Natural History Museum Library 000163719 ■*'v V. V t f c r t V :i f « iJ IT i '*-■ I 1 I J r PHILOSOPHICAL TRANSACTIONS, GIVING SOME ACCOUNT OF THE Prefent Undertakings, Studies, and Labours, OF THE INGENIOUS, IN MANY Confiderable Parts of the WORLD. VOL. LV. For the Year 1765. LONDON: Printed for L. Davis and C. R e v m e r s, Printers to the Royal Society, againft Gray s- Inn Gate, in Holbourn. mTdUc.lxvi. t •< >• t. ADVERTISEMENT. The Committee appointed by the Royal Society to diredl the publication of the Philojbphical Tra?ifa5hons, take this opportunity to acquaint the public, that it fully appears, as well from the council- books and journals of the Society, as from repeated declarations, which have been made in feveral for- mer ’TranfaShons^ that the printing of them was al- ways, from time to time, the fingle a6t of the re- fpedlive Secretaries, till the Forty-feventh Volume. And this information was thought the more neceflary, not only as it has been the common opinion, that they were publilhed by the authority, and under the di- redlion, of the Society itfelf; but alfo, becaufe feveral authors, both at home and abroad, have in their writ- ings called them the PranJaSlions of the Royal Society, Whereas in truth the Society, as a body, never did intereft themfelves any further in their publication, than by occafionally recommending the revival of them to fome of their fecretaries, when, from the par- ticular circumftances of their affairs, the 'TranfaSliom had happened for any length of time to be intermitted. And this feems principally to have been done with a view to fatisfy the public, that their ufual meetings were then continued for the improvement of know- ledge, and benefit of mankind, the great ends of their firfi: inftitution by the Royal Charters, and which they have ever fince Readily purfued. But the Society being of late years greatly inlarged, and their communications more numerous, it was thought advifeable, that a Committee of their Mem- bers thou Id be appointed to reconfider the papers read before them, and fele<5t out of them fuch, as they a 2 Ihould ADVERTISEMENT. fhoiild judge moft proper for publication in the future Tra?jfa6iions ; which was accordingly done upon the 26th of March 1752. And the grounds of their choice are, and will Continue to be, the importance or fingu- larity of the fubjedts, or the advantageous manner of treating them ; without pretending to anfwer for the certainty of the fadts, or propriety of the reafonings, contained in the feveral papers fo publiflied, which muft dill reft on the credit or judgment of their re- fpedtive authors. It is likewife neceflary on this occafion to remark, that it is an eftablifhed rule of the Society, to which they will always adhere, never to give their opinion, as a body, upon any fubjedt, either of nature or art, that comes before them. And therefore the thanks, which are frequently propofed from the chair, to be given to the authors of fach papers, as are read at their accuftomed meetings, or to th« perfons, through whofe hands they receive them, are to be conftdered in no other light, than as a matter of civility, in re- turn for the relpedt ftiewn to the Society by thofe communications. The like alfo is to be faid with regard to the feveral projedts, inventions, and curio- fities of various kinds, which are often exhibited to the Society ; the authors whereof, or thofe who ex- 'hibit them, frequently take the liberty to report, and even to certify in the public news-papers, that they have met with the higheft applaufc and approbation. And therefore it is hoped, that no regard will here- after be paid to fuch reports, and public notices ; which in fome inftances have been too lightly cre- dited, to the difhonour of the Society. C O N- C ON TENTS T O VOL. LV. I. /IN Account of the Pholas Conoides, by J. ^ Parfons, M. D. F. R. S. p. i. JI. An Account of the Cafe of a young Lady who drank Sea Water for an Inflam7naiion and Fumour in the Upper Lip. Communicated by Dr, Lavington of Taviftock, in Devon, to John Huxham, M. D. and F.R.S. p. 6. III. A Letter to the Right Honourable the Earl of Morton, Prefident oj the Royal Society. Coiitaining Experiments and Obfervations on the Agreement be- tween the Specific Gravities of the feveral Metals^ and their Colours when united to Glajs^ as well as thofe of their other P rgpctrtmts : By Edward Delaval, F. R. S. M. A. Fellow of Pembroke Hall, Cam- bridge. p- lO. IV. An Account of the Cafe of an extraneous Body forced into the Lungs : By William Martin, Efquire^ of Shadwell. Communicated by Mr. Emanuel Mendez da Cofta, Librarian oJ the Royal Society. P- 39- V. Aji CONTENTS. V. An Account of an Earthquake felt at Llfbon, December 26, 1764: In a Letter to the Rev. Samuel Chandler, D. D. F. R. S. p. 43. V J . An Account of the White Negro Jhewn before the Royal Society : In a Letter to the Right Nonourahle the Earl' of Morton, Prefident oj the Royal Society ^ from James Parfons, M. D. F. R. S. p. 45. \"1I. An Account of an Improvement made by Mr. Peter Dollond in his New Felefcopes : In a Letter to James Short, M. A. F. R.S. with a Letter of Mr. Short’s to the Rev. Thomas Birch, D. D. Secret. R. S. p. 54. VIII. Some Account of a Salt found on the Pic of Teneritte, by W. Heberden, M. D. F.R. S. p. 57. IX. Short and eajy Methods for finding ( i .) Fhe ^puan- tity of Time contained in any given Number of Mean Lunations -y (2.) Lhe Number of Mean Lu- nations contained in any given ^antity of f ime ; (3.) The Number of Froy Pounds contained in any given Number of Avcirdupoife Pounds^ and vice verfa; (4.) Fhe ^lantity and Weight of Water ' contained in a full Pipe of any given Height y and Diameter of a Bore-y and confequenthy to fnd what Degree of Power would be required to work a com- mon Pumpy or any other Hydraulic Engine, when the Diameter of the Pump- bore, and the Height to which the Water is to be raifed therein, are given. Communicated by Mr. James Fergulbn, F. R. S. p. 61. X. A Recommendation of Hadley’s S^uadrant Jor fur - vcyingy efpecially the furveying of Harbours, together with a particular Application of it in forne Cafes of Pilotage. By the Rev. John MichelJ, B. D. F.R. S. p. 70. XI. An 5 CONTENTS. XI. An uncommon Anatomical Ohfervaiion addrejjed to the Royal Society^ by John Baptift Paitoni, Phy~ fician at Venice : Pranjlated from the Italian, p. 79. XII. An Account of a New Improvement of the Port- able Barometer. By Edward Spry, M. D. of Totnefs, Devon: In a Letter to the Right Ho- nourable James Eatd oj Morton, Prefdent of the Royal Society. P* ^3* XIII. A Letter from Mr. Woolcombe, Surgeon at Plymouth Dock, to Dr. Huxham, F. R. S. con- cerning the Cafe of a Locked faw. p. 85. XIV. A Defcription of a beautiful Chinefe Phea- fant', the Feathers and Drawing oJ which were fent from Canton to John Fothergill, M. D. F.R. S. By Mr. George Edwards, F.R. S. p. 88. XV. A Catalogue of the Fifty Plants from Chelfea Garden, prefented to the Royal Society by the wor- fdipful Company of Apothecaries^ for the Tear 1764, purfuant to the Dirediion of Sir Hans Sloane, Bart. Med. Reg, et Soc. Reg. aliquando Prcefes : By John Wilmer, M. D. clarijf. Societatis Pharmaceut . Lond. Soc. Hort. Chelfean. PrafeSlus et Praledlor Botanic. P- XVI. A Courfe of Experiments to afcertain the fpe- cific Buoyancy of Cork in different Waters : The refpelHve Weights and Buoyancy of fait Water and frejh Water : And for determming the exaSi Weight of human and other Bodies in Fluids. By John Wilkinfon, M. D. F.R. S. of London a?jd Got- tingen. p. 95. XVII. An Account of the Difeafe, called Ergot, in French, from its fuppofed Caufiy viz. vitiated Rye. In a Letter Jrom Dr. Tiflbt, of Laufanne, to George CONTENTS. George Baker, M. D. F. R. S. Communicated to the Rev. Thomas Birch, D. D. Sec. R. S. p. io6. XVIII. Obfervations for fettlmg the Proportion^ which the Decreafe of Heat bears to the Height of Situa- tion. FxtraSied from a Letter of Thomas Heber- den, M. D. F. R. S. to William Heberden, M. D. F R. S. p. A 26. XIX. An Account of a Stone voided without Help from the Bladder of a Woman at Bury. Communi- cated by William Heberden, M. D. F, R. S. p. 128. XX. ^ Letter from John Bevis, M. D. to the Rev. Thomas Birch, D. D. Secretary to the Royal So- ciety i containing Afronojnical Obfervations^ made at Vienna, by the Rev. Father Jofepli Liefganig. p. 130. XXL An Account of the Cafe of a fuppofed Hydrophobia : In a Letter to the Rev. Thomas Birch, D. D. • Secretary to the Royal Society, from the Right Ho- nourable James Earl of Morton, Prefdent of the Royal Society. p. 139. XXII. Fwo theorems, by Edward Waring, M. A. Lucafian Profefor of Mathematics in the Univerjity of Cambridge, and F. R. S. In a Letter to Charles Morton, M. D. Sec. R. S. p. 143. XXIII. A fOifertation on the Nature of Evaporation, and fever al Phenomena of Air, Water, and boiling Liquors: In a Letter, to the Rev. Charles Dodgfon, D. D. F. R. S. From the Rev. tiugh Hamilton, D. D. F. R. S. Profefor of Natural Philo fop by in the Univerfity of DuhWn. p. J46. XXIV. Phyfjcal and Meteorological Obfervations, Con- jeAures, and Suppoftions. By Benjamin Franklin, LL. D. and F. R, S. p. 182. • XXIV. Hifo- CONTENTS. XXIV. Hifiorical Memoirs relating to the PraSiice of Inoculation for the Small Pox, in the Britifli Anie- rican Provinces, particularly in New England : Addrejjed to John Huxham, M, D. F. R. S. By, Benjamin Gale, A.M. p. 193. XXV. An Account of a Balance of a new Confirublion, Juppofed to be of life' in the Woollen Manufadiure. By W. Ludlam, B. D. Fellow of St. John’s Col- lege, Cambridge. p. 205. XX Vl. An Experimental Enquiry into the Mineral Elafic Spirit, or Air contained in Spa Water ; as well as into the Mephitic ^lalities of this Spirit. By William Brownrigg, M.D. F. R. S. p. 218. XXVII. Extradi of a Letter from Mr. Benjamin Gale, to a Phyfciaii in New England, to John Huxham, M. D. F. R. S. concerning the fuccefsful Application of Salt to Wounds made by the Bitmg of Rattle Snakes-, dated at Killingworth in Con- ne, V i I • . i # ,♦ i y I I \ • I. An Account of the Pholas Conoides, by J. Parfons, M* D, F. R, Read Jan. lo, "I" D O myfelf the honor of laying be- ' X* learned Society a fpecies of Pholas, very little known, and but feldom feen among the naturalifts', being the firft of them that has come to my hands. [Vid. Tab. I.] This Ihell is pivflurcd by RurnphtuSy and called by the name of Pholas lignorum j in Dutch, Hout^ Mojfely Wood Mufcle, becaufe it is found burrowed in timber. The fpecimen before you is one of" infinite numbers that were thus bedded in the keel of a Spani/h Ihip, which was brought from the Weft-Indies, a piece of which accompanies the' fh^ll, to Ihew' how they lie in wood, ftone, or any other hard bodies, that entertain them. Buf this name is altogether too vague and uncertain, unlefs it could be alferted that this is the only kind that inhabits pieces '-of wood: for every fpecies of Vol.lv. B Pholas [ o Phelas penetrates that and other folid fubftances like- syife, and fo do various other fhell-fifli. Therefore, as all fubjedis, in natural hiflory, fhould have fome precifion in the appellations which diftinguifh them from each other, the bed: and mod clear method of giving names to them, is certainly to call them after lome ftriking character proper to them fpecifically : and, therefore, I have ventured to give this fpecies the above title, viz. Pholas ConoideSy being very dif- ferent in its form, from the oblong, the broad, the pointed, the cilindrlcal, and every other Pholas I have feen. And a5 the figure given by Rumphius is fo imperfedf, and this name fo general, it was neceflary to give an accurate account, as well as an exaft re- prel'entation of fo curious a fpecics j and, therefore, I drew it in four views, and fhall deferibe it as follows : If we obferve this fpccimen, as it is intire, it will appear to confift of two great valves, an ante- riour long piece, a pofteriour long piece, and an or- bicular detach’d piece at the end of this, at that ex- tremity which may be called the bafe of the Cone, Thefe make but five pieces to compleat the whole, unlefs the white fmooth parts, at the broad ends of the great valves, are accounted feparate pieces, which they really are not, but abfolute portions of the fame valves ; and, as to the circular piece on the back, it appears to me to be intire, and not divided into twoj if it may be counted two, then the whole would confift of fix pieces, according to Monf. de la Faille's opinion, who feems fond of that num- ber in the Pholades. It is an inch and half long, and three quarters of gn inch thick at the bafe j and this appears to be its utmoft C 3 ] utmoft fize, becaufe the others, which are in this piece of wood, feem nearly of the fame magni^ tude. The great valves are of a duflcy white, inclining,- towards the bafe end, to a purplilh cad: ; where the Jhice arc very fine and minute, running upwards to- meet thofe which are larger on the main body, in a weavy curve diredion j and the fmooth parts of thefe, as well as the other pieces, are perfectly white, and without any ftriae at all. The bafe end of this fifli feems covered with three plates that are white and* fmooth ; but thefe are only the two fmooth pieces of the great valves, and the circular pofterior plate,, mentioned before : and where thefe meet, there are two depreflions, which terminate in two holes in the bafes of the great valves, which are half covered by the pofteriour circular piece. The apex is. round' and flatidi, and- forms almoft a^ flaarp edge by the concurrence of the two great valves and the fore and back edges are united, by the long; pieces fpokeii of already; The wood in which they lie was faid to be cedar; but it rather feems to be of fir, having a fiflile grain., like common deal wood, and is as eafily. fplit as that,;, it is allb extreamly light, and its fibres- are very loofe',, nor has it the lead Imell like cedar they have the- fame colour, which is of a yellowifh call; ;, but the- cedar has- a clofe fmooth graiuj though it is a light wood, and foft in itlelf : whereas this does not feem; to be as hard as what we call white deal, which is. efteemed the lighted and tendered, of ail the clafs of, firs. B 2. The.* [ 4 ] The texture of the fhell is very- thin and brittle; and therefore it is wonderful to 'fee the holes they lie in fo fmooth and uniform, as if bored with a hard fharp inftrument. The bafe end is always inward, and the hole which opens from them outwards very fmall ; and this is the cafe of every kind which are thus lodged whether in wood or done j fo that one muft conclude that they are depofited there in a very minute date, and not in a date of maturity ; for then they muft bore their way inwards, and the hole would be as wide outwards as inwards, and confe- quently be of equal diameter. But how thefe ani- mals maintain and increafe the cavity, as they grow larger, is a queftion which it will be very difficult to refolve, and has puzzled feveral ingenious naturalifts in the enquiry. It is faid they have a power of turning themfelvcs about wdth a fwift motion, and fo make themfelves gradual room ; but this will be hard to conceive, if we confider that a fifh clofely ffiut up within its valves, and comprefled on all fides, can have no power of motion. We cannot imagine any animal can move itlclf, when thus confined, without fome fulcrum or point of effort, from which to begin fuch motion ; and if they had fuch tentacula as were capable of feizing upon the wood, in order to exert themfelves, there can be no room for it, for it is in clofe contadt with themfelves in every point. That this is the cafe, is very clear, from confidering the ftate of toads, frogs, and other animals, inclofed in blocks of marble, trunks of trees, &c. which have no communication with the atmofphere at all. Thefe are foft animals, and their fhape not at all fit for turning about and I boring [5] boring’ their cavities ; and they are found In moulds as exactly fitted to their bodies, as thofe are to melted matter caft into -them by a founder. It may, however, be fuppofed that the ftone and wood does actually give way to the growth ol the animal within, becaufe the fadfs are well attefted ; but how this comes to pafs,in thefe Pholades and cylindrical Mulcles, and by what means, toads, &c. can receive aliment 'to caufe their growth, without any external commu- nication, mufi: yet remain among thofe fecrets of nature, which we cannot but admire, without knowing how they are brought about. Explanation of 'the Table*. Fig. I. Is a view of the furface of one of the great valves, with the edges of the two longi- tudinal pieces, and with portions of the fmooth parts at the round extremity or bafe. II, Shews the anteriour edge of the Pholas co- vered by the long fmooth white piece, and, at the bafe, having part of the fmooth portions of the great valves in view. III. Reprefents the pofteriour edge of the Pholas, with the round white piece upon the bafe end, and the long ditto, which is larger than that of the fore edge, running to- wards the apex. IV. Is [6] IV. Is a view of the bafe extremity, which Is round like a hemifphere, fhewing the two holes, one at the end of each great valve, juft where the procefles of their fmooth portions, and the edge of the round piece, meet. The apices of fome of thefe conoide Pholades are a little curved ; but that of this fubje(5t defcribed is ftrait. We muft: al fb obferve that, befides thefe, there were great numbers of Cojjiy or worms, in the bot« tom of the Spanifti fliip ; the veftige of orre or two of them, if vifible in this piece of wood, and the channels they make, which are in all diredions, arc lined with a thin white incruftation, and are of equal dimenfions all along. II. An Account of the Cafe of a young Lady who drank Sea Water for an Inflamma- tion and Lumour in the Upper Lip, Com- municated by Dr, Lavington ^Taviftock, in Devon, to John Huxham, M, D, and F, R, S, Read Jan. 17,, \ Young lady of Launcqfton, aged 1765. ftxteen, very tall, of her age, and of a thin delicate conftitutiqn, very weak and fickly when a child, enjoyed for fome years paft a tolerable ftate of health. However being incom- moded [73. moded now and then with an inflammation and fwelling of the upper lip, which was thought ftru- mous, was advifed to drink fea water, which fhe ac- cordingly did every morning, to the quantity of a pint, for ten days fucceflively ; during which (he was as well as ufual, till on a fudden ihe was feized with a profufe difcharge of the catamenia. This continued fo immoderate and alarming that Dr. La- vington was confulted. Upon inquiry, he found not only that the uterine flux was exceflive, but alfo that file was perpetually fpitting blood from the gums ; and likewife had innumerable petechial fpots on her neck and bread; ; and withall a great many large livid fpots on her arms and legs. Her pulfc was very quick, though pretty full j her face ex- ceedingly pale, and fomewhat bloated ; and her flefh in general was very foft and tender. She was often taken very faint, but foon recovered tolerable fpirits. The flux from the uterus at length abated, but that from the gums increafed to fuch a degree, that her apothecary took a little blood from her arm. From the orifice blood ouzed continually for feveral days, notwithftanding many endeavours were ufed to {launch it. At lafl: blood iifued from her nofe perpetually, attended with frequent faintings, in which fhe at length expired, choaked as it were with her own blood. But before fhe died, it was very re- markable, that her right arm was quite mortified from the elbow to the wrifl : and it is to be further noted, that though blood, drawn from her fome weeks before {he began the ufe of the fea water for an inflammation in her lip, was found fufliciently denfe, and in a pretty good {late ; yet that drawn off in / [8] in her laft ficknefs was mere putrid difTolved. gore. To this account Dr. Lavington fubjoincd the 'fol- lowing queries. Whether or no, a fcorbutic ftate of ‘the animal juices may not be produced by fait water, as well as by fait provifions ; efpecially if, as in the prefent cafe, it doth not pafs of¥ freely by the ufual evacu- ations, which often happens when drank for a con- fiderable time, and the body is accuftomed to it ? Whether the thin tender delicate fibre is not a morbid difpofition, fomewhat different from the too vifcid or too lax ? and whether to fuch a conftitution, attended with a loofe texture of the blood, or a hedlic habit, a fait water courfe may not be likely to increafe the acrimony of the blood, rupture the veffels, and bring on a dangerous hsemorrhage ? And whether, even to flmmous patients thus circum- flanced, the Cortex Peruvianus is not more adapted ? To which Dr. Huxham replied nearly as follows : “ Jn many cafes I have known very good effedls “ from a courfe of fea water, when drank in pretty Jarge quantities, and long continued; but it was when it purged gently, and now and then puked “ fomewhat. With the thin, tender, and hedtical, it feldom agrees. The grofs, heavy, and phlegma- “ tic, commonly bear it with advantage. I have “ known it bring on colical pains, diarrhcea, dyfen- “ tery, and bloody fiools, cough, hedtical heats, “ wafting of the flefh, and an haemoptoe. It ge- *' nerally renders the body liable to very great con- “ ftipation, after it hath been drank for a confiderable “ time.” Sea . . Sea fait is a kind of neutral fait, that will not pafs off through the pores of the fkin (except perhaps in an ammoniacal ftate fome of it may). Its proper outlets are by ftool and urine. It appears by expe- riments to be very little alterable by the powers of the animal oeconomy. If fo, when not duly difcharged by thefe paffages, in a courfe of drinking fait water, the marine fait muff be greatly accumu- lated in the mafs of blood, make it continually more and more aferimbnious ; and by the mutual attraction of its particles, when fo abundant, run into molecula too large to pafs the minuted: veffels, occafion ffag- nations ; and by irritating thefe capillaries increafe the impetus a tergo^ and often bring on ruptures of thofe veffels, extravafations, blotches, fpots ; in a word, all the fymptoms of the fcurvy in the higheff degree. Indeed it is very well known, that the mod: healthy failors cannot long live in drinking mere fait water for common drink. VoL. LV. C III. A [ 10 ] III. A Letter to the Right Honourable the Earl of Morton, Prfident of the Royal Society, Containing Experiments and Ob- fervations on the Agreement between the Specific Gravities of the fever al Metals^ and their Colours when united to Glafs^ as well as thofe of their other Prppad^ions: By Edward Delaval, F. R, S. M. A, and Fellow of Pembroke Hall, Cambridge. My Lord, Read Jan. 24, T" T A K E the liberty of laying before >765* Jl^ your Lordlhip the following paper, containing a variety of fad:s and experiments, which I have endeavoured to apply to fome Optical in- quiries. Befides the experiments originally contrived and made by myfelf, I have repeated moll of thofe which I have quoted from others. Sir Ifaac Newton, in his Optics, has fliewn hy a feries of experiments, that the feveral differences of colours, exhibited by thin tranfparent plates, are occafioned by their feveral thickneffes; and that therefore the tranfparent parts of bodies do, ac- cording to their different fizes, refledt rays of one colour and tranfrnit thofe of another; and confe- quently that the bignefs of the component parti- cles of natural bodies may be conjedured from their colours ; fince the particles of thofe bodies moft probably exhibit the fame colours as a plate 4 of of equal thicknefs, provided they have the fame denfity. He concludes this whole dodtrine in thefe words : I have hitherto explained the powers of bodies to refledl and refradt, and (hewed that “ thin tranfparent plates, fibres, and particles, do, according to their feveral thickneffes and denfitiesy “ refledt feveral forts of rays, and thereby appear “ of feveral colours \ and by confequence, that no- thing more is requifite, for producing all the “ colours of natural bodies, than the feveral fisc,es “ and denfities of their tranfparent particles.” Though he has accurately fhewn what colours arife from the feveral changes of thicknefs, I do not find that any one has attempted to explain in what 7na?mer the differences of denfty, in the component particles of bodies, contribute to produce the feve- ral differences of colours: and therefore I thought, that if inftances could be produced of bodies whofe feveral differences of colour appear to be propor- tioned to their feveral degrees of de77fity, it would tend to illuftrate this part of Optics. To this purpofe, however, are conducive all thofe experiments and obfervations, from which Sir Kaac Newton has inferred that bodies have their refradiive and refleBive powers nearly praportional to their denfities ; and that the leaf refrangible rays require the greatef power to refledt them : which is deducible froni/ hence, i. that the rays are refledted at the greatef obliquity of incidence, and the nsiolet at the leaf, 2. that the niolet is refiedted, in like circurnftances, at the leaf thicknefs of any thin plate or bubble, the red at iht greatef thick- nefs, and the intermediate colours at intermediate C 2 thickneffes. [ 12 ] thicknefles. 3. The fame appears from the table (p. 206.) in which the thickneffes of air, water, and glafs, and the colours produced by them are fet down. Thefe experiments are applied by him to tranf- parent bodies and the colours exhibited by them; but they are equally applicable to permanently coloured bodies : and it appears from them, that denfer fubftances ought, by their greater rejiedtive power, in like circumftances, to refledl the lefs re- frangible rays, and that fubftances of lefs denjity Ihould reflect rays proportionably more refrangible, and thereby appear of feveral colours in the order of their denfity. In confirmation of this reafoning, I fliall give inflances of natural bodies, which differ from each other in denfty, though circumftanced alike in other refpeds ; and fhall fhew that they differ in colour, in the fame order they do in denfity, the denfefi being red, the next in denfity orange, yellow, &c. In fuch an inquiry metallic bodies feem to de- ferve our frfl and principal attention, as their fpecific gravities have been afeertained by well known and repeated experiments. Without enter- ing into a minute chemical theory of the princi- ples of metals, it is fufficient to obferve that they are univerfally allowed to confift of i. an inflam- mable or fulphureous matter, which is of the fame kind in all the metals ; 2. of a fixed matter or calx, which appears in each of the metals to be fpecifically different in weight, as well as in other properties. ' 2 Af [ T3 ] As the fulphureous matter, in the intire metals, ads ftrongly on the rays of light, it is neceffary to calcine, or to divide them into extremely minute particles, in order to examine feparately the adion of the calx, or fixed matter, on the rays of light. In order to examine all the metals in like cir- cumftances, by reducing them into the fmallefi: particles, and depriving them of their fulphur as far as was pradicable, I expofed each of them, united with a proper quantity of the pureft glafs, without any additional ingredient, to the greateji degree of fire they are capable of bearing, without having all colour whatever dejiroyed. In this flate it appears, from a variety of experi- ments and fads, that they adually do, without any exception, exhibit colours in the order of their denfities, as follows. Gold Red. Lead — — — Orange. Silver Yellow. Copper — — Green. Iron — — — Blue. GOLD. [ 14 ] * > GOLD. GOLD, which is the denfeft of all the metals,, imparts a red colour to glafsy whenever it is divided into particles fo minute, that it can be intimately mixed with the ingredients of which the glafs is made ; and it feems indifferent in what manner it is reduced to this ftate. Thus 1. From the powder obtained by rubbing gold with a pumice ftone, ufed by the goldfmiths in polifhing it, mixed with nitre, borax, and potafh, a beautiful red glafs is produced [d that the different manners of preparing copper have producad different colours, f have experienced that by calcining copper per fe, without any addition, I could produce all the elfeds that the author t.eaches us to bring about by different preparations of that metaU lx [ 21 ]■ If a quantity Jalfs be added in the prepara -• tion, they will, by attenuating the mixture, and confequently lejfening its fpecijic gravity^ make the glafs incline to blue, tbe colour next in order [/] ^ but this happens only when the fire is. moderate for in a greater degree of heat, the redundant falts, even thofe of the mofi: fixed nature, are expelled \u\. It is true.,' that> copper is mentioned by feme- writers, as an ingredient: in red glafs and enamel i but the redy which is the colour of the metal not difiblved or mixed with the glafs, remains only while the compofition is expofed to fuch a degree of heat as is too fmall to melt and incorporate it; for, if it be fufiered to remain in the furnace afew^ minutes ^ after the copper is added, the mafs will turn green inftead of red [w] : in efied, the pre- paration of copper recommended on this occafion, is exadly the lame as. that ufed in tinging glafs green^ [/] Flora Saturnizans, chap, xu art. 6-.. When a , green, colour IS to be given to glafs, care muft be taken «lue glafs. El 2 ' GOLD [ 28 ] GOLD. GOLD precipitated from aqua regia, and wafhed with hot water or boiled in a folution of alcaline fait, becomes red on being expofed to a flight heat. Lewis, Hiftory of gold, p. io8. 2. The fame colour is produced when this precipi- tate of gold is ground with oil of vitriol, or fpirit of fulphur; or if it be mixed with fulphur, and the fulphur burnt away. Junker, tab. xxxiii. P* ^59- 3. The fmoaking fpirit of Libavius, mixed with gold and afterwards drawn off from it by diftil- lation, changes it’s colour to a blood red. — Sol fine vefte, exp. 19. Junker, tab. xxxiii. p. 861. 4. Gold is reduced into a red powder, by amalga- mation with mercury, and expoling it for a conliderable time to a flow heat. — Boyle’s Abridg. vol. ii. p. 77. Junker, tab. xxxix. p. 987. 3. if fix parts of antimony are fufed with one of gold, and the antimony driven off by the blaft, a red powder of gold is left behind. — Caffius de Auro, cap. 10. 6. if gold leaf be cemented and ground with decre- pitated fait, hartfliorn, pumice, or chalk, and expofed to a proper heat, the metal becomes red, and may be precipitated from a folution of thofe fubftances in a red powder. — Junker, tab. XXXIII. p. 854. Lewis’s Hiftory of gold, p-74. Sol fine vefte, cap. 6. 7 . A red [ 29 ] 7* A red tindlure may be prepared from gold by feveral methods mentioned byLibavius, Alchem. lib. ii. p. 130. Junker, tab. xxxiii. p. 868. 8. A folution gold in aqua regia prepared from fal ammoniac may be fublimed of a blood red colour. The fame is effedled by diffolving the calx, or crocus of goldy in other menftrua. Lewis’s Hiftory of gold, p. 100. Junker, tab. XXXIII. p. 857. 9. A folution of gold in aqua regia, evaporated pro- perly, affords cryftals of a bright red colour.— Caflius de Auro, p. 109. Junker, tab. xxxiii. p. 862. 868. Lewis’s Hiftory of gold, p. 99. 10. Aurum fulmmans moiftened with water, has been found to tinge gems deeply of a fine red. Phil. Tranf. N°. 179. 1 1. A folution of gold tinges ivory, cotton, the fkin, and other fubifances red. Rubies being frequently found in gold minesy it is very probable that they receive their colour from that metal ; and from this circumftance, before the experiment had been made, Libavius rightly con-’ je(Sured that a folution of gold would communicate a ruby colour to glafis. Libavii Alch. p. 88. It does not appear that, excepting the colour natural to gold in its intire date, any other than’ red can be obtained from preparations of this metal : it is from this colour, which gold affumes when- ever its metallic brightnefs is deflroyed, that writers in chemiftry call it leo ruber \i\. [e] Libavius de natura inetallorum, lib. i. cap. 4. de auro. " In iuo manifefto cittinum eft, in occulto fummam continet rul?e- 2 LEAD. [ 30 ] LEAD. THE only coloured preparation of leady is that produced by calcination in the furnace. The firft of the primary colours produced by this procefs is yellow, the calx paffing from that colour through orange into red. It is remarkable, that, though in the calcination previous to the reverberatory heat in which thefe colours are produced, the lead is diminiJJjed in weight j yet in the reverberatory fire it gains con- fiderably, and in proportion to that increafe of gravity, it paffes from the more refrangible to the lefs r frangible colours ; fo that while the calx re- mains of a lefs weight than that of the lead originally,^ it’s colour is yellow, with the next mcreafe of weight it paifes to orange, which is the colour of dlnem ; unde et non tantum tin£lum ipfum eft, fed et tin£luram ruhedlnis confert abundante'm. Dum c'ltrinum dicitur, externus vultus qualis eft poft excodti- onem refpicitur : ilia tamen citrinitas igne caementi et in opere philofophico fumma rubedtne permutatur, Itaquehinc eft philo- Ibpliorum axioma, quod in dtrinitate lateat rubedo excellemiftinia,_ qualis eft rubedini gemmae. V oces occultum, manifeftum, non ita pueriliter funt accipiendae, quafi in fuperficie fit flavum, in centro rubrum: fed progrefliones colorum in perfedlione artiliciali notantur, quod naturali pro- cfivitate et difpofuione poft citrinitatem abolitam, alTuinat rubedinern. Leo ruber non folet vocari, ante quam ab arte eleboratum, et aftrale, ut aiunt, fadtum. Potentia tamen etiam fimplcx et natu- rale aurum ita vdcare non eft abfurdum, cujus tindiura appella, tur ejus fanguis, quo vocabulo et fcrnienturn denotatur. glaft \ ;[ 31 ] glafs of lead ; and when the calx is increafed more in weight, fo that it’s gravity is become greater than that of the lead originally^ it paffes into red, the next colour in order. Thefe three colours fucceeding each other in proportion as the gravity of the metal increafes, , feem to prove that, in this cafe, the greater denfity produces the lefs refrangible colours : and as orange is the colour of this calx, when in a middle degree of weight, between that which is lighter and that which is heavier than the original metal, it appears that orange is the colour natural to lead when it’s weight is neither much increafed nor diminidied. SILVER. THE only preparation of fiver, which is of any primary colour (except the yellow it im- parts to glafs, and other vitreous fubftances, as earths or falts) is luna cornea, which Mr. Boyle fays is of a J air yellow, Shaw’s Boyle, vol. i. p. 255. Phyfical EjSays, Edinburgh, 1754, vol. i. p.310 [yj. [y] Art. 10. Remarks on chemical folutions and precipita- tions, by A. Plummet, M. D. When either a muria of fea fait, a folution of fait ammoniac, or fpirit of fea fait (for thefe three have nearly the fame efFedls) is put into a folution of ftlver \ it becomes milky, and, as it were, crudled, and at length a white powder fubfides to the bottom : this powder, being wafhed with warm water and dried, is foftand impalpable j it’s weight exceeds that of the filver diflolved by COPPER [ 32 ] COPPER and I R O N. I T appears then that all the preparations of goldj lead, and fiher, invariably retain the colours peculiar to the order of their denjities, and that they are the fame ^uoith thofe njohich they co7nmunicate to glafs. The two mod: imperfect metals, copper and iron, being very ealily adled on by almoft all men- Itrua, the colours of their folutions, &c. viz. green and blue, are apt to change into each other’s order; the copper in lome folvents becoming blue and the iron green, and in other folvents vice verfa ; this probably depending on the increafe or diminution of their denfities. The folutions of copper, in the acids of nitre and fea flit, and in the vegetable acids, are green. But if copper be attenuated, by folution in volatile alcalies, it becomes blue. Theophraftus and others have obferved, that emeralds are frequently found in copper mines ; and it is probable that they obtain their tinge from that metal. I melted fome emeralds with twice their weight of falts, and found that they had formed a fine geren glafs, fuch as would have been produced from the fame quantity of a vitrifiable earth, and about a hundredth part of its weight of copper. t more the one fixth part. This powder comes much fooner to fufion than filver, but does not recover the appearance or pro- perties of that metal ; for it looks like a piece of yellowijh glafs, femiopaque and brittle, yet bending or yielding a little, whence it gets the name of luna cornea. Iron [ 33 J rron diffolved by the vitriolic acid is' green ; bat if further attenuated by a chemical procefs, it pro- duces that beautiful colour called 'Prujjiaii blue, Phil. Tranf. N®. 38. Henckel, Differt. 6. A fimilar blue may be obtained from the iro7i contained in the alhes of all plants. Henckel, Flor, fat. chap. 8. parag. 55. Having expofed a pound of wood aflies in a luted crucible, to a pretty Ifrong fire, for thirty hours, the greatefl part of them became tinged by the iron contained in them. A blue may be alfo extradled from a martial *vitriolj by fpirit of wine. Henckel, de appropria- tione, chap. 2. parag. 257. An inftance of a mineral fubflance changing it’s colour from green to blue on it’s fpecijic gravity being dhninijhedf appears in a ftone defcribed by Dr. Grew in the Mufeum of the Royal Society : this gem is a kind of emerald, which, when expanded. by heat, becomes blue, and remains of that colour till cold, in which ftate it returns to it’s ufual colour, which is green. Tin is not capable of being vitrified, or impart-' ing any colour to glafs ; nor are any preparations of it of any primary colour. F VoL. LV. • MERCURY. [ 34 ] MERCURY. THERE is no body of an intermediate weight between gold and mercury ; and it is probable that a great part of the difference between their fpeci- he gravities depends on the Jhiidity of the one and the folidity of the other. Mercury is not capable of communicating any colour to glafs, being fo volatile that it will not bear the degree of heat neceffary to incorporate it with the glafs in fufion. But it is well known that it’s calx, either pre- pared per fe, or by diffolving it in an acid and evaporating the menftruum, is red, 2. A folution of mercury tinges the fkin, 6cc. red, as gold does. P L A T I N A. THE fpeci/ic gravity platinahtingntOivly equal to that of gold, it feems neceffary to examine whe- ther the colour of it’s preparations correfpond with thofe of gold. On looking into a differtation written by Dr. Lewis on that metal, in the Philof. Tranf. I find that the precipitates and cryjials obtained from folutions of platina are red: and that a folution of that metal in aqua regia to perfe6t faturation is of a dark red, though, when diluted, ; in the fame manner that ‘‘ a red liquor (as Sir Ifaac Newton obferves) in a conical glafs, looks of a pale and dilute [ 35 3 dilute yelloWf at the bottom, where it is thin ; and a little higher, where it is thicker, orange \ ‘“where it is thicker Hill, it becomes red-, and “ where it is thickeft, the liquor is deepeji and dark- “ eft." Newton’s Opt. p. i6o. H AV I N G gone through thefe experiments and fadts, which feem to {hew that the metals mvzx'vdkAg exhibit colours in the order of their denfities, when melted with glajs^ under the circumftances above mentioned j and that the other preparations of the fame metals, for the moft part, aftume the fame colours', it feemed probable that the caufe, on which the colour of natural bodies depend, may fometimes be conjedlured from the chemical ana- lyfis of fuch fubllances. This I have attempted with regard to the colour of plants. It is known from the experiments of Lemery and others, that all earth is impregnated with iron ; that the ferruginous matter is received into the roots of plants in their growth, and makes part of their fubftance, and is univerfally diifeminated through them j and. that iron may be feparated by a magnet from the afhes of all vegetables [^]. It has been already obferved, that the green colour of thc^/<^ ufed in making bottles, is caufed by the iron contained in the materials of which it is made ; and I have cited Becher’s opinion, that the green or blue colour in glafs is an indelible mark of it’s vegetable origin. \^g'] Lemery’s Mem. cle I’Academ. anno 1706. Memoirs of the Acad, of Upfal and Stockholm, of the cafth found in vegetables, by J.G. Wallerius, 1760. F 2 This . [ ,36 ] This obfervatlon of the conftancy of that cotour in glafs made of vegetable ajhest and it’s being caufed by irony led me to conjecture, that the colour of the intire vegetables arifes alfo from the iron, fo univerfally diffufed throughout their fubftance in their growth. Green is the colour which iron aflumes conftant- ly, when diilblved by the acid in the airy that metal thus diffolved being a true green vitriol of iron [/»]; and as this ferruginous or vitriolic matter is univer- fally difleminated through the leaves and branches of plants, thofe parts of it which are at the furface will, by their contaCt with the air, alTume the colour peculiar to its fait or vitriol. Mod: vegetables, when they grow in fuch a man- ner as to be defended from the contaCt of the air, are prevented from becoming green. This happens to the roots of trees, and as much of their flem as is covered with earth ; grafs grow- ing under ftones, or other bodies, that accidentally lie bn it, is white \ not having the lead green, but as the air has accefs to it : and it is a method commonly ufed by gardeners, to cover with earth thofe parts of plants which they would preferve white : by that means hindering them from being tinged green by the contaCt of the air, as the parts [/>] Shaw’s Notes to Boerbaave’s Chemiftry, vol. i. p. 94. Iron is eafily difl'olved in falts, dew, air, &c. By the a£Uon of any of thefe it contradis a ruff, which js nothing but the flowers ,of iron, or iron difl'olved, and lorfakcn by it’s diilblvent ; for ircn examined with a microfcope when it full becomes rufly, fhews it’s furface covered with a number of pellucid vltrieik lamella:, or glebes, which, being afterwards dried by the fluid menftruum’s evaporating, become a ruddy caU. expofed C 37 3 cxpofed to it are ; though it appears from experi- ment that the prefence of light, as well as of air, is neceffary to the produ7^5- Jl^ before this learned Society on Thurfday laft, came to me with his mafter on Sun- day afternoon ; and according, to the defire of your lordfhip and the gentlemen prefent, I made the ne- celhary inquiry into the feveral circumftances relative to his being born of black parents, and find the fol- lowing notices very fatisfaftory ; to which I have added fome obfervations which, I hope, will not be foreign to the fubjedl. It appears that the father and mother of this boy were brought down above three hundred miles from an in-land country to the Gold Coaft in Africa, and were bought among a great number of others, and put on board a flaip bound to Virginia j where they arrived in the year 1755. They became the property of colonel Benjamin Chambers, of the Falling Springs, in Cumberland County, in Pennfilvania; and are now employed upon an eftate in Virginia, which the colonel pofefTes in right of his lady, whom he married in that province, although [ +6 ] although he lives with his family in Pennfilvania, where he fold the boy to his prefent mader ; of which fatfl, I faw the bill of fale that palled between the colonel and him. The father and mother of this child are pcrfeflly black, and were both very young when landed; the woman not being above fixteen years old, and her liulband not more than fix years older ; and when they landed, being afked, how far flie was gone with child ? anfwercd, fo as to be underftood to mean, that Ihe was with child fomething more than fix moons, and that this was her firft pregnancy. They alfo declared, that they had never leen a white pcrlbn before they came to the fhore where Euro- peans were employed in buying black Haves. The prefent owner of this boy is Mr. James-Hill- Clark, whom I informed of what had pafied be- tween Dr. Franklin and myfelf, on Friday morning laft on this fubjedf; for I paid him a vifit, and in the courfe of our conveiTation he informed me, that while he was in England before, he received a letter from his lady, in which was fome of the wool of a white negro child’s head, by way of curiofity ; and when I mentioned it to Mr. Clark, he alfured me that this very boy was fhewed in Pennfilvania as a great rarity ; and that, to his knowledge, the wool lent in the letter was taken from this child’s head. He was born about fix or feven weeks after his pa- rents landed in Virginia, in the year 1755; and was purchafed by Mr. Hill-Clark of colonel Chambers in 1764, fo that he appears not to be quite ten years old ; and his mother has had two children lince, who are both as black as the parents. 4 / Now, [ 47 ] Now, though this deviation of colour In the child, from the contrary hue of both parents, is very fingular, and fomething preternatural, yet in dances of the fame kind have happened before. We had one about four years ago here in London, which was a white girl, fomething younger than this boy, but exadlly fimilar in colour, wool, &c. and was faid, by the perfon who made a fliew of her, to have been the offspring of a black father and mother. I did not go to fee her ; but I read an advertifement, con- cerning her, feveral times in the public papers, wherein fhe was called a white negro girl ; and was informed by thofe that faw her, that fhe anfwered the defcrip- tion in the advertifement very truly. She was fhewn in town for fome months every day. To this remarkable cafe I diall fubjoln two others, one of which I faw myfelf, and the other was given me by a gentleman of undoubted veracity j which, though they differ in fome circumflances from the above, yet have fo much relation to each other, as will prevent their being cenfured as digrelfions from the fubjedl. The fird is of a black man who married a white woman in York feveral years ago 3 of which I had an account from an eye-witnefs. She foon proved with child, and in due time brought forth one in- tirely black, and in every particular of colour and features refembling the father, without the lead par- ticipation from the mother. This was looked upon as a very fingular cafe, becaufe people naturally ex- pe(fl the iffue of fuch a marriage would be tawny ; which indeed is the ufual effe(5t produced by the coii- grefs of black and white perfons. The . [ +8 ] . The fecond cafe was of a black man, fervant to a gentleman who lived fomewherc in the neighbour- hood of Grays-Inn. This black man married a white woman, who lived in the fame family ; and,' when die proved with child, took a lodging for her in Grav’s-inn-lane ; when Ihe was at her full time, the mafler had bufinefs out of town, and took his man with him, and did not return till ten or twelve days after this woman was delivered of a girl, which was as fair a child to look at as any born of white parents, and her features exactly like the mother’s. The black at his return was very much didurbed at the appearance of the child, and fworeit was not his; but the nurfe who attended the lying-in woman foon fitisfied him j for the undrelTed the infant, and fliewed him the right buttock and thigh, which were as black as the father, and reconciled him im- mediately to both mother and child. I was informed of the fadt, and went to the place, where I examined the child, and found it true ; this was in the fpring of the year i 747, as my notes fpecify which I took upon the fpot. As I was willing to add as much as polhble to the above account, I took an opportunity of enquiring about matters of this fort, in a worthy family who came to live in Red-Lyon-Square not many months agoj and had lived in Virginia feveral years in a confpicuous light ; and was informed by the lady of the family of the two following curious parti- culars : About nineteen years ago, in a fmall plantation near to that of this family, which belonged to a widow, two of her flaves, both black, were mar- ried ; I * [ 49 ] lied; and the woman brought forth a white girl, which this lady faw very often ; and as the circum- ftances of this cafe were very particular, I lhall make mention of them here, both for the entertainment of the Society and to fliew that this is exadly fimi- lar to the cafe of the boy before us. When the poor woman was told the child was like the children of white people, flie was in great dread of her huf- band, declaring, at the fame time, that die never had any thing to do with a white man in her life ; and therefore begged they would keep the place dark that he might not fee it. When he came to afk her how (lie did, he wanted to fee the child, and wondered why the room was (hut up, as it was not ufual ; the woman’s fears increafed when he had it brought into the light ; but while he looked at it he feemed highly pleafed, returned the child, and be- haved with extraordinary tendernefs. She imagined he diifembled his refentment till die diould be able to go about, and that then he would leave her; but in a few days he faid to her : “You are afraid of me, and “ therefore keep the room dark, becaufe my child is “ white ; but I love it the better for that, for my “ own father was a white man, though my grand- “ father and grand- mother were as black as you and “ myfelf ; and although we came from a place where “ no white people ever were feen, yet there was al- “ ways a white child in every family that was related “ to us.” The woman did well, and the child was diewn about as a curiodty ; and was, about the age of fifteen, fold to admiral Ward, and brought to London in order to be fhewed to the Royal Society ; but, finding that one of the failors had debauched VoL. LV. H the [ 50 ] the girl and given her the pox, he foon put her un- der the care of a captain returning to America, and fent her back to her own country. The other account is, that admiral Franklin had taken a Spanifh fliip, in war time, and brought her into Carolina j and, upon fearching, found a pidlure of a boy who was as beautifully mottled ail over with black and white fpots as any dog that ever was feen 5 it is uncertain which was the ground, or which colour the fpots were of; but this lady fays, that feveral copies of the picfturc were taken in Ca- rolina ; and that they faid it was the portrait of a child born of negro parents upon the Spanifh main ; the fhip was bound to old Spain ; and this lady does not doubt but the admiral may have the pidurc in his cuftody now. If thefe fails are afcertained by thefe two gentlemen, they will be worth recording with the prefent fubjeil, which I will take the trou- ble of enquiring into further. Thefe deviations of colour are indeed very extra- ordinary among the African negroes, but they are not peculiar to them ; fome parts of America have alfo limilar variations from the common colour of the inhabitants ; and as I edeem it a great happinefs when I can contribute to the entertainment of this learned body, I cannot excufc myfelf from adding to the above, what Mr. Wafer’s account of the Idhmus of America gives us upon the like objects in that country. See page 134 of his Defcription, See, London, printed for Knapton in Paul’s Church-yard, in 1699; where, after having deferibed the natural copper-coloured complexion of the people, he fiys, ‘‘ There is one complexion fo fingular among a fort “ of [ 51 3 of people of this country, that I never faw nor heard of any like them in any part of the world. “ They are white, and there are of them of both “ fexes 5 yet there are but few of them in compa- “ rifon of the copper-coloured, poffibly but one to “ two or three hundred. They differ from the other Indians chiefly in refpedl of colour, though “ not in that only. Their fkins are not of fuch a “ white, as thofe of fair people among Europeans, ‘‘ with fome tindlure of a blufli or fanguine com- “ plexion *, yet neither is it like that of our paler peo- “ pie, but it is rather a milk-white, lighter than “ the colour of any Europeans, and much like that of a white horfe. “ For there is this further remarkable in them, “ that their bodies are befet all over, more or lefs, “ with a fine fliort milk-white down ; for they are “ not fo thick fet with this down, efpecially on the cheeks and forehead, but that the lldn appears di- “ flindt from it. Their eye-brows are milk-white “ alfo, and fo is the hair of their heads, and very ■“ fine withal, about the length of fix or eight inches, “ and inclining to a curl. “ They are not fo big as the other Indians; and “ their eye-lids bend and open in an oblong figure, “ pointing downwards at the corners, and forming “ an arch or figure of a crcfcent with the points downwards. From hence, and from their feeing “ fo clear as they do in a moon-fhiny night, we “ ufed to call them moon-eyed. For they fee not well in the fun, poring in the cleareft day ; their “ eyes being but weak, and running with water if i‘ the fun fliine towards them ; fo that in the day- II 2 “ time [52] time they care not to go abroad, unlefs it be a cloudy dark day. Befidcs, they are a weak people in comparifon of the others, and not very fit for hunting, or other laborious exercifes, nor do they delight in any fuch. But, notwithflanding their being thus fluggifli and dull in the day-time, yet, when moon-fliiny nights come, they are all life and activity, running abroad into the woods, and fkipping about like wild bucks, and running as faff by moon-light, even in the gloom and fhade of the woods, as the other Indians by day, being as nimble as they, though not fo ftrong and lufty. The copper-coloured Indians feem not to refpedt them fo much as thofe of their own com- plexion, looking on them as fomething monftrous. They are not a didindl race by themfelves ; but now and then one is bred of a copper- coloured father and mother ; and 1 have feen a child of lefs than a year old of this fort. Some would be apt to fufpedl they might be the offspring of fome European father j but befides that the Europeans come little here, and have little ccm- merce with the Indian women when they do come j thefe white people are as different from the Europeans, in fome refpeds, as from the copper- coloured Indians in others. And, befides, where an European lies with an Indian woman, the child is always a Modefe, or Tawny, as is well known to all who have been in the W efl-Indies, where there are Modefas, Mulattoes, &c. of feveral gradations between the white, and the black or copper-co- loured, according as the parents are, even to de- 4 “ compounds. C S3, ] “ compounds, as a Mulatto-Fina, the child of a Mu- “ latto man and Moftefa woman, &c. But neither is the child of a man and woman< of thefe white Indians white like the parents, but copper-coloured as their parents were. For fo “ Lacenta told rne, and gave me this as his conjec- “ ture how thefe came to be white, that it was “ through the force of the mother’s imagination looking on the moon at the time of conception “ but this I leave others to judge of. He told me ‘‘ withal that they were but fhort-lived.” N. B. Lacenta was the king of the Indians among whom Mr. Wafer lived. If my time would have permitted, I fliould have madefome remarks upon thefe feveral cafes; butimuft feize feme other opportunity for this purpofe; and am. My Lord, Your Lordfhip’s mofl refpeflful and moft humble fervant, J. Parfons** Wednefday, Jan. 30, 1765. VI. % C5+] VII. An Account of an Improvement made by Mr, Peter Dollond in his New 7^- If copes : In a Letter to James Short, M, A, F. R, S, with a Letter of Mr, Short’s to the Rev, Thomas Birch, D, D, Secret, R, S, Dear Sir, Surry-Street, Feb. 7, 1765. IH AV E fent you, inclofed, a letter which I re- ceived this morning from Mr. Dollond, concern- ing an improvement which he has made in Iiis new telcfcopes. He, fome months ago, fent me a tele- fcope, in this new way, of 3 i. feet focal length, with an aperture of 3 ^ inches ; I examined it, and I ap- proved of itj I have tried it with a magnifying power of 150 times, and I found the image diftind, bright, and free from colours. You may, if you pleafe, lay Mr. Dollond*s letter before the Royal Society. I am. Dear Sir, Your moft obedient, and humble fervant, James Short. [ 55 ] S 1 R, Read Feb. 7, 1765. I Take the liberty of fending you the following fliort account of an improve- ment I have lately made in the compound objedt glafles of refradting telefcopes. The diffipation of the rays of light may be per- fedlly cor reded in objedt glaffes, by combining me- diums of different refradlive qualities ; and the errors or aberrations of the fpherical furfaces may be cor- redted by the contrary refradlions of two lenles, made of the different mediums; yet as the excefs of re- fradtion is in the convex lens, and though the fur- faces of the concave lens may be fo proportioned as to aberrate exadUy equal to the convex lens, near the axis i yet as the refradlions of the two lenles are not equal, the equality of the aberrations cannot be con- tinued to any great didance from the axis. In the year 1758, when my father had condrudled fome objedl glaffes for telefcopes in this manner, viz. with one convex lens of crown glafs, and one con- cave lens of white flint glafs ; he attempted to make fliort objedl glaffes to be ufed with concave e)^ glaffes; in the fame manner ; but as the field of view, in ufing a concave eye glafs, depends on the aperture of the objedl glafs, the limits of the aperture were found to be too fmall : this led my father to confider that if the refradtion of the crown glafs (in which the excefs was) fhould be divided by means of having two lenfes made of crown glafs inflead of one, the aberration would thereby be decreafed, and the aper- tures might then be larger; this was tried with, fuccds j in [ S6 ] in thofe obie£t glafles, when concave eye glafTes were ui'ed, and thefe have been ever fince made in this manner: fome trials were likewife made, at the fame time, to enlarge the apertures of longer objedt glaffes, where convex eye glaffes were ufed, by the fame method ; but thefe not fucceeding, in the fame man- ner, the method of making them with one lens of crown glafs, and one of white flint glafs, -was con- tinued. As I could not fee any good reafon why the me- thod, which was pradiced with fo much fuccefs, when concave eye glaffes were ufed, fliould not do with convex ones ; 1 determined to try fome further experiments in that way. After a few trials, I found it might be done; and in a fhort time I finilhed an objed glafs of 5 feet focal length, with an apperture of 3 ^ inches, compofed of two convex lenfes of crown glafs, and one concave of white flint glafs. Thinking that the apertures might be yet admit- ted larger ; I attempted to make one of 3 4. feet fo- cal length, with the fame aperture of 3 4 inches, which 1 have now completed, and am ready to ffew the fame to the Royal Society, if defired. The difficulty of procuring good glafs of fo large a diameter, and of the thicknefs required, added to the great exadnefs of the furfaces, in order to cor- red the aberration in fuch large apertures, has pre- vented me from attempting to extend them any farther in that length. I am, S I R, Your moft obedient, and moft humble fervant, Peter Dollond. VIII. Some C 57 ] VIII. Some Account of a Salt found on the Pic ^TenerifFe, by W. Heberden, M. D. F. R. S. Read Feb. 7, v ]SJ the account of a journey up the Pic jI. of Teneriffe, by Dr. Thomas Heberden, printed in the Philofoph. Tranfadions, Vol. XLVII. N° 57. there is mention made of a fort of fait, as well as of brimftone, with which fome parts of the Pic are covered. There is no difficulty in conceiving how brimflone may be forced up by fubterraneous hres; and it is no uncommon thing to find it in other places : but it is not fo eafy to underfiand how a fait of fo fixed a nature, as this is, ffiould be fublimed to fuch a height without being cooled and fixed long before it arrives at the furface of the earth, where no fenfible heat is perceived. Neither am T able to ex- plain, how it happens, that a fubftance, fo eafily melted in water, is not difiblved and wafhed away, as fafi; as it can be produced, by the dews, and rains, and melted fnow. By means of my brother Dr. Thomas Heberden, I have procured a parcel of this fait collected from the Pic, a fpecimen of which, together with fome of the fulphur, is here prefented to the Society ; both which, though fo very pure, are juft 2,s they were taken up. My brother informs me, that the fait is found not far from the verge of the crater, and that it is called, by the Spanilli inhabitants of the Vol. LV. I ^ ifland, C 58 ] ifland, falitron j which is the name given by them to falt-petre ; and that it is fold for about five pence a pound. It appears to be the natron or nitrum of the anti- ents, or, as it is fometimes called, the foflil alkali, which is the bafis of fea-falt: the fame which is procured from the Spanifii barilla, and from our own kelp. The mineral alkali differs from the vegetable in its ready cryftallizing without any addition of fixed air, which is neceffary to make the latter take the form of cryftals * ; and in its not melting in a moift air ; and on this laft account it is a much more com- modious ingredient in medicinal powders, than the vegetable alkali ; as it is not like this apt to run per deliquium ; but on the contrary, .inftead of attracting moifture from the air, it is robbed by the air of its own moifture, fo that its cryftals foon lofe their tranfparence, and are turned to powder. The natron liquefies in a very gentle heat : it refembles the vege- table alkali in tafte and fixednefs, and like that is ufcd in making foap and glafs ; and they are both ap- ' plicable to moft of the fame purpofes. Of the cryftals of natron, when very dry, but yet with fcarce any white powder on them, i oo grains may be diffolved in 384 gr. of water, when Farhen- heifs thermometer is at 37. Such cryftals quite dry, and juft- inclining to grow white, will lofe of their weight if dried, with a heat fufficient to fcorch paper. * See Dr, Black’s experiments in the Edinburgh Eflays, Vol. II. page a 1 8. 2 ‘‘ The [ 59 } “ The vegetable alkali has a ftronger affinity to « the acid fpirits of vitriol^ nitre, and marine fait, “ than the foffil j” for (r) If the common alkali be added to a faturated folution of Glauber’s fait in water,, the fpirit of vi- triol will leave the natron-; and uniting itfelf with the vegetable fixed fait will form vitriolated tartar ; which being of difficult folution, much of it will cryfiallize and .fall to the bottom, while the natron, robbed of the vitriolic acid, remains difiblved toge- ther with a fmall portion of the vitriolated tartar. (2) Gr. 1 66 of quadrangular nitre were difiblved by heat in a folution containing gr. 138 of pearl- affies. On cooling, there ffiot fome cryftals of com- mon nitre, the nitrous acid having left the foffil al- kali, which is the bafe of quadrangular nitre, to join itfelf with the pearl-aflies. (3) Gr. 500 of fal-gem, which feemed quite free from fal catharticus amarus, were difiblved by heat in a folution of gr. 654 of pearl-affies. There ffiot a confiderable quantity of fal fylvii mixed with foffil alkali, which had been expelled by the pearl-affies from the marine acid. Thefe experiments were made and communicated to me by the Hon. Henry Cavendifli. Befides the properties, which have been mentioned, the natives of the Canary iflands have found out, that they can make matches by dipping paper or tow in a flrong folution of natron, which will then burn, except that they do not fparkle, almofl; as well as if they had been dipped in a folution of nitre, though upon trial no nitre appears to be mixed with it. The fait of barilla and kelp 1 find, by experience, to have I 2 this [ 6o J this property, but in a lefs degree,' which may be owing to their not being perfedly free from other falts. It may be doubted whether the mineral alkali be not generated upon the Pic, where it is found, by the- - litnefs of that fort of earth to attract out of the air fome of the principles, of which it is made : for there; is often feen upon walls a faline efflorefcence, which proves to be this very faltj and fome earth, as that at the bottom of a lake in Egypt, is faid to produce it, fo as to make a conftant lupply of a great quan- tity, which is every year dug up and carried away. The natron mufl be in great abundance in the air or earth, as it is the bafe of that fait, which is the commoneft of all in almoft every part of the world ; but though it be every where found, when united to the acid of fea-lalt, yet there are but very few es, where we have been able to procure it ^ IX. Shcrl [ 6i 3- IX. Short and eafy Methods for finding- (i.) "The §^a?2tity of "Time contained in ary given Number of Mean Lu?iations ; (2.) T*he Number of Mean Lunations contained in' any given §fuantity of Litne ; (3.) Lhe Niwiber of Iroy Fou?ids contamed in any give?! Number of Avoirdupoife Pounds^ and vice verfa ; (4.) Lhe Quantity and Weight of Water contamed^ in a full Pipe of any given Height y and Diameter of Bore ; and coifequently^ to find what Degree of Power would be required to work a common Pump^ or any other Hydraulic Engine^ when the Diameter of the Pump-bore^ and the Height to which the Water is to be raifed therein^ . are given. Communicated by Mr, James . Fergufon, F, R, S. Read Feb. 7> O O M E time ago, jufl: as I was finifli- ^ table for (hewing the quantity of time contained in any given number of mean lu- nations within the compafs of 6000 Julian years, in- tending tliereby to examine how near our prefent aftronomical tables would (hew the times of fome antient eclipfes which we have on record, when the proper equ ations of the folar and lunar motions were I ‘ taken [ 62 ] taken into the account j I was vifited by my friend William Rivet, Efq; of the Inner Temple, who faid he wilhed he had come fooner, hecaufe he could have put me upon a much fliorter method of com- putation. I defired him to (hew me his method, which he did mofl; readily and chearfully. “ It was “ only to reduce the odd hours, minutes, feconds, “ and thirds, &c. above the integral days of a luna- tion, into the decimal parts of a day j which niim- be of days and decimal parts, being nine times added together, will be equal to the time contained in nine mean lunations. And from thele, the “ time contained in any other affigned number may “ be found, as follows. A Table fliewingthe quantity of time contained in any given number of mean lunations. The mean luna- tion being 29 days 12b 44' 3" a'" ; or 2q.i;3o<;908<;io8 days. Lun. Days. Decimals of a Day, 29*530590^5^08 59.061 18170216 3 88.59177255324 4 1 1 8.12236340432 5 '47-65295425540 6 I/7-'^3545'o64*^ 7206.71413595756 8:236.24472680864 91265.77531765972 Explanation. For tens of lunations, remove the decimal point one place forward j for hundreds of lu- nations, two places; for thou- fands, thiee places ; and fo on, as in the aiinexed example ; and then the remaining deci- mals may be reduced into hours, minutes, feconds, Sic. by the common method of re- ducing decimals to the known parts of an integer. Example. C 6^ ] « Example. In 74212 mean lunations. Qu. How many days, hours, minutes, and feconds ? Lun. Days Dccim, of a Day. 70000 2067141.3595756 4000 1 18 122.36340432 200 5906.1 18170216 10 295'3°59'=85io8 59.061 18170216 2 74212 1 2191524.20824034896 Anf, 2191524 days and .20824034896 decimal parts of a day. And by redudion, 2191 524 days contain 6ooo Julian years, 24 days, and .20824034896 decimal parts of a day, contain 4 hours, 59 minutes, 51 feconds, 57 But in pradice, it is fuf- hcient to take in four or five of the decimal figures. Having got this hint from Mr. Rivet, I reverfed it into a way of finding the number of mean luna- tions contained in any given quantity of time j for which purpofe I calculated the following table, upon the above length of a mean lunation j which comes the neareft to the truth of any length I have yet found, when carried back from the prefent times to the recorded times of antient eclipfes, if the proper equations depending upon the anomalies of the fun and moon are applyed to the mean times of new and full moons. A Table [ 64 ] A Table fhewing the number of mean lunations contained in any given quantity of time. Y. , Decimals of a ^ ' Lunation. 1 12.36853003S63 2 24.73706007726 3 37.10559011589 4 49.47412015451 5 61.842650193 14 6 74.21118023176 7 86.57971027039 8 98.94824030Q02, 9 111. 31677034^65 H. Decimals of a 1 ' Lunaticn, 1 c. 00141096024 2 0.00283193248 3 0.00423289872 4 0.00564386496 s . 0.C0705483120 9 0.00846579744 7 0.C098707636S 8 0-0 1 128772992 9 0 01269869616 s. " DecimpU of a " I.unatinn, 1 3 3 4 !s 6 7 8 9 i,ccooco;oi93 % 000COO7S387 3.0CO001 J75S0 4.000001 56774 5.00000195567 6.00000235161 7.000002743 54 1.00000313548 9,00000352741 D. j Decimals of a Lunation, M. Decimals of a Lunation. Th: Decimals of a Lunation. X 0.033863x897600 X 0.00002351610 1 0.00000000653 2 0.0677263795200 2 0,0000^.70^221 • 2 0.00200001306 3 0.1015895692800 3 0.00097054831 3 0.000COO01959 4 o-i3S4S*759'340o 4 0.0000.9406442 4 0.00000002613 5 0.1603150488000 .5 0.00011758052 .5 G.00000003 266 6 0.203179x385600 6 C.000141C9662 6 0.00000003919 7 0.21704.23283200 7 o.'Coci646i273 7 0.000000,04573 8 0.2709055180800 8 0.00018812883 8 0,00000005226 9 0.3047687078400 9 0,00021164494 9 0,0000^005879 Explanation. For tens of years, days, hours, minutes, orfeconds, remove the decimal "point ‘one place forward 5 for hundreds, two places j for^thoufahds, three places j and fo on, as in the annexed example, which is the . . f j . .. I • : 'li Mi' -r { Example. i [ 65 ] Example. In 6000 Julian years, 24 days, 4 hours, 59 mi- nutes, 52 feconds, How many mean luna- tions ? Years 6000 Days j ^ 20 * 4 Hours ... “ 4 Minutes ■ > 50 1 9 Seconds - r 50 1. ^ Lun. Dec. of a L. 7421 1.18023 176 0.677263795 0.135452759 0.005643865 0.001 175805 0.00021 1645 0.000019596 0.000000784 Anfwcr 74212.000000009 This (hort method may be ufeful in many other cafes ; but, as yet, I have only applied it to two. The firft of which is, to find the number of troy pounds contained in any given number of avoirdupoife pounds, and the reverfe. The fecond is to find the quantity and weight of water that would fill an up^ right pipe of any given diameter and height : and confequently, to know what power would be required to work a common pump, or any other hydraulic engine, when the diameter of the bore of the pump, and the height to which the water is to be raifed, are given j proper allowance being made for fridfion. Thefe two cafes are as follows. VoL. LV. K [ 66 ] ^roy weight compared with avoirdupoife weight. One troy pound contains 5760 grains j and One avoirdupoife pound contains 7000 grains. Therefore, 175 troy pounds are equal to 144 avoird. pounds \ and 175 troy ounces are equal to 192 avoird. ounces. On thefe principles, the tu^o following Tables are conftru(5ted. I. A Table fhewing the number of avoirdup. pounds contained in any given num- ber of troy pounds. 2. A Table Slewing the number of troy pounds con- tained in any given number of avoirdupoife pounds. Troy Avoirdupoife pounds and Je- Pounds cimah of a pound. Avoir. -Troy pounds and decimals of a Pounds pound. 1 2 3 4 5 6 1 8 9 0,822857142857143 1.6457142857 14286 2.468571428571429 3.291428571428572 4.114285714285715 4,937142857142857 5 . 7&0000C00000000 6.582857142857143 7.4057 T42857 14286 1 2 3 4 5 6 7 8 9 1.215277777777778 2-430555555555556 -3-645833333333333 4.861 1 1 1 1 1 1 1 1 1 1 1 1 6.076388888888889 7.291666666666667 8.506944444444444 9.722222222222222 10.937500C00000OCO Explanation. For tens of pounds, remove the decimal point one place forward ; for hundreds of pounds, two places ; tor thoufands, three places j and fo on, as in the following examples. Example i 67 1 Example i. In 175 troy pounds, How many avoirdupoifc pounds? Troy Avoirdupoife 100 82.2857142857143 70 57.6000000000000 5 4.1 142857142857 175 144.000000000000 Anfwer, 144, Example 2.’ In 144 avoirdupolfe pounds, %. How many troy pounds ? Av. Troy 100 i2t.5277777777778 40 48.61 II mill III 4 4.8611111111111 144 175.C000000000000 Anfwer, 175. When any fignificant decimal figures remain in the fum, after integral pounds, they are eafily re- duced into the known parts of a pound : feeing that, in troy weight, 24 grains make one penny- weight, 20 penny-weights make an ounce, and 12 K 2 ounces [ 68 ] ounces make a pound. And, in avolrdupolfe weight, 1 6 drams make an ounce, and i6 ounces make a pound. A Table by which the quantity and weight of water in a cylindrical pipe of any given diameter and. perpendicular height may be found. Diameter of the cylindrical bore one inch. Feet Quan, of water high, in cubic inches. Weight in troy ounces. In avoirdupoife ounces- 1 2 3 4 5 6 7 % 9 9,4247781 1 8,8495562 28.2743343 37.6991124 47. 1 228QOS 56.5486686 65-9734467 75.3982248 84.8230029 4.9712340 9.9424680 14.9137020 19.8849360 24.856170Q 29.8274040 34.7986380 39.7698720 44.741 1060 5-454^539 10.9013078 16.3624617 21.8166156 27.2707695 32.7249234 38-1790773 43-633231-2 49.0873851 Explanation, For tens of feet high, remove the decimal point one place forward j for hundreds of feet, tv/o places , for thoufands of feet, three places, and fo on : and you will have the quantity and weight of water in the cylindrical pipe, fuppofing its diameter to bs one inch. The contents of cylinders of equal heights are to one another as the fquares of their diameters. There- fore, having found the quantity and weight of vva^ ter in a cylinder of one inch bore, you may find the fame for any other larger bore, by multiplying the above-found quantities by the fquitre of the diameter [ ^9 ] of the given bore, taken in inches. Thus, fiippofe* the given bore was lo inches in diameter (the fquare of which is loo) and the height of water in the pipe of lo inches bore was 85 feet, The quantity and weight of the water ?, F.high. Cubic inches. Troy ounces. Avoird. ounces. 80 753.982248 397.698720 43(>.3323i2. 5 47 123890 24.856170 27.270769 85 801 .106138 422.554890 493.603081 Mult, by 100 100 100 Anfw. 80110.613800 42255.489000 46360.308100 Which number (801 10.6) of cubic inches being divided by 231, gives 346.8 for the number of v/ine gallons i and the refpedfive w'eights (42255.489 troy ounces, and 46360.308 avoirdupoife ounces) being divided, the frit by 12, and the laft by 16, give 3-521.29 for the number of troy pounds, and 2897.513 tor the number of avoirdupoife pounds. And fo much would be required to balance this quantity of’ water in a pump, or any other hydraulic engine, and as much more to raife it as would be fufficient to overcome the fridtion of the engine. The realbn for removing the decimal points one - place forward for tens, two places for hundreds, &cc. is- evident : for, when any number confids of integer and decimal figures, tlie fetting of the decimal point one place forward is the fame thing as multiplying the number by lO; two places forward, the fame as multiplying the number by 100 j and fo on : as- tlie tables, tbemfelves are calculated only from.-, i to 9. [ 70 ] I to 9. But I multiplied by 10 produces 10, and 9 multiplied by 10 produces 90, And lo on for all the intermediate units. X. A Reco7?tmendation of Hadley’s Quadrant for furveymg^ efpectally the furveymg of Harbours^ together with a particular Ap- plication of it m fome Cafes of Pilotage, Py the Rev. John Michel), B. D. F. R. S. Read Feb. 14, T 1765. H E ufe of Hadley’s quadrant, as ' an inftrument to take altitudes at fea, is already fo well eftablifhed, that it wants no farther recommendation but there are feveral other purpofes, to which it may be applied, with great advantage, which, though obvious enough, feem yet to be hardly fufficiently attended to. There is no inftrument fo well adapted to many kinds of fur- veying, cither for exadnefs or conveniency, and par- ticularly the laft; but the furvcying of harbours, or fuch fands, as lie v/ithin fight of land, may often- times be performed by it, not only with vaflly more eafe, but alfo with a much greater degree of preci- fion, than can be hoped for by any other means, as it is the only inlfrument in ufe, in which neither the exadnefs of the obfervations, nor the eafe with which they may be taken, are fenfibly affeded by the motion of a veffel : and hence a fingle obferver, in a boat, may generally determine thefituation of anyplace he [ 71 ] he pleafes, with a fufficient degree of accuracy, if, with this inftrument, he takes the angles fabtended- by two or three pairs of objedls properly chofen uporii the (hores round about him ; but it will be ftill bet- ter to have two obfervers, one of whom, being in a boat, muft, at the time he takes the angle fubtended by fome two objedls upon the ihore, make a fignal to the other obferver, who, being placed at one of the objedls, as a flation, muft at the fame time obfervethe angle fubtended by the boat and the other objedt. By this means, two angles in a plain triangle being given, together with the diftance between the two> objedts, as a bafe, the whole triangle, and the fitu- ation of every part of it, will be given likewife. By fuch obfervations, as thefe, provided the boat be at red: during the time of making them, and they be made carefully, with good quadrants, though without the afiidance of telefcopic fights, the fitua- rion of places may be eafily determined to twenty or thirty feet upon every three or four miles. Befides the ufe of Hadley’s quadrant in furveying, it may upon fome occafions be very ad vantage on fly employed in piloting fliips into harbours, the great readincfs, with which it may be ufed, making it a very convenient inftrument for this purpofe : but that this may be done to the greatefl advantage, it will be necefiary to have a proper provifion made for it upon the charts, by exprefiing upon them the angles fubtended by given objedts, by means of which, to- gether with the bearings, a flilp may be enabled to know her fituation with areat exadlnefs. The well- O known property of the circle, that angles in the fame fegment are equal to each other, may be often- times . 72 ] - times very conveniently applied upon this occafion j for if, through any two given objects, we defcribe fe- veral fegments of circles, in which thofe objeds (hall fubtend the angles of * 120°, 90°, 8c°, yo", &c. refpedively, we fhall then know immediately, upon finding the two objeds fubtend any one of thefe angles, that we are fmiated fomewhere in the cir- cumference of the correfponding fegment ; and, the bearing alfo from one of the objeds being known, our precife fituation will be determined with great accuracy. The manner of deferibing thefe fegments, through two given points, may be performed in the following manner. Let B and C [Tab. II. fig. i.] be the given points : then, joining thefe two points, bifed the line B C in A, and draw the indefinite right line DE, perpendicular to B C, through the point of bi- fedion. Upon BC, at the point C conftitul'e the angles DCB, F C B, G C B, H C B, &c. refpec- tively equal to the difference between the angles, which correfpond to the feveral intended fegments and 90'’; and on the oppo-fite or fame fide of the line C B with thofe fegments, accordingly as they exceed or fall diort of 90°. Then will the points D, F, G, FI, &c. where the lines CD, C F, C G, C H, &c. interfed the line D E, be the centres of * The number and frequency of thefe fegments, as well as the magnitude of their , rel'peftive angles, muft be determined, according to the particular circumflances of the occafion, upon which they are appli^^d : I have mentioned no greater angle, than 120°, as there are few cafes, in which this v.nll not be fiifficicnt ; and indeed it is the greateft, that Hadley’s quadrant, tile only inflrument fit for this purpofc, will eafily admit, accord- ing to the prefent conftruiSlion of it. I the [ 73 ] . the intended fegments j but, if the angle, corre-* fponding to the intended fegment, is to be neither greater or lefs than 90°, the point A, which bifects the line B C, will be the centre of the intended fegment. Thus, if I would have the angle in the intended fegment, to confift of 120'', 1 conftitute upon B C, at the point C, the angle D C B equal to 30°, the difference between 120° and 90°, and on the oppofite fide of C B from its correfponding fegment, becaufe it exceeds 90°, Then with the centre D, and radius D C, I defcribe the fegment C 120 B, in every part of which the two points C and B will fubtend an angle of 120°. In like manner, if I would have the angle in the intended fegment to conlifl of 80°, I conftitute upon B C, at the point C, the angle BCG equal to 10°, the difference between 80° and 90"", and becaufe the intended angle is now lefs than 90°, I place G on the fame fide of B C with its correfponding feg- ment. Then with the centre G, and radius G C, I defcribe the fegment C 80 B, in every part of which the two points C and B will fubtend an angle of 80®. Laftly, if I would have the angle, in the intended fegment, to confifl of 90°, with the centre A and radius A C, I defcribe the femicircle C 90 B, in every part of which the two points C and B will fubtend an angle of 90° * If we want a fegment, the angle in which is to be the half of one we have got before, the centre is already found to our hands j for it will be the point of interfedlion of the former fegment with the perpendicular line DE. Thus the point, VoL. LV. L The [ 7+ ] - The demonftratlon of all. this is fo well known to every geometrician, that it needs not to be inferred ; but it may not perhaps be amifs to exemplify what I mean, by applying to it a particular cafe. The prefent inconvenient and indeed dangerous htuation of the two lights at the mouth of the Humber, commonly called the Spurn Lights, mull probably foon make it necelTary to remove them ; for the ground, upon which they formerly flood, is now fo far wafhed away, as not to leave fuflicient room to eredl them at a proper diflance from each other ; and frefh ground being grown up to the fouthward, fo as to make the point above a mile di- jflant from them, fliips are frequently thereby liable to be deceived. Jn cafe therefore thefe lights fliould, at any time hereafter, be removed nearer to the point, I think the foregoing principle might be very con- veniently and advantageoufly applied, fo as to enable entire flrangers to enter the Humber, with the greatefl where the fegment, correfponcHng to 120", iiiterfefts the liixe DE, will be the centre of the fegment correfponding to 60°: the point, where the fegment correfponding to 80°, interfedfs the line D E, will be the centre of the fegment correfponding to 40°, &c. There is another method of finding the centres of thefe feg- ments, which, if great cxadlnefs is required, will perhaps be found preferable, in practice, to the former, efpecially in the larger fegments. The method, I mean, is to fet them off by a fcale, in which cafe the diftance of the feveral centres, from the point A, muft be refpc(ffively proportional to the co-tangents of the angles in their correfponding fegments, or, what is the lame thing, refpedlively proportional to the tangents of the angles D C A, F C A, GCA, H C A, ^^c. confiituted upon the line AC, at the point C; for, making A C the radiu-, the lines D A, F A, G A, H A, &c. arc the rcfpe