with a tremulous motion, round the eaftern limb of Venus, whereby it appeared to me that the whole body of Venus was then within the difk of the Sun. The tremulous appearance of the rays of light, I at firft at- tributed to my telefcope refting againft the fide of the ob- ervatory, but afterwards apprehended might be owing to their pafling through the atmofphere of Venus.” The ASTRONOMICAL PAPERS. — 49 The committee having defired me to ufe the large re- fle&tor mentioned above, I chofe that power which magni- fies the diameters of objects 300 times; with which I ob- ferved at 2". 13’. 48”. apparent time, an obfcuration on the north-eaftern limb of the Sun, gradually advancing forwards with a tremulous motion, which, from its irre- gular and dufky appearance, I concluded was occafioned by the refraction on the Sun’s rays through the atmofphere of Venus, which atmofphere foon afterwards became very obfervable to us all. From this I was led to conclude that the contac did not happen till about 15 or 16 feconds af terwards, when there was a large and evident impreflion | made on the limb of the Sun; but as the precife moment of the external conta& cannot be noted by an obferver, the body of Venus not yet being interpofed between the Sun’s limb and the eye; this contaét muft have happened about the time that her atmofphere made the abovementioned ob{cu- ration, and therefore lam of opinion that the truetimeof the contact fhould be accounted at 2". 13’. 48”, or it may be 3 or 4 feconds fooner, when nothing but the atmofphere of Venus, which preceded her body, appeared on the limb of the Sun. About the time that the center of Venus approach- ed the Sun’s difk, I faw the whole body of Venus, her eaftern edge being furrounded with a faint light which was doubtlefs occafioned by her atmofphere refracting the Sun’s rays. At 2". 29'. 11" mean time, or 2". 31/. 26" apparent time, I {aw the internal contaét, when the whole body of Venus was introduced within the difk of the Sun, and the thread of light had compleatly furrounded her, although not as bright as it became in two feconds afterwards. From what has been faid, it appears that the apparent times of the contaéts may be reprefented at one view in the following table, as they were noted by the different obfervers. ft Exeter. Contact, aft Inter. Contad. Magnifying hm. fee, h. m. fec. Powers, Tofeph Shippen, Bfy. 2%. 13. 47 Ap. T. 2. 31. 34 Ap. T. 80 times, Dr. Williamfon, % 23. 46 2. 31. 25 to 27 90 times. Mr. Pearfon, G13. 50 ee es és ie Mr. Thompfon, - ee %. 81. 26 to 30 Bese Mr. Prior, @. 13. 42 2 3X. 28 100 times. Mayfelf, a 13. 48 a 31. 26 300 times. A well-defined black r dent in ©’s limb, att eo Gaus Vou. 1, G After 50 | MATHEMATICAL anp After the obfervation of the contaéts, I applied myfelf to the micrometer to meafure the diameters of the Sun and Venus, and the diftance of their limbs at fundry times du- ring the tranfit. I had indeed frequently meafured the ‘equatorial diameter of the Sun before the day of the tranfit, and always found it to be 6 feconds lefs than what is given in thenautical almanac. The mean of 6 meafures on that day is 31’. 31".6, which differs but o”,3 or three-tenths ofa fecond from what is given in the faid almanac leffened as above. ‘Therefore I have ftated it at 31’. 31.3 in the following reduétions and calculations. Six meafures of the diameter of Venus on the Sun made it 58 feconds. I attempted to meafure it both ways, with the beginning of the divifions of the vernier advanced on the feale of the micrometer and the contrary, that the er- ror of adjuftment might have been thereby taken away. But the micrometer did not admit of it, the diameter of Venus being a fmall matter too large for this operation, However I took fome meafures this way, but they gave the diameter no more than 55”.4, which appearing too {mall were therefore rejected. About 20 minutes after the contacts, I began to mea- fure the neareft diftance of the limbs of Venus and the Sun, and continued untill the Sun was fo low, that the meafures could not be made with fufficient accuracy any lonyer. Some of the meafures appear to difagree too much with the others, and therefore fhould not be depended on; but I could not prevail upon myfelf to negle& the inferting of them; leafithe unufual agreement among fo great a num- ber fhould raife a fufpicion, in the minds of aftronomers, that they had not been honeitly tranfcribed from our mi- nutes; efpecially as there are enough, to anfwer all the purpofes defigned by them, which agree in giving the neareft diftance of the centers with fufficient precifion. Although thefe meafures are fet down in the following ta- ble with the parts of a fecond, we would not therefore be fuppofed to affect an impoflible accuracy in them ; but they are fach as the micrometer has given them when properly reduced. : Mean ASW RONGMECAL 9PAP ERS. gt a M, Time, | Ap. Time. [Nearelt dif [ Neareit dif] Par. of | Par.of ; Par. of 2 i. tance of thi tance of | 2 inthe] 9 inher} perpendic. — limbs of @] their cen- |Vertical.| Path. | to her path. | 2 1769. and 2 cers. iy June 3d, } hem, “feces hi om. fee. | mi fec, m. fee. fee. fec. fec. | Bip hu Bs 4O4m S5s* 59 de ts 8,46 | 14. 28,19 3595 13,20 4:56 | Slo fe SL iG. BT | Aes | ts. $742 14,60 13.9 . 4,04.) 373) Te Bee ra. ab 18. aor 3. 19,16 14,92 14,20, : Aj Ge td 71 3, tO OG |e. Toa | te.) Gia 15,05 14, °3 | Bote FAs 78) Be Bas 23) 8. 47 | ae 35 07 15,60 14,70 j : OG 2h. 4513. ot 0 lo. 33,08 | io. 34,3 15,76 I4,90 | a Pie or AT ST To Oy, Se ok Bea | to. 25,00 15,75 15,02 \ 8] 3) 44. gL] 3.-46, 46+) 3, 18,86] 11. 37,89 | 16,55 15,80 i GA, 2 Bila 4, 46 | 3. 53,64 |.1t. 95,65 | 17,38 | 16,56 | TO) 4c a Ao 56's oe eG tai $0,799 | To. 26,86 | 90,84 19,34 37 [6 2% 39/6. 4. 53] 4 49,49 | 10. 27,16 | 20,90 | 19,38 $510. 8 7 1G. IO Of | dv, 44529-| 10. 92,38 |. 26,96 19,42 39 | 6. to. 4)6. 12. 18 | 4. 43,52 [ 10. 33,13 21,0 19,44. 40 |G. 18. 37/0. 46. 57 | 4. Gos8 lic. 46,07 41,04 19,46 Al |O: O1..40|6. 54. 3.) 4: 34,061 10. 53,50 21,10 19,48 42 | 6. 96..13 6. 98. 27] 4 13,81, tr. 0,84 | at,14 19,50 43 \6. 32. 18/6. 34, 32] 4 1,46] 1%. 14,19 | 21,18 | 19,50 44.|6 33, $5 |6. 36. O11 4 3,42 | 11. 13,23 21,20 19,46 4510. 3%. OIG. 35. 43 13. 58,50 [1 15,45 21,22 19,43 46|6. 38 5516 at. 9 | 3. $4,290 | 18. 22,30 | 21,24 £9,40 9 Ov aks. 89:| Ouodbe 58) 2be 4073 | at 26,92 21,26 19,36 48 |6. 43. 571}6. 46. 11 | 3. 44,94] 1%. 31,71 | -21,28 F 4916. 46. 2516. 48 39] 3. 42,98] tr. 33,67 | 21,29 : 50.16. 48, 4916. Gh 3.) 3» 36,40] tI. 39,19 21,30 SiG. Fa PPO 5h. «311° 3s 28,64) 11. 48,01 a1,34 Sa 7.9. 117.24 15 8 C8 | im 7457,| 238 Ooty. & B41 7: 6. 47 | 3-4 4,52] 12. 12,13 21,39 54 1% 201 11. 40 | 3 5,92 | 1a. 11,83 21,40 52 MATHEMATICAL anpb The foregoing nearefl diftances of their centers are de- duced from the meafured diftances of their limbs, taking their diameters as they are ftated above: And the paral- -laxes are not computed, but meafured from a projec- tion of the difk of the earth as feen from the Sun, the pro- jection being 21 inches and an half in diameter. The latitude of our ofervatory in Philadelphia is deter- mined from the obfervations of Meffrs. Mafon and Dixon with the above mentioned fector. From a mean of thirty obfervations of the paflage of fome ftars over the meridian, they found the latitude of the moft fouthern point of the city of Philadelphia to be 39°. 56’. 29”,2. Our obferva~ tory is north of this point, 26,2 feconds, and therefore its latitude is 39°. 56’ 55"54. In order to determine the parallax of the Sun, from the foregoing obfervations, it is neceflary that our longitude from fome fixed meridian fhould be afcertained with the moft rigorous precifion. For this purpofe we have obfer~ ved various eclipfes of Jupiter’s fatellites, that they might be compared with the correfpondent obfervations made at Greenwich and elfewhere, when we are furnifhed with them. Eclipfes of JUPITER’s SATELLITES, obferved at Philadelphia, with a two fect refletor. D. hy in. fess D. i. m. fée. 1767, April 3, 7. 11, 23 Em. 2d. Ap. T.| 1769. April 3, 14. 50. 48 Im. 17. Ap. 'T. May 30, 10. 15, 3% Em. 1. If, 9. 49. Ta Int. 3d. | Fune 13, 9. 18. 6 Em, 2d. 1%, 11. 15. 49 Im. 17, 1768. Mar. 3, 9. 46. 49 Im. 17. May §, It. 30. 28 Im. 17, April 9, 19. 37. % Em. Tf. With a four feet reflector, G35 0° Be 56. 50 Em. rf. fine 4, Br 44. 37 Em, a7, May 12, 10. 33. 9 Em. 2d. 22, 8. 27. 35 Em. 17, 1769. Feb. 16, 14. 21. 51 Im. Tf, 29, 10. 21. 55 Em, 1. bo, 15: 42. 1 Im. 2, Ang. 23, 12% 15. 48 Em. rf, ay, 16. 10. 21 Im, 1/7. Sept. 11, 7 44. 41 Ein. a, Mar.7, 1% 45. 21 Im. ad. Since the foregoing account has been drawn up, we have been furnifhed with fome obfervations of the eclipfes of Jupiter’s fatellites, made by the revd. Mr. Mafkelyne, aftro- nomer royal, at Greenwich. By comparing thefe with the like obfervations made at Philadelphia and Norriton, we are enabled to fettle the longitudes of our obfervatories, But ASTRONOMICAL PAPERS. 53 But as there are but two or three of them correfpondent with ours, we muft have recourfe toanother method; which is firft to compare them with the calculations in the nau- tical almanac, which were made for the meridian of Green- wich, that the error of the tables may be difcovered by the mean of them; and then to compare ours with the fame calculations, applying the errors of the tables to the longitude deduced from this comparifon. We may depend upon the refult of this method with much more confidence, than upon any fingle obfervation. Here follow the Apparent Times of the Greenwich Obfervations compared with the calcula- tions of the Nautical Almanac, 1769. D. h. m. fee. Mar. 29, 12. 2§. 7 Im. tf obf. at Green. 29, 12. 24. 26 Do. p. calc. of N. Al. 41 Error Welt. Apr. 11, 14. 50. 23 Im. 2d obf. at Greenw. II, 14. 50; 4 Do. p. calc. of Nv Al eee mmm einen gnc mat 1765. Iv h,- mr, feo, a April 28, 14. 35. 17 Im, 17 obf’ at Green. 28, 14. 36. 14 Do. p, calc, of N, Al. 57 Urror Eaft. May 6, 11. 51. 2 Im, ad obf, at Greenw. 6, 11. 51. 45 Do. p. calc. of N. Al. 43 Error Eaft. May 16, 9. 3% 15 Em. 1fobf.at Greenw. 16,. 9: 31. 7 Do. p. calc. of N. Al. 19 Error Weft, 12, 16. 16. 13 Im. 1/ obf. at Greenw. 12, 16, 16, 13 Do. p. calc. of N. Al, one te ee Ae 60 | 1. 8 Error Weit. Fune 8, 9. At. 16 Em, 1f obf. at Green. | uly 1, 9. 50. 24 Em. 1f obf. at Greenw. 8, 9. 41. 26 Do. p. cale. of N. Al. I, 9. 50. 37 Do..p. calc. of N, Als peer gene ee nr 13 Error Eaft. etna eam pt io Ertor Eat, 35, 1. 35. 53 Eni. if obi wt Green. 15, TI, 34 §5 Dovp, cale. of N.-Al, athe Ga Error Weft. Now although the errors of the firft fatellite appear confi- derable, yet if we reje&t the obfervation of the 16th of May as being too near to the time of Jupiter’s oppofition with the Sun; the mean of thofe, which give an eaftern meri- dian correfponding with the calculations of the nautical almanac, exactly counterbalances the mean of thofe which give a weftern meridian correfponding with them, 'There- fore we have nothing to-do but to reduce all our obferva- tions at Norriton and Philadelphia to the meridian of Phila- delphia, and then compare them with the calculations in the nautical almanac. The 54 MATH EMA YIGAL \4+p The Norriton obfervations of the eclipfes of Jupiter’s firit Satellite are as follow. ; Dy: heemy-fees ’ 1769. Dy: h. m.:fec, 1769. Feb. 16, 14. 21, 10 Im. If. May 14, 10. % 14 Em. 17 doubtful, 43, 167 05. Imi, at} °Il.) 53-13) im, 3c April 3, 14, 49. 25 Im. 1. Yune 0, 10. 1.32 Em. 1% 10, 16. 46, © Im.-1f. 9, 8 436-44 Emme ad ti, i704. 377m. 1/7, T9319 de Tob Li, May 5, 1x. 29. 27 Im. If. Now if we compare the correfpondent obfervations at Philadelphia and Norriton on the 16th of February, the 12th of April, the 5th of May, and the 7th of June 1769, the difference of our meridians will be found from. the mean of them to be 57 feconds of time. _ This is farther confirmed by the obfervations we have made on the tran- fit of Mercury over the Sun, on the gth of November, ‘1769, which being compleated before thefe fheets were printed off, we have judged proper to infert. Apparent Time. he th. dec. j "The external contact wasat 2. 36. 9 by the meanvof 4 obfervations at Philadelphia, And at 2. 35. 17 by the mean of 3 obfervations at Norriton, The difference is 5% The internal contaét was at 2. 37. 34 by the mean of 4 obfervations at Philadelphia, Andat - - - 4% 36. 34 by the mean of 3 obfervations at Norriton, The difference is nae Therefore the mean of both thefe makes the difference’ of our meridians 56 feconds of time, which muft certain- ly be more accurate than what is deduced from a few cor- refponding obfervations of the eclipfes of Jupiter’s fatel- lites; both becaufe they afford 24 comparifons, all nearly agreeing among themfelves, and becaufe thefe tranfits, in the judgment of moft aftronomers, afford the beft oppor- tunities of fettling the longitude of places. Hence if we add 56 feconds to the time of the Norriton obfervations of the eclipfes of Jupiter’s fatellites, they will be reduced to the meridian of our obfervatory in Philadelphia, and may be ufed in fixing our longitude from Greenwich, in the following manner. The ASTRONOMICAL PAPERS. 55 The calculated time per Nautical ; ‘The obferved The Norriton | Lhe difference Almanac. Time at obf. red. to the | of merid. of Gr. . \ Philadelphia. merid. of Phil, | and Philadel. Dr hs my fee. Die hi ete | is he. i Tees D. h. fec. 1767. May 30, 15. 165 TO Hind fy | $0, 10715639) es fe 5, Oo 36 Fune 13, 14. 17. 37 Bm. ad. | 13, 9. 18. 6 “ss 4, $9. 3t 1768. Mar, 1, 14. 48. 24 Im. Tf. t,o, 40 ap pe ee ee April 9, 15. 36. 34 Em, rf Gin G7 oe |= = = = 4, 59: 3% Os, XG. $7. AO bth 1 35, 8 56 $01 = = = = = #0. 50 May12. 15. 34. 11 Em. Qe. °7.10, 15 83 9 i* Ss = = * 3s ty 1769. Feb. 16. 19. 2% 2gim. Tf, | 16, 14. 21. 5E | - - = = = s 6, 38 16, 19. 22. 29 Im. 1f - = =e TO, 14. 43 «6 ©, O23 BO; 20a. So Is Ga] 80, as. Ae Teor SS 4, @. i a3, 91, 20.95 lt. afe | 395,20. 16 or | * eos Sy Oe t4 99, 21. 16. 35 Im. Tf, - es a3; 36. 4 87 Be Gc 98 War 1% 17,46; elie Qe [E71 dd. aT fe M8 Be Or 4G April 3, 19. §1. 24 Im, tf. 3,014. JO. 48 | = <8 eG BG 3, 19. §1. 241m. if. soe oes 4, Tay 50: Ot de 8 To, 21, 47. 141m. rf. - - = = To, 16. 46. 56 s 6. 16 fi; Ta. $6", 4im. So Pit, 0, 49. TA Ae es 5; Oc 5° ia; TOO. te mY ka, 11. 25, ag |= = = a GO. BA £2, 10, 10, tg ihn Tf] = = = Ta. Tr. Tse 33 5,70 40 May 5, 16. 31. 20 Im. 1/7. $) 11, $0.39 | = =, = «+5- 4. O58 ‘SyerGy, 81.20 im,’ 17. - «ss S57 t8.-G00 23 SO 87 aI, 16. 56. 49 Em. if, = eos OI, Ti. £6.7-9 $5. 0: 40 Sfune 6, 15. 12. §9 Em. rf - = ee 6, 10. 12. 20 fe Oe 7, 13. 45. 13 Em, 2d, a, 30. Ad 37 | = 8 ¥. 0, 50 4, 13. 45+ 13 Em, 2d. == "= y, 8. BA: 39 5 O34 13, 17. 6. 31 Em. 17, ot ee B9s 00s 5589 5s O34 ao, Toe Oe Ge EMER F225 R47 35.) en So 3S 49, 15. 22. 17 Em. Hi, | 25; IG, 2155 {= = = = = ¥, 0, 16 Aug. 23, 12 15. 49 Em, afc =| 2Qy) 9s T§uA@el= = > oe = houa oOo nT Sept. 11, 12. 45. 10 Ems ad. | It, 7. 44:40 [= = - s, 6. 35 Now if we take the mean of all the 21 foregoing deter- minations of our longitude from Greenwich, by the eclipfes of the firft fatellite, rejecting only thofe of March ift, and April gth, 1768, which differ moft from the others, the refult will be 5". 0’. 35" for the difference of our me= ridians. ‘Thefe ought evidently to be rejected, as they dif- fer near twice as much, from the mean of the reft, as any other of the determinations do, yet the retaining of them will make no difference in the refult. If the mean deter- mination of the longitude be taken from the immerfions alone, rejeQing that of the ift of March, 1768, it will be s". o!. 36", and if from the emerfions alone, it will be fc. oo’. 34", when the obfervation of the oth of April, 1768, is excluded. Therefore the mean of both, (which fhould always be preferred.) is gel aneds Asa farther confirmation of this conclufion; if this dif- ference of meridians be applied to the Greenwich obfer- vations . ig 56 MATHEMATICAL anp vations, of the firft fatellite, rejeCting that of the 16th of May, to reduce them to the meridian of Philadelphia, and if they are then compared with the calculations in the nau- tical almanac; we fhall have the fame refult from them allo. The calculated time per Nautical Al-'Greenwich obfervations re-| Difference of meridian of manac. ‘duced to the meridian off Greenwich and Phila» Philadelphia. delphia. E769. De he mutec.. D. he m. fee, he. im: lec, Mari 29, %4. 44. 26 Im, iil: 2, 7 Fh, 3a Anon 54. April te, 46, 16, 43 Tm, xi, Id; Ht. 15, 38 So Oe a8, 14. 36. 14 Im. af, 28, 9.34. 49 5 B34 Sune 8, G 41. 26 Emit S, 40 4G, At 5 Ge a 32; Sas OG em Igy 6,-3.4. 50 ge hor 37 Fuly %, g. $0. 97, Hm. rit, In 4. 49s 49 $1. On 48 April tt, 4 50. 4 Im. ad. B15 9.1495: 48 3 6, 16 May 6, 4. 51. 45 Im. od. G, 470, JO. 49 5 yy. 18 The mean of thefe determinations of the longitude, from the Greenwich obfervations of the firft fatellite, is 5°, 0’. 35". But farther if we take the mean of all the determina- tions, derived from the eclipfes of the fecond {fatellite, it will be found to be 5°. 0’. 37". And laftly, if the mean of all the determinations from the eclipfes of both firft and fecond fatellite be chofen, the deduced longitude will be 5". of. 35". So that we may fafely conclude, that the dif- ference of meridians between Philadelphia and Greenwich, is 5". o'. 35"; and that Norriton is 56” of time weft of Philadelphia, and its longitude is 5°. 1’. 31”. weft. With this determination we muft be contented until farther ob- fervations are made, by which it may be confirmed, or ren- dered liable to exception. Thefe obfervations are fufficient to determine every thing relative to the theory of Venus, and the parallaxes of the Sun and planets, as may be feen by the annexed projec- tion of the tranfit, and the following calculations. Al- though the parallax of the Sun may be obtained from the obferved neareft diftance of the centers of the Sun and Venus, yet this method cannot be fo much depended on, as the comparifon of the contaéts of the limbs obferved in proper places, where the abfolute difference of time is confiderable. Neverthelefs, as the public feem very impa- tient ASTRONOMICAL PAPERS. 57 tient to know the refult of what was done in this place, I have endeavoured to deduce it from our obfervations alone; and flatter myfelf, that in the conclufion it will be found pretty accurate; as it is nearly the fame with what I had before found it to be, by an hundred and forty determina- tions of it, from the obfervations of aftronomers on the tranfit of 1761; and alfo from another method, the in- vention of the celebrated Mr. Stuart, of Edinburgh; both which I have now annexed to the following calculations. Having thus collected together all the elements neceflary for the enfuing calculation, before I proceed to it, I mutt in juftice to Dr. Williamfon and Mr. Prior, obferve, that of the micrometer meafures, the 2d, 3d, 19th, 20th, aif, 22d, 23d, 24th, and 25th were made by Mr. Prior, and the 35th, 43d, 44th, and 54th by Dr. Williamfon, with the fame adjuftment of the focus, that I ufed in the others. I have taken the trouble of making above fifty determi- nations of the middle ef the tranfit, and find from a mean of them, that the neareft approach of their centers was at 5°. 21’. 27" mean time, or 5". 23’. 41",7 apparent time, which was haftened by parallax 4’. 48” at Philadelphia; and therefore, that the central apparent time of the middle of the tranfit was 5". 28’. 29",7, according to our meridian. By comparing together eighteen determinations of the neareft diftance of the center of the Sun and Venus, I find the mean of them to be 10", 3",58, as feen in Philadelphia. But fhe was then depreffed 6”,91 by parallax; and there- fore, the geocent. neareft diftance of the centers was 10’. 10” ,49=610",49. ‘Therefore fay, As 72626,45 the diftance of 9 from the ©: 28879,55 her dilance from © 3: 610,49: heliocentric diftance of their centers. 4. 861,0949 4, 460,5904, , 2, 985,6785 a@e 7. 246,2689 % 385,1740==2242!',7583==4'. 2!",7583 the heliocentgic diftance of their centers. As, 3°. 23.! 20! the incl. of Q orbit to the eclip.: R::8, q/. 2”,758 : Sine of ©’s ditt. from the node of 9, 8. 771,6803 TOv = ee 7-_970,2506 8. 291,570321°. &. 20',23 © ditt. from the node of 9. VOU oh gi Now 58 MATHEMATICAL ann Now fuch is the peculiarity of the orbit of Venusand her horary motion at that time, that we may indifferently fay, ‘As$, 1°. 8. 207.23: Rad::5, ro/. 10,49: 8, of the angle of her vifible path with the ecliptic 8°. 33/. 11,5. ant Or asl’, 4/. 2.7583: T, 10. 107,49 +: S, 3°. 23/. 20: S, of the angle of her vifible path= 8°. 2 ip Tooke “ oriattly, “it thould be deemed more eligible to deduce her horary motion from the foregoing meafures, and from a comparifon of it with the horary motion of the Sun, to deduce the angle of her vifible path, it may be done in the following manner, and will be found to be nearly the fame. For let A B reprefent the horary motion of @==2'.392375 (fec fig.'2. pl. 4.) B A C=sthe inclination of the orbit of 9 with the ecliptic==3°. 23'. 20//. A C=the horary motion of 9 =3'.952942, as it may be deduced from the faid meafures. ‘Then the angle DBC will reprefent the vifible path of 9 with the ecliptic, and may be found as follows: : . Let 2/.392375=horary motion ©) 3.922942—=horary motion =237!. 17652 whole Log. is Q 375. 0716 — As 6.345317=fum of their horary motions «= < = '* 0.80245 34 Isto 1.560567=-difference of their horary motions - = = 0.193,2825 So is cots of Half of 3°: 93/. 20, arcot. 19. ail. gos” = = I1.528,9452 To 'T, of half the diff. ofthe angles at B & C==83°. 8! 27! 9==10.919,774% To which add half the fum of do. - - 88.. 18.20 171. 26 47,2andthe fupl: ofthisis 8° 33’. 12.8 = ==the angle of the vifible path of @ 916,65=the difference of the femidiameters of © and Q 610,49=sthe geo. neareft diftance of their centers, Sum, 1527,14==3- 183,8789 Diff. 306,162. 485,9484 2)§. 669,8273 the log. of the fquare of half the tranfit line between the in- ternal contacts. 1s 2. $34,9136—the log. of half the tranfit line between int. cont.=+683!,776 247! 17652=:2. 375,0716=the log. of @ hor. mot. ; ao ©. 459,8420=2h. 88298a==ah. 52/. 58/,7—=the femidu. between the in, cont, 974,65==the fum of the femidiameters of © and Q 610,49==the geo. neareft diftance of their centers. Sum, 1585,14 3. 700,0677 Dif. 364,16 2. 561,2922 —— et 2) 5+ 76153599 ; 3. 880,6799==the log. of half the tran. line between the ext. co.==7597,766 a. 375,0716=the log. of 2 hor. mot. . 0. 505,6083== 3h. 20338==3h. 19/. 12/,168=the femiduration between the external contacts. AsR: Sec. 3°. 33/. 11,5 1: 610,49 : geo. latitude of 8 IO -- - 10. 004,85 7% a, 785,6785 4. 790,535 7==617",356== 10. 17!,336 = = |§$ 49 54 /Tobolfki, ; - “17. O21 12. 49. 2O$|13, 7% 39% | 5 i. 50 Cape G. Hope, | - ” _ z WEG SS. a oe Bo - : Rodrigues, - - - “ Id, 35. 47 |1% 5g. 18 - - Calcutta, ” ~ | 8, 20. 58 T4. If. 34 |t4. 37. 38 br FOr 36 Madrafs, Fopghe lO oh Fe 470 55 13. 39. 38 |13- 55. 44 5. SI. 43 'Tranquebar, ” - - . a alae es Wor, 38 Great Mount, | - % ” 7 é of- = = = | 5. 51, 20 N. of ASTRONOMICAL PAPERS, 65 IN. of Plac Latitude, i f Pl 8 atitude fae, eee aces, | Latitude, | Longitude re Jae ae "sa P79 fr. Greenwich, Greenwich, 51. 28, 39N.lo. 0, 0. ar os SS if Shirb.Cafle, 51. 39. 22 Noo 4! rw. |] Camenimh [69:38 ON.| 4. ar. 28 Sav. Houfe, - = 10 o 3a. WwW. Aen ot: “i 40. 30N.J 1. 5. 39 E Spit. Square,| = = 10, 0: 16zw. || Tors 00. 27. ON 3. 28. 33 E |Chelfea, oc = Clore wo we tl catch 65. 50, 5ON.| 1, 36, 48 EF Letkard, — |s0. 26. 55 Nio. 18. 32 w. {| 'Toboliti. 64. 13. 30N] 3. 51. 50k Paris | 4 obolfki, 58. 12. 22 N, a E 9 48. 50, 14 Nio, 9.16 FE Capea. Hi Sel Ms 340 52 Bologna, [44. 29. 36 Njo. 45. ar. E. || Rolirigues, ise, 35° 42 S| T 13 35 E Rome, Al. $3. 54 Njo. ek ane 19. 40. 40 S| 4. 12. 34 E Drontheim, |63. 26. 10 No. 44, °3 E Yalcutta, 2% 30. ON, 5. 53. 44 E Upfal ee | oe is & ON 5.gege @ Sth khol 59 SI. 50 Nit. Io. 26. E. || Tranquebar, |10. 56. oN 3. 8d, — olm, [59 20. 30 Nit. 12. 26 KE. |] Great irate - ae x be P , : ¢ Parallax of the SUN, sane 3 tide ~ ae ce eae of the Limbs of the SUN and ’ “anfit o, . Cape of Good Hope & i Cape & Sherburne Cajile, Cape & Ch elfea, h. ma. fec. WT. any tee. Paral. h Parall., 9: 39. 50 Cape, & 8] 9% 39: 50 6° oho. ve - : ‘é awe Diff. Longitude, pals diff. longitude, I. 14. 1s ay | - oy o 22. TA 8. 2 | ee 5. 34 i are Lefeard, ; a ABS. 14 Sherborne 1,32] 8. 18 4 Chelfea, 1%. 14 : i : . Seen 7+ 20 7" 30 ea | es Par B65, ‘ebeeaibea Suis Par. 87,73)? \ gp ea a ini se { e Oe Saville cen es 8| 9 a oe Spittal Sores Pe igs Cape & Greenwich. ; ace . ‘| 9: 39» 50 6.8 | I. 14; I. 13 | vt Ie 3, | Ea an ie it eee e 2 5 | meee ? — 8. 18. AI Spit. Sg. I. 1 : 8. 19. 0 Greeaw, 3. 14 Sun's Par. 8 + 19 qs 16. 7- IQ 7. 15 o. ae Sun’s Par, 8,497 Sun’s Par. 8,42 ? Cape & Paris. , Cape & Drontheim. Cape & Bi ; | 9 39- 50 6 8] 9: 39. 50 a 4 T9 |_O« 29: 32 ©. 28. 14 . 8.3%. 31 to. 8 ro Er ok By 9. II. 36 8. a8. a7 0 54/9 tag m 38] 9. 4. 57 oi 7 4 qc 8. 29 C4o to é, 39 . ere Sun’s Par. 8,54 Sun’s Par, 8,23 Sun’s Par 8 54 Or. i Gape & Rome. Cape & Calmar. y a Sas ey eee 94390359 6. 8] % 39 te 6 8] 9. 39. ry 6 8 0. 23+ 4% Bele ake) oO. 3. 9 O. 10r 8 9+ 31. 54 “9. 36. aL 9.9. 36 Oy 1g | O34 F591 9. 28 6 Ay on 6. 32 6 a1 8. eh Ce am er Ee -Reagert Sun’s Par. 8,74 |___Sun’s Par. 8,62 Sun’s Par. 8,60. be Cape 8 Hernofand. ~~ | Cape & Stockholm. ee ee 9 39. 50 bee 8) 9 89. $0 6 8 ee oe. os 9 0. tg Se ier ' or 3% a3 | 9. 38 4m raat 9. 28, 52 2. 26 | 9s gO: 10° 2, 18 | 9. 45. 59 a 38 8 Fs B34] 8. 31 Be BOe Bag. Cees Sun’s Par, 8,78 _ Sun’s Par. 3,58 Sun’s Par, 8,68. . Cape & Tornea. Cape & Cajanebury. a Ope K: Tololfi oO 39:50 oe. 8 9: 39: 50 bi § 9. 39. §0 « “% HELO, 3. 33 jbo. 38. 15 3.39.. 17 Ge Gr 8 | To. 18 § Td. 59. 07. hs 8 SE 8 a ae | _% 59 ia. 49. 20 a 45 | 8. 55 G13 | 9. 6 9. : —— i Sun’s Par. 8,22 Sun’s Par, Sag Voy Par. 8,6 oe i Vou. I. = Cape atrooemamataenee ee Se ae 66 MATHEMATICAL anp Av 20 4. Sun’s Par. 8,80 Capes Madrafs. Cape & Calcutta. Gape & Rodrigues. Parall, Parall. Parall. h. m, fee, ee les sees hh Tee: wo | he m. fee poet g- 39. 50 6 8. | 9+ 39. §0 6 8 | 9 39 50 by 8 de 0s 35 : 4. 49. 9 % 50. 59 13. 46. 25 4. 19. 59 12. 38. 49 E3. 39-38 00-36 \t4. Lin 34 M% TA ia. 35. 47 oie ae 6 8. 25 8. 2 oF yt Sun’s Par 8.74 Sun’s Par. 8,55 Sun’s Par. 3,54 Rodrigues Lofkard. Rodrigues & Sherburn _ Rodrigues & Chelfea. 12. 35+ 47 3 7 \E% 35. 47 7 tee Gee AT. OG he Bt. 6 4A. 2G. 35 4, Te TA 8. 42 | 8.09. 12 + Wd 33 Gor at Tr. 4 | 8. 15, a to A ae a os i, it ree Ag eee 4. sun’ 3 Par. 8,00 29 : Tban't Par. 8,86 Rodrigues F Saville houfe. Rodrigues & Spittal fquare. © ci? s Par. 3,60 4. 18 12. 35. 47 3: 7 [2% 35. 47 a7 4. 13. 4 Av 1% 50° 8, 2% 43 8. 22. 549 8. ve oY) 17 rr |. 19; 4r I. Ir . 16 Ci, 4 Sun’s Par. 8,44 Rodrigues & Greenwich. 12, 35. 47 7 A 12, 34 pS. 93, 13 io. 49. 0 i 4f A. 13 4 16 Sun’s Par, 8,33 Rodrigues F Paris. 7 Rodrigues & Drontheim, Rodrigues & Bologna, 12. 35- 47 3. ‘(es 35: a | o - x 7 fe 350 3. 28. 3. 27. Or 3% 29 qe = 9. 8 34 8, 27 0. 54 is, I. 45 % 38 |_9. 4 57 0. 4 at ee meee 5. 45 3-37, 3: 36 * sun’ s Par. 3,53 Sun’s Par. 8,05 Sun’s Par. 8,54 b Rodrigues & Rome, j Rodrigues & Galmar. Rodrigues & re T% 35+ 47 5.. 9 Ae oS 47 3. 7 [Ed 35s “4 9 (3. 4% 4t 3. 6. 55 3. % 8 | arr eaey 4 i Os 5% 9- 33° 39 . 6 G13 “ 43» % tr. 59 |_9: 28 In 24 3. 30 3. 20 Be 1d, 0 5 33, 5. Sun’s Par. 8,92 Sun’s Par. 8,67 oe ald 8,62 Rodrigues F oe ; Rodrigues SF Stockholm, bai 558 Ag & ~ ; aes rn nea eae 9. Sar AL 5. 39 9. 51. 40 4 nd be 2. 26 “ a Ms 18 | 9: 45+ 59 30 abe 4B 5. ga |. 3: 39. “bas 5+ 47, 5 gre es iS, pePar, ares “4 he's Par. 8,51 a 8 at fe Rodrigues (oa Torna Rodrigues & Gajaneburg. ei ee o ia i. ; ry eee a 5 ee SEs S 10. 15. 3 12:36). 2 ‘ 54. 8 + BS NO) 8. 59 a 5g | ts oP 3. 35 sear 6, 1 e eb . AS O43 ean Par. 8,07 as Sci Par. 8,45 Sun's Par. 8 156 Rodrigues & Calcutta, Rodrigues & Madrafs. eS ae i & ne vt * oe a ae ee ng sae ta 10. 2. 43. 23. « 56 t4, 10. 37 1G. 43 22 Ve Se § 14. It, 34 % Th \13. 39 38 0. 36 tort = 4 Soy) 5. Ot 3. 45 3. a5 , aaa Par, 8,55 Sun’s Par, 8,58 “sun? s Par. 8, 16 Lobolfki ASTRONOMICAL PAPERS, 67 TF ebolhi to Chey Fe. Tobolfti & Saville =. Lobol/ki & Spittal Square. P I. I Sun’s Par. 8,39. I. 22 Sun’s Par. 8,61 Paral, Aled arall, Hy ta. feos h. m, fee. , Dy th. fee, sa: 12. 49 20 . Fe T%. 49. 20 $. 35 11%: 49. 20 << = 4. 33. 3% Ay 33. 42 a ga 9 8. 13. 48 BP th. $8 t. 16, 2 8. 18. 4 ty Ir | 8. re. on oth Ue |. S38. 4r mr IF a. 16 % 24 2 34 % 4A 2.30 oer Sun’s Par. 8’,02 Sun’s Par, 8,99 Sun’s Par. 8,85 Tobolfki SF Greenwich. Tobolfki & Paris. Tobolki & Bologna. 12. 49. 20 3s 3 [IRE 49 20 35 [14° 49: 20 3 Ay 3% §% A. 3. 36 3: 47+ 3h “B. \TO. 28 8.25. 44. Gi ag 8 Ip 6 ton | & : . 27 O 54.1.9 4 57 O. 29 | ai 3 a Ade % At a8 x 6 OT Sun’s Par. 8,97 “ine s Par. 8,60 Sun’s Par. 8,59 Tobol{ei F Kome. Tobolfti & Calmar. Tobolfei & Upfal. 12. 49. 20 3. 35 12> 49 20 gi 3g) [Tek ag 20 3. 35 3. Am 59 3+ W7- 13 3. 22. 26 g. O..at 9. 2a. 7 O26. 54 9: 9» 36 O13 | 9. 23. 40 i. 59 | 9. a8 6 % Ot 3. IS a 2% Te 33 Te 36 I 1% ig Sun’s Par. 8,20 Sun’s Par. 8,23 Sun’s Par. 8. a TLobolfki {F Stockholm. Tobolfki & Calcutta. Tobolfki & Madrafs. 12. 49. 20 3: 35 [12 49. 20 of So eRe 498 20 3: 935 3. 20. 26 1.90, 5% O. 47. 18 g. 28 14. 10. 12 13. 36. 38 : 30. .- » T4i Tt. 34 Bs IA 118s 39. 38 o 36 6 Te 17 Tee OT 2. 59 oo Sun’s Par. 8°55 Gajaneburg © dsawille houfe. Cajenburg &F Spittal oe Cajaneburg F Greenwich. Pe . Sun’s Par. 8,30 Gajaneburg ww Lidar oe to. Bi 39) «89 3. 23~ 20 £3; 37) as » 38 0. 36 TQ 2. 23 ahs s Par, 8.27 ~~ Stockholm & Paris. 9. 30.10 218 Ts fe 16 an Oo 8. 28, 29 oO. 54 1.37 24 x Sun’s Par. 8,80 104,38). 59 me 59 |t0. BF 59 © $9 |TO & 59 a 59 I. $2. 20 t Fae 7 I. 51. 50 8. 16. 39. 8. 16. 5% 8.17, 9 8 180 22 4. 12 | 82 28 42 ur a? EU le 43 re 48 foe AQ ‘oS 48 < I 48 Sun’s Pari 8) 11 Sun’s Par. 8,58 ia 8 Rar. 8,94 Cajaneoury F Paris. Cajaneburg (9 Rome. : Cajaneburg {9° Bologna. 10. & 59 . 59 to. 8 59 % 59 110 8 59 % 59 T. 42 34! pi. % 7 Ty 6. 39 8. 26. 95 o. Oo: 5a fe ae gO §. o8e 27 O $4 | ov. o 36 a3 9. 4. 57 O29 a 44 % 46 a. 27 . §0 a. Sun’s Par. 8,33 Stockholn & Spittal | Jquare. QF 30.16 2 18 I, 12 43 B. des a7 triad qT. I ee el Sun’s Par, 8,12 "Stockholm “Bologna. 9. 30 10 Qe Oo 47. 5 ee) 9. 4 57 0. 29 I. 49 L.. 52, Sun’s Par. 8.73 9. 3¢. 10 a. 18 Ov 4% 33 ves 37 9 36 O. 13° = ee 2 2 Sun’s Par, 8,33. Stockholm &F Greenwich. 9. 30, To a 18 1, 12, 20 | o t7, 8. 19. i: rr fi 1. : Sun’s Par. 8,88 Stockholm °S Rome. 59 Sun’s Par. 8,09 Stockholm 68 MATHEMATICAL anp Stockholm (F Madras. Opal & Lefeard. Opal & Saville ae Parall. Paral ike. Me ti, aC, { HN Mefec: (. U1 he me fee. Qs 3°. 10 % 18 | 9. 28 6 %. 21.1 9.28, 6 Se 41 4. 7. 44 1. 28. 58 I. Io. 56 £3. 376 54 7.59. 8 8. 17. 10 13. 39- 33 a 36 | 8. o 21 I 47 8 a. 4% — I. 44 I, 42 tT. 13 Le To Sun’s Par. 8,67 Sun’s Par. 8/,06 Sun’ acs 8” io Bigs ty Paris. Upfal & Bologna. ae to Rome 19. Ge 9-4 G. 28. 6 %. 4} 9. 28 6 4 41 I. aS es O45. § 2 20! 33, 8. 26. 56 §. 3 1 Mg Yieae 8. 28, 27, 0. 54.19 A 57. 0. 291 9. 9. 26 On, 14 Te gt 47 I. 56 f. $4 Cas) wo Sun’s Par. 8,89 Sun’s Par. 8,0 Sun’s Par. 8,17 Upfal F Madras. Galcutta and Saville Houfe. Calcutta & Paris. 9. 28. 6 mM at [14. Tl. 34 % 14 |1t4. Ile 34 ee pe tL Se 5a 14 ka iy 37. 50 8. 17. 20 6.270 6 13. ag 38 Oe 36 | 8 18. 22 I. Il] 8 = a7 O54 48 ba te 2 re. 3 “feat Te 90 "sen! s Par. 8,74. Sun’s Par. 8,37 eel s Par. 8, a Calcutta & Bologna. Calcutta & Madras. Abo & Lefeard. ide Tl. 34 a 4 |l4. TI. 34 a 4 | 9. 45+ 59 4% 30 5. 8. 23 cia a eth LSE | Gy goat” 13. 38. 0 7. 58. 54 4057 0. 29° TH 390938 Or 9044 & O.-3t rT 4 ee bdo I 45 I. 38 1, 38 27 26 Sun’s Par. 8,58 Sun’s Par. 8,50 Batt Tats eee Abo & Rome. Hernofand & Rome. Calmar & Madras. 9. 45- 59 ce eee 4 26 | 9. 23. 40 1. 59 0. 38. 40 O. 21. 35 4: 34, Bt 2. us : 9: 7 17 to: -36. tr = 9.30 0. 1319. 9. 36 Os 35 [15s 39+. 38 0. 36 2 17 4 | 2 19 13 Z29 tee ed Sun’s Par. 8,50 Sun’s Par. 8,88. Sun’s Par. 8,91 : Sherburne & Lornea. Greenwich & Paris. Greenwich & Lefkard. 9. is, 12 Te 12} 3. fp. 3 I. I ae 0 I. 12 I. 40. 49 sr Stas yar: y Boel & oO a8 9. 54 8 3 5 | 8. 28. 27 C. 541 8 0. 24 Bien ee 84 i 58 37 1 7 eS Sun’s Par. 8,50 5un’s Par. 8,50 Sun’s Par. 9,50 The parallax of the Sun may alfo be deduced from the total duration of the tranfit, as obferved in different places, in the following manner. Tranquebar & Galmar. Aosiri i tie Lec, " Be §le 33 a 2A kk) fs N 5A Sun’s Par. 8”,05 Tranquebar & Upfal. Parrall. i. Mm. dec: toy $: St 33 6, 94 5. 50. 26 es eee) e Sun’s Par. 8/25 Tranquebar & Abo, P h. m. fee. a 5+ 5%. 33 6 24 see 9 7 AG By) I. 24 T Sun’s Par. 8/97 Lranquebar ASTRONOMICAL PAPERS. 69 Tranquebar & Cajaneburg. Lranquebar & L obolfki. Adadras & Siockbolm. Parall. Parall. Parall. h, mi, fec, 1. © hem. fee, cu too 5. 51. 33 6. 24 | 5. 51. 33 G 44 (5. §T 43 6. 33 5: AQ: 54 8. 5 | 5. 48. 50 9:3 | S$. 50. 42 34) I. 39 i at a. 43 a) es fo oy Sun’s Par. 8,34 ____Sun’s Par, 8,67 __ Sun's Par, 8450. Madras & Tornea. Great Mount & Abo. | Great Mount & “‘Tobolfki. 5. 51. 43 6 33 | 5. $1. 20. 6 38 | §. gh. 00 6. 33 i357 af eS 7.46 | $. 48. 50 ms I. 34 I. 34 I. If t, 23 G30 % 30 Sun’s Par. 8,50 Sun’s Par. 8,26 Sun’s Par. 8,50 Cajaneburg & Upfal. Cajaneburg & Calmar. Tobolfhi ty a 5. 49. 54 8 5 | 5. 4% 54 oe ae tO ; |. bone a2: 33) Ss $89 got Sse 8 eae 3% 3% eae 44 ss) ae Sun’s Par. 8,50 Sun’s Par. 8,70 Sun’s Par, 8,7 The parallax of the Sun may alfo be determined, by comparing the times of the internal contaéts, as obferved in various places, with the time of their happening as ob- ferved at the center of the earth. For this purpofe the following elements are ufed, as they were calculated by Mr. Short, from the meafures made at the tranfit in L761, viz. the diameter of the Sun 31’. 31”, the diameter of Venus 59”, her horary motion 3’, 59",8, the angle of her path 8’. 30".10, the neareft diftance of their centers g'. 32", and the difference of their horizontal parallaxes 21",35. Hence the apparent time of the rft and 2d in- ternal contacts was 2" 22’. 3”, and 8". 20’, 4", reckoned by the meridian of Greenwich, without parallax, and the central duration was 5". 58’. 1”. Central Time & Op/al, Central Time & Up/al, Cental Lime oc szerngand, Parall. Paral, Paral! h. m. fec. Poel ae fet Qe Bde 8 Oo fae OO] 2 oa 3 o a6 it. 10. 26 I, 10, 26 t. 2%. 63 3. 9h 29 3+ 3% 29 3+ 33+ 3 3.37. $6 be Td | G3 8S Je 14) 3. 38. 35 ee 5. 27 , 5s 1h 5. 4 : Sun’s Par. 8,91 Sun's Par. 87455 Sun’s Par, 87,33 Central Time & LHernofand. Central time & Cajanedure, Central Time & Stockholm. maa 4 Ob <6 || 4 aa 3 Ge Os] aaa 3 cS 866 J. It. 28 Ut. St. 59° T, 12. 26 3a. Be 4- 13. $3 3+ 34. 29 3, 3& 26. §, tol A i oF 5+ 6} 3. 39. 29 $16 A 5S 5. Td 3 Sun’s Par, 8,09 Sun’s Par. 8,66 Sun’s Par. 8,07 Wow K Central 70 MATHEMATICAL AND Central Time & Abo. Central 'Yime & Tornea. Central Time & Calmar, Parall. Parall. Parall. i ibs li wt / “ imei ears Or ae 8a GF G7 Op a.hae3 Oo 9 1, 28.34 f, 46. 49 Th. 30 3+ 50. 39 ; a RO. SE Br Ov -Am 3. 55: 50 ¥, 16 4 4 0 ng 2 oa Ss Ss U2 5-14 Css ‘ 5s 43 Sun’s Par. 8,44 Sun’s Par. 8,69 Sun’s Par. 8,52 Central Time & Tobolfhi. Gentral Time & Madras, | Central Time & Calcutta, We UM 3 OF Of er aes 5 GO | a We 3 oO. Ae 3h. 8D 5+ 20, 50 5a An Oe $4. 55 | Te Ad 13 8. 15+ 47 7. 28 ge 98 7 Ae SS 5. 97 | 8. 20. 58 je 10 5+ 33, 5. 4% fe TE : Sun’s Par. 8,63 } san’ s Par. 8 8, 14 -Sun’s Par. 8,36 The Sun’s parallax deduced from the obferved and calculated times of the ed internal contatt. 7. Th "Sob Par. 8,50 Central Time & Spittal Square. {Central Yume cael 4 Central Time & Paris. Parall. Parall Parall, f “| h, m. fec. ' 1 h. m. fec. Je oth 8..20: 4 oO 01.8. 70. 4 O& 0) 3 20 4 es Me oO. ot 0. 0, 30 2 pe » 19. 34 Eee i. Ir] 8. x 2% 1, 2 4 i 54, iis Sain i 1% “gun's Par, 8,01 "Ban's Pat. 3,62 Sun’s Par. 8,34 —Gontral Time & Bologna. | Central Time me & Cape. Central Time & Up/al. 8..20. 4 @- 0| 8.20% 4 Co © 20. 4 Oo 0. 45. 21 1, 13. 35 I. 10. 26 Q Ss 2S ~ ” | 9: 33: 39 P - 9. acs 30° sagt it ? 9. 39- 5° . BL Ge 28. 9 : . ap a ‘ | 6. : We UL Sun’s Par. 8,21 sun’ s Par- 8,58 Sun’s Par, 330 . | —~Gentral Time & Up/al. Central ‘Time & ae 2 Central Lime 8 Stockholm. 8. 200 4 o o| 8 20. 4 8. 20. 4 6 Ce I. 10. 26 I. 0. 26 I 12. 26 g: 30 30 9. 30. 30. 9G» 32. 90 9. 28. 7 a. at | 9. 28. 3 a wa | 0 See a. 18 ntact per deanna ee 4, Qe. 27 a 19 sun" s Par. 8,62 Sun’s Par. 8,86 Sun’s Par. 8,56 Gentral Time & Stockbolm. — Central ‘Time & Abo. Central Time & ie Page . 9. 20. 4 0 0 | 8 20 4 o. of 8 20. 4 0, y to, 26 ie. 28.33 I. 51. 50 §- 32. 30 9. 48: 37 aE Ee me ; 9e 30. 8 m 18 | 9. 45: 59 isi ge (ou cS oe Soo, Qe UX % 38 aha pane Sun’s Par. 8,75 Sun’s Par. 8,95 un’s Par. 6,31 Central Time & Tobolfhi. Central Lime & Galmar. Central Time & Rodrigues. $20... 4 O 8. 20. 4 6 | o 2. 4 ere Ae 320 52 ti 3139 As de 34 12. 5% 56 9. a5» 43! 12. 32. 38 12. 49+ 20 ae 35 Gee oe, 1. 59 \1% 35+ 47 ee a. 36 % 3 sey: Sun’s Par. 8,54 Sun’s Par. 8,78 Sun’s Par. 8,59 Central Lime & Calcutta. 8,.20. 4 o. 0 5. 55 AA SJ 4,13. 48 fA. Pls I. 34 2, t4 The gp ASTRONOMICAL PAPERS 71 The Sun’s parallax is alfo found, by comparing the to- tal duration between the internal contacts, as it was ob- ferved in different places, with the duration at the center of the earth, viz. ance Cent. Duration & at Her 7 54 Sun’s Par. 8,89 arall hy me tec. 7 ceca Go 6 5. 50 7 7 38 ‘|b. m. fec. fe 5. 58. 2 a 5 $+ 50. 26 7 33 7 35 Sun’s Par. 8,54 Cent, Duration & at Calmar. 5. $e, & elma, 5: 49. 54 8 5. oe 7 Sun’s Par. 8,53 aan Gent. Dur. & at Stockholm. ge $0.1 Oz 6 bala ete ve oH . 16 Sun’s Par, 8,16 | y 44 Sun’s Par. 8,65 | Cent. Duration & at Abo. | 5. 58 OG. 6 5. $09 7. 46 7+ S% Sun’s Par. 9,61 Cent. Duration & at Up/ul. fo 5h t ou 6 5. 50s ® 7 59 ee Sun’s Par. 8,98 $e Sey. I oS 5: 49) $4 a 6S 8 — 2 Sun’s Par. 8,53 Cent. Dur. & at Upjal. Parall. Cent. Dur. & at Herngfand. Sse. Tt eo} 5: $0. 17 7 36 Cent. Durat, & at Cajaneburg. Cent. Duration & at Tornea.| Parall. he wma. fee: tot fe F853 kt oF 6 JS: 50. 15 % 9 : sun's Par. 8,13 Cent. Duration & at Todol//ki S50. ft oS oh the £0, %. 3 p. 21 : Sun’s Par. 8,63 “Cent. Duration & at Calcutta, 5. 58 oo 5+ $0. 36 7s. 30 7+ 45 Sun's Par. 8,40 Cent. Dur. & at Tranguebar. i o. 5. 58 2 ° 5. 51. 23 6. 24 poker 6. 28 : Sun’s Par. 8,59 5+ 50 26 7. 36 7 35 Sun’s Par. 8,48 Cent. Dur, & at Hernofand. | Oe 0 5. 5o fF : oO. ° oh 43 6. 33 . 18 Sun’s Par, 8,17 Cent. Dur. & at Stockholm. . So” as G20 5s $0. 4% 7 34 7 19 Sun’s Par. 8,22 Cent. Duration & at Madras, “Cent. Dur. &at Great AZount, “fe tee 4 S 6 §. 51. 20 6.7 33 6. 41 Sun’s Par, 8,67 The mean of all the preceding determinations of the Sun’s parallax is 8’52 on the day of the tranfit, in June, 1761, which gives 8"65 for his horizontal parallax at his mean diftance from the earth. Mr. Stuart of Edinburgh, whom I mentioned before, deduces the parallax and diftances of the bodies that com- pofe the folar fyftem, from, the Newtonian theory of gra- vitation, and the periodical times of the Sun and Moon. As he proceeds upon the fuppofition that the diftance of the Sun from the earth is very great, it would therefore feem, that the conclufion fhould be accurate, in propor- tion to the greatnefs of that diflance, His method de- pends oe re MATHEMATICAL. ann pends upon a feries of propofitions, with long and difficult demonftrations; fo that the rules of calculation are not very obvious, without a confiderable knowledge of geo- metry, in general, and a particular acquaintance with his very ufeful and ingenious treatife. I was defirous of fee- ing what agreement there was between the refult of his method of calculation, and the obfervations made on the tranfit of Venus; and therefore amufed myfelf in a leifure hour with the comparifon. As it may be agreeable tofome, who have not time to read over the book, and to others, whofe acquaintance with the mathematics will not admit of it, to have the practical rules of computation deduced from his propofitions; I fhall annex them to the foregoing calculations, together with the determination of the Sun’s parallax and diftance derived from them. A Calculation of the horizontal Parallan and diftance of the Sun, according to Mr. Stuart's method froma the principles of gravitation. D Let P=the periodical time of the earth round the Sun==365. 256417824 p=the periodical time of the Moon round the earth 27. 32162036 a=her revolution from apogee to apogee in time, UI. 5SAS3BS m=zher mean dift. from the earth, in femidi, of the earth== 60. WA t==the tangent of the Sun’s horizontal Parallax, at his mean diftance. S==the dittance of the Sun from the earth. nod P2 a5-—p} an Af Inng m2 42 "Then according to Mr. Stuart’s method, 4-——¢ anes ae : pr Sab-3p% I—-9 m 242 4/ T-gm ete p25 05-393 3m XI 1.5 Now if CS then S== — nearly Pp appz ay i-.50X 14-26 a 3X ate Nearly. 0S is greater than the firlt, and lefs.than the leaft And § i He in thefe theorems, a Vv Tn. 5¢X Ifo 1.50 But the parallax and diftance of the Sun, may he found nearly, ina fhorter method, by the following rules, derived from the fescue) by faying, ; 1. As the cube root of the fquare of the Moon’s periodic revolution or a the Earth, viz. 2732162030) Is to the cube root of the fquare of her revolution from apogee ve a % apogee, viz» 275545351 So is 1 toafourth number, which call A==-1.0056748164. a. Ass A—m3:A2:: 1: a fourth number, which call B.==.002797833==the mean difturb. ing force of the Sun; the ’s force==t. 3. As the rectangle of B and the {quare of the periodic time of the Earth % round the Sun, viz. BX365,2564) Is to the fqnare of the periodic time of the moon round the Earth t 2 viz. 2732102036 So is 1, toa fourth number, which call C=1,999840899. a 4. As C—t):12::C+toa fourth number; to which add 1, and from the {quare root of that fum fubtraét 1, and multiply the remainder by the half of C—1, or 0,4999204495, and call that produ&t D==1,9999715505. 5. Subtract ASTRONOMICAL PAPERS. 7 5. Subtra& D from 2, multiply the remainder by D, and call the fquare root of the pro- duct E.==.007543089. i 6. Asthree times the Moon’s mean diftance from the Earth, in femidiameters of the Rarth. isto H, fo isR, tothe tang. of the Sun’s horary parallax, at his mean diftance,==8/,65. . As B: 31: the Moon’s mean diftance in miles: the Sun’s mean diftance in miles== 94,982,600. In determining the parallax of the Sun, from the ob- fervation made in our obfervatory on the 3d of June, 1769, I have only made ufe of the time of the internal contact, as I noted it on that day, together with fome of my own micrometer obfervations, without attending to thofe of the other gentlemen who obferved with me. But as the So- ciety has a right to expect a full account of the refult of the other obfervations, which were made on that occafion; and as fuch account may tend to corroborate the foregoing calculations, | have, with Dr. Williamfon’s permiffion, fubjoined a calculation of his, founded entirely on his own obfervation, which being very fhort, | have inferted entire in his own words, except what refers to the manner in which he judged of the contacts, &c. which I have tran- fcribed in another place, (fee page 46.) From this, which is very fimilar to the obfervations made by the other gen- tlemen on that committee, the Society will perceive, that our obfervations muft have been made with confiderable accuracy, as the refult of the calculation is nearly the fame. Dr. WILLIAMSON’s Determination of the PARALLAX of the SUN, from his Obfervation of the TRansir of VENUS, at Philadelphia, ‘une 3d, 1769. - ITH a refracting telefcope, 24 feet long, which magnified near 100 times, I obferved, The external conta& at 2". rr’. 31" re a Internal do. at be lequiae n Time. “ With a micrometer of Dollond’s conftru€tion, fitted to a Gregorian reflector, which magnified 100 times, I meafured the diftance of Venus from the limb of the Sun; alfo the diameters of the Sun and Venus, as follows: Mean 74 MATHEMATICAL anp Mean Time. Neareft Diftance of the Center | Neareft Diftance of the Limbs of © and @. of © and @. Tis 18, .fecy m. fec. m. fee. Ati 5s AB. UF IO. 14,12 5. 453 6. 3%. 18 II. 14,19 4. 1,46 6. 33 55 IX. 13,23 de 3,a% q. Gi 3 0% in, 85 4 58% *“* | meafured the diam. of Venus on the Sun, and found itto be 55",42. I alfo frequently meafured the diam. of the Sun, on the day of obfervation, and the next day, and found it to be 31’. 31530. ss “¢ From thefe data, I fhall attempt to deduce the Sun’s par. except that I fhall make no ufe of the meafure at 6°. 32'. 18”, which I fufpeéted was not accurate at the inftant it was made, wherefore I immediately made another mea- Ore; ViZ.'at Oe 94.5 85 “ The neareft dift, of the limb of the Sun from that of Venus at 5". 43'.17” And at6 33. $3 give the apparent neareft dift. of their centers 10’. 3”,7, or 603",7, and the parallax of Venus was at that time fouth 6",91 nearly. Therefore, the geocent. neareft dift. of their centers was 610",61. ‘Then, “ As 72626,3 the relative neareft dift. of Venus from the Sun, “ Ts to 28894,9 her dift. from the earth. - «© So is 610",61 the geocent. neareft dift. of the cent. of the Sun and Venus, ; “ To 242”,936=4'. 2,936, the heliocent. dift. of their centers at the neareft approach. “ As Sine 3°. 23’. 20” the given inclin. of Venus’s or- bit to the ecliptic: Is to Radius, * So isS, 242”,936, the heliocent. dift. of the cent. of the Sun from Venus, at the middle of the tranfit, “To the Sine of 410",5=1°. 8’. 25", the Sun’s difk, from the node of Venus at the ecliptical conjunction, “As S, of 1°. 8’. 25”, the Sun’s dift. from the node of Venus, . « Ts to 10’. 10",61, the geocent. neareft dift. of their centers “ So mean time compared together, ASTRONOMICAL PAPERS. 75 * So is Rad: to the S, of 8°. 32’.57",6, the angle of Venus’s vifible path with the ecliptic. “ From 8°. 32’. 576, the angle of Venus’s vifible path,. “© Subt. 3. 23. 20, the inclination of Venus’s. orbit with the eclipt. and the remainder is 5°.9'. 37,6. Then “ As S,. 5°. 9’. 3756 the diff. of the angle of Venus’s vifible path and the inclin. of her orbit, &c. “ Ts to S, 8°. 32'. 57,6 the angle of Venus’s vifible path with the eclipt. “ Sois 2',392375 the given hor. motion of the Sun. * To 3',954.12 the hor. motion of Venus. “ As Rad. Isto T, 8°. 32’. 57”,6 the angle of Ve- - nus’s vifible path. : “ So is S, 1°. 8’. 25” the Sun’s dift. from the node of Venus. “ To T,, 10’. 17”,2 Venus’s geocent.. latitude, “ As 72626,3 the relative dift. of Venus from the Sun,. “ Is to 28894,9 her diftance from the earth. “ So is 617",2 her geocent. latitude. To 24.5",56 her heliocent, latitude. “ From 15’. 4.5”,05 the femid. of the Sun, “ Take 27",71 the femid. of Venus, and the diffe-- rence is 15’. 17°94.) the dift. of the center of the Sun from the center of Venus at the inter. contact. But the geocent. neareft dift. of their centers was found 610",61. From thefe (b. Euc. 1. 47) the length of half the tramfit line between the int. contaéts is found to be 68 5. 9397 which divided by the hor. motion of Venus gives the fe- miduration of the tranfit between the two internal contaéts. gi San 20 ee «¢ In the fame manner, from the geocent, lat. of Venus, and the neareft dift. of her center from the center of the Sun, we find the time of Venus paffing from: the eclipt, conjunction to the middle of the tranfit. 22’. 44",9. Then from 5", 28’ 47", which I find to be the central time of the middle of the tranfit, dedu@ 22’. 44",9, and the re- mainder, viz. 5". 6". 2,1, will be the apparent time of the ecliptical. 76 MATHEMATICAL anp ecliptical conjunétion when the Sun’s place was 2°. 13°. a7’. 20",5, as calculated by the aftronomer royal, on the fuppofition that our obfervatory is weft of Greenwich 5°. 0’. 35". To the Sun’s place in the eclipt. add his dift. from the node of Venus 1°. 8’. 25”. The fum is 2°. 14°. 35’. 45"55, the place of Venus’s afcending node. “ From the micrometer meafures above given, it ap- pears that the center of Venus was at her neareft approach to the center of the Sun at 5°. 21’. 44” mean time, or 5°. 23", 59" appar. time. But on account of the parallax of Venus, the appar. timeat the center of the Earth was 4’. 48" later, which brings it to 5". 28’. 47” as I have menti- oned. From this deduct the femidurat. 2", 53’. 20, and the remainder 2". 35’. 27” is the time of the internal con- tact at the center of the earth. This contact 1 obferved as above, at 2",'29'. 10” mealtime, or 2". 31’. 25” ap- parent time. This differetice, therefore, viz. 4’. 2”, is the obferved effeéts of Venus’s parallax both in latitude and longitude. © *¢ But on the fuppofition that the Sun’s horizontal pa- rallax, at her mean dift. from the earth was 8”,65, as Mr. Short has ftated it at the former tranfit, then his ho~ rizontal parallax, on the 3d of June, the day of the tran- fit, would have been 8”,5204, in which cafe the total effet of her parallax, to haften the internal contact at Philadel- phia, fhould be 4’. 1", Therefore, @: Ag g'l4 is to. 4". "2,° 10 18 8"; 5204 “to Be e6, the Sun’s horizontal parallax on the day of the tranfit, accord- ing to the foregoing obfervations. “© Hence we have 8",685, the Sun’s horizontal parallax at his mean diftance from the earth. ‘Then fay, « As the Tang. of the Sun’s horizontal parallax: is to the femidiameter of the earth, “¢ So is Rad. to the diftance of the earth from the Sun, viz. 94791100 Englifh miles, taking the earth’s mean femidiameter at 3985.4 miles, An i ‘The place of the Sun & Mercury at the Ecli ptical Conjundiion 7 17 50 AT The place of the afcending Node of Mercury =~ I 15 35 29 ‘The Sun’s Diftance from the Node of Mercury ~ . - a 15 1% The Angle of his vifible path gute Helptie = 3 21 18 ‘The Horary Motionof Mercury == > <2 5 55-6 "Phe Semidiameter of the Sun on the Day of the Tranfit - - 16 10.1 "Phe Semidiameter of Mercury at whemanctine 4-938 "Fhe Geocentric Latitude of Mercury at the Ecliptical Conjunction 4 39-905 . 16 34-558 His Heliocentric Latitude at the fame time - - - "The apparent time of the Ecliptical Conjunétion accordingtothey oh!’ " Meridian of Philadelphia == = - i The time of the neareft approach of the Centers of the Sun ee a | ee ae as i xg 1 30 ‘The central Semiduration of the Tranfit between the External Contacts2 25 4% "The centralSemiduration of the Tranfitbetween the Internal Contaéts 2 23 44 The apparent time of the External Contact obferved at Philada. %.36° 9 The apparent time of the Internal Contact obferved at Philada. he 37 30 - re 0 o Projected for the Latitude of Philada. 39 56 54% Longitude 75 8 45 Weft of Grecuwich by JOHN E WING 5 12 46.5 aan { ae. a 3 a oo 40 | ASTRONOMICAL PAPERS, 97 An Account ofthe Tranfit of MERCURY over thes UN, on Noveribee Gan Ne N.S. ‘ N the judgment of moft aftronomers, the tranfits of Mercury and Venus over the Sun afford the bet op- portunities, for fettling the longitudes of places on the earthy éven preferable to that derived from the eclipfes of ‘Jupiter’s fatellites, when the parallax of the Sun is pre- vioully known. Thofe of Mercury happen frequently, and although they are of but little importance in deter- mining the parallax of the Sun and the dimenfions of the - folar fyftem, by reafon of his great diftance from the earth, and the difference of their parallaxes being lefs than that of thé Sun; yet they have been carefully obferved, for the purpofe of fettling his theory, and the longitudes of the places of obfervation. The fociety therefore fenfible of the importance of this pheenomenon, both to the perfection of aftronomy in general, and particularly for completing the purpofes defigned to be anfwered by the obfervation of the tranfit of Venus, have appointed the fame committee, with the addition of two other gentlemen, to obferve the tranfit of Mercury on the gth of November, 176y, in Phi~ ladelphia, that had been before appointed to obferve that of Venus. i » Having fll the fame inftruments in our obfervatory, which we ufed on the former occafion, together with a new time=piece made by Mr. Duffield of this city, with an ingenious contrivance of his, in the conftru@ion of the pendulum, to remedy the irregularities arifing from heat and cold; we paid the utmoft attention to the going of. the clock both before and after the tranfit. From com= paring afufficient number of correfponding altitudes of the Sun’s limbs, we found that our clock was too flow for mean time 1’. 20” and the equation of time being 15’. 49",6 or to avoid fractions 15/. 59"; 17'. 10” were added to the times of all our obfervations, as they Were written down in the obfervatory, to-reduce them.to apparent time. “SInthis. a manner 78 MATHEMATICAL anpb manner we obtained the time of the fubfequent obfervati- ons. Dr. Williamfon, Mr. Shippen and myfelf ufed the fame telefcopes, we had ufed before in oblerving the tranfit of Venus; excepting that on this occafion I chofe that power of the telefcope which magnifies the diameters of objects an hundred times. Mr. Evans ufed the reflecting telefcope formerly ufed by Mr. Biddle at the Capes. On the day of the tranfit, we aflembled together at the obfervatory, adjufted our telefcopes to diftin& vifion, ap- pointed an affiftant to count the clock with an audible voice, and agreed that no other perfon fhould fpeak, nor move from his telefcope, until both contacts were over; but write down his own obfervation feparately by himfelf, that it might be compared with the others. The fky being very ferene, and the limb of the Sun well defined in our telefcopes, we obferved the contacts, as they are exhibited in the following table, Obfervers. External Cont, | Int. Cont, Par. in{ Par, p. | Par. in his f Vert. | to hisP. Path, h, m, tec i. m. fee, " " ul Dr. Williamfon, \ 2: 36. SAp.1'.] % 37. 30 3,74 3,44 1,48 at the External Mr. Shippen, 26 360.24 9», 370 AO Contac. Mr. Evans, 4, B6...9 2 39. 38 3,745 | 3,44 1,49 at the {nternal Myfelf. % 36. 9 % 37+ 30 Contact. I happened to have that part of the limb of the Sun, on which Mercury entered, in the middle of the field of my telefcope, with my eye intent upon it; fo that Iam cer- tain, that there was not the leaft impreffion on the Sun’s limb, perceptible by my telefcope, a fingle fecond of time before [ difcovered it. So that 1 am not furprized that Dr. Halley, who had obferved a.tranfit of Mercury in the Ifland of St. Helena, concluding that, that of Venus would be equally inftantaneous, expected, that the conta& of her limb with the Sun might be determined to a fingle - fecond of time. The atmofphere of Venus renders it quite otherwife, and produces an uncertainty of 5 or 6 feconds of time, in judging of the contacts; whereas no fuch thing was perceptible in Mercury. The firft appear- ance of Mercury, on the Sun’s limb, wasa fleady {mall {peck, ASTRONOMICAL PAPERS. 7 {peck, black, well-defined, and not larger in my telefcope thanthedot ofa pen. But that of Venus was tremulous, ob= {cure, and ill-defined, growing gradually darker as fhe ad- vanced on the Sun. If Mercury has an atmofphere, it muft be fo rare and low, that his diftance from us renders it abfolutely imperceptible with the telefcopes that we ufed. At the internal contad,, the crefcent of light round the body of Mercury clofed inftantaneoufly, fo that it might be judged of with more precifion than that of Ve-~ nus; his atmofphere giving us no difturbance in this cafe. We could not have a fairer opportunity,. for afcertaining the truth of thefe conclufions; as our telefcopes were in. good order, and well adjufted, and the fky was remarka- bly clear and ferene, on both of thefe days. On the firft of them, not a cloud appeared from morning till evening, and on.the latter, none till about four o’clock, when the Sun was. very low; and both the tranfits began between. two and three o’clock, in the afternoon. About three o’clock, I applied mydelf to the micrometer, to meafure the diameters of the Sun and Mercury, and the: neareft diftance of their limbs; while Dr. William/on read off the divifions of the micrometer, and a third perfon wrote'them down, withthe times of making them. Thefe: meafures make the diameter of the Sun on the gth of No- vember 1769, 32'. 20,2. or his femidiameter 970",1 fe- conds, and the femidiameter of Mercury 4",238. The meatures of the leaft diftances. of their limbs. reduced to minutes and feconds of a degree, with the parallaxes of _Mercury adapted to the apparent times of the obfervations, as they are determined. from a very large projection of two inches to a fecond of. his hor.. parallax, are {et down in the following table. Apparent 80 MATHEMATICAL awnp "Apparent ‘Time. { Nearcit diftance of | Parrallax of % | Par. per.to his | Parallax in his limbs of © & % in the vert. path. path. ho m, fee." : | A $9 49 v.54l/,1 3,!'8E eo ld V,725 gt 8 I 056% fe OB BT » * 35396 3,73 Bu 2 hi IE %. 8,284 3,32 ; 35393 3,745 Bu ot BO Qh, 20,83% 3,825 3539 1,765 B06 86 2. 26,048 3,826: 3,306 i 1,78 3. Io, 33 2. 48,216 3,835 | 3538 1,83) 3 1a 6 2 57,444 gyeat My 89879 1,84 Bi An. 56 3> 2556 3844 35376 1,85 3 iF 3+ 13,744 3,850 oo 1,865 Sez EO. 3. 26,032 3,856 3,369 d 1,87 Ga 10. 18 3. 30,596 3,86 : 35366 1,888 %. 21, 30 3. 43,6 3,864 3,363 : 1,915 he o 3- 51,684 35875 3136 1,95 a eS 4. 20,8 35895 3534 L 7,0 3. 33. 30 Ay 355744 3590 31338 21,0 3. 36. 40 Ay 5T,444 35905 | = 8333.4 31,04, 3. 37- 40 ; 3 39 45$ 5+ 4,202 35915 3533 2,065 oe. Ale a a dd FO 5. 21,406 35930 gas 2,09 3. 40. 5S Se 37,184 3,935 33% 4,145 Bi 85S 334 6. 8,48 3,96 330 Qy% A: 594 15 6. 26,084 3,97 3549 2,%A, 4. 98, FO 7. 54,756 4,0 354% 254% 440456 $, 35,18 4,02 3515 2,51 N. B. In the above table, the meafure at 2°37’. 40" was taken between the neareft limb of the Sun and the in- terior limb of Mercury neareft to the Sun’s center, and 18 5’. 2"202, the fame with the diftance of their nearelt limbs at 3° 39'. 25": So alfo the diftance between the neareft limb of the Sun, and the interior limb of Mer- cury, at 3 a1’. 10”, was the fame with the diftance of their neareft limbs at 3% 42’. 50", viz. 5’. 21",406. The fame is to be faid of the laft meafure, which was taken from the neareft limb of the Sun to the limb of Mercury neareft to the Sun’s center. . If acomputation be made from the above meafures, the apparent neareft diftance of their centers will be found to be 451",914. But Mercury was then deprefled by paral- lax 3,11; fo that the geocentric neareft approach of their centers was 455",024, which happened at 5" 1’. 15" ap- parent time, when his par. in the vert. was 4,042, and in his path 2",93, and perpend. to his path 3",11. The horary motion of Mercury as feen from the Earth is alfo determined from the above meafures to be 5 ASTRONOMICAL PAPERS, Sr 5'+ 56",941=5",94856, which is nearly the fame with What is given by Dr. Halley’s tables of Mercury. On the day of the tranfit, he moves, by them, at the rate of 15"5334 per hour. The Sun’s horary motion on that day is {tated in the nautical. almanac at 2”,¢16, and their dif ference, viz. 12',818 is his horary motion from the Sun,. as feen at that diftance. Then fay, " As the diftance of 8 from, isto his diftance from ©, Sois this horary motion to his ho-- rary motion from ©), as feen from =) 4. 830,2920==log. of 67653.8' Ae AYS,3305==log. of 31284.6: I. 107,8203==log. 12.818: 5. 603,1508" ©. 772585 885". 92733==5'..55",6398 & hor: mot. from ©, as feen frome. 15. 334==horary motion 8. 4». §16=shorary motion ©, As 17, 850meT. 251,6382=sthe fum of horary motions ® and y. Isto 12, 818—=1.. 107,8203==their difference,. So is cot. 3°. 29/. 4o/aart. ssa eoe the log. cot. of half the incl. of %’s orbit with the eclipticae4 6°. .59/, 20. I2i- 32.2,0270 ee a GRC To Log. Tang. 11. 070,3888=:85°. 8. a2//, 86. 30, 205-4 fup. of 6°, 35720", Sums=171.. 38. 42 The fupplement whereof is 8, ax 18=+the angle of 8's vifible path. with the écliptic, i pe Rad } Sec, 8° 21/, 18”: : geo. neareft dift. : the geo. Jat. of on IG, 000,0000 IO. 004,6342 2. 658,0343==455",024=—geo. neareft diftance, % 662,0685==454!',905==g¢0. Jat. of ¥ ==7!. 39/, 908: As ditt, of 8 from © : his ditt. from © ++ geo. lat. : -his-heliocent. latitude. 4+ 49553305 | 4 4. 830,2920° %. 662,6685 7. 492,9605 3. 997)6300==994",558 the hel. lat. of Y ==16'.. 34/,558 As T, 6°. 59/. 207 : Ris T,.16" 34,558 : Sine of ©’s dift, from the node of u. 9. 088,4133 10 = = = 7. 683,0140 8. 594,6007==2°. 15/, 12!",22=@'s dift, from the node of 459,905==eocent. lat. 8. 4$5,024==yeocent, neareft dif. of © and Xf, Sum==914,929=2. 961,3373 Difh== 4,881==0. 688,5088 ey %)3. 649, 896% %. 824,94808 82 MATHEMATICAL anp-> I. $24,94805 =-66",8264—) the length of part of the tranfit line between 4% § 51,0104 % hor. moto the middle of the tranfit and the eclipt. con- ——— in feconds. ) junction. : : —I. 273,9376=oh. Pe 265 Sool. 1, 16,45 8=the time between the middle and ecliptical conjunction. ; ; 9,74,338=sthe fum of the femidianreters of @ and 8. 455,024—=the geo. neareft dift. of their centers.. Sum=1429,362==3. I55,142% Diff= 519,314==2.. 715,4300 inne half the length of the tranfit line f Is. 9352861= 860", 561 i pe Hor hd do t . tranfit line ae the %. §§1,cTO4-=the horary motion of % on @, as feen from @. 0. 334,2757—=2h. 422567—=2h.'422567—=9h. 25!. 21!',24. the femidura- tion from the external contact. : 965,862 the diff. of the femidiameters of @ and 3. 455,024 the geo. neareft diftance of their centers.. Sum—=1420,886—3. 152,569% Diff.=510,738==2. 708,2833 a) 5. 860,8524 ras dancin 851,974==the length of half the tranfit line from the %. 930,4262==§ internal contact. : 2. §§1,0104==hor. mot. of 3%. 0. 379,4158=2h. 39561=2h. 23. 44,196 Now to 2h. 36/. 19” the time of the external contaé, Add 2. 25. 21 the femidur. between the external contacts, eel The Sum, 5. I. 30 isthe time of the neareft approach of their centers, To this add, 11. 16,5 the time from the middle to the ecl. conjunction, ‘The fum, 5. 12. 46,5 isthe apparent time of the ecl. conjunction at Philadelphia, "To this add, 5. © 35 the diff. of meridians between Greenwich and Philadelphia. The fum, 10. 13. 21,6 isthe time of the ecl. conjunction at Greenwich, when the Sun’s place, according to the Nautical Almanac, is 7s. 17°. 5o/. 42”, and that of Mercury is zs.17°. 50'. 41”, by Dr. Halley’stables. From this fubtract 2°. 15’. 12”, the Sun’s diftance from the node of Mercury, and the remainder 1s. 15°. 35’. 29/,is the place of his node at that time. The PROJECTION of the TRANSIT of MERCURY, Pi. V. THE following projection of the tranfit of Mercury over the Sun, on the gth of November, 1769, was made from the foregoing meafures and calculations, on the fup- pofition that the Sun’s horizontal parallax, at his mean dif- tance is 8",65, and therefore, 8",7437 on the day of the tranfit. In this cafe, the horizontal parallax of Mercury, at his mean diftance, will be 14”,1132, and on the day of the tranfit 127856, and therefore his horizontal pa- rallax from the Sun on that day is 4.”,0419, being the dif- ference of their parallaxes. The delineation was made in the fame manner as that of the tranfit of Venus. The elements for it were collected ( trom i ican ASTRONOMICAL PAPERS. 83 from the preceding calculation, and the parallaxes of Mer- cury were meafured upon a very large projection, for that purpofe, adapted to the apparent times of the micrometer meafures, and applied to the projection. By thefe, the apparent places of Mercury were determined, as feen at Philadelphia; and {mall circles were drawn round them, with the radius 4.”,238, to reprefent his difk on the face of the Sun. From the limbs of the Sun and Mercury, lines were drawn in the direction of their centers, of the precife length exhibited in the foregoing table of mea- fures. Upon the whole, [have given a full and faithful account of our obfervations of the tranfits of Venus and Mercury, in the foregoing fheets; and if they fhould be found, in the conclufion, to contribute any thing to the advancement of aftronomical knowledge, it muft refle& an honor on our new obfervatory, and give pleafure to all the lovers of {cience, as well as to, : Gentlemen, Your moft obedient And very humble fervant, Philadelphia, July 19th, 1769. + JOHN EWING. An Account of the Tranfit of Venus, over the Sun’s Dilk, as obferved near Cape Henlopen, on Delaware Bay, Fune 30, 1769. By Owen Biddle, Joel Bailey, and se Drawn up By Owen Biddle. GREEABLE to the appointment of the American Philofophical Society, to obferve the tranjit of Venus at the light-houfe, near Cape-Henlopen, | fet out by wa- ter from Philadelphia, accompanied by Joel Bailey, and Richard Thomas, the latter of whom had offered to accom- pany us at his own expence, and proved very ferviceable in the affiftance he gave us, ; Onthe 26th ofthe 5th month (May) we arrived at Lewes- Town, and immediately endeavoured to gain fuch informa- tion i. J ll i 84 MATHEMATICAL and tion as might enable us to determinethe beft place for our obfervations; and, on mature deliberation, we fixed ona place about one quater of a mile’S. W. of the town of Le- wes, where a convenient houfe was to be had, in a retired fituation, and having an open view of the fky. We found on our firft landing on the beach, that neither the Light-foufe, nor any place near the fea-fhore, would be fuitable for our obfervations; as it would be difficult to keep our inftruments fteady, or defend either the glaffes of the telefcopes, or the eyes of the obfervers, from receiv- ing injury by the fand which is wafted about by the wind. Having chofen our place, we fixt up our inftruments on the 27th of the month,and had fome good corref{pond- ing altitudes of theSun that day by which we fet our clock, and took fome equal altitudes of fixt ftars in the evening. The four following days continued cloudy, with frequent rains. But that we might not be idle in the mean time, and have it in our power to afcertain our latitude and lon- gitude, in cafe we fhould be difappointed of celeftial obfer- vations for that purpofe; Joel Bailey and Richard Thomas, went to take the courfes and diftances from our obfervatory, to the provincial weft line, which was run from Fenwick’s Ifland to the middle point of the peninfula; fo that our ob- Jfervatory might thereby be connected with Meflrs. Mafon and: Dixon’s ‘meridian, Hinpyo17 Sqn Ft snen Woowtlo 4 The 1ft of the 6th month (June) my affociates returned from this fervice; and by their care and {kill, I make no doubt, they performed it with the neceflary precifion. We had concluded that it would be a more expeditious way to take the courfes, &c, from our obfervatory to the weft line, rather along the neareft public road than to run: in one dire courfe through the woods; as by this laft me=! thod, both the expence and delay of openinga vifta, would’ have been neceflary. As the fixing the latitude and longitude of our obferva- tory muft depend chiefly on this part of the work, I {hall here infert the field notes, before I proceed to draw the conclufions ASERONOMTGAL’ PAPERS 8 conclufions from them. AndIthink it the more neceflary to be particular in this requeft, that 1 may comply with the defire of the aftronomer royal, expretfed in his note to Dr. Franklin, as follows, viz. Greenwich, December 11, 1769, “ Mr. Mafkelyne presents bis compliments to Dr. Franklin and fhall be obliged ta him, when he writes to Philadela phia, for enquiring of Mr, Owen Biddle, what is the beare ing and what the abfolute diftance of Lewestown from the Stone on Fenwick's Ile in Engh/b miles ; or elfe what is the difference of latitude and departure inEnglifh miles? He may alfos if he pleafes acquaint Mr, Biddle, that the latitude of the Middle Point between Fenwick’s Ile and Chefapeak Bay, as found by Meffrs. Mafon and Dixon, is 38°, es » $4; and the length of a degree of latitude, as measured by them, ts 68,896 flatute miles. “© Mr. Mafkelyne would alfo recommend it to Dr. Smith, and the other Norriton-oblervers, to fettle the bearing and diftance in Englifh miles between Norriton and the fouthere moft point of the city of Philadelphia, or elfe the State Houfe fquare ; as this will fill further confirm the fituation us Norriton-obfervatory, by connecting it with Meffrs. afon and Dixon's meridian line, “© Mr. Mafkelyne hopes, the Pennfylvania-obfervers will be fo kind as to fend us their obfervations of the Tranfit of Mercury, which happened November oth, if they were fore tunate enough to fee it; and any other obferwations, they have made, which have not yet been fent here, tending to cfablifh the difference of longitudes.” The Vou. I. M 86 MATHEMATICAL anp The COURSES and DISTANCES from the Obfervatory near Lewestown, to the Provincial W oft ; Line, between Benwick’s Ile and Chefapeah-Bay, are as folloxus : Courfes. Diftance Courfes. Diftance ~ Courfes. | Diftance ao | in | in Oo Perches. [| o ? Perches. | oO F Perches. 8. 43. 5 W. 495 S. a7. 15 W. LIL Si: ae. 0. We 56 6. 7, 30 ©, 5 Be 4g: 0 We 23 B t4: 0 fe] itt 8. 4g. a7 W. 446 Si 64. 0. W. 58 5. 43, 0 2. 5A Oy Ae OW. 70 5. 50.. © W. 26 Bi Phu. O Bs 25 S$, 68; 19, W. 44 S. 20.. 40 W. 98 8.64, oO le 65 By Age OW Bt Se 407.0 Ws AL S. 29. OF, 2% 5. 35. 30 Ws 52 8 3m, 0 E. 74 8. 13. 10 £. Sr 5. 28...0: W. 3% 8. 44. Oo We 5% 8.90 30 Bat Gr S. 8%. 15 W. SO. §,<21., 30. Wa, 3.79. 0 Wilh, 2A N. 76. oW. 30 AcrofsInw | C60 & 8.556. SOA. + 36% tO, 4Se 5 We 10% dian Ri- 997 §.25.. @ Wi. 84 27. Os 57 ver. 8) ar, 30 2. 40 Si 64. 0 We 33 HS. 5O 55 OL Wie 131 S$. 40, 0 de 57 5. 44.0 W. 4G 1.5. 64, © W. 78 5. 16,0 Be 26 Sree eo We 4S 8.951 Oo Wi 96 8. ta. OE. 48 Orel. OW 138 Ni 80. 0 Wat « J% §. 40 © Wid -96 S. 30. 30 W. 216 S. 85. 30 W. 44 Si a6, 50. Wil +86 S. 28. 40 W. 76 oD. 900 5O.Wy . 62 SAtde..0 H. 56 By 5. 0 W 104 S. 86. o W. 70 Go. 70. 0 Wil 46 South, « = AG 8. 65. o W. 66 S. 16. 10 E. 48 8... 8a OW. 96 &. 24, 0 W. 50 oe 6 OB, 26 5. fg. 5. 56 6.18, 45 Wa. 93 8.8 Oo Wi. sg 5. 96. o W. 80 S; 12.-0 8. A S.. 4%. .0 E. 46 5, 27..39 WwW. 159 8 6. 6 48 a oO WG 20. Ss, 8-0: W. 270 S&S. tt, Ot 174 8. Aa. 02, 42 8. 29. 0 W. 58 S. 6. 0 E. 73 8. 22, OF.) 30 $11.20 E. | 164 8. 1d, | O We 38 S. 48 0 Wil 46 8. 45., 0. E. 44 §,. 11.0 Es 11a Std, 0, Ey at §. 28, 30 E, 58 8) 6? O'R. 35 § 18. oF, 48 S..40. 39 Ex 200 8. 19. 0 W; 16 i S$. 346 Go. BE. 52 B. 30> § es: 45 Bilge OL Ws 22 8: az. OE; 49 §.4o, 5°, 16 S. 29. o W. 46 §3 yo... 088, 44 5.: 58. 0.E. 44 5. 50, @ Ev 145 By td. 0 Wand 210 8. to; 0 W. 58 5,-6%. Of8 48 South - - 31 §..19%-20.E, 4% Bio. Gib. 36 8. 40; 0B. 26 S. ta, 0 Ey 84 S. at. 30 W. 110 Sb4i' ods W% 8 14.08, 178 S. 104.10) We. | 5, 8Or 8.4%. & Wel . 4, 13 S, to, ©. &. AA 8%. 40 & 1 ee Here the line from Fen. 5. jy ge Ee 56 §. 27, 30-2. 34 wick’s Hle to the Middle §, 45.0 60 S. 12.,;0 I 38 Point was interfected at 6. at. or Ws 62 S10. o W 30 » gmiles 86 perches, from $. ati..0 We 40 5.28. 0 W. 30 the ftone in Fenwick’s Bi fs 0 We 18 §, 38. *O W vA Ife. ti The needle, with which thefe courfes were taken, being compared with out meridian line, and alfo with the Prov. W. line, was found to have 3°..55/. variation W. which was allowed for in reducing the work. : ‘ Hence, from the above work, we get the obfervatory near Lewestown, Weft of the Stone on Fenwick’s Ifle 1895,5 perches,==5 miles 295,5 perches, Eaft of the middle point, - - 9286,3 perches,==29 miles 6,3 perches, North of the middle Point, - - 7007,5 perches,=19 miles 4,3 perches, The latitude of the middle point is - - - 38° 27% 34! The fum is the latitude of the obfervatory 38. 46. 38,3 Thus ASTRONOMICAL PAPERS, 8% Thus the latitude of the obfervatory was fixed, and fo would its longitude have been fixed by the above work alfo, if we had known either the longitude of the middle point, or of the ftone on Fenwick’s Ifle. But this not appearing from any part of the work of Meffrs. Mafon and Dixon, left among their public papersin this province, the American Philofophical Society ordered us in the sth Month, (May,) 1770, to take the courfes and diftances from New-Caftle Court-Houfe, to the obfervatory in the State-Houfe {quare, by which means the middle point, and confequently our obfervatory at Lewes might be con- nected with the Philadelphia and Norriton obfervatories, and fo the longitude of the two latter being known, the longitude of the former would be known alfo, Our work. is as follows. Courses. |Diftance Courtes, Perches, Courfes, Perches, Begun at the cen-| in Ne GBC 85 258 Mit 6 E. 189 ter of Newcattle; perches, WN, 45: 5 E 168 Nu 5% 0 £, 116 Court-Houfe. N. ga: (30 E 98 Wr 3% °° 40 -E, 438 ; N. 60,. 20 HE. 23% N. 58. 0.E, 406 rN, 39% «=O Wi 3,52 Ni 78. 30 8. aas Ni 4 33 rs0 Ns 32. | 40 E, 40 N, 62, g ui 132 Noah. 4078, 66 Nida (CO Bf 50 N. 69 Oo 188 N. gh URE 42 N. 50 E. 80 Newt, o E, 135 B44, G6. E 38 Nt 56 Wa ta N. 4p. o &, Tos N. 83. 30 E. a7 N. 19. OB. ya N. 58, ° 11z B. 90, «40 E, 16% Ny 36. 99-5, |< 32 N, 67, 45 E 123 N. 73, 30 EK. 4§ VN. te go Bil 66 N. 49. OB, |. Ios N, 50 3028, | 790 N. 99.0 (0 Ed 199 N. 74, O B.] 140 8, 88. 15 E.-| 100 Ni ase 2 Eel 8 N, 64. OE. 76 § 7% go R, | 189 N. 19. o W. 50,24|| N. 59. Oo: 14% 8. 89, o£, 1O4 North. - > 89 N. 473...,%5 8 148 Ni55: .. OB. | 430 Ne 3. o Wil ver » 58 30 E, 93 8. 77% 40 B. | 35,8 Neo 7 0 B. |: 56 N, 26,. 30 We | 32 Bouth. +» « 18 Ni ay, 6 & ao Ni 56. 30 BE. | 136 Nv so... §6 Bil eoaa Bey ok. 124 To the center of the obfere Neat SO 7 N. 34 95 E. | 126 | vatory in the State-Houfe Ni fr 30 Eve 276 Ni 61 oO B 289 Square. Nigig. 26 & 48 N. 62. ° 13 & 320 N.B. The variation efthe needle by which thefe courfes were taken was 3° 1' Weft, which was allowed for in reducing the wor Thus by the above work we get- : Perches. Hew Cate Toerhoule welt of Philadelphia obfervatory * . e OILS Middle point of Peninfula weit of New-Caitle court houfe - “ = 92ta,2 int wett of Philadelphia obfervatory Peres Their fum gives the middle point welt o ia obfe : os 9223,7 But (p- 86.5 the middle point is welt of the Lewes obfervatory * ‘ aa0'g Their difference gives the Lewes obfervatory eaft of the Philadelphia obfervatory 62,6 "This difference of fixty-two perchesdoes not give quite a fecond of time difference of longitude. And 88 MATHEMATICAL anp And as, both by the Philadelphia and Norriton obfervations, the longitude of the Philadel phia obfervatory, welt of Greenwich, is Ss it « gh. of. 35! ‘The longitude of Lewis obfervatory Weft of Greenwich isintime 5. 0. 34 Or, in degrees and parts of the equator the longitude of Lewis obferva- tory welt of Greenwichis =~ - - f 75% 8.! 30)? And its latitude as above - ~ - - 38. 46. 38,3 North. For the advantage of navigation, we alfo took the courfes and diftances from our obfervatory to the Provincial light-houfe near the Cape; and on reducing the work, we find the light-houfe north of our obfervatory 132,83 perches,=29",8; and caft of the fame 944 perches=3!. 16,8. —W hence ‘Fhe latitude of the light-houfe, is - - 38°. 47’. 8/5 North. And its longitude, weft of Greenwich = - bite I now proceed to give an account of the remainder of our obfervations. The 2d of the month we had feveral good correfponding altitudes of the Sun for fetting our time-piece. . The 3d being the tranfit-day, was as fine in every re- {pect for our obfervation, as we could defire; the air calm, and not acloud in view. We had a feries of good corref- ponding altitudes of the Sun, taken in feafon, not to in- terrupt the obfervation of the tranfit, About 12 o’clock we direéted our telefcopes to the Sun, determined to keep it conftantly in the field, till the con- taéts fhould be paft; and in the mean time we fet our boys (whom we had tutored for that purpofe) to count the fe- conds by the clock, each boy counting one minute alter- nately, leaft they fhould be wearied, and not perform it with fufficient exactnefs. During the whole a perfon was ftanding by to overlook them, calling out each minute as it elapfed, and noting it down. We had agreed with each other to attend to our tele- fcopes one minute by turns, until about 7 or 8 minutes before the expected time, leaft by too fteady attention, we fhould impair our fight, and difable ourfelves from dif- cerning the contaét clearly. I had left my telefcope the minute preceding the conta&, intending to apply myfelf fteadily to it before the minute was fully elapfed; and not to quit it again until the contact occurred. When the 48th fecond was called, I applied myfelf to the telefcope, and by the time three feconds more were elapfed, I per- ceived on that part of the Sun’s limb, where | had expected the ASTRONOMICAL PAPERS. 89 the contact to take place, a {mall impreffion, which prov- ed to be the limb of Venus in contact with the Sun. All the limb of the Sun which appeared at that time in the field of the telefcope had a {mall undulatory motion, which. I apprehended was occafioned by the afcent of denfe va- pours at this place (being near the fea). On the firft ap- pearance of Venus, it was like one of thefe {mall waves on the limb of the Sun, enlarged in fo {mall a proportions that I remained doubtful for feveral feconds, whether it was any thing befides. It continued making a deeper im- preflion with that tremulous motion for about ro feconds,. when the tremor difappeared where Venus was in contact, and the indenture became truly circular with an even ter- mination. My abfence from my telefcope, juft before the contact occurred, deprived me of the opportunity of judging whether there was any appearance of an atmofphere pre- ceding the weftern limb of Venus as it came in contact ;. but when Venus had entered near one half her diameter on the difk of the Sun, my companion and-I both faw a - Jaminous crefcent, which enlightened that part of Venus’s. circumference which was off the Sun, fo that the whole of her circumference was vifible;. but it did not continue fo, until the firft internal contact took place. At the time of the internal contact, agreeable to what was noted by fome of the obfervers at the tranfit 1761; « the eaftern limb: of Venus feemed to be united to the limb of the Sun by a black protuberance or. ligament, which was not broke by the entrance of the thread of light,” until 4 feconds after the regular’ circumference of. Venus feemed to coincide with the Sun’s. For this obfervation ufed a reflecting telefcope, mag- nifying about I so times, which was in exceeding good or- der at the time, and: defined the limb of the Sun, and fpots on its dif, very nicely. Thad applied’a polar axis to it, and had altered the rack work, by which I could keep the fame part of the limb in the field with. eafe, My 9 MATHEMATICAL anv My companion Joel Bailey was not fo well provided with a telefcope. He had one of Dollona’s double objet lens refracting glafles of about four and an half feet length. This, with a ball and focket, was fixed to a poft, which made it very convenient for obfervation. Thus furnifhed we found the contacts take place as follows. Joel Bailey’s external contaé& was loft by an accident, but feen by him after ithadtakenplace,at 2".14'. 30" ap. t. The’ intertiar comtatr, Dy to, Neg, Seen ee ~ External conta, as feen by Owen 2, 1g Biddle, rs Oe ‘aide The internal contact by do. age Thefe obfervations are reduced to appar, time, And it muft be noted, that the time of the internal contact, as given by Owen Biddle, is 4 feconds before the thread of light had broke the dark ligament by which Venus’s limb was united to the limb of the Sun, that being the time he eftimated the two limbs to be in contact. Alfo, that as the external contact occurred {peedily after he went to his te~ lefcope, he will not prefume to affert that he has the time to a fingle fecond, yet he conceives he has given the exact time of that contact, as he is not fenfible of any error therein. The foregoing being an exact diary of our tranfations, we fubmit the fame to the fociety, and hope for their ap-~ probation. OWEN BIDDLE, P. 8, Since the foregoing was drawn up, 1 received from Dr, Smith the following note; which gives me pleafure to find fo little difference between the refult of Charles Maton and. Jeremiah Dixon’s meafurement and our own, Drar Sir, : SINCE you finithed your meafurement from Newcaftle Court-Houfe tothe Philadelphia obfervatory in the State-Houfe Square, the 58th volume of Philofophical Tranfadtions has come to hand, containing the whole work of Meflrs. Mafon and Dixon in meafuring a degree of lati= tude; and it is with great pleafure I find, that the longitude of the middle fee of the penin fula (and confequently of your obfervatory at Lewes) in refpect to Philadelphia, will come out almoft entirely the fame from their work as from yours, although obtained is different routs*, LONGITUDE * The refult by Mr. Biddle’s rout is got, by going from the State-Houfe obfervatory to Newcaflle Court-Houfe, agreeable to his meafurement; thence by the ram. radius and tan. gent line to the middle point. ‘The refult by Meffrs, Mafon and Dixon’s work is got, by bes ginning at the fouth point of the city of Philadelphia, (or the place of their obfervatory,) on the north fide of Cedar-ftrect, between Front-ftreeetand Delaware; thenceto their obfervatory in the Forks of Brandywine, which is 31 miles Weft, and 10,5 South of the fouthermoft point of the city; thence + the other lines of latitude and departure, wherewith they conneét the obfervatory in the Forks of Brandywine, with the middle point of the Peninfula, See their work in the volume of Tranfactions, quoted above, ASTRONOMICAL PAPERS. gt LONGITUDE of the Middle Point, and of the Lewes Obfervatory Weft of the Philadelphia Odfer- tory, agreeable to the lines of Mejrs. Maton and Dixon.. Obfervatory in the Forks of Brandywine Welt of the South point of the city mil. ch, lin. of Philadelphia, : 31. ©0. 00 Middle point of the Peninfula Ealt of obfervatory in the Forks, ee) The diff. gives the middle point of Peninfula W. of S. point of Philadelphia, 28. 74. 51 But 8. point of Philadelphia is E. of obfervatory in State-Houfe Square, Oy 28.98 The diff gives the middle point of Peninfula Weft of State-Houfe obfervatory, 28. 45. 76 But by your work the middle point is W. of. the Lewes obf. 9286,3 perches,==29. 1. 57 _ The difference gives Lewes obfecvatory Eaft of the State-Houfe obfervatory, from Mafo: and Dixon’s lines, Gi" 3s. or But by your: .eafure to Newcaftle the Lewes obfervatory was Eaft of the State-Houfe obfervatory, 62,6 perches, ==" O. TS. 65: So that Mafon and Dixon’s lines give your obfervatory more aft than your own work, only ©. 20. 16 "Thus, by their work, we get your obfervatory not quite 2, and by your own not quite 1” Eatt of the obfervatory in the State-Houfe Square. Wherefore 1 being taken asa mean, and applied to sh. of. 35!’ the longitude of the State-Houfe obfervatory Weft of Greenwich; the longitude of the Lewes obfervatory may be well depended. onas {tated from your own work, to bein time Weft of Greenwich, sh. of 34! N. B. As Britith mariners generally take their departure from the Land’s end of England, as by Mr. Bradley's obfervations of the late tranfit of Venus, the longitude of the Lizard Point is now determined to be 5°. 15’ W. of Greenwich, if that be fubtracted from 75°. 5’. 13/’,95 it will give the longitude of the Provincial Light-Houfe near the Capes W. of Lizard Point, 69°. 50/. 13,2 re oil think the above can be of any ufe, you may add it to the end of your account. 1. think there is no miftake in bringing out the different refults; but if I canfind leifure I will re- examine the work before the fheet is track off. Iam, with greatregard, your’s, &c. Philad.. Fuly 213, 1770: WILLIAM SMITH. 2st) ‘| ‘Mr, Owen Bippue. An Abftraét of Mr. BENJAMIN WES'T?s Account of the tranfit of Venus, as obferved at Providence, in New- England, June 3d, 1769. S it appears by fome letters of the aftronomer royal, which have WA been communicated to this Society, that moft of the Northern obfervers, both in Rufia and Sweden, were greatly difappointed, by the unfavourable flate of the weather, in their noble and public {pirited endeavours to ebferve the late tranfit; the American obfervations have become of the greater importance, in order to a comparifon with thefe of Greenwich, and therefore the Society think it very material to pre- ferve in their tranfaétions, fuch of the obfervations made on this conti- nent as they have been favoured with. The account of the Providence ebfervations, drawn up by Mr. Wesv, was tranfmitted by Mr. Josnpu Brown, and being laid before the Society by Dr. SMirHy the following abfiraét thereof was ordered to be publifbed at a meeting, May 18th, 1770. WHEN 92 MATHEMATICAL ann W H EN it became more generally known that there would be a tranfit of Venus in 1769, and the advantages which were like to accrue to aftronomy, and confequently to navigation and chronology, from pro~" per obfervations of it, Mr. Joszren Brown”™, a very re- {pectable merchant of Providence, being very defirous, if poflible, to obtain an obfervation of it, was pleated to ad vile with me, concerning an apparatus fuitable for fuch an obfervation, and to know if we fhould be able to obierve the tranfit with the neceflary precifion for anfwering the important defign? My anfwer gave him fo much fatisfac- tion in the matter, that he immediately fent his orders to his correfpondent in London, to procure the inftruments, His orders were accordingly executed with fidelity and difpatch; and the inftruments arrived in Providence about one month before the tranfit, Our apparatus was made by Meffieurs Watkins and Smith, London; it confifted of a three feet refleCting telefcope, with horizontal and ver- tical wires for taking differences of altitude and azimuths, adjufted with fpirit-levels at right angles, and a divided arch for taking altitudes; a curious heliofcope, together with a micrometer of a new and elegant conftruction, with rack motions, and fitted to the telefcope, Befides the be- fore mentioned inftruments, we had a fextant belonging to the government, made in Newport, by Mr. Benjamin King, under the direction of Jofeph Harrifon, Efq. now colleétor of his Majefty’s Cuftoms for the port of Bofton; its limb was divided to five miles, and by a vernier index to five fecondst. We had two good clocks, one of which ‘was made in Providence, by Mr, Edward Spalding.” was * Reading Mr. Winthrop's account of the tranfit in 1761, wae what firft occafioned Mr, BROWN to fend for a telefcope, fitted in the manner Mr, Winthrop there defcribes; after. wards, taking notice of the application of the American Philotophical Society to the Affembly of Pennfylvania, for an apparatus for obferving the tranfit of Venus, he found the orders he had fent were incomplete + Fe then advifed with the author, as mentioned above, and there» upon ordered a micrometer to be added,m——My, Brown's expence, in this laudable undertak- ing, was little lefs than one hundred pounds ferliug, befides near a month’s time of himfelf and fervants, in making the neceflury pies experiments and preparations, And here we rmuft not forget the Hon, Abraham Redwood, thy » OF Newport, who, in order that Newport aud Providence might both be fupplied with a fextant, for this fingular occafion, ordered one made at his own coft, for the ule of the Revd. Dr, Stiles. 1am fenlible en for fo public {pirited an sdtion, will receive the thanks of every wellewifher to {cience, : | | Risin esti ene Pec? ESN ASTRONOMICAL PAPERS. 93 “* We had nothing to learn refpecting the apparatus, excepting our new catadioptric micrometer, which, I have lately learned, is of Dollond’s conftrution; not having any author by us, from which we could get the ufe of that curious inftrument, we were obliged to have recourfe to experiments. When the micrometer was fixed upon the telefcupe, it was found by trial, that objeéts could not be feen with the fame-focal diftance as when it was off, and we were obliged to fcrew up the {mall fpeculum nearer to the cye; for which there is an optical reafon. From whence it was concluded, that objects fhould always be ob- ferved in the moft diftin@ point of view, the fame with the micrometer on, as when it was off. The next thing to be done was to find the apparent diameter of an object (or the angle fubtended ‘at the eye by two objects) by this inftrument. In order to this, we ftretched a cord, as ftraight ‘as poflible, one’ thoufand feet in length; which was meafured feveral times over, in order to avoid miftake. At the end of the cord was fet two circular objects, made of white paper, in a line perpendicular to the cord, and ex- actly ten feet apart; ftanding at the other end of the cord, and by opening the micrometer, we could bring the two images into an exact coincidence, or could make one of the images appear like two, and by bringing their limbs into contact, the diftance of their centers was fhewn on the {cale, to the five hundredth part ofan inch. Now from the rules of trigonometry, the angular diftance of the two ob- jects was 34’. 22",58; from thence it was known, how many inches and parts of an inch were anfwerable to that angle. ‘Thefe experiments were repeated every fair day (for no other was fuitable for thefe obfervations) till we could many times going find the diameter of a body toa fecond of a degree. From thefe obfervations we were en- abled to make a table for the micrometer, as far as the fcale extended. _ Thefe experiments were carried yet far- ther; for, by looking at two bodies whofe diftance from each other was known, .we could tell their diftance from the Vows 1 N place ‘94 MATHEMATICAL ann place of obfervation, to a critical exaGtnefs; and this was proved by accurate menfuration. 'Thefe were certainly very diverting experiments to an inquilitive mind! The gen- tlemen whoaffifted us through thefe experiments, and like- wife in the reft of our work, were the Hon. Stephen Hopkins, Efq. Mr. Mofes Brown, Dr. Jabez Bowen, Jo- feph Nath, Efq. and Capt. John Burrough. “ The regulation of our clocks, being of the utmoft confequence in this affair, was what next commanded our attention. In this part of the work we endeavoured to arrive at as great a degree of certainty as the nature of the cafe would admit.—Several workmen were employed in laying a platform of feafoned pine plank, as fmooth and le- vel as art could make it: This was fecured from rain, or other moifture, that it might not warp when expofed to the Sun. We examined this platform three times a day (when the weather would admit of it) with a very long level. On the fouth fide of the platform, and exactly per- pendicular to it, we erected a ftile ten feet high; this was likewife examined three times a day. We next perfor- ated a piece of board, into which was fixed the glafs of a {cioptric ball, fo that the center of the glafs was exaétly in the center of the perforation; this board was fo cut, and let in at the top of the ftile, that it turned upon an axis, in fuch a manner, that the center of the glafs did not alter its pofition. The Sun’s rays were tranfmitted through the lens upon the platform, where they were formed into a bright {pot, and very diftinétly defined. From the cen- ter of the lens was let fall a perpendicular upon the plat- form; from that point, asa center, was drawn a great number of concentric circles, for taking correfpondent fhades, in order to trace a meridian line; and, as our wifhes would have it, the weather proved favorable for this work. When the line was drawn*, I found from cal- culation, it declined 3” in time, eaft of the true meridian; this * The magnetic needle, being placed on his exact meridian linc, was found to differ from it 6° 4 weftward. ’ encima ASTRONOMICAL PAPERS. 95 this error arofe from the increafe of the Sun’s declination, between the times of forenoon and afternoon fhades; this {mall equation of 3” was allowed for in regulating the clocks. “ As we were willing to have every corroborating cir- cumftance to prove our work, we made ufe of the method of correfponding altitudes of the Sun, forenoon and after- noon. ‘The fextant and refle€tor were both employed in this bufinefs for feveral days preceding the tranfit (and the day following) in order to afcertain the going of the clocks. In the Jaft method (as in that of correfponding fhades) the equation of time, anfwerable to the increafe of declination. ought by no means to be neglected. The whole procefs was conducted with the utmoft caution, that no errors might efcape our notice. We found upon the whole, a furprifing agreement in thefe two methods of regulating clocks; they were feldom found to differ a fingle fecond. « Being in this readinefs, the morning of the third of June was ufhered in with that ferenity the bufinefs of the day required; all wascalm, and not a cloud to be feen. The gentlemen concerned in the bufinefs convened very early at the place of obfervation, to fee that every thing was in order; and at the fight of fuch a morning, the gladnefs of their hearts was vifibly expreffed, by the plea- fure of their countenance. : ** At noon we examined the going of the clocks, as the Sun paffed the meridian, and found them very regular. “© We began to look for the firft conta& of Venus with the Sun, at leaft 15 minutes before the time given by cal- culation, to get as early a fight of it as poflible. Venus was firft perceived, by making a dent upon the fuperior limb of thé Sun, at 2" 29°. 43". P.M. apparent time. But, as it is likely the exterior contaéts will be given dif- ferent, by different obfervers, they can be of but little con- fequence in this affair. The greateft attention was given to the interior contact; this was at 2 46’. 35.” apparent time”, 96 MATHEMATICAL ‘anv time*. From a mean of a number of good obfervations, the apparent diameter of the Sun was 31. 40',66, and that of Venus 58",66; though I could not make it myfelf more than 58", which was the fame we found it about a fortnight before the tranfit. ‘Fhe proportion of their dia- meters was neatly as 1 to 33. ‘Phe neareft approach of their centers, at the middle of the tranfit, was taken with the micrometer, and found to be ro’ ..5". “ The proportion of the diftances of the Sun and Venus from the earth, at that time, was as 3,514.3 to 1; then (allowing the Sun’s parallax at his mean diftance to be 8”,68 the fame it was found the 6th of June, 1761) the parallax of Venus was 30",04; the difference of their parallaxes 21",49 is the parallax of Venus from the Sun. The angle between the vilible way of Venus.and theeclip~ tic, 8°. 34’. 17”; and the angle made by the axisiof the ecliptic and equator, 7°. 3'..7"; their fum, 15°. 37'. 24", was the angle between the axis of the vifible way of Venus, and the Earth’s axis. The tranfit line, from total ingrefs to the middle of the tranfit (meafured in time by the yi- fible motion of Venus) was 2 55’... 36”; but Venus was more accelerated in her orbit (by parallax in longitude) at the middle of the tranfit, than at total ingrefs; this dif- ference of acceleration was 1’. 33"; therefore from the to- tal ingrefs to the middle of the tranfit was 2" 54’. 3", Thence [ conclude, that the + Firft conta& was ato - = = 2% 28'.' of But feen by us, as above, at 2. 29. 43 ¢ ap. time, Interior contact, ~ wid. AOS ge Middle of the tranfit, - - 5. 40. 38 “ Venus’s * At the moment of interior contact, the Srn’s altitude was taken with the fextant, by Mr. Mofes Brown, and bythe file by Captain John Burrough; and both gave the time with the clocks within two feconds. Fhe total ingrefs was not fo inflantaneous as I did expect it would be, but the bright cufps of the Sun, as they encompafled Venus, were much more ob» tufe, and there feemed to be a faint junction of their lintbs for at leaft 4 feconds; the moment this penumbral ligament broke, J proclaimed the time; at firtt 1 fufpe@ed the telefcope was not adjufted to a proper focus; but afterwards, by looking at the folar fpots, &c. I was con- vinced of the contrary, During the time we faw Venus upon the Sun, fhe appeared to be furrounded by a ring of a yellowith colour; its width was about one tenth of the diameter of Venus. We faw nothing that might be taken for a fatellite. + When calculated this tranfit, 1 fuppofed the longitude of our place to be much lefs than we have fince found it by obfervation. By correGing that error, the error in calculation will appear to be inconfiderable. I | 4 i i al ll : | ASTRONOMICAL PAPERS. 97 ** Venus’s parallax in longitude, at the middle of the tranfit, was 18",7; this was paffed over by Venus’s vifible motion in 4’. 44"; fo thatthe middle of the tranfit, as feen from the center of the earth, was at 5" 43. 6” mean. time. The true conjunction was 23' 21” before the middle of the tranfit, as feen from the earth’s center; con- fequently the true conjundtion was-at 5” 19.45%, mean time. At which time, the place of the Sun and planet was Gemini 13°. 27'. 3"; and the’ geocentric latitude of Venus ro’ 19",8 north. But her heliocentric latitude was 4’. 6",515 and by the rules of {pherical trigonometry, the: afcending node of Venus was 1°. 9’. 23,5. in.confequence: of the Sun, or in Gemini 14°. 36'. 26", 5% “ From the foregoing calculation it appears, that the mean motion of Venus is.37" forward of what it ftands: in Dr. Halley’s tables, and her afcending node a’. 41". “ It is probable Dr. Halley’s folar numbers need. fome correction. likewife; the following may not. be far from truth, viz. add to Dr. Halley’s mean motion of the Sun, for any year of the chriftian era, 25", and to the apogee. 6'. 18"; for each century after 1700 add 14,666 to the mean motion, and to the apogee 3'. 53”; then by ma- king ufe of the Parifian* equation of the Sun’s center, his place may be had within a {mall matter of truth. “© By taking the mean of a number of obfervations, the latitude of our obfervatory: was found to be 41° 50’. 41” north}. The longitude was obtained by obferving the emerfions of Jupiter’s fatellites, compared with the corref-. ponding obfervations made at Cambridge, in New-Eng- land, by Mr. Winthrop, which he was fo kind.as to fa» vour * According to the Parifian hypothefis, the eccentrity ofthe earth's orb is 1680 parts, of which the mean diftance of the earth from the Sun is 100,000. + The latitude of the place being of great confequence, and the fextant and ftile not giving: it exa@y alike, the perfevering Mr. Brown contrived to make ufe of the micrometer asa lens, which he placed on his houfe, twenty feven feet high, and exactly perpendicular to a center on a horizontal platform below, on which was drawn a meridian line; the Sun’s image on this platform was feen to move very fenfibly. By this the latitude was finally determined. "The Sun’s meridian altitude, being taken for feveral days by this long ftile, the latitudes thence found did not differ from each other more than rs feconds. At the time this was done, we had {een no account that a glafs had been made ufe of, as here defcribed; but fince this went to the prefs, we learn from Dr. Long’s aftronomy, that he found the latitude of Cambridge, in England, by the fame method, 98 MATHEMATICAL: a£n'p vour us with; and for which we return him our fincere thanks. Providence was found to be 16’ in longitude weft from Cambridge. Mr. Winthrop has hitherto found the longitude of Cambridge to be 71’. weft from the royal obfervatory at Greenwich; fo that the longitude of Provi- dence is about 71° 16’ from the royal obfervatory. “| fhall now give the reader a fhort account of the parallax herein mentioned, and how the planets are affected thereby. ‘© The horizontal parallax of the Sun is that angle at the Sun’s center, which is included between two lines fup- pofed to be drawn, one from the Sun’s center to the cen- ter of the earth, the other from the Sun’s center to the furface of theearth. Or, in other words, it isthe angle, under which the femidiameter of the earth would appear to an eye, at the center of the Sun. The way that parallax affects the Sun and planets is, it makes them appear below their true pla~ ces in the heavens, except they be in the zenith of the ob- ferver; in that cafe parallax hath no effec at all; and the reafon is, becaufe the obferver is in that right line which joins the centers of the earth and planet. Parallax may af- fect the planets places feveral ways; asif theobferver fhould view the planet upon a vertical, cutting the ecliptic at right angles; inthis cafe, parallax will affect its placein refpe&to latitude only; but if the obferver be fituated in the plane of the ecliptic, it willthen alter its place, inrefpect to longitude only; and if the planet be viewed in an oblique pofition, with refpect to the ecliptic, parallax will affect its place both in longitude and latitude. ‘The horizontal parallaxes of the planets are to each other in a reciprocal proportion to their diftances; that is, the planets which are neareft have the greateft parallax, and thofe which are moft remote, the leaft. Thence it follows, if two planets are viewed together, that which is neareft will appear juft fo much below the other, as what the difference of their parallaxes is. The nearer a planet is to the horizon of the obferver, the greater is its parallax, and inthe horizon it is the greateft poffible; and is then called the horizontal parallax. oe cace | | } | I f | ASTRONOMICAL PAPERS. 99 “© Hence comes the method of inveftigating the Sun’s parallax, from: obfervations of Venus on his difk. At the time of the tranfit, the third day of June, Venus was much nearer to the earth than the Sun was, and, of confequence, was much more affected by parallax. This effect was pro- duced in a twofold manner, in refpect to us in the nor- thern regions of our earth. Firft, Venus was. deprefled upon the Sun, by parallax in longitude, bringing her to a conjunction with the Sun fooner to.our point of view, than. to a fpectator at the center of the earth. In the fecond place, fhe was carried nearer to the center of the Sun, by- parallax in latitude, thereby lengthening the tranfit-line; both which. effects confpired to. accelerate the time of firft interior contadt.. Now. to an obferver in Great-Britain,. parallax had a ftill greater effet, by what is faid before :- That is, fome minutes. paffed after the contact was formed. to the obferver there, before it was feen.by us. Now the difference of longitude, between the two places of obfer- vation,, being accurately known, the effect of parallax, between the two places, is. likewife Known; for the dif-. ference of longitude, by thefe obfervations, will be con~ fiderably lefs than the true difference. «© The method of calculating the Sun’s parallax, from: thefe obfervations, is by trial; the parallax will be fup- pofed of that quantity, which the obfervations found it in 1.7613. hence the total effect of parallax, at each place of. obfervation, muft be computed; and if it fhould be the fame as given by obfervation, it will prove. the aflump- tion to be juft; but if, by obfervation, it fhould be greater or lefs than by calculation, the Sun’s parallax will turn out to be greater or lefs in the fame proportion.—When the Sun’s parallax is known, the. diftance of the earth, and of all the planets, from the Sun,. will be known like-. wife,” OBSERVATIONS. 100 MATHEMATICAL awnopb OBSERVATIONS of the Transit or VENUS over the SUN, and the Eciipse of the SUN, on Fune 3d, 1769, made at the ROYAL OBSERVATORY, Greenwicu. By the Revd. NEVIL MASKELYNE, B.D. £. &. S. and Aftronomer Royal. Communicated to the Society by Dr. Sm1tH, and ordered ta publifoed at a meeting, May 18th, 1770. HE weather, which had been cloudy or rainy here, with a fouth wind, for the greateft part of the day, began to clear up at four o’clock in the afternoon, the wind having returned to the weft, the fame quarter in which it had been the afternoon before, which was re- markably fine and ferene, though it changed early in the morning preceding the tranfit. Towards the approach of Venus’s ingrefs on the Sun, the fky was become ayain very ferene, and fo continued all the evening, which af- forded as favourable an obfervation of the tranfit here as could well be expected, confidering that the Sun was only 7°. 3’ high at the external, and 4° 33’ at the inter- nal contact. I obferved the external contact of Venus at 4", 10’. §8' apparent time, with an uncertainty feemingly not exceeding 5”; and the internal contact, by which I mean the completion of the thread of light between the circumferences of the Sun and Venus, at 7 29’. 23" ap- parent time, with a feeming uncertainty of only 3"; for fo long was the thread of light in forming, or the Sun’s light in flowing round and filling up that part of his cir- cumference, which was obfcured by Venus’s exterior limb. Neverthelefs, I would not hence infer, that obfervations made by aftronomers in diftant places thould agree together within fuch narrow limits; for I know they will not even in the fame place, and that a difference in the fkill or judgment of the obfervers, in the telefcopes, and perhaps in fome other little circumftances, not eafily diftinguifhed, may produce much greater difagreements, elpecially if the Sun be low, as it was here; in like manner as in ob- ferving cB ASTRONOMICAL PAPERS. tor ferving the eclipfes of Jupiter’s fatellites, the immerfion or emerfion fhall often feem inftantaneous, or nearly fo, equally to two obfervers in diftant places, and yet the ab- folute times of the obfervations may differ a minute of time or more from each other, owing to the difference of tele- {copes, weather, or other circumftances. Indeed, in the prefent cafe, the limit of differences is certainly much nar- rower; but what itis I fhall not at prefent venture to fug- geft, as that may better be done, when all the obfer- vations that fhall have been made of the tranfit are col- lected together. The telefcope which I ufed, was an ex- cellent reflecting one of two feet focus, made by the late ingenious Mr. Short, and is the fame with which the lat tranfit was obferved here by Mr. CharlesGreen. I applied the magnifying power of 140 times, and ufed fmoaked glafles to defend the fight, which are much preferable to black or red glaffes, as fhewing the objeéts more diftin®, and being much more pleafant to the eye. - I fhall now endeavour to defcribe, as accurately as I can, fome other phoenomena which I noted during the immer- fion of Venus, and to mention fome others, which by fome ingenious perfons were expected to have been feen, but which I could not difcover. It had been thought by fome, that Venus’s circumfer- ence might probably be feen, in part at leaft, before the entered at all upon the Sun, by means of the il- lumination of her atmofphere by the Sun; I therefore looked out diligently for fuch an appearance, but could fee no fuch thing. I was alfo attentive to fee if any penumbra or dufky fhade preceded Venus’s firft impreffion on the Sun at the external contact, {uch a phoenomenon having been obferv- ed by the Rev. Mr. Hirft, F. R. S. at the former tranfit of Venus, in 1761, which he obferved with much care and diligence at Madrafs, in the Eaft-Indies; but I could not difcern the leaft appearance of that kind. I would not, however, be therefore thought to call in queftion either Vou. hi et”, Mr. 102 MATHEMATICAL anp Mr. Hirft’s difcernment or fidelity; as 1 am fenfible that the tremors of the limbs of the Sun and Venus, occafioned by the vapours at the altitude of 7°, might eafily obfcure a faint objec. When Venus was a little more than half immerged in- to the Sun’s difk, I faw her whole circumference complet- ed, by means of a vivid, but narrow and ill-defined border of light, which illuminated that part of her circumference which was off the Sun, and would otherwife have been invi- fible. This [ might, probably, have feen fooner, if I had at- tendedto it. [continued to fee it till withina few minutes of the internal contact, and grew apprehenfive that it would prevent the appearance of the thread of light, when it came to be formed; but it difappeared about two or three mi- nutes before, as well as I can remember: After which the regularity of Venus’s circular figure was difturbed towards. the place where the internal contact fhould happen, by the addition of a protuberance, dark like Venus, and project- ing outwards, which occupied a fpace upon the Sun’s cir- cumference, which bore a confiderable proportion to the diameter of Venus. Fifty-two feconds before the thread of light was formed, Venus’s regular circumference, fup- pofed to be continued as it would have been without the protuberance, feemed to be in contact with the Sun’s cir- cumference, fuppofed alfocompleted. Accordingly, from this time, Venus’s regular circumference, fuppofed defined in the manner juft defcribed, appeared wholly within the Sun’s circumference; and it feemed, therefore, wonderful that the thread of light fhould be fo long before it appear- ed, and the protuberance appearing in its ftead. At length, when a confiderable part of the Sun’s cir- eumference, equal to one third or one fourth of the dia- meter of Venus, remained ftill obfcured by the protube- rance, a fine ftream of light flowed gently round it from each fide, and completed the fame in the {pace of three feconds of time, from 7". 29’. 20” to 7". 29’. 23” apparent time; and Venus appeared wholly within the Sun’s lucid circumference; ASTRONOMICAL PAPERS. 103 circumference; but the protuberance, though diminifhed, was not taken away till about 20” more, when, after be- ing gradually reduced, it difappeared, and Venus’s circu- lar figure was reftored. An ingenious gentleman of my acquaintance having defired me to examine if there was any protuberance of the Sun’s circumference’ about the point of the internal contact, as he fuppofed fuch an appearance ought to arife from the refraction of the Sun’s rays through Venus’s at- mofphere, if fhe had one; I carefully looked out for fuch a circumftance, but could fee no fuch thing; neither could Ifee any ring of light round Venus, a little after the was got wholly within the Sun: But, I confefs, I did not re- examine this latter point afterwards, when the was further advanced upon the Sun, at which time other perfons at the obfervatory faw fuch an appearance. How far from the ring of light, which I faw round that part of Venus’s circumference which was off the Sun, dur- ing the immerfion, may deferve to be confidered as an in- dication of an atmofphere about Venus, I fhall not at pre- fent inquire; but [think it very probable, that the protu- berarice, which difturbed Venus’s circular figure at the in- ternal contact, was owing to the enlargement of the dia- meter of the Sun, and the contraction of that of V. enus, produced by the irregular refraGtion of the rays of light through our atmofphere, and the confequent undulation of the limbs of the two planets; the altitude of Venus being only 4° 48’, though the Sun’s limb was more diftiné and fteady than ufual at that altitude. This conje€ture feems corroborated by two circumftances: one is, that Venuis’s limb, from its firft appearance to the total immerfion, as well as afterwards, was very ill defined, and undulated very much; the other is, that her horizontal diameter, which I meafured foon after the internal conta& with an excellent achromatic objet glafs micrometer, fitted to the two feet reflecting telefcope, was only fifty-five and three fourths of a fecond, by a mean of eight trials, or about 2 : lefs 104 MATHEMATICAL anp lefs than it fhould have been, from the obfervations made, with the like inftrument, atthe tranfit of Venus, in 1761, by Mr. Short, Mr. Canton, Mr. Haydon, and Mr Mafon, when the Sun was at a confiderable altitude; and moft likely the Sun’s diameter was enlarged in proportion, though it might have been difficult to have afcertained it by aétual meafure, had time allowed me to make the ex~ periment with the fame micrometer before the Sun entered into a black cloud near the horizon. Six other perfons alfo obferved the contacts of Venus here, and noted fome other phoenomena. Their names are, the Rev. Malachy Hitchins, a gentleman well ac- quainted with aftronomy and aftronomical calculations, who has made and examined many belonging to the nau- tical almanac, and has been fo obliging as to come here and affift me in making aftronomical obfervations, during the abfence of my affiftant, Mr. William Bayley, who is gone to the North Cape, by appointment of the Royal Society, to obferve the tranfit of Venus there. The others are, the Rev. William Hirft, who obferved the former tranfit of Venus, in 1761, at Madras; John Horfley, Efq. a gentleman whom I had the pleafure of firft com- mencing an acquaintance with during my voyage from St. Helena to England, in the Warwick Eaft-India fhip, and who then, and in feveral voyages fince to the Eaft-Indies and home again, obferved and calculated the longitude from diftances of the Moon from the Sun and fixed ftars with the greateft accuracy; Mr. Samuel Dunn, who has had a good deal of practice in making aftronomical obfer- vations, and who carefully obferved the former tranfit of Venus, in 1761, at Chelfea; Mr. Peter Dollond, whofe great fkill in conftructing achromatic and reflecting tele~ {fcopes; and Mr. Edward Nairne, whofe fkill likewife in the fame way, and in making all kinds of mathematical and philofophical inftruments, are fufficiently known to the public, : ; Mr, al ASTRONOMICAL PAPERS toy Mr. Horfley and Mr, Dunn obferved with me in the great room; Mr. Hitchins and Mr. Hirft, in the eaftern fummer-houfe; and Mr.-Dollond and Mr. Nairne in the weftern fummer-houfe; by three clocks placed in the re- {pective rooms, which were compared with the clock in the tranfit room, before the external conta@t, and again after the interhal contact was paft; whence the times of the obfervations, as noted by the clocks, were reduced. to the. time of the tranfit clock, and thence to apparent time. Their obfervations, together with my own, are given: in the following table, as reduced to apparent. time.. Regular’ cir- (Thread oflight Magni-- External — jeumferencesin] compleated, | Telefcopes made ule of. fying contact. contact, or, the inter- power. nal contact. h. m. fec. Dim. 166.) Re. hi fee, , N. Mafkelyne} 7 xo 58 7. a8 3t 7 29 23 2 feet reflector, 140 | M. Hitchins 9 10 354 7 ao ay 7 a8 54 6 feet reflector. 9° W. Hirtt Metts tt me ceeeene: 7 ay 38 a feet reflector. 55 J. Horfley 7 IO 44 o oe 1s 7 29 28 | Iofeet achromatic. | 50 S. Dunn P10 BF 7 ay 28 7 29° 48 3% feet achromatic. 140 P. Dollond 4 IL Ig hein sae 7 29 20 34 feet achromatic. 150 i. Nairne, 4 II 30 eet enaenne 7 49 20 a feet refleor, 120 Mr. Dollond and Mr. Nairne ufed telefcopes of their own conftruction;. but they did: not wait ’till the thread of light was formed at the internal conta&, but noted the time, when they judged it was jultready tobe formed. The three and an half achromatic telefeopes were thofe made with three object glaffes. The differences between the different obfervations feem: pretty confiderable, and greater than I expected, confide~ ring that all the telefcopes. yor be reckoned pretty nearly equal excepting the fix feet refleCtor, which is much fupe= rior tothem all; and to its greater excellence and diftinct- nefs I principally attribute the difference of 26", by which Mr. Hitchins faw the internal contact before me; as I can depend upon his obfervations. Poffibly the greatnefs of the differences might arife from the low altitude of the Sun and Venus; and then the like differences would ‘not be fo much to be feared in places where the obfervation: ; may 106 MATHEMATICAL anp' may be made at higher altitudes; otherwife the Sun’s pa- rallax will not be deducible from the tranfit of Venus with that accuracy which has been expected. The other appearances about Venus, noted by the fix obfervers, which they have communicated to me are as follows : Mr. Hitchins remarks, that, at the firft conta, though there was a tremulous motion in the Sun’s limb, yet that part of it which the planet entered was very well defined, and the firft impreflion of Venus appeared to be inftantane- ous, andasa black, fharp point. At theinternal coincidence of circumferences, the fluctuation of the Sun’s limb was increafed, and the limb of Venus being affected in like man- ner, there was an uncertainty of about 10” in eftimating the faid coincidence; but at the breaking in of the thread of light between the limbs, there was not a greater uncer- tainty than a fecond and a half of time. At the internal coincidence of circumferences, the limb of Venus next to that of the Sun being protuberant, her vertical diameter appeared to be longer than the horizontal one; but when the Sun approached the horizon, and was fcarce above a de- gree high, Venus’s horizontal diameter appeared to be fen- fibly longer than the vertical, which was, probably, owing to refraction. After the internal, contact, there appeared a luminous ring round the body of Venus, aboutthe thick. nefs of half her femidiameter; it was brighteft towards Venus’s body, and gradually diminifhed in {plendor at greater diftances, but the whole was exceflive white and faint. This radiancy round the planet feemed to him to be greater in Mr. Nairne’s two feet telefcope than in the fix feet Newtonian reflector. After the fecond or internal contaét, Mr. Hirft left off obferving with Mr. Dunn’s two feet reflector, and had a fight of Venus in the fix feet Newtonian refleQor, in which he thought he preceived a glimmering of light about the upper part of the circumference of Venus, or that part of the planet which entered laft into the folar difk. After ASTRONOMICAL -PAPERS, 107 After Venus was got within the Sun’s difk, a light a little weaker than that of the Sun, of a purplifh colour, appeared to Mr. Horfley, to the left hand of Venus, which is really totheright, the telefcope inverting objects. This light he faw for fix or feven minutes. From 7" 28’ 26” to 7" 28” 30" apparent time, Mr. Dunn faw a very faint rim of light at Venus’s exterior limb. After Venus was wholly on the Sun, he faw a faint ring of light furrounding her,. both with the three and a half feet telefcope, and Mr. Nairne’s two feet reflector. When one third of Venus’s:diameter was entered upon the Sun, Mr. Dollond firft faw a light about the exterior limb of the planet: This light,. during all the time of its continuance, appeared rather reddifh, and in all refpects like irregular refrated light. After Venus was wholly entered upon the Sun, he faw a faint ring furrounding her, After Venus was wholly entered upon the Sun, and her. exterior limb was near one of her femidiameters diftant from theSun’s circumference, Mr. Nairne faw a faint light’ round the planet, rather brighter and whiter than the bo- dy of the Sun. _ Fortunately, the weather was.as favourable for the ob- fervation of the eclipfe of the Sun, the next morning, as it had been the evening before for that of the ingrefs of Venusupon the Sun; which is of the more confequence, as the comparifon of it with the obfervations which may be made of it in the northern and eaftern parts of the world, will ferve to fettle the longitudes of thofe places, and con- fequently render the obfervations which may be made there of the tranfit more ufeful and valuable. I obferved the beginning of the eclipfe at 18". 38’. 54", and the end at 20" 23’. 30” apparent time, with the two feet reflector, ufing the magnifying power gotimes, And at 19" 29/. 31” apparent time, I obferved the greateft eclipfe, at which time I found the remaining lucid parts of the Sun 15’. 15”, with Dollond’s micrometer, affuming the sd, Caecss aknaste Getee cee dees 108 MATHEMATICAL AND the horizontal diameter of the Sun 31’. 31”, whence the value of the fcale of the micrometer was determined for the prefent purpofe. Hence the eclipfed parts of the Sun were 16’. 16", or 6 dig. 11',62 on the northern part of his difk. Mr. Hitchins obferved the beginning of the eclipfe with a three and an half achromatic telefcope magnifying 150 times (the fame with which Mr. Dollond obferved the con- tats of Venus) at 18™ 38’. 59", and the end of the eclipfe with the fix feet refleCtor with the magnifying power go, at 20" 23°. 35” apparent time. And Mr. Samuel Dunn obferved the beginning of the eclipfe at 18" 39’, 9”, and the end at 20" 23'. 33” with the other three and an half feet achromatic telefcope, magnifying 140 times, the fame with which he obferved the contaéts of Venus. Several inequalities in the Moon’s circumference, feen upon the Sun’s difk during the eclipfe, were diftinly difcerned by all of us, the air being very clear, and the objects fleady, ‘The whole feries of meafures of the lucid parts, which 1 took with the achromatic objedt glafs micrometer applied to the two feet telefcope, was as follows, seed Se time. Lucid parts, . mm, fee. m. = fec. 19 2% %3 ee ee 15 40,5 24 4 — ee 1g 46,5 26 9 — ew Is 20,9 28 26 — ee 15 45,6 30 14 —--—--- 15 14,5 31 44 —— 15 16,4 32 80 “me is. 36, 33 19 —— oe 15 19, 34 28 -——— = 15 25,4 36 19 — 15 3559 37 500 ee 15 49,4 Some Account of the TRANSIT of Venus, and Ecuipsé of the Sun, as obferved at the Lizard Point, June 3a, 1769. By Mr. Joun BRaDLey. R. Mafkelyne, the aftronomer-royal, who has drawn up this fhort account, mentions that having had fome doubts that neither the latitude nor lon~ gitude of the Lizard Point were duly fixed, “ he had pro- pofed thofe doubts to the Board of Longitude, who being fenfible of the importance of determining the pofition of a place ASTRONOMICAL PAPERS. tog place of fo much confequence in the Britith navigation, refolved that proper aftronomical obfervations fhould be made at the Lizard for that purpofe; and the tranfit of Venus appeared a convenient opportunity, itfelf affording one of the beft means of determining the longitude of places; and the eclipfe of the Sun which was to happen the morning after, affording another of determining the fame. wef * Accordingly Mr. John Bradley, nephew of the late Dr. Bradley, and formerly his affiftant at the royal obfer- vatory, was appointed to make thefe obfervations. The inftruments which he was provided with, were an equal- - altitude and tranfit inftrument in one, an aftronomical quadrant, and a reflecting telefcope of two feet focus, all made by Mr. Bird; and an altronomical clock, with a gridiron pendulum, made by Mr. Shelton. “« Mr. Bradley ftaid at the Lizard 51 days, viz. from May 13th to July 3d, during which time he was lucky enough to make a great many ufeful obfervations; fome of the principal of which were the following, Viz— Several meridian altitudes of the Sun and pole flar; by which the latitude of the Lizard Point was determined to be 4.98! 5:7! a go"saNac, The tranfit of Venus and eclipfe of the Sun. viz 1769 Apparent time. June 3d. 6°. 50’. 754 External contaét of Venus and the Sun, very exact, the eye be- ing fixed on the place. 7. §. 25 Internal conta&; doubrful to 4 or 5", a cloud having hid Venus fo long; and at the cloud’s go- ing off, 2” after the time fet down, a thread of light appear+ ed very diftind between the circumferences of the Sun and Venus. 18. 14. 54 Begin. of the eclipfe of the Sun] Both 19. 57. 17 End of the eclipfe. HS on. I. oe es good * Thefe ee i er a ener oer a Li i 110 MATHEMATICAL awnpb « Thefe obfervations were made with the 2 fect reflect- or, and the magnifying power 120. havi fec. . June §. 9. 20, 14 Em. rft fat. of Jupiter. Jupiter had not been from under the clouds 10 when he faw the fatellite, yet he reckons the obfervation good. Juners. 11. 13. 46 Em, wit fat. A thin haze about: Ju- piter, but the obfervation pretty good. ‘Thefe emerfions were ob- ferved with the fame telefcope, but with the magnifying power 100. Comparing the obfervation of the contaéts of Venus at the Lizard with his own at Greenwich, making a fmall allowance for the difference arifing from the effet of par- allax at the two places, Mr. Mafkelyne makes the differ- ence of meridians of Greenwich and the Lizard.— By the external contaét of Venus 20’. 53" : By the internal contact of ditto 21 1 tof time, The mean by the contacts ao 0837 By the two emerfions, making a {mall allowance for the difference of brightnefs of the telefcopes, he makes the difference of meridians as follows, viz. By the firft emerfion - Rally woh: By the fecond emerfion - 21. 52 . The mean of thefe is - =, ac, 2009 The mean by thecontadls - 20. 57 ~ enone teatenmnnnsen tenement Mean of the two means - 21. 13525 But Mr. Mafkelyne, till he has time to compare the o- ther obfervations, fixes on 21’. o” of time=5°. 15’. of the equator, for the difference of longitude of the Lizard weft of Greenwich. The above is taken from the nautical almanac for 1771; and it was thought might be a proper addition to the foregoing account of the tranfit of Venus, at Greenwich, drawn up by the Aftronomer Royal. ALETTER ASTRONOMICAL PAPERS. ir ALETTER from the Revd. Nevil Mafkelyne, B. D. F. R. S. Aftronomer Royal, to the Revd. William Smith, D. D. Provoft of the College of Philadelphia; acknow- dedging the receipt of the NORRITON Objervations of the Tranfit of Venus, and giving Jome account of the Hud- fon’s-Bay and other Northern Obfervations of the fame. Read at a meeting of the American P hilofophical Society, May 18th, 1770+ Greenwich, Dec. 26, 1769. Revd. SI Ry “WRETURN youmany thanks for the account of the va- luable obfervations of the late tranfit of Venus, made at Norriton by yourfelf and two other gentlemen. which I have communicated to the royal fociety. It is ordered to be printed in the volume of their tranfactions for this year, and I will take care to fee that it is printed correQly. “© T fent to the Honourable Mr. Penn, a good while ago, my obfervations of the eclipfes of Jupiter’s firft fatel- lite made this year, defiring that he would communicate them to you, and I hope you * have received them. “© By a mean of your five firft /mmerfions (rejecting that of May sth as too near the oppofition to the Sun) compared: with the nautical almanac, the difference of our meridians. is 5°. 1’. 32”. But bya mean of my two firft immerfions,. - the correction of the nautical almanac fora 2 feet reflector of Short’s is + 20",5 which applied to 5". 1’. 32” gives 5". 1. 52", for the difference of the meridians of Green- wich and Norriton by the zmmerfions. “ By a mean of your emerfions, June 6th and 13th,. compared with the nautical almanac, the diff. of our me- ridians is 5". 1! 28",5; and by amean my of two emer- fions June 8th and July 1ft the correction of the nautical almanac is—11’,5, which applied to 5”. 1’. 28”,5 gives 5°. 1’. 17" for the difference of our meridians by the emer- jfions; but, by the immerfions it was found above, 5°. 1/. 52',5. The mean of thefe two refults is 5°. 1’. 34",7 for the * They are inferted above p. 19. 112 MATHEMATYOQOAL Awop the true difference of our meridians, which happens to agree to a fecond with what you deduced from a comparifon of all the obfervations with the almanac alone. J “ Jf any further obfervations of the eclipfes of Jupiter’s fatellites {hall be made the enfuing feafon, I fhall be obli- ged to you for a communication of them; which will ferve further to confirm the difference of our meridians. ‘© The many curious optical phenomena: noted: in your account [of the orriton obfervations] cannot but be very acceptable to philofophical readers. ‘The Sun was too low here to give mean opportunity to obferve the firft im- preffion of Venus (perhaps J ought to fay of her atmofphere) in the fame manner you faw it. Mr, Hirft’s account of his obfervation of the former tranfit 1761, at Madras, feems to have a great refemblance to yours... But L have feen.no fimilar * account with refpect to the prefent tranfit.. Per- haps none of the obfervers had the Sun fo bright and clear as you had. ie 3 «“ Your meafures of the neareft diftances of the limbs of the Sun and Venus determine very well the neareft ap- proach of Venus to the Sun’s center, which was a very important obfervation, and could not be made here. — If the appulfes of the limbs of the Sun, and Venus’s center, to the hairs of the equal altitude inftrument fhould + arrive in time, I will take care that they be inferted in the place left for them. “ T fee Mr. Rittenhou/e, in making his projection, af- fumed 8",65 for the Sun’s horizontal parallax at the mean diftance; but, by the obfervations of the tranfit in 1761, Mr. Short } and myfelf both found that to be the parallax on * Ajl the obfervers in this province noted much the fame phenomena as thofe referred to in this letter. + They were not inferted in our own printed account, for the reafons given in p, 33, } Mr, Rittenhoufe affumed the parallax 8”,65 from Mr. Short’s paper in Phil. ‘Tranf. vol. 52, part 2d. page 621, where the parallax of the Sun on the tranfit day, 1761, is certainly made by Mr. Short 8,52 and the mean horizontal parallax 8,65 as taken in our projection. Mr. Short’s wordsare very clear. , After going through his laborious and accurate calculations, from. the different obfervations of the tranfit 1761, he concludes asfollows——-«« The parallax of the Sun being thus found, by the obfervations of the internal contact at theegrefs == 85%, on the day of the tranfit, the MEAN HORIZONTAL PARALLAX of the Sun is 8,65,” We prefume then there muft be fome fuhfequent paper of Mr, Short’s, and the aflronomer royal, (which we haye not yetfeen) thatm akes the parallax of the Sun 8,65 on the day of the tranfit1761/ However the {mall difference of lefs than two-tenths of a fecond will not materially affect the projeGion ee ASTRONOMICAL PAPERS. 113 on the day of the tranfit; whence the Sun’s mean horizon- tal parallax fhould be 8",84. But whatit will be as refult- ing from the obfervations of the late tranfit, cannot be known without a number of laborious calculations, which I have undertaken. uot «ee «“ The Swedesand Ruffians were very unfuccefsful. No complete and thorough good obfervation of the total dura- tion is come to hand from the north, Our obfervers at the North Cape faw the ingrefs only, and that in a very bad ftate of air. « The Hud/on’s-Bayobfervers, Mefirs, Dymond and Wales, had better luck, and obferved all the contacts, and neareft approach of the centers, as follows. | we ‘qf External conta 0", 97". 455. 7... rft Internal conta 2. 19. 23). ' ad Internal conta 7. 0.4795 ad External contact 7s IQs 21. J “The laft very hazy. “ At 4%. 5’. 30", apparent time, was the neareft ap- roach of Venus to the’ Sun’s!center; when the diftance of her interior limb from the Sun’s limb was 6'..22". The diameter of Venus was's9",5 and the San,s horizontal dia~ meter! 31/. 3254. Hence the neareft approach of Venus to the Sun’s center was about 9’. 54", or 7” lefs than by your obfervations; undoubtedly owing to a greater parallax. Their latitude'is 58°. 47' 30" north. They could only ob- ferve five occultations’ of ftars by the moon to determine their longitude, and [ have not yet found any obfervations made in Furope, or elfewhere, correlponding to them. “ { could with that the differenceof meridians of Norriton and Philadelphia, could be determined by fome meafures and bearings, within one-fiftieth or one-hundredth part of the whole; in order toconnect your obfervations with thofe made at Philadelphia and the Capes of Delaware, as alfo to conneét your obfervations of the longitude of Norriton with thofe made by Meflrs. Mafon and Dixon, in the courfe of meafuring the degree of latitude. I hope to be gfitieg mes favoured P All’ appatitime, 114 MATHEMATICAL awnp favoured with an account of your obfervations of the late tranfit of Mercury, if you made any, and of the late eclipfe of the moon. I fhallbe obliged to you for the continuance of your correfpondence, and am, Sir, yours, &c. NEVIL MASKELYNE. Account of the terreftrial meafurement of the difference of longitude and latitude, between the obtervatories of Nor- riton and Philadelphia. | | To the AMERICAN PHILOSOPHICAL SOCIETY, &c. GENTLEMEN, GREEABLE to the appointment you made (at _ the requeft of the aftronomer royal) Mr, Lukens, Mr. Rittenhoufe, and myfelf, furnifhed with proper in- ftruments, met at Norriton early on Monday, July 2d, for the above fervice; and took to our affiftance two able and experienced furveyors, viz. Mr. Archibald M‘Clean, and Mr. Feffe Lukens. ‘The firft thing we did, was accu~ rately to afcertain the variation of our compafs, which we found 3°. 8', by Mr. Rittenhoufe’s meridian line. We then carefully meafured our chain, and adjufted it to the exact ftandard of 66 feet. In the execution of the work, whenever the inftrument was duly fet, each courfe was taken off, and entered down feparately, by three different perfons, who likewife kept feparate accounts of all the diftances, and fuperintended the ftretching of every chain, and the levelling and plumbing it, whenever there was any afcent or defcent in the road, July 4th. We finithed the furvey ; and Mr. M‘C/ean, Mr. Feffe Lukens and myfelf, then agreed to bring out the dif- ference of latitude and departure feparately on each courfe and diftance to four or five decimal places; and there was fo great an agreement in this part of the work, when exe- cuted, that we had all the fame refults to a few links, and the whole was at laft brought to agree in every figure, by comparing ASTRONOMICAL PAPERS. 115 comparing the few places where there was any difference, which fcarce ever went farther than the laft decimal place. Mr. M‘Clean and Mr. Lukens took the trouble to bring out their work by multiplying each diftance by the natural Sine of the courfe, to the radius unity, for the departure; and by the cofine for the latitude. Mine was done by Ro- bertfon’s tables. The whole follows, and we think it may be depended on for corre¢tnefs. Courfes and Diftances from Norriton obfervatory to the ob- fervatory in the State-Houfe Square, Philadelphia, and from thence to the obfervatory of Meffrs. Majfon and Dixon, at the fouth point of the city of Philadelphia; taken Fuly 3d and ath, 1770: With the 4 diese dd longitude and latitude, between the faid oblervatories, thence deduced. o 2, ; Magnetic Diftances : 8 Courfes, chains. links] *Northing. Southing. Eafting. Welting. “Ts, 27°, oo! W.|, 13,00 “s+ 11,5831 “ee. 5,9018 a9. 68. 00 E,| . 11,00 "2s 41207 10,1990 “<= * 3,N. 89. oo E, 8.29 00,1447 8,2337 - oom as. 66. 00 E.| 19,77 “#4 2 = 959077 7612937 “42 = 5\S. 80. @0 E.| 10,00 “= «© 1,7365 9,848% — 6S. 70. 20 EB. 22,00 es es 754040 20,7166 os < ©. p ae 68 30 E.| 60,00 “- 2 41,9900 55,8250 « » 6 « 8. 72, TO E.| 6,00 «ne « 97,9624 pot o 2 ® gS. 70. 00 E.| 69,00 “= = =] 23,5993 64,8388 wie wee tol§. 50. 00 H.| 20,22 “ss * 12,9971 15,4894 = 6 ee Sumsin 2ocourfes.| 257,28 00,1447 98,6208 26,1900 5.9018 TiS. 4%. 00 E.[ 12,00 “ae os 8,917 80296 ~ eres 12S. 45. 00 E.f 40,00 “se 28,2843 28,2843 ‘ s-- & 13/5. 60. 00 E. 8,87 - 2 ee 414350 97,6816 ~_s + © 14/8. 27. 30 E. WA, 14 a tes 2X, 41a4 11,1466 «ae. 15S. 15. 30 W.| 11,00 poles ig 10,5999 fe 6 259396 168. 34. 30 E.| 9350 coe 758292 53809 “* 19S. 49-. CO E.| 44,50 <= = 7 {.. 21946 335848 sua 18S. 42. 45 E. 19,00 "47, ey; * 13,9541 12,8972 ea oe 1515, 92. 00 fy |.t900 | =m 4° 7,6165 951175 oe 408...9. go.E,) 20,80) | soe = =|) 96,7745 1,1690 oe Sumsin 20courfes.} 472,09 |__ 00,1447 467,6370 34uabrs 1 8 Bar4 No. *'The Northin Southing, Eafting and Wefting, are in chains and deci ‘n, to the ten thoufan th part; or may be read chains an links, calling the 96. peter Sous of the decimal, links, and the two other figures hundredth parts of links, 116 MATHEMATICAL awpb al sid 2 Magn Diftances. £3 5 ; te ‘ ee 2 | ae chains. links} Northing... Pourhipg, Eafting. Wefting. : | ‘. fon = sr go sei le Setcgmesin 5 Sums in 20C.'| 472,09 00,1447 967;6370° | -g4rs4br5 * 8,844 a brought over. i : ne ee 2 | aii3. 10°, OO Wa 4,00 Co. e« 339392 era 0940 aS. 206 930/Es | $m56. aot APL) SOA 19,1073 snot 23)5. §5- 15 E.| 31,80 ~ 35 * 18,1259 26,1284, ~ ote AMET 590, WO BETS 780 OT) PER. = mG 7O0 al ees ecpaeeananiaa Raids AO, OO B14 OLOG | ~ bonis) 03.2500 65,4599 ‘| - soos abls: fo. “5°. )? I0,00 as es 9,4504 32694 a ew 4715. 44. 30 W.| 10,00 = se pray : oe) 40091) « BSS. Ocal. | 18,28 “= se 18,2689 0,6380 - = os 4619. 4. 40 Me ag .t4 oes ), O1gt 15,6829 we ae xc[5._ 49. 30 E. 0,00 : “4 Oh0A5 Mc 70RdE Ng, = 8 Sumo gocourles. | "782,17 | _00,1447 486, 4584 1 507,947 | HFA — 31/9. 44.. 45 E.| 12,00 os 8,522 854482 - - e219. 20. OO. | 21,50 - - - 19,3241 954250 "o - aoe Gs 30 E. '* 19390 = seo 19,0357 4, 506% “2 5 3415+, Ae 00. Ws) 11,77 Be eae I1,7413. , 454103 815. 2. 30W.| 17,60 <2 = -| 17,5832 peas a 0,7677 sghS. t9- 5 E. | 33,28 see =] © 31,3249 10,9391 - - 60\S. 40. 40 E.|] 30,58 Je ew 23,195% | 195 9276 ey Sumsin 60courfes. | 1376,33 00,1447 1° 991,6774 1 77% 9784. V 031, 8607 61S. 42. 50 E.| 52,00 - = = =( 38,3384 Be i307) 8 we ore 6219: 20. 40 EB. | 335,00 = os - 30,9102 10,5508 - - 63/8. 23. 45 E.| 17,46 < se = | 7 15,9813 750319 = 64)8- 28. 00 E. [© 33,980 - = 26,0043 40,3163 ee ke 65\5. 2%. 60 BE.) 24,54 ae ae 2249101 8,7943 "= = = 66/8. 29. 00 E.| 35,40 -- +: 30,9615 17,1623 os + 4915, ie 00 E.| 22,72 - = = =| 15,4950 16,6163 - es §8)5. oo W.} 34,00 a 33,1286 “2 2 - 748g. 59S. ne 00 E. 1,79 - = - ©,4027 1,7741 - To the center of Philadelphia obfervatory. ‘Yotal Sums, [163079 | 00,1447 | [ 95, 8095 Th eae 39,5180 ely ae 60,1447 39,5180 ee ‘Total Southing, I 205,6648 1 051,8436 Votal Baiting. Then ASTRONOMICAL PAPERS, 117 Chains. Log. Then NA diff. of lat. 1205,6648 3. 0812265 To AE depart. 851,8436 2. 9303599 As Rad, IO.« = « To Tang. of ENA the (le of the courfe 35° 14/. 33/,08 t 9 8491334 And Sine of 35° r4/. 33,08 9. 7612048 To Rad. TO. 4) oo As 851,8436 % 93035 To NE, the diftance in a {trait — line=1476,2336 Chains, 3, FOOTSST ’ A But the courfe of NE being 35°. 14/. 33”. E. with refpect only to NA the maguetic fouth ; add the variation = = += 3, 8 0 Which gives 38. a2. 33 E. for the courfe of NE with refped& to NS the true meridian, ‘So that the true courfe and diftance from Norriton obfervatory to Philadelphia obfervatory, in a ftraight line, NE is S. 38°. 92’, 33” E. 1476,2336 chains. of Then Rad. £0, ef = To cofine of 38°, 22, 33” g. 8942913 _ As NE 1476,2336 3. T69IS5E ‘To NS true diff. of lat. I157,3013 3+ 0634464 And Rad. IO. = = «@ To fine of 389, 29/.. 33! 9 7929639 As NE. 1476,2336 3. 1691551 To SE true diff. of long. 916,4713 a 9621188 Thus we have-= Chains. Feet. Norriton obfervatory, North, 1157,30=276381,8==12/. 35,9 difference of latitude. from Philad. obfervatory, 4 Weft, 916,47==60487,02==00!, 52/ of times=13/ diff. of longi- tudes=9/,95 of a great circle, or geographic nile. But the obfervatory in the State-Houfe Square, Chains. Feet, with refpect to the fouth point of the city of ( N. 40,0685 ==2644,5==26,16 diff. of lat, Philad. (to which Mefiis. Mafon & Dixon re- Oe ee a fer their obfervations), is, W.. 28,7695 1898, 8:c21,6 of time. Therefore Norriton obfervatory, with refpect to the fouthernmoft point of Philadelphia is, Chains. Fect. North, 1157,30 -—-40 0685=21197, 36852279026, 3==13'. o1,86 difference of latitude. Welt, 916,47 +-28;7695=—= 945,2395=62385,8==00/. 53,6 of time, Hence, by the above meafurement and work, we get Norriton obfervatory 52” of time weft of the obfervatory in the State-houfe {quare; which is exadtly what we got, by that excellent clement, the external contact of Mercury Von. I. Q_ with 18 J MATHEMATICAL And with the Sun November gth, 1769. The iternal contact gave it fomething more; owing no doubt to the difference that will arife among obfervers, in determining the exact moment when the thread of light is compleated; and the mean of all our other obfervations, gives the difference of meridians, between Norriton and Philadelphia, only 4" of time more than the terreftrial meafurement, and the exter- nal conta& of Mercury gave it, which may be taken as a very great degree of exactnefs for celeftial obfervations; if we confider that the difference of meridians, between the jong eftablifhed obfervatories of Greenwich and Paris, as Mr. De La Lanpve writes, November 18th, 1762, was not then determined within 20" of time. For he fays “ fome called it 9". 15”; others 9’. 42"; but that he him+ {elf commonly ufed 9’. 20”, though he could not tell from what obfervations it was deduced.” And it may be need- lefs to add that a fhort diftance is as liable to the differences arifing from the ufe of inftruments in celeftial obfervations, asa greater one. Neverthelefs, if we apply the difference of meridians between Philadelphia and Norriton, got by this meafurement (viz. 52", inftead of 56”,) to the Revd. Mr. Ewing’s colletion of Jupiter’s fatellites, (p. 55), rejecting thofe of the 2d fat. and alfo the immerfions of May sth, as too near the oppofition, we fhall get Philadelphia, 5 o'. 37", and Norriton, sh 1'.29", weft from Greenwich. This refult is what ought to arife from a diminution of 4” of time in the difference of meridians, by dividing that dif- ference, and bringing the one meridian 2” more weft, and the other 2” more eaft; and we believe future obfervations will confirm this as exceeding near the truth. The latitude of Norriton comes out, by the meafurement, 25,09 lefs north, with refpeét to the fouthernmoft point of the city of Philadelphia, than Mr. Rittenhoufe’s obferva- tions give if; and if the latitude of that point of the city be taken, as fixed by Meflts. Ma/on and Dixon, at 39°. 56’. 29",4 then the lat. of Norriton (neglecting fractions of fe- conds) will be 40°. 9/ 31" inftead of 40°. 9’. 56”. How- ever, ASTRONOMICAL PAPERS) rig ever, as both were fixed by celeftial obfervations, and ex- perienced men, the fmall difference ought perhaps to be divided; and if a mean be taken to reconcile it with the terreftrial meafure, the lat. of the fouth point of Philadel- phia would be 39° 56’. 42”; and that of Norriton 40° 9’. 43”. But. as Mr. Rittenboufe had only Sifon’s two and an half feet quadrant, and Meflrs. Ma/on and Dixon were furnifhed with a compleat aflronomical fector, and did their work to fix the lines of two. provinces, it may be thought that their determination is moft to be relied on, Never- thelefs, the whole difference of 25” in the celeftial arc is fo inconfiderable, as not to give 40 chains on the furface of the Earth. - All the refult in the above work are got without any fen- fible error, by plain trigonometry, as the different arcs are fo very fmall.’ In eftimating the length of a degree, to de~ ‘duce the difference of latitude between the two obfervatories, the {pheroidal figure of the earth was taken into confide- ration; and the degree meafured by Mefirs. Ma/on and Dixon, in mean latitude 39° 12',= 363771 feet, wasmade the ftandard, which being lengthened in the ratio of sg, 7866 to 59,8035 gave 363874 for a degree of the meridian in the mean latitude between Philadelphia and Norriton, which is only 103 feet more than the deg. in lat. 39° 12‘, and makes but a fraction of a fecond difference in the lati- tude, fo that it might have been difregarded. With ref- pect to feconds of time in longitude, no fenfible difference can be obtained in the {mall diftance of about rr miles, whether we confider the earth as a {phere of {pheroid. In bringing out the 52” of time diff. of long. a degree of the equator was taken in proportion to Meffrs. Ma/on and Dixon's deg. of the merid. in lat. 39”,12, in the ratio of 60 to 59,7866, (agreeable to Mr. Szm/pon’s table) which gave 365070 for a degree of the equator. By taking a de+ eree of longitude as fixed at the middle point by Mr. Ma/~ kelyne m lat. 38° 7'. 35", and faying as the cofine of that lat. is to cofine of mean’ latitude between Philadel- phia a ee 120 | MATHEMATICA‘L awn phia and Norriton, fois the length of a degree of long. at the middle point (viz. 284869,5 feet) to the length of a deg. in mean lat. between Norriton and Philadelphia, the refult was got 52",13; being only thirteen hundreth parts of a fecond of time more, The above account of the work was thought proper, that thofe who will take the trouble may examine and correc itif in any part neceflary. Philadelphia, Auguft 17,4770. WILLIAM SMITH. ane To the AMERICAN PuiLosopuicaL Socrety, held at Philadelphia for promoting ufeful knowledge. GENTLEMEN, GREEABLE to the order of laft meeting, we have A collected into one general and fhort view (from the laft, or s9th vol. of the philof. tranfactions), the following. account of the different obfervations of the late tranfit. of. Venus made in Europe and other diftant places; contain- ing the apparent times of the contadts; the latitude and: longitude of the places of obfervation, fo far as known to us, with fuch other circumftances, as we judged proper: for anfwering the end youhad in view; namely theafford- ing materials to. perfons of a curious and mathematical. turn, who might be defirous of enquiring what parallax. of the Sun, may be deduced from a. comparifon of thefe diftaut obfervations, with thofe made in this Province, by your appointment. We are, &c. WILL14M SMITH, Hucw WILtiamMson, Nov. 166 1770. © JOHN EWING, THomas ComBer, Owen Brippir, D, Rirrennouse. ne ty we Ett old Kap ap iin ERAN EMC Tots, Oh MIDDLE TEMPLE. lat. 51%. 3o/. 50!" Nu lon, 25/ of time * Welt. By Mr. Hor/z/all, with a Gregorian reflector; mag. power 100 times. . # ey penumbra obferved to firike into @’s limb. At 3” more, viz. iz. 13% Q had made a vifible dent mear the vertex of @’s limb. a8. 49% internal conta. ‘Vhe light juft clofing round @ . oS SHIRBURN * 'The different longitudes are fet down in time, Eaft or Weft with refpect to the royal ob. fervatory of Greenwich, as the firfl meridian, ASTRONOMICAL PAPERS. tar SIURBURN CASTLE, the feat of Lord Afacclésfield, lat. 51°. 39’. 2al’, N. long. 3’. 54! Welt. Hi. m. fec. 7% 7 4 Ext. contact 2? By Mr. Bartle, Lord Macelesfield's obferver ; with 14 fect refragor, 7+ 35, 26 Internal ditto § mag, power 60 times. 7: aMs 288 laternal contact, by Lord Macclesfield; judged by the thread of light clofing round @ . Witha treble object glafs refractor 34 f. power 150, times, . 164 internal contact, by Lady Adacclesfield, witha 6 f. refractor. OXFORD Lat.51°. -45/. 15! N..Long. 5’. 4 Weit. By Mr. Horntby, Sav. Prof. Aftr, The Ext, Cont. _ witha raf. refrac~ : tor, Power 68. (int. Contact judged of by the completion of the thread)... - j oflight. About 10” later than this, viz.- 7h. 24/. 23!’ ae pe eh _— external contact to have happened a few feconds fooner than this: 16. Reg. circumferences in contact: ys of Venus’s diameter entered on the Sun, he judges the 58 i} thread of light appeared in: breadth= y of Q’s diam. fo : z 1334 that he. concludes the.true internal contact was about 1/ ? hel or ae _ fooner, viz. at 7h. a3! 15”. Q’s diameter meafured, on maGtOr (a. , a mean.of fix meafures, 58”,1:. , Power 90 times perceived afimall impreflion feveral fe- a. 6 feet. Acrom. telefcope pow-~ External contac certainly paffed, having) By Mr. Lucas of New-College, with. 12 : } conds fooner. er 60.. Int. contact, thread of light entircly com-2 By Mr. Clare of St. Johin’s-College Te Mies OE > hated cy x with the fame ssletoooe. : a: 6 © Q fomewhat entered By Mr. Sykes of Brazen-Nofe Col- - Int.. contact, or thread of light: com+¢— lege, with 34 feet Acromatic To Mh WM pleated... * "Telefeope. : “By ‘Mr. Shuckburgh of Baliol College, who thinks that at » 7h..23'. 16” the center of 2 was removed more than 7, 6s 8 External contact. half her diam. from’©’s limb, and that the true In= 7.44. 2§ Thread of light complete. ternal Contact was then actually pafled. He thinks : at leaft 8” or 10! are.to be allowed for the comple tion of thread of light. 7. 6: 44: Ext. Contact j By Mrs Niditi : 7 : re Nikitin of St. Mary Hall, 7,24. 154% Internal ditto y - : “Both with {mall te» efopes. 4 60 29% Ext. Contact 5 ‘Hanlon. 7.24. 10% Internal ditto Bye Walideafe se ath Ss Ext, Contact j B witha : ae da 28 Viternal-dito 3. By Samuel Horfley, LL. B. with an 18 inch Reflector. * When there are fractions of feconds, it is not to be imagined that feconds were divided in pronouncing the times of the contacts by the clocks; but the fractions arife ia applying the equation to reduce mean into apparent time, poy 4, LO. 7. 28. 7 28. iro. 42.29. ~ KEW..1/. 14’ Wett.. _Afudden boiling or tremor on ©)’s limb, 2 A final indembeaadl fignal given for External Contact, Limbs tangentical, but 2 quite entered on ©, though ' } | By Dr. Bevis, with a 34 feet Reflector of 6 inches aperture, and a magnifying power of 120 times. {till joined to his limb by a flender tail or ligament, but not fo black as her dik, 17 The tail vanifhed fuddenly, SPITAL SQUARE, Lat. 52°. 31. 15 Long. 17'"W, 44% Ext. Conta@,. §By Mr. Canton, with a Telefeope magnifying 95 times. Q's 15q Internal ditto j diam. 59 ona mean of 4 mealures. ©’s diam. 31/, 35/4, HAMMERFOSY 122 MATHEMATICAL anp HAMMERFOST ISLE, (in Danifh Lapland) near the North-Cape of Europe. Lat. 70°. 38/. 22/",5 N. Long. th. 34’. 55". B. — — — Ext. cont. at Ingrefs not feen, by reafon of clouds; but Mr. Yeremiah Dixon, (who conducted the obfervation, with a 2 f. Refractor) had an inftantaneous view of the Sun through a thin cloud; when Venus feemed completely entered, but no thread of light; the air at this time very hazy, and the Sun was imme- diately hid again in a cloud, N. B. Mr. Dixon’s clock was kept near fiderial tinge, and as fhe appears at the noon of June 3d, to be gh. 49/. 3/ fatter than apparent time, gaining thereof 3/. 59”,6 per day, fhe was at the time of the above hafty glimpfe of the internal contact, 4h, 47’. 33” fafter than apparent time. At 13h. 50/, o!/ per clock, Or 9. 4%. 27 ap. time. ISLE MAGGEROE, (near the North Cape of Europe) lat. 71°. o/. 47, N. long. th. 44/, 6” of time Eaft. — —- = tft Cont. not feen, the Sun being in acloud. a @’s outer limb in cont. with ©’s limb, but ftill join- | eddes P ; ed by a black protuberant ligament. ir aMteb at 9.14. 56 The ligament broke; but the air very red and hazy, & ah Le wie Green~ in 10! or 15" 9 appeared 1th part of her diameter fled we 1a 2 fect within ©’s limb. CERIO: LEICESTER ; lat 52°. 37’. 3 N. long. not given; beginning of © ecl, 18h. 35/. 21”, but may be deduced from ¢ end of ditto - = 23. at, 2, 7. 7. ¥ Ext, cont.? By Rev, Mr. Ludlam, with a triple object glafs acromatic telefcope of 7.45. 9g Int. ditto. 33% inches; its mag. power 54 times. : By Mr. Bayley affittant obferver at the royal UEBEC, viz. Captain Holland’s Houfe, S. 56°. W. of the Caftle of St. Lewis, 2 : we icc, | : Lat. 46°. 47/. 17". N. long. 4h. 44!. 41. W. 4s, 2 Z miles. . 30. 3% ft external contak) 4 ee 3a at internal ditto, f By Samuel Holland, Elq. Surveyor-General of the Northern pe itee wear laade Diftri@ of America. With aDollond’s refractor, "The external contact was likewife obferved at the fame inftant, viz. at 2h. 30/, 3, apparent time, by Mr. St. Germain of the feminary of Quebec, with a two feet reflector of Short’s, The above latitude of Captain Holland’s place of obfervations, is taken from a mean of feveral refulcs of the latitude, deduced by himfelf, He has not deduged his longitude, but he has given the following eclipfes of Jupiter’s firft fatellite for that purpofe, obferved with his Dollond’s refractor, viz. 1769. Immerfions. Apparent time. Emerfions. Apparent time. March 11, 4h. 50/. 47",7 May 28. 4h. 5’. 44",9 April 3. 15. 7. 94 June 6. 40. 28. 2,6 Tdro 13, 24) 41,58 By a mean of the aie three immerfions, compared with the Nautical Almanac, and apply- ing the correétions which, (by the immerfions obferved at Greenwich), the almanac eens td require at this time, the difference of meridians of Greenwich and Captain Holland’s obferva- tory is 4h. 44!. 35”. ; ‘ By a mean of the two emerfions, compared with the almanac, and applying the neceffar correction, the difference of meridians is 4h. 44’. 47!. y The mean of thefe two refults, viz. 4h. 44’. 41” is the longitude fet down above, ISLE COUDRE; lat. 47°. 17’ oo! N. long. Eaft of Quebec’ 3/. 6”. or gh. Al, 26! W. of Greenwich. ; J 2. 34. 56 A {mall impreflion on ©’s limb; external contact afew fecondspaft. %. 50. 19 @ completely round; or regular cir. ferences in contact. 2% 50. 50 ‘Thread of light compleated, or in- | ternal contact. SWEDI6b8n OF SERV A 210 NS; CAJANEBURG; lat. 64°. 13. 30% N. long. th. 50. 47". Eo of Greenwich, By Mont. Planman; with a 20 feet reflector 9. 20. 45% xt internal contact ; lig. He miffed the rft ext. conta& ina cloud and jutt breaking, after the 1ft int. contact a night of thunder and ftorm enfued; yet next morning, a little after 15. 3% 27 ad external contact; or to- the adint. contact the Sun fhone out, a By Mr. Wright, Deputy Surveyor of th Northern iftrict of Amnericr: with ‘ two feet reflector, and gave tal egrefs, @ fhining cx him an opportunity of obferving the total eorcf; refs, ( a ortun x thetotal egre tremely bright. to yreat fatisfaction, at the ns soarked ig he margin. STOCKHOLM, ASTRONOMICAL PAPERS. 123 >TOCKHOLM; lat. 59°. 20. 30” N. long. th. 12/: 26’ E. Ey mm. Tec. 8. aq. 8. rh ext. contac. 2 By Monf. Ferner, with a 10 feet acromatic &. 4x. 48. ft int. ditto. 4 telefcope, magnifying power go times, 8. 24. § wt external contact. 8. 41. 2 Regular circumferences in contact. Monf. Wilcke, with 17 feet reflector. Gas ‘The ligament broke, and 9 * 44. 45 ¢ appeared fomewhat within@) $. 23. 52 External contact. 7 8. 41. 32 Circumferences incontact internally, ¢ Monf. Wargentein, with 1 feet refractor. 8. 41. 47 Int. contac; the ligament broke. UPSAL; lat. 59° 51’. so” N. long. W. of Stockholm v. 40", or th. 10!. 46” E. of Greenwich. - = « « External contact not feen. 8. 39. 58 Regular circumferences in contact. 3 2 Internal contact, the ligament broke, Wee 37¢ and circumferences feparated. Monf. Stroemer with a 3 feet reflector. 8. 2% %& External contact. . 8. 39. 57 Citcumferences in contact internally. M. Melander witha 20 feet refractor. 8. 40. 12 Thread of light completed, or int. contact. - « = External contac not feen. 8. 40. 9 ‘The ligament broke at the int. sie a Mont. Bergman witha 21 feet refractor. a2, 1% External contact ee 40. 12 Internal ditto, the ligament broke. Monf. Profperin with a 16 feet refractor. 39. 46 Regular circumferences in contact. . 40. 15 ‘Thread of light completed, or int. contact. gedit gogo se 90.00 aa 15 External contadt; a diftinét dent in @’s a Monf. Salenius, with a 12 feet nd > GLASGOWS lat. 55° 53/ 32/N. long. reckoned 17’. r1/, * Weft. 6. 54. 32,4 External contact. ; ; é f Int contact; judged by the completion ait i a sien i Guiee Aftronomy 7 TI. 597 ¢ of the thread of light round 9. ae ee 6. 54. 28 External contact. ; : 7 7. 10. 24 Reg. circumferences judged in | By Dr. Williamfon and Dr. Reid, throwing contact. the @’s image of about fix inches diameter, a. 1% 94 Int contact judged by the com- on white paper, into a dark room; through pletion of the thread of light} a Dollond’s refrador of 29 inches focus. round 9. 6. 54. 28 External contact. By Mr. Wilfon (fon of Profeflor Wilfon) 7. 12. 24 Int. cont. Thread of light compleated§ with a reflector of & £. of Short’s. N. B. Dr. Wilfon writes, that his fon thinks, he would have given the extetnal contact 8’ fooner, had he beem obferving apart ;_ but was kept in doubt whether the impreffion he firft faw wasreally Q on ©, by finding that Dr. Reid had not then obferved any impreffion. The internal contact, he adds, was noted by his fon, without any notice of the time given by the other two. : HAWK BILL; the feat of Lord Alemoors, lat. 55°. 57'. 30” N. long. 12/. 45” Welt. 6. $9. 484 External ge By Lord Alemoor, with an 18 inch reflector. 4, 16. A474 Internal ditto, § i o 6. 59. 454 External contaét.¢ By Mr. ‘fames Hoy, with a 3} feet acromatic telefcope, 7, 16. 504 Internal ditto, ‘ power r5o times, ; ‘ » §. 46 External contact. Dr Zi a fen a 5 “ : 7, 16. 5% Internal ditto, Pvt tiny With Sieh tone. Power T60: Dr. Lind writes, that he fufpects all the external contacts at this place were too late. The internal contacts were all carefully judged of by the completion of the thread of light round and the time accurately noted down. ‘The above latitude of Hawkhill, which lies about 14 mile * See p. 19. Some eclipfes of Jupiter's fatellites for the further afcertaining the longitude of Glafgow, in refpect of the Royal obfervatory, Greenwich, 124 MATHEMA‘TICAL anpb mile N E. of Edinburgh is given from Dr. Lind’s lateft obfervations; and the longitude (viz. x2/. 45! of time) is taken from a mean of two refults, deduced by the aftronomer royal from Dr. Lind’s obfervation of the oe ae -of the Moon in December, 1769. ‘The longitude of Hawkshill may be further deduced from the end of the Solar clipe ebtemved there June 3d, 1769, which was at 20h. 19’. 45" apparent time, MS TOR KN EW TO Ny lat. 55° g4!. 30 ON, i,m, icc. 4. 14. 28% Internal contact. Judged of by the completion of the thread of light. ‘This obfervation was made by the Rev. Mr. Bryce. He did not fee the external contaét; nor has he fixed the longitude of his place of obfervation. He fays it is 17 miles Weft of Hawkhill. But the longitude may be deduced pretty near the truth from the end of the folar éclipfe, which was obferved here at 20h. 18’. 23/ apparent time. : GIBR & let A RB: lateg6? oak ae 6. 51. 8 External contad. oA ee th ° 21 Internal contact. tay OCDE arene, The longitude of this place is not fixed; but for fixing the fame Mr, Yardine gives the fol- lowing obfervations, viz. June 8th, rf fat. emer. gh. 22/. 34” clock 1/. 16”2 before mean time. sth, rf fat.emer. 11. 15. 544 clock 1. 28 before mean time, asth, 3d fat. emer. 13. 59. 56 clock 1. 44 before mean time. CAMBRIDGE, New-England; lat. 42°. 25’. N. long. gh. 44’. Welt. 2. 30. 4 External contact.) By Yoha Winthrop, Efq. B. R. 8. Hollifian Profeffor of 4. 47. 30 Internal ditto, Mathematics. He makes O% horizontal diameter at 9 in the morning==31/. 33!,2; and Q’s diameter 58,6, the lea: diftance of the centers 9’. 59/575 fo that the true duration of the ingrefs fhould be r8/. 56; but this being contracted at Cambridge 15” by parallax leaves 18/. 41”, and there fore he thinks the 1f contact happened nearly 1’. 15/. before the impreflion was difcovered by him, ‘The time of the neareft approach of the centers he makes at sh, 37; all apparent time. Mr. Winthrop, with a power of the great telefcope, magnifying 260 times, could perceive no fuch dufkinefs round 9 when on@, ashe faw at the internal conta@, nor that imperfect light which Mr. Dunn mentions in refpect to the tranfit of 1761. He gives the above longi- tude asnear the truth; but for the better fixing his longitude, he adds the following eclipfes of Jupiter’s fatellites, as obferved at Cambridge, New-England, viz. 1768. Apparent time. rft Sat, 1769, Apparenttime. xft Sat. April 25. gh. 13!. 52// May 14. Ioh.19/, 7/ May 18. 9. 27. 27 AUS. 23. = 9 31-96 June 10. 9. 37. 25 July 3. 9. 45. 54 June: 7, 9, . t ty ad Sat, PRENCH OBSERVATION 6. Y¥ ACR ol 8, fe ma, dees M. Mefier, with an acromatic telefcope, 12 feet focus, aperture I 4 * 98048 3% inch. Power 180. i 38, 33 Int. cont. Mo Du Sejour, Cet all Jefe 9. 98» 43 M. Cafinithe fone§ “? MOUSE telercopes: “ae ME U T 2) near Paris; 7. 38 45 Internal contact. Meff. de Mouchy, Bailly, de Borry, and two opticians, ROYAL OBSERVATORY of PARIS; lat. 48°. 50/. 14!. N. long. 9/.15! E, 4. 48. 53 eo Caffini de Thury, | Both with 3% feet acromatic telefcopes of 9. 38. 57¢ Int. cont. @ Duke de Chaulnes Dollond. 9. 38. 50 M. Maralidi, with a 3 feet ditto, made at Paris. be, MO 8 oR 1, 38. 52 Internal contact. M. Le Mannier. BO 8 D0 FA Us, . 38. 50. Internal conta, M4. Hoguere, a ~ BRE eo 3 4, 38, 58 Internalcontact. M. Verdun. ASTRONOMICAL PAPERS. ras All the above obfervations of the Internal Contaé, are reduced to the time of the royal obfer- yatory of Paris, et, for the difference of meridians, &c. N. B. ‘The External Contaét was miffed by all the French obfervers, the Sun being in a cloud. Mont. Mefier meafured the diameter of 9, and found the greateft meafure Ou! 3 and the lealt 53/4. CAPE FRANCOIS; Lat. 19°. 47’, Long. not given, Hi, mk tee, z He ‘ = dienes ¢ Monf. Pingré, with a 5 feet acromatic telefcope. Mook Rd oN 1 oO. 2s, Bie t4 Bas fito. ¢ By amiffionary. Neither Jatitude nor longitude given. 3. 390 67 ints ditto, AUSTIN AFFAIRS, London; 3" of time eaft of St. Paul’s*; that is 18/4 welt of Greenwich, oath ae om MG et aha un re San ae limb was completed, _ — WINDSOR CASTLE; lat. 57°. 28. 15. N, long. 2/, 24/5 W. 7. 8 ag% Ext. cont. as Mr. Harris, matheniatical mailer, of Chritt’s og mabe with Js 2), ook Int. ditto. f 7 : an 18 inch reflector of Sdort’s power 55 times. Q’s diameter he 7. 26. 37% Int. ditto. makes $94; ©’s diameter 31. 43!, : EAST DEREHAM, Norfolk; Lat. 52°. 40, By Rev. Mr. Wellafton; who likewife obferved the, Ext. cont. Beginning of ©’s eclipfe at x8h, qa’. 39” 7 U4. Sag moi End of the fame at 20... 30. 23. P. S. The following lift of correfpondent eclipfes of My fatellite are given, for the better afcertaining the difference of meridians of Greenwich and Glafgow. GLASGOW OBSERVATORY. 1962, Apparent Time, _ Sept. rz, Im. roh. 55’. 33” . Od. 4. Imy PY. 13. 22 - Good. 1763. Nov. t. Im. 9, 28. 29 4. 1765. Dec.22. Im. 15. 54. 25 indiff, ‘The above obfervations were made by Dr. Wi/on, witha reflector of Shori’s of 18 inches. 1762. Apparent Time, CorresponpIna Onservarions, Sept. 11. Im, rth, 12/, 43" Surry-firect, 2 feet reflector; by Mr. Ma/kelyne, + 4 Im It 32 £2 oy peop, 5 rybyi Movs x. Ime ge Ay 9g Surry-firect. 2 feet reflector; obferved by Mr. Short. 1765. Dec. 2% Im. 16. 1% 19 Greenwich, 6 fect reflector; hy Mr. Maj/telyne. N. B. Mr. Short’s houfe in Surry-/reet, where three of thefe four obfervations were made, is 26" of time weft of Greenwich. By comparing the three firft obfervations in each of the above lifts, making an allowance of 4!’4 of time for the difference of the two reflectors; Glafgow Ob- fervatory comes out 17. 10”, weit of Mr. Short's houfe in Surry-freet, or 17! 36/% of tithe welt of the royal obfervatory but in the above lift it is only reckoned 17/, 11” welt. By an im mediate comparifon of the two immerfions of December 22d, allowing 20” of time for the difference of aperture of the 6 feet reflector, and the reflector of 18 inches, Glafgow will come out 17, 34! welt of Greenwich; agreeing within 2” with the refult obtained from the three former obfervations. 1, An Account ofthe Contaé?s of the limbs of VENUS and the SUN, Sune 3d, 1760, as obferved by the Right Hon, WILLIAM Sarl of STIRLING, at his feai at Bafeenvidge, New=Ferfey. Apparent Time. Lat. 40° 40/. N. long, gh. 58. of time weft, ah. 16.’ co! Firft difcovery of the external contadt at the ingress, % 34. 12 ‘Total ingrefs, The above account is extracted from his Lordfhip’s letter of June 29th, 1770, to the Rev. Dr. Smith Provoll of the College of Philadelphia, and was communicated to the Society, July acth * St. Paul’s London is 22/4 Welt of the royal obfervatory; and its latitude 53°, a0. 4g". N. B. 'The latitude of the royal obfervatory at Greenwich, is 51°. 28/, ay! Vou. I. R following, 126 MATHEMATICAL awnpb following, together with his Lordfhip’s obfervations of the comet, which are inferted below. He writes that he had no opportunities of making any other obfervations refpedting the tran/it of Venus except the contacts, and that his clock was properly regulated. 2, Obfervation of the contacts of the limbs of VENUS and the SUN, Fune 3d, 1769, made by Mr. William Poole, at Wilmington, in Pennfyluania. Lat. * 39°. 44/. 37. N. Long. sh. 2/. 9”, W. Extracted from a letter to Mr. Ozwen Biddle, and communicated to the Society, Dec. arf 1770, a With a refraGtor of 12 feet magnifying power about 50 times. : : Mr, Poole thinks the external contact was feveral feconds ge igh ey 1h Be eal before the time marked in, the margin. fo AL fan nag dite * P'The internal contact was taken juft as the Sun’s light began eo et to furround the planet; though his limb was not vifible ‘ beyond the planet, till a fecond or two afterwards, shin To the AMERICAN PuiLosopuicaL Society, held at Philadelphia for promoting ufeful knowledge. GENTLEMEN, TAKE the liberty. of communicating to you an im- I provement in the conftruction of Godfry’s double re- fleGting quadrant, which I have difcovered about two years ago, which may be of fervice to fuch as ufe that excellent in- ftrument. The greateft inconveniencies arifing from the former conftruction of it are owing to the badnefs of the glaf- fes, the planes not being ground parallel to each other, and to its ftanding in need of a new and careful adjuftment almoft every time it is ufed. Both thefe imperfections, I appre- hend, are thoroughly removed by the new conftruction pro- pofed. I have heard, that Mr. William Grant, an ingeni- ous mathematician of London had alfo made fome improve- ment in that inftrument; but I had not heard it before eighteen months had elapfed, after I had perfected my de- monftration of it, and fpoke to the workman to conftruct it accordingly. As the propofed alteration makes the inftrument capable of affording a number of obfervations, the unavoidable er- rors * Mr. Poole had no opportunity of afcertaining the latitude or longitude of Wilmington by celeftial obfervations, but they are both to be gotten with fulficient exactnefs from Mr. Biddle’s meafurement between New-Caftle and the Philadelphia obfervatory p. 87. From that mea- furement, we get Wilmington weft of Philadelphia obfervatory 67414 perches==23/. 38/,8 diff. of meridians, or 1/. 34,6 of time; and fonth of the fame 47324 perches==12/. 52/,6 diff, of latitude. Whence the latitude and longitude of Wilmington in refpect to Greenwich, ar as above fet down. W BM LT ASTRONOMICAL PAPERS. 127 rors arifing from them may be greatly leflened, by taking a mean of them: So that angles may be meafured by it with much greater precifion than can be attained by the common quadrants. This will make it peculiarly fervice- able for finding the longitude at fea, from the obferved dif- tance of the Moon from the Sun, or from a known ftar near her path. For unlefs this diftance is meafured accu- rately, it will occafion a confiderable error in the deduced longitude. That the inftrument may an{wer thefe purpofes, it is de- figned that the arch fhall contain an hundred and twenty whole degrees, and be numbered from the middle to 120 both ways, and that inftead of one central fpeculum two fhould be affixed to the index, and inclined to each other in an angle of 60 degrees. When they are once adjufted to this inclination, let them be {crewed faft by the inftrument maker. Now the largenefs of the arch will enable us to meafure much greater angles than can be meafured by the fore ob- fervation of the common odtant. If the Sun be within 30 degrees of the zenith, the double fextant will give his al- titude either above the fouthern or northern horizon, as may be moft convenient; or for the fake of greater precifion, both may be taken in the fame manner as by the fore obfervation ; and then half the difference between their fum and 180 de- grees, being added to the leffer altitude when the fum is lefs than 180 degrees, or fubtracted from it, when greater, will give his true altitude from neareft horizon more ac~ curately than either of them feparately could give it. This may be done by one central {fpeculum alone and one half of the arch. ‘Fhe fame may be repeated by the other, and the mean of all the four obfervations taken as ftill nearer to the truth. Hereby the error of adjuftment is taken a- way, and that of the obfervations, leflened. Or thefe er- rors may be corrected by the mean of four obfervations, when only one horizon can be made ufe of, in the follow- ing manner. Let the altitude be taken in the common way, 128 MATHEMATICAL anvp way, as by a fore obfervation, by one central fpeculum and noted; let the index be pufhed ftill farther along the arch and the image of the Sun will again be brought down to the horizon by the other central fpeculum, which affords another obfervation of the altitude to be noted alfo; count- ing from the end of the arch next to the obferver in the firft cafe, and from the middle of it in the latter. Then let the arch of the inftrument be held upwards, and the center downwards, and the index be moved the contrary way; this will give two other altitudes: The meanof any two of thefe obfervations that depend on the fame glafles gives the true altitude free from the abovementioned errors. The fame may be faid of taking any other angles. __ The inverting of the inftrument is not neceffary in tak- ing angles, when it is indifferent which of the objects is brought to the other by reflection; as in meafuring the dif- tance between two ftars. But when one of the objects is brighter than the other, it is neceflary to bring the bright- er to the other by reflexion, in that cafe it is neceflary to invert the double fextant. In other cafes it will be found _ more convenient to make all the obfervations, by only mov- ing the index both ways. . When the diflance of two objects is continually chang- ing, and expedition is neceflary in the obfervation; two or more pieces of brafs fhould be made to flide on the arch of the inftrument, that the degrees noted by the index may be marked, by bringing one of them up to the index and {crewing it faft to the arch, where it muft remain, un- til all the obfervations are made. In the fame manner may all the obfervations but the laft be marked; that no time may be loft in reading off the degrees and minutes and writing them down. When the obfervations are com- pleted, they may be read off, by bringing the index clofe . up to the abovementioned pieces, and written down at leifure. That the moving the index backwards, will give the alti- tude of the Sun or ftar above the horizon, when the arch hangs ASTRONOMICAL" PAPERS. 429 hangs downwards, will appear very evident, by confide- ring, that the image of the Sun is brought down to the horizon, by pufhing the index from the obferver, and con- fequently the image of the horizon is alfo funk as much belowthe true horizon; therefore, when the index is moved in a contrary direction or towards the obferver, the image of the horizon is thereby raifed up to the Sun in the Hea- vens, and their diftance is fhewn on the arch. But as it is requifite to bring the image of the Sun tothe horizon, by moving the index both ways, this is effected by invert- ingthe inftrument; holding the arch downwards, while one obfervation is made, and upwards while the other is: made, «: = 4 ots The above illuftration is fufficient to anfwer all the pur- pofes of a demonftration to fuch as are acquainted with the theory and principles of this infrument; as it fhews, that the demonttration is nearly the fame for the obfervations made both with the arch hanging down, and with it invert- ed. But as it may. be defired. by fome, 1 fhall infert the demonttration for the obfervation with the inverted: double fextant, which will fhew more clearly the reafon of gra~ duating the arch both ways from the middle. Let the double fextantinverted be reprefented by APQR; (See Plate 1V. Fig, H.) QAR being the common fextant, and QAP the additional part propofed ; in which it is to be proved, that while the index moves from the pofition QGA, tothat of AFD, the folar image will move twice as far from S$, down to the horizontal line IDG, and will be feen by the eye at I, in the horizontal line IG, parallel to HO; fo that the angle QAD fhall be half of the angle SEH, which is the Sun’s altitude. Let SF be a ray of light from the Sun at S, falling on the fpeculum at F, and from thence reflected to the {pecu- lum at G, and from thence refleed again to the eye at I, where the folar image will be feen in the horizontal line IG; the fpeculum at G, being fet parallel to the line AQ, or to the larger fpeculum at F, when the index is at Q, or the 130 MATHEMATICAL aynp the beginning of the graduations. Now it is to be proved, that the angle SIH, is equal to twice the angle QAD, which is the diftinguifhing peculiarity of this inftrument. dy te Mids Rak Mee ddd alte Since NGM, is parallel to CBA, the angle NGC, is equal to GCB, and theangle MGB, isequal to GBC, being alternate; but the angles NGC, and MGB, are equal from the laws of reflexion, which make the angle of incidence equal to that of reflexion. Therefore GBC is an ifofceles triangle, having the angles at B, and C, equal. Again, fince HFS4+SFD=(HFD=QAD+FEA=QAD+ 4+DEA=QAD+FBC=QAD+QAD +BFA=2QAD+ BFA =1QAD+GFA=) 2QAD+4SFD, Therefore, HFS—2 AD. That the inftrument may be held with greater eafe, an handle may be affixed to the back of it, or another fextant might be added directly oppofite to the middle of the other two, and the index continued to the oppofite arches, mov- ing on the center; which would have its advantages e{pe- cially on land. And as the errors of adjuftment and ob- fervation may be corrected without the fecond central fpe- culum, it may be neglected. This improvement of an inftrument, which was firft in- _ vented and conftruéted by Mr. Godfrey of this city, and which, I do not hefitate, to call the moft ufeful of all aftronomical inftruments that the world ever knew, I hope will make it ftill more ferviceable to mankind. But how- ever this may be, it is fubmitted with all due refpeét to the fociety, by Their very humble Servant, 1 O FN. EW IN... ASTRONOMICAL PAPERS, 131 To the American PuitosopuicaL Society, held at Philadelphia, for promoting ufeful Knowledge. "GENTLEMEN, INCE my delivering in the fhort account of the im- _y provement, which I propofed in the conftruction of Mr. Godfrey’s double reflecting oCtant, at a late meeting of this fociety, I have been induced to fubjoin a relation of the manner in which I was firft led into it, and of the time when it was effected. In the beginning of the year 1767, finding that the common arch of the octant was too fhort, for taking large angles by a fore obfervation, I thought that it might be conveniently enlarged; and foon after found that this enlargement might anfwer valuable pur-~ pofes both at fea and on land. I communicated, to Mr. Benjamin Condy, mathematical inftrument-maker of this city, my propofal for making the inftrument with double the ufual arch, and the addition of a fecond fpeculum on the index, inclined to the other in an angle of half the length of the arch; as appears by his certificate, which I have here inferted in the following words, viz. 6 Te IS is to certify, That fometime in the /pring or Jum~- mer of the year 1767, the Revd. Mr. Fohn Ewing, of this city, communicated to me a propofal of his, for ma- hing Godfrey's Sextant with double the ufual arch, and the addition of another fpeculum affixed to the index, and inclined to the other in an angle of half the enlarged arch ; and. that we had frequently converfed together on the purpofes . defigned to be anfwered by this new conftruction. As wit~ nefs my hand this roth day of January, 1770. BENJAMIN CONDY.” About two years after [had thought of this conftruction of the inftrument and perfected the demonftration of it, which I laid before the fociety on the original {crap of pa- per, on which it was firft written, [ learned by “Oe with ae Ae i | with Mr. Wilhkam Grant, an ingenious mathematician and merchant of London, who came to this city about April or May 1769, that he had alfo propofed an improvement inthe fame inftrument, but different from mine in thefe re{pects, viz. His was a complete femicircle, having the horizon glafs and place of the eye fixed on the arch, and without the fecond {peculum on the index; which anfwer- ed nearly the fame purpofes, with mine; excepting that by its wanting the above mentioned fpeculum, it afforded but half the number of obfervations which my conftruction admits of. ‘The firft intimation J ever had of his improve- ment was from the Rev. Dr. William Smith, provot of the college in this city, in May laft; to whom I had fome time before mentioned, that I had thought of fomething, which might be deemed an improvementin the conftru@ion of Godfrey’s quadrant. This Dr. Smith intimated to Mr. Grant, upon his informing him that he had improved that inftrument before he left London; which circumftance in- duced the Dogtor to promife him an introdu€tion to my acquaintance, as appears by his certificate in the following words, viz. . ainoilot ad)ai bojila: sad sues Philadelphia, rath Jan. 1770, “ REV, SIR, ” g® anfwer to your requeft, that J fhould certify the oc~ cafion of my introducing Mr. Grant to you, T do well remember it to have been as follows.---That ingenious gentleman having been recommended to my acquaintance, by Jome of my friends to the northward, we happened, one day about the beginning of laft May, to fall into converfation upon fome literary fuljects. Among other things, Mr. Grant mentioned an improvement which he had made in the confiruction of Godfrey’s quadrant, and with a truly com~ municative fpirit feemed willing to explain the nature of his improvement, by making out a draft or fhetch of it for me. It happened that I was to fet out the day following, on a journey to Northampton County, and Mr. Grant was appre- henfive ASTRONOMICAL PAPERS. 133 henfive that he fhould leave Philadelphia before my return. f then recollected what you had told me fome time before, concerning your improvement of Godfrey's quadrant, and Jpoke to Mr. Grant as follows: I am Sorry, Lam obliged to £0 out of town to morrow, as I could wifh to have some further converfation on this fubject; but there is a gentle- man of this city, the Rev. Mr. Liwing, who fome time ago mentioned to me an improvement of a fimilar nature, which he had made, and I beheve he has engaged a workman to Jinfb a quadrant for him, on the plan he has projected. Are you acquainted with Mr. Exwing ? If not, Twill bring you together, for [ would wi/b you tocompare your fchemes, and to havea conference with each other. Mr. Grant ex~ preffed his defire to be acquainted with Mr. Ewing, and I accordingly introduced them to each other, before J went w a aces WILLIAM. SMITH.” To the Rev. Mr. Ewing. Thefe things I have mentioned not from a folicitude a- bout the invention, but to fhew, that, what has often been fuppofed probable in affairs of this nature, has adtually taken place in the prefent inftance ; that men at the diftance of many thoufand miles might fall nearly upon the {ame inventions, about the fame time, without any previous correfpondence or acquaintance with each other. J. E. Le ee Ne An ESSAY on the Ufe of COMETS, and an Account of their Luminous APPEARANCE; together with /ome Conjec- tures concerning the Origin of HE AT. ByHUGH WILLIAMSON,. m™ D. Read before the Society, Nov. 16th, 1770. A COMET is a folid dark body revolving round the Sun in ftated periods, receiving light and heat from. the Sun. Comets revolve as other planets do in an ellipfis, Vo. I. =e one 134 MATHEMATICAL anp one part of which is much farther from the Sun than ano- ther; fome of them are very eccentric; that which appear~ ed Anno 1680 was twelve thoufand millions of miles from the Sun in aphelio, it was not half a million in perihelio. The period of the comet which appeared Anno 1758 is 75 years. That of 1661 is 120 years. And that of 1680 is 575 years. ‘Though comets doubtlefs move in an ellipfis, yet from the extreme length of their path, the {mall part that falls under our obfervation, the difficulty in determining the comet’s abfolute diftance or velocity, &c. we have obtained no certainty concerning the period of any comet except the three I have mention-~ ed, nor fhall we ever determine their periods in all proba- bility, except by a feries of obfervations on the return of each particular comet, which may require feveral thou- fands of years. Comets receive their light and heat from the Sun, for they appear to have no light of their own, and are thence invilible, except on their near approach to the Sun. .In the year 1723, an aftronomer had the fortune to difcover a comet by means of his telefcope before it was bright enough to become vifible by the naked eye. The great comet which appeared Anno 1743 feemed no larger than a ftar of the fourth magnitude when firft difcovered; as it came down towards the Sun it acquired a tail, and increaf- ed gradually in fize and luftre till it obtained that amazing form with which it terrified half the world. As this co- met departed from the Sun, its tail decreafed, it loft its brightnefs, till in a fhort time it became invifible; this has alfo been the fate of every other comet; hence it is plain that their light, like that of other planets, is borrowed from the Sun. Having juft mentioned thofe general properties in which comets evidently agree with other planets, I fhall now try to account for that luminous train which attends them on their approach to the Sun, from which they are generally denominated blazing flars, and are fuppofed to differ ef fentially ASTRONOMICAL PAPERS 135 fentially from every other planet or ftar. IfI fhould be fin- gular in any part of my opinion on this fubjeat, I prefume I fhall be indulged, fince it is matter of mere hypothefis. Comets are not blazing ftars, they do not burn at all, noris there any remarkable heat in that tail which has fo often terrified the nations, and been thought to portend diffolution to the world itfelf. The comet of 1743 had acquired a tail fome thoufands of miles long above two “months before he paffled the Sun, while he was yet three hundred millions of miles from the Sun. Surely this could not be a flame of fire kindled by the Sun, elfe comets take fire ina place where every drop of water on this globe would inftantly freeze. Thereis nogreater reafon tothink that comets burn by their own heat, fince their tail, what- ever it be, as well as their light, evidently depends on the Sun, as we have already explained. Philofophers have differed greatly in their attempts to account for the tail of acomet. One imagines that comets are furrounded on all fides by a lucid fiery vapour, or at~ mofphere, which on account of the Sun’s fuperior light, is only vifible in the dark, whence we fee no part of it but that which is in the fhadow of the comet on the fide op- pofite to the Sun. According to him their atmofphere extends in all directions feventy or eighty millions of miles, for fome comets have appeared with a tail of that length, fo that from the near approach of comets to the earth we mutt frequently have been enveloped in that fame lucid atmofphere. ; From the extreme viciflitudes which comets feem to en- dure, at one time penetrated with intolerable cold, at ano- ther time blazing with deftructive heat, fome have irre- verently conjectured that they were defigned as a place of future refidence for the unhappy tran{greflors in this ftate, and thus vainly fuppofe that fifty or an hundred worlds were created for the fake of punifhing the inhabitants of this little globe. It is fufficient to have mentioned fuch conjectures, The 136 M-A T-HOE MA-TILCAL awp The great Sir J/aac Newton was of opinion, that comets were deh pnb; among other purpofes, to nourith and re- freth this earth and all the neighbouring planets. He imagined that by vegetation and putrefaction, a great deal of radical moifture is confumed or changed into earth; that the tail of a comet isa thick vapour exhaled from the comet by the heat of the Sun, which vapour is feattered through the planetary regions, and part of it being receiv~ ed within our atmofphere, occafionally fupplies our lofs of moifture. Whatever properties have been afcribed to heat, it feems very clear that evaporation cannot be performed unlefs by means of an atmofphere whereby the fluid is attracted, fufpended and carried off. Therefore if we fuppofe that the earth and all the planets are fupplied with radical moifture from the comets, we muft alfo fuppofe, that the folar fy{- tem is univerfally filled with an atmofphere fufficient for attrating and fufpending fluids, which hypothefis would certainly deftroy our prefent fyftem of aftronomy. Befides this we may obferve, that from the moft accurate chymical analyfis, there feems great reafon to believe, that all the apparent chanyes in matter depend on combination and folution alone. That water may be combined with earth and again feparated from it; but, that fince the creation, this globe has not fuftained the abfolute lofs of one ounce of water, or gained one ounce of earth. Therefore we do not require any nourifhement from the vapour of comets. I fee no reafon to doubt that comets were created like this world, to be the refidence of intelligent beings; fome: of them nodoubt which travel toimmente diftances through the Hleavens, may be inhabited by an order of beings, greatly fuperior to this fhort lived race of mortals, and much better fitted for comprehending and admiring the works of their divine original, which they behold in greater perfection. One of the primary ideas we form of the Supreme Being is, that he is the fource of life, intelligence and happinefs, and delights to communicate them; the carth ASTRONOMICAL PAPERS. 137 earth we tread, the water we drink, and the very air in which we breathe, {warm with living creatures, all fitted to their feveral habitations. Are we to fuppofe that this little globe is the only animated part of the creation, while the comets, many of which arelarger worlds, and run a nobler courfe, are an idle chaos, formed for the fole purpofe of being frozen and burnt in turns. We cannot admit the thought; the comets are doubtlefs inhabited. The great viciflitudes of climate, is the only plaufible obje@tion that has been made to this opinion. The comet of 1680 came within one hundred thoufand miles of the Sun, but the Sun’s whole diameter is more than feven hundred thoufand miles. ‘lhe comet’s heat was then fuppofed to have been two thoufand times hotter than red hot iron; but the fame comet was about twelve thoufand millions of miles from the Sun, at his greateft diftance, when it is fuppofed, that he perceived ten thoufand times lefs heat than we ufually enjoy. Hence it is fuppofed, that fuch a planet could never afford a comfortable refidence for rational creatures. But here philofophers have taken for granted that the heat of every body is inverfely as the {quare of its diftance from the Sun, a proportion which I greatly fufpet; for I apprehend that it is contrary to experiment. Were heat a certain body proceeding immediately from the Sun, the quantity of heat in any {pace would doubt- lefs be inverfely as the fquare of its diftance from the Sun. ‘But I fee no reafon to believe that heat comes from the Sun, while there is much reafon to think that it does not. We perceive that light comes from the Sun. We alfo perceive that heat is produced in the bodies on which the rays of light fall, hence we are apt to confound light and heat together, though it be demonftrable that light is not heat and that heat is not light. So contracted is our knowledge of the primary conftituent parts of bodies, that we cannot readily determine why any particular caufe fhould not excite heat. with equal facility in all bodies. But we are taught by experience that different quantities are 138. MATH EMATICADR 4x5. are produced by the fame caufe, according to the medium on which it operates. It alfo appears that the particular aptitude of any body to be heated is nearly as the elaftici- ty of that body, or the cohefion of its parts. Whatever produces a tremulous motion in the particles of any body, excites heat in that body, and vice ver/a whatever excites heat produces a tremulous motion in the particles of the body. Does heat therefore confift in nothing elfe than the rapid vibrations of the minute particles of any body? or is there an elementary principle of fire diffufed through all bodies, which is only excited or brought into action by any caufe which produces.a tremulous motion in the particles of thofe bodies? The latter feems moft probable, though in folving the prefent hypothefis there is no dif- ference whether heat depends on the fimple vibration of the particles of matter, or whether it depends on the fire which was only brought into action by the vibration of thofe particles, provided it fhould appear that the heat in every body is uniformly as the vibratory motion of the particles of that body.—This I apprehend is the cafe, and fhall beg leave to mention fuch evidence as feems _ to render the matter at leaft very probable. Philofophers have enumerated five methods by which heat it generated, viz. 1. by attrition, 2. chymical mixture, 3. fermentation, 4. inflammation, and 5. by the Sun. In all thefe cafes it appears that the heat depends on a vibratory motion which by one means or another is excited in the particles of the body. 1. Heat is produced by attrition, or by the ftriking or rubbing of one body againft another. In this cafe there can be no doubt that the heat depends on the vibratory motion of the particles, hence bodies are fooneft heated where the friétion is confiderable, provided the bodies have alfo a proper degree of elafticity. For the motion once communicated to the particles of an elaftic body, are re- tained a confiderable time, and increafed by every fucceed- ing ftroke of the caufe which put them into motion. ‘The quantity ASTRONOMICAL PAPERS. 139 quantity of heat produced in any body by friction, de- pends greatly on the body being fit to preferve the motion once communicated. Thus a faw fixed in a hand vice fo that it may long retain its tremulous motion, will foon be heated, whil{t the file with which it is rubbed is not foon heated, being held in the foft unelaftic hand, whereby the vibratory motion of its particles are immediately deftroyed. The facility with which fome bodies are heated before others, and with which the fame body may be heated in one pofition rather than in another, abundantly prove that the quantity of heat produced in any body by fri€tion will not be as the motion communicated, but as the ftrokes communicated, together with the number of vibrations re- tained and communicated in confequence of each ftroke. 2. The heat which is produced by chymical mixture has been the fubjeét of much fpeculation.—There are fun- dry bodies which joined together produce confiderable heat as water with oil of vitriol; others produce cold, as falt of nitre with water. Why fhould one union produce heat the other cold? It appears in general that all mixtures, properly fo called, produce heat, all folutions produce cold. But in every mixture the bodies undergo a certain change im their qualities, whereas bodies undergo no: change by folution. This may point out to us the true origin of heat in one cafe, and cold in the other, and the pores of the one body are fo conftituted as that the minute particles or atoms of the other body may penetrate into them, a general diffolution of the conftituent parts of the body muft enfue, the minute particles being rent afunder by the attractive force of the parts; fuch diflolution of the conftituent parts of a body neceffarily alters the qualities of that body. We may eafily perceive that in the rapid union of fuch bodies by which the minuteft particles are rent afunder, the vibratory motion of thofe parts muft be greatly in creafed. Hence the generation of heat by mix- tures. Hence too the heat in fuch mixtures, feems to be in proportion to the number of particles, which in any : body 140 Mea tT HE MAD CALS awn body of a determinated bulk, rufh into union with and de- ftroy the texture of one another. In folutions or cooling combinations no change is pro- duced in the qualities of the bodies, Thus by a folution of nitre in water cold is produced, and the falt may be depo- _ fited from the water, or the water be evaporated, and neither of the bodies undergo the leaft change. In this cafe it appears, that there is no diflolution of the conftituent parts of either body, by the attractive force of the other, or by the conftruation of their parts; but that the globules of one body adhere fuperficially to thofe of the other, and the particles of the fluid are fimply charged with thofe of the folid, by which means the vibratory motion of the particles is diminifhed, whence cold is neceflarily produced. It has been obferved that {pirit of nitre mixed with water produces heat, while the fame {pirit mixed with fnow pro- duces the moft intenfe cold. This may be probably urg- ed as an objection to the above theory of heating and cool- ing combinations, under the apprehenfion that {now being nothing elfe than frozen water, fhould on thefe principles produce the fame effets, on combination with any third body. But it muft be obferved, that one is a mixture, the other a folution. Water joined with {pirit of nitre produces amixture, the bodies undergo a change of qualities, and heat is generated. Pour the fpirits of nitre into fnow and nothing will follow, at leaft nothing has followed but a {olution of the {now in the fpirit. For thefe experiments have always been made when the temperature of the {pirits was much below the freezing point of water, fo that the {now could not be melted by fuch combination. Hence there being no intimate union of the parts, nor any thing elfe than a proper folution, cold was generated as in all fimilar cafes. 3- Heat produced by fermentation or putrefaction, may be accounted for in the fame manner as that produced by chymical mixture, there being no doubt that new mixtures are conftantly forming in every putrefcent or fermenting body. 4» Heat ASTRONOMICAL PAPERS. 141 4. Heat which is produced, by inflammation feems alfo to depend on the chymical mixture of bodies. In all bo- dies which blaze there is found an acid and mephytic air, which feem to abound in thofe bodies in proportion to their different degrees of inflammability. The feparation of thefe two bodies conftitutes a flame; this we obferve can only be effected by means of a third body, viz. common air. The union of the acid with the water that is fuf- pended in the air, and the union of the mephytic with the common air, produces two heating mixtures. Hence heat is excited by flame, 5+ Heat is produced by the Sun: Does that heat pro- ceed immediately from the Sun, as is generally fuppofed, or is it mechanically excited by the action of the rays of light; The latter is moft probable. We havefeen a variety of methods by which heat is produced. They appear in different forms, but they all terminate in the fame thing; they are different methods of exciting a tremulous motion in the particles of the body. By fome of them the moft intenfe heat is produced, and yet in no cafe is there any adtual addition of fire. When heat is excited by the Sun, there is alfo a tremulous motion excited in the particles of the body, they are expanded, %*c. The phenomena re- femble thofe of heat excited by other means, whence it feems unphilofophic to fuppofe that there fhould be an ac- ceffion of fire in this cafe more than in the others. I there- fore fuppofe that all the heat which ts caufed by the Sun, depends on a tremulous motion excited by the rays of light, in the particles of the body which is heated. Hence ‘it will follow that the heat of any body will not be according to its diftance from the Sun, but according to the fitne/s of that body, to retain and propagate the feveral vibrations which are communicated to its particles by the rays of light. Hence it is that the air which is very elaftic. when well com- prefled by the weight of the incumbent atmofphere, will receive a great degree of heat near the furtace of the earth, while the light thin air whofe particles are removed Non. dL, fe to 142 MATHEMATICAL awnpb to a confiderable diftance, as on the top of a high moun- tain, is always in a freezing ftate within the torrid zone. Let us fee how this theory of the generation of heat may be fubfervient to the inhabitants of the cometary worlds. It is evident that comets are furrounded with an at- mofphere very different from that of our globe; the heighth of our atmofphere is hardly fuppofed to exceed 60 or 70 miles, while that of a comet is frequently 8 or 10,000 miles. Why fhould they have fuch a weight of atmo- fphere more than us? This is doubtlefs fubfervient to fome very extraordinary purpofe. We may alfo fuppofe with great probability, that the atmofphere of a comet differs greatly from ours. The particles may be f{maller, more fubtile, elaftic, and much more eafily heated, whence the Sun’s rays may be enabled to warm fuch an atmofphere comprefled together by the weight of eight or ten thoufand miles, at a diftance from the Sun, in which we {fhould perceive the moft intenfe cold. This will explain the man- ner in which the inhabitants of a comet may be fufficiently warm at their greateft diftance from the Sun; but if they were proportionably heated on their neareft approach to the Sun, their fummer heats would be intolerable; but this muft certainly be the cafe if their atmofphere were ina permanent ftate, and continued in all feafons of equal. den- fity and weight. We are certain however from obferva- tion, that this is not the cafe; for as the comet approaches the Sun, we can eafily perceive its atmofphere greatly rarified, and thence rendered lefs fit for generating or re- taining heat. But this is not the principal relief which cometarians receive from the fummer’s heat. The atmo- fphere of a comet feems to undergo a change which is pe- culiar to itfelf. It is removed by the rays of light, and thrown off to a confiderable diftance behind the planet. It is demonftrable that the rays of light pafs with amazing velocity, they travel above thirteen millions of miles in a minute; fuch amazing velocity multiplied into their weight, however % ASTRONOMIGAL’ PAPERS. = 143 however {mall they be, muft give them a confiderale mo- mentum or impelling force, which muft be great in regions near the Sun; by this force they repel the extremely fub- tile and light particles of air, and drive them off to fuch a. diftance behind the comet that their weight is hardly per-, ceived on its furface. The atmofphere being thus repelled by the Sun’s rays, and thrown as it were into a thelter be- hind the planet, will be there extended longitudinally in the form of a fhadow, being very rare towards the top. Every particle near the furface of this immenfe ftream of air muft be illuminated by the refraction and reflection of the Sun’s rays, whence they will exhibit the faint appear~ ance of a blaze. Thus we are apt to imagine that a comet is intenfely hot, and that a prodigious flame proceeds from it, while we fee nothing elfe than its enlightened atmo-~ {phere. As the inhabitants of comets are not prefled by day, when they come near the Sun, with a thoufandth part of the atmofphere which ufually furrounds them, and which is doubtlefs the mediate and principal caufe of their per- ceiving heat, we may eafily fee how they may be tole- rably cool at noon day, on their neareft approach to the Sun. If we might form any conjecture concerning the life of a cometarian, from the annual periods of the world which he inhabits, we fhould apprehend that he far exceeds the years of anantedeluvian. Or might we attempt to mea- fure the continuance of this globe, from the length of time which will be neceflary to bring the aftronomy of comets, as well as every other fcience to that perfection at which they muft doubtlefs arrive, we fhould infer that a {mall portion of that time is yet elapfed. On which ever of thefe fubjeéts the mind is fuffered to ftray for a few minutes, it will find fufficient fubject of a pleating {peculation. A letter 144 MATHEMATICAL awnp A letter from David Rittenboufe, A. M. of Norriton, to William Smith, D.D. Provoft of the college of Phila- delphia ; containing obfervations of the COMET, which appeared in ‘fune and Fuly, 1770; with the elements of its motion, and the Trajectory of its path. Communi~ cated to the Society, Auguft 3d, 1770. REY, SIR, EREWITH fend you the fruit of three or four days labour, during which F have covered many Sheets, and literally drained my ink fland feveral times. [t, zs an account, gc. of the Comer which lately appeared, and I have no objection toits being made public. 1 might, indeed, have been a little more careful to have the precife. time of my obfervations, as the near approach of this Comet required ten times the accuracy, that is neceffary for com~ puting the place of any planet. I am, however, quite fatis- fied that the fituation I have given its orbit will be found very near the truth. H Ecircumftances moft remarkable in this comet were, its prodigious apparent velocity, the fmallnefs of its fize, and the fhortnefs of the time it continued vifible. Its velocity was at firft furprifingly accelerated, and before it difappeared again retarded, from which its near approach to the earth may be inferred. I did not fee it till Monday the 25th of June; and from its fituation at that time, I expected it would have been vifible for many weeks, if not months; and therefore did not prepare, with fuch expedition as I might have done, for obferving its place with accuracy. Butfrom the 27th to the 30th, the weather continuing fair, every evening about nine, I took the diftance of the comet from Lucida Lyre and Lucida Aquile, with a common Hadley’s quadrant. July the firft, it was cloudy in the evening. At 10 however, I faw both lucida lyre and the Comet through the clouds, and obferved their diftance; but the comet was ASTRONOMICAL PAPERS, 145 was again hid before I could take its diftance from the pole ftar, which feemed to be about 5 or 6 degrees. This even~ ing it was diftant from: lucida lyre 49°. 17‘. whereas the evening before it had been but 5°. 4.2’. from the fame ftarat gh. It had therefore moved above 45°. in the laft 25 hours, and now appeared much brighter than it had been before; there being alfo fome appearance of a tail on the fide oppofite to the Sun. July the 2d it was cloudy with rain in. the evening; but in the morning of the 3d about 3". IT obferved its diftance from the pole ftar, from Ca- pella, and from a ftar of the fecond magnitude in Caffio- peia, which was the laft time I faw it. From the above obfervations, and many very laborious calculations, | have endeavoured. to fettle the elements of this comet’s motions (fuppofing it to move in a parabola, and to be governed by the Sun’s attractive force) as follows,. viz. The place of the afcending node - Leo 14°. 21’. 45". The place of the perihelion - - Pifces26*.19'. 28". Inclinationofthe orbit - = = - = 1% 49). 5". Periheliondiftance from theSun, ) in fuch parts, as the earth’s > 62757,5Log.9.7976653 mean diftance is 100000 ~The logarithmof itsdaily mean motion = 0.2636300 Time of the comet’s being in perihelio,. Auguft 8th,, 1g". 26’. equal to Auguit 8. 80965 : Its motion: direct; that is, according to the order of the’ 1¢ns. tion thefe elements, and Dr. Halley’s tabula generalis motuum cometarum, in arbe parabolico, it will be eafy to compute this comet’s vifible place for any time; during its ftay in the planetary regions, in this manner, Find the difference between the time propofed and the time of the perihelion; that is, Augult 8. 80965, in days and decimal parts of a day; and to the log. thereof add the log. of the daily mean motion. The fum is the log. of . the mean motion from the perihelion. To the mean motion fo 146 MATHEMATICAL anp fo found, take the angle correfponding out of Dr. Halley's table abovementioned, which angle being added to or fub- tracted from the place of the perihelion, as the time pro- pofed is after or before Auguft 8th, 194. 26’, gives the heliocentric place of the comet in its orbit; and, as that is fo nearly parallel to the plane of the ecliptic, 1 have, for the more eafy calculation, neglected the reduction entirely, which could fcarcely exceed 50” at any time. Likewife, to the mean motion, take out of the table aforefaid the Logarithmus pro diftantia a fole; from which fubtra& the compliment of the log. of the perihelion diftance, viz. 2023347 always, and you have the log. of the comet’s diftance from the Sun. ‘The inclination and geocentric place may then be found by the fame method we ufe for the planets. py . Examrre. Let the vifible place of the Comet for June a7th, 94. be required, From Auguft 8. 80965 Subtract June 27. - 345 Remain days 42%. 43465 log. 1.62947207 Log. daily motion add ~ + = 0.2636300 Mean motion before perihel, 7.86652. 1.8913507, : Angle correfponding 80°; 5/. 12, Log. re diftantia = © = 59320440 Sub. from perihelion }€ 26°. 19’, 28”. | Compliment log, aaa! omen | dit, fubtract *2023347 bane wa ct 19. 6°. 14 261 C ‘ 6 8 ti Soo Ee met’s heliocen- + 0°,.34 ¥ omet a 107082,2 Y. §.02970¢ tric longitude Oa © 101678,2 Log. Biber ants Sub. from longitude Q vp. 6°. 16. 7! seem ' ~~ | Comet dO 5404 Log. 3.7347155 Difference eet’, 51 ‘Tangent. 6, 7308977 ‘ Add the Log. of © diftance 4 © 5.0072280 , , Sum 11.7381257 Subtract the Log. of the Comet 4 © 37327153 Remains Tangent ‘ 34/. Aol 8,005 4104 ‘Which fub. from vg. 6°, 14. 16” The heliocentric longitude, ; Remains «-¥P. 5°. 39. 28 The Comet’s vifible place. Place of the node tw 14° 24/. 45” Defcending. Argument of lat. — 55, 799! Sine 9-7905493 -{-Sine inclin, of orbit. = 1. 4g/. 5! .SOLAILE —Rad,=Sine heliocent, lat. 1°. 7/, 20! 8.2919604 ji ? J enamel Tangent ditto 8 2920434 -+Log. Comet a @ ; 5.0297093 Sum 13.3297527 Log. Comet 8 Q=3.7327153 ‘Sa, 3. 7327668 + Secant 34/, 48—Rad, =5 15 renee ns matt Remains Tangent vifible lat, 91°, 13/, = 9.5889859 Obferved Pe en eT ae eRe ee eT ASTRONOMICAL PAPERS. 147 Obferved diftances of the COMET, | From Lucida | Lucida \Capella \In flexura Longitude | Longitude |N. Lat.'N, Lat. Lyre, | Aquila. ad Coxas' obferved. | computed. lobferwed. comptited. D: - = . = \Cafiopeiae | \ June 27. G.| 40% Hal] 22% Ole = ww fem ee = YP 5% aE! [v9 5% 39/91", 5/22 13! : 29. 9.|2% 25 | 18. 8\----|-+-- - VP 10. 9 |rP ro. 12 49- Bed. Aq BO. 410 F. 24S) Sati 86 VP 23. 36 IVP 23. 3864. 0/64. © July I§.| <2 = = [= = = = [2° 735° av \1t 24. 32 [TT a4. 35|33- $0133. 29 3. 15,5] 95. gle <=] 8. TB ee TT 27. 29 [TT 97. agiat. Zola. 35 pat This laft obfervation was taken by the Rev. Mr, Ewinc. ‘In making the above obfervations, the time (as hath been already hinted) was not ftri€tly noted to minutes; and therefore a perfec? agreement, between the ob/erved and computed places, cannot be expected. _Befides, the comet approached fo very nigh, that an error of 1’. in computing its heliocentric place, might produce an error of a degree in its vifible place, and more than two degrees. in its longitude in the figns. al It is remarkable of this comet, that in any future re- turns, whilft it continues to move in the fame orbit, it can never approach the earth nigher than it did this time. On the firft of July, it was about one fixtieth part of the Sun’s. diftance from us. Perhaps, if the apparent diftance of the Nuc evs, from Jome fixed far near which it paffed, had been meafured with a micrometer, at different places on the earth conve~ niently fituated, the SUN’s PARALLAX might, by this means, have been determined nearer than we can ever hope fory by any other method. This comet, notwithftanding its nearnefs, appeared but {mall and continued vifible but a few days; and, in all probability, had it pafled the earth’s orb but three weeks: fooner, we fhould never have feen any thing of it. This. affords ground for a probable conjecture, that there are numbers of thefe wandering bodies, which traverfe the vatt {pace encircled by the planets, entirely unperceived by us. | I remember one, about ten or twelve years ago, that appeared much f{maller than this, moved very faft,, and difappeared in a few days likewife. Nothing: 148 MATHEMATICAL awnpb Nothing but the{mallnefs of the prefent Comet can pre- vent its being feen at this time (if indeed it be not feen); for it muft rife in the morning before day, and continue todo foforfome months; but willatlength retire to a prodi- gious diftance beyond the reach of the beft glafles, in the 26th degree of Virgo, and very little north of the ecliptic. The earth’s place June 27th, 14°. at the meridian of Greenwich, is computed to be 9* 6°. 16’. 7” and the ex- centricity of its orb 168 fuch parts, as its mean diftance is roo00. If any one would compute the vifible place of the Comet, from the principles above laid down, he mutt find the Sun’s place, or rather the earth’s, by the tables he makes ufe of, to June 27, 14°. at Greenwich, and as much as he finds it fafter or flower than 9° 6°. 16'. 7” fo much muft he add to, or fubtract from, the place of the ' perihelion, net neglecting feconds, otherwife a very. great difference might arife in the calculation. a If the reduction to the plane of the ecliptic be applied, 50” may be fubtracted from the place of the perihelion. Norriton, July 24,1770. ©. D. RITTENHOUSE. Cee Deaay dow James eS. aes VE DEAR SIR, WAS much pleafed with a paragraph in the Gentle- J man’s Magazine, for July 1770, by which it appears, that M. Meffier difcovered the laft Comet in France, ten or twelve days fooner than we did here; becaufe it affords another opportunity of comparing this Comet’s motion with my theory. According to M. Meflier’s obfervation, on the night be- tween the rsth and 16th of June,, the Comet’s right af- cenfion was 270°. 57’. 37” with 15°. 55’. 24.” South de- clination. The hour of the night is not mentioned, but the place of the Comet was no doubt determined by its paffing the meridian, which he fays was about midnight, that is at Philadelphia, June rth, 7’. Time ASTRONOMICAL PAPERS. 149 Time of the perihel, Aug. 8. 8096 Subtract June 15. 2916 Remain Days, 54. 518 Log. 1,736540 Add the log. of the daily mean motion, 2263630 Mean motion, 100,04. Log. 2,000170 Angle ig ake 90°. o. 54” Log. pro diftantia & Sole 0, 301260 Which fub. rom 6 iy 08 Subtract, » " 3202335 the perihel. opr 2) neces : meee | Comet’s dift. from ©@=CS 125,581 Log. 0,098925 Comet’s heliocent. Earth’s diftance from ditto Toi,627 Log. o,oo7orr long. 8s. 26°. 18/. 34/==266.18.34 | Secant, 1°, 33'. 41/—Rad. fub. 165 @do. 8.24. 44. 53 cena, Siren rt PS - IOI, 590 Log. 2006850 differ, tT. 33. at Sub. from CS=125,581 +-Tang. 1°. 33/.. 41" 8,435490 Let 8, (Plate I. Fig. 3.) be the Seeatamtaee ened place of the Sun; E, the place} Rem. CP== 3,991 Sum, 10,442340 of the Earth; and C, of the Sub. CP. Log. 1,380048 Comet. fe a ‘ mn emains Tang. ECS=6°, 356/, 4/on 062292 4-heliocent.long. 86, 26°, 1 ga" nbt99 The fum is the geocent. place of the Comet, 8. 2°. 53° galt Long. of the defcending node ros. 14°. a2/. agit Sub. heliocent. long. of Com. 8. 96. 18. 34 Argument of latitude, 48. 4. 15 Sine, g8rtsas +The Sine of the inclinat. of orbit 3. 49. 5 1501454 Rad. ==Sine heliocent. latitude, I. ar. 9 8,373002 As the Cofine of 6°, 35’. 3"==ECS 9,997126 Ts to Radius - - . To, = = SoisCP=23,991 = - = 14,3829 talaiennces To CEs=94,1s028 + As CE==24,15028 To CS==125,582 1,380048 1, 38293 2,098925 So is tang. heliocent, lat, 1%. 21/. 9/==8,373094 To the rig} of me 9°, of geocent. lat 10,472016 9089094 Hence the vifible place of the Comet was 4? 2°. 53/. 37! with 7°. O North latitude. The right afcenfion and declination I find as follows. Let C, (Plate I. Fig. 4) be the baka of the Comet; A, the firft point of Aries; AP, a por- i tion of the ecliptic; CP, perpen declination. cular to it; AR, part of the equator; and CR, perpendi- cular thereto. ‘hen fhall AP, be equal to the complement of the Comet’ and PC, its North latitude=7°, o!, 5 longitude==879, »/, AR, the complement of right afcenfion; and RC, the Cofine AP=879%, 9! « «= = = 8,70T589 Coline CP=7, 0 -~ - + = 95996755 Rad. =Cofin, AC=87°, 8. 20/==8,698340 Rad.-Sine 79,0 ~ = « —Sine 87°, 8, a0 = « . . meSing «§ = « 987, = 6 Vout. I. arnt 19,085 895 - 9,999458 emer, 9,086437 ==Sine 150 MATHEMATICAL anon axing = —- «704 -U, = 2 =. 0,000487 Sub. from 3+ 28 obliquity of the ecliptic. Rem, 16%.27' Sine, 5452060 9 4Sine - - - 87. 8. 20! 92999458 —Rad. =Sine 16, 26—=-CR= 9451518 Rad.f-Cofi. 87°. 8. 207 18,698340 “Coline - - 16. 26; 95981886 =:Cofine AR=87. 1 8,716454 Which fubtracted from 360, leaves 272°. 59/. right afcenfion. Right Afcenfion. ‘Declination South... Therefore, by calculation from Bs — the theory, we have 4 et OF 2 16°. 26 But by Mr. Meflier’s obfervation, B72 bIR 1g. 55% The difference in right afcenfion is, 0% WE and 0° 304 in declination. Hence it appears, that the obfervation of M. Meflier entirely agrees with the magnitude I have afligned the Comet’s orbit, and likewife with the time and place of the perihelion; but the inclination of the orbit ought perhaps to be increafed four or five minutes. I am, Ever yours, &c. December 2, 1779 D. RITTENHOUSE. To Rev. Dr. SMITH. | aoe 0 ere ak Eas Oh ae” Sas eae oe © Mr. Rittenhoufe, when he wrote his firft paper, ex- preffed his hopes of obtaining a further confirmation of his theory of this Comet’s motion, by {eeing it on its afcent from the perihelion. But.it was not then feen (fo far as we have yet heard) by any perfon in America. This dif- appointment, however, he did not afcribe to any defect in a theory which he had endeavoured to eftablith from the beft principles, and with great labour of calculation, but to the difficulty of finding a body of fuch {mall fize in the heavens; efpecially with fuch a large unwieldy refractor, as he himfelf was obliged to ufe. The account, there- fore, of M. Meflier’s obfervation, who faw the Comet ten or twelve days fooner than we did here, being fo accept- able to him, (as it gave a further opportunity of confirm- ing his theory by the above paper of December 22d) [ imagined that any account of the Comet, after its return from ASTRONOMTGAL “PAPERS. ag from the Sun, would be ftill more acceptable; and there- fore, when the Gentleman’s Magazine, for Augutft laft, fell into my hands, I loft no time in fending him the fol- lowing, viz, | . “ Though we were not lucky enough in America to ** difcover the late Comet in its afcent from the Sun; yet *‘ | have the pleafure to acquaint you, that it was feen in “‘ England. I find in the Gentleman’s Magazine for Au- “ guft, that Mr. Szx fays, he had the unexpected pleafure “(to you it would not have been unexpected) of feeing “* the Comet on its aicent from the Sun towards its Aphe- “ fon, and though not vifible to the naked eye, yet with “a telefcope magnifying 25 times, it appeared much like “the Nebula in Andromeda’s Girdle. Augult 22d, half paft ** two, mané, it had 106°. 20. right afcenfion, and21°.N, “declination. The two fucceeding days its longitude in- ** creafed daily 1°. 15’. but its latitude both days not more “than 5’. Its apparent motion, he fays, was nearly pa- “ rallel to the ecliptic. If thefe fubfequent obfervations agree as well as Mr. Meffier’s previous obfervation, with “your theory on this Comet, I think it will thereby be “ eftablifhed paft doubt. Iam yours, &c. WILLIAM SMITH.” Mr. Rirtenuouse’s An/wer. December 26th, 1770. I was favoured with your extract from the Gentleman’s Magazine, for Auguft, by which I find Mr. Six was lucky enough to difcover the Comet with his telefcope, after it had paft its perihelion, though it was not vifible to the naked eye. I have computed the Comet’s place to Au- guft 22d, half paft two in the morning, and make its right afcenfion 108°. 46’. with 21°. 0’. North declination; agreeing with Mr, Szx’s obfervation entirely in declination, but differing from it about 2°, in right afcenfion, which I cannot think material, unlefs I knew what method he took to determine the right afcenfion of a heavenly body, out of the meridian. Dio N. B 152 MATHEMA TIAL? and N. B. In the Parabohe Trajectory of this Comet (Plate I. Fig. 2.) fuppofe that part, from A to B, a little elevated above the plane of theecliptic; and the remainder, from B to C, as much deprefled below it; the two planes interfe@- ing each other in the line of the nodes, at an angle of 1° 49". Some account of the fame COMET, ina letter from the Right Honorable Witt1aM Earl of Stiriine, to WiL~ Liam SmiTH, D. D. Provof of the College of Phila- delphia. Communicated to the Society, Aug. 17,1770; VIZ. Ae aie De BASKENRIDGE, Fune 29, 1770. OU have reafon to think me negligent in not com- municating (according to my promifes, to you) my obfervations of the laft Tranfit of Venus. I now fend them*, and you fhould have had them before, but I have been fo. much engaged in bufinefs the laft twelve months, that I have had but little time to think of any thing elfe. Laft night, about ten o’clock, I difcovered a new flar, about 78°. diftant from the pole. It would pafs the me- ridian, I imagine, about midnight, and a little before lyra. Its appearance was larger than a ftar of the firft magnitude, of a dull light, with a bright fpeck or nucleus, in the cen- ter. Itake it to be a comet, and that its tail is from us. But whether it be a comet or not, will be determined in a few days; for as it changes its place, and the earth moves on in its orbit, the pofition of the tail, with regard to the earth, muft be altered, and will then appear to encreafe in length. June goth. Laft night I again obferved the new difco- vered ftar. Its appearance was much as it was the night before, but I think rather larger. Its fituation was about 70° from the pole, and it paffled the meridian with lyra almoft half after eleven. I think I have its place fo well marked, * They are inferted above, P. 125. ASTRONOMICAL PAPERS. 163 marked, that in two or three evenings I fhall be able to determine its courfe. What further obfervations I make before I have an opportunity of fending this, I will add hereto. July rft, The new ftar, which, I no longer doubt, is a comet, on his way to the Sun, paffed the meridian laft night about twelve o’clock, and nearly half an hour after lyra, and was advanced to within 48° of the pole, being alittle to the northward of our zenith. It feemed to me to be encreafed in fize, the fhape rather more oval than circular, the nucleus no longer in the center, but advanced towards the northern part of the whole appearance. July 2d, laft night at twelve o’clock, the comet was nearly Eaft from the pole ftar, and about 8° diftant from the pole. July 4th. The night before laft, being cloudy, the comet was not vifible; and laft night, (July 3d) although the fky was clear, the ftars bright, and myielf on the watch for it till day light began to appear in the Eaft, I could not dif. cover any appearance of the comet. Jt muft now be gone to the region of light, and we {hall not fee it more until its return from the Sun. The apparent velocity of this comet, for the laft three days of its appearance, has been prodigioufly great, which, toyether with its apparent fize, induces me to think, that its real fize is but {mall; and that its path lay at no very great diftance from the earth. But thefe matters may be better determined, if we have an opportunity of feeing the comet again, inits return from the Sun. Tam, Dear Sir, Your moft humble Servant, PL LT Wwee EQUATION 154 MATHEMATICAL awnp EQUATION of EQUAL ALTITUDES of the SUN, for the Latitude of Puitapenrata. Calculated by JOHN EWING, } Months | Sun’s | Half the Interval of the Obfervations in ‘Time. and = |Longi-|h, os 30u[ 3h. Oy ea 30'.[4h. of.) gh. 30/. -— Osh. 30/. oh OF Davs. | tude. _ ee ee |= ee pas NM 6 ee 7 Me HNN He ghee Wo SE Te Decom.s Wy, 9. y 6! Or Ch Oye Ol Ores O10. CG, OFC, - 8,0, . Ol Os 9 26, S(T. $3, Ti $3) Mees Zt Ts Fai. FB) Ts S31 we galt 55. | 1. 56 0. a 31; To] 3. 42] 3. 42] 3. 43) 3+ 43] 3- 43] 3¢ 44] 3- 45) 3. 49 | 3 ST Fan. Sse. 15) 5. 29| §- 29) $+. 28) S. 20) §. 29] 5. 32) G+ 35) S- 38) | 5. 43 7 8 10, 20 6.7 Te 7) Te OQ) 7+ ANT Je TSP 7. LYE 7. 23 | 7. Bt Ti. 2 oF 37\ 8. 38| 8. 391 8. 49] 8. 4518. Sol 8. 5519. 3 | 9. 15 Z0,410.. O 5O|1O. tO. GO/10, G|lo. I: {tO. 1Oj10, 2s(10. 36 | 10. 51 Ay 5)EI. 29’. act. ¥ ig av The fide ¢ 6 is the horary motion ? 4 © as feen from the Sun=95",418; which encreafedinthe ratio of 9 ’s diftance frome, to her diftance from ©, gives her horary motion in the vilible way=2 39’ ,8g1. Now, returning to fig.7; we had got |_ 9., .) 0» ssthersoetidiokt angle CVD, Bt | — Ba". 54. 23", But we had before ZVP, or DVL=49".5 5'.33 And we have now got the angle} Rea of the vifible way, CVN, 35> °°79°5 Subt. their fum from CVD, and we have LVN,=24. 29.23, Wherefore, in the right-angled triangle LNV (which being {mall may be refolved as a plain triangle) having found one angle LVN and the hypothenufe LV, we get the remaining fides, viz. VN the parallax in longitude=10”* 592. LN the parallax in latitude= 4. 8245. Now the parallax of longitude VN contributes to accele- rate the contact of Venus and the Sun, by its whole length; but the parallax of latitude LN contributes to accelerate the fame by a {pace different from its whole length. There are feveral ways of explaining this matter, and of converting the fpace LN into a proportionable part for acceleration. The following method, given by Mr. Rit~ tenhoufe, is that which we made ule of, and is as plain and ftritly mathematical as any. “ Let ge, 24, 58 * This angle, in the Norriton account of the tranfit, ‘was called 8°. 28’, 27’, that is near 1 lefs; the fide & 29 being computed from Helley’s tables, not having Mayer’s tables at that time, a id a a 7 168 MATH EM ATIOAL@ ann “« Let S (plate III. fig. 6) be the center of the Sun and of the circle ABC, whofe radius=975” the fum of the femidi- ameters of the Sun and Venus. Let D Lobe the true tran- fit line, and D the place of Venus’s center at the time of the external contact, as feen from the earth’s center; and B its place as feen from any part on the furface of the earth, fuppofe Greenwich. MakeB E perpendicular toDo; then will D E be the parallax in longitude, andEB in latitude; and. D L hall be the whole fpace by which Venus is brought fooner into contact with the Sun to a fpectator at Green- wich, than as feen from the center of the earth. “« Now if the parallax of longitude only took place, the center of Venus would be removed thereby only along her true path from D to E, and fo the tranfit would not yet be begun. But the parallax of latitude EB makes her cen- ter appear to be removed in another direétion from Eto B, and brings her to touch the Sun’s limb by the {pace E L fooner than if only the parallax of longitude took place. The length of this fpace E L, (which is here lefsthan E B) may be determined as follows. : “© Having affumed the Sun’s horizontal parallax as be- fore it follows from the Norriton obfervations, that the leaft diftance of the centers of the Sun and Venus, as feen from the earth’s center, was 610". Make therefore, o S =610", perpendicular to Dor; and om=half the parallax of latitude BE, calculated as above for the given place. Drawn mI, parallel to o L; join S I, which shall be per- pendicular to B L, Make S p, perpendicular to S I, or parallel to BL. Then the triangles BEL, 1m S, arefimi- lar; for they are both fimilar to S m p; whence I m: m S:: BE: EL. But m S,=610—m 0, half the parallax of latitude already found; and ¥S12 m mS mn. T htts, the three firft terms of the proportion being known, the fourth E Lis known alfo. “« Inlike manner let F be the geocentric place of Venus’s center, and H its place as feen at Norriton at the time of the external contaé&t. Draw H G perpendicular to D Lo. Then ASTRONOMICAL PAPERS. 169 Then F G will be the parallax of longitude, and G H of latitude. Make o n=half the parallax of latitude found a- bove. Draw qn K parallel to D Lo. Join SK which fhall be perpendicular to H L. Thenthe triangles FHG, KS hiare fimilar; and Rin:nS::HG:GL.° Thus GL may be found. Letus, foranexample, take Norriton. HG the parallax of latitude (under the denomination of LN) was already found =4",8245; whence #6 =2",41 22=0n. And oS—on=nd; thatis 610’—2",4122 = 607",5878=nS. Moreover YSK?nS2 Kn; That is ¥ 9752 607,5878~762"536=K n. Wherefore fince Kn: nS:: HG: GL; we have 762",536:607",5878::4",824¢: 3",8432=GL. Thus the parallax of latitude HG=4",824 sf keg accelerates the contact only by GL aR To which add the parallax of longitude EG, found above for Norriton And we havethe whole fpace F Lby which) =1454.352 ‘ =10,592 encores the contact is haftened at Norriton, by the parallaxes both of longitude and latitude Now as the motion of ?in an hour is 239”,891; the will require 216”,624 of time, to pafs over the above paral- lactic {pace of 14",4352- And by fo much will the ex- ternal conta&t be accelerated at Norriton in time; viz. 216",624. . By the like procefs for Greenwich, (ufing fig. 8, where we had fig, 7 before), we fhall find the whole parallaétic {pace, DL=27",0441 Gr Oewi igs ee for the acceleration of ext. which gives in time=405 1846} "ont ie Coben: But, 216,624.was theacceleration at Norriton. The difference 189",222, is the abfolute time, by which the external contact {hould have been feen fooner at Green- wich thanat Norriton, ifthe Sun’s horizontal parallax. were truly afflumed=8",5212 on the tranfit day. . But at Norriton theext. contact was obferved, at 2".12'. 50” Add 170 MATHEMATICAL awnp ; : : : Ei, tec, Add for the diff. of merid. of Greenw. & Norriton, ¢. 1. 20 TheSum gives the time for Greenwich, if diel: aed were no parallax : apes But the contact was obferved at Greenwich, at 7. 11, 2 ne ee ee The difference is the obferved effect of paral.=3'.17"=197" But this obferved effe& 197” is greater than the calculat- ed effe&t 189",222 and therefore the Sun’s true parallax on the tranfit day is (by this comparifon) greater than the parallax affumed for the calculation, and will be found 8",8715. For 189/222: 197" 2; 8",5212:8",871 5. In like manner, for the internal contacts, after comput- ing the parallaxes of ? 4 gin long. and lat. for the refpea- ive places and times of obfervation, agreeable to the fore- going rules, the parallaxes in latitude were reduced to their proportionable {pace for acceleration, by taking the differ- ence of the femidiameter of and ?=918" for the radius of the circle (Plate III, Fig. 6) inftead of their fum =g75". In all other refpeéts the operation is the fame as for the external contacts. So far concerning the neceflary preparations. The fol- lowing table contains the names of places, their latitudes and longitudes, and fuch other requifites as enter into the comparifons for deducing the Sun’s parallax from the obfervations.— EXTERNAL CONTACT. | 3 ¢ |Calculated Names of Longitude in Time | rftext. cont. |. 8 acceleration places. Latitude from from app. time. Em in time, by, North. Greenwich. '‘Norriton, \| |S Jpar. % 3 Pieamifece = ph mifec. th, miles, |= |e” Greenwich, §1928'.47!, 0.00. 0d gy: VeRO |e Tie 3° 159 7 AOA Spital Square, EX. 9% TS Os 0. 17 We | Sy de D2 |e 20. Ade LT 405. 85% Middle Vemple,| 51.30. 50 | 0, 00. 95 Wi] Ie 4 || 7 1te 4] | 405. Sar esos —— — {oo 114 Wi] 5.015 | 7 10.444 12 | 405, 755 Windfor Caftle,) 51. 28. 15 | 0. 2 a4hW.| 4.59. 44] 7 8.30 |X | 405, 664 Shirburn Caltie,| $1; 50.22 | 0 B57 Wal geg7. ge 7 7d 1h | dob. Ase Oxford, ‘ ASS 10,8 AW) A S0n co ioe Se beds, | AOs, 236 Glafgow, Serb 32 1 0: V7. TL Wi A, gave 107) Or Fae 29 3 | 460. 867 Upfal, 59:-g%.50 | 1e.t0,746 E. 16,02, 15 |.8. 22. of) 3 398. 632 Stockholm. So. ho. 30 |. 12. 26 Hy |G, 13. 55 18. 24 2" 4s | soy: 988 ——Wean oe a cae pak! a oes | 7+ 2230,55| % | 403. 853 Norriton 40. 9+ 3I |5. 1. 29 W.. 0.00.00 a Ig, 36 216. 624 Diff, 5. 9. 40,25 | — | 187. 229 Thus ASTRONOMICAL PAPERS. r71 Thus fubtradting the time of the external contact at Norriton, from the mean of the ten ex- ternal contads inthe above table, we have sh. 9/. 40!/,25 for the mean difference of longitude by the obfervations. But the true mean diff. of long. is sh. 12/, 44!,95. The difference of thefe twosng/. 4/,7==184",7 is the mean obferved effedt of parallax.. But the mean calculated effedt==18 9",229, : Whence 187/229 . 184”,7: : 8!,5212 : 8",406. Thus, by one fingle comparifon of the mean of the above ten obfervations with the Norriton obfervation, we get the Sun’s parallax op the tranfit day==-8/,406, agreeing to the laft decimal place with:what is got by ishing all the comparifons feparately, and taking the mean of the refults, as in the following table. It would therefore have been nceedlefs to enter down thefe feparate comparifons; if it were not to fee how they differ from each other, and which (if any)-ought to-be fejected.. i Norriton and Greenwich. Norriton and Spital Square, ff. my tec. feconds. EL. ma fea. feconds. 4. 12. 50 Norriton 405,846 Greenw. | 2. 12. $0 Norriton. 405,852 Spital Sq.! 5. 1. 2g==diff. of merid, 216,624 Norriton. | 5. 1. T2==diff, merid. — 216,624 Norriton,). Fekge Td 139,222 oe ees) 169,228 be Th a Greenwich. 9"',778 7, 46. 44h Spital Square. of 852% 3. 17197" 3. 175==197",75 tue ‘Sun's Parallax=8",8715 ss |__ Sun’s Parallax 87,9055. Norriton and Middle Temple. Norriton and Kew. ae % 1% 50 Norriton 405,841 M4. Temp.| % 12. 50 Norriton, 405,755 Kew, 5. 1. qe=diff, merid. 216,624 Norriton. | 5. 0 15==diff. merid. 216,624 Norviton. reakge St: 189,217 713. § 189,132 7. It. 53 Mid. Temple. —20!,967| 7. 9. 59 Kew. — 3,131 a. 484==168",25 3. 6==186". } ' Sun’s Parallax==7!,5776. . Sun’s Parallax==8”, 3804. ee Norriton and Windfor Gafile. . WNorriton and Shirburn Cajile. ; 2. 12. 50 Norriton — 405,064 Windfor, | % 12. 50 Norriton. © 405,452 Shirb. Caf. (4. 59. 44=ndiff. merid, 216,624 Norriton. | 4+ 57» 3a=diff. merid, 216,624 Norriton, 9. TI. $44 189,04 7. 10. 2% 188,828 : 4. 8. 30 Windfor. 15,46 | 7 7 4 Shirb. Gaftle. +9", 17% . WAd=204",5 3«. T5198 3 Sane Parallax==9/',2181. Sun’s Parallax=8/,9351. Norriton and Oxford, ; Norritoa and Glafgow. % 1% §0 Norriton 405,236 Oxford. % 12. 50 Norriton. 400,867 Gla/row,| 4. 56. ase=diff. merid. 216,624 Norriton. | 4. 44. T8=sdiff. merid, — 216,624 Norriton, ———— —— “enemy eres nee coer teae et : m. 40y LS 188,612 6:89, 8 184,243 9. §+ 58 Oxford. 8,388] 6. 54. 29 Glafporw. 955243 ere erin cmenrtmencemner meat hee eS ee gc. Dyeeto7” “< 2 39==159". i Sun’s Parallax==8',g002. : un’s Parallax==7/, 3537. Norriton and Upfal.- Nurriton and Stockholm. a. 12. 50 Norriton. 398,632 Up/al. 2. 12. 50 Norriton. 339,388 Stockbolm: 6, 12 1s=diff. merid, 216,624 Norriton, | 6. 13. 55==diff. merid.. 216,624 Norriton, io, age 8 187,008 8. 26. 43 182,764 8. 2a. 9 Upjal. wm 6/008] 8. 24. 1 Stockholm. 18,764, | een teenie te RR AT I TCT RN %. S6ee176" 2. 4qe=t64"' Sun’s Parallax=8",23399. Sun’s Parallax=7",6464. Mean of the whole, 8,403. Names 172 MATHEMATICAL anp LN ER NAT. CONT A.C. T. | is _ |. Calcul.|) Thread a s{ Long. in Cal. acce- Namesof Reg. cir- , #|/Long, in accelera- || of light | 2 & time,from | leration places. cumf. in 5 5 |time,fromjtion in |} com- |8 4 Norriton. | in time, pea S| Norriton.|time, by} plete. aS by pa- f 26 Parallax. |) BS rallax, h.m,fec.| [hem fec | feconds. {(h. m. lec. h. m.fec. feconds. Greenwich, 7: 48. 31) 3 15. 1. 29 E1423, 898 (7, 29. 18) 6 |5. 1. a9 B, 424,768 fia) SqUSr ey, lt wie | tenet | = Sele bye Pek ae uF #3 DPA Leni sels teeta 424,741 Middle'femple,| ~~ mf tro fe te 7098 god} rls. 1. 4g laagzor ew, At Aditi lemesiere staf cae lI 9s) 9Bot Lok olga Cots. —ladayasa Mindior Calle, fs 5 ot) 7.26. 371% |4. 59. 4% |qndyaar Siiryurn Calle) a Glee le 6 | ae 7-25 94) 3 |4. 59.3% 1424,103 Oxford, Fee afi of Pe Pa fe cele hen BOL ldo 566 BE (423,956 Glafgow. ev meee oe ee Oe as 421,01 Upfal, 8. 39. 54] 3 |6.%9. 15 [418,247 118. 40.16] 5 16. 12, 15 «148,947 Stockholm, 8. 4t. 17) 2 16.13. 55 |416,769 |/8. 41. 47 £316. 35 ys lard h oe Mean 8. 16. 344 = 15+ AQ. 13 [azg.Pi23 one : EE £2. 44,95 (422,617 Norriton, |2. 30. 6| 3 [serene oye gees pa ae laa8iore Dit.” 15. 40. 981 = 1 - =~ < [11,6123 lls.i0.11,81 - |: 2 ee 1 183,642 Thus the true mean diff. of !| In like manner, for the ten places, meridians of Norriton and which noted the completion of the the three places where ? 5. 49. 13 thread of light, for the internal con- the reg. circumferences tad; we have are noted in contac, is Mi diff. merid, 5. 14, 44,95 Both the mean diff, of me« i But, by the obfer. ridians, by the ohare 5. 46 28 ; vations, the meng §: 1d, 14,8 tions, is diff. merid, is ! : a ee ae ‘The diff. of thefe two, is The diff. of thefe | the mean obferved effect ==%, 45=n165/ two, isthe mean of Parallax??? “ss obferved effedt (433) 15=15 3515 But the mean calculated effect of 181,612 of Parallax, Parallax,is - - « = - ae But the mean calculated 83.8 effect of Parallax is ts ee . And, 181/,6123 ::165" :: 8,521: 9,742, And, : : Whence, 7",742%==@’s Parallax, 183/84 2 153/153: 8,sar9 : 4!',08 Whence 4!,08==@’s Parallax. Both thefe refults are the fame asthe mean refults of their refpective clafles, got by the fepa~ rate comparifons in the following table. ae : INTERNAL CONTACT, Comparifons from the regular circumferences in Contact. ‘ "Naerriton ‘and Greenwich. e } — Worriton and Opfal. Hi mitted 6 arcuseconds,”* Pe mivtec ' 2. 30. , 30. 6; Norriten, 418 5. 1. 29.==diff, merid. 238, Norriton. | 6. 12. 15.==diff. merid, 238 seovanunsencn enamine aan etna feconds, 1447 Upfal, so=~ WNorriton, %; 33,45; 185,824 By dar 21, 180,247 9. Ub» 31. Greenwich, wet!,8ar | 8. 39. 54, Upfal. —=33",247 3. 4==184". 2. 27=—T4y!l, Sun’s Parallax—=8/,44, Sun’s Parallax6",95, Norriton and Stockholm, ‘The mean of thefethtee comparifons gives the 2. 30. 6» INorriton. 416,769 Stockholm,\Sun’s Parallax Vt 4s 6. 13. Sgemediff, merid, 238,--2 This year there fhould be two ftakes to a vine, one on each fide, to faften the branches to, by this means they are {pread at a diftance from each other, and grow the ftrong~ er and better; the Sun, air, and winds come to every part; the wood ripens well, and the buds fill, and they are the better prepared to become fruitful in due time. Whereas, when they are huddled altogether, and faftencd up to one ’ flake, 204 CULTIVAT ION or tHe VINE. flake, they fuffer greatly for want of the Sun and air to dry them after rains; mifts and heavy dews; and in clofe muggy weather, they will mildew and rot. Let therefore the branches be tied up fingly to the ftakes on each fide, with a foft band, as foon as they are long enough, leaft they be torn off by hard winds, which would ruin the vine, I need not tell you again, that your vineyard is al- ways to be kept clean and free from weeds and grafs; and the dryer the ground is, and the hotter the weather, the more effectually they are deftroyed, by hoeing, ploughing and harrowing. But remember never to meddle with your ground when it is wet, you do more hurt than good. This fecond fummer your main branches fhould be fuf- fered to grow about five feet long; and then the ends of them muft be nipped off, in order to curb them, to keep them within proper bounds, and to hinder them: from growing wild, The lateral or fecondary branches fhould be nipped off at the end, when they are about a foot long, the nephews alfo fhould be nipped off when they are about fix inches long. This is much better, than the'taking all thefe fmaller branches clean away, which is the practice of fome, who are more nice than wife. For Uhave found, by experience, that, when. thefe fecondary branches are clean taken away, the main branches fuffers they grow flat, and appear diftorted; which plainly fhews, that nature is deprived of fomething, that is effentially neceflary to her well being. It is quite neceflary to nip off the ends of the main branches, when they are grown about five feet long. They grow the larger and ftronger, the wood ripens the better, the lower buds are well filled, and better prepared for the bearing of fruit. Befides it teaches the vines to become reconciled to a low and humble ftate, it curbs their pride and ambition, which is always to climb and mount up above every thing that is near them, and educates them to bear fruit within your reach. Some time after the tops of the main branches are nipped off, they will fhoot out a fecond time, and then they generally throw out, from near CULTIVATION or tute VINE. 205 near the end, two branches inftead of one; fo prone is the vine to fhoot and extend itfelf, thefe alfo muft be nipped off; at the fame time the lateral or fecondary branches mutt be looked to and nipped off, if any of them are fhoot- ing out anew. In the fall of the year, as foon as the leaf begins to wither and fall off, which happens earlier or later, accord~ ing to the weather, cut the branches down again to one good bud each, and take away the earth round the heads of the vines, as before directed, and cut away the day roots, and manage them juft in the fame manner as you did the fall before. Now as fome of your forward vines will bear fruit the third from the planting, which is the nest year, and as it is natural for you to defire fruit, and. efpecially to know what fort of fruit, and how good, your different vines will bear; to fatisfy your curiofity, 1 would advife you to fet afide two or three at moft, of each fort of your moft thriving vines for that purpofe, and inftead of cutting down all their branches to one bud each, like the reft, leave two branches.on each of thefe vines, with two or three good buds each, which will fhew fome fruit to your fatis- faction. But be perfuaded to prevent the reft from bear- ing fruit till the fourth year, and the weaker vines till the fifth year, and your vineyard will make you ample {atisfaction, for this, piece of felf denial. For it greatly weakens a vine to bear fruit when fo young; and however fond moft men may be of their vines bearing much fruit, the over- bearing of vines is allowed on all hands, to hurt them greatly, ‘To prevent which, in wine countries, where it is common to leafe out vineyards to hufbandmen, whom they call Vignerons, they have very ftriGt laws, obliging them to leave four, fix, or eight bearing branches on a vine, according to the age of the vineyard, the ftrength of the vines, and the goodnefs of the foil, and according to the cuftom of different countries where good wines are held in repute, to prevent their hurting the vines, and the reputation of their wines. Thefe Vignerons are likewife Vou. I. Dd obliged 206 CULTIVALETOWN! on yre VINE. obliged, after three fruitful years, if fo many happen fuc- ceflively, to let their vineyards reft one year without bear- ing fruit, that they may have time to recruit and gather freth ftrength. ; The third fummer you are to manage your vines in the fame manner you did the fecond, tying up all the branches to the ftakes, one above another; only of thofe vines that are to bear fruit, the fruit bearing branches fhould be tied up above the reft, that the fruit may have the benefit of the Sun, the air and winds, all which are necef- fary, and confpire to bring the fruit to maturity; and this fhould always be the practice. This year a third ftake is provided, which in the {pring is drove down juft on the north fide of the vine, upona line with the reft, for order fake. To this ftake the branches that bear fruit, there be- ing but few of them, will be beft faftened, becaufe there will be the more room for the branches of referve, which are to: ~ bear fruit the next year, to be diftin@ly faftened to the fide ftakes. Thefe branches of referve are now of great importance to the owner, as the next crop will depend up- on the right management of them. They are, therefore, to be carefully tied up at proper diftances to the fide ftakes, » that they may grow well, that the wood may ripen, and that the buds may be well filled. When they are grown about five feet long, the ends muft be nipped off, the la~ teral branches kept fhort, and the nephews reftrained, if they grow too long, fo fhall the main branches appear full and round, and ina natural, healthy and flourifhing ftate; whereas, if they are all tied up to one ftake, as is the practice with fome people, the wood remains green and fpungy, and does not ripen, the buds do not fill well; and where the band is, all the branches mildew and rot; which plainly thews the badnefs of fuch management, As to the few vines that bear fruit this fummer, let the fruit bearing branches be nipped off five joints above the fruit, and let the fide branches and nephews be kept fhort as above direéted; fo fhall the fruit come to perfection. In CULTIVATION or tne VINE. 207 In the fall of this third fummer, preferve two of the beft fhort jointed branches of referve, one on each fide of the head of the vine, for bearing fruit the next year: The reft cut down to one good bud each. If fome of your vines be very ftrong and flourifhing, you may preferve four branches for bearing fruit, but by no means more, one on each quarter of the vine, fo thall they bear fruit the better, As to the branches on the few vines, that bore fruit this year, they muft be cut down to one good bud each; for the fame branch muft never be fuffered to bear fruit two years running, unlefs you fall fhort of branches of referve, in that cafe you muft do what neceflity requires, and let the old branch bear a fecond time, but they fel- dom or never bear fo large clufters, nor fo fair fruit. On thefe vines, that bore fruitthis year, not above two branches on each, fhould be kept for bearing fruit the next year, fo thall you preferve their ftrength from being exhaufted when young; they will laft the longer, and bear fruit the more plentifully hereafter. The reft of the management is the fame with that of the laft year; only fome time in the latter end of November, or fomewhat later, if the hard weather keeps off, a {mall long trench on each fide of the vine is dug with a hoe, and the branches that are kept for bearing fruit, are laid down gently into them, without forcing them, fo as to crack them, or fplit the bark, or {train the wood too hard, and muft be covered over with the earth. If any part appears above ground, it muft be well covered with ftraw, bog, or falt hay, and indeed if the whole that are buried were alfo covered in the fame manner, with ftraw, &c. it would be beft; for the branches being of an elaftic nature, they are very apt, upon the thawing of the ground, to rife with their backs above the ground, and remain expofed to the weather, fo that your crop may be loft notwithftanding your trouble, which a {mall covering of ftraw or hay will prevent. If any of them fhould be fo ftiff and fubborn as not to bend down, then bind ftraw round them and the flak e. In z08 CULTIVATION ov tHe VINE. In the fpring of the fourth year, the branches that have been preferved for bearing fruit, muft be carefully trained up to the fide ftakes, the higher the better; and the branches that fhoot out from the head this {pring, which are called branches of referve, and are defigned to bear fruit the next fucceeding year, muft be tied up to the ftakes below the fruit bearing branches, and one or two to the middle ftake, if there is room, for often times the fruit bearing branches, occupy the middle as well as the fide ftakes, and efpecially in a plentiful year. The management of the vine in its bearing ftate, calls for a clofe and particular attention. Some gentlemen, and thofe who have written beft upon this fubje@t, recommend the taking away all the lateral or fecondary branches and the nephews, clofe to the body of the fruit bearing branch, and to leave only the main leaves of that branch, thinking, by this method, that all the nourifhment of the vine is thrown into the fruit. They alfo order the top of the branch to be taken off, with- in three joints of the uppermoft clufter of grapes. Others again are for following nature, and fuffer all the branches to extend themfelves as they will. Thefe I look upon to be, two extremes, and think that a middle way, is every way beft, moft rational and fafeft. The lateral branches, the leaves and nephews are {uppofed by naturalifts to draw off and perfpire the crude and thin juices and to hinder them from entering and fpoiling the fruit, and alfo ferve as lungs for refpiration; the circulation of the air through all the parts being neceffary to vegetation, and for bring- ing the fruit to perfe&t maturity. That this is fo, or how it is, lam not fo well acquainted with the operations of nature, as to'determine; but this I know, that when thefe {maller branches are taken clean away, the main branches inftead of growing round, full and plump, which is their natural ftate, become broad, flat and diftorted, and have an unnatural appearance. Befides thefe branches, when kept within proper bounds, ferve to fhade the fruit from the fcorching rays of the Sun, and to fereen them from vio- lent CULTIVATION or Tue VINE. 209 lent winds, from hail and beating rains, from damps and fogs and cold nights dews, which are all injurious to the fruit, as well as the cold dry north-eaft winds, and the cold driving north-eaft ftorms. But let not this lead us into the other extreme, for if the vine be left to herfelf, and all be fuffered to grow, fhe will run wild, and ruin all by her own excels. ‘This is the method of managing vines when. the head is formed near the ground, which is now prac- tifed in moft vine countries in vineyards, (except fome parts of France, where they are ftill fond of efpaliers.) and this method muft be continued as long as the vines latt, which moft writers do affirm, will be above a hundred years. As to the management of vines in gardens, again{t walls, and for forming of fhady places, and many other ways to pleafe the humour and phantafy of the owner, that is not to be regarded, it has no relation to vineyards. Here | would propofe a new method of managing vines, the heads of which are formed near the ground, by way of trial; I have not yet made the experiment, if it fhould. anfwer, it would fave a good deal of trouble, and be more fecure again{t the feverities of the weather; I have been told that it is the pra@ice of fome to cut all the branches down, and to truft to new fhoots for bearing of fruit; and I have read the fame account in a treatife publifhed by Fames Mortimer, Efq; fellow of the royal fociety, in the year 1707, but thefe accounts are fo vague, fo general and fuperficial, without entering minutely inte any par- ticulars, that I could have no dependence upon them; nor could any man form a judgment of the manner of doing it. However from thence I have taken the hint, and fhall now propofe a method which may be worthy on trial. If the fall of the third year of the vine’s age, inftead of fav- ing two or four branches for bearing fruit, cut down thefe to two buds each, and the reft cut down to one bud each; the upper buds of thefe branches that have two buds, are defigned to bear fruit, this next year, the lower buds and the buds of all the reft are defigned for fruit the year after, and la ato CULTIVATION or tur VINE. and therefore if any fruit thould appear upon them, they mutt be taken away as foon as the clufters appear; in the fall of the fourth year, cut all the branches that have born fruit clean away, and leave thofe that did not bear fruit; and then according to the ftrength of the vine, cut as many of thefe down totwo buds, as you think your vine ought to bear, andcut the reft down to one bud, always remembering that the branches that have but one bud, and the under bud of thofe that have two, are to bear no fruit. When your vines come to be ftrong and able to bear it, cut down all the branches to two buds, and then you will have eight bearing branches in one year, which are quite enough for the ftrongeft vines; however if you have a mind to ftrain your vines, and to try how much they will bear, you may then cut as many branches as you think fit down to three buds, two of which may bear fruit, while the under buds are kept for branches of referve. In the fall, all the fruit bearing branches are cut clean away. If this method fhould fucceed to your mind, and you think it preferable to the method firft laid down, I mean that of preferving branches of referve to be laid down and covered in winter, which is the German method, and the general practice of. the Rhine, &c. then in order to bring your older vines into this method, cut down the fruit bearing branches to one bud the firft year, and the branches of referve you may cut down to two or three buds each, as you think your vines are able to bear it. In this you form your judgment, from the ftrength of your vine, the goodnefs of your foil, the diftance of your vines from one another, and the quan- tity of fruit they have born the three preceeding years: for vines, as well as men, muft have time to reft and recruit, if you mean them to laft, and to return to their work with vigour. Now for the covering of thefe vines in the winter feafon, I would advife a handful of foft hay, that is free from grafs-feeds, to be laid on the head of the vine, and a flight box made of rough cedar boards, or of pine, (which any fervant CULTIVATION or roe VINE. att fervant may make, only let the top piece cover the whole,) be put over the head, which will be a fafe and fufficient covering. Otherwife a {mall fheaf of ftraw, bound well round the ftake, and the bottom brought handfomely all round the head of the vine, and fecured by a band from blowing open, will do very well. The vines fhould not be covered till hard weather is ready to fet in, and they fhould be dry when covered. | gt te Before I proceed to the management of vines for the frame or efpalier, it will be neceflary to acquaint you with fome things of a general nature, which you will find wor- thy of notice. i When vines are trimmed in the fall, which they ought to be as foon as the vintage is over, or as foon as the leaf withers and falls off, they feldom bleed, and never fo as tohurtthem. If vines have been neglected and not trimmed in the fall, and this work muft be done in the {pring, let it be done in February, if good weather happens, or early in March. If it be done later, they will bleed too much, and endanger the crop. Searing the wound, as foon as it is made, witha hot iron, it is faid, and I think with rea- fon, will prevent the bleeding. In trimming, keep about two inches from the bud, or half way between bud and bud: fo fhall the upper bud that is left befree from danger. The rule is, to cut flopping upward, on the oppolite fide to the bud, that the flope may carry off the tears from the eye, but I never found this any kind of fecurity to the eyes below. If therefore fearing every wound with a hotiron be thought too much trouble, the only remedy, befides that, which I have yet been able to difcover, is, to wath the branches that are wounded and bleed, and efpecially the buds, with a rag dipped in warm water, without touching the wound, which in 8 or 10 days will ftop of itfelf; the liquor form- ing a ftiff jelly upon the wound, like coagulated blood, and drying by degrees, heals up the wound. The wafh~ ing muft be deferred till they have done bleeding. Unlefs this is done, the eyes below will be in danger of being blinded, a a i i | 212 CULTIVATION or rue VINE. blinded. For fo glutinous is the fap, that it binds up the bud it reaches, fo that the leaves cannot open and unfold at the time of vegetation. In cutting off large limbs from old vines, it fometimes happens that ants fall upon the pith, eat their way in, and make a hollow, where the water fettles and rots it. In this cafe the remedy is, to cut fuch branches clofe down to where it is folid and green, and it will bark over and heal. ae It is common for large buds to fhoot out two or three branches each. One only on each fhould be fuffered to grow; if you expect fruit on them, be not in a hurry to {trike them off ’till you know which is moft fruitful, and fave that. Vines that are clofe planted in a vineyard, can- not be expected to bear fo much fruit, as fingle vines, or as thofe that are planted ata diftance. Their roots are too much confined, fo that they cannot gather nourifhment in fo {mall a compafs of ground, to fupport and bring: to per- fection a large quantity of fruit; and this is a fufficient reafon for reftraining them, and for limiting the number of bearing branches, if you mean to make good wine, to keep your vines in full vigour and to preferve them for many years. Befides the deficiency is fully made up, by a greater number of vines; and the planting them clofe, enables you the better to keep them low and within pro- per Donde = Ft Be ehh GH Ban » Is an arm with a claw at the end, marked 6, the the ratch-whee] 2; this ratch-wheel is fixed upon an axis, which carries a {mall trundle head or Pinion R, on the oppolite ends this takes into a piece SSSSS, which is ins dented with ‘teeth, and {crewed firmly againtt one fide of the carriage CCCC, and by means of this the carriage hag TT, Is a clamp for faftening one end of the file in the place or bed on which it is to be cut. V, Is another clamp or dog at the oppolite end, which works by a joint W, firmly fixed into the carriage CCCC. Y, A bridge, likewife {crewed into the carriage, through which the {crew X pales, and prefles with its lower end againft the upper fide of the clamp V, under which clamp the other end of the file 77 » 18 placed and held firmly in its place while jt is cutting, by the preffure of the {aid clamp or dog 7.) » 2, T'wo catches, which takes into the teeth of the ratch- wheel , to prevent a recoil of its motion, 3» 3> Isa bridge to fupport one end of the axis 4, of the ratch-wheel 9, 5,A ftud to fupport the other end of the axis of the tatch-wheel, 9, When the file or files are laid in their place, the ma- chine mutt be regulated to cut them of the due degree of Vow, 5 finenefs, MISCELLANEOUS PAPE finenefs, by means of the regulating fcrew, L, wt {crewing it further through the arm, M, wi files finer, and vice ver/a, by unfcrewing i make them coarfer; for the arm GG, can have liberty to rife the higher, which w arm PP, with the claw, to move further along the peri- phery of the ratch-wheel, and confequently mmunicate a more extenfive motion to the ma eneft fight; for, by ftri ci of the cutter or chife t work, and, by repeating vith. er, the files on one fide will at cut; then they mut be turned, and the opera : ed, for cutting the other fide. It is needlefs to enlarge much on the utility or extent of this machine; for, onan ‘examination, it will appear to perfons of but an indiffer - ent mechanical fkill, that it may be made to work by water as readily as by hand, to cut coarfe or fine, large or {mall files, or any number at a time; but it may be more par- ticularly ufeful for cutting very fine fmall files for watch- makers, as they may be executed by this machine with the greateft equality and nicety imaginable: And as to the materials and dimenfions of the feveral parts, I fhall leave ‘that to the judgment and {kill of the artift, who may have -occafion to make one, only obferving, that the wole fhould _ be capable to bear a good deal of violence. — method with the hammer on the he pule the ftroke ; length be eee PiarE VII. Ky a x se. ee Se lh Se i Sais CU ailing Fine! Be Z A ( Ross G Bene ’ ‘ < \ te \ NASD YX ac Kot 6 BX. — ai lol » ER, SAS Sea, See ny, aus ee ae Trp fot She bs tog pity, Ge Dolled - perry The A peor wv Onna by iy! Mok Lents Views aie aie oe [| +3004) Srcr. IV. PAPERS. M- An Analyfis of the CHALYBEATE WATERS of BRISTOL, in Pennfylvania; in two letters from Dr. Joun DE Nor- MANDIE, of Briftol, addrefed to Dr. Yuomas Bonn, one of the Vice Prefidents of the American P hilofophical Society, held at Philadelphia; and by him communicated to the faid Sooi i Be istrottogt ged oor viptol, in Pennfylvania, Sept. 10 DEAR SIR, z ; i : N fecing amongft the many ufeful purpoles of infti- tuting the American Philofophical Society, that of communicating to the public new methods of curing and preventing difeafes, is defervedly included; I take the li- _ berty of requefting you to prefent my moft refpectful com~_ pliments to the worthy members of it, and beg their fa- - yourable acceptance of the inclofed Analyfis of the Briftol - mineral water, and of an account of the means whereby " avillage, long unhealthy, has been rendered remarkably “healthy. a eT i ‘adelphiay eC. ‘cAN Puitosopuican Sociery, held at ements. the laft and the prefent e healing art, the encouragement hyfic by the eftablifhment of me- \merica, and efpecially in your city, es of medicine are regularly taught, enfible pleafure to every humane an encouragement to all who are of their fellow creatures, to exert every difcovery which may tend to ss the difpofition, at interefted in ¢ themfelves in 369 MEDICA, PAPER S: the relief of the fick, or the reinftatement of an impaired conftitution. From thefe confiderations, I have undertaken to try the following experiments upon the Chalybeate waters of Briftol, in Pennfylvania, with a view to difcover their.. contents, as a guide to the further inveftigation of their virtues and ufes; and particularly, their application in the cure of difeafes. For although it muft be confeffed, that a chymical analyfis is, in fome meafure, an uncertain teft of the medical virtues of any compound; and that ‘the qualities of its conftituent parts, when feparated, may not only differ from, but are fometimes oppofite to, thofe of the mixture; yet when we want the teftimony of experi- ence, a chymical analyfis is the beft means of inveftigating the truth, and difcovering the virtues of the compound. Thus, if from the following experiments it hall be found that the waters of Briftol, are impregnated with the principles of thofe of Bath or Spa, it will be no forced conclufion to fay, they may be beneficial in cafes fimilar to thefe that have been happily cured by the latter, _ Experiment I. A {mall portion of white oak bark, in- fufed in the waters, induced an immediate change from tranfparency toa dark purple colour, which it retained 24 hours, without depofiting any fediment. I]. Some of the fame water, after being made hot, or expofed for a few hours to the open air, in a great mea- fure loft its irony tafte, and received no other colour than a common tinture from the white oak bark. IIIf. One drop of ftrong oil of vitriol, in two ounces of the water, produced no fenfible alteration; and the water after ftanding fome time continued tranfparent, without depofiting any okerith or other fediment to the fides or bottom. be Bp Upe : IV. Ol. tart. pr. deliq. dropt in fome of the fame water, induced a change in the colour, rendering it fomewhat yellow; and in time precipitated to the bottom of the cup a fine gold coloured. oker, ised V. Sixteen MEPIGALIBPAPERS. 370 V. Sixteen ounces avoirdupois, carefully evaporated toa ~ drynefs in a China bowl in B. M. left one grain of a yel- lowith brown powder of the tafte of tart. tartariz. VI. Linen, moiftened with the fcum floating on the top: of the ipring, is tinged with a ftrong iron mold. VIL. This water in weight is exactly the fame as that of rain water, From thele few experiments, it is fufficiently evident that this water, in its natural ftate, contains a large portion of iron diffolved, in pure water by means of an acid, which acid is extremely volatile, and probably of the vi- triolic kind; principles fimilar to thofe of the much cele- brated waters of the German Spa, with which they like- wife agree in the effedts which immediately follow upon drinking them; {uch as quickening the pulfe, exciting an agreeable warmth in the ftomach, promoting the appetite, and occafioning a flow of {pirits, and a greater degree of chearfulnefs, - Hence we may juftly conclude, that like thofe they will be, very beneficial in all that numerous train of difeafes, which arife froma debilitated and relaxed ftate of the folid parts of the human body, brought on by living in warm climates, immoderate evacutions, &c.. fuch as hypochon-~ driacal complaints, melancholy, lofs of appetite, and in- digeftion, with habitual ficknefs and pains of the ftomach and. bowels, and all their unhappy. confequences;) rickets, lamenefs, and fome paralytic complaints; and: that they will likewife prove powerful deobftruents and alteratives,, opening obftrudtions, and difcharging what is obnoxious. by the feveral emundtories,: Nor indeed are thefe! virtues attributed to them from. conjecture and analogy only; but in fome meafure, from: the teftimony of fact and experience. _ For although it would not be! very ‘eafy, till the waters become more ge= nerally known, to colle& any number of accurate and well attefted cafes, yet, from the ftrideft enquiry from perfons, who have {pent their lives, near thefe {prings, it is certain 371 MEDDOALIPAP RK a certain they have, for a long time, been remarkable for their falutary effects, ftrengthening the ftomach, reftor- ing loft appetite, &cc. And that numbers have left’ the place perfectly cured of difeafes' which, for many years, had eluded the moft powerful remedies. But as Briftol was formerly an unhealthy place, and prejudices againft it may ftill remain in the minds of num- bers of perfons, who otherwife would be willing to try the benefits of thefe waters, it may not be improper to aflign the caufes why it wasthen fo, and how from their re- moval, it is now become an exceeding healthy fpot. The town of Briftol is fituate on a high dry bank, with the river Delaware to the eaftward and fouthward. There is a quantity of low ground to the fouthward and weft- ward, which in its natural ftate, was overflowed by every {pring tide; to the northweft there is a large pond of wat- er, which, when filled by the winter’s rain, overflowed the neighbouring hollow clayey ground, and thete re- mained ftagnant, until exhaled by the fucceeding warmer feafons, which was feldom before the middle of autumn; at which time agues, remitting, intermitting, and conti- nued fevers, and indeed every {pecies of autumnal diford- ers, prevailed, not only amongft ftrangers, but even the inhabitants. This continued to be the cafe until the owners of the low marfhy grounds, to the fouthward and weftward of the town, embanked and improved them; and a few public {pirited inhabitants employed perfons to cut ditches to drain off the fuperfluous water, as it flowed out of the pond. After thefe improvements, the place became healthy; the inhabitants were no longer particu- larly fubject to fevers of any kind, and, for feveral years paft, have enjoyed as much health, as any people in any part of America. ) , eee BEET Bee Te STR, ‘ OME months ago, ina letter to you (communicated to the public by the Philofophical Society) T gave you a fhort analyfis of the Briftol Chalybeate waters, I have MEY. DLUIZCSA -G. APALPTELR YS. 372 Thave fince had opportunities of profecuting that fub- ject farther, by a number of additional experiments, which, together with the hiftories of feveral cafes, that have oc- curred in my attendance here, will more clearly afcertain the contents of thefe waters, and determine the effects which may be expected from their ufe, in the cure of difeafes. ; I therefore take the liberty to tran{mit you the follow- ing account, which I flatter myfelf, will be favourably re- ceived as an ufeful {upplement to my former letter. The experiments I related to you in my laft, tended chief= ly to fhew that nee waters owed their chief impregna- tion to iron kept in folution, by means of an acid, which I judged to beof the vitriolic kind. tas Thofe which I am now to communicate to you confirm this opinion, and at the fame time difcover fome other principles, in their compofition, with which I was before unacquainted, and which probably increafe their medical virtues. . / _ Experiment 1. Upon the addition of Sp. Sal. Arom.. to the water a flight effervefcence enfued, and upon ftanding about an hour, alight yellow matter was feperated and floated on the top of the liquor. ‘ II, From a mixture of lime water, the fame feparation was made, but fell to the bottom of the liquor. IIL Powder’d chalk added to the water produced. the fame feparation, but not in fo fhort a time, as in the pre- ceding experiments. te IV. Therefiduum, after a flight calcination, was ftrongly attracted by the magnet, V. A folution of crude Sal. Ammon, being mixed with the water, was fucceeded by the fame appearance as the addition of lime-water. | VI. The refiduum after evaporation in Baln. Mar. be- fore calcination, difcovered to the tafte a confiderable por-- tion of falt, which left a coldnefs on the tongue, and when feparated by folution, filtration and evaporation, appeared of 373 NE DICUA LSPA RIELRSS. of the colour of falt of amber, and fhott into right angled cryftals, which through a microfcope appeared beautifully feathered; and from every experiment was found perfect- ly neutral. (as it 1 VIL. Silver immerfed for fome time in the water acquir- eda flight yellow colour. VII. The refiduum thrown on a red hot iron fparkled very much, and emitted a fulphureous {mell, what re- mained on the iron had not the leaft perceptible tafte of falt. IX. The waters, and the folution of the chryftalized falt, changed fyrup of violets, toa fine light green. The firft four of thefe experiments, in which the wa- ters were decompofed as well by a volatile alkali, as by lime water, and an abforbent earth, and the refiduum (af- ter a flight calcination) being attracted by the magnet, evi- dently prove that they are impregnated with a confiderable portion of iron, . The fifth experiment (in which a decompofition takes place by means of a double elective attraction) fhews that the acid in thefe waters, has a ftronger affinity with alka- lies, than that which is the bafis of Sal. Ammoniac, (which is the marine acid,) and mutt be either the nitrous or vitri- olic. And from a decompofition taking place, on the ad- dition of common nitre with the Chalybeate waters, in about the fame time as when left expofed in the open air, we may rationally conclude the acid to be of the vitriolic The fixth experiment fhews that there is a fmall portion of neutral falts in thefe waters, which from the coldnefs with which they affect the tongue, and the appearance of the cryftals, are probably of the ammoniacal kind, . The feventh and eighth experiments together with the {mell of the bath and the confiderable feetor which the waters acquire when kept for any time, evidently thew that they contain a third principle, which is fulphur, This indeed (as wellasthe falt) isin afmall quantity, yet it may contribute fomewhat to the medicinal virtues of thefe fprings. The MDL CAL APE RR &. 374 The ninth experiment feems to prove them to tend ra- ther to an alkaline nature, but as this was in a very trifling degree, it may be accounted for from the efcape of the acid which is extremely volatile. Thefe experiments compared with thofe I have already communicated to you fufficiently difcover the conftituent parts of thefe waters. : From fome other experiments I find they inftantly la- ther with foap, are fomewhat lighter than common water, that they no ways coagulate milk, even when boiled with it, and that when mixed with an equal quantity of it, they pre- vent in fome meafure its acefcency; from the firft and fe~ cond of which facts, we may naturally fuppofe them more powerfully deobftruent, and from the two laft we may draw this ufeful corollary, that they may not only be ufed with fafety along with a milk diet, but that they realy in a chymical fenfe prevent the ill confequences which often attend fuch a diet in a weak ftomach. From this circum~ ftance their efficacy muft be in many cafes greatly increafed. When drank, they act as a quick diuretic, always in- creafing the quantity of urine. They generally at firit drinking prove cathartic, always tinge the excrements black, and fometimes, from the ftate of the ftomach prove emetic. They exhilarate the {pirits, and in fome inftances produce a momentary intoxication. They communicate an immediate vigor and ftrength to the whole conftitution, as is evident to many patients, who with fatigue walk to the wells; but in returning home, are not fenfible of any wearinefs or languor. They promote digeftion, flrengthen the flomach and create an appetite. ‘Thefe are their conftant and immedi~ ate effects in almoft every ftate of the body, from which one might reafonably conclude, that they would be highly beneficial in many difeafes. But as the beft teft of their | utility are facts, I fhall fele& fome few out of thote cafes, which this feafon has already afforded me. ; Vou. I, B3 Cafe if, 475 MEDICAL PAPERS. Cafe if. W. A, Alabouring man, of a fallow dufky complexion, who for twelve years paft, had been afflicted with phegadenic ulcers in his legs, and for the laft eight years a {chirrous liver and {pleen, for which the moft pow- erful deobftruent, aperient, and alterative medicines had been prefcribed without effect, was employed in finking the Bath, and digging drains, to carry off the wafte water for ten days, during which time he was generally up to his knees in mud, ochre, and water. In that time the ul- cers on his legs,intirely healed up, without the ufe of any kind of medicine or drefling, except a piece of linen cloth over the fores. He was then retained as bath keeper, in which ftation his bufinefs led him into the bath feveral times every day; and in eight weeks (during which time he conftantly drank the waters) the diforder in his liver and fpleen gradually gave way; and at this time, without the ufe of any medicine, he has perfectly recovered his health and complexion. To him the waters at firft proved gently purgative, and afterwards diuretic. ad W.W. Aged about nineteen years, for two years paft had been afflicted with violent rheumatic complaints, to fuch a degree that at the time of his coming to the bath it was with difficulty he could raife himfelf when feated, and the mufcles of his neck were fo rigid and contracted that he could not move his head; he found fenfible benefit from the firft ufe of the bath, and by continuing it for about feven weeks, perfeCtly recovered his health, and the ufe of his limbs. 3d. L. M. Had for near two years been afflicted with a weaknefs at his ftomach, inability in the organs of digef{- tion to perform their office, and at times a general laffi- tude and wearinefs over every part of his body, brought on by too violent exercife. Upon drinking and bathing a fhort time, he received very fenfible benefit, all his com- plaints ceafed, and he gained a much better appetite than he had ever we ey while labouring under his diforder. 4th. Mrs. 4. For five years had been afflicted with a violent MEDICAL PAPERS, 376 violent cough, attended with pain in her breaft and a hectic fever which never had abated from the ufe of medicine. By drinking and bathing for four weeks, fhe perfectly re- covered her health without any medicine, and returned home with a very good appetite. . sth, Milfs A. For two years paft had been fubjec to pains in her ftomach and head, obftructions in her liver, flight cough, perpetually feverifh, with lofs of appetite, and reftlefs nights, for which a variety of medicines had inefrectually been ufed, they only affording a temporary relief. . In this flate fhe came to the wells, in fo lowa condition that the could not walk the length of a {treet but with the greateft difficulty. At firft the daily rode to the bath, but after ufing it for fome time, fo far recovered, that the could walk without any inconvenience, and after ftaying about five weeks, returned home very hearty, had a good appetite, and refted well. 6th. F. F. For the laft five months fubjeQ to an incef- fant cough, the effect of a violent cold, came to the wells and drank the waters for ten days, in which time his cough by degrees abated, and he returned home perfectly cured, | 7th. Mrs..K, Had complaints fimilar to thofe mentioned in the cafe of Mifs R. but attended with frequent acrid, black ftools, which afforded no relief from her complaints. She drank the waters, and went into the bath for five weeks, in which time fhe recovered her complexion and flefh, and a much better ftate of health, than the had en- joyed for a number of years. 8th Mifs H. About five weeks before fhe was brought to the bath, was feized with {pafmodic contractions in her left arm, a paralytic complaint over all the fame fide, her {peech. was much affected, one fide of her mouth drawn up, and fhe had hardly any power over one hand and foot, - from which the beft adapted medicines and the ufe of a common cold bath had afforded no relief. Immediately on ufing the Ghalybeate bath, her {pafins began to abate, ‘ and 377 «MEDICAL PAPERS: and foon left her. She ftill remains at bath, has perfeally recovered her fpeech, and at this time, without the ftrict- eft examination, you cannot difcover the leaft remains of her diforder; fhe can now work with her needle, and drefs herfelfas ufual. She took fome few nervous ftimu- lating medicines during the time of bathing. oth. Mr. D: Who had been for fome years conftantly fubje&t to a nervous cholic, which rendered his life a bur~ then to him, came to Briftol, and, after ufing the bath and drinking the waters for two weeks, left the place per- _ fe&tly cured without the ufe of any other medicine. toth. Mrs. — For the laft twelve years of her life was fubje&t to obftructions in her liver, attended with an al- moft conftant menftruation, lofs of appetite, oedematous {welling in her legs and feet, and difturbed and reftlefs nights. At the folicitation of her friends, fhe came to Brifto] with a conftitution almoft wore down, and witha prepoffeflion that her cafe did not admit of any relief. Af- ter a fhort time bathing, and drinking the waters, the {welling in her feet and legs abated, her appetite and fleep returned, the diforder in her liver, and every other com- plaint abated, her colour returned, and fhe now enjoys a much better ftate of health than fhe had experienced for a number of years, with the Pernt profpect of a perfect recovery. From thefe cafes, as well as from the fenfible effects upon firft drinking thefe waters, it is evident that they are a fafe and active Chalybeate, exerting the moft powerful effets upon the human conftitution, and agreeing with the moft delicate fubje€ts; and that they are fafely and fuccefsfully drank in many cafes where the common and ufual preparations of iron are attended with dangerous confequences; which perhaps may be owing to the ex- treme fubtlety and minutenefs of its parts, and the inter- pofition of fo large a quantity of pure water; or it may poflibly depend on the nature of the mixture, which can- not eafily beimitated by any artificial preparation, In ~ oren RARAMTT ga MEDICAL PAPERS. 398 In particular, thefe cafes teach us, the moft happy ef- feéts are to be expected from thefe waters in old and ob- ftinate ulcers, which they quickly and readily difpofe to. heal. That they penetrate the moft remote and minute veflels of the body, prove powerful deobftruents, and re- move the moft obftinate of difeafes, glandulous obftruc- tions, even after they had refifted the moft powerful me- dicines. And hence they may prove highly beneficial in ftrumous and ferofulous cafes of children, in jaundice, and other obftru@tiions of the liver, fpleen, and myfenteric glands, which lay the foundation for fo many and fuch obftinate chronical complaints; as alfo in cafes of obftruct-. ed catamenia, and where, from relaxation, the flow is too abundant. They likewife, as appears from the cafes of 7. W. and. L. M. cure moft obftinate rheumatifms, and that languor and uneafinefs which often arife from too violent exercife, . and which are nearly allied to the rheumatifm. And however prejudices may operate againft the ufe of Chalybeate waters in diforders of the lungs, nothing is more certain than that thefe I am now treating of, have afforded effe€tual relief in violent coughs, even where they have been of long ftanding, and when attended with hectic complaints; as is evident from the cafes of Mrs. 1. Mifs R. and 7. F. which laft was the only cafe in which drinking the waters without bathing.completed the cure. Nor indeed is this doétrine of the ufe of Chalybeate wa-- ters in pulmonary and hectic complaints intirely new. Morton prefcribes them in the phthifis pulmonalis, in which he does not ftand fingle. And there have been in-. {tances of confiderable relief afforded by them even in the laft {tages of aconfumption. Some reftrictions and cauti- ons are certainly neceflary in their ufe, but they would be too tedious to mention here, and mutt be left to the jugd- ment of the phyfician. In nervous diforders arifing from relaxation, one would . naturally expect from them the happicft effects, and in fact 499 MEDICAL: RAPERS fact they have been found very effectual in palfies and nervous cholicks, as in cafes of Mifs Hand Mr. D. In fhort, thefe waters, in every difeafe which arifes from that fruitful fource of complaints, relaxed and weakened ftate of the folids, may with great propriety and truth be termed {pecific; but in no cafes have their good effects been more evident or remarkable, than in a depraved and dibilitated ftate of the organs of digeftion, arifing from in- activity, and a fedentary life, from continuing too long in warm climates, or from.exceflive and free living; here the remedy is immediately applied to the feate of the difeafe, and of confequence mult produce the moft immediate effects, nor indeed has there been one inftance, in which, if pro- perly perfevered in, they have failed of affording relief. _ Every particular here afferted is confirmed by experi- ments that have been carefully made, and by many cates, from which thefe few are felected, and in ftating of which the public may reft aflured, that the moft fcrupulous fide- lity has been obferved, by oy ages Dear Sirs Yours, &c. Oc. 6th, 1769. FOHN DE NORMANDIE. To Do&or Tuomas Bonn. The Cafe of a TETANOS and LOCKED JAW, cured by amazing quantities of Opium, by Dodtor ArcuiBAaLD GLOSTER, of St. John’s, Antigua; communicated to ,Joun Morcan, M.D. F. B.S. Profeffor of Phyfic, in the College of Philadelphia; and by him laid before the American P hilafophical Society. NEGRO, aged forty years, having fuffered the ex- ceflive heat of the fun in the day, imprudently laid himfelf down and flept on the damp earth in the night. The next morning, he perceived a ftiffnefs in the mufcles of MEDICAL: PAPERS, he of his jaws, with a fomewhat painful, or rather uneafy fenfation in thofe of the neck; having no other complaint at the time, he was blooded, and had an emolient lini- ment for the parts affected, and was ordered a lenient purge, ex Mann. & Sal. Glaub. This operated immedi- ately. The day following the pains in his jaws increafed, the mufcles of his back and neck were frequently feized with violent fpafms, which proceeded to the mufcles of his thighs: and legs, rendering them quite rigid. He could fearcely refrain from crying out at thele times, and could not, but with difficulty, open his teeth, fo far as to admit a knife between. Luckily for him his under jaw projected naturally beyond the upper jaw, fo that his food pafled between his teeth, and he had no great diffi- culty in {wallowing liquids. His pulfe was flow and fmall, and his fin was below the natural heat: He had no fleep, for fo foon as he dofed, fevere fpafms would roufe him. Having obferved in the London Medical Effays, that thefe complaints had been fuccefsfully treated with free exhibitions of opium, and having before this obftinate cafe came under my obfervation relieved patients by very libe- ral dofes of it, [ thought nothing in the Materia Medica would be fo likely to yield relief in this cafe. 1 therefore prefcribed on the evening of the fecond day as follow, viz: Fune 7th. ®. Pulvs Contrayero: Com': 3 ifs. Nitre: pur: Camph: Opic pur: ana s/s. M Din P- Ai ex. Cap: unam 3t1a quaque bord. 8h. He was no better, his ftiffnefs continued with fre= quent fpafms fevere and painful. The powders were re- peated with 57 of opium. — th. Hehad no fleep, no difturbance in his mind, nor the leaft affection of the Senforium Commune which could be attributed to the opium. His powders were repeated as yefterday; he took liquid food, fuch as weak broths, gruels and ptifans. A general’bath was’ ordered, in which he was put ftiff as a flake, andthe {pine with all the rigid parts. 381 MEDICAL: PAPERS. parts were well rubbed after the ufe of it, with a lini- ment, ex Camph. 31. folut: in OL: Oliv: 507. Tenet: Tebaic: s1ij7. M: toth. The powders were repeated with 32 of opium to be given every two hours as ufual. A particular bath likewife, confifting of emollient and difcutient herbs, was direéted for the mufcles of his jaws and neck, which were moft feverely convulfed; indeed the maffeter mufcles were to the touch like wood. 11th. The patient was no better: I began to defpair of him: Emollient clyfters were thrown up morning and evening, he being very coftive, as well from the ule of the opium, as from the effects of the difeafe. His mind was clear and undifturbed, he had no fleep, nor even drowfinefs; nor did there appear any of the ufual effects of opium given in much fmaller quantities. However I knew that nothing but opium could anfwer our purpofe, and though I had gone as great lengths with it as any one in thefe parts would venture, yet I not only perfifted in its ufe, but increafed its quantity to 32/5. in fix powders, ufing lefs nitre and camphor. 12th. Having taken the laft fix powders, he thought his fpafins recurred lefs frequently. Yet there was no relax- ation of the mufcles of the jaws, nor any other favourable alteration. His clyfters were repeated, the baths and lini- ment continued, and his powders were again ordered. 13th. Every thing continued the fame. He had no fleep, nor any relaxation of the mufcles. His difcharges by the clyfters were hard dry fcybals; his mind was ftill calm, and not a funétion of it impaired, or in the leaft altered. He was wakeful in the day as ufual, and inthe evening had an inclination to reft, but continued to be difturbed by thefe dreadful {pafms. Still between hopes and defpair I ordered fix powders with two drachms of opium which was twenty grains of pure folid opium in each dofe, to be given every three hours. 14th, Re COA Le oP APE RS, 382 14th. Having taken all thefe, he was rather eafier, his {fpafms were lefs frequent, yet no perceptible relaxation of the mufcles of his lower jaw followed, His diet was continued as above. His clyfter produced the fame dif. charges as before. He was ealier always after the general bath, and the rubbing in of the liniment, all which were continued, and as I had ventured as far with opium as I thought it prudent, I ordered as follows : R Pul. Contray. Comp. . Cinnab, Antim. ? ana 3/3. Opiipur. =" - Motch. Chinens. s/ to be divided into fix parts, and one to be given every three hours. 15th. He faid he was eafier, had a very little fleep; his fpafms were lefs frequent, and he was in better {pirits, ‘This encouraged me to hope for a relaxation of thefe cruel {pafms, which have been fatal to fo many. I therefore boldly returned to the former dofe of opium, and gave 377 in the powders with the mufk and cinnabar, 16th. The patient found himfelf much the fame as yef~ terday. His baths, liniments, clyfters, friGions and pow-~ ders were. repeated. _ 17th. He found himfelf much eafier to day, his pow- ders were repeated, and his fpafms were much relaxed every where, except in his right leg which was very painful, The mafleters gave way a very little, fcarcely perceptible, 18t4. He was much the fame as yefterday, having ained however a little ground. The fame means were continued, and his powders repeated. 19¢). He was rather better, and more free from pain; he could fit up; the mufcles of the back part of the body were fo far relaxed as to admit of that pofture, without much pain, He moved his lower jaw from fide to fide with fomeeafe. The fame powders, &c. were continued, 20th, He could open his mouth fo far as to admit my little finger into it, but this was done with a horrid grin, and I was afraid the fpafm would return with the effort, which is very common. ‘The medicines were repeated. Vous I C 3 21ft, Si MEDICA Lb’ EXPER. aif. He was much in the fame condition; till had fpafms at greater diftances, had fome fleep, and faid he could eat, but I was unwilling to hazard the experiment. His liquid food was continued, his medicines were repeat- ed, and every thing obferved with the fame care as before. 22d. He continued to mend; has had fome fleep; the mafleters were relaxed ftill more; the fpafm recurred lefs frequently. He complained of lownefs of fpirits, and was defirous of tobacco to fmoak, which was allowed. He had a mixture of four fpoonfuls of old rum in a pint of warm water. His powders were ordered as before with 37 of opium, and the ufual quantity of mufk, to be given every four hours only. 23d. He was much better, had fome fleep, opened his mouth, could chew, and ftill enjoyed a calm undifturbed mind. His powders were repeated with o77 of opium which makes fifteen hundred grains of folid opium taken in Jeventeen days. 24th. He had better reft laft night and more fleep than during his illnefs before. He eat a bit of lamb, could open his mouth no farther than yefterday, but his fpafms recurred lefs frequently. His powders with 977 of opium were ordered as before. 25th. He was much better in all refpects; he flept pretty well laft night, and could move his legs and arms -very freely. There was ftill a fpafm on. his maffeter mulcles, as he could not freely open his mouth. Nothing was ordered but a continuance of his baths, liniments, cly{- ters, frictions. The powders ordered for him yefterday not being yet expended. 26th. He continued to mend, although he had not tak- en about twenty grains of opium the two preceding days. There was no alteration in his fpirits. The fpafms were more relaxed. From this time he was vifited lefs fre- quently, his medicines given more irregularly, but as he had fpafms which recurred now and then “till the 15th of July he had his bath: continued, and took about ai/s of mufk, and 96 grains of opium in that fpace. Fuly 20th. MEDIGAL.PAPER SS wy July 20th, He is now perfectly well, in good fpirits, and finds no inconvenience from his preceding ficknefs, nor any mifchief from the amazing quantity of opium he has {wallowed down. It is to be noted that from the 16th he was put upon a courfe of nervous pills ex G. Affafoetid, and Cinnabar of Antimony without any opium, Left any perfon fhould imagine the opium which was made ufe of in this cafe, might not be good, I think pro- per to add that it was frefh, and appeared to be very good, being procured from Meflrs. Beaven, Druggifts in Lon- don; and that it always anfwered to the ufual effets of opium in the common dofes, in every other inftance, hav- ing made fufficient ule of it in my practice, to be certain of its quality, . ee RNTABR An account of the effects of the STRAMMONIUM, or Thorn-Apple, 4y Benyamin Rusu, M. D, Profe/~ Jor of Chymifiry, in the College of Philadelphia. WAS called to a child, (between three and four years old) a few days ago, which appeared to be ill with a vio- lent fever, delirium, tremors in her limbs, and a general . eruption on her fkin, accompanied with a confiderable {welling, itching and inflammation. As the feafon for in- flammatory difeafes was now over, (it being the beginning of Auguft) and as I had neither feen, nor heard, of any cafes which bore the leaft refemblance to this in the city, I acknowledge I was much furprifed at it, and knew not what caufe tocallin, to account for a fever attended with fuch acute fymptoms, at a time of the year, when moft of people, efpecially children, were fubject to complaints of a very different nature, As her pulfe was pretty full and ftrong, I immediately ordered her to loofe a little blood, and gave her a few laxative medicines. Befides thefe, I ordered her to be put into a warm bath, and recommended the application of ftimulating cataplafms to her feet. The ; opening 483. MyEpDelcOpApL 9 Pe Ay Poh B & opening medicines operated the evening after I gave them, and brought away a great number of the afcarides worms which I far from thinking were the caufe of her diforder, as the fymptoms full continued with as much: violence as ever. I cannot help remarking here, that two of the moft powerful vermifuge medicines we are acquainted with, viz. the Anthelmia, or Worm Grafs of Jamaica,* and the Carolina Pink Root, are both confiderably narcotic, and when taken in too large quantities produce effe€ts fomewhat fimilar to thofe of the Strammonium. Do their vermifuge depend upon their narcotic qualities alone? Are all narcotic fub- ftances vermifuge? Or may not they be rendered fo, by adminiftering purges after them, in the manner we are direéted, after ufing the worm grafs or pink root? Thefe are queftions, which are perhaps foreign to our prefent fubjeét, and yet when refolved, may have their ufes in me- dicine. But to return; the mother of the child finding moft of the remedies we had ufed ineffectual, informed me for the firft time, that they had a quantity of Stramonium growing in their garden, where the child generally play- ed, and that fhe recollected that fhe had been once difor- dered in a flight manner, from eating fome of the feeds of it. ‘This led me immediately to treat her complaints in a very different manner from that I had formerly done. [ gave her a puke of two grains of Tart. Emetic, diffolved in water by fpoonfuls. It vomited her feveral times, but brought nothing but phlegm from her ftomach. After this I gave her {weet oil in large quantities, mixed with a little of the oleum Ricini, which in a little time brought away a great number of the Strammonium feeds. The relief fhe got from this evacuation, encouraged me to re- peat the fame medicine, which I did every day for near a week, till I began to flatter myfelf they were all difcharged from the body. But notwithftanding this, the was far from recovering fo rapidly as we wifhed. ‘The tremors ill continued in her hands at times; her delirium abated, but * See Dr. Brown’s Natural Hiftory of Jamaica, MEDIO A Li PAPE RS 386 but it left her ftupid and blind. The pupils of her eyes were much dilated, and fhe catched at the bed clothes and at every thing around her, in the fame manner as a perfon in the laft ftage of a fever. As I was perfuaded the oil the had taken, had evacuated all fuch of the feeds as were in the guts, I began to fufpect, that her complaints were fill kept up by a few feeds which ftill remained in her fto- mach, Itherefore gave her four grains of Tart. emetic, in the manner [ formerly mentioned, and had the pleafure to find, that it brought up above eighty of the feeds, the fecond time it puked her. Finding the ftupor and blind- nefs ftill continue, I repeated the puke, which brought up above twenty more. Upon this all her complaints va- nifhed, and ina few days fhe appeared perfe@ly well. It may perhaps appear furprizing to fome, how fo many of the feeds of the Strammonium fhould be lodged fo long in a child’s ftomach, without producing much worfe ef- feéts than thofe we have mentioned, efpecially when we confider the accounts which Dr. Stork has given us of the effeéts of a very {mall quantity of it. In order to account for this, we mult remark, that the feeds the child fwal- lowed were of the laft year’s growth, and were become fo dry and hard as to refemble little pieces of Horn, Be- fides the feeds of the narcotic plants in general contain but very little of their virtues; even the feeds of the poppy itfelf may be taken in large quantities, without producing any of the effects of opium. Dr. Sfork’s experiments were made entirely with the extract of the Strammonium, two grains of which contain more of the narcotic quality of the plant, than three hundred of the dried feeds. My chief defign in relating the above cafe, is to make ‘two obfervations, which may be of ufe in other cafes. 1. We learn the wonderful connection between the fur- face of the fkin and the alimentary canal. Eruptions upon the fkin are generally attributed to an acrimony in the blood. In the prefent cafe we fee an eruption occafi~ oned by acrid fubftances irritating the ftomach and bowels. It SS a = 387 MEDICAL: PAPERS, It would be eafy to point out feveral other matters both of a vegetable and animal nature, which produce effects of the fame kind almoftas foon as they are received into the ftomach, and long before they are fuppofed to have un- dergone its action, or of being mixed with the blood. [It is impoflible to tell, what fpecies of the eruptive difeafes are occafioned by the prefence of morbid matter in the primz vie; but in all thofe cafes, where it is doubtful, it would not be amifs to fufpe& it, and to order our medicines ac- cordingly. Dr. Korr (of St. Croix) informed me, that he had once an obftinate humour upon his arm, which alter- nated with a complaint in his ftomach, arifing from the too great predominance of an acid, and that he was never able to remove it with all the applications he could ufe, till he cured the diforder in his ftomach by bitter and aftringent medicines. A fecond obfervation upon the above cafe, which I would beg leave to make is, that pukes may often be given to evacuate the contents of the ftomach, and not- withftanding they work tolerably well, may not anfwer the purpofes we intended by them. How often do we difcover the ftrongeft marks of worms being lodged in the ftomach, and yet how feldom are we able to bring them up from thence, by the ordinary pukes we adminifter. In this, and like cafes therefore, it fhould be our prac- tife to increafe the dofes of our vomits, or to give fuch fubftances as will deftroy the life, or virus of. thofe things we would with to expel from the ftomach. Had the laft puke, which I gave to the child, which had eaten the Strammonium feeds, failed of bringing them up, I have no doubt, but what the plentiful ufe of acids *, (which are fuch powerful antidotes to other narcotic fub- ftances,) would have rendered them harmlefs. And if we may be allowed to reafon from analogy, I think we may prefume, that there is {earcely a poifonous fubftance in na- ture but what has an antidote provided for it. What thefe antidotes * Since writing the above, J have had the pleafure of hearing from Dr. Thomas Bond, and Dr. Harris, an account of the good effects of lemon juice ina fimilar cafe, after the ftrongeft pukes had been given to no purpofe. MEDICAL PAPERS. . 368 antidotes are, can never be determined by reafoning a priori, but muft be found out by experiments alone. Con- fidering the frequency of the accidents which arife from poifons, and the little relief we are able to afford in them, I cannot help thinking an enquiryinto this fubje& a mat- ter of great importance, and well worthy of the attention. of the faculty of phytic. . } gi MEDICAL. PAPER'S. on firft. One child, however, lived under thefe circum ftances tothe eighth day; and the day before he died, his breath and what he expectorated, was fomewhat offenfive ; but this was the only inftance in which I could difcover any thing like a difagreeable {mell, either from the breath or expectoration. Out of fixteen cafes attended with this remarkable fuf- focation in breathing, feven died; five of them before the fifth day, the other two about the eighth, Of thofe who recovered, the difeafe was carried off in one, by a plenti- ful fallivation, which began on the fixth day; in mott of the others by an expectoration of a vifcid mucus. I diftinguith between the fallivation and expectoration, becaufe in one the difcharge feemed to come from the fali~ vary glands, and was attended with little or no cough; in the others it manifeftly came from the trachea, and was at~ tended with an inceflant cough; and 1] judged the falliva~ tion to have been a natural crifis, as the patient had taken but grs. vi of calomel before it came on, Her gums were not inflamed, her teeth were not loofe, nor had her breath, or faliva, the fmell of perfons under a mercurial falivation. In this cafe the voice, in the fpace of a few hours, from being pretty ftrong and loud, became fo low as to be with difficulty heard. One of the firft families in which this difeafe appeared, was that of Mr. William Waddell of this ‘place. He had feven children in his family, all of whom were taken ill one after another; the four firft had the difeafe as I have juft now defcribed, and three of thefe died; the one who recovered was the inftance I mentioned, in which the dif- eafe was carried off by a fallivation, The other three were the youngeft. They had not the difficulty of breath- ing, but in its ftead very troublefome ulcers behind their ears. Thefe began with a few red pimples, which foon ran together, itched violently, and difcharged a great deal of very fharp ichor, fo as to erode the neighbouring parts, and in a few days fpread all over the back part of the ear, and down upon the neck, They all had a fever, particu- larly Spa TTI ETh rer cc ne San epee rae tn int MEDICAL PAPERS, 392 larly at night, and one of them had a perpetual tenefmus. This fymptom appeared in feveral who had the difliculty of breathing, but in none to fo remarkable a degree as in this child. After this, many other children had fimilar ulcers be- hind their ears; and fome of them feemed flightly affec- ted with the difficulty of breathing; but it never became alarming while this difcharge continued. .Thefe ulcers would continue for feveral weeks, and appeared covered in fome places with floughs, refembling thofe on. the tonfils ; and at laft grew very painful and unealy. In fome cafes they were attended with {wellings of the parotid and fublingual glands, which fubfided on the eruptions appearing behind the ears, and difcharging free— ly, and again {welled upon the difcharge being checked. I met with but two inftances of any thing like this com" , , plaint in adult perfons. Both of thefe were women; and one of them had aflifted in laying out two of the children. / that died of it. At firft her fymptoms refembled rather \ an inflammatory angina, but about the third day the ton- fils appeared covered with thick floughs; her pulfe was | low and feeble; fhe had a moift {kin; a deje@tion of {pi- rits; and fome degree of anxiety, though nothing like the difficult breathing of the children. The other was a foldier’s wife, who for fome time, be~ fore fhe perceived any complaint in her throat, laboured. under a low fever. Her tonfils were {welled, and entirely covered with floughs, refembling thofe of the children; but her breath. was. more offenfive, and the had no fufFocation.. I have had an. opportunity of examining the nature and. feat of this difeafe, from diflection, in three inftances.. One was a child of three years old. Her firft complaint was an uneafinefs in her throat” Upon examining it the tonfils appeared fwelled and’ inflamed, with. large white floughs upon them, the edges of which were remarkably: more red than the other parts of the throat. She had no. great forenefs in her. throat, and could fwallow with little. or no difficulty. She complained of a pain under her left. 393 MEDICAL SGAPERS, left breaft; her pulfe was quick, foft and fluttering. The heat of her body was not very great, and her fkin was moift; her face was {welled; fhe had a confiderable pro- firation of ftrength, with a very great difficulty of breath- ing; a very remarkable hollow cough; and a peculiar change in the tone of her voice. The next day her dif- ficulty of breathing was increafed, and fhe drew her breath in the manner before defcribed, as if the air was forced through too narrow a paflage, fo that the feemed incapa- ble of filling her lungs: She was exceedingly reftlefs, tof- fing perpetually from fide to fide, was fentible, and when afked .a queftion, would give a pertinent anfwer, but otherways fhe appeared dull and comatous. All thefe fymptoms continued, or rather increafed, untill the third night, on which fhe had five or fix loofe ftools, and died early in the morning. ~ Upon examining the body, which was done on the af- ternoon of the day fhe died, I found the fauces, uvula, tonfils, and root of the tongue interfperfed with floughs, which ftill retained their whitith colour. Upon removing \/ them, the parts underneath appeared rather pale than in- flamed. I perceived no putrid {mell from them, nor was the corps in the leaft offenfive. The cefophagus appeared as in a found ftate. The epiglottis was a little inflamed, on its external furface, and on the inner fide, together with the infide of the whole larynx, was covered with the fame tough white floughs, as the glands of the fauces. The whole trachea, from the larynx down to its divifion in the lungs, was lined with an infpiffated mucus, in form of a membrane, remarkably tough and firm; which, when it'came to the firft fubdivifions of the trachea, feemed to grow thin and difappear: It was fo tough as to require no inconfiderable force to tear it, and came out whole from the trachea, which it left with much eafe; and refembled more than any thing, both in thicknefs and appearance, a fheath of thin fhammoy leather. ‘The inner membrane of of the trachea was flightly inflamed; the lungs too ap- peared inflamed as in peripneumonic cafes; particularly the MEDICAL PAPERS. 304 the right lobe,.on which there were many large livid {pots, though neither rotten or offenfive;.and the left lobe had {mall black {pots.on it, refembling thofe marks left under the {kin by gun powder. Upon cutting into: any of the larger fpots, which appeared on the right lobe, a bloody fanies iffued from them without frothing, whereas upon cutting thofe parts which appeared found, a whitith froth, but flightly tinged with blood, followed the knife. This is a faithful hiftory of this complaint, as it ap- peared in all the cafes I have met with. Dr. Douglas, of Bofton, in the year 1736, publifhed an account of the firft appearance of the difeafe in this country; from which I find that it put on much more ma- lignant and putrid fymptoms at that time, than it has late~ ly been attended with, efpecially in this city, where dif- eafes of the putrid. kind feldom occur; and was fo con-~ ftantly attended with the erylipelatous fymptoms, that he terms it an eruptive miliary fever, with an angina ulcuf- culofa. And even in this-place, fome of the oldeft, and moft refpectable practitioners, aflure me, they have {een, but a few years ago, the fame difeafe of which I am now treating, attended both with-the eryfipelatous appearances and highly putrid fymptoms. Upon the whole, I am led to conclude that the prefent difeafe, as well as other fimilar difeafes, which have made their appearance at different times, and in different places, arofe from a particular difpofition of the air, or mia/mata fui generis; which more or lefs, according to particular circumftances, generate an acrimony in the humours, and difpofe them to putrefaction;. and which have a fingular tendency to attack the throat and trachea, affecting the mucous glands of thefe parts, in fuch a way, as to occafi- on them to fecret their natural mucus, in greater quanti- ties than is fuflicient for the purpofes of nature: And which in this particular fpecies, when fecreted, is either really of a tougher or more vifcid confiftence than natural, or is difpofed to become fo from reft and ftagnation, The Ve 395 MEDPGAL. ? &4P'E RS. The difeafe I have defcribed, appeared to me to be of an infectious nature, and as all infe@tion muft be owing to fomething received into the body, this, therefore, what- ever it is, being drawn in by the breath of a healthy child, irritates the glands of the fauces and trachea, as it pafles by them, and brings about a change in their fecretions. The infetion, however, did not feem in the prefent cafe to depend fo much on any generally prevailing difpofition of the air, as upon effluvize received from the breath of infected perfons. This will account why the diforder fhould go through a whole family, and not affe& the next door neighbour; and hence we learn a very ufeful leflon, namely, to remove all the young children ina family, as foon as any one is taken with the difeafe; by which cauti- on, Iam convinced, many lives have been, and may again be preferved. I fhall now proceed to deliver the method of cure, which was found moft fuccefsful in the difeafe, as far as it fell under my own obfervation. And in the firft place, as from all the fymptoms related, it is evident that this dif- order is not always, and in every ftage, attended with any remarkable degree of putrefcency; and from the diffedti- ons it appears, that an inflammation of the lungs, if not the caufe, may at leaft be the confequence of the diftemp- er, one would imagine that V. S..and evacuations were not totally to be forbid; and accordingly we find Dr. Dou- gla/s directing us, that if the fever is high, and the pati- ent is plethoric or accuftomed to venefeétion, to take away fome blood, but with difcretion: And if the tonfils are much inflamed, with great pain and difficulty in fwallow- ing, to ufe venefection in the jugulars. And Auxham ac- knowledges, in the ulcerous fore throats of which he treats, “ That there were certainly fome of them with a “« pretty {mart fever that bore bleeding at the beginning “* with advantage, and that he was obliged in feveral to “ give nitre with diaphoretics.” But Lothergill {peaking of the fore throat’ diftemper, which came under his notice, and whieh feems to be of a ’ more MEDIGAL PAPERS! 496 more highly putrid kind, affures us, that although in fuch cafes he has been induced to order bleeding, yet it did not appear to have any advantageous effects; and concludes, that nothwithftanding the vehemence of the fymptoms, it is proper in general to omit this evacuation; nor can | hear of any perfon who has ufed it, in the fore throat (which appeared lately amongft us) with fuccefs; fo that | hardly dare venture to prefcribe it, but mutt leave it to the diferetion of the phyfician, until farther experience fhall confirm its utility, or forbid its ufe. There is fomething very fingular in the tendency of the virus in this difeafe, as I have already hinted, to attack the throatand trachea, nor are the effects its produces there lefs remarkable, Dr. Fothergill, in his account of the pu< trid fore throat, deferibes the floughs on the tonfils, as mortified efcars; but in that fpecies of fore throat | met with, they appeared as in the trachea, to be nothing more than the mucus of the part, preternaturally thickened into the form of amembrane, At firft ] imagined this to be only a peculiar kind of pus, which is fometimes found upon the furface of internal inflamed membranes; but uponremoving it, the membrane of the trachea did not ap~ pear to have been fufficiently inflamed, to juftify fuch an opinion, And in a cafe I lately had an opportunity of examining, where the patient died of a very violent inflam~ mation of the internal membrane of the trachea, there was no fuch mucous lining to be difcovered upon it. Nor can [ think it the effect of any fpafm or conftriction of thelungs, as I never knew it remarked as occuring in fuch as have died of {pafmodic afthmas, nor is it long fince | had an op- portunity of being fatisfied as to this particular, in the cafe ofa failor, who actually died in a violent fit of a fpafmo-~ dic afthma, which had lafted for feveral days; and yet there was not the leaft appearance of any fuch mucous membrane after death, either in the large or fmaller branches of the trachea, This morbid appearance ig par- ticularly noticed by feveral gentlemen who hove favoured us with an aegount of the diffections.of thofe who have diad \é ere 397 MEDtCGAL + BA? ER & died under an angina*. Dr. Monro, fen. found it in feve-. ral he diflected, and + Rolandus Martin, Profeflor of Ana- tomy at Stockholm, mentions a very remarkable inftance of it, where this mucous membrane de{cended into the minuteft branches of the trachea arteria, growing thinner as it defcended deeper into the lungs, until it refembled the membrane which lines the fhell ofanegg. He adds, that the lungs were not inflamed, nor in the leaft injured, fo that the infant died merely from the fuffocation. And even thofe who have written of the ulcerous fore throat, as Drs. Huxham and Douglas, and have not given the ap- pearances from difleGtion, yet have mentioned many mu- cous linings being expectorated, which Douglas compares to the cuticle raifed by verfications, and Huxham con~ ceived to be really pieces of the internal membrane of the the trachea. So that this is a circumftance which feems to be peculiar to the difeafe; and I believe thofe who die, on thefecond or third day, with the ftrangulated breathing, are generally fuffocated by this membrane. The affection therefore, of the mucous glands, muft be confidered as the proximate caufe of this difeafe, and readily accounts for all the other fymptoms; and from it only, efpecially in the beginning of the complaint, can we fafely draw our indications of cure; paying at the fame time a conftant at- tention to any fymptoms of putrefcency that may occur. And it is from viewing the difeafe in this light only, that we can account for the ufe of Mercury in it; a medi- cine, which if we confider it as a fpafmodic complaint, cannot poflibly have any good effe&; or if we look upon it merely as a putrid difeafe, feems direly contrary to every intention of cure; but which, neverthelefs, undoubted ex- perience has proved to be highly beneficial. And indeed, if we confider the peculiar acrimony which this difeafe oc- cafions in the fluids in general, independent of putrefac- tion, and the infpiffation of the mucus of the trachea, we might reafonably conclude a priore, that Mercury, which in general corrects acrimony in a very remarkable manner, thins * See Dr. Withering’s Thefis on the Angina Grangrenola, + Idem. MEDICAL PAPERS, 398 thins all the mucous 4ecretions, particularly thofe of the mouth and fauces, and affects the breath very early, would be beneficial in it, and either prevent the formation of this membrane, or promote its feparation and expulfion, when already formed. Dr. Douglas viewing the matter in this light firft tried it, and meeting with fuccefs, afterwards recommended it to others; and in a very few words has explained both his theory and practice in this particular. « Any affedtion of the throat (fays he) does frequently “ produce a natural ptyalifm, Mercurials ufed with difcre« « tion, area kind of fpecific in fuch like ulcers and ulcul+ * cula, and in fact here moiften the throat and mouth, flop “ the fpreading of the uleufcula, and: promote the cafting “ off of the floughs; and as an acceflary advantage, the pa- « tients being moftly children, deftroyed worms. Amongtt « all the preparations calomel anfwered beft. The gentle « yomiting and few ftools that it occafioned in fome, “ did not confound the natural courfe of the diftemper. “ Turbith produces too ftrong a revulfion, and the erup- « tion is thereby too much diverted, This diflemper did « pot well bear anyother evacuation but Mercurials, And in another place, fays, “ the defpumation of this acrid in« “ quination of the juices in our diftemper, that is, its na~ « tural crifis, feems to be by the patent and falutary emunc~ « tories of the fauces and fkin, In corrofive taints, v2. «¢ venereal and others, a mercurial ptyalifm, and fudorific s decoétion of the woods anfwer beft, this gave us the “ hint of promoting the tendency of nature in our illnefs, “ by mercurials and gentle breathing {weats in bed, which « with good management feldom failed, excepting where « the necrofis was irremediable from the beginning.” There is a fingularity in this Gentleman’s ftile, but his obfervations are accurate and judicious; and, ashe fays hime felf, being founded upon real, not imaginary cafes, muft therefore be of permanent truth. And indeed the cafe I met with, in which the diforder (and in no trifling degree) was carried off by a very copious falivation, is, of itfelf, Vou. I 4 almott 499 gMyEeDylyGpA Lp oP peek yg hgh. almoft a fufficient vindication of this praGtice; and toge- ther with the cafe of that child whofe body I firft opened, where J faw the moft powerful antifeptics faithfully admi- niftered, which not only failed of fuccefs, but did not even mitigate the fymptoms, was what firft led me to enquire more minutely into the nature of the difeafe, and of the remedies which had been ufed with moft fuccefs in its cure.— Upon reading Dr. Dougla/s’s little eflay, (which gave me the greater fatisfaction becaufe he wrote upon the difeafe as it appeared in this country, and under his own immediate obfervation,) I found he placed his chief de- pendence upon mercurials, which I was the more readily induced to make trial of, from the appearance I found from diffeétion, and the idea I thence naturally formed of this complaint; and the experience I have had of their good effects, fully juftifies the recommendation Dr. Doug- fofs has given of them; as the more freely I have ufed them, the better effeéts I have feen from them. Calomel is what I have commonly ufed, and have given it to the quantity of 30 0r 40 grains, in five or fix days, to a child of three or four years old; not only without any ill effects, but to the manifeft advantage of my patient; relieving the difficulty of breathing, and promoting the cafting off the floughs, beyond any other medicine. That it may more immediately enter the blood, and acl more power- fully as an attenuant, it fhould at firt be joined witha mild opiate; and what is a little remarkable, is, that given in this way, it feldom or never raifed in children any fa- livation; though indeed I fhould be apprehenfive of no il confequences from it, if it fhould. After the firft or fecond dofe, the opiate fhould be ommitted, as then the mercury will not be fo apt to go off by the inteftines, and the opiate if. continued will, by leflening the fenfibility of the tra- chea, counteract in fome meafure the attenuating effects of the calomel, and alfo increafe the coma. ‘The opera- tion of the calomel, as an expectorant, will be very much promoted by a prudent ufe of oxymel of f{quills, or leaft that Wee TOA bP AR ERS, 4.00 that fhould purge, by ipecacuahna, given fo as to puke - two or three times. ; But although I confider mercury as the bafis of the cure, efpecially in the beginning of this difeafe, 1 by no means intend to condemn, or omit the ufe of proper alexiphar- mics and antifeptics; of which the ferpentaria, contrayerva, and peruvian bark are the moft powerful, and have been ufed with the greateft fuccefs. Sweating is certainly one way, by which nature carries off this difeafe; infomuch that Muxham declares he did not remember to have had one patient mifcarry, who fell into a foft, eafy, univerfal {weat: And therefore,-whatever method of cure was pur- {ued, this fhould be always connected with it, The pati- ent fhould be kept in bed, and as the difeafe has a putrid tendency, the diaphoretics fhould he of the alexipharmic and antifeptic kinds. The bark is certainly a moft pow. erful antifeptic, and when the fymptoms of putrefaction, fuch as a moift clammy fkin, highly putrid breath, and haemorrhages appear, muft be attended with advantage, But early in the difeafe, while the {kin continues dry, at~ tended with a great difficulty of breathing, and the fymp- toms of inflammation rather than thofe of putrefaction pre~ vail, it fhould be omitted; and here the removal of the dif. order fhould be attempted, chiefly, by mercurials and mild fudorifics. And indeed I think the whole art, in the cure of this difeafe, depends upon properly timeing thefe reme~ dies, and infifting upon one or the other, as the fymptoms of putrefaction do, more or lefs, prevail. But befides a falivation, and {weating, nature frequently carries off this difeafe by an eruption on the fkin, ulcers behind the ears, or in other parts of the body, or an exter- nal {welling of the throat, all of which feem evidently to indicate the ufe of blifters. And accordingly Drs. Fother-= gill and Huxham vecommended them; particularly Dr. Huxham, who fays he has fometimes bliftered the throat from ear to ear with great fuccefs, It has indeed been faid, that they fometimes produced mortifications, and that even the V 401 MEDIC aL PAPER S the difcharge they occafioned, feemed to be more than the patient could bear; but as I have never heard this remark confirmed, I cannot help imagining, that the cafes in which they were tried, were particularly unfavourable, and more — remarkably putrid than is ufual; for in the child, who died on the eighth day, I applied blifters behind the ears, and they had not‘the leaft appearance of mortification or gangrene, even after the child’s death. And ina cafe of very great danger, which I lately met with, they were cer- tainly of great fervice, and very effectually fupplied the place of thofe natural difcharges, by which nature carries off this difeafe. I would recommend their application early in the difeafe, from the fame principle that they are applied in inflam- matory angina’s or pleurifies; to relieve the throat and trachea, and to derive the flow of humours from the inter- nal, to the external parts. As the cafe to which I refer was a very remarkable one, in which the difeafe was attended with fome of the worft fymptoms I ever faw, and the method I have been advifing was ftrily purfued, and attended with fuccefs, I cannot help confidering this fuccefs to be in fome meafure a proof of the propriety of the treatment, and for that reafon fhall here infert the cafe at large. The patient was a child of about two years and a half old, who had complained for about a week ofa fore throat and hoarfenefs. The day before I faw her the had fome difficulty of breathing, which on that day was greatly in- creafed, and exaétly refembled the breathing of the children whofe cafes I have before related, when moft ftrangulated. Upon examining her throat I found the tonfils fwelled, inflamed, and covered with floughs of a yellowith colour, Her breath was not in the leaft offenfive; her pulfe was fmall and fluttering, and her {kin pale and clammy. Two very large blifters were immediately applied, one behind each ear, fo as to meet at her throat. She took four grains of calomel, with a quarter of a grain of opium, and was directed MEDHG AL. .P-Ac?P ER.S; 402 directed to drink a decoction of ferpentar : virg : difguifed with old metheglin, as a common drink; and as her {kin was pale and clammy, fhe hada clyfter of one drachm of cort. peruy. and ten grains of ferpent. virgin. in milk, ta be adminiftered every fix or eight hours; but of thefe fhe received but one that night; and as we found the did not retain them, they were foon difcontinued; nor could the be prevailedon to drink but very little of the decoction. I {aw her feveral times during the firft day, and fhe ap- peared worfe at cachtime, About cight that evening the had fomething like a fit; and, at nine the ftrangulation in her breathing was much increafed; her pulfe was funk;: her countenance changed; her nofe appeared to be pinched. up; her eyes were fixed and glafly; a blue ring was ob- fervable about her mouth, and ihe was comatous. I left,. her, expecting fhe would {oon die. Her blifters had been. dreffed a little before; had rifen well; and difcharged free- ly; and, within two or three hours, as 1 was informed by the watches who fat up with her, fhe feemed to revive. The next morning I was greatly furprifed, not only to find her. living, but in a fitting pofture, eating her breakfaft, with. little or no difficulty of breathing, having her natural coun- tenance returned, -with fome colour in her cheeks, and her: pulfe rather rifen. At twelve o’clock however her breath- ing grew more difficult, and though not fo ftrangulated as the day before, was very quick-and uneafy. From this. time for five days fhe remained in a very dangerous fitu- ation, and gave but little reafon to. expect her recovery. Her breathing continued quick and laborious, and her voice was almoft entirely gone; her pulfe was quick and’ low; the fweated profufely, particularly at nights, and conftantly lay in her bed in a comatous fituation, given however diftin& anfwers when fpoken to. I could difco- ver nothing difagreeable in her breath, though fometimes what fhe brought up was alittle offenfive. During this time, and for many days after, the blifters difcharged con- fiderably, and the matter of the difcharge was fo tharp and corrofive be po 7 ‘ v 403. MED CAL (PAPER & corrofive as to inflame and erode the fkin almoft from the chin tothe ferum, She conftantly took twice a day three erains of calomel; and, except the firft dofe, without opi~ um, until fhe had taken upwards of thirty grains; and continued the ufe of the decoction of ferpentar : In as large quantities as fhe could be prevailed on to take it. On the feventh day from the time I firft faw her, fhe began to cough a good deal, with which fhe expectorated pretty freely, and brought up fome very tough mucus. She breathed more freely, opened her eyes and looked about with fome fprightlinefs, and drank a glafs or two of wine. From this time fhe gradually grew better, and by the fif- teenth day from the time I faw her, all her fymptoms had left her, except great weaknefs, and fo remarkable a hoar~ fenefs, or rather lofs of voice, that it was with great dif ficulty the could be heard; and a peculiar fenfibilityof the larynx with regard to fluids, fo that the moment fhe attempted to drink fhe fell into a fit of coughing, although fhe could {wallow folid food without difficulty. This however foon left her, but her weaknefs and lownefs of voice continued, a much longer time, fo that in two months fhe could hardly walk alone, or {peak in a tone above a whifper. When ulcers appear behind the ears, or in different parts of the body, they require a particular treatment ; the difcharge fhould be encouraged by frequently wafhing them with warm milk and water, and poultices of bread and milk be applied to them; but greafy applications al- ways do harm, as they check the difcharge: Nor will they bear digeftives. I was in fome cafes, however, after the difcharge had continued for a great length of time, oblig- ged to check it, with a very weak folution of vitriol. alb. which I found anfwered this intention well; nor did I ever obferve any ill effects from it: But Lalways ufed it with great caution, and never ventured on it, until I had cor- rected the general virus of the difeafe, by a previous uf- of mercurials. In refpect to gargles, I would entirely fole low MEDICAL PAPERS. — 404 low Dr. Fothergill’s advice. Fomentations applied to the breaft, and fumigations with the fteams of fome mild aro- matic herbs, and warm vinegar, not only give eafe, but ferve, in fome meafure, to attenuate the mucus in the tra- chea; and by gently {timulating the lungs, raife a flight cough, and promote the expectoration. The treatment of any accidental fymptoms, after endeavouring to form a juft idea of the difeafe, muft be left to the difcretion of the phyfician. Such are the fentiments, which, from an attentive ob- fervation of the fymptoms, and progrefs of this difeafe, I have entertained ofits nature, and moft proper treatment, which nothing, but a real defire of contributing to the ftock of medical facts, has induced me to offer to. the no- tice of the public; thefe being the only foundation of a certain and rational practice; and I can anfwer for the fidelity and candor with which I have related, what are here perferved. ; siiceniemiieerieis cS a SuBSTANCE of fome PAPERS that could not be inferted in: their proper Place.. The following account of an Aurora Borealis was recerved from a Correfpondent, at Lancafter,; in Penn/ylvania, viz. “PH AT about half an hour after feven in the evening of January 5; 1769, there was’feen at that place, a bright crepufculum, rifing out of the North; which in: about a quarter of an hour extended itfelf from. N. E. to. N. W.—The upper part was: deeply notched, and rofe in: one place to the height of near’ 40°. above the horizon. “At three quarters after eight, it was fo light in the Northern hemifphere, that a perfon, who felt no decay or. infirmity of eye-fight, might eafily have read a book print- in Double Pica Roman. ; . «¢ At nine o’clock, five columns or pyramids, of avery vivid red, rofe perpendicular to the horizon, in the N. W. — They: gos HORIZONTAL WIND-MILL —They were unequal in their heights: For, whilft two of them rofe almoft to the zenith, others did nott-exceed 45°. They changed colours alternately from a fiery red to a purple; from that toa yellow; from yellow to a flame co~ lour; and then to red again. Thefe changes were fo fud- den and quick that they affected the fenfe fo ftrongly as to raife horror. “Ata quarter after nine, the columns changed their perpendicular pofition to an oblique one, and immediately began to move towards the Weft. They foon blended to-= gether, and formed a dirty red fky, tinged with yellow. «“ N. B. There were no ftreamers, corrufcations, tre- mulous or dancing motions, as are common to fuch pha- nomena. This was a quiet one, except that it changed colours, and moved towards the Weft, as already defcribed. “ During the appearance the air was uncommonly {e~ vere and chilling; and, though the Heavens were ferene and befpangled with ftars, the atmofphere felt damp and heavy. “A little before ten o’clock, the whole funk below our horizon and difappeared.” A a Sa Mr. Thomas Gilpin hath prefented a model of a Horizontal Wind-mill; and writes to the Society as follows. HAT to obviate the difficulty of turning the houfe, or frame, of common wind-mills to the wind, he had contrived a model of a horizontal wind-mill, which he had fixed to three pumps, as he apprehended the chief ufe of fuch a mill would be the applying it to raife water out of mines and quarries, and likewife out of wells, or brooks for watering meadows. He thinks alfo it might be further applied to anfwer the various ufes of other wind- mills, without the inconvenience in turning or fhifting them as the winds fhift. 6 The HORIZONTAL WIND-MILL. 406 _« The model is three pumps erea, in a triangular po- fition; in the center isa crank ereét ina ftep, and fteddied. by a neck in a frame, from the ears of the pumps; on the top of the crank are eight arms, and at the ends of each is a fail which alternately draws with the wind, and folds againft it, which gives a powerful motion to the crank,. which, by a handle to each pump, works. them in a regular fucceffion.”” ie ay Mr. John Jones, of Indian River, Worcefter County, Ma-- ryland, gives the following account of a Species of Grape Vines which he had difcovered, different Srom all others Bie ad ever feen— 7 HE bark (he fays,) is of a grey: eolour, very fmooth,. - and the wood.of a firm texture.. They delight ina: high fandy foil;. but will thrive very well in the Cyprus fwamps.. The leaf is very much. like that of the’ Englith grape vine, fuch as:is propagated in the gardens near Phi-- ladelphia for table ufe. “ The grape is muc fhape, and, when qu an the Englifh, of an oval The pulp is a little like the Fox-grape; but in tafte more delicious... Thefe grapes are ripe in October, and yield an. incredible quantity’ of juice, which, with proper manage-. ment, he doubts not, would make a valuable wine. « He employed a ‘perfon to gather about three bufhels* and one peck of them when ripe, and immediately had’ them prefled ; which, to his furprize, yielded twelve gallons of pure juice, though a good quantity muft have been loft. in the’prefling. = pene Ee oy “ In about twelve hours after: putting the juice in a keg, . it began to ferment, and he fuffered it to goon till it got to be fo violent, that it might be heard all over a large room. It continued in that {tate for three days. He then Vot.I. rE checked “is black, adorned with a» number of pale red {pecks, which, on handling, rub off.. 4o7 Specizs or VINE GRAPES. checked it, fearing it might turn acid, though, he fays, he | was afterwards convinced that ifhe had fuffered it to fer-— ment as long again, it would have feparated the vinous parts from the flefhy, and given greater finenefs to the liquor. « After this it was racked off, and before cold weather buried in the garden, the top about fix inches under ground; where having continued till the fummer follow- ing, he could not difcover that it had in the leaft altered, either in tafte or colour. He obferves farther that, after eating a quantity of them, or drinking the juice, they leave an aftringency, as claret is apt to do. “ There is:an immenfe quantity of thefe vines growing on the beach, open to the fea; and they are alfo found in great plenty upon the ridges, and in the fwamps. Since their difeovery he has tranfplanted a number of them into his vineyard, from which, ina year or two more, he ex- peéts to make a wine much better than is commonly im- ported.” END of tus FIRST VOLUME,