twin Ibl Si; University of California • Berkeley n Xc THE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON, FROM THEIR COMMENCEMENT, IN 1663, TO THE YEAR 1800; Sibritiscti, WITH NOTES AND BIOGRAPHIC ILLUSTRATIONS, BY CHARLES HUTTON, LL D. F.R.S, GEORGE SHAW, M.D. F.R.S. F.L.S. RICHARD PEARSON, M.D. F.S.A. VOL. VIII. FROM 1735 TO 1743. LONDON: PEINTED BY AND FOR C. AND R. BALDWIN, NEW BRIDGE-STREET, BLACKFRIARS. 1809. i?/8 1 2. •; t*:*5»:' / ¥C> j^Z. LOAN STACK CONTENTS OF VOLUME EIGHTH. Page Isaac Rand, catalogue of 50 PlanU .. 1 Ja. Hodgson, Eclipses of Jupiter's Satel. . . ibid . — , On the same ibid , Again on the same ibid Ste. Gray, on the Electrical Light 2 Wm. Braikenridge, Description of Curves 5 Geoffroy, on Seignette's and other Salts . . 10 Biograph. Notice of M. Seignelte ibid Desaguliers, on ventilating close Rooms . . 12 , Velocity of the Air in Ventila- tion 13 , Uses of the Machine in ditto . . 15 Rd. Reynell, on a Cataleptic patient .... ibid Hunauld, on the Fistula Lacrymalis 17 Biog. Notice of Fr. Jos. Hunauld ibid Geo. Hadley, on the general Trade Winds 19 Paul Dudley, Earthquakes in New-England 22 Dr. Cookson, Magnetism by Lightning . 24 , on the same 25 C. L. Gersten, an Arithmetical Machine . . ibid Ja. Stirling, Figure of the Earth 26 Dr. Vater, Mexican Filtering Stone 30 Dr. Mortimer, on Catesby's Nat. Hist. Ca- rolina 32 Revillas, a Halo observed at Rome ibid John Cope, on an Ancient Date ibid John Ward, on the same ibid John Cope, Ancient Indian Dates 37 John Ward, on the same 39 Colin Maclaurin, Description of Curves ... 41 . , On the same Subject .... 4.3 Ste. Gray, Electrical Experiments 51 Wm. Barlow, Number of Persons at Stoke Damerel 53 C. Amyand, Foramen Ovale open 54, Isaac Rand, Catalogue of 50 Plants ibid Ja. Hodgson, Eclipses of Jupiter's Satellites ibid J. Hadley, Combinations of Lenses ibid Dr. Ed. Hody, A bony substance in the Womb 56 Ja. I/)gan, Impreg. of the Seeds of Plants . . 57 Geo. Lynne, Eclipses of Jupiter's Satellites. . 58 Tho. Jones, High Tide in the Thames .... 59 Dr. Vater, Singular Cutaneous affection . . ibid Dr. Derham, Vibrations of Pendulums .... 60 John Colson, on Spherical Maps 61 Roger Gale, on an Ancient Chirograph ... 64 Ste. Gray, Electrical Rotations in Bodies . . 65 De Lisle, Quicksilver Thermometer, &c. 6'6" VOL. VIII. Dr. Houston, Perforations in the Thorax . . 6"8 Weidler, Observ. Astron. Phys &c ibid Ja. Logan, Zigzag Figure of Lightning . . . ibid Andr. Celsius, Aurora Borealis 69 Dr. Rob. James, Exper. on Mad Dogs .... ibid Biog. Notice of Dr. Robert James ibid Dr. Mortimer, on Catesby's Nat. Hist. Carol. 73 Dr. Rob. Barker, Catoptric Microscope ... 73 Martin Folkes, Standard Measures at Rome 74 Weidler, Observ. Astrop. Pbys. &c 76' Cap. Middleton, on the lat. and Variations, &c. 76 ■ Desaguliers, Damps or foul Air in Mines . . ibid John Maud, on Inflammable Air 77 Henry Forth, Account of a Storm 78 John Belch ier. Bones coloured red by Food 79 Dr. Stuart, a white Liquor from blood ... ibid Dr. Madden, a Plum-slone in the Rectum 80 Celsius and Revillas, Solar Eclipse at Rome 82 John EUicott, Expansion of Metals by heat ibid J. Belchier, Bones changed red by Food . . 83 J. Hodgson, Eclipses of Jupiter's Satellites 84 Dr. Burton, Remedy for the Bite of Vipers ibid Dr. Mortimer, on the same, and on Mad Dogs ibid J. Fames, on Newton's Fluxions by Colson 88 CI. Amyand, Inguinal Rupture, &c 89 Boerhaave, Experiments on Quicksilver . . 9,; Weidler, a Lunar Eclipse 96 Duke of Richmond, Earthquake in Sussex ibid Dr. Edw. Bayley, on the same ibid Jos. Wasse, Earthquake in Northampton . . 98 Boerhaave, Experiments on Quicksilver . . . ibid Mart. Triewald, Improv. on the Diving Bell ibid Sam. Dale, tlie Moose Deer, a Stag, and a Flying Squirrel 102 Desaguliers, on the Horizontal Moon 105, io(j Dr. Atwell, on the Bite of Vipers !07 J. Logan, on the Horizontal Sun and Moon 112 Isaac Rand, Catalogue of 50 Plants ns A. Celsius, on some Runic Characters. .. 114 Lunar Eclipse, by Graham, Halley, Celsius 1 16 The same, by Dr. Bevis iip- Biog. Notice of Dr. John Bevis ibid The Lunar Eclipse, by Mr. John Milner . . 118 Alexis Clairaut, on the figure of the Earth ibid Biog. Notice of Alexis Claud. Clairaut .... ibid Ste. Williams, Cure for the Bite of Vipers J 24 De Lisle, Measure of the Earth in Russia . . ibid De Ijisle, Measure of a Base for tlie same . . 134 Tim. Neve, Parhelia and Aurora Borealis,. . ibid II CONTENTS. Weidler, on two Parhelia 136 Martin Folkes, on three Mock-suns 137 Chr. Wolfe, Rupture of the lleunn 138 DesagLiliers, New Statical Experiments . . . 139 Ja. Hodgson, Eclipses of Jupiters' Satellites 141 John Gray, Peruvian or Jesuit's Bark 142 J. Eames, Account of MuUer's Conic Sec- tions 145 Biog. Notice of Mr. John Muller ibid Dr. Bevis, Moon's Transit by Aldebaran . . 147 Lunar Eclipse, by Graham, Bevis, Weidler, and Middleton ibid Dr. Bevis, Observation of a Solar Eclipse . . 148 Occult, of Mars, by Graham and Bevis .... ibid Geo. Graham, 'Transit of Mercury ibid On the same, by Manfredi and Weidler . . . 149 J. Bradley, on the Comet of 1737 ibid On the same, by Revillas, at Rome 153 Dr. Kearsley, on the same, and a solar Eclipse ibid On the same Comet, by Dr. Fuller and M. Sartori 1 54 G. R Vanbrugh, on the same Comet .... 155 Dr. Bryne, on Mammoths' or Elephants' Bones ibid Dr. Cantwell, Tumour in the Pelvis, &c. . , 158 Isaac Rand, Catalogue of 50 plants l60 Dr. Steigertahl, Narhwal, or Unicom Fish ibid Dr. J. H. Hampe, on the same l6l M. Klein, an undescribed Water Insect . . ibid On the same, by L. Brown and Dr. Mortimer l63 Geo. Hadley, Meteorological Diaries .... ibid Solar Eclipse, by Graham, Bevis, and Mac- laurin I69 The same, by Sir J. Clark, &c 175 The same, by Revillas, Weidler, &c 176 Dr. E. Latham, New Celestial Globe .... ibid John Senex, on the same Contrivance .... ibid Biog. Notice of Mr. John Senex ibid J. Machin, Solution of Kepler's Problem . . 177 M. Triewald, New Water-bellows 192 Sig. Poleni, Meteorological Observations . . 196 Hen. Beighton, on Orme's and other Baro- meters 198 J. P. Seip, Sulphurous Cavern at Pyrmont 204 J. Fuller, on Darapier's Powder for the bite of a Mad Dog 204 Bite of a Mad Dog, by Da. Hartley and Fr. Sandys 205 Biog. Notice of Dr. David Hartley ibid Al. Clairaut, on the Figure of the Planets. . 207 Abbe NoUet, Experiments on Ice 223 Biog Notice of the Abbe Nollet ibid Cap. Middleton, the Magnetic Needle affect- ed by Cold , 224 Dr. Cantwell, Palsey of the Eyelids 225 J. Belchier, on an Arm torn off by a Mill . . 226 Ld. Carpenter, a bullet lodged near the gullet 227 CI. Amyand, Biliary Ducts and Gall-bladder 228 Dr. Alex. Stuart, on the same case 232 Mat. Bell, on the Copper-waters in Mines 235 C. Amyand, on a Bubonocele ibid Ja. Hodgson, Eclipses of Jupiter's Satellites 236' Dr. Mortimer, on Catesby's Nat. Hist. Carol. 236 Wm. Gregory, a Pin in a Child's Bladder . . 239 M. de Caumont, Calculus in the Bladder . . 240 M. Salien, on the same Ca.se 241 Sir Hans Sloane, on the same Stone 242 J. Maud, Oil of Sassafras crystallized 243 Benj. Cooke, Foul Air in a Well 244 J. Eames, Magnets with more than 2 Poles 246 Desaguliers, Magnetical Experiments .... ibid , On the same Subject . . 246, 247 Dr. Mortimer, Roman Stamps like Printing 248 Dr. Bevis, Occult, of Mercury by Venus . . 251 Cap. Middleton, New Azimuth Compass . . ibid Dr. Zac. Pearce, Account of Bell's Hist, of Hungary 253 J. Eames, Account of Kersseboom's Essay on the number of Persons in Holland 253 Wm. Mailland, Answer to Kersseboom's Es- say as to the Numb, of Persons in London 257 Cha. Leigh, a Water-level to Davis's Quadr. 260 , Mercurial I,evel to the same . . 262 J. Ferguson, Loss of part of the Spleen . . 263 Benj. Cooke, a Ball of Sulphur supposed to be generated in the air 264 Dr. Tho. Stack, Account of Dr. Huxham's book de Acre et Morb. Epidemicis .... 265 M. Dufay, Cure for the Bite of Vipers 267 Dr. Patouillet, Poison of Henbane Roots . . ibid Tho. Steward, Buckshorn Plantain as a Cure for the Bite of a Mad Dog 269 Abr. Demoivre, Reduction of Radicals .... 271 Isaac Rand, Catalogue of 50 Plants 278 Dr. Jurin, Motion of Effluent Water ibid Mat. Bell, two Caverns, the one icy, the other of noxious Effluvia 293 Jer. Pierce, large Tumour in the Knee 294 John Clayton, on the Spirit of Coals 295 , on Nitrous Particles in the Air 296 Dr. Rutty, Poison of Laurel- water 297 Dr. Jurin, on Effluent Water, part 2d 29» Solar Eclipse, by Graham, Short, Celsius, Weidler, and Manfredi 306 Gr. Wheeler, Electrical Experiments 306 Dr. Mortimer, on the same Experiments . . 313 Gr. Wheeler, on Mr. Gray's Electrical Cir- cular Experiment 3l6 J. Ellicott, Influence of 2 Pendulum Clocks on each other 320, 322 Tho. Baker, Wound in the Cornea of the Eye 324 Dr. Cantwell, of a monstrous Boy 32i sm CONTENTS. Ill B". Sherman, Three Cases in Surgery 3?o J. Cl;i)'lon, Manners and Customs in Virginia 328 . , Force of Water Steam 335 J. Green, on a Girl who was a quarter of an hour in water without drowning 337 Mr. Cox, on a Pestilential Fever by Tapping a Corpse dead of a Dropsy 338 W. Hoxton, Variation of the Compass .... 339 Desaguliers, on the Cause of Electricity . . 340 , on Electrical Experiments .... 346" , on the same 350. 351, 352,353, 357 Dr. Moehring, Botanical Observations . . . 358 Weidler, on an Authelium ibid Chr. Kirch, Occulta of Aldebaran ibid Weidler, on the same ibid — — , on a Solar Eclipse 359 J. Derby, a Whirlwind at Come- Abbas . . . ibid J. T. Klein, Letters within a Tree . ibid Sir John Clark, EtFects of Thunder on Trees and on a Deer's Horn within an Oak . . . 360 Dr. Mortimer, Rereiarks on the same .... 36 1 Aragona, Eruption of Vesuvius ibid English Gentleman, on the same 368 Fouchy, on the Lunar Atmosphere 37 1 P. H. Zollman, large sinking of Ground . . 376 Dr. Baster, Worms that destroy Timber . . 378 Biog. Notice of Dr. Job Baster ibid A. Vizoar, Loud Explosions in the Air 383 Sam. Shepheard, on the same 384 Isaac Rand, Catalogue of 50 Plants ibid Superville, on Generation and Monsters . . 385 J. T. Klein, Gigantic Bregma, &c 388 Dr. Zac. Pearce, Account of Fourmont on the Histories of the Ancients . . 389 Biog. Notice of Dr. Zac. Pearce 389 Da. Nicholson, Scurvy- grass of Greenland 391 Edm. Stone, two new Curve Lines 392 Biog. Notice of Mr. Edm. Stone ibid Mr. Harris, New Terrestrial Globes 393 C. Smith, Catodioptrical Telescopes ibid H. Temple, Earthquake at Naples 401 Tim. Sheldrake, a Monstrous Child ibid Wm. Barlow, Sun-fish, and its Glue .... 40'2 Wra. Sloane, Aretina, near Naples 403 Mr. Crocker, a Meteor in the Air ibid Dr. Bevis, Luminous Appearance 404 Da. Hartley, a Calculus through the Perin. 405 J. Sisley, a Calculus through the Scrotum ibid Mort. Gilks, Petrifactions at Matlock 406 Abbe Pluche, on the Smut in Corn 408 Biog. Notice of the Abbe Pluche ibid Dr. Bartram, Teeth of the Rattle-snake . . . 409 Jos. Breintnall, Meteors at Philadelphia .... 409 C. Lucas, Cave of Kilcorny ibid M. Malfelguerat, Tumour on the Thigh . . 410 Ja. Short, Aurora Borealis 412 J. Freeke, Exostosis on a Boy's Back 413 J. Eames, Account of Celsius on the Figure of the Earth ibid J. Alexander, a Place near New York to measure a Degree of Latitude 419 J. T. Klein, Antiquities of Prussia 420 Du Harael, Madder Root tinges the Bones ibid Biog. Notice of Hen. Louis DuHamel .... ibid Isaac Rand, Catalogue of 50 Plants 424 M. de Sigome, Impossibility of Vortices . . ibid Da. Hartley, Account of Dr. Trew on the ditf. of the Body before and after Birth . . 425 H. Baker, a Beetle lived 3 Years without Food 426 Biog. Notice of Mr. Henry Baker ibid H. Baker, a Plant in Seniine 429 Wm. Barlow, Weights and Measures .... 432 Account of Weidler on Parhelia 433 Ste. Williams, Barrows in Cornwall 433 C. Pademi, Herculaneum at Porlici 435 Geo. Knaptou, on the same 437 Mr. Crispe, on the same Subject 43$ J. Cagua, Wound in the Head cured 439 J. Mackarness, Stone voided per Anum . . 441 H. Baker, Leuwenhoek's. Microscope .... 443 Anonymous, Dry or Wet Summer 447 B. Ehrhart, Observ. in the Tyrol Alps .... 4 j 1 Biog. Notice of Baltha.sar Ehrhart ibid Sam. Jenkins, Grinding I^enses ibid Dr. Breyne, Calculi in the Stomach, &c. . . 452 S. Kirkshaw, Two Roman Pigs of Lead . . 453 H. Ettrick, Machine to reduce Fractures . . 454 J. T. Klein, on le Bruyn's Petrified Oysters 455 Biog. Notice of Cornelius le Bruyn ibid Chr. Kirch, Observ. of the Planet Mars . . 457 On the Red Lights seen in the Air 457 J. Eames, Account of Jurin De Vi Motrice 461 N. Sherwood, on Stones in the Kidneys . . 462 J. Fuller, the lake Malholm Tarn 463 M. de Breraond, Magnetism by Lightning ibid P. Pott, Softening of the Bones 464 Wm. Watson, Part of the Lungs coughed up 468 Tho. Short, on several Meteors 469 Dr. Bevis, Conjunc. of Venus and Mercury 470 G. Graham, Occultation of Aldebaran .... ibid Mr. Short, a Solar and Lunar Eclipse .... ibid Desaguliers, Expers. on Electricity 470, 472, 473 Dr. Huxhani, a Hernia Inguinalis 474 Ja. Short, on the Satellite of Venus 476 Dr. Bevis, and Ja. Short, Occult, of Jupiter 477 Dr. Parsons, Account of his book on Henna- phrodites jbij Wm. Barlow, Ancient Date at Rumsey . . 473 H. Baker, Black Currant Jelly 479 Desaguliers, Electrical Experiments ibid Dr. Huxhatn, Extraordinary Venereal Cas-e 480 Wm. Hanbury, Coal-balls at Liege, &c. . . 483 Dr. Mortimer, Account of Dr. Stuart's Paper on the Structure of the Heart ibid M. Le Cat, Foramen Ovale, and the Urethra 485 Biog. Notice of Claude Nicholas Le Cat . . ibid Geo. Lynn, on the Weather, Kc +80" 2 1\' Wtn. Bromlield, Foetus 9 Years in the Ab- domen 489 Biog. Notice of Wm. Brorafield ibid J. Powell, Hairy Substances voided by Urine ibid Sir Hans Sloane, on the same 490 T. Knight, on the same Subject 491 Dr. Graham, on Watery Cystises 492 Wm. Watson, Hydatids per Vaginain .... 494 M. Lc Cat, on the same Subject 495 , on a singular Hernia 497 H. Miles, Circulation of Blood in an Eft . . 501 Dr. Eb. Latham, on the Ancient Sphere . . ibid Revillas, Aurora Borealis at Rome . . . 502 H. Beighton, New Plotting Table ibid Wm. Wright, Fracture of the Thigh Bone 503 Wm. Gregory, on a Monstrous Foetus .... ibid A Needle passed tlirough the Arm andBreast 504 A. Orme's Pectoral Syrup 505 H. Miles, Seed of Fern ibid J. I. De Torres, a Heart upside down .... 508 J. Castillion, the Cardioide Curve 509 J. Ai Segner, Machine for Solar Eclipses . . 510 S. C. Hollman, Observ. de Sceletorum, &c. 513 M. Johnson, Earthquake at Scarborough . . 514 Cap. Middleton, on Frozen Sea-water .... ibid Col. Maclaurin, Merid. Parts on a Spheroid 515 S. Zanotti, Parabolic Orbit of a Comet ibid Bp. of Cork, Extraordinary Skeleton, and a Man who gave Suck 5l6 Caesarian Operation, by a Butcher 517 J. Payne, Force of Steam 518 A. Godfrey Hankewitz, West Ashton Well Waters 522 G. H. Senckenberg, Cheltenham waters . . 523 J. Marty n, on the Dulwich waters ibid Dr. Mortimer, Aurora Borealis 525 J. Martyn, on the .same Subject ibid Tim. Neave, on the same 526 Arch. Cleland, New Catheter for the Stone ibid , lustrum, for the Eye and Ear 528 Ste. Fuller, Hurricane in Huntingdonshire 530 T. Sympson, Roman Hypocaustum at Lincoln 532 Dr. Mortimer, Capricorn Beetle, and Horn of a Fish stuck in a Ship 535 , on Frobenius's Spiritus Vini . .^thereus 536 Ld. Beauchamp, Fire-ball Explosion 540 J. Fuller, on the same Subject ibid Wm. Gostling, on the same Meteor 541 Chr. Mason, on the same ibid Edw Milwardj Antidote to the West-Indian Poison 542 Edw. Nourse, on Stones in the Bladder .... 545 Dr. Desaguliers, Observ. on Electricity . . . 546 Cap. Edw. Legge, on a Lunar Eclipse .... 548 H. Miles, Unusual Warmth of the Air . . ibid Tim. Sheldrake, a Steel-yard Swing 549 Sir Tho. Mostyn, on a Golden Torques .... 550 Benj. Cooke, on a Fire-ball ibid CONTENTS. I'agc J. Fames, Account of Klein's Hist, of Fishes Mat. Plant, on Earthquakes in America . . Dr. Mead, on Sutton's Ventilators H. Miles, on some Parhelia Dr. Cha. Parry, on the Waters of the Dead Sea, &c Geo. Bell, on Stones in the Bladder , J. F. Gronovius, on preserving Fish-skins Cap. Wm. Gordon, on a Fire-ball Wm. Gostling, on the Fire-ball Wm. Watson, on Sutton's Ventilators .... C. J. Geoffroy, on Soap-making P. R Pedini, Earthquakes at Leghorn .... J. Castilion, on Newton's Binomial Theorem Dr. Burton, Cases of Internal Cancers .... Dr. L. Stocke, Falling Dew and Snow Flakes M. Triewald, Veget. of Old Melon-seeds . . S. C. Hollman, Heights of Barometers . . . Dr. Huxhara, Polypi in the Heart Mr. Stackhouse, Account of Bridgenorth . . Ld. Petrie, Effects of Lightning Dr. Tho. Milner, of a Meteor Desaguliers, Electrical Conjectures H. Baker, on a Person speaking without a Tongue C. Warwick, a Remarkable Birth Sir. I. Newton, on a Reflecting Instrument for taking the Moon's Distance from Stars Cap. Middleton, Observ. at Hudson's Bay . . Committee of the R.S. Expers. in Gunnery Ld. Lovell, a Meteor in Norfolk Committee of the R S. on the English and French Weights and Measures G. Heinsius, Gold-coloured Glazing Revillas, Meteorological Register J. F. Gronovius, on a Polypus Dr. Eb. Latham, on the Ancient Sphere . . Dr. Tho. Short, Extraordinary Dropsy .... A Cambridge GSentleman, on the Polypus . . J. Catlyn, Calcul. of the Transit of Mercury R. Campbell, on a Man living 18 Years on Water Geo. Hadley, Meteorol. Observations .... Dr. Parsons, Account of Dr. Le Cat's Trea- tise on the Senses Dr. Schlichting, Medico-Chirur. Observat. Dr. Baste:, 'I'wo Medical Cases M. Trembley, Expers. on the Polypus .... S. Poleni, Pendulums afJec ted by centrifiigal Force Ja. Hodgson, Astron. Observ, at Pekin . . J. Van Rixtel, Account of Kersseboom's Treatises on the Number of People in Holland Jos. Hobson, Great Increase of Seeds .... J. A. Beurer, on the Nature of Amber .... Col. Maclaurin, Account of his Fluxions . . A. Leprotti, Calculus voided by Urine .... M , Le Cat, a Hammock for dressing Patients Paee 551 552 553 555 ibid 557 559 ibid 563 560 565 568 571 572 577 577 578 580 581 583 ibid 584 586 589 590 591 598 604 ibid 606 ibid 607 ibid ibid 609 613 616 617 619 620 622 623 627 628 ibid 631 ibid 632 653 654 CONTENTS. Page Wm. Watson, Account of Haller's Enume- ratio Methodica Stirpium Helvetiae, &c. 655 Biog. Notice of Albert Haller ibid Dr. Parsons, on tlie Phoca, or Sea-calf .... 6"58 M. Le Cat, the Ambe of Hippocrates, &c. 659 Col. Maclaurin, Account of his Fluxions con- tinued 667 H. Miles, of the Eels in Vinegar 674 C. Maclaurin, Grandgor or Venereal Dis- ease 675 M. Folkes, fresh- water Polypus 676 B. Robins, Account of his Gunnery 677 Fa. Frantz, on a Comet observed at Vienna 681 Cha. Bonnet, Observations on Insects .... 682 S. Bevan, Bones becoming soft ibid Dr. Lining, Stat. Expers. on himself 683 Duke of Richmond, on Polypi 685 Dr. Wm. Hunter, Articulating Cartilages 686 Biog. Notice of Dr. Wm. Hunter ibid Tho. Lord, Worms living after cut in parts 692 Dr. Parsons, Nat. Hist, of the Rhinoceros . . ibid Biog. Notice of Dr. James Parsons ibid Committee of the R.S., Standard Weights and Measures 698 Page J. Freke, Instrument for reducing dislocated Shoulders 706 Dr. P. Dodd, Bloody Urine in the Small Pox 708 C. Maclaurin, Cells of Honey-comb 709 J. Winthrop, Transit of Mercury 713 — , On a Lunar Eclipse ibid Geo. Graham, Transit of Mercury 714 , On a Lunar Eclipse 715 Bp. of Corke, Ancient Temple and Stone Hatchet ibid G. Hughes, on a Zoophyton 717 R. Pickering, Seeds of Mushrooms 718 Wm, Watson, Remarks on the same .... 721 G. Heinsius, On Saturn's Ring 722 Dr. J. Green, Nat. Hist, of Greenland .... 722 H. Baker, on a dried Polype 724 Jos. Miller, Catalogue of 50 Plants 725 Dr. Bevis, Transits of Mercury ibid M. GeofFroy, a Monstrous large Child .... 727 Dr. Banyer, Extraordinary Haemorrhage . . ibid , Ascites cured by Tapping ibid T. Needham, Malmy Concretions 729 , Farina of Red Lilly ibid , Worms in Smutty Corn .... ibid THE CONTENTS CLASSED UNDER GENERAL HEADS. Class I. Mathematics. 1 . Arithmetic, Political Arithmetic. AP'ge Page RiTHMETiCAL Machine, C. L. Gersten 25 Numb, of Persons in London, &c.Wm. Mait- Numb. of Persons at Stoke-Damerel, Barlow 53 in Holland, 8cc. J. Eames 253 land . 257 in Holland, J. Van Rixtel 628 2. Algebra, Analysts, Fliuxions. On Newton's Fluxions, J. Eames . 88 Newton's Binomial Theorem, Castilion . . . 5/ i MuUer's Conies and Fluxions, J. Eames . . 145 On Maclaurin's Fluxions, Maclaurin 632, 667 Reduction of Radicals, Demoivre 271 3. Geometry, Surveying. Description of Curves, Brackenridge 5 Two New Curves, Edmund Stone 392 , C. Maclaurin .... 41, 43 New Plotting Table, H. Beighton 502 Muller's Conic Sections, J. Eames 145 Cells of Honey-comb, C. Maclaurin 709 vi CONTENTS. Class II. Mechanical Philosophy. 1 . Dynamics. Page Vibration of Pendulums, Derham 6o On Jurin'» De Vi Motrice, Earaes 46l Page Pendulums affected by Centrifugal Force, Poleni 627 2. Statics. Statical Experiments, Desaguliers 139 Weights and Measures, Wm. Barlow 3. Astronomy, Navigation, Chronology. 432 Eclipses of Jupiter's Satellites, Ja. Hodgson . 1, 54, 84, 141, 235 _ — , Geo. Lynn 58 Astronomical Observations, Weidler . . 68, 76" Solar Eclipse, Celsius and Revillas 82 On a Lunar Eclipse, Weidler 96 Horizontal Moon, Desaguliers 105, 106 Horizontal Sun and Moon, Ja. Logan .... 112 Lunar Eclipse, Graham, Halley, Celsius.. Il6 On the same. Dr. Bevis 117 . , John Milner 118 Occultation of Aldebaran, Dr. Bevis 147 Lunar Eclipse, Bevis, Weidler, Middleton 147 On a Solar Eclipse, Dr. Bevis 148 Occultation of Mars, Bevis, Graham ibid Transit of Mercury, Geo. Graham ibid , Manfredi and Weidler 149 Comet of 1737, Ja. Bradley ibid . , by Revillas at Rome 153 , and Solar Eclipse, Kearsley ibid , Fuller and Sartori 154 . — , G. R. Vanbrugh 155 Solar Eclipse, Graham, Bevis, Maclaurin i6"9 , Sir J. Clerk 175 -, Revillas, Weidler, &c 176 New Celestial Globe, Dr. E. Latham ibid ____^ , John Senex 176" Solution of Kepler's Problem, J. Machin . . 177 Figure of the Planets, Clairaut 207 Occult, of Mercury by Venus, Bevis 251 New Azimuth Compass, Middleton ibid Davis's Quadrant, Leigh 260, 262 Solar Eclipse, Graham, Short, Celsias, Weidler, Manfredi 306 Occulta, of Aldebaran, Kirch, Weidler .... 358 On a Solar Eclipse, Weidler 359 On the Lunar Atmosphere, Fouchy 371 Impossib. of Vortices, De Sigorne 424 On the Planet Mars, Chr. Kirch 457 Conjunc. of Venus and Mercury, Bevis . . . 470 Occulta, of Aldebaran, G.Graham ibid Solar and Lunar Eclipse, Ja. Short ibid On the Satellite of Venus, Ja. Short 476 Occulta, of Jupiter, Bevis and Short 477 The Ancient Sphere, Dr. E. Latham 50t Machine for Solar Eclipses, Segner 510 Mend. Parts on a Spheroid, Maclaurin .... 515 Parabolic Orbit of a Comet, Zanotti ibid Lunar Eclipse, Cap. Edward Legge 548 The Ancient Sphere, Dr. Eb. Latham .... 607 Transit of Mercury, J. Catlyn 6l3 Astron. Observ. at Pekin, Hodgson 628 A Comet observed at Vienna, Frantz 68 1 Transit of Mercury, J. Winthrop 713 A Lunar Eclipse, J. Winthrop ibid Transit of Mercury, Geo. Graham 714 A Lunar Eclipse, Geo. Graham 715 Saturn's Ring, G. Heinsius 722 Transit of Mercury, Dr. Bevis 725 4. Projectiles, Gunnery. Experiments in Gunnery, Committee 598 Account of Robins's Gunnery, Robins 6^7 5. Mechanics. Influence of two Clocks on each other, J. Ellicott 320, 322 6. Hydraulics. On Effluent Water, Dr. Jurin 278, 298 7. Pneumatics. VentUating Close Rooms, Desaguliers 12, 13, 15 Trade Winds, Geo. Hadlcy .'. 19 CONTENTS. VII Page Foul Air in Mines, Desaguliers 76 Inflammable Air, John Maud 77 On Barometers, H. Beigliton 198 Foul Air in a Well, B. Cooke 244 Force of Steam, J. Clay tonr 335 I' age Force of Steam, J. Payne 518 Sutton's Ventilators, Dr. Mead 553 , Wm. Watson 56o Heights of Barometers, 8. C. HoUman . . 578 8. Optics. Combinations of Lenses, J . Hadley 54 Catoptric Microscope, Dr. Barker 73 Catoptric Telescopes, C. Smith 393 Leuwenhoeck's Microscopes, H. Baker . . . 44S Grinding of Lenses, Sam. Jenkins 451 A Reflecting Instrument, Sir L Newton . . 590 g. Magnetism, Electricity, Thermometry. The Electrical Light, Stephen Gray 2 Magnetism by Lightning, Dr. Cookson . . 24,25 Electrical Experiments, Stephen Gray .... 51 Electrical Rotation in Bodies, Stejjhen Gray 65 Quicksilver Thermometer, De Lisle 66' Magnetical Variations, Middleton 76 Expansion of Metals by Heat, Ellicott ... 82 Magnet. Needle aft'ectcd by Cold, Middleton 224 Magnets of more than 2 Poles, J. Eames . . 246 Magnetical Experiments, Desaguliers. . 246,247 , Gr. Wheeler ... 306 On the same Experiments, Dr. Mortimer. . 313 On Gray's Electrical Rotations, Wheeler.. 3l6 Variation of the Compass, W. Hoxton . . . 339 Cause of Electricity, Desaguliers 340 Electrical Experiments, Desaguliers 346,350,351, 352,353,357 ,470,472,473,479 Magnetism by Lightning, De Bremond . . . 483 Observations on Electricity, Desaguliers . . 546 Uncommon Warmth of Air, H. Miles . . . 548 Electrical Conjectures, Desaguliers 584 Class III. Natural History. 1. Zoology. Catesby's Natural History of Carolina, Mor- Phoca, or Sea Calf, Dr. Parsons 658 timer 32,73,235 Eels in Vinegar, H. Miles 674, Moose-Deer, Stag, Flying Squirrel, Dale 102 Fresh -wrater Polypus, Mart. Folkes 67S Narhwal, or Unicom Fish, Steigertahl. . . . ]60 Observations on Insects, Bonnet 6821 — , Dr. J. H. Hampe . . 16I On Polypi, by the Duke of Richmond .... 685 Uncommon Water Insect, Klein ibid Worms living after cut, Thomas Lord .... 692 , by Brown and Mortimer l63 A Zoophyton, G. Hughes 717 Worms that destroy Timber, Dr. Raster . . 378 A Dried Polype, H. Baker 724 Sun-Fish, and its Glue, Wm. Barlow 402 Worms in Smutty Com, T. Needham 7J9 Teeth of the Rattle Snake, Dr. Bartram . . 409 2. Botany. Catalogue of 50 Plants, Isaac Rand 1,54,113, 160,278,384,424 Botanical Observations, Moekring 358 Letters within a Tree, Klein 359 Deer's Horn in an Oak, Sir J. Clark 360 Remarks on the same. Dr. Mortimer . . Scurvey-grass of Greenland, Nicholson Haller's Enum. Math. Slirp., Watson . . Catalogue of 50 Plants, Jos. Miller . . . . 3. Mineralogy. Copper-water in Mines, Mat. Bell 236 Spirit of Coals, John Clayton 295 Nitrous Particles in the Air, Clayton .... 296 Petrifactions at Matlock, Mort. Gilks 406 Le Bruyn's Petrified Oysters, Klein 455 Coal-balls at Liege, &c. Hamburgh . . Observ. at Hudson's Bay, Middleton Nature of Amber, J. A. Beurer . , , . Malmy Concretions, T. Needhara . . . 361 391 655 725 483 591 631 729 VIU CONTENTS. 4. Geography and Topography. Page Figure of the Earth, J. Stirling 26 Spherical Maps, John Colson 6l Figure of the Earth, Clairaut 118 Measure of the Earth in Russia, De Lisle. . 124 Measure of a Base for the same, ditto .... 134 Cavern at Pyrmont, J. P. Seip 204 Bell's Hist, of Hungary, Dr. Pearce 253 Two Curious Caverns, Mat. Bell . .' 293 Manners in Virginia, J. Clayton 328 Eruption of Vesuvius, Aragona 36l The same, by an English Gentleman ...... 368 Sinking of Ground, P. H. ZoUman 376 New Terrestrial Globes, Mr. Harris 393 Page Aretina near Naples, Wm. Sloane 403 Kilcorny Cave, C. Lucas 4.09 Celsius's Figure of thfe Earth, Fames .... 413 Degree of Lat. near New York, Alexander 419 Herculaneum at Portici, C. Paderni 435 , Geo. Knapton . . . 437 , Mr. Crispe 438 Observ. in the Tyrol Alps, Ehrhart 4.J1 Lake Malholm Tarn, J. Fuller 463 Dead Sea Waters, Dr. Charles Parry 535 Account of Bridgnorth, Stackhouse 581 Of Hudson's Bay, Capt. Middleton 591 Of Greenland, Dr. J. Green 722 Mexican Filtering Stone, Dr. Vater 30 High Tide in the Thames, Tho. Jones .... 59 Hydrology. Diving Bell, Mart. Triewald 98 Class IV. Chemical Philosophy. 1. Seignette's and other Salts, Geoflfroy 10 Experiments on Quicksilver, Boerhaave. . 93j98 Experiments on Ice, Abbe NoUet 223 Oil of Sassafras Crystallized, J. Maud .... 243 Chemistry. West-Ashton Waters, G. Haukewitz .... 522 Cheltenham Waters. Senckenberg 523 Dulwich Waters, J. Marty n ibi< Frobenius's Spir. Vini ./Eth. Mortimer .... 53i 2. Meteorology. Earthquakes in New England, P. Dudley 22 Halo observed at Rome, Revillas 32 Zigzag Figure of Lightning, Ja. Logan ... 68 Aurora Borealis, Andrew Celsius 69 Of a Great Storm, Henry Forth 78 Earthquake in Sussex, D. of Richmond ... ^6 On the same. Dr. Edward Bayley ibid Earthquake in Northampton, J. Wasse. ... 98 Parhelia and Aurora Borealis, T. Neve ... 134 Two Parhelia, Weidler 136 Three Mock-Suns, Martin Folkes 137 Meteorological Diaries, J. Hadley l63 Meteorological Observations, Poleni 196 Sulphur gener. in the Air, B. Cooke 264 An Anthelim, Weidler 358 Whirlwind at Come Abbas, J. Dorby 35? Effects of Thunder on Trees, Sir J. Clark 360 Explosions in the Air, A. Vievar 383 On the same, Sam. Shepheard 384 Earthquake at Naples, H. Temple 401 Meteor in the Air, M. Crocker 403 Luminous Appearance, Dr. Bevis 404 Meteors at Philadelphia, Breintnall 409 Aurora Borealis, James Short 412 On Weidler's Parhelia 433 Dry or Wet Summer, Anonymous 447 Red Lights seen in the Air 457 Several Meteors, Thomas Short 469 Weather, &c. George Lynn 486 Aurora Borealis at Rome, Revillas 502 Earthquake at Scarborough, Johnson 514 Aurora Borealis, Dr. Mortimer 525 , J. Martyn ibid , Tim. Neave 526 Hurricane in Huntingdonshire, Fuller .... 530 Fire-ball Explosion, Lord Beauchamp .... 540 , J. Fuller ibid , William Gostling .... 541 , Charles Mason ibid , Benjamin Cooke 550 Earthquakes in America, M. Plant 552 On Parhelia, H. Miles 555 On a Fire-ball, Capt. Wm. Gordon 559 , Wm. Gostling 56O Earthquakes at I-eghorn 568 Dew and Snow-flakes, Dr. L. Stocke .... 577 Effects of Lightning, Lord Petrie 583 A Meteor, Dr. Thomas Milner 583 Meteor in Norfolk, Lord Lovell 604 Meteorological Register, Revillas 606 Meteorological Observations, G. Hadley . . 6l7 CONTENTS. IX. Class V. Physiology. I . Anatomy. Page Foramen Ovale open, C. Amyand 54 Bones of Mammoth or Elephant, Bryne .. 155 Gigantic Bregma, &c. Klem 388 Monstrous Child, T. Sheldrake 401 Stuart's Structure of the Heart, Mortinaer 483 Foramen Ovale and Ureflira, Le Cat 485 Monstrous Foetus, Wm. Gregory 503 Page Heart upside down, De Torres 508 De Sceletorum, &c. S. C. HoUman 513 Polypi in the Heart, Dr Huxham 580 Sfieaking without a Tongue, H. Baker .... 586 Articulating Cartilages, Wm. Hunter .... 686 Monstrous Large Child, Geoffroy 727 2. Physiology of Animals. Bones coloured Red by Food, J. Belchier 79,83 A Monstrous Boy, Dr. Cantwell 325 A Girl a Quarter of an Hour in Water with- out Drowning, J. Green 337 Generation and Monsters, Super\'ille 385 Bones tinged by Madder Root, Du Hamel 420 Dr. Trew on the Difference between the Body before and after Birth, Da. Hartley 425 A Beetle lived 3 Years without Food, Baker 426 On Hermaphrodites, Dr. Parsons 477 Circulation of Blood in Efts, H. Miles 501 Extraordinary Skeleton, and a Man who gave Suck, Bishop of Cork 5i6 Remarkable Birtli, C. Warwick 589 On a Polypus, J. F. Gronovius 607 , a Cambridge Gentleman . . 609 A Man who lived 18 Years on Water, R. Campbell 616 Experiments on the Polypus, M. Trembley 623 Stat. Experiments on himself. Dr. Lining 683 Worms living after cut, Thomas Lord .... 692 Cells of Honeycomb, Maclaurin 709 3. Physiology of Plants. Impregnation of Plant Seeds, Ja. Logan . . 57 Oil of Sassafras Crystallized, J. Maud 243 The Smut in Corn, Abbe Pluche 408 A Plant in Semine, H. Baker 429 Seeds of Fern, H, Miles 505 Veget. of Old Melon Seeds, Triewald 577 Great Increase of Seeds, Hobson 63 1 Seeds of Mushrooms, R. Pickering 718 Remarks on the same, Wm. Watson .... 721 Farina of Red Lilly, T. Needham 729 4. Medicine. On a Cataleptic Patient, Rd. Reyuell .... 15 Experiments on Mad Dogs, Dr. James ... 69 Bones Coloured by Food, J. Belchier 79 Remedy for Vipers bite. Dr. Burton 84 On ditto, and Mad Dogs, Mortimer 84 Bite of Vipers, Dr. Atwell 107 Cure of t)ie same, Ste. Williams 124 Peruvian or Jesuits Bark, John Gray 142 Dampier's Powder for Canine Madness, J. Fuller 204 Bite of Mad Dogs, Hartley and Sandys . . 205 Biliary Ducts and Gall-bladder, Amyand . . 228 On the same case. Dr. Stuart 232 On Dr. Huxham's Book De Aere et Morbis Epidemicis, by Dr. Stock 265 Cure for Viper? bite, Dufay 267 Poison of Henbane Roots, Patouillat .... ibid Cure for Canine Madness, T. Steward .... 269 Poison of Laurel Water, Dr. Rutty 297 Limgs coughed up, Wm. Watson 46'8 VOL. VIII. 1 Black currant Jelly, H. Baker 479 Extraordinary Venereal Case, Huxham. . . . 480 Hairy Substances voided by Urine, Powell 489 On the same, by Sir Hans Sloane 49O On the same, by T. Knight 491 Watery Cystises, Dr. Graham 492 Hydatids per Vaginam, Wm. Watson .... 494 On the same by Le Cat 495 On Orme's Pectoral Syrup 505 Antidote tothe Westlndian Poison, Milward 542 Stones in the Bladder, E. Nourse 545 On the same Subject, George Bell 557 Extraordinary Dropsy, Gronovius 607 A Man living 18 Years on Water, Campbell 616 Two Medical Cases, Dr. Raster 622 Calculus voided by Urine, Leprotti 653 Grandgor, the Venereal Disease, Maclaurin 675 Bones becoming Soft, S. Bevan 682 Bloody Urine in the Small- Pox, Dr. Dodd 708 CONTENTS. Fistula Ljicrymalis, Hunauld Bony Substance in the Womb, Dr. Hody. . Perforations in the Thorax, Hauston Plum-stone in the Rectum, Madden Inguinal Rupture, &c. Amyand Rupture of the Ilium, Chr. Wolf. Tumour in the Pelvis, Dr. Cantwell Palsy of the Eyelids, by the same Arm torn oft' by a Mill, Belchier Bullet lodged near the Gullet, Ld. Carpenter Biliary Ducts and Gall-bladder, Amyand . . On the same Case, Dr. Alex. Stuart On a Bubonocele, C. Amyand Pin in a Child's Bladder, W. Gregory .... Calculus in the Bladder, De Caumont .... On the same Case, Salien On the same, by Sir Hans Sloane Part of the Spleen lost, J. Ferguson Tumour in the Knee, Jer. Peirce Wound in the Cornea of the Eye, T. Baker Three Cases in Surgery, Sherman Pestilential Fever by Tapping a Corpse dead of a Dropsy, Cox Calculus through the Perin. Hartley Calculus through the Scrotum, Sisley .... Tumour on the Thigh, Malfalguerat Exostosis on a Boy's back, Freeke . Surgery. Page Page 17 Wound in the Head cured, Cagua 439 56 Stone voided per Anum, Mackarness 441 68 Calculi in the Stomach, Dr. Breyne 452 80 Machine to reduce Fractures, Ettrick .... 454 89 Stones in the Kidneys, N. Sherwood 462 138 Softening of the Bones, P. Pott 464 158 Hernia Inguinalis, Dr. Huxham 474 225 Foetus 9 years in the Womb, Bromfield . . 489 226' Hair}' Substance voided by Urine, Powell. . ibid 227 Singular Hernia, Le Cat 497 228 Fracture of the Thigh, Wm. Wright 503 232 Needle through the Arm and Breast 504 236 Caesarian Operation by a Butcher 517 239 Catheter for the Stone, A. Cleland 526 240 Instrument for the Eye and Ear, Cleland . . 528 241 Steelyard Swing, T. Sheldrake 549 242 Klein's History of Fishes, Eanies 551 263 Preserving Fish Skins, Gronovius 559 'i9i Internal Cancers, Dr. Burton 572 324 Le Cat's Treatise on the Senses, Dr. Parsons 619 326 Medico-Chirurg. Observ. Schlichting 620 Hammock for dressing Patients, Le Cat . . 654 338 Ambe of Hippocrates, Le Cat 659 405 Instrument to reduce dislocated Shoulders, ibid Freke 706 410 Extraordinary Haemorrhage, Dr. Banyer . . 727 413 Ascites cured by Tapping, Banyer ibid Class VI. The Arts. 1. Mechanical. Standard Measures at Rome, Folkes 7* New Water Bellows, Triewald 192 Weights and Measures, Wm. Barlow .... 432 Grinding Lenses, Sam. Jenkins 451 English and French Wts. and Mea. Comm. 604 Standard Weights and Measures, Committee 698 2. Chemical. On Soap-making, GeofFroy 565 , - 3. Fine. Gold-coloured Glazing, Heinsius 606 4. Antiquities, On an Ancient Date, John Cope On the same, John Ward On the same again, J. Cope Again on the same, J. Ward Ancient Chirograph, R. Gale Runic Characters, Celsius Roman Stamps like printing, Mortimer Antiquities of Pnissia, Klein Weights and Measures, Barlow Barrows in Cornwall, Williams 32 Herculaneum at Portici, Pademi ........ 435 ibid On the same, by Geo. Knapton 437 37 On the same again, Crispe 438 39 Roman Pigs of Lead, Kirkshaw 453 64 Ancient Date at Rumsey, Barlow 478 1 14 Roman Hypocaustum, Sympson 532 248 A Golden Torques, Sir Tho. Mostyn 550 420 Standard Weights and Measures, Committee 698 432 Ancient Temple, and Stone Hatchet, Bp. of 433 Cork 715 CONfENTS. XI Class VII. Bibliography ; or, Account of Books. Page Newton's Fluxions by Colson, Eames 88 Muller's Conic Sections, J. Earaes 145 Bell's History of Hungary, Z. Pearce 253 Huxham, De Acre et Morb. Epid. Stack. . 265 Fourmont'sHistoriesof the Ancients, Pearce 389 Celsius on the Figure of the Earth, Eames 413 Dr. Trew on the Difference of the Body before and after Birth, Da. Hartley 425 Le Bruyn on Petrified Ousters, Klein 455 Page Dr. Stuart on the Struc. of the Heart, Mort. 483 Klein's History of Fishes, Eames 551 Kersseboom on the Number of Persons in Holland, Van Rixtel 628 Maclaurin's Fluxions, Maclaurin .... 632, 667 Haller's Enumeratio Methodica Stirpium Helvetiae, &c. Watson 655 Robins' Principles of Gunnery, Robins. . . . 677 Class VIII. Biography ; or. Account of Authors. Page Page Bevis, Dr. J , 117 Du Hamel 420 Baster, Dr. Job. . 378 Ehrhart, B 451 Baker, Henry . . , 426 Hunauld 17 Bruyn, C . 455 Hartley, Da 205 Bromfield.W... 489 Haller, Alb 655 Clairaut 118 Hunter, Dr. Wm. 686 Page James, Dr. R. , , . 69 Le Cat 485 Muller, J 145 NoUet 223 Pearce, Zac 389 Pluche, Ab 408 Pot, Percival . , . 464 Parsons, Dr 692 Seignette 10 Senex, John .... 176 Stone, Edm 392 REFERENCES TO THE PLATES IN VOLUME VIIL Plate I, Fig. I, II, III, 6; IV, V, 7; VI, 8j VII, VIII, IX, 9; X, 10. II, . . 1, II, 12} III, 13; IV, 32; V, 26j VI, VII, 56; VIII, 100. ni, . . I to V, 44; VI, VII, 45; VIII, IX, 46; X, XI, 47; XII, XIII, 48; XIV, 49;. XV, XVI, 50. IV, ..I to V, 74; VI, 82; VII, 103; VIII, 104; IX, X, 105; XI, 106; XII, 120; XIII, 121 ; XIV, 122. V, . . I to X[V, 114; XV, 136; XVI, 138. VI, .. I, l6l; II to V. 162; VI, 163; VII, 183; VIII, 192; IX, 208; X, 209; XI, XII, 210; XIII, 212; XIV, 213; XV, 217. VII, . . I, 241; II, 249; III, 260 and 262; IV, V, 284; VI, 286; VII, VIII, 342ir IX, X, 343; XI to XIV, 344; XV to XVIII, 345. VIII, .. I, 353; II, 357; III, 371; IV, 372; V, 375; VI to XIII, 382. IX, . . I, II, 393; III, 395; IV, 396; V, 400; VI, 429; VII, 434; VIII, 454; IX, 478. X, . . I, 454; II, in, 459; IV, V, 486; VI, VII, VIII, 486; IX, 508; X, 507. XI, . . I, 509; II, III, 510; IV, 511; V, 519; VI, 521. XII, . . I to VII, 528; VIII to X, 529; XI to XIII, 530, XIII, . . I, II, 532; III, IV, V, 533. XIV, . . I, II, 535; III, 536; IV, 550; V, VI, VII, VIII, 577; IX, 590; X, 623; XI, 654; XII, 655. XV, . . I, II, 659 ; HI, 661; IV, 659. XVI, . . I, 661 ; II, III, 662; IV to IX, 662 and 663. XVII, .. I to XIII, 666 and 677. XVIII, .. I, II, III, 686; IV, 691; V, VI, VII, 698. XIX, .. I to IX, 698, XX, . . I, 717; II, 706. XXI, . . I, II, 710; III, 712; IV, 718; V, VI, VII, 720; VIII, 725, THE PHILOSOPHICAL TRANSACTIONS OF THS ROYAL SOCIETY OF LONDON; ABRIDGED. ji Catalogue of the 50 Plants, from Chelsea Garden, presented to the Royal Society by the Company of Apothecaries, for the Year 1733, pursuant to the JDirections of Sir Hans Sloane, Bart. By Isaac Rand, Apothecary, F. R. S. N" 436, p. 1 . Fol. XXXIX. JL HE 12th annual present of the 50 plants, making in all 60O. A Catalogue of the Eclipses of Jupitei-''s Satellites, for the Year 1736, computed to the Meridian of the Royal Observatory at Greenwich. By J. Hodgson, F. R. S. Master of the Royal Mathematical School in Christ's Hospital. N° 436, p. 5. Mr. Hodgson's usual catalogue of these eclipses, precalculated, to compare with observations when they should be made. The Apparent Times of such of the Immersions and Emersions of Jupiter s Satellites, as are visible at London, in the Year 1736, with their Configura- tions at those Times. By Mr. Hodgson. N° 436, p. 13. O the same nature, and for the same use as the former. Account of the Observations of the Eclipses of the First Satellite of Jupiter, com- pared with the Tables. By the same. N° 436, p. 15. By comparing 244 eclipses of Jupiter's first satellite, observed between the years l677 and 1731, with the Flamsteedian tables, corrected by Mr. Hodgson, he finds there are 74 that do not differ 1 minute from the tables ; 127 that do VOL. vm. B 2 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. not differ 1 minutes; 181 that do not differ 3 minutes ; and 214 that do not differ 4 minutes ; the rest not differing above 5\ minutes. Experiments and Observations on the Light, produced by communicating Electri- cal Attraction to animate or inanimate Bodies; ivith some of its most surprising Effects. By Mr. Stephen Gray. N° 436, p. l6. The several new electrical discoveries made by M. Dufay, especially that im- portant luciferous one, mentioned in a former Transaction, led Mr. Gray to make the following experiments : — He began first with some common utensils that were at hand, as the iron poker, tongs and fire-shovel ; any of these being suspended on lines of the largest sewing silk, and then the excited tube being applied first to the knob of the poker, and afterwards to the hand, the snap and pricking were felt ; and the effect was the same, when the tube was first applied to the other end of the poker. He had by him a three-pronged iron instrument, made many years be- fore ; being designed for propping up the observatory table, when he observed the spots in the sun. The prongs were about 4- an inch in diameter, two of them about 22 inches, and the third about 8 inches long, and pointed. This being laid either on cylinders of glass, or cakes of rosin and bees-wax, or on a cake of sulphur, the tube being applied to the end of any of the legs, while the hand or cheek was applied near the other, both the other legs had the same effect, as that to which the tube had been applied ; but by holding his cheek near any of the points of the legs, the pricking or burning pain was much more sensibly felt, and even sometimes for several minutes after. As to the success in repeating M. Dufay's experiment at Mr. Wiieeler's, they procured silk lines strong enough to bear the weight of his foot-boy, a good stout lad : then having suspended him on the lines, the tube being applied to his feet or hands, and the finger of any one that stood by held near his hands or face, he found himself pricked or burnt, as it were, by a spark of fire, and the snapping noise was heard at the same time: but it did not succeed when they applied their hands to any part of his body through his clothes, except upon his legs, where he felt the pain through his stockings, though they were very thick ones. They took also a large white cock, and suspending him on the lines, first alive, the effect was the same as on the boy, whether they applied their fingers to any part of his body, or their cheek to his beak, or comb or claws. The cock was then killed, and put on the lines again ; when they found very little, if any difference, from the effect it had when the cock was living. They then VOL. XXXIX.] rHILOSOPHICAL TRANSACTIONS. 3 caused the cock to be stripped of all his feathers ; and the difference was still not very considerable. They took a large surloin of beef, and suspended it on the silk-lines : then, on holding the fingers near any part of it, there was a snapping, and the fingers were pushed or pricked : but the snapping was thought not to be quite so loud, as when the experiment was made on the cock. They caused to be made an iron rod, 4 feet long, and about half an inch diameter, blunt pointed at each end. This was suspended on the lines : then the tube being rubbed, and held near one end of the rod ; and then the finger or cheek being put near either end of it, the effect was the same as when an animal was suspended on the line, with respect to the pricking pain. At night they made the luminous part of the experiment ; suspending the iron rod on the silk lines ; then applying one end of the tube to one end of the rod, not only that end had a light on it ; but there proceeded a light at the same time from the other end, in form of a cone, the vertex being at the end of the rod ; and it plainly consisted of rays of light, diverging from the point of the rod ; and the exterior rays incurvated. This light is attended with a small hissing noise ; and every stroke given to the tube, causes the light to appear. The hissing seems to begin at that end of the rod next the tube ; and as it comes, increases in loudness ; but it is so small as not to be heard without good attention, and by those only that stand at the end of the rod from whence the said light proceeds. Mr. Gray repeated the experiments, by laying a rod of iron on a cake of shell-lac, which was laid on a glass-vessel : and the effects were much the same as mentioned above. Having caused to be made 3 iron rods, one 4 feet long, and two 3 feet long each ; one of these was made tapering towards the ends, and pointed as that of 4 feet was ; the other pointed at one end, and the other end not pointed, the diameter of the rods about half an inch ; they were first forged, then filed and burnished. With these Mr. Gray made the following experiments : when any of them were laid on the brims of hollow cylinders of glass well warmed, or on cakes of rosin and bees-wax, or on those of sulphur, the phenomenon was the same, as when they had been suspended on silk lines. But now he dis^ covered a very surprising one, viz. that after the tube had been applied, and the light seen at both ends, on going to the other end of the rod, when there was no light to be seen, and holding his hand at some distance from it, then moving his hand towards it with a pretty swift motion, there issued from that point of the rod a cone of light, as when the tube had been applied to the end : and on repeating this motion of his hand, the same phenomenon appeared for 5 or 6 B 1 4 PHILOSOPHICAL TRANSACTIONS. [aNNO J 735. times successively, only the rays were each time shorter than the former : and these lights were attended with a hissing noise. The light which appears on that end next the tube, when it is held obliquely to the axis of the rod, has its range tending towards it. All the time he is rubbing the tube, these flashes of light appear on every motion of his hand, up or down the tube; but the largest flashes are produced by the downward motion of the hand. When several rods are laid either in a right line, or forming any angle with each other ; and either touching, or are at a small distance from each other ; the tube being applied to one of their ends, the farthest end of the farthest rod exhibits the same phaenomena, as one single rod does. An experiment with the rod pointed at one end only. When the tube is ap- plied to the other end, the point exhibits the same appearance, and a like effect, as the rods that are pointed at each end ; but the great end of the rod, when the hand or cheek is applied near it, gives but one single snap ; though this is much louder than the greatest of those from the pointed end, and it gives a little more pain. Having forged an iron ball, 2 inches diameter, and then turned and burnished it; having placed it on a wooden stand with a small concave on the top, in which the ball was placed: the stand being set on a cylindric glass, and the excited tube being applied near the ball, a stream of light proceeded from it, with a small hissing noise : but putting his finger or cheek near the ball, no snapping nor pain was felt ; yet a very bright light appeared. The rod, of 4 feet long, being placed on a stand, having a cross arm, with a groove in it, to receive the rod ; and then the stand being placed on the glass cylinder, they were set at such a distance, as that one of the points of the rod might just touch the ball over against its centre ; then going to the other end of the rod with the excited tube, he applied it as usual ; when he came to the ball, the hand or cheek being near it, caused a loud snap, compared to those made by the points of the rods, and the pain of pricking or burning was more strongly felt ; the light was also brighter and more contracted. The rod being then placed with its point at an inch distance from the ball, and applying the rod as before, then touching the ball with his finger, there not only appeared a light on the ball, but there also proceeded a pencil of light from the point of the rod, after the same manner as when the experiments were made with the rods only. The following experiment was made with the 4-foot rod, and a brass plate 4 feet square. This was placed on a stand, so that the plate stood perpendicular, the stand being set on the cylindric glass ; then the rod with its stand and glass was set in such a manner, that one point of it was about an inch from the centre VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 5 of the plate ; then the tube being applied to the other end of the rod, and after going to the plate, on striking it gently with the finger on the backside, a light appeared on the plate, and at the same time the pencil of light issued from the point of the rod ; and when the hand or cheek was held near any of the angles of the plate, a light issued from thence, with a small hissing noise, and the pricking was felt, as when the experiments were made with the pointed rods. A pewter plate being laid on the stand, which had been set on a glass cylin- der, applying first the tube, and then the finger, a light appeared on the plate, and the end of the finger was pushed ; and when the cheek was held near the edge of the plate, a snapping was heard, but not so loud as when the iron rods were used. On filling the plate with water, and applying the tube and finger as before, there was the same light, with the pushing of the finger and snapping, as when the experiment was made with the empty plate. When the experi- ment is made with water by day-light ; by applying the end of the finger near the surface of the water, it appears to rise in a little hill, but on the snapping noise it falls down again, putting the water into a waving motion, near the place where the water had risen. He then took a wooden dish, and placed it on the stand, first empty ; then applying the tube and the finger near the dish, a light appeared, but no pushing of the finger, nor snapping. He then filled the dish with water, and the tube being held over the surface of it, there appeared a greater light than when the finger had been applied to the empty dish, but no snapping ; till by holding the tube, after it had been well rubbed, within 2 or 3 inches of the finger that was held near the surface of the water ; for then the finger was pushed, and a snap- ping noise wafe heard, as when the experiment was made with the pewter plate. By these experiments we see, that an actual flame of fire, with an explosion, and an ebullition of cold water, may be produced by communicative electricity; and though these effects are at present but in minimis, it is probable that in time there may be found out a way to collect a greater quantity of it ; and con- sequently to increase the force of this electric fire ; which, by several of these experiments, seems to be of the same nature with that of thunder and lightning. A General Method of describing Curves, by the Intersection of Right Lines, moving round Points in a Given Plane. By the Rev. IVm. Braikenridge. N° 436, p. 25. Translated from the Latin. The following general method of describing lines of any order, by the inter- 6 PHILOSOPHICAL TRANSACTIONS. [anNO J 735, section of right lines moved round poles, Mr. Braikenridge thinks is much more simple than that of Sir I. Newton, and will give a solution of many difficult pro- blems, which he doubts if they can be found by any other principles. The author gave only one particular case of this in his Geometrical Exercitation, printed at London in 1733, not thinking it convenient to explain the whole method at that time, though he was then, he says, well acquainted with that method. It is now, he says, 3 years since he fell upon the general theorem, which he had many reasons for concealing ; being determined to let 2 years at least pass, after the publication of that Exercitation, before disclosing this general method : for he doubted not, that if any others were possessed of this invention, they would, on the publication of a particular case, especially as they were provoked to it, embrace the opportunity to publish their general method, if they had really discovered one. About 3 given points, as poles, a, b, c, fig. 1, pi. 1, in any plane, let there be turned 3 right lines, ans, bos, cno, which may intersect each other in the points s, n, o ; and let the two points of intersection s and n be drawn along the right lines dks, knk, given by position ; then the remaining point o will describe a conic section ; as is demonstrated in the Exercit. prop. 1. — If through the points a, b, c, be drawn the right lines ab, ac, meeting each other in a, and the right lines rk, dk, given by position, in r and m ; then the figure de- scribed will pass through the 5 points b, c, k, m, r. And hence appears a new method of describing a conic section through 5 given points, much easier than any yet invented. See Exercit. prop. 3. Let there be moved around 4 points a, b, c, d, fig. 2, as poles, in any plane, as many right lines ans, bos, cno, dpo, three of which, ans, bos, cno, may intersect each other in three points, s, n, o ; and let the two points of inter- section s, N, be drawn along the right lines dK, rk, given in position ; and at the same time let the right line dpo, drawn from the 4th pole d, pass through the remaining point o, and cut the right line ans in p : then that point p will describe a line of the 3d order : as is demonstrated prop. 1 1 of the exer- citation. Through the poles a, b, d, let there be drawn the right lines abr, bdh, meeting each other in b, and the right lines kr, Kd, given by position, in r and H : then the figure described by the motion of the point p, will pass through the 3 points a, d, h, k, r, of which a will be double. Hence is de- duced a method of describing a line of the 3d order through 7 given points, one of which may be double. For let a, d, h, k, p, m, r be given, fig. 3, one of which A is to be double. Through the two points h, r, and another k, let the right lines hk, rk pass ; also join the points a, r, and h, d, and produce ar, VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 7 HD, to meet each other in b. Then through a and the points p, M, draw the right lines apms, amhs, cutting the right line kr in n and n, and the right line HK in s, s ; tlirough these points s, s, to the point b, draw bs, bs ; and through D, to the points p, m, draw the lines dpo, dmt, meeting bs, bs, in o and t. Draw ON, xn, produced to meet in c. Then about the points a, b, c, d, as poles, let there be revolved the lines as, bo, co, do, of which the three as, bo, CO intersect in s, n, o ; and let the two s, n move along the lines hk, kr, while the line do always passes through the remaining point o, and cuts ans in p ; then this intersection p, of the right lines as, do, will describe a line of the 3d order, passing through the ^ given points, a, d, h, k, m, p, r, and doubly through the given point a. Lines of the 3d order also are more generally, but less commodiously, de« scribed after this manner, which also comprehends the former. About 5 given points. A, b, c, d, e, fig. 4, as poles, let as many right lines ans, bos, cno, dpo, EPS, revolve, of which the three ans, bos, cno intersect each other in the points n, s, o; let the two s, n be moved along the lines dK, kr given in position ; and through one s, of the two n, s, and the remaining point o, let the lines eps, dpo pass, being drawn through the poles e, d, and meeting in p: then this point p will describe a line of the 3d order, with a double point in the pole E. In like manner may lines of the 4th order be described. About the 5 given joined points a, b, c, d, e, fig. 5, as poles, in any plane, let as many right lines, ans, bqs, cno, dpo, EPa, be moved ; of which the three ans, bqs, cno meet ' in the three points s, n, o ; let the two points of intersection s, n be drawn along the lines dK, rk, given in position, while the line dpo, moveable about the 4th pole d, passes through the remaining point o, and cuts the line ans in p ; then let the line epg, drawn from the 5th pole e, be drawn through p, and be produced both ways to meet the lines sas, cno, in q and w : then will the points a and w describe lines of the 4th order ; as is demonstrated by prop, ll of the Exercitatio. Through the poles a, e, and b, d, let the lines aeh, bdf, pass, meeting dK, given by position, in h and f ; join de ; and through the poles d and a, the line ad being drawn, meeting dK in v; from which point v let the line vb be drawn to the pole b, and cut the line de in g. Then the figure described will pass through the 5 points b, e, g, f, h, and triply through the pole B. Through the poles a, b, let there be produced the line abr, meet ing the line kr, given by position, in r ; then the curve will also pass through the points r, k. Hence is derived a method of drawing a line of the 4th order through Q given points, one of which is a triple point. For let b. e. f, g, h, l, m, t, a be given, ^ 1 8 PHILOSOPHICAL TRANSACTIONS. [anNO J735. one of which b is to be triple, fig. 6. Join the points bf, fh, he, and pro- ducing these three lines ; and through the points eg, gb, let the lines egd, BGV be drawn, of which let egd cut bf in d, and the other line bgv cut fh in V. Then having joined v and d, and produced vd to meet he in a, draw the line dABR through the points a, b. Then from the points b, e let the lines Has, EPQ be inflected to the given point q, of which let the first Bas meet fh produced in s ; and through the points a, s having drawn as, meeting eq in p, let DPO be produced through p and d, and meet Bas in o : and note the point o. In like manner, from the same b, e, to another given point t, let the lines BTS, EpT (supply the figure) be inflected, of which let bts meet fh in s ; and having drawn as cutting EpT in p, draw npz through p and d, meeting bts in z, and mark the point z. And thus let lines be drawn from the same b, e, to the other given points m, l, and drawing lines from a and d as before, let the points so found be marked x, y. Then through the 4 points thus found, o, z, X, Y, and the given point b, let a conic section be described (see prop. 3, exercit.), cutting fh in the points i, k, and the line dAB in b, r. Through the points A, I draw the line ax, cutting the conic section in i and c ; join the points K, R, and let this line kr be produced. Now about the 5 points a, b, c, d, e, as poles, let as many lines, as, bs, cn, do, Ea, revolve, of which three as, bs, ON meet each other in n, s, o ; and let the intersections n and s, of the lines as, on, and as, bs, be drawn along kr and fhk, while the line dpo passes through the pole d, and the intersection o of the lines bs, cn, and cut the line as in p ; and through p and the pole e, let EPa be produced to cut bs in a : then this intersection a will describe a line of the 4th order, passing through the 9 given points, b, e, f, g, h, l, m, t, a, one of which b will be triple. By a method not much unlike this, a line of the 4th order may be described through 8 given points, 3 of which are double; as also a line of the same order through 1 1 given points, 2 of which are double ; with many other cases of that kind. As to the number of points which determine a line of any order, Mr. B. says, that if n denote the number of the dimensions of a line ; then tr + 1 will be the number of points through which the line may be described. For instance, a line of the 2d order through 5 points, one of the 3d order through 10, of the 4th order through 17, of the 5th order through 2d points. And hence is deduced, that if a line of the 11th order have an « — 1 multiple point, it may be described through 2n + 1 points. For instance, a line of the 3d order, with a double point, (viz. n — 1 = 2) through 7 points, and a line of the 4th order with a triple point, through Q, &c. And generally, if p, q, r, &c. denote multiplex points, the number of which is m, a curve can be described through VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. - Q w'^ — p'^ — q- — r^ -\- m -\- \ points, of which there are m multiplex points. Thus, a line of the 4th order, with 3 double points, may be described through 8 points : for n = 4, /) = 9 = r = 2, m = 3, and l() — 4 — 4 —44- 3+1=8. There is another method also of describing lines of the 4th order, not much different from the former, but a little more complex. About 7 poles. A, b, c, d, E, F, G, (fig. 7), let there revolve as many lines, as, bs, cn, ds, en, fo, gt, one of which ANS, by revolving, cuts the lines dK, kk, given by position, in the points s, N ; let the lines cn, bn be drawn through one of them n, and the lines BS, ds through the other s, and meet the lines cn, kn, in the points o, t, describing conic sections as above; while the lines fo, gt, drawn from the poles F, G, pass through the same o, t, and meet in p : then the intersection p will describe a line of the 4th order, with a double point in both the poles f, g. But not to dwell longer on these, Mr. B. now gives the following general theorem. About the poles a, b, c, d, e, f, g, h, &c. (fig. 8), whose number is n, let as many lines as, bs, cn, dp, eq, fw, gx, hy, &c. revolve, of which the three as, bs, cn intersect each other in the points n, s, o ; let two, s, n, be drawn along the lines dK, kr, given in position; while through the third o and the pole D, passes the line dp, cutting as in p ; and through p and the pole e draw the line Ea, cutting bs in a ; and from a through the pole f let Fa be drawn, cutting as in w ; also through w and the pole g draw gw, cutting bs in X ; and then through x and the pole h draw hy, meeting sa in y ; and so on : then the concourse y, of the line hy, drawn from the last pole h, with either of the lines as, bs, will describe a line of the n — 1 order, and have the n — 2 multiplex point in the pole a or b, like as it was described by the inter- section of the line as or bs. The points o, p, a, w, x, y, &c. will describe lines of the 2d, 3d, 4th, 5lh, 6th, 7th, &c. order. But if all the poles a, b, c, d, e, F, G, H, &c. be situated in the same right line, then those points o, p, a w x Y, &c. will also describe as many right lines. The Newtonian description of curves is also greatly promoted by this method. It is well known, that if the given angles oan, obn. revolve about the given points a, b (fig. 9) and the intersection n, of the legs an, bn, be drawn along the line nr, given in position ; then the concourse o, of the legs ao, bo, will describe a conic section. Now let another point c be taken, about which let the line ocp be moved, which shall always pass through the intersection o of the legs AO, bo, and meet the other leg an of the angle a in p : then the in- tersection p will describe a line of the 3d order, passing doubly through the pole a. In like manner, if by the intersection of the leg bn, of the angle b, a curve be describedj it will be of the same order, and have a double point in the VOL. VIII, C 10 PHILOSOPHICAL TRANSACTIONS. [anNO 1735. pole B. And hence also it appears, how a line of the 3d order may be described through 7 given points, one of which may be double. Let the angles oan, obn, be moved as before, about the given points a, b, (fig. 10) ; and through the intersection o, of the legs oa, ob, let the line ocp pass, drawn from another given point c, meeting the side an, of the angle a, in p ; then through p, and a 4th given point d, draw the line dpq, meeting the leg Ao in Q ; then the point a will describe a line of the 4th order, having a triple point in the pole a. And thus, by increasing the number of the poles a, b, c, d, &c. so that their number at length may be n, the line described will be of the same order n. But it may be noted, that if for the angle obn, there be substituted a right line, re- volved about the pole b, the description will become easier. j4n Account of M. Seignettes* Sal Polychrestus Rupellensis, and some other Chemical Salts. Bij M. Geoffrey. N" 436, p. 37. M. Seignette's sal polychrestus rupellensis is a soluble tartar, composed of cream or crystals of tartar, and the fixed salt of the kali of Alicant,-|- well de- purated. This salt is very singular: for, though it be a fixed alcaline salt, it has the peculiar property of crystallizing; nor does it easily dissolve in the open air ; as other fixed salts do ; but on the contrary calcines in it like vitriols or Glauber's salt. Another peculiar property M. GeofFroy observed of it is, that if it be saturated with vitriolic acid, and the liquor be evaporated, there results a salt that resembles Glauber's salt, and has all the properties requisite to make M. Seignette's salt. To produce this, take of the salt of kali [of Alicant] well depurated, 1 lb ; dissolve it in water, add about 1 lb. ss. of crystals of tartar ; boil the whole, to dissolve the crystals : but the exact proportion of crystals of tartar can be de- termined no more in this operation, than in making the soluble tartar ; either because the salt of kali has retained more or less humidity in its crystallization, or because the tartar has more or less impurities in it. But if there be too much tartar in the alkaline liquor, after the fermentation is over, filtrate the liquor, and as it cools, the superfluous tartar will fall to the bottom. After the sepa- ration of the tartar from the liquor, evaporate the lixivium by a gentle fire ; set it in a cool place to crystallize, and you will have very fine crystals. If the * M. Seignette was an apothecary at Rochelle, whence this salt has been called Rochelle salt. t The kali of Alicant is a marine plant (Salsola sativa Linn.) from which, by incineration, is ob- tained the fossil alkali or soda, which uniting with the superfluous acid of the crystals of tartar, forms a triple salt, compounded of tartaric acid, potass and soda, and denominated in the modern chemical nomenclature tartrite of potass and soda. VOL. XX XIX. J PHILOSOPHICAL TKANSACTIONS. 11 liquor be evaporated a little too much, there will be no crystals of salt formed, but the liquor will be converted into a hard transparent mass, not unlike glue. But by dissolving this mass again, it is made to crystallize, as on dissolving M. Seignette's salt. This salt purges very well, from I to 2 oz. dissolved in a quart of water. M. GeofFroy employed himself in perfecting this salt, and in examining the salt of kali, and comparing it with borax. From the salt of kali he extracted Glauber's salt, by mixing it with oil of vitriol. He next made experiments on borax. A mixture of 4 oz. of borax with 1 oz. and I dr. of vitriol, on sublimation, gives the sedative salt, described by M. Homberg ; and the residue exposed to a strong fire, afforded Glauber's salt.* M. GeofFroy found out a method *o shorten this operation : for, instead of subliming this salt, he procured it by crystallization in light foliated laminae. This salt, whether sublimated, or crystallized, has the property of dissolving in sp. of wine ; and when this sp. of wine is set on fire, its flame is green. Sp. of wine has no effect on borax ; the oil of vitriol, digested with sp. of wine, communicates no greenness to its flame; it is therefore requisite that the borax be united with an acid, in order to pro duce this green flame. Sedative salt, made by crystallization, crystallizes in a peculiar manner : this operation is performed with 4 oz. of borax, 1 oz. and 1 dr. of concentrated oil of vitriol, the most fixed and weighty that can be had. The borax is put into a glass retort ; the oil of vitriol is poured on it ; and then -J- oz. of common water. This mixture being exposed to a fire, gradually increases, after the phlegm has passed off, and even while it is passing there rise flowers, or a volatile salt, in very beautiful foliated laminae, some of which melt by the heat of the fire. After the operation, the finest of these flowers, which are round the neck of the retort, are gathered ; and those that are grey are thrown on the remaining mass ; which mass is dissolved in water, filtrated and evaporated slowly. Some- times even without evaporation, the shining talcous laminse are to be seen in the liquor. In 24 hours the liquor is poured from these laminae ; they are washed in fair water, set to drain, and then to dry in a stove. -j~ If these crystals do not calcine in the stove, or in the sun, it is a sign there is nothing crystallized but the sedative salt : if they do calcine, it is a sign that there is some Glauber's salt mixed: and then this salt must be dissolved again in • Borax being compounded of a peculiar acid termed boracic acid and soda, its own acid is ex- pelled from the alkaline base by the vitriolic or sulphuric acid of the vitriol here employed ; which unites with the said alkaline base, and forms with it Glauber's salt, i e. sulphate of soda. t The product here termed sedative salt, is now known to be the acid of borax. 02 J2 HHtLOSUFHICAL TRAK8ACTIONS. [aNNO 1735. hot water, and re-crystallized. No one before M. GeofFroy thought of extract- ing this salt by crystallization, being always before sublimed. An Account of a Machine for changing the Air of the Room of sick People iti a little Time, by either draiving out the foul Air, or forcing in fresh Air ; or doing both successively, without opening Doors or Windows. By Dr. J. T. Desaguliers, F. R. S. N''487, p. 41. Fig. ] , pi. 2, represents a case, secb, containing a wheel of 7 feet diameter, and 1 foot thick ; being a cylindrical box, divided into 1 2 cavities, by partitions directed from the circumference towards the centre, but wanting 9 inches of reaching this, being open towards the centre, and also towards the circumfer- ence, and only closed at the circumference by the case, in which the wheel turns by means of a handle fixed to its axis a, turning in two iron forks, or half concave cylinders, of bell-metal, such as a, fixed to the upright timber or standard ae. From the middle of the case on the other side behind a, comes out a trunk or square pipe, called the sucking-pipe ; which is continued quite to the upper part of the sick person's room, whether it be near or far from the place where the machine stands, or in an upper or lower story, or above or below the ma- chine. There is a round hole in one of the circular planes of the machine, of 18 inches diameter round the axis, just where the pipe is inserted into the case, by which the pipe communicates with all the cavities ; and as the wheel is turned swiftly round, the air which comes from the sick room, is taken in at the •centre of the wheel, and driven to the circumference, so as to go out with great swiftness at the blowing-pipe b, fixed to it As the foul air is drawn away from the sick rooms, the air in the neighbour- ing apartments gradually comes into the room through the smallest passages : but there is a contrivance to apply the pipes which go to the sick room to the blowing-pipe b, while the sucking-pipe receives its air only from the room where the machine stands. By this means fresh air may be driven into the sick room, after the foul has been drawn out. This machine would be of great use in all hospitals, and in prisons : it would also serve very well to convey warm or cold air into any distant room ; or even to perfume it on occasion. Fig. 2 represents the inside of the flat of the wheel, which is farthest from the handle, and next to the sucking-pipe. 1,2,3, 4, represents the cavity or hole which receives the air round the axis, having about it a circular plate of iron, to hold all firm ; which plate is made fast to the wood and to the iron VOL. XXXIX.] PHILOSOPHICAL TKANSACTIONS. 13 cross containing tlie axis, ggg, bj a pricked circle, denotes a narrow ring of thick blanketing, which (by pressing against the outside case, while it is fixed to the outside of the flat of the wheel) makes the passage into the wheel tight. HHH is another circle of blanketing, likewise fixed to the outside of the wheel, and rubbing against the case ; that the air violently driven against the inner cir- cumference of the case, may have no exit, but at the blowing-pipe at b. On the outside of the other flat of the wheel, where the handle is fixed, is a ring of blanketing, like hhh, opposite to it, but none opposite to ggg; be- cause the wood there is not open, but comes home close to the axis. Fig. 3 gives a vertical section of the wheel and case, a little forward of the flxis, drawn to a scale twice as large as that of the other two figures. Aa the axis, supported by the irons A, a, cylindrically hollowed, except the upper part, where a pin keeps in the axis, bd the case with the sucking-pipe sa. ea the prop for one end of the axis. 1, 2, the opening into the wheel, gg the emi- nence of the wood, to which is fixed the small ring of blanketing. The four black marks, one of which is near h, represent the sections of the two other rings of blanketing. A Calculation of the Velocity of the Air moved by the new-invented Centrifugal Bellotvs, of 7 Feet in Diameter, and 1 Foot thick within. By J. T. Desa guliers, F. R. S. N° 437, P- 44. When the wheel revolves on its axis, which is performed in this machine every revolution in about half a second, the air may be considered as divided into as many concentric circumferences, as there are particles of air contained between the least and the greatest circle ; consequently the centrifugal forces will be as the radii, that is, in an arithmetical progression. Let R = radius of the greatest circle 3.5 feet, r = radius of the least circle O.75, m = radius of the middle circle . •• 2. 125 = 4.R -j- ^r, t; = the velocity, or space described in a second, "S in the middle circle, on the supposition that .2Q.ll, the wheel makes two revolutions in a second j s = space described in a second by the action of gravity }l6.1. * = the space that a particle of air, receding from the centre, would describe in a second, by the action of the centrifugal force at the circumference of the middle circle. Then 2m'.v::v:s\ therefore ^ = «, by Huygens's rule. Let g and c. 14 PHILOSOPHICAL TRANSACTIONS. (^ANNO 1735. express the force of gravity, and the centrifugal force at the middle circle. Since the spaces described in the same time, by the action of two forces, are as those forces, s : 5 :: g : c, and — := c; then substituting in this expression, -— instead of s, we have - — = c; and putting -^r + t'" instead of its equal m, -. — ■—: = c. So that the ratio of gravity to the centrifugal force, at the middle circle, is that of g to '^ , or that of 1 to —^ ; which (R + r) X s' (a + r) X s ' being multiplied by the number of the revolving circles u — r, gives for the pressure of the column of air r — r, proceeding from gravity, r — r, and the pressure proceeding from the centrifical forces ■ ■— , where r — r being a factor common to both, may be thrown out of the expression; and since the velocities produced from different pressures, are as the square roots of the pressures, the velocity gravity would give from the natural weight or pressure of R — r, will be to the velocity the same column would have from the pres- sure occasioned by the centrifugal force, as ^Z J , or 1 , to t/- r . •' ° '(R + r)xs Lastly, since the velocity proceeding from the action of gravity, on a column = R — r, is always a known quantity, it may be called = a, equal in this case to 15,38 feet per second, and consequently the velocity proceeding from the centrifugal force will be a X /: c , or av X \^ , — :— r , or ,■ , -=^; ^ ' (R + r) X s- (r + r) X s' v(r -|. r) x s 1 5-38 X 26 71 that is, in this machine, . .'. — = 40.67 feet per second. And if we add to this, the velocity of the outer circle in the tangent of which the air escapes, which, in the supposition we made of two revolutions in a second, is 44 feet per second, we shall have = 93.67 feet per second. Note. — This calculation supposes the bore of the sucking-pipe sufficient to furnish as much air as would escape, according to this velocity ; but in this machine the sucking-pipe being no larger than the ajutage or blowing pipe, the velocity proceeding from the pressure occasioned by the centrifugal force, and from the velocity in the tangent, which may be represented by a column of air of sufficient height to give the velocity of 93.67 feet, which is 145. 882 feet, must be divided into two equal parts, one half employed in sucking, and the other in blowing; therefore the half of 145.882 feet, which is 72-941 feet, will represent the height of a column of air, that would occasion the same pressure with which the centrifugal force and the circular motion act in this machine; and a column of this height producing a velocity of 68.53 feet per second. This number will express the velocity with which the air is sucked into the wheel; and the same number will also express the velocity of the air VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 15 out of the blower, proceeding from the centrifugal force, and the circular velo- city of the outer circle, which is the real velocity of the stream of air out of the blower of this machine, viz. 68.53 feet per second, which is at the rate of a mile in about 77 seconds, or about 7 miles in Q minutes. The Uses of the foregoing Machine. By the same. N° 437, P- 47. Besides the uses of this machine for sick rooms, for prisons, or large assem- blies, for warming, cooling, or perfuming any chambers at a distance, it may also serve in a man of war, to takeaway the foul air between decks, occasioned by the number of men in the ship, and to give them fresh air in a few minutes. In every part of the vessel, every foul hole may be rendered wholesome, and even the stench and foul air from the surface of the bulge water may be carried oft". Also for mines the machine must prove of excellent use; for as the damps, either fulminating, which taking fire, destroy the men and ruin the works, or arsenical, which kill by their poisonous nature, are some specifically lighter, and some specifically heavier than common air, this centrifugal wheel can in a little time drive down air through wooden trunks, or launders, of 7 inches bore, in such quantities into the deepest mines, as to cause all the light damp to come out at the top of the pit; or, by only altering two sliders, suck away all the heavy poisonous damp, while wholesome air goes down from above ground into the pit, so as to fill all the subterraneous caverns with fresh and wholesome air. Likewise a great many of the difiiculties which attend the carrying on sub- terraneous passages, for the conveyance of water from mines, called soughs, adits, or drifts, may be removed by the help of this wheel ; for the fresh air may be driven in a very little time to the place where the men are at work, though at the distance of 2, 3, or 4 miles, and therefore also to any interme- diate space; whereas the practice now is, either to make a double drift, with communications between the two for the circulation of the air, or to sink per- pendicular shafts or pits, from the top of the hill over the adit: both which methods are very expensive, and inferior to the application of this machine. The Case of a Cataleptic Woman. By Richard Reynell, Jpolhecary, London. N" 437, p. 49. Ann Billiard, a servant, about 21 years of age, had been for some time irre- gular in her menses, and very much afflicted for the loss of a friend. July 10, 1730, she complained of a pain in her head, sickness in her stomach, with a general disorder ; and took Gascoign's powder for a sweat; next morning. \6 PHILOSOPHICAL TKAN8ACTIONS. [aNXO 1735. July Jl, about p o'clock, she was found in bed, senseless, stiff, and void of feeling, with her eyes shut, and seemed to be dead. When Mr. R. came, he found her in a true cataleptic fit, senseless, without motion, her limbs very stiff, but warm, and not easy to be bent; but in whatever posture any limb was put, it continued in the same, whether erect or reclined; her respiration was good, but her pulse low and irregular; she had no calchings, or convulsive motions, but could not, by any means used, be brought to herself. A vein was opened in the arm, and 12 oz. of blood were taken away; she bled freely, and came a little to herself, but could not speak. Mr. R. then gave her some volatile and anti-spasmodic medicines. In a few hours she came to herself. She complained of a dizziness in her head, with a violent pain in the fore part of it, and sickness in her stomach, and was a little feverish. H«/ gave her a vomit at 4 o'clock in the afternoon, which worked kindly, and she seemed relieved by it. About 6 in the evening another tit returned, much in the same manner as before; but she soon came out of it, and then took the medicines with the volatile salt of hartshorn, as before. Mr. R. moreover applied a large blister to her back, and two more to her arms; about Q the same evening she had a strong convulsion fit, with catchings, grinding of the teeth, and a great tremour; neither of which she had had before: she had a stool the preceding night, but none that day. He gave her a draught with tinct. hier. at night going to rest; she continued taking the volatile medicines, &c. every 4 hours. July 12, she had been light-headed all night, with little or no rest; the blisters were dressed, which discharged plentifully, and the tincture had given her 3 stools in the night, which had made her a little faint; her pulse was low, and her water pale. Mr. R. saw her in the evening, when she had slept pretty well, with which she was refreshed; the pain in her head but little, her stomach easy, and he found her in every respect better. The medicines were continued. July 13, in the morning, Mr. R. found her head easy, her water higher co- loured; she was allowed broth, and food of easy digestion, which agreed very well with her. She sat up in the afternoon, but was faint, and her head giddy; but when in bed she was better. She had no stool that day. The volatile me- dicines, &c. were continued with a purge the next morning. July 14, the purge worked 5 times; she eat a light dinner, and was easy; but on walking about the room, her head was giddy, and she trembled very much ; but when in bed, she was better. Mr. R. gave her a draught with sp. c. c. and tinct. castor. July 15, she complained, when up, of a numbness in her legs, and a pricking in them, like what happens when the legs are what we commonly call asleep: her appetite was better, and she was in every respect mended. Mr. R, then gave her some medicines composed of valer. castor, asafoetida, &c. The VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 17 blisters were kept running as long as could be; and when they were dried up, Julv 19, he gave her the same purge as before. July 22, she had continued very well, without any return of a fit; but on cutting an issue in her arm, she fell into a third fit, in which she continued near 1 hours; but then came to herself, and was well that evening. July 29 the purge was repeated. August 6 she complained of ,a pain in her head, sickness in her stomach, and some days before she had the menses, and had vomited near 1 lb. of blood, and was costive; Mr. R. then advised her to take 2 spoonfuls of tinct. sacra every, or every other night, going to bed, as she found it necessary, and 40 of the fol- lowing drops: R spt. c. c. opt. jiij. tinct. helleb. nigr, 3V. to be taken twice a day in camomile tea. She took these medicines about 3 weeks, which an- swered expectation, and he left her well. He saw her about 12 months after, and she told him she had continued very well ever since. Sennertus, Med. Pract. lib. 1. c. 30, says, that a catalepsy is so rare a case, that it is supposed hardly one physician in a hundred has seen a cataleptic patient; so that when this disease occurs, its history is carefully to be noted. Thoughts on the Operation of the Fistula Lacrymalis. By Francis Joseph Hunauld,* M. D. F. R. S. and Member of the Royal Academy of Sciences at Paris; in a Letter to Tho. Slack, M. D. N° 437, p. 54. Mr. H. omits giving the history of the fistula lacrymalis, of the different species of the distemper, or the various methods of treating it, as things suffi- ciently known; and only remarks that the intention in destroying theos unguis, and saccus lacrymalis, through which the tears naturally distil into the nose, is to procure them a new passage thither, by the hole thus artificially made. In order to keep the sides of this hole asunder, to prevent its filling up, and render the flesh, which forms its circumference, hard, and as it were callous, a tent made of prepared sponge, &c. is put into this new passage, where it is con- tinued a month or two. Notwithstanding this precaution, it happens but too often, that the tears, instead of keeping the road prepared for them with such care, flow over the lower eye-lid, as before the operation, and occasion a weep- ing, which is now become past remedy. It is easy to prove, that those very means, which are used after the operation to make the tears distil into the nose, are generally the cause of the subsequent • M. Hunauld succeeded M. du Verney in the anatomical professorship at Paris. He wrote a treatise on the bones of the cranium, besides various papers inserted in. the Memoirs of the French Academy of Sciences. He was possessed of a good collection of anatomical preparations, which was purchased by the academy after his death. This happened in 1742, when he was in his 41st year. His fort lay in osteology and the diseases of the bones. VOL. VIII. D 18 PHILOSOPHICAL TRANSACTIONS. rANNOl735. weeping; for by filling the wound with small pledgets, and putting a tent into the hole, the orifice of the little common canal, that serves to convey the tears into the lacrymal duct, sufl^ers a compressure, and is rendered hard, thick and callous; by which, as its diameter is very small, it is easily stopped up. The contusion made on this small orifice, and round about it, brings on a suppuration ; after which the parts coalesce, and the orifice of this small canal closes up. The pus or sanies, which in the course of the distemper flowed back, both through the common canal, and the small canals, which are a con- tinuation of the puncta lacrymalia, has sometimes occasioned excoriations; in consequence of which there happens a regeneration of flesh during the dress- ings, a small matter of which is sufficient to stop up such slender ducts. Indeed those small canals, through which nothing passes for a month or two, that the dressings last, either close by their own elasticity, or their diameters are lessened by their small vessels becoming varicose. It is true, that injections are some- times made through the puncta lacrymalia; but the propelling force of these injections overcomes those resistances, which the cause that naturally drives the tears into the puncta lacrymalia, is not in a condition to overcome. Thus it appears, from the detail of the accidents here enumerated, and which generally happen more or less, that while the artist is endeavouring to preserve a clear passage for the tears into the nose, he labours, without designing it, to stop the entry of the upper part of their canal. Mr. H. hopes to make appear, that the best way to avoid part of these accidents, and keep open the new canal from the eye to the nose, is precisely to do nothing. This is what experience has confirmed, and what theory too, well understood, will give us a clear con- ception of. It is not very easy to determine, how the tears, and the liquid that is conti- nually found on the surface of the eye, to preserve the cleanness and transpa- rency of the cornea, can pass through the puncta lacrymalia. It is also ob- served, that when we lie in bed, this liquid enters into those puncta lacrymalia, which in that position are higher than the eye, as well as into the puncta lacry- malia of the opposite eye. The ascent of liquors in capillary tubes above the level, might be proposed to explain this last fact. We might also in certain circumstances conceive the road which the tears keep, to pass from the eye into the nose, to be a syphon, the short leg of which is divided into two. It is strange that these two ideas, which strike by their simplicity, have never been oflTered by any one. It must be allowed however that they are not entirely sufficient to account for the phenomenon under consideration. The following rationale seems quite as simple, and more accurate. The air present at the orifices of all the ducts, which have any communica- VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. \Q tion with the trachea, is by its proper weight deteraiined to enter them, when the resistance happens to be diminished. Thus as, during inspiration, it passes through the mouth and nostrils, so it Hkewise enters the puncta lacrymalia; and must necessarily carry with il, towards these puncta and their small canals, the moisture that lubricates the surface of the ball of the eye, as it mixes with it. Therefore it is easy to perceive already, that to preserve to the tears their new and artificial road into the nose, we need only commit the whole care to the continual passage of the air and tears. It is well known in good surgery, that it is very difficult, not to say impossible, to effect a reunion in a part, that serves as an emunctory to a liquor constantly flowing to it. Now let us exan)ine, if nature alone can stop the hole made by the operation. It will not be imagined, that from the remains of a bony lamina, so thin as the OS unguis, a sufficient quantity of ossifying juice can work out to stop it up. The periosteum and saccus lacrymalis are too much lacerated, to think it possible for them to repair of themselves what they had lost. Nor will it be believed, that the membrana pituitaria can easily fill up the hole made in it. Those are the parts concerned in the operation : but even if they are granted to be more disposed to a re-production than they really are, still the air and tears will always be able to preserve themselves a passage into the nose. Therefore, after having destroyed the saccus lacrymalis and os unguis, in- stead of introducing an extraneous body capable of making the orifice of the small common canal into the ductus lacrymalis become callous, and of drawing on a suppuration, the communication between the nose and eye must be left entirely disengaged, and liberty by this means be given to respiration, to make both the air alone, and the air mixed with the tears, to pass continually through it. Also, the action of these fluids may be assisted by the application of col- lyriums, and by making frequent injections into the puncta lacrymalia ; which besides the common effects that may be naturally expected from them, will con- tribute to prevent the juice, that re-unites the wound made in the skin, from over-straitening the canal. On the Cause of the General Trade- Winds. By Geo. Hudley, Esq. F. R. S. N° 437, p. 38. Probably the causes of the general trade-winds have not been fully explained by any who have written on that subject, for want of more particularly and distinctly considering the share the diurnal motion of the earth has in their pro- duction. For though this has been mentioned by some among the causes of those winds, yet they have not showed how it contributes to their production ; D2 ''■•■^'"' ' '■ ■■'■ 20 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. or else have applied it to the explication of these phaenomena, on insufBcient principles. That the action of the sun is the original cause of these winds, it seems all are agreed ; and that it does it by causing a greater rarefactio-i of the air in those parts on which its rays, falling nearly perpendicular, produce a greater degree of heat there, than in other places ; by which means the air becoming specifically lighter than the rest round about, the cooler air will, by its greater density and gravity, remove it out of its place, and make it rise upwards. But it seems that this rarefaction will have no other effect, than to cause the air to rush in from all parts, into the place where it is most rarefied, especially from the north and south, where the air is coolest, and not more from the east than the west, as is commonly supposed. So that, setting aside the diurnal motion of the earth, the tendency of the air would be from every side towards that part where the sun's action is most intense at the time, and so a n. w. wind be produced in the morning, and a n. e. in the afternoon, by turns, on this side of the parallel of the sun's declination, and a s. w. and s. e. on the other side. That the perpetual motion of the air towards the west, cannot be derived merely from the action of the sun upon it, appears more evidently from this : if the earth be supposed at rest, that motion of the air will be communicated to the superficial parts, and by little and little produce a revolution of the whole the same way, except there be the same quantity of motion given the air in a contrary direction in other parts at the same time ; which is hard to suppose. But if the globe of the earth had before a rotation towards the east, this by the same means must be continually retarded: and if this motion of the air be sup- posed to arise from any action of its parts on each other, the consequence will be the same. For this reason it seems necessary to show how these phaenomena of the trade-winds may be caused, without producing any real general mo- tion of the air westwards. This will readily be done by taking in the considera- tion of the diurnal motion of the earth: for, let us suppose the air in every part to keep an equal pace with the earth in its diurnal motion ; in which case there will be no relative motion of the surface of the earth and air, and consequently no wind : then by the action of the sun on the parts about the equator, and the rarefaction of the air thence proceeding, let the air be drawn down thither from the N. and s. parts. The parallels continually enlarge, as they approach to the equator, and the equator exceeds the tropics, nearly in the ratio of 1000 to gi7 ; consequently their difference in circuit is about 2083 miles, and the sur- face of the earth at the equator moves so much faster than the surfiice of the earth with its air at the tropics. From which it follows, that the air, as it moves from the tropics towards the equator, having a less velocity than the parts of the earth it arrives at, will have a relative motion contrary to that of VOL. XXXIX.] PHILOSOPHICAL TKANSA.CTIONS. 2t the diurnal motion of the earth in those parts; which being combined with the motion towards the equator, a n. e. wind will be produced on this side of the equator, and a s. e. on the other side. These, as the air comes nearer the equator, will become stronger, and more and more easterly, and be due east at the equator itself, according to experience, by reason of the concourse of both currents from the n. and s. where its velocity will be at the rate of 2083 miles in the space of one rotation of the earth or natural day, and above 1 mile and -^ in a minute of time ; which is greater than the velocity of the wind is sup- posed to be in the greatest storm, which according to Dr. Derham's observa- tions, is not above 1 mile in a minute. But it is to be considered, that before the air from the tropics can arrive at the equator, it must have gained some motion eastward from the surface of the earth or sea ; by which its relative mo- tion will be diminished ; and in several successive circulations, may be supposed to be reduced to the strength it is found to be of. Thus it appears the n. e. winds on this side of the equator, and the s. e. on the other side, are fully accounted for. The same principle as necessarily ex tends to the production of the west trade-winds without the tropics ; the air rarefied by the heat of the sun, about the equatorial parts, being removed, to make room for the air from the cooler parts, must rise upwards from the earth ; and as it is a fluid, it will then spread itself abroad over the other air, and so its motion in the upper regions must be to the n. and s. from the equator. Being got up at a distance from the surface of the earth, it will soon lose great part of its heat, and thus acquire density and gravity sufficient to make it approach its surface again, which may be supposed to be when arrived at those parts be- yond the tropics where the westerly winds are found. Being supposed at first to have the velocity of the surface of the earth at the equator, it will have a greater velocity than the parts it now arrives at ; and thus become a westerly wind, with strength proportionable to the difference of velocity, which in several rotations will be reduced to a certain degree, as before said of the easter- ly winds, at the equator: and thus the air will continue to circulate, and gain and lose velocity by turns from the surface of the earth or sea, as it approaches to, or recedes from, the equator. To solve the phasnomena of the variations of these winds at different times of the year, and- different parts of the earth, would too far extend this paper. From what has been said it follows : 1. That without the assistance of the diurnal motion of the earth, naviga- tion, especially easterly and westerly, would be very tedious, and to make the whole circuit of the earth perhaps impracticable. 2. That the n. e. and s. e. winds within the tropics, must be compensated by as much n. w. and s. w. in other parts : and generally all winds from any one quarter, must be compen- 22 PHILOSOPHICAL TRANSACTIONS. [anNO 1735. sated by a contrary wind some where or other ; otherwise some change must be produced in the motion of the earth round its axis. jin Account, of the several Earthquakes ivhich have happened in New-England, since the first Settlement of the English in that Country, especially of the last Earthquake, Oct. IQ, \717* By Paul Dudley, Esq. F. R. S. N° 437, p. 63. That this country (New England) is subject to earthquakes, is certain ; many instances of which have occurred since the first settlement of the English here, which now is about 100 years. The first and most considerable earthquake in our history, and which seems to have been much like the last, was June 2, l638. This is said to have been " a great and fearful earthquake : it was heard before it came, with a rumbling noise or low murmur like distant thunder; it came from the north, and passed southward ; as the noise approached near, the earth began to quake ; and it came at length with such violence, as caused platters, tiles, &c. to fall down. The shock was so violent, that some per- sons without doors, could not stand, but were obliged to catch hold of posts, &c. In less than half an hour after, came another noise and shaking, but not so loud nor strong as the former : ships and vessels in the harbour were shaken, &c." In l658, there was another very great earthquake, but no particulars are related. In l66o, Jan. 31st, a great earthquake. In i6f)2, Jan. 26th, about 6 o'clock at night, there happened an earthquake, which shook the houses, caused the inhabitants to run out into the streets, and the tops of several chimnies fell down. About the middle of the same night was another shake ; also in the morning following the earth shook again. In l665, and in l668, and l66g, the earth was shaken. Since which we have also had several tremors of the earth, but not very considerable, till the terrible earthquake, Oct. 2g, 1727, which amazed and terrified the inhabitants from one end of the country to the other. Gilbertus Jacchaeus, in his Institutiones Physicae, cap. Terras Motus, distinguishes earthquakes iinto four species ; in which he agrees with Aristotle and Pliny, with whom the first species is a shake or trembling, which they com- pare to the shaking fit of an ague. Our motion of the earth was not that which Aristotle and Pliny call a pulse or an intermittent knocking, but one continued shake or trembling ; and therefore must be ranked under the first species, viz. a tremor or shake, without altering the position of the earth, * See another account of this earthquake in p. 348, Vol. vi. of these Abridgments. vol,. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 23 leaving all things in the same state, except the falling down of the tops of some chimnies, stone walls, &c. without dobrs; dishes and some other things within doors, &c. That this earthquake was of the first species, is also proved from the sound that accompanied it ; since tremulous and vibrating motions are proper to pro- duce sounds. The noise that accompanied, or immediately preceded it, was very terrible and amazing. Some people took this noise to be thunder ; others compared it to the rattling of coaches and carts on pavements, or frozen ground. One compared it to the shooting out of a load of stones from a cart under his window. Mr. Dudley himself, being perfectly awake, tliough in bed, thought at first the servants, who lodged in a garret over his chamber, were dragging along a trundle-bed : but indeed the noise that accompanies an earthquake seems to be sonus sui generis, and there is no describing it. This noise was instantly succeeded by a shake much more terrible. His house, which was large and well built, seemed to be pressed up together, as if a hundred screws had been at work to throw it down ; and every thing in the house, particularly the bed, and the building itself, shook so violently, that there was great fear it would have tumbled down. As to the degree of the shake ; this will be best known from its effects. Be- sides some circumstances before mentioned, a country farmer said he had 40 or 50 rods of stone wall thrown down by it; another person walking abroad at the time, could hardly keep his legs : another that was riding says, that his horse stood still, and, during the shake, trembled so that he thought he would have fallen under him : some dogs barked, others howled and made strange and unusual noises. Nor was the earth only affected with this shake, but the sea also in the harbours, and the shipping were much moved by it. The extent of the shake was felt from Boston to Kennebeck River to the eastward, and at Philadelphia to the westward, 1 60 leagues distant from each other on a w. s. w. and e. n. e. course nearest : and no part of the intermediate country, escaped it ; the colonies of Rhode Island, Connecticut, and New York being all affected, though not equally, particularly at Philadelphia they write, it was a small shock. A person at Boston, who had a well 36 feet deep, about 3 days before the earthquake, was surprised to find his water, which used to be very sweet and lympid, stink so that they could make no use of it ; and thinking some carrion had fallen into the well, he searched the bottom, but found it clear and good, though the colour of the water was turned wheyish or pale. In about ^ days after the earthquake, the water began to mend, and in 3 days more it returned 24 ' PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. to its former sweetness and colour. It was also credibly asserted, that several springs and good watering places were some of them lowered, and others quite sunk and lost by the earthquake. A divine, in a town about 20 miles distant from Boston, said, that immediately after the earthquake, there was such a strong smell of sulphur, that the family could scarcely bear to be in the house for a considerable time that night ; which is confirmed also from other places. Persons of credit also affirm, that just before, or in the time of the earthquake, they perceived flashes of light. A gentleman of probity, from Newbury, a town situate between 30 and 40 miles to the n, n. e. of Boston, writes, that at 40 rods distance from his house, there was a fissure of the earth, and near 20 cart-loads of fine sand thrown out where the ground brake, and water boiled out like a spring, and mixing with the sand, made a sort of quagmire ; but at the date of his letter, which was the 21st current, the spring was become dry, and the ground closed up again. It is also said, that the ground where this sand is thrown up, and round about it for a considerable distance, is a solid clay for 20 or 30 feet deep, and nothing like sand ever to be found there before; so that the exhalation forced this great quantity of sand through a very deep stratum of clay. Of an Extraordinary Effect of Lightning in communicating Magnetism. By Dr. Coohson of JVakefield in Yorkshire. N°437, p. 74. A tradesman at Wakefield in Yorkshire, having put up a great number of knives and forks in a large box, some in cases or sheaths, and others not, of different sizes, and of different manufactures, in order to be sent beyond sea ; and having placed the box in the corner of a large room, there happened a sudden storm of thunder, lightning, &c. by which the corner of the room was damaged, the box split, and many of the knives and forks melted, the sheaths being untouched. The owner emptying the box on a counter where some nails lay, the persons who took up the knives, that lay on the nails, observed that the knives took up the nails. On this the whole number was tried, and found to do the same, and that, to such a degree as to take up large nails, packing- needles, and other iron things of considerable weight. Needles or other things placed on a pewter-dish, would follow the knife or fork, though held under the dish, and would move along as the knife or fork was moved ; with several other odd appearances. Also, though the knives be heated red-hot, yet their power is still the same when cold. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 25 A further Account of the extraordinary Effects of the same Lightning at JVahe- Jield. By Dr. Cookson. N° 437, p. 75. This storm of thunder and lightning happened the latter end of July, 1731, and not only broke the glass and iron frames of the cross-chamber windows, but at the same time split some studs in the corner of a wood-house, and passing into a room, split likewise a large deal box, which stood in the south corner of the room, where the lightning entered, and dispersed a great many dozen of knives and forks, which were put up in the box, all over the room. On gathering up these knives and forks, some of them were melted, others snapped in sunder; others had their hafts burnt; others their sheaths either singed or burnt ; others not ; but what was most remarkable, on laying them on a counter where there were iron nails, rings, &c. it was observed, that when any of them were taken up, there hung a nail or ring at the end of each of them; most of them were tried, and found to do the same. , Query. The polarity of the compass has been altered by lightning, as is to be seen in the Philosophical Transactions: now how should lightning be capable of communicating such a power in this case, since it is plain that it has taken it away in another? The Description and Use of an Arithmetical Machine invented by Christian Ludovicus Gersten, F. R. S. Professor of Mathematics at Giessen. N° 438, P- 79- • Sir Samuel Morland was, it seems, the first who undertook to perforn) arithmetical operations by wheel-work. To this end he invented two different machines, one for addition and subtraction, the other for multiplication, which he published in London, in the year l673, in 12mo. He gives no more than the outward figure of the machines, and shows the method of working them. The last for multiplication, is merely an application of the Napierian bones on flat moveable disks; consequently his invention alone is not fit to perform justly all arithmetical operations. After him the celebrated Baron de Leibnitz, the Marchese Poleni, and Mr. Leupold, attempted to perform it after difi^erent methods. The first published his scheme in the year 1709, in the Miscellanea Beroli- nensia; giving however only the outer figure of the machine. Signor Poleni communicated his, but explaining at the same time its inner construction, in his Miscellanea of the same year 1709. Mr. Leupold's machine, with those of Mr. de Leibnitz and Signor Poleni, were inserted in his Theatrum Arith- VOL. VIII. E 26 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. metico-Geometricum, published at Leipzig in 1727, after the author's death, yet imperfect, as it is owned in the book itself. Besides these, the French journals show that Charles Pascal invented one. M. Gersten took, the hint of his from that of Mr. de Leibnitz, which put him on thinking how the inner structure might be contrived. The structure is then described, and the mode of performing the arithmetical operations; but the whole so intricate and operose, as incapable now of exciting any attention. Of the Figure of the Earth, and the Variation of Gravity on the Surface. By Mr. James Stirling, F. R. S. N° 438, p. 98. The centrifugal force, arising from the diurnal rotation of the earth, depresses it at the poles, and renders it protuberant at the equator; as has been lately advanced by Sir Isaac Newton, and long ago by Polybius, according to Strabo, in the second book of his Geography, But though it be of an oblate spheroid- ical figure, yet the kind of that spheroid is not yet discovered ; and therefore we may suppose it to be the common spheroid generated by the rotation of an ellipsis about its less axis; though by computation it appears, that it is only nearly, and not accurately such. Let us also suppose the density to be every where the same, from the centre to the surface, and the mutual gravitation of the particles towards each other to decrease in the duplicate ratio of their dis- tances; and then the following rules will follow from the nature of the spheroid. 1. Let adbe, fig. 5, pi. 2, be the meridian of an oblate spheroid, de the axis, AB the diameter of the equator, and c the centre. Take any point on the surface, as f, from which draw fc to the centre, fg, perpendicular to the surface at f, meeting cb in g, and fh cutting the line cg, so that ch may be to gh as 3 to 2. Then will a body at f gravitate in the direction fh ; and the mean force of gravity on the surface, will be to the excess of the gravity at the pole above that at p, as the mean diameter multiplied into the square of the radius, is to -J- of the difference of the longest and shortest diameters multiplied into the square of the co-sine of latitude at p. 2. The decrement of gravity from the pole to the equator is proportional to the square of the co-sine of latitude; or, which comes to the same, the incre- ment of gravity from the equator to the pole, is proportional to the sqaure of the sine of latitude. Hitherto we have considered the variation of gravity which arises from the spheroidical figure, while it does not turn round its axis ; but if it does, the direction of gravity will be in the line fg, perpendicular to the sur- face; and its variation now arising from both the figure and centrifugal force, will be 5 times greater than what arises from the figure alone; as will appear VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 1^ from the proportion of the lines ph and fg, the former being to the latter, as the whole force of gravity at p, while the spheroid is at rest, to the force with which a body descends at f, while it turns round its axis. 3. From this last article it appears, that \ of the variation of gravity is occa- sioned by the figure of the spheroid, and the remaining f by the centrifugal force. And whereas the earth could not be of an oblate spheroidical figure, unless it turned round its axis, nor could it turn round its axis, without put- ting on that figure; therefore the diminution of gravity towards the equator, known by the experiments with pendulums, prove both the rotation and oblate spheroidical figure of the earth. A. The mean force of gravity on the surface, is to the centrifugal force at any point f, as a rectangle under the radius and mean diameter, to a rectangle under the co-sine of latitude, and 4- of the ditFerence of the longest and shortest diameters. And at the equator, where the co-sine of latitude becomes equal to the radius, the mean force of gravity is to the centrifugal force, as the mean diameter to -f of the difference of the longest and shortest diameters. This ar- ticle is found from the proportion of the lines fh and gh ; the former being to the latter as the force of gravity to the centrifugal.force. 5. The proportion of the diameters of the earth will be found in the following manner: the moon revolves about the earth in 27'* 7*^ 43*", or in 39343 minutes: and her mean distance is about b<^\ semidiameters of the earth, according to La Hire's and Flamsteed's tables; but near 604- by Halley's tables. We shall therefore take 60 for the mean distance, till it be better known; then according to the nature of gravity, as the cube of the moon's distance is to the semidia- meter of the earth, or as 216000 to unity, so is 1547870000, the square of the periodic time of the moon, to 7^66, the squaje of the number of minutes in which another moon would revolve about the earth at the distance of its semidiameter. And as this last number is to 2062096, the square of 143(), the number of minutes in a sydereal day, so is unity to 287-7 5 which would show the proportion of the centrifugal force at the equator, to the mean force of gravity, by corol. 2, prop. 4, lib. J, Princip. were it not for the action of the sun on the moon. Therefore, by corol. 17, prop. 66, lib. 1, Princip. as the square of the sydereal year is to the square of the periodic time of the moon, that is, as 179 to unity, so is 287.7 to 1.6; which being added to 287.7 makes 289.3. And therefore, as unity to 289, neglecting the fraction, which is un- certain, so is the centrifugal force at the equator to the mean force of gravity on the surface. And thence, by article 4, as 28g to -f, so is the mean diameter to the difference of the longest and shortest ; and therefore, as the axis is to the equitorial diameter, so is 2307 to 2317, or in smaller numbers, as 231 to fi 2 28 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735, 232, the same as Sir Isaac Newton found in a different manner; for he makes it as 230 to 231, and as 230 to 231, so is 231 to 232.004. 6. In the same manner the proportion of the diameters of any planet may be found, if it lias a satellite; for instance, in Jupiter, he turns about his axis in 9*^ Sd™, or in 5q6 minutes: and his third satellite revolves about him in 7'' 3^ 42™ 36% or in 10302.6 minutes, at the distance of 1 5.141 of his semidiameters. Therefore, as the cube of 15.141 to unity, so is the square of 10302.6 to 30579, the square of the number of minutes in which a satellite would revolve about him at the distance of his semidiameter; and as this last number is to 355216, the square of 596, so is unity to I 1-f, or the centrifugal force at his equator, to the mean force of gravity on his surface. There is no need of correcting this number, as in the former article, because the periodic time of Jupiter round the sun is vastly greater than that of his third satellite round him. The third satellite is here chosen before any of the rest, because its greatest elongation was observed by Dr. Pound, with a micrometer adapted to a telescope 123 feet long; and he also took the diameter of Jupiter by the transit of the satellite, which is a much more exact way than with a micrometer. But as the planes of Jupiter's satellites almost coincide with the plane of his equator, the diameter, determined by the transit of the satellite, is his greatest; and the distance of the satellite, which ought to have been given in his mean diameters, is assigned in his greatest; for which reason the force of gravity already found, must be augmented in the triplicate ratio of his greatest diameter to his mean one; that is, if a represent the mean diameter, and d the difference of the longest and shortest, in the proportion of 2a + 3d to 2a very nearly. Hence, as the centrifugal force at his equator, is to the mean force ot gravity on his sur- face, so is unity to 1 l-f X -^ — • ■^"^' ^^ ^^^^^^^ ^t 1 '-f X •^-—- — : 1 :: a : ^d, or 20 aa = \%%ad + 27Qdd; which makes a to d, as 108 to 10; and hence the axis is to the equatorial diameter, as 108 — 5 to 108 + 5, or as 103 to 113; that is, as 12 to 13-J-; which agrees nicely with the observations of both Dr. Pound and Mr. Bradley, made with Huygens's long telescope; the former making it as 12 to 13, and the latter as 25 to 27, which is very nearly the same. And if this theory agrees so well with observations in Jupiter, there is no doubt but it will be more exact in the earth, whose diameters are much nearer to equality. 7. By experiments made at Jamaica, Philos. Trans. N° 432, in the latitude of 1 8°, with a very curious clock, contrived by Mr Graham, it was found that the London pendulum went slower there by 2"" 6% in a sydereal day, than at London. But it was found by experiments made with thermometers, that 9^ VOL. XXXIX.] PHILOSOPHICAL. TRANSACTIONS. 2Q were to be allowed for the lengthening of the pendulum by heat; and therefore it was retarded only 1"' 57* by the decrement of gravity. So that while a pen- dulum of London makes 86164 vibrations, the number of seconds in a sydereal day, the same at Jamaica gives only 86047 vibrations. Therefore the force of gravity at London, is to that in the latitude of 18°, as the square of 86 164, to the square of 86047 ; that is, very nearly as 1 106 to 1 103. And, by article 1 and 2, if a denote the mean diameter of the earth, d the difference of the greatest and smallest, then a will denote the force of gravity in general in any latitude, whose co-sine is to the radius as c to r; where, if instead of c there be substituted the co-sines of 51° 32' and 18°, that is, of the lati- tudes of London and Jamaica, we shall have the force of gravity at the former, to that at the latter, as a — 3870(i to a — Q045d, that is, as II06 to 1103. Hence the mean diameter of the earth, will be to the difference of the axis and equatorial diameter, as 191 to unity; and thence, by article 4, as the mean gravity on the surface, is to the centrifugal force at the equator, so is 191 to 4, or so is 239 to unity. In order to show that this cannot be, we may observe, that when the moon's distance was supposed 60 semidiameters of the earth, as in article 5, it was found that the mean force of gravity was to the centri- fugal force at the equator, as 28^ to J. But if the proportion now found be true, the moon's distance of 60 semidiameters must be augmented in the sub- triplicate ratio of 289 to 239, ^^^ then it will become 64 semidiameters. In like manner, if we compute the ratio of the mean force of gravity to the centrifugal force, by presupposing the magnitude of the earth, as Sir Isaac Newton and Mr. Huygens did, we must suppose a degree to be above 80 English miles, to bring it out 239 to unity. Now whereas it is certain that the distance of the moon is about 60 semidiameters of the earth, and that a degree is less than 70 English miles; therefore, that the conclusion, which seems to follow from the Jamaica experiment, cannot be allowed to be true. And the experiments made by Richer, in the island of Cayenna, would still make a greater difference between the diameters of the earth, than those made in Jamaica. And the lengths of the Paris and London pendulums compared together, would make it greater than -j-f,- part of the whole, as it was found in article 5. 8. From all the experiments made with pendulums, it appears that the theory makes them longer in islands than they are found in fact. The London pen- dulum should be longer when compared to the Paris one, than it really is; the Jamaica pendulum, when compared to the London one, which vibrates in a greater island, should be longer than is found by experience; and the pendulum in Cayenna, a smaller island than Jamaica, should be still longer. This defect 30 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. of gravity in islands is very probably occasioned by the vicinity of a great quan- tity of water, which being specifically lighter than land, attracts less in propor- tion to its bulk. And we find by computation, that the odds in the pendulums, between theory and practice, is not greater than what may be accounted for on that supposition. We may also observe, that though the matter of the earth were entirely uniform, yet the hypothesis of its being a true spheroid is not near enough the truth to give the number of vibrations which a pendulum makes in 24 hours. And suppose the true figure were known, the inequalities of mountains and vallies, land and water, heat and cold, would never allow theory and experiments to agree. But after the French gentlemen, who are now about measuring a degree, and making experiments with pendulums in the north and south, shall have finished their design, we may expect new light in this matter. Of the Mexican Filtering Stone. By Dr. Abraham Voter, F, R, S. &c. N° 438, p. 106. Abridged from the Latin. This stone has the name filtre from its porosity, by which it suffers liquors to pass through it : and for this reason pots and mortars are made from larger pieces of it, to strain liquors, particularly water to drink: for it is thought, that the water filtered through this stone is freed from all its impurities, and becomes clearer and purer, and more wholesome. Hence these stones are highly valued in Japan, and sold at the price of gold; because the Japanese, who know nothing of the stone or any other disorder in the kidneys, and who prefer health far before all other blessings, are of opinion, that these petrified fungi have the power of prolonging life. This species of fungus, it is said, grows on the rocks in some places of the gulph of Mexico, about 100 elns under water, and spontaneously hardens and petrifies in the air. Dr. Vater does not attempt to determine the origin of the filtre stone, nor its produc- tions, though both appear to be very suspicious, and invented only to prevent its being thought a common stone. For Lentilius writes that there are vessels made of two sorts of it ; one of a dark grey colour, like the lapis scis- silis from Canada, and sold at a dearer rate; and others of a tophaceous colour, of the growth of Italy. And, according to Le Clerc, in his physics, it is like- wise dug up in the bishopric of Liege, and much used in Holland. Dr. Ehrhart of Memmingen, presented Dr. Vater with a choice collection of fos- sils, among which was a tophus very porous, found about Memmingen, and which he was assured would strongly imbibe water. For, no sooner does it touch the surface of the water, but the water ascends, and is carried quite VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 3i through its porous substance, as in sugar, salt, filtering paper and sponge. This immediately suggested the hint, whether it might not be used instead of the Mexican filtre to strain water. He accordingly made a hollow in a little bit of it, and on pouring water into it, it strained very fast through the pores. He then took the tophaceous tubes of osteocoUa, and stopping one extremity, he poured water on it; when it transuded very fast through its porous substance. He also recollected that he had a sponge for several years, which when he lived at the Caroline bath, he had put in a pipe that conveyed the hot waters, and by this means the sponge being incrustated with the ochre, which the hot waters carry along with them and deposit in their passage, degenerated into a tophus: he made a pit in the sponge, and filled it with water, when it ran very fast through it. On this he resolved to make trial with a tophus of the hot bath, of which he had a pretty large piece ; and for this purpose he had it hollowed into a mortar, to see whether the water would pass through that dense and solid stone: and it answered his expectation; as the water strained through in the same manner as through the Mexican filtre and other tophi; but by reason of the density of the stone, slower than through more porous stones. Hence the Dr. thought, that the tophus of the hot baths is generated from the water depositing its ochre, in flowing through the pipes, and is in- sensibly concreted ; in like manner might the sea, beating on the rocks, deposit saline earthy particles, from whose successive concretion this stone is gene- rated, and rather grow on the rocks, than like rock-mushrooms, spring from them. But considering the remarkable density of the hot bath tophus, through which water filtrates, he had a mind to try the same experiment with the com- mon stone used in building. The success answered expectation : for, a mortar made of such stone served instead of the Mexican filtre, the water straining equally clear through both. The water strained in this manner acquired at first an earthy taste, which yet on repeated filtration it lost. As to the purifying quality of these filtres, the Dr. does not deny, but that muddy and slimy waters may, by straining through such stones, become clear and pellucid ; because these impurities do not dissolve in the water or inti- mately incorporate with it, but only float in it. But besides these, no other waters can by any means become purer, as he learned from repeated expe- riments, both with the filtre from Holland, and with those made from the tophus of the Caroline hot baths and common stone, on several kinds of river and spring water; and with an hydrometer examining their weight both before and after filtration, he found little or no difference. , , A -lol ?ii 33 PHILOSOPHICAL TRANSACTIONS. [anNO 1735. A Continuation of an Account of an Essay towards a Natural History of Ca- rolina and the Bahama /stands, by Mark Catesby, F. R. S. fVith some Extracts out of the Seventh Set. By Dr. Mortimer, R. S. Secret. N° 438, p. 112. This 7th set consists of the description of fishes. A Halo observed at Rome, Aug. 11, 1732. By Sig. De Revillas. N° 438, p. 118. From the Latin. 1 From 9 o'clock in the forenoon, till 2 in the afternoon, a simple halo was observed to surround the sun. It was exactly circular, and well defined; and its breadth equal to the sun's apparent diameter. The innermost colour was red; the rest pretty dilute, and analogous to those in the rainbow, but termi- nating in a whitish brightness. :ii Concerning an Ancient Date found at JVidgel-Hall in Hertfordshire. By Mr. John Cope. N° 439, P- ^ •O- Fig. 4, pi. 2, represents an ancient chimney-piece, as Mr. Cope was informed, found on pulling down part of Widgel-Hall in Hertfordshire. There is cut on it a date expressed part in Roman numerals, and part in Indian figures ; which is the earliest instance he has met with of the Indian figures being used here in England, viz. 99- l6, or I0l6; that at Colchester being in the year lOgO. See Philos. Trans. N° 266. The carving is very fair, the letter 31^ and the figure project out above a quarter of an inch. The whole chimney-piece is of English oak plank, and is now very firm, though T iS years old, and was never painted over; it is 4 feet S\ inches long; the part under the l6 was broken off in taking it down in August, 1733, when the house was on fire. ♦ * * Remarks on the foregoing Ancient Date, found at Widgel-Hall near Bunting- ford in Hertfordshire, on an Oaken Plank. By John Ward, Rhet. Pr. Gresh. and F. R. S. N° 439, P- 120. m April 4, 1734, a curious draught of an ancient date, carved in an oaken plank, at Widgel-Hall, the seat of Francis Gulston, Esq. was laid before the Royal Society, as the most early instance of our common figures, usually called Arabian, which had ever been observed in England. It was read 3l9l6, and thought to express the year 1016, the 2|B being taken for a Roman numeral, and the \Q for Arabian figures. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 33 Doctor Wallis had, in l683, communicated to the R. S. the draught of a mantle-tree, somewhat like this, which he saw at the parsonage-house at Helmdon in Northamptonshire. The date, which was likewise carved in mixed characters, expressed the year &} 133, as the Doctor read it. This being the oldest monument of that sort, which had then been discovered among us, was published first in the Philos. Trans. N" 154, and afterwards in the Doctor's Algebra, cap. 4, p. 14. In 1700, another draught of a date at Colchester, which had been sent to Dr. Wallis by Mr. Luffkin, who copied it from the under cell of a wooden window, and read the figures lOQO, being all Arabian, was printed likewise in the Transactions, N° 266, as more ancient than the former. None earlier than these last two had yet appeared, till that from Widgel- Hall. On the sight of this, Mr. Ward thought the reading given to it looked very plausible. The mixed characters were no just objection, which Dr. Wallis had accounted for in the Helmdon date, and Mr. Ward himself observed in some manuscripts. Yet one difficulty seemed to remain, which was the want of some character in the place of hundreds. And therefore soon after going into Hertfordshire, he took that opportunity to wait upon Mr. Gulston, in order to see the original. That gentleman afterwards informed him, by letter, that the house was always esteemed ancient : that before it was burnt, on the timbers there were several old coats of arms ; some were considered as belonging to the family of the Scalers, who were possessors of Widdihale, with other estates, soon after the conquest ; and at the time of the conquest it was in the possession of a considerable follower of Harold. Widdihale, in Hertfordshire, in the time of the Conqueror was parcel of the estate of Hardwin de Scalers, as appears by Domesday Book, fol. 141. It con- tinued in that family for several generations, till it came to Anthony Widvile, by the marriage of the daughter and heir of Scalers. But when he would not comply with Richard the Third to destroy the young Princes, all his lands were seized, and the manor continued in the crown, till Henry the Eighth granted it to George Canon and John Gill: George Gill, the son of John, marrying the daughter of George Canon, obtained the whole. In this family it continued till the beginning of the reign of James the First, when it was sold to John Goulston, Esq. whose descendants now hold it. The piece of timber was the top of a door-way, in a timber built house, and plastered over with mortar. From the date on the plastered wall, the door had not been used at least 343 years ; for on the outside was plainly to be seen the VOL. VIII. F 34 PHILOSOPHICAL TBANSACTIONS. [aNNO 1735. date 1390. Part of the room this was found in, was burnt too much to repair again. On considering the characters on this plank, and those of the other two dates mentioned above, with the accounts given by learned men of the time when the Arabian figures were first introduced into these parts of the world, and the various forms they have since received, as exhibited in fig. 4, pi. 1. Mr. Ward was at last satisfied, that none of these 3 dates prove they were ever used among us, in less than 100 years after the reading given to the latest of them. Most writers, who have treated of the use of these figures, have thought they came first from the Persians or Indians, to the Arabians, and from them to the Moors, and so to the Spaniards, from whom the other Europeans re- ceived them. This was the opinion of John Gerard Vossius, (De Natura Art. lib. iii, cap. 8, § 6,) Mr. John Greaves, (De Siglis Arabum et Persarum Astro- nomicis, p. 2, where the form of them may be seen,) Bishop Beveridge, (Arithmet. Chronolog. lib. i, cap. 5,) Dr. Wallis, (De Algebra, cap. 3, p. 10,) and many others. And the Arabians themselves acknowledge that they had them from the Indians, as both Dr. Wallis (Ibid. p. 9), and Mr. Greaves (De Siglis Arabum, &c.) have shown from their writers. But Isaac Vossius thought the ancient Greeks and Romans were acquainted with these figures, and that the Arabians took them from the Greeks, and the Indians from the Arabians, (Observat. ad Pomp. Mel. p. 64). For the proof of this he refers to Tyro and Seneca's Notes, (Vid. Grut. Inscript. vol. ii, ad fin.) and the treatise of Boethius De Geometria, (Lib. i, sub. fin.) But as to the notes of Tyro and Seneca, they seem to have no affinity with these figures, either in the number or nature of them ; for they are not limited to 9, but are many times that number, and all different in form. Nor are they simple signs of numbers, but complex characters of several letters of those numeral words which they stand for in the Roman language, like our short-hands ; and there- fore vary in their shape, as they are designed to express cardinals, ordinals, or adverbs of number. This will appear by the table of characters annexed to these papers, in which are given the first 10 of each. But as to what Vossius says concerning Boethius, Mr. Ward observed in a curious manuscript of that writer, now in the library of Dr. Mead, nine characters, which he says were invented and used by some of the Pythagoreans in their calculations ; while others of them made use of the letters of the alphabet for the same purpose. Boethius calls them apices vel characteres, (Lib. i, sub. fin.) These also are inserted in the table, to show the great affinity between them and the Arabian figures, as these latter were written two or three centuries since. VOL. XXXIX. ] PHILOSOPHICAL TRANSACTIONS. 35 The opinion of Daniel Huetius differed from either of the former ; for he imagined, the Arabian figures were only the letters of the Greek alphabet, cor- rnpted and altered by ignorant librarians, (Demonstrat. Evangel, prop. iv. c. 13, p. 17 '2.) From this summary account of the rise and antiquity of these figures, it seems probable that they might owe their original to the Greeks, those com- mon masters of all science, and passing from them first to the eastern nations, come round to these western parts, in the manner before described. We have no other author, who speaks of this matter, near so ancient as Boethius, whose words are very express, and much strengthened by the similitude of his cha- racters with the Arabian figures. And therefore we may rather suppose they took their rise from these, than from the small Greek letters, with which Huetius compared them ; since these latter are neither so like them, nor so old as the time of Boethius, And though what the Arabians say may be true, that they had them from the Indians, and not the Indians from them, as Isaac Vossius conjectured ; yet it may be equally true, that the Indians had them first from the Greeks, and those Arabian writers, who are not very ancient, not have known it ; nor are there any Indian monuments of sufficient antiquity to render this opinion questionable. >\;ii' But whichever of these suppositions may be esteemed the most credible, with respect to the origin of these figures ; Joseph Scaliger thought they were not received by the Europeans, as they came of later ages from the Arabians, long before the year 1300, (Lib. iii, Ep. 223.) But John Gerard Vossius, was of the opinion they began to use them about the middle of the 13th century, or the year 1250, (De Natur. Art. lib. iii, cap. 8, ^7-) Father Mabillon, in his treatise De Re Diplomatica, was necessarily led to attend to the use of these figures, particularly in dates. And he informs us, that they were rarely used before the 14th century, except in some few books of geometry and arithmetic. And presently after he says, it was not much to his purpose to treat of them, since he did not design to carry his work lower than the 13th century, (Lib. ii, c. 28, § 10.) By which he seems to intimate, that he had met with very few, if any, instances of Arabian figures, in such instru- ments at least, before the year 1 300. But no one appears to have examined this subject more carefully than Dr. Wallis ; who has off^ered some arguments to prove that Gerbert, a monk, who was afterwards advanced to the papal see, and took the name of Sylvester II, had before the year 1000 learned the art of arithmetic, as now practised, with the use only of g characters (whatever their form then was) from the Saracens F 2 36 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. in Spain, which he afterwards carried into France, (De Algebra, c. 4, p. 17). But the Doctor thinks those characters or figures were known for a long time after only to such artists, and principally used by them in astronomical calcula- tions ; the Roman numerals being still retained in common use to express smaller numbers, (Ibid. p. 1 1, 15, l6.) Nor has he given the figures used by any of those writers before Johannes de Sacro Bosco, who died in the year 1256; and Maximus Planudes, a Greek, who flourished after him ; which are here copied from him, in fig. 4. Mr. David Casley, in his Catalogue of the Manuscripts of the King's Li- brary, &c. has published a specimen of a manuscript from the Cottonian Library, called Calendarium Rogeri Bacon, (Plate xv.) and dated I2g2. The figures in this book are Arabian, and, as Mr. Casley says, the oldest that he remembers to have met with in either of those libraries: for which reason they have a place also in the table. It appeared exceedingly difficult, how to reconcile the opinions and observations of these several writers, concerning the first use of the Arabian figures in these western countries, with the time assigned even to the latest of the dates above- mentioned. And it could not but seem very strange, that no date of any writ- ing should have been produced in those figures, or any other use of them dis- covered (except perhaps in some mathematical calculations, or books of arith- metic) long before the 14th century ; and yet that a date should be found, so carved in a piece of wood, before the middle of the I'ith century, for so com- mon a purpose as the mantle-tree of a chimney. But on a closer examination of the characters, Mr. Ward found reason to think, this was not really the case ; and that instead of 1 133, they ought to be read 1233, what has been taken for a 1, being designed for a 2. This reading seems to be confirmed by the shape of the two 33 that follow it, from which, if the bottom curve towards the right hand (as it was often made formerly) was taken off, the upper part would make the 2. Which agreement between those figures is not only usual at present, but often found in manuscripts of the 14th and 15th centuries. Though sometimes indeed it is otherwise ; and the 2 has an angle at the top, when the 3 is round, which would not so well have suited this square hand. The reason which occasioned the carrying this date so high, has probably been the similitude between the small i over the preceding abre- viated word domini and this 2. And he believes this date may claim the pre- ference of being the oldest of the sort that has hitherto been discovered. The antiquity ascribed to the Colchester date, namely lOQO, has, it seems, been occasioned by a mistake in the copy ; for the 0 in the place of hundreds, should have been made a 4, by drawing down an oblique stroke on each side VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 37 from the bottom, which makes it 149O, before which time the 4 had long re- ceived that shape. As to the date from Widgel-Hall, which gave occasion to this inquiry, it seems plainly intended to express the year 1000, and no more, by the Roman ^ in the escutcheon on the right side. For the characters in the other escutcheon cannot, Mr. Ward thinks, stand for figures, but must be the initial letters of two names I. G. as W. R. in the Helmdon date ; and were very pro- bably designed in both to denote the persons who erected those buildings. The omission of a character in the place of hundreds, is still an argument, that these last two were not made for figures. But what seems to put the matter past all doubt, is the want of evidence that the figure 6 had received that form till some ages afterward : and when it was introduced, the upper part was not at first made so erect, as it is here, but carried in a small arch just over the top of the circle. On the other hand, what looks here like the modern 6, was at that time the usual form of the capital G. This Mr. Ward found fully con- firmed by a large collection of original grants, made by our ancient kings and others, and preserved in the Cottonian Library, (Augustus II.) On consulting these for half a century at least, both before and after the year IO16, the g is so written in a great number of them. For these reasons therefore he makes no question, but that character was designed for a g, and not a 6. And it is plain from other circumstances in Mr. Gulston's letter, that the building might very probably be as ancient as the year 1000; which renders this relic of it, considering how firm and sound it still is, a remarkable curiosity. The use which may be made of these observations, is this : that so far as yet appears, any coin, inscription, or manuscript, with a supposed date before the 13th century, expressed in Arabian figures, may be justly suspected either not to be genuine, or not truly read ; unless its antiquity be certain, from other clear and undoubted circumstances, and the date will bear no other reading ; and, if it be a copy, that it has been taken with exactness. Some Considerations on the Antiquity and Use of the Indian Characters or Figures. By Mr. John Cope. N° 439, p. 131. The ingenious invention of figures by the sagacious Indians, is of such vast importance in numbering, that it can never be too much admired, though now their use is become so familar among us, that very few consider what a loss the want of them would be to people of every station in life : for, to consider only, that such a number as not long before the conquest would take up a good arithmetician whole days to count by the literal characters, is now by the help 38 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. of figures commonly expressed by a child in a few minutes. This consideration of the vast use of figures, put Dr. Wallis, and others since him, on inquiring at what time they were first happily introduced into this island. Dr. Wallis informs us, that we had the figures from Spain, into which nation they were brought by the Moors. The Moors had them from the Arabians ; and the Arabians from the Indians. And it was the Doctor's opinion, that they were first brought into England about the year I J30; for that the first instance of their use which he had met with, was a date upon a chimney-piece, which date was St^ 133, the character S19 which the Romans used to express 1000, being mixed with figures, as Dr. Wallis observes, was often done at their first coming in ; and since that, in Philos. Trans. N° 266, is mentioned a date IO9O, all in figures. Lately too Mr. Cope produced a date on a chimney-piece at Widgel-Hall in Hertfordshire, which was fj^ 16, the 01 for the lOOO, being here again mixed with figures. And he now produces a still earlier instance of the use of figures in England, being a draught of an inscription over a gateway at Worcester, built, it is believed, in the reign of King Edgar, and is this (i')Xl> 97^, which is 158 years before the date of Dr. Wallis's, 41 years before that Mr. Ward produced last year, and is now 76O years standing. The account of this date Mr. W. had given him by Mr. Joseph Dougharty of Worcester, who is an in- genious and reputable person, and lives in the house over the gate-way on which this inscription is : he also said, that his house goes by the name of the oldest house m five counties ; and it is the current opinion there, and reported by the ancient people in that place, that the house was built by King Edgar, where they say he sometimes kept his court : and all historians agree that Worcester was then a very considerable bishopric ; and that Dunstan and Oswald, who were both successively bishops there in Edgar's time, were both his great favourites, especially Dunstan, for whom King Edgar had a very great regard : for it appears that the first thing Edgar did after he came to the crown, was to recall Dunstan from Flanders, where he had been 3 years in exile, and was immediately made prime minister, favourite, and confessor, as first bishop of Worcester, and afterwards Archbishop of Canterbury ; on which last pro- motion his great friend Oswald succeeded him in the See of Worcester : and it is very likely that either Dunstan or Oswald, as having so much power, interest and riches, might erect a building there, of which this gate-way might have been a part ; for as Edgar died in the same year 975, if we suppose the date to be fixed on the building the year it was finished, as is now commonly done, Edgar could not live or keep his court there, unless it was in some part of that year in which we suppose it to be finished. VOJL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 3p Remarks on the foregoing Ancient Dale, over a Gate-way, near the Cathedral, at Worcester. By John IVard, F. R. S. N° 439, P- 136. Mr. Ward having lately communicated to the Royal Society some remarks on an ancient date, carved in wood, that was found at Widgel-Hall near Buntingford in Hertfordshire, with the characters 21^ 1 6 ; which had been read 10l6, supposed to be mixed numbers, the 319 Roman, ^"d the two others Arabian or Indian, as they are indifferently called. This led him to consider two other dates of the like kind, formerly published in the Philos. Trans. ; one found at Helmdon in Northamptonshire, in mixed characters expressing, as was thought, iH^ '33; and the other at Colchester, said to denote the year lopo, wholly in Arabian figures. But on searching into the origin of those figures, and the time when they were first brought into these parts of the world, he could meet with no examples of them in any manuscripts, before some copies of Johannes de Sacro Bosco, mentioned by Dr. Wallis, who died in the year 1256, which was 123 years after the latest of the three dates above- mentioned. As it could not therefore but seem very strange, that workmen should have made use of those figures for such common purposes, so long be- fore they appear in the writings of the learned ; so on a closer examination, and further inquiry, he found there was no reason, from any of these dates, to suppose it was really true in fact. For the Helmdon date, instead of M) 133, should be read 21^233; the Colchester date 14gO, instead of JO9O; and that at Widgel-Hall has no Arabian figures in it, the characters 1 and 6 not being numbers, but the initial letters of two proper names I G, in the usual form of those letters in that age. But there had been soon after read before the Society, an account of a date at Worcester, more ancient than any of the 3 former; namely OtIOj or 97^, in which the unit is a Roman numeral, and the other two are taken for Indian figures. Now Mr. Ward observed in his former paper, that such mixtures were sometimes found in ancient numbers; though in what manner they were so used, he did not then explain, but for brevity contented himself with refer- ring to Dr. Wallis's Algebra. The Doctor thought it necessary to take notice of this, in order to account for his way of reading the Helmdon date, in which the a? only is a Roman numeral. And Mr. Ward had met with a few instances of it in Dr. Mead's manuscript of Boethius, as 00029 'Jnd docSs, where the hundreds are numeral letters, and both the decimals and units Arabian figures, (De Arith. lib, ii.) But it is observable, that this is not done promiscuously ; for the larger numbers are always letters, and the less figures ; as in the Helm- 40 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. don date. And MabUlon has observed, that in a curious manuscript copy of Thomas k Kempis, written in the 15th century, some of the pages are so numbered, (De Re Diplom. tab. xv.) Which method, so far as appears, was always attended to, and never in any one instance inverted. So that this Worcester date, which has a Roman numeral in the place of units, and the two preceding characters are supposed to be Indian figures, is not only without example, but directly contrary to all other instances of such mixed numbers. Which consideration alone might be of sufficient ground to think, there must be some mistake in the reading. But the middle figure, taken for a seven, is as remarkable ; which turning towards the left hand, forms two obtuse angles, one above, and the other be- low. This shape of the seven was never seen before, and seems by no means to suit that age. In the specimen of the figures taken from Johannes de Sacro Bosco, by Dr. Wallis, the figure seven is made in this form A, like the two legs of an isosceles triangle. And in Roger Bacon's Calendar, dated 12Q2, there is only this variation, that the leg to the left hand is somewhat shortened. And this form continued till printing was introduced among us ; as is evident from Caxon's Polychronicon, and other books printed about that time. Nor is it found till later times in any other shape ; unless that in Bishop Beveridge's table of Indian figures, the two legs of our ancient seven are drawn parallel, and arched at the top, instead of meeting in an angle; (Arith. Chron. lib. i, cap. 4.) and Planudes, a Greek writer, has kept the true Arabian form V, like the Ro- man five, which the Europeans inverted. The last alteration this figure re- ceived among us, was by raising the shorter leg horizontally. But no instance of it parallel to this in the Worcester date, or any thing like it, has before ap- peared. As there seems therefore no reason to suppose it a seven ; so a proba- ble conjecture may be offered, what it was designed for, and that is, the Roman numeral ten, which was made in this form, like an X ; to which character, in our old square hand, this supposed seven ^ would very well agree, by sup- plying only the two extreme parts to the right hand, in this manner X, which may easily be thought to have been decayed, and worn away by length of time. As there is no reason to take the middle character for seven, so neither is there any to suppose the first was intended for a nine, being thus placed before two Roman numerals, as Mr. Ward takes them both to be. It has indeed some similitude with that figure ; but that is nothing more than what was anciently, and still is, common to the letter OQ in that hand, which resembles a double Q, with an oblique stroke turned inwards from the bottom of that to the right hand ; so that if the other to the left be taken away, that which remains will appear in this form ^ > I'ke what is here called a nine. And every one knows. VOL. XXXIX.J PHILOSOPHICAL TKANSACTIONS. 41 who has any acquaintance with ancient inscriptions, that letters frequently perisl) in this manner, one part before another. Upon these suppositions the true reading would be mxv. But since the old date is now destroyed, and modern figures put in its place, this must remain uncertain. But tiiough the precise year of tliis date cannot now be determined with certainty, it is sufficient to have shown, that neither the order of the characters, their shape, nor the oldest examples of Arabian or Indian figures, any where found, do in the least countenance the reading given to it; but, on the contrary, all of them afford the highest probability, that it cannot be genuine. On the Description of Curve Lines. By Mr. Colin Maclaurin, Math. Prof. Edinb. F.R.S. N° 439, P- 143. Mr. Maclaurin was informed that some papers had lately been presented to the Royal Society, concerning the description of curves, in a manner that has a near affinity to that which he communicated to them formerly, and had carried farther since; and that it would not be unseasonable, nor unacceptable, if he should send an account of what he had done further on that subject since the year 17 IQ. The author* of those papers taught mathematics at Edin- burgh privately for some years, and some time ago, viz. in 1727» mentioned to Mr. M. some theorems he had on that subject; which, at the same time, Mr. M. showed him in his papers. Some time before that, he showed him a theorem which coincided with one of those in Mr. M.'s book, though he seemed not to have observed that coincidence ; and indeed methods of that kind, are often found coincident that do not appear such at first sight. Mr. M. is unwilling to be the occasion of discouraging any thing that is truly inge- nious, and renounces any pretensions of appropriating subjects to himself; but on the contrary, wishes justice may be done to every person, or to any per- formance in proportion to its merit ; yet finding it fit he should take precautions, lest any one should take it in his head afterwards to say, he takes things from him which he may have had long before him; and therefore Mr. M. sends the following abstract of what he had done in this matter since the year 1719. Mr. M. has so much on this subject by him, that he declares himself at a loss what to send; but at present he only gives an abstract of those propositions, which he takes to be more nearly related to those which this author has offered to the society from the conversations he had with him. In 1721, Mr. M. printed several sheets of a supplement to his book on the description of curve * Mr. Braikenridge. See p. 5, of this volume. VOL. VIII. G 42 I'HILOSOPHICAL TRANSACTIONS. [aNNO 1735. lines, which he hud not published, having been engaged for the most part in business of a different nature, and in pursuits on other subjects since that time. He first gives an abstract of that supplement, as far as it was then printed, and subjoins an account of some theorems he added to it the following year, viz. in 1722. He was led into those new theorems by Mr. Robert Simson's giving him at that time a hint of the ingenious paper, which has been since published in the Philosophical Transactions. Mr. M. had tried, in the year 17 ig, what could be done by the rotation of angles on more than two poles; and had ob- served, that if the intersections of the legs of the jingles were carried oyer right lines, as in Sir Isaac Newton's description, the dimensions of the curve were not raised by this increase of the number of poles, angles, and right lines; and therefore he neglected this at that time, as of no use to him, confining hiuiself to two poles only, and varying the motions of the angles as in his book. He found this by inquiring in how many points the locus could cut a right line drawn in its plane, and found, by a method often used in his book, that it could meet it in two points only. Having found then, that three or more poles, were of no more service than two, while the intersections were carried over fixed right lines; he thought it needless to prosecute that matter then, since by increasing the number of poles, his descriptions would become more complex, without any advantage. But in June or July, J 722, on the hint he got from Mr. Simson of Pappus's porisms, he saw that what he has there ingeniously demonstrated, might be considered as a case of the abovementioned description of a conic section, by the rotation of any number of angles about as many poles; the intersections of their legs in the mean time being carried over fixed right lines, excepting that of two of them which describes the locus. For by substituting right lines instead of the angles, in certain situations of the poles and of the fixed right lines, the locus becomes a right line; as for example, in the case of three poles, when these three are in one right line, in which case the locus is a right line, which is a case of the porism. It was this that led him to consider this subject anew; and first he demon- strated the locus to be a conic section algebraically ; and found theorems for drawing tangents to it, and determining its asymptotes. He also drew from it at that time a method of describing a conic section through five given points.* This encouraged him to substitute curves for the right lines, to see if by this method he could be enabled to carry on his theorems, about the descriptions of * The paper on this subject I have, says Mr. M. is dated July 31, 1722, at sea, being then in my way to London, going for Cambray. Orig. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 43 lines through given points, to the higher orders of lines. Some of the tiieo- rems he ft)un(l at that time accompany this. In November 1722, looking into Sir Isaac's Principia, he saw that the description of the conic sections by three riglit lines, moving as above, about three poles, could be immediately drawn from his 20th lemma, which itself is a case of this description. This gradually led him to seek geometrical demonstrations for the whole, as far as it related to the conic sections. He sent some leaves of this paper, dated at Nancy, No- vember 17 22. Since that time, he had not added much to this subject, but what relates to drawing tangents, determining the asymptotes, and the puncta duplica, or multiplicia of these curves. He considered it the less, as he did not find it more advantageous in any respect, than the method he had consi- dered in tiis book, nor more general. In 1727 lie added to a chapter in his algebra, an algebraic demonstration of the locus, when three poles are employed; and the method of describing a conic section through five given points, subjoining at the same time, that if more poles are employed, and angles or right lines, the locus was still a conic section ; which he thought was a remarkable property of the conic sections, not observed before. These things he intended to put in order, and publish in the supplement to his book, a part of which had been printed since the year 1 721. He intended also to give several other things in that supplement; two of which he only just mentions at present, as they are foreign to the present affair. He subjoins a problem determining the figure of a fluid, whose parts are supposed to be attracted to two or more centres; and a solution of a general problem about the collision of bodies. The author of the papers given in to the Royal Society will not deny, that Mr. M. showed him the theorems, now sent, in 1727. He owned it last sum- mer at least; Mr. M. intended to publish these very soon. Whether he has carried the subject farther, he leaves to the judgment of the gentlemen to whom they were referred. As to the demonstrations, it would take some time to put them in a proper form to be published. He could send those that are algebraic easily; but did not care to send those that are geometrical, till more leisure. An Abstract of ivhat has been printed since the Year 1721, as a Supplement to a Treatise concerning the Description of Curve Lines, published in 1719, and of what the ^-Juuhor proposes to add to that Supplement. By Mr. Maclaurin. N°439, p. 148. I. In the first part of the supplement, a general demonstration is given of the theorem, that if two lines of the orders or dimensions, expressed by the G 2 44 PHILOSOPHICAL TRANSACTIONS. [aNNO J 735. numbers m and n, be described in the same plane, the greatest number of points in which these lines can intersect each other, will be mn, or the product of the numbers which express the dimensions of the lines, or the orders to which they belong. II. In the next part, theorems are given for drawing tangents to all the curves that were described in that treatise by the motions of angles on given lines. Their asymptotes are also determined by more simple constructions than those which are subjoined to their descriptions in that treatise. Of these we shall give one instance here. Suppose the invariable angles, fig. 1 and 2, pi. 3, pcg, ksh, to revolve about the fixed points or poles, c and s. Suppose the intersection of the two sides OF, SK, to be carried over the curve bom, whose tangent at the point q is sup- posed to be the right line ae ; and let it be required to draw a tangent at p to the curve line described by p the intersection of the other two sides cg and sh. Construction. — Draw qt constituting the angle saT, equal to caA, on the opposite side of s«, that aA is from cq; and let qt meet cs, produced if neces- sary in t. Join pt, and constitute the angle cpn equal to spt, on the opposite side of cp, that pt is from sp; then the right line pn shall be a tangent at p, to the curve described by the motion of p, which is always supposed to be the intersection of cg and sh. The asymptotes of the curve, described by p. are determined thus. Find, as in the abovementioned treatise, when these sides become parallel, whose intersection is supposed to trace the curve; which always happens when the angle cas becomes equal to the supplement of the sum of the invariable angles fcg, KSH, to four right ones; because the angle cps then vanishes. Suppose, in fig. 3 and 4, that when this happens, the intersection of the sides of, sk is found in a. Constitute the angle saT equal to caA, as before, and let aT meet cs in t. Take cn equal to st, the opposite way from c that st lies from s. Through n draw DN parallel to cg or sh, which are now parallel to each other; then dn shall be an asymptote of the curve described by the motion of p. If instead of a curve line bqm, a fixed right line ae be substituted, then the point p will describe a conic section, whose tangents and asymptotes are deter- mined by these constructions. In this supplement, it is afterwards shown how to draw the tangents and asymptotes of all the curves which are described in the abovementioned treatise by more angles and lines. III. The same method is afterwards applied to draw tangents to lines described by other motions than those which are considered in that treatise ; of which the following is an instance. Suppose that the lines CP and sp, fig. 5, revolve VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 45 about the poles c and s, so that the angle acp bears always the same invari- able proportion to asp, suppose that of m to n. In the line cs, take the point T, so that ST may be to ct in that same proportion of ot to n; then this point T will be an invariable point; sin(;e cs is to ct. as ot — n to n. Draw tp, and constitute the angle spn, equal to cpt, so that pn and pt may lie contrary ways from sp and cp, and pn shall be a tangent of the curve described by the motion of the point p. Several other theorems of this kind are subjoined here. IV. After these, lines or angles are supposed to revolve about three or more poles, and the dimensions of the curves with their tangents and asymptotes are determined. Suppose in the first place, that the three poles are c, s, and d, fig. 6, and that lines or rulers ck, sq, qdr, revolve about these poles. The line which revolves about d, serves only to guide the motion of the other two, so that its intersection with each of them being carried over a fixed right line, their intersection with each other describes the locus, which is shown to be a conic section. The intersection of qdr with sq, is supposed to be carried over the fixed right line af ; the intersection of the same auR with cr, is supposed to be carried over the fixed right line ae ; and in the mean time, the intersec- tion of the right lines sa, cr, that revolve about the poles s and c, describes a conic section. This conic section passes through the poles c and s; and if you produce dc and DS, till they meet with Aa and ar in f and e, it will also pass through f and e: it also passes always through a the intersection of the fixed lines qf and ER; from which this easy method follows, for drawing a conic section through five given points. Suppose that these five given points are a, f, c, s, and e: join four of them by the lines af, fc, ae, es, and produce two of these FC, es, till they meet, and by their intersection give the point d. Suppose infinite right lines to revolve about this point d, and the points c and s, two of those that were given, and let the intersections of the line revolving about D, with those that revolve about c and s, be carried over the given right lines AE, af; then the intersection of those that revolve about c and s with each other, will, in the mean time, describe a conic section, that shall pass through the five given points a, f, c, s, and e. It is then shown, that when c, s, and d are taken in the saine right line, the point p describes a right line, fig. 7> as also when c, s, and a are in the same right line; which also follows from what is demonstrated in that very ingenious paper concerning Pappus's porisms, communicated by Mr. Simson, professor of mathematics at Glasgow, published in the Phil. Trans. N" 377. In the next place it is shown, that if four right lines revolve about four poles 46 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. c, s, D, and e, and those that revolve about d and e, serve only to guide those that revolve about c ands; so that a and h, the intersections of that which revolves about d, with those that revolve about e and s, be carried over the fixed lines ab and af; and m the intersection of that which revolves about k with that which revolves about c, be carried over a third fixed line bp; then the intersection p of those that revolve about c and s, will, in the mean time, de- scribe a conic section, and not a curve of a higher order. The conic section degenerates into right lines, when cp and sp coincide at the same time with the line OS, that joins the poles c and s, as in the preceding description ; which coincides again with what is demonstrated in the abovementioned ingenious paper. After this it is shown generally, that though the poles and lines revolving about them be increased to any number, and the fixed lines over which such intersections, as we described in the last two cases, are supposed to be carried, be equally increased, the locus of the point p will never be higher than a conic section; that is, let a polygon of any number of sides have all its angles, one only excepted, carried over fixed right lines, and let each of its sides produced, pass through a given point or pole, and that one angle, which we excepted, will either describe a straight line, or conic section. Thus, if a hexagonal figure lqrpmn, fig. 8, have all its angles, excepting p, carried respectively over the fixed right lines Aa, sb, og, nh, kIc; then the point p in the mean time will describe a conic section, or a right line. The locus of p is a right line when cp and sp coincide together with the line cs. All these things are demonstrated geometrically. V. After this, angles are substituted instead of right lines revolving about these poles; and it is still demonstrated geometrically, that the locus of p is a conic section or right line. Suppose that there are four poles c, s, d, and e, fig. 9, about which the in- variable angles pca, psk, rdm, meu revolve; and that a, m, and r, the inter- sections of the legs cq and eq, of em and dm, and of dr and sr, are carried over the fixed right lines Aa, sb, Gg, respectively; then the locus of p is a conic section, when cp and sp do not coincide at once with the line cs; but is a right line when cp and sp coincide at the same time with cs; and never a curve of a higher order. VI. Having demonstrated this, which seems a remarkable property of the conic sections, or lines of the second order; it proceeds to substitute curve lines instead of right lines in these descriptions, as is always done in the treatise concerning the description of lines, and to determine the dimensions of the locus of p, and to show how to draw tangents to it to determine its asymptotes. VO?.. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 4ij and other properties of it. Mr. Maclanrin had observed in 1719> that by in- creasing tlie number of poles and angles beyond two, the dimensions of the locus of p, did not rise above those of the lines of the second order, while the intersections moved on right lines; and therefore he did not think it of use then to take more poles than two, since by taking more, the descriptions be- came more complex, without any advantage. When the intersections are car- ried over curve lines, the dimensions of the locus of p rise higher, but the curves described have double, or multiple points, as well as when two poles only are assumed; and therefore this speculation is more curious than useful. How- ever, he subjoins some of the theorems that he found on this subject, con- cerning the dimensions of the locus of p, and the drawing tangents to it. 1. If, in fig. 6, you suppose q and r to be carried over curve lines, of the dimensions m and n respectively; then the point p may describe a locus of Imn dimensions. 2. If, in fig. 8, you suppose L, a, r, m, n, to be carried over curve lines of the dimensions wi, n, r, s, t, respectively; then the locus of p may arise to Qimnrst dimensions, but no higher; and if instead of lines revolving about the poles, you use invariable angles, the dimensions of the locus of p will rise no higher. 3. He then assumed 3 poles, c, d and s, (fig. 10) and supposed one of the angles snl, to have its angular point n carried over the curve an, while the leg NG passes always through s, as in the description in the treatise of the ge- neral description of curve lines, while the angles odr, rcp, revolve about the poles D and c : he supposes also the intersections a and r to be carried over the curve lines sa, gr, and that the dimensions of the curve lines an, Ba, gr. are m, n, r, respectively; and finds that the locus of p may be of Smnr dimensions; but that the point c is such, that the curve passes through it as often as there are units in 2mnr. 4. If any number of poles are assumed, so as to have angles revolving about them, as about c and d in the last article, and the intersections are car- ried over other curves, the dimensions of the locus of p will be equal to the triple product of the number of dimensions of all the curves employed in the description. 5. If the invariable angles pnr, pmg, (fig. 11 ) move so, that while the sides PN, PM, pass always through the poles c and s, the angular points n and M describe the curves an and bm; and at the same time, the invariable angle RDQ, revolve about the third pole d, so that the intersections r and a describe the curves er and go. ; then the dimensions of the locus of p, when highest, shall be equal to the quadruple product of the numbers that express the dimen- 48 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. sions of the given curves an, er, oa and bm, multiplied continually into each other. If more poles are assumed, about which angles be supposed to move, as RDQ moves about d in this description, and the intersections of the sides be still carried over curves, as in this example ; the dimensions, of the locus of p, when highest, shall still be found equal to the quadruple product of all the numbers that express the dimensions of the curves employed in this description. 6. Suppose that the three invariable angles pqk, klr, rnp, (fig. 12) move over the curves gq, el, an, so that the sides pq, kl, pn produced, pass al- ways through the poles c, d, s, and that the intersections of their sides k and R, at the same time move over the curves fk and br ; then the dimensions of the locus of p, when highest, shall be equal to the product of the numbers that express the dimensions of the given curves multiplied by 6. If more poles, with the necessary angles and curves, are assumed between c and d, as here D is assumed between c and s, and the motions be in other respects like to what they are in this example; then in order to find the dimensions of the locus p, when highest, raise the number 2 to a power whose index is less than the number of poles by a unit; add 2 to this power, and multiply the sum by the product of the numbers that express the dimensions of the curves employed in the description ; then this last product shall show the dimensions of the locus of p when highest. The author is able to continue these theorems much further : but it is not worth while, especially since there is not any considerable advantage obtained by increasing the number of poles, above the method delivered in the above- mentioned treatise, of the description of curve lines. On the contrary, the descriptions there given, by means of 2 poles, will produce a locus of higher dimensions by the same number of curves and angles, than these that require 3 or more poles; and are therefore preferable, unless perhaps in some parti- cular cases. 7. However, he has also found how to draw tangents to the curves that arise in all these descriptions : of which he gives one instance, where 3 right lines are supposed to revolve about 3 poles, and 2 of their intersections are supposed to be carried over given curve lines, and the third describes the locus required. Let the right lines ca, sn, dn, (fig. 13) revolve about the poles c, s, d ; where that which revolves about d, serves to guide the motion of the other two ; its intersection with ca moving oyer the curve oa, while its intersection with SN moves over the curve fn. Suppose that the right line ah touches the curve ca in a, and that the right line Aa touches the curve fn in n. In VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 4^ order to draw a tangent to the locus of p ; join dc, ds and cs, and constitute the ; ngle dqr, equal to cqb, so that gr lie the contrary way from gd that qb lies from gc, and let qr meet dc in r. Constitute also the angle dnt, equal SNA, with the like precaution, and let nt meet ds in t. Join kt, and produce it till it meet cS in h ; then join ph, and make the angle cpl equal to sph, so that PL and ph may lie contrary ways from cp and sp; then pl shall be a tan- gent at p, to the locus described by p, the intersection of cq and sn. Mr. Maclaurin has also applied this doctrine to the description of lines through given points. But he supposes he has said enough at present on this subject ; and concludes, after observing that in the abovementioned treatise, he has given an easy theorem, for calculating the resistance of the medium, when a given curve is described with a given centripetal force in a resisting medium, which he here repeats, because it has been misrepresented in a foreign Journal. Let V express the centripetal force with which the body that is supposed to describe the curve, is acted on the medium ; let v express the centripetal force with which the same curve could be described in a void ; suppose z = -, then the resistance shall be proportional to the fluxion of z multiplied by the fluxion of the curve ; supposing the area, described by a ray, drawn from the body to the centre of the forces, to flow uniformly. Let this theorem be compared with what the celebrated ma^iematician mentioned by that Journalist has given on the same subject, and it will easily appear what judgment is to be made of his assertion ; and since several persons, and particularly the gentleman men- tioned above in this paper, testify that Mr. Maclaurin communicated to them this theorem, before any thing was published on this subject by the learned mathematician he nauies, his observation on this occasion must appear the more groundless. From this theorem, the author draws this very general corollary; that if the curve is such as could be described in a void by a centripetal force, varying ac- cording to any power of the distance, then the density of the medium in any place, is reciprocally proportional to the tangent of the curve at that place, bounded at one extremity by the point of contact, and, at the other, by its intersection with a perpendicular raised at the centre of the forces to the ray drawn from that centre to the point of contact. Let al be the curve described by a force directed to the point s (fig. 14) ; let lt touch the curve at l, and raise st perpendicular to sl, meeting lt in t ; then the density in l shall be inversely as lt, if the resistance be supposed to observe the compound propor- tion of the density, and of the square of the velocity. Besides what is here observed, he proposes to illustrate and improve several VOL. veil. H 50 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735. Other parts of the treatise concerning the description of curve lines in this supplement. That treatise requires these additions and illustrations the more, that though the whole almost was new, it was published in a hurry, when the author was very young, before he had time to consider sufficiently which were the best ways of demonstrating the theorems, or resolving the problems, for which this supplement he hopes will make some apology. The following paper, dated at Nancy, Nov. 27, 1722, is that which the author mentions in his letter. Section I.— Pkop. 1. Which respects the Description of Lines. — About the poles c, b, d, (fig. 15) let the lines cd, Bm, nr be moved; and let the concourse of the legs sm, nr be drawn along the given line pg, and the con- course of the legs cd, nr along the given line pa; then the concourse of the legs cd, sd will describe a conic section. Draw rt parallel to the line bd given in position, meeting Bd in t; joint pt, producing it to meet bd in f ; and it will give the point f. For as the ratio of ru to rt is given, being the same as that of dg to db, because of the similar triangles omBG and rmta ; and since ru is to rt, as og to qf, the ratio of qf to ug will be also given ; so that, because of the given line qg, there will be given qp, and hence the point f and the line pf. Since there- fore Btand cr cut off the parts pt, pr, from the ITnes pf, pa, given in position, their intersection d will always be in a given ratio in a conic section, by Lem. 20, lib. \, Newton's Principia. If the point d be taken anywhere in the right line bf; and if dg be always to aG, as bd to qf ; the conic section will be the same as d describes. The conic section passes through c, p, b and a, by completing the parallelo- gram psav. It also passes through l, where the line bg produced meets pv, as also through k, where cd cuts the given line pg. Hence the pentagon pkclb is inscribed in the section. And if the 5 points ckpbl be given, through which the conic section is to be drawn, or if the conic section is to be cir- cumscribed about the given pentagon clbpk, let any 2 sides, ck, lb, be pro- duced to their intersection d ; then join the rest pl, pk, and let the intersec- tions of cd, Dr, and sd, dk, be silways drawn along those lines pl, pr ; then the intersection d will describe the section. Prop. 2. About the given points f, c, g, s, (fig. l6) as poles, let the lines FQ, cn, gq, sl be moved ; and let the intersections of the lines fq and cn, FQ and Ga, Ga and sl, viz. the points m, a, l, always touch the lines ae, BB, HL, given in position ; then the intersection of the lines cn, sl will describe a conic section. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 51 Let the lines am, hr meet bq in e and h. Join cf and gs, meeting in D ; join Da, meeting cm and sl in n and r : then if en and hr be joined, these will be lines given in position, by Lemma 1 . For since the points f, c, d, are in the same right line ; and the intersections of the lines fm, cm, and Fa, Da, run over given lines, the intersection of the legs cm, do will also touch the given one. And, for the like reason, since s, d, g are in the same right line, the intersection of do and sl will also touch the given one. Therefore, omitting the poles f, g, there is to be found the curve which the intersection p, of cn, sl, will describe, while by the lines cn, dn, sr, revolv- ing about the poles c, d, s, the concourse of the two cn, dn touches the given line en, and the concourse of the two sr, dn touches the given one hr; and that this is a conic section is plain from the foregoing proposition. Some Experiments relating to Electricity. By Mr. Stephen Gray, F. R. S. N°439, p. 166. Feb. 18, Mr. Gray tried what effect would be produced on several sorts of wood with respect to the luminous part of electricity : the wood was made into rods of the same form with those iron ones mentioned in a former letter on this subject ; the woods were fir, ash and holly ; these being successively disposed on electric bodies, after the same manner as the iron rods had been, the tube being applied to one end, there appeared a light on it, but not with so great a force, nor did the light extend to so great a length ; neither was the form of it conical, but rather cylindrical ; but its extremity seemed to consist of a short fringe of light ; when the light, that was given to the rod by the application of the tube, ceased, on a motion of the hand towards the point of the rod, the light came out again, as has been mentioned of the iron rods ; but when the hand or finger was held near the point of these wooden rods, there was no pricking or pushing of the finger felt, as when the iron rods were used. He had some of these rods made much larger at one end than the other, and now applying his finger to the larger end, there not only appeared a light, but the finger was pushed, especially when the holly rod was used, and the cheek was a little pricked, but the smart was not near so great as when the iron rods were used ; the large end of the rod was pointed with a much greater angle than the smaller one, yet there was very little, if any difference, in the form or size of the light from either end. Having procured two pair of lines made of worsted yarn, one of them of a mazareen blue, the other of a scarlet colour ; on the 3d of April, he sus- pended the boy first on the blue lines, and found that all the effects were the H 1 52 PHILOSOPHICAL TRANSACTIONS. ' [aNNO 1735. same, as when he was suspended on lines of blue silk. He then suspended him on the scarlet lines ; but now, though the tube was as well excited, and the experiment often repeated, yet there was no effect produced on him, either of attraction of a pendulous thread, nor of pricking nor burning, by apply- ing a hand near him : one of the iron rods being then first on the blue lines, all the same effects were exhibited, as when the same rod had been laid on silk lines of that colour; but on laying the same rod upon the scarlet lines, no manner of attraction, &c. was perceived. In the Philos. Trans. N° 422, Mr. Gray gave an account of the experiments made on the communicative electricity of water, and found that water is at- tracted by the tube ; with several remarkable circumstances with which this attraction is attended ; but he has now found, that when the stand with those little ivory cups there mentioned, are set on any electric body, the same phae- nomena are produced, not only by holding the tube near the water, but when that is removed, and the tip of the finger placed over the water, viz. there is a little hill, or protuberance of water of a conical form, from the vertex of which proceeded a light and a small snapping. May the 6th, was made the following experiment. The boy being sus- pended on the silk lines; and the tube being applied near his feet, as usual; on holding the end of his finger near a gentleman's hand, that stood on a cake made of shell lack and black rosin ; at the same time another gentleman stand- ing at the other side of the boy with the pendulous thread; the boy was then bid to hold his finger near the first gentleman's hand, on which it was pricked, and the snapping noise was heard; and at the same time the thread, which was by its attraction going towards the boy, fell back, the boy having lost a great part of his attraction; on a second moving his finger to the gentleman's hand, the attraction ceased: then the thread being held near that gentleman, he was found to attract very strongly; but having since repeated this experi- ment, though the attraction of the boy is much diminished, yet he does not quite lose it, till 2, 3, and sometimes 4 applications of his finger to the hand of him that stands on the electric body, but without touching him. At another time three persons stood, one of them on a cake of shell lack, &c. the other on one of sulphur, the third on a cake of bees-wax and rosin ; the persons all holding hands, the boy applying his finger near the first man's hand, they all three became electrical, as appeared by the attraction of the thread, when held near to any of them. June the 10th in the morning, were repeated the experiments with the wooden rods, the most material of which were made with the holly rod : this being laid on the glass cylinder, and a fir board, about a foot square and ,v of / VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 53 an inch thick, being placed erect on a stand, set on another glass cylinder, so that the centre of the board was placed near the point of the rod, but not to touch it by near i- inch ; then the tube being held near the thick end of the rod, there issued out a light from the small end, which was that next the board; and it came along with a hissing noise, and struck against the board : when the boy touched the board, there was a light ; and at the same time another on the end of the rod, but he heard no snapping nor pricking of his finger, as when the brass plate and iron rod were used. Experiments with the Scarlet and Blue Worsted Yarn repeated. — When the boy was suspended on the scarlet lines, he attracted the white thread at a very small distance ; but the attraction ceased in about 6 or 7 seconds of time. Then the boy being taken off, an iron rod was laid on the lines, but there was no attraction of the thread by the body of the rod; but when the thread was held near either of its pointed ends, it showed a small repulsion, and in the dark a very small light was seen at each end of the rod. When the boy was suspended on the blue lines, he attracted the thread to him when it was held at least a foot from him, and he continued his attrac- tion to near 75 seconds, the iron rod continued its attraction not more than 36 seconds. When he was suspended on the blue lines, he continued his attraction 50 minutes, on the scarlet lines 25 minutes, on the orange coloured lines 21 minutes. By these experiments we see the efficacy of electricity on bodies sus- pended on lines of the same substance, but of different colours, and also that the attraction continues much longer on silk than on yarn, and consequently silk is the properest body we can make use of, to suspend those bodies on, to which we would communicate an electricity. An Account of the Births and Burials, with the Number of the Inhabitants at Stoke- Damerel, Devonshire. Communicated by the Rev. Mr. fVm. Barlow.. ]S° 439, p. J7I. On taking a survey, about Michaelmas 1733, of the inhabitants of Stoke- Damerel, in the county of Devon, the number of persons, men, women, and children, residing in the parish, amounted to 336l. By the register, it appears that in the same year, 28 couples were married, 61 males and 61 fe- males baptized, and 61 people buried. Whence it appears that the number of persons who died, is only one more than half the number of children born ; and that about 1 in 54 died. 54 VHILOSOPHICAL TRANSACTIONS. [aNNO 1736. An extraordinary Case of the Foramen Ovale of the Heart, being found open in an Adult ; communicated by Claudius Amyand, F. R. S. N° 439, p. 1 72. A person dying at the age of 22, of an illness that had perplexed his phy- sicians, was opened, to discover an imposthume, which was apprehended in the belly. As nothing was observed there worth notice, excepting a great re- laxation of the viscera, the cause of his death was looked for in the thorax ; there the lungs were strongly attached to the pleura on each side, and a large collection of water in each cavity, especially on the left, where the pos- terior lobe was inflamed, and tending to suppuration; the quantity of water in the pericardium was greater than usual, and the heart much larger than could be expected in so great an atrophy as the patient was reduced to ; in it the foramen ovale was found open, so as to give passage to a large finger, when a fungous substance, which grew from the circumference of the foramen, and stopped up the same, was removed. The valve was hardly perceptible, it being callous and furled up. The ductus arteriosus was found close as usual. This patient had enjoyed great health till lately, and had given no sign of this opening of the foramen ovale, which is preternatural in adults. A Catalogue of the Fifty Plants from Chelsea Garden, presented to the Royal Society hy the Company of Apothecaries, for the Year 1734, pursuant to the Direction of Sir Hans Sloane, Bart. P.R.S. By Isaac Rand, F.R.S. N''440, p. 173. This is the 13th catalogue of this collection, completing 650 plants. The Apparent Times of the Immersions and Emersions of Jupiter's Satellites, which will happen in the Year 1737. Computed to the Meridian of the Royal Observatory at Greenwich. By James Hodgson, F. R. S. N" 440, p. 177. Another repetition of the catalogue of these eclipses, pre-computed, and published for the accommodation of gentlemen intending to make observations on them. A Proposition relating to the Combination of Transparent Lenses with Rejecting Planes. By J. Hadley, Esq. V. Pr. R. S. Communicated Jan. 9, 1734. N°440, p. 185. Having proposed the use of a telescope with the instrument for taking angles vol.. XXXIX.3 l-HILOSOPHICAL TRANSACTIONS. 55. which Mr. Hadley formerly laid before this Society, (See N° 420) it gave oc- casion to consider the effects of combining several kinds of telescopes with re- flecting planes, and, among others, led to the following proposition : That if two lenses, of equal focal length, be put together in the form of a telescope, and a plane speculum be placed before one of them, so that the axis of the telescope make any angle with its surface, and a ray of light, the line of whose direction lies in a plane perpendicular to that surface, and passing through the axis of the telescope, fall on it, and be reflected from it, so as to pass through the telescope ; then the line of its last direction, after passing the telescope, will make an angle with that of its first direction, before its incidence on the speculum, very nearly equal to double the angle made between the axis of the telescope, and the surface of the speculum. Lemma. — Let the line fg be the common axis of the two lenses id and ke, of equal focal lengths, fig. 6, pi. 1 ; to which let the lines ad, db and be, be each equal ; and let a ray of light, issuing from a point in the axis p, fall on the lens id at i, and be there refracted into the line ig, cutting the axis in g, and meeting the lens ke in k ; where let the ray be again refracted into the line KH, cutting the aforesaid axis in h : the angles ipd and khe are very nearly equal, Demonstr. — It is known from dioptrics, that the lines pi, I6, kh, and fg, are all in the same plane ; and by the construction the lines ad, db, and be are equal ; and by prop. 20 of Huygens's dioptrics, the lines fa, pd, and fg are continually proportional ; consequently fa is to ad as pd to dg ; and dividing, PA is to AD as PD — pa (= ad) is to DG — AD (= bg). Therefore ad is to bg as FD to dg. By the same prop, the lines bg, eg, hg are also continually proportional, and be (=: ad) is to bg, as eh is to eg. Hence it follows, that the lines pd, dg, and eh, eg, are proportionals. But pd is to dg, as the tangent of the angle igd or kge, to the tangent of the angle ipd ; and eh is to eg, as the tangent of the angle kge to the tangent of the angle khe. The tangent of the angle kge therefore has the same ratio to the tangents of each of the angles ifd and khe, and consequently those angles are equal, a. e. d. In the demonstration of the above-cited proposition of Hiiygens, the thick- ness of the lenses are neglected, and the distance of the points i and k, from the line fg, supposed very small ; so that if either of those are too great, there may arise a sensible difference between the angles ifd and khe. Let DP and cg, fig. 7> represent the two lenses, put together as before, having their common axis in the line bl ; and bn a plane speculum, to which that line is inclined in the angle ghn ; and let ab be a ray of light falling on the speculum at b, as is before expressed, and let it be there reflected towards 56 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. the point c of the lens cg, where it is refracted towards the point d of the lens DF, and there again refracted into the line de, cutting the axis in k. The angle AOP contained between this last line de, continued backward, and the first line of incidence of the ray ab, will be very nearly equal to double the angle of in- clination of the axis of the lenses el, to the plane of the speculum bn ; i. e. double the angle ghn. Demonslr. — Produce the lines of incidence and reflection of the ray ab and BC, till they meet the axis of the two lenses in i and l ; and through the point B draw BK perpendicular to the plane of the speculum, and cutting the same axis in k; then the angles kbl and kbi are equal. The angle klb is the differ- ence of the angles ikb and kbl ; and the angle hib is the sum of the angles ikb and KBI = to KBL : therefore the angle ikb is equal to half the sum of the angles hib and klb. But by the foregoing lemma, the angles klb and fed are very nearly equal. Therefore the angle ikb is nearly equal to half the sum of the angles hib and fed ; that is, to half the angle pob ; and its complement bhi or GHN is nearly equal to half the angle aop, the complement of pob to a semi- circle, a. E. D. If the first incidence of the ray be supposed to be in the line ed, it will pro- ceed in the same track as before, but with the contrary directions ; so that the angle eob made between the first incident ray, and the last reflected, will still be equal to the double of ghn, as before. It is evident that on this principle an instrument might be constructed, the effects of which would in a great measure resemble those of that before-men- tioned (N° 420) : but it would be liable to the errors arising both from the spherical figure of the lenses, and also the different refrangibility of the rays of light, when the object is seen at a distance from the axis of the telescope ; though those errors, by a proper disposition of the parts of the instrument, may be reduced to a very small quantity. However, for this reason, and also be cause the instrument seemed to be attended with greater inconveniencies, both in its construction and use, than the other, Mr. Hadley did not think it neces- sary to give any more particular description of it. Of a large Bony Substance found in the fVomb. By Edward Hody, M. D., F.R.S. N°440, p. 189. In examining the pelvis of a woman, 57 years of age. Dr. H. found a large bony substance, contained in the womb, and so strictly united to it, that they seemed to be one and the same body. On cutting the substance asunder, he observed, that the ossification went no farther than the thickness of a shilling; VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. fl/ the part immediately under the ossification was like firm flesh, and this flesh was softer and softer the nearer to its centre. He thinks it unnecessary to remark, that the woman never had but 1 child, of which she was delivered about 1^ years before she died. Her chief complaints, for some years, were a short cough, great difficulty in breathing, frequent uneasiness in making water, or in going to stool, and a constant weight, or bearing down, on the parts of generation. But the immediate cause of her death was an asthma; for she had only one lobe of the lungs left that was perfectly sound ; the rest adhered firmly to the pleura, were very much contracted, and in some places scirrhous. i Experiments concerning the Impregnation of the Seeds of Plants. By James Logan, Esq. N° 440, p. iQ2. As the notion of a male seed, or the farina foecundans, in vegetables, is now very common, Mr. Logan only mentions such observations concerning it, as may have some tendency to that subject. And first it appears, from Miller's dictionary, that M. GeofFroy, from the experiments he made on maize, was of opinion, that seeds may grow up to their full size, and appear perfect to the eye, without being impregnated by the farina, which possibly may in some cases be true ; for there is no end of varieties in nature. But in the subject he has mentioned Mr. L. believes it is otherwise, and that Mr. G. applied not all the care that was requisite in the management. In the spring Mr. Logan resolved to make some experiments on the maize, or Indian corn. In each corner of his garden, he planted a hill of that corn, and watched the plants when they grew up to a proper height, and were push- ing out both the tassels above, and ears below ; from one of those hills, he cut off the whole tassels, on others he carefully opened the ends of the ears, and from some of them cut or pinched off all the silken filaments ; from others he took about half, from others ^ and ^, &c. with some variety, noting the heads, and the quantity taken from each : other heads again he tied up at their ends, just before the silk was putting out, with fine muslin, but the fuzziest or most nappy he could find, to prevent the passage of the farina; but which would obstruct neither sun, air nor rain. He fastened it also so very loosely, as not to give the least check to vegetation. The consequence of all which was this ; that of the 5 or 6 ears on the first hill, from which he had taken all the tassels, from whence proceeds the farina, there was only one that had so much as a single grain in it, and that in about 480 cells, had but about 20 or 21 grains ; the heads, or ears, as they stood on VOL. VIII. I 58 PHILOSOPHICAL TRANSACTIONS. [aNNO 1 736. the plant, looked as well to the eye as any other ; they were of their proper length, the cores of their full size, but to the touch, for want of the grain, they felt light and yielding. On the core, when divested of the leaves that cover it, the beds of seed were in their ranges, with only a dry skin on each. In the ears of the other hills, from which he had taken all the silk, and in those that he had covered with muslin, there was not so much as one mature grown grain, nor other than as mentioned in the first : but in all the others, in which he had left part, and taken part of the silk, there was in each the exact proportion of full grains, according to the quantity or number of the filaments left on them. And for the few grains found on one head in the first hill, he immediately accounted thus : that head, or ear, was very large, and stood prominent from the plant, pointing with its silk westward directly to- wards the next hill of Indian corn ; and the farina, he knew, when very ripe, on shaking the stalk, will fly off in the finest dust, somewhat like smoke. He therefore judged that a westerly wind had wafted some few of these particles from the other hill, which had fallen on the styles of this ear, in a situation well fitted to reieive them, which none of the other ears, on the same hill, had. Mr. Logan is positive, by his experiment on those heads, that the silk was taken quite away, and of those that were covered with muslin, none of the grains will grow up to their size, when prevented receiving the farina to im- pregnate them ; but appear, when the ears of corn are disclosed, with all the beds of the seeds, or grains, in their ranges, with only a dry skin on each, about the same size as when the little tender ears appear filled with milky juice before it puts out its silk. But the few grains that were grown on the single ear, were as full and as fair as any ever seen ; the places of all the rest had only dry empty pellicles, as described ; and probably the same holds generally in the whole course of vegetation ; though it may not be safe to pronounce absolutely upon it, without a great variety of experiments on different subjects. But there are few plants that will afibrd so fine an opportunity of observing on them, as the maize, or Indian corn ; because its styles may be taken off or left on the ear, in any proportion, and the grains be afterwards numbered in the manner abovementioned. ^Some Observations of the Eclipses of Jupiter s Satellites, made by Geo. Lynn, Esq. at Southwick, Northamptonshire. N° 440, p. 1Q6. The account of these eclipses is of no use now. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 5Q Concerning the High Tide in the River Thames, on Feb. J 6, 1735-6. By Mr. Tho. Jones N" 440, p. IQS. Mr. Jones having in a former Number given an account of the tide's flowing on the 8th of March, 1725-6, which then flowed 20 feet 5-j- inches, as he took it by a level from that high water mark to low water the next morning, and was 4 inches higher than had been known for 40 years before. He now adds, that having marked that high tide on a post, on Monday the l6th instant, (Feb. \(), 1736) the tide rose at the same place 6^ inches above that mark, and flowed near 2 feet the last half hour but one before high water. If the tide had flowed its full time, it would have flowed half an hour longer, and would have drowned the whole level. A Singular Cutaneous Affection, By Ahr. Vater, M. D. Professor of Anatomy and Botany in the University of fVittemberg and F.R.S. An Abstract from the Latin. N° 440, p. IQQ. In the Phil. Trans. N^ 424,* a history is given of a very uncommon case of diseased skin, occurring in a young labourer. A case parallel to this occurred in Germany in a young girl, who had been previously affected not only with swellings of the limbs and body (to which various domestic and empirical reme- dies had been applied) but also with a large, hard tumor between the shoulders, which was removed by discutient applications. But after the discussion of these tumours, a dry and hard crust or scab began to form, on the feet and hands, especially in the soles of the feet and palms of the hands, and this incrustation projected so much from the ends of the fingers and toes, that the patient could neither lay hold of any thing nor walk. The incrustation scaled off at intervals, especially after the use of various ointments ; but at such times the girl was always ill, being swelled in her body, and troubled with a sense of oppression, and griping pains of the bowels, which symptoms continued until the incrusta- tion was removed. She was at length cured by laxative mercurial medicines, and decoctions that purify the blood. Examined by the microscope, the in- crustation appeared to be nothing more than the cuticle expanded and in- durated. Dr. V. was informed of another similar case occurring in a young wo- man, likewise a German, whose hands and feet, with the fore-arm, were covered with a crust or scab, which scaled ofl^ twice a year, and resist'^d all the. remedies which had then been tried. This patient laboured under an ob- * Vol. vii, p. 543 of these Abridgments. I 2 60 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. struction of the menses, which was supposed to give rise to the diseased state of the skin. Experiments on the Vibrations of Pendulums. By the late W. Derham, D. D. F.R.S. N°440, p. 201. The account Mr. Bradley gave in Philos. Trans. N°432, of observations made at Jamaica by Mr. Campbel, with a nice pendulum-clock of Mr. Graham's making, brought to mind some experiments Dr. Derham made some years be- fore, which may be of use in observations of this nature. The first he notices are some experiments made in the year 1 704, with ex- cellent instruments, on the vibrations of pendulums in vacuo ; which were published in the Philos. Trans. N° 294. The sum of which is, that the vibra- tions in vacuo were larger than in the open air, or receiver unexhausted : also that the enlargement or diminution of the vibrations, was constantly in pro- portion to the quantity of air, or rarity, or its density, left in the receiver of the air-pump. And as the vibrations were larger or shorter, so the times were augmented or diminished accordingly, viz. 2 seconds in an hour slower, when the vibrations were largest, and less and less, as the air was re-admitted, and the vibrations shortened. But notwithstanding the times were slower, as the vibrations were larger, yet he had reason to conclude, that the pendulum really moved quicker in vacuo, than in the air, because the same difference, or enlargement of the vibrations, as -^ of an inch on a side, would cause the movement, instead of 2 seconds in an hour, to go 6 or 7 seconds slower in the same time ; as he found by nice experiments. The next experiments he made at several times, in 1705, 1706, and 17 12, by the help of a good month-piece, that swings seconds. The weight that then drove it, was about 12 or 13 pounds, and it kept time exactly by the sun's mean motion : but by hanging on 6 pounds more, the vibrations were enlarged ; but yet the clock gained 13 or 14 seconds in a day. And as the increase or diminution of the power that drives the clock, ac- celerates or retards its motion, so doubtless does cleanness or foulness affect it, as also heat and cold ; for all have the same effect on the jiallets and pendulum. The last experiments he made in 1716 and 17 18, to try what effects heat and cold had on iron rods of the same length, or as near as he could to those that swing seconds. He made many experiments with round rods of about a quarter of an inch diameter, and with square rods, of about three quarters of an inch square. The effects on both which were the same. / VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 6l At first he took the exact length of the rods, in their natural temper. Then he heated them well in a smith's tire, from end to end, nearly to a flaming heat; by which means they were lengthened -i^ o( an inch. Then he quenched them in cold water; which made them y^ of an inch shorter than in their natural state. Then he warmed them to the temper of his body; by which means they were about -j-i-5- of an inch longer than in their natural temper. Afterwards he cooled them in a strong frigorific mixture of common salt and snow, which shortened them -pf-j- parts of an inch. Afterwards he measured these rods, when heated in a hot sun, which length- ened them -T-*Tr parts of an inch more than their natural temper. All these experiments seem to concur in resolving the phenomenon of pen- dulum clocks going slower under the equator than in the latitudes from it; but yet he has too good an opinion of Sir Isaac Newton's notion of the spheroidal figure of the earth, easily to part with it; and therefore he leaves it to the con- sideration of others, how far the figure of the earth, and how far heat and cold, and the rarity and density of the air, are concerned in that pheno- menon. The Construction and Use of Spherical Maps, or such as are delineated on Por- tions of a Spherical Surface. By Mr. John Colson, M. A. F. R. S. N° 440, p. 204. Geographical maps, and hydrographical charts, though representations of a convex spherical surface, were first delineated on planes, as being the most easy and obvious, though not the most natural and accurate representations; and they are sufiiciently near the truth, when the part of the earth or seas described, is not of a very large extent. Such as these have been usually called chorogra- phical and topographical maps ; but when the map is any thing general, or is to contain any large tract of the earth or seas, suppose, for instance, one of the four quarters of the world, then, when they are projected, or represented on a plane, the parts must necessarily be distorted, one way contracted beyond the truth, another way dilated, so as to give no just idea of the whole. Nor can this distortion be possibly avoided, when any considerable part of a spherical surface, by any projection whatever, is to be represented on a plane. This distortion is indeed always regular, and according to certain laws; so that knowing the nature of the projection, it may tolerably well be allowed for. But to do this scientifically, requires much skill and accuracy in the maker, as well as proficiency and experience in the peruser; and therefore not so proper for an introduction to learners, in the rudiments of geography. Young minds 62 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. are apt to receive wrong notions and prejudices from them; at least they cannot be rightly and easily instructed by them. To obviate this inconvenience, geographers have contrived the terrestrial globe, on which they endeavour to delineate all the parts of the earth's surface in their natural state, as to longitude, latitude, distance, bearing, magnitude, &c. which being a true and genuine representation of the whole superficies of the earth, as far as it is yet known, is the best adapted for conveying just no- tions to young minds, and for preventing all false conceptions and preposses- sions. After the first rudiments of geography have been imbibed from hence, they will be then prepared for the use of plain maps; and they will afterwards find, that large projections of particular countries, kingdoms, and provinces, in piano, will be of excellent service for their further improvement in this useful and necessary science. Nor will they now be in any danger of being misled by such maps, though they are not so just and niatural representations of the terrestrial globe. Now the same conveniencies that may be derived from the whole globe, may, in proportion, be had from any notable portions of it; as a hemisphere, a quadrant, a sextant, an octant, or other part. But with this advantage besides, that these partial spherical maps will not only be much less cumbersome, and more manageable than a whole globe, but may be made much more accurate and particular, as they are capable of being formed to a much larger diameter, than a globe can conveniently be made to. The maps may first be printed on a plane, as is usual in the common globes, and then pasted on thin convex shells of pasteboard, formed to the intended radius. The forming of these spherical coats of pasteboard will be a matter of no great difficulty, even to as large a diameter as shall be desired ; but the chief art will be required in projecting the maps in piano, after the simplest and exactest manner, so as they may adapt themselves, with as little error as possible, to a spherical surface. For a plane surface cannot be converted into a spherical surface without some error. The best method of doing this, with the least possible error, may be as follows. Instead of the usual slips or gussets, as is the manner of globe-makers, which are comprehended between two meridians at some distance, and are formed only tentatively and mechanically, without the help of any just theory, we may divide the whole spherical surface into parallel portions, or zones; that is, into parts terminated by two parallels to the equator, at the distance suppose of 10 degrees. As if the first of these portions, or zones, were at the equator itself, and ex- tended to 5 degrees of latitude on each side of that circle; the second zone would be at the parallel of 10 degrees of latitude, and would extend to 5 de- VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. GA grees of latitude on one side, and to 15 degrees of latitude on the other side of that parallel ; and so of the succeeding zones. Now we may conceive the first of these portions, or zones, to e converted from a spherical surface to a plane in this manner, without sensible error; let the middle line of this zone, that is the equator, continue in its situation, and let the segments of the meridians on each side be conceived to unbend them- selves gradually, till they are extended into right lines perpendicular to the equator; then will that which was before a zone, or portion of a spherical surface, with a small alteration become a portion of a cylindrical surface, cir- cumscribed about the sphere; whose breadth is every where equal to 10 degrees of the sphere, and whose circumference is equal to the equator. And thus every parallel to the equator, as far as that of 5 degrees of latitude on each side, will be stretched and extended into a circle as large as the equator; but they will all keep the same distance from one another, and from the equator, that they had before. This extension, or alteration, will be every where regular and uniform, and will be but very little, even where it is most; for the least of these circles, which is the parallel of 5 degrees of latitude, has the same pro- portion to the circle it is stretched to, or the equator, as the sine of 85 degrees has to the radius, or as 996 1 947 to 10000000; which approaches very near to a ratio of equality. And now it will be easily conceived, that without under- going any other alteration, or distortion, this portion of a cylindrical surface may be rectified, or extended into a plane parallelogram, whose length will be equal to that of the equator, and whose breadth will be equal to an arch of 10 degrees of the same equator. Consequently, by an operation that will be just the reverse of this, if on a plane we delineate such a parallelogram as this, we may then lay down all the places that are contained in it very exactly, in their proper situation of longi- tude and latitude, and then apply its middle line, or equator, to that of a globe of a due magnitude, which will then become a portion of a cylindrical surface, circumscribed about the globe. Then by pressing it close to the body of the globe, we shall cause it to contract itself a very little, but regularly, which contraction will be only according to longitude, and not at all according to lati- tude; and then the cylindrical surface will be changed into that of a sphere, and will become the first spherical zone before described, with all its delineations in their due position, without sensible error. In like manner in the second spherical portion, or zone, comprehended be- tween the parallels of 5 and 15 degrees, whose middle line is the parallel of 10 degrees, we may conceive the segments of the meridians to unbend gradu- ally on each side, and to extend themselves into tangent right lines, which 64 PHILOSOPHICAJ. THANSACTIOX8. [aKNO IJSO. therefore will form a s^ment of a conical surface, still touching the globe in the parallel of lO degrees of latitude. The axis of this cone will coincide with the prolonged axis of the globe, and the side of the cone, which is to be esti- mated from the vertex to the circle of contact, will be the co-tangent of the latitude, or the tangent of 80 degrees. Now this portion of a conical surface may easily be conceived to be unrolled, or to be expanded into a plane surface, without undergoing any other alteration, and then it will become a portion of a sector of a circle ; which portion will have for its length, or middle line, an arch of a circle described with the said tangent, as a radius, whose length will be the same as the parallel of contact, and its breadth will be equal to an arch of the equator of lO d^rees, as before. This s^ment of a sector of a circle, so produced, may therefore be easily described in piano, and within it may be inserted all the places belonging to it, according to their longitude and latitude. Then it must be applied to the globle, so as that its middle line shall coincide with the parallel of JO d^rees; then by pressing it may be bent to the surface of the globe, every meridian to its respective representative, by which it will imiformly contract a little according to longitude, but not at all according to latitude. And thus the globe will be covered as ^r as 15 d^rees of latitude. The next zone, or that belonging to the parallel of 20 degrees, may be thus constructed a priori. On a plain paper, with radius equal to the tangent of JO degrees, describe an arch, whose length is equal to that of the parallel of 20 d^ees; as also two other concentric arches on each side, at a distance from the middle arch equal to an arch of 5 degrees. This will be the required s^- ment of the circular sector, in which are to be inserted all the places belonging to it, according to their longitude and latitude. Then the middle line or arch is to be applied to tlie parallel of 20 d^rees on the globe, and the segment of the conic^ surface thence arising, is to be duly contracted as before, or pressed close to the globe ; by which means this zone will also be completed. And in the same manner we are to proceed to the succeeding zones, till the whole globe is covered. And the method will not differ in any material circumstance, if instead of a whole globe, we are to construct any part of it only, or what is here called a spherical map. ^ Copy of an anderu Chirograph, or Conveyance of Part of a Sepulchre, cut in Marble, lately brought from Rome, with sotne Observations on ii by Roger Gale, Esq. r. P. S. N»44l, p. 211. Tliis marble lately arrived from Rome, and dqxjsited in the noble museum of Sir Hans Sloane, is a most valuable piece of antiquity, exhibiting a complete formula of a chirograph, or conveyance of one part of a burying-place from one VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 65 family to another, but neither of them of any note, seeming by their agnomina to have been only liberti, or descended from such. Agricola indeed is a Roman name, but those of his wife Lacena, and his son Protus, are both Greek. By this chirograph Herennius Agricola obtains from Titus Flavins Artemi- dorus, a right to 4 ollaria, which were niches or repositories, where they placed cineraria, urns, or vessels of stone or earth, containing the ashes of the dead, and were here 53 in number. This monument was situated on the left side of the Via Salaria, which ran to the north-west of Rome from the Porta Collina. It stood in the ground of Volusius Basilides, and the consideration for the conveyance of it is one Sesterce. It is very usual in sepulchral inscriptions to find the monument of one family in the field of another, the prpprietor of the monument reserving the right of that to himself when he sold the ground; or purchasing so much ground from the owner as was suflicient for erecting the monument. All sepulchres, when once a body was interred therein, were esteemed as religious and sacred, and were not to follow the possession of the field. The stone is turned with an arch at top; the whole length of it is 17\ inches; the breadth at the bottom is lOj^ inches, and at the base of the arch 12^, as it widens gradually upwards. The letters are cut in a small indifl^erent character; that of the E and the F are remarkable, being always formed in this manner E,/. It was probably placed over or between the four niches, or ollaria, granted to M. Herennius Agricola, in this monument, by T. Flavius Artemidorus, to de- clare and assert the right and possession of them to the former, and his family, till they were all filled. Of the Revolutions which small Pendulous Bodies, by Electricity, make round larger ones from West to East, as the Planets do round the Sun. By Mr. Stephen Gray. N° 441, p. 220. Mr. Gray made several new experiments on the projectile and pendulous mo- tion of small bodies by electricity, by which they are made to move about larger ones, either in circles or ellipses, and that either concentric or excentric to the centre of the larger bodies about which they move, so as to make many revolutions about them; and this motion constantly the same way that the planets move about the sun, viz. from the right to the left, or from west to east; but these little planets, if they may be so called, move much faster in their apogeon than in the perigeon parts of their orbits: which is directly con- trary to the motion of the planets about the sun. VOL. VIII. K 66 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736, On the Construction of a Quicksilver Thermometer ; also Observations on the Eclipses of Jupiter s Satellites, Anno 1731 and 1732. By M. Jos. Nic. De risle, F.R.S. N°441, p. 221. In order to have surer grounds for experiments of natural philosophy in Russia, and that they might be compared with those of other countries, M. De risle applied this winter to the construction of thermometers of mercury, regulated by the expansion of that fluid proportionably to its bulk. This ex- pansion is indeed not very perceptible, considering that Dr. Halley, in the expe- riments he made on it above 40 years since, N° J97 of the Phil. Trans.; found that the said expansion, by the heat of boiling water, was no more than the 74th part of the bulk of the mercury. M. Amontons also relates, in the Memoirs of the Royal Academy of the year 1704, that this expansion of the mercury is only the 115th part of its bulk from the greatest heat to the greatest cold that is felt at Paris. But M. De risle found in the great cold at Petersburg, on the -t-f Jan. 1732-3, in the morning, that the bulk of the mercury was condensed almost a 50th part of the extent it had in boiling water. The cold on that day, the wind being at east, was one of the severest ever felt there. His new thermometers of mer- cury he had made of a good large size, and in such manner that, having divided in each the whole quantity of contained mercury into 100,000 parts, and having marked the extent of the bulk of that mercury in boiling water, he can at any time see on the divisions of these thermometers, by how many parts the bulk of the mercury is condensed through the present temperature of the air. And though he has made four of these thermometers, which differ very much as to their size, and the quantity of mercury they contain, yet they agree within a very few of these parts. As pure mercury is of the same nature every where, and not liable to any alteration from being inclosed in a tube; and as it is probable, that taking it equally purified, it will in different countries be subject to the same expansion, if exposed to the same degree of heat ; for this reason it is probable, these thermometers may very well serve to compare the temperature of dift^erent countries; especially as he found by experience, that these thermometers may be rendered fit enough to mark sensibly the increase or diminution of the bulk of the mercury, within one or two parts out of the 100,000 contained in the whole bulk. This kind of thermometers has also this advantage, that as they mark the proper expansion of the mercury in each temperature of air, they may serve to show every moment the correction to be made in the height of the mercury in simple barometers; which will serve for reducing them to the height VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. (JjT they would have in an equal temperature of air; and one might, for this end, chuse and agree on the heat of boiling water, as a fixed term, which, in all appearance, will be the same all over the world. If the Royal Society should approve this new construction of thermometers, and should order some of their members to make the like, we might hereafter be able exactly to compare the temperature of England with that of this country, and other places where the like thermometers should be made. In order to reap this advantage from his experiments, M. De I'lsle proposes to communicate to the Royal Society all the observations he has made for 4 or 5 years past, on the barometer and thermo- meter. M. De risle was informed, that 4 or 5 years since, the Royal Society sent to M. Abraham Vater, at Wittenberg, large thermometers of spirit of wine, made and regulated by an instrument maker of the Royal Society, to compare the observations to be made in Germany, by means of those thermo- meters, with the observations made in England by the like thermometers, the one being regulated by the others. M. Weidler, professor of mathematics at Wittenberg, mentions in the account which he gave of his meteorological ob-, servations for the year 1729, that he has furnished himself with one, which he intends to make use of hereafter for his meteorological observations. He also says, that the observers of the Royal Society of Berlin make use of a like thermometer; and M. De I'lsle had received from thence, observations on the heights of the thermometer of spirit of wine, made probably with that instru- ment, for the whole year 1729, and for the first 3 months of 1731. Those observations are engraved on copper plates, where the heights of the spirit of wine are expressed in parts of the French, English, and Rhinland foot. If the Royal Society approve of this kind of thermometers, and are desirous he should compare them with his; if they also desire that meteorological observa- tions with those thermometers of spirit of wine should be made in Russia, he begs you would send him several of them ; but then he begs that those sent him may be well regulated, and exactly compared with those the observers of the Royal Society make use of; supposing that some person of their body is appointed to keep journals of these observations. M. De I'lsle will send in exchange to the Royal Society, if they desire it, some thermometers of mer- cury regulated by and compared with the four large ones he made at Peters- burg, After this, M. De I'lsle inserted the last observations on the satellites of Jupiter, which were made at Petersburg, since those inserted in the 3d volume of the Memoirs of the Academy of Petersburg, to the present time, but are omitted now, as of no use to repeat on the present occasion. K 2 68 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. Experiments on the Perforation of the Thorax, and its Effects on Respiration. By IV. Houston, M. D. F. R. S.* Communicated by Philip Miller, F. R. S. , An Abstract from the Latin. N" 44, p. 230. Tliese experiments, 6 in number, were made upon dogs and puppies. The admission of the external air into the cavity of the thorax (even when both sides were perforated) did not impede either the respiration or the barking of the animals. When the dogs howled, the lungs protruded through the wounds made in the thorax, and when the dogs ceased making a noise, the lungs again went in. But what may seem paradoxical, the dilatation of the lungs, in some of these experiments, was observed to be synchronous with the con- traction of the thorax, and e contr^. This phenomenon the author supposes to have been owing to the violent convulsive action of the abdominal muscles, whereby the lower part of the lungs becoming suddenly pushed up, the air would be accumulated in their upper part, which would consequently be dis- tended. It is not to be supposed that this is the case in the natural, undis- turbed respiratory action. From these experiments it was evident, that in the natural state the lungs occupy the whole cavity of the chest, their surface being in close contact with the membrane which lines the thorax. Observations, Astronomical, Physical, and Meteorological, for the Year 1 733, made at fVittemberg. By John Fred. Weidler, Professor of Mathematics, and F.R.S. N°44], p. 238. These meteorological and other observations, being temporary, are now of no use. Concerning the crooked and angular Appearance of the Streaks or Darts of Lightning in Thunder-Storms, By James I^ogan, Esq. N° 441, p. 240. Mr. Stephen Hales, in his Statical Essays, vol. ii, p. 291, mentions this phenomenon of the streaks or darts of lightning in thunder-storms appearing crooked and angular, as a thing not yet accounted for, and therefore he guesses at a solution of it. The clouds are generally distinct collections of vapours, like fleeces ; and therefore the rays of light through them must pass through very different den- sities, and accordingly suffer very great refractions : from thence, therefore, that appearance must undoubtedly arise. For it is highly absurd to imagine, * These experiments were made while Dr. H. was at Leyden in the years 1728 and 1729. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. - 69 that fire darted with such a rapidity, can from any assignable cause deviate in fact from a right line, in the manner it appears to us. And this, if duly con- sidered, may probably be found a plenary solution. Observations on the Aurora Borealis made in England. By Andr. Celsius, F. R. S. a7id Sec. R. S. of Upsal in Sweden. N° 42 1 , p. 24 1 . Here are registered several instances of the appearances, more or less, of the aurora borealis ; from which M. Celsius infers, that In several of these observations he is certain as to the time of tlie clock: so that if it has happened that others have observed the same phaenomena, the longitudes of places may be determined by them with greater exactness than by the satellites of Jupiter ; which he takes to be the principal use that may be made of these observations, especially in making maps of the northern coun- tries, where these lights more frequently occur. Some Experiments made on Mad Dogs with Mercury. Dated June 3, 1735. ^ By Dr. Robert Jaines* of Litch/ield. N° 44 1 , p. 244. Dr. James here gives an account of some experiments made on mad dogs • Dr. Robert James was descended from a family of great respectability in Staffordshire. After studying at Oxford, he practised physic first at Sheffield, next at I,itchfield, then at Birmingham, and lastly in London. In 1755 he was, by the king's mandamus, admitted to the degree of M. D. at Cambridge. His first publication appears to have been the above paper, afterwards reprinted with considerable additions, in a separate form. After this appeared his Medicinal Dictionary in 3 vols, folio, 1743 j a compilation which proves that the author was well acquainted with the writings of the physicians of antiquity, as well as with the most esteemed medical publications of his own days. For whatever relates to the history of the medical art and the histories of diseases, this dictionary may be consulted with advantage; but much of the physiology and patliology which it exhibits is now exploded; nor are the curative directions, in many instances, the best that could have been given. In the materia medica too much notice is taken of the virtues attributed to different medicinal substances by the ancients; and with regard to the pharmaceutical part of this work, that is now become almost useless j for, during the 60 years and upwards which have elapsed since the publication of this Dictionary, phar- macy, in consequence of the improvements and discoveries made in chemical science, has undergone a complete reform. Add to this, that most of the articles in this compilation are discussed with too much prolixity. The work should have been less bulky, and more select. Dr. James's other publications are as follow. A Translation of Ramazzini de Morbis Artificum j a Practice of Physic, in 2 vols; a Treatise on Canine Madness ; for the cure of which he proposed mercury ; a remedy which had been before recommended in another form by M. Desault, of Bor- deaux, in a Treatise published in 1733. A Dispensary; and a Dissertation on Fevers. The last mentioned publication was written chiefly in recommendation of his celebrated Fever Powder ; a pre- paration of antimony, to which the pulvis antimonialis of the new London Pharmacopa-ia is sup- posed to be analogous. 70 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. with mercury, which he had reason to believe to be the most effectual pre- servative against, and perhaps even a cure, for the hydrophobia. About Michaelmas, \734, Mr. Floyer complained that he was afraid of a madness among his hounds ; for that morning one had run mad in the kennel, and he was apprehensive that most of the rest were bitten by him : Dr. J. took this opportunity of telling him that he had long believed that mercury would, if tried, prove the best remedy against this infection; and that if the idea he had formed of this poison was just, he was pretty sure the medicine would answer, notwithstanding the difficulty there is of determining the effects of a medicine a priori; and that it was at least worth while to try. Mr. Floyer neglected this advice till the Feb. following. Mean time he tried the medicine in Bates, commonly known by the name of the pewter-medicine ; as also every thing else which was recommended to him by other sportsmen, but to no pur- pose ;■ for some of his hounds ran mad almost every day after hunting. On this he took his hounds to the sea, and had every one of them dipt in the salt- water ; and at his return, he brought his pack to another gentleman's kennel, 6 miles distant from his own. But, notwithstanding this precaution, he lost 6 or 7 couple of his dogs in a fortnight's time. At length on further persuasion, Mr. Floyer tried the experiment on 1 of his hounds that were both very far gone. They refused food of all sorts, particularly fluids, slavered much, and had all the symptoms of a hydrophobia to a great degree. That night he gave 12 grains of turpeth mmeral to each of the 3 dogs, which vomited and purged them gently. Twenty-four hours after this, he gave to each 24 grs. and after the same interval he gave 48 more to each. The dogs salivated considerably, and soon after lapped warm milk. At the end of 24 hours more, he repeated to one dog 24 grs. more, and omitted it to the other. The dog that took this last dose, lay on the ground, salivated extremely, was in great agonies, and had all the symptoms of a salivation raised too quick; but he got through it: the other relapsed, and died. To all the rest of the pack he gave 7 grs. of the turpeth for the first dose, the second 12, at 24 hours distance, which was repeated every other day for some little time. The method was repeated at the 2 or 3 succeed- ing fulls and changes of the moon. From this time he lost not another Dr. James died in 1776, aged 73. A spirited vindication of Dr. J.'s character from the c))arge of empiricism, in consequence of the patent he obtained for his Fever Powder, has been written by Dr. Heathcote. This is a subject respecting which there will always be a difference of opinion. With regard to Dr. J.'s merits as an author, if he is not distinguished for much originality of thought or conciseness of expression; yet he has shown himself to be a faithful and industriou* collector of medical information down to bis own time; and it must be confessed that few have surpassed him in point of erudition. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 71 hound ; and though several were afterwards bitten by strange dogs, the turpeth has always prevented any ill consequences. Dr. J. and his friends tried the same thing on many other dogs, and it had never failed in any one instance ; though dogs bitten at the same time, and by the same dogs, have run mad after most other methods had been tried. As to the experiments made on mankind, Dr J. had opportunities of making only three. The first was on a girl about 14 years of age. The calf of her leg was so torn by a mad dog, that the surgeon was obliged to use means to prevent a mortification from the bite. She was vomited by the turpeth. Three days before the next change of the moon, the vomit was repeated, and again the very day of its changing. The same method was pursued the next full moon. The girl is very well. The 2d was on a boy of about 10 years of age. He had 4 holes in one of his legs, made by a mad dog. The turpeth was given as above, and the wounds dressed with digestives, and he continues well. The 3d case was that of a young man of about J 8 years of age. The bite was on the hand. A great number of dogs were bitten at the same time, in the town where he lived. About 6 days after the mischief was done, several dogs that had been wounded ran mad ; on which he applied to Mr. Wilson, apothecary in Tamworth, to whom the Dr. had communicated the success of the turpeth in this case. The young man was at this time very melancholy and dejected, had tremors, and slept very little for some nights before, though he was not apprehensive that the dog which had bitten him was mad. He had a dry scab on his hand : on applying to Mr. Wilson, he was vomited with Vin. Benedict. §ij. The next thing he took was made according to the following prescription ; viz. R Turpeth. Min. gr. xij. Lap. Contrayerv. 3i. Ther. Androm. q. s. M. F. Bol. N° 3, sumat unum singulis noctibus hora decubitiis snperbibendo Julap. seq. Cochl. iv. R Aq. Rut. §vj. Theriac. §ij. Syr. Paeon, c. gift Tinct. Castor 3ij. M. F. Julap. On taking these, the patient sweat very much, and had 2 loose stools every day after them : his tremors went off, and he slept better. After this he went into the cold-bath, and continued perfectly well. But what is remarkable in this case is, that the wound ran a thick digested matter after this method, and threw off the scab like an eschar; after which it healed of itself. Instead of endeavouring to explain the action of mercury in these cases, Dr. J. makes an observation or two on the antiquity of this disease; which he the 72 PHILOSOPHICAL TRANSACTIONS. [ANNO 1736. rather chooses to do, because Caelius Aurelianus, in his account of it, does not seem to build so much on the authority of Homer, as, in his opinion, he might have done. Indeed he quotes a passage out of the 8th IHad, where Teucer calls Hector jtui/a ^^uo-o-nTtif a, but he does not seem to think this sufficient to prove that Homer was acquainted with this madness. But he omits two more passages in the same author, which, joined with this, amount to a demon- stration that Homer was by no means ignorant of it. The first is in the 9th Iliad, 1. 237, where Ulysses is on his embassy to Achilles. He describes to the last mentioned hero, the distress the Grecian army was in through his ab- sence ; and when he has painted Hector as terrible as he can, he compares his fury to the rage of a mad dog. Maii/fxai ixTTxyXu;, TruruK)? An, sSi ti rut Ai/i^xi; iSi ©{85* xf«T£fr) Si i Kh(r(ra SiSvKiv, Hector vero valde trucibus oculis adspiciens Furit terribiliter, fretus Jove : nee quicquam honorat Viros neque Deos ; ingens autem ipsum rabies invasit. If Homer had designed as a physician to describe a mad dog, he could not have expressed his looks by a more proper turn than B\iiJi,t»lvuv. It must also be considered, that this discourse is directed to Achilles, who, having studied physic under Chiron, was consequently more capable of receiving an idea of the mischief Hector did to his countrymen by this metaphor. In the 13th Iliad, Hector is again called Aua-a-wJ*)?, by Neptune. It must be observed that Awo-a, Xua-a-rnr]^, and Xva-a-uh;, can properly, and in their natural signification, be applied to no other madness, than that which is peculiar to a dog, though metaphorically it may, as in the instances Dr. J. has given, as also in Sophocles and Euripides. The word Xvaa-x or Aurra is used to signify the mad- ness of dogs by Aristotle, Galen, and Dioscorides. And Ava-a-ohxro; is used by the last mentioned author to signify a man bitten by a mad dog. Auro^aw is used by Aretaeus in this sense, and AuTTtoo-ait by Plutarch, to express the same thing. What the Dr. would infer from this is, that Homer was certainly acquainted with the madness of dogs ; and if dogs in his days ran mad, it is probable they would bite men, and if so, to be sure, an hydrophobia would be the conse- quence ; and yet Plutarch will have it that it was first noticed in the days of Ascle- piades, famous for his practice in Rome before the death of Mithridates. Another strong evidence of its antiquity, is that instinct which directs every dog to avoid some that is mad, on smelling, seeing, or even hearing him. If this is not instinct, it is reason ; and that in a higher degree, than we our- VOL. XXXIX.3 PHILOSOPHICAL TRANSACTIONS. 73 selves can pretend to. Now instinct must be coeval with the creation, or at least the fail ; and therefore [canine] madness cannot be much younger. A Continuation of an Account of an Essay totvards a Natural History of Caro- lina and the Bahama Islands. By Mark Catesby, F. R. S. with some Extracts out of the 8th Set. By Dr. Mortimer, Seer. R. S. N°441, p. 251. This part contains some account of the different kinds of snakes and vipers found in those parts. A Catoptric Microscope. By Robert Barker, M. D., F.R.S. N°442, p. 259. Though microscopes, composed of refracting glasses only, have been vastly improved, as to their effects of magnifying ; yet they have been attended with such great inconveniences, that their application to many arts, in which they might be very convenient, is not so common as might be expected, and man- kind have reaped but a small part of the advantage obtainable from so surprising and useful an instrument. Among the inconveniences mentioned, the following are the most con- siderable : 1. That in order to magnify greatly, it is necessary that the object-glass be a portion of a very minute sphere, whose focus being very short, the object must be brought exceedingly near; it will therefore be shaded by the microscope, and not visible by any other light than what passes through itself; in this case therefore, opaque objects will not be seen at all. 2. Objects, illuminated this way, may be rather said to eclipse the light, than to be truly seen, little more being exactly represented to the eye, than the out- line ; the depressions and elevations within the out-line appearing like so many lights and shades, according to their different degrees of thickness or transpar- ency ; though the contrary happens in ordinary vision, in which the lights and shades are produced by the different exposure of the surface of the body to the incident light. 3 . Small parts of large objects cannot easily be applied to the microscope, without being divided from their wholes, which in the case of vivi section de- feats the experiment, the part dying, and no more motion being observed in it. • " •'*' 4. The focus in the dioptric microscope being so very short, is exceedingly nice, the least deviation from it rendering vision turbid ; therefore only a very small part of an irregular object can be seen distinctly this way. To remedy these defects. Dr. Barker has contrived a microscope on the VOL. VIII. L - • 74 PHILOSOPHICAL TRANSACTIONS. [aNNOIJSS. model of the Newtonian telescope, in which he has been greatly assisted by that excellent workman, Mr. Scarlet, jun. As to the effects of this instru- ment, it magnifies from the distance of Q to 24 inches. Fig. 1, pi. 4, represents the entire microscope, mounted on its pedestal, on a proper joint, contrived so as to direct the instrument towards any object. Fig. 2, the section of the instrument ; in which ab is the larger concave metalline speculum ; CD the lesser concave metalline speculum ; ef a hollow brass screw, to fasten in the 1st dioptrical glass, or plano-convex lens; gh an- other screw fastening on the hollow cylinder efik (in which the dioptric glasses are contained) to the body of the microscope ; ik a cap with a small perfora- tion, serving as an aperture to the eye-glass, or 2d lens, convex on both sides; ML is a long screw passing through the nuts p and v, serving to bring the small speculum to a proper distance from the larger; Na a sliding piece moved by the screw, carrying the stem an, and the little speculum cd ; yx a screw for the cap at fig. 3 ; that at fig. 4, is to be screwed on the aperture jk. Fig. 5, shows the construction of the microscope ; in which i is an object supposed erect ; from which rays falling on the speculum ab, will be reflected to the focus k, where they will form an inverted image ; and being reflected by the small speculum cd, they will pass through the perforation of the great speculum, and falling on the plano-convex glass ef, converge again, and form an erect image at I ; which being brought very near to the eye, and so con- siderably magnified, will be distinctly seen through the eye-glass gh. yin Account of the Standard Measures preserved in the Capitol at Rome. By Martin Folhes, Esq. V. P. R. S. N° 442, p. 262. In the wall of the capitol is a fair stone of white marble, of the length of 8 feet 5 inches English, and of the breadth of 1 foot 9-f inches ; on which are inscribed the standards of several measures with these respective inscriptions : Piede Ro : Pal. iiii. One. xii. Deti xvi. Piede Greco. Canna di Architet. Palmi x. Staiolo Pal. v. Quar. iii. Canna di Merca. Palmi otto d'altra misura. Braccio di Merc. Pal. iii. d'altra misura Braccio di Tessito di Tela. Curante Lu. Poeto. The lines, that represent these measures, are cut in the marble, pretty deep; but as they have, consequently, a considerable thickness, it is somewhat difii- VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 75 cult to be very exact in taking off their dimensions. Mr. Folkes however did it as nearly as he could, by setting the point of his compasses in the middle of the cross lines, that are drawn to determine the beginnings and ends of the measures. The palm of the architects is easier to give than the others, be- cause the whole canna is inscribed on the stone : this he therefore took off, and then divided it into 10 equal parts. Afterwards his chief attention was given to the Roman foot, as of greater consequence than the other measures. They all however follow, a^Hhey occurred to him, in such parts as the London foot contains 1000. The Roman foot 966 +. This is divided on the stone, first into 4 palms, and then on the upper part into 12 unciae, and on the lower into 16 deti, accord- ing to the inscription. The Greek foot 1006 -|-. This is also divided like the Roman. The canna of the architects 7325. It is divided into 10 palms, each of which, is therefore 732-i^ of the English foot. The staiolo, being 5 palms and \, is 4212 —. The canna de mercanti, divided into 8 palms of another measure, 6 feet 6 inches 4-1-. The braccio de mercanti, divided into 4 palms of another measure, 2 feet 9 inches -14. The braccio di tessitor di tela, divided into 3 parts, 2 feet 1 inch^x- The palm of the architects is assigned by Mr. Greaves 732 of the English foot ; and the same is given by M. Picart to the Paris foot, as 4944- to 720 ; ' which reduced, becomes 732 -|- of the English foot, as before, and as it came out from this trial. The Roman foot is given by Picart, from this very stone, 653 ,V of such parts, as the Paris foot contains 720 ; that is, by reduction, 967 + of the English ; and the same by Fabretti, who also measured it on this stone, is assigned to the palm of the architects, as 2040 to 1545 ; which reduced on the former measure of the palm, is 966-^ of the English foot. These measures come out as near as the nature of the standard can possibly allow ; and as it was somewhat fresher in Picart's time, than it is now, Mr. F. would make no dif- ference in the proportion he has assigned ; but supposes the Roman foot on this marble was intended to be such a one, as should contain 967 parts of the English very nearly, Mr. Greaves had long before assigned the measure of the Roman foot from Cossutius's monument, to be 967 of the English, and had preferred that mea- sure to the others he had taken from the tomb of Statilius, and the Congius of L 2 76 PHILOSOPHICAL TRANSACTIONS. [aNNO 1/36. Vespasian. And there seems no doubt but Cossutius's foot was the foot in- tended to be inscribed on this marble ; though that monument is itself now lost. For the Greek foot, there seems to be no further mystery, than that it was intended to be made to the Roman, in the proportion collected from Pliny, which is, that 6'25 Roman feet made 600 Greek ; by which account the Greek foot should contain 1007 of such parts as the Roman contains 967 ; and the actual quantity Mr. F. took off, was 1006. Some Observations, made at fVittemberg in 1734. By John Fred. PFeidler, F. R. S. N" 442, p. 266. These observations, like those of former years, by M. Weidler, are chiefly on the aurora borealis, the weather, &c. ; and no longer useful. Observations made of the Latitude, Variation of the Magnetic Needle, and Weather, by Capt. Christopher Middleton, in a Voyage from London to Hudson's Bay, Anno 1735. N° 442, p. 270. These observations are nearly alike with those before printed. Vol. vii, p. 465 and 617, of these Abridgments. An Experiment, to show that some Damps in Mines may be occasioned only by the burning of Candles under Ground, without the Addition of any noxious Vapour, even when the Bottom of the Pit has Communication with the out- ward Air, unless the outward Air be forcibly driven in at the said Com- munication or Pipe. By the Rev. J. T. Desaguliers, LLD., F. R. S. N°442, p. 281. Exper. 1 . — In a cylindric glass-receiver, open at both ends, whose lower end is plunged in water, and upper end covered with a plate, having a hole of near an inch bore, a candle of 6 in the pound will not burn quite the time of one minute, before it goes out. Exper. 2. — A candle will burn almost as long when the receiver is quite covered. Exper. 3. — The receiver having the hole of the plate open, and a pipe at bottom communicating with the external air, will burn but a little longer than in the first experiment ; and by blowing in at the pipe with your mouth, it will go out rather sooner. Exper. 4. — Blow in at the pipe with bellows, and the candle will burn as long as you will. VOL. XXXIX.3 PHILOSOPHICAL TRANSACTIONS. fj A Chemical Experiment, serving to illustrate the Phenomenon of the Inflammable Air shown by Sir James Lowther, Bart, as described in Phil. Trans. N" 429. Bi/ Mr. John Maud. N° 442, p. 282. Sir James Lowther made an experiment on some air which he collected out of a coal-mine, and brought in bladders, close tied, by sea to town; the effects of which was, that the air being pressed out of the bladder through the small orifice of a tobacco-pipe, would catch fire from a lighted candle, and burn like an inflammable spirit, till it was all consumed. On considering that the cause was only a great quantity of sulphureous vapours fluctuating in that air, Mr. M. was naturally induced to make an essay, by an artificial mixture, to produce the like eflfect. It is very well known (he observes) to every one versed in chemical affairs, that most metals emit great quantities of sulphureous vapours, during the effervescence they undergo, in their solutions in their respective menstrua, or solvents. Of these fumes, iron emits a great quantity while it is dissolving in oil of vitriol, which are very in- . flammable, and not easily to be condensed. These fumes Mr. Maud collected into a bladder with the desired success, and having produced before the Royal Society two bladders of this fictitious air, at the same time that Sir James Lowther made trial of his, they both exhibited the same phasnomena. A par ticular account of the preparation made use of is as follows. Mr. Maud took jij of oil of vitriol, and mixed it with jviij of common water, which he put into a glass with a flat bottom, about 10 inches wide, and 3 deep, with a long neck ; to this he added jij of iron filings : there instantly arose a great heat, with a violent ebullition, and the iron was wrought upon very fast, with a copious exhalation of fumes. To the end of the neck of the glass he luted a bladder, void of air, the neck of the bladder being fastened to a tobacco-pipe ; the fumes arising from the dissolving metal soon puffed up the bladder to its full extent, when that being taken away, the neck of it being first tied close with a string, he applied another in the same manner : thus may be got as many bladders full as you please, while the effervescence lasts. Two of these bladders were tried before the Society, and exhibited a flame like those of Sir James Lowther's, very like in the smell, though somewhat different in the colour of the flame. After Mr. M. had pressed part of the air out of the blad- der, by drawing back the hand, the flame was sucked into the bladder, which set on fire what inflammable air remained all at once, and went off like a gun, with a great explosion. It is worthy of notice in this experiment, that all the air which filled the 78 PHILOSOPHICAL TRANSACTIONS. [aNNO ] / 36. bladders was, as it were, generated de novo out of the mixture, or else re- covered from being locked up in the body of the metal in an unelastic state. This experiment will easily explain a very probable cause of earthquakes, volcanoes, and all fiery eruptions out of the earth ; for nothing more is re- quisite than iron, a vitriolic acid, and water. Now iron is generally found ac- companied with sulphur ; and common sulphur may be analized into an inflam- mable oil, and an acid liquor like oil of vitriol. This acid therefore in the bowels of the earth, by being diluted with a little water, surrounds the iron and works upon it in the same manner as described above ; an effervescence and intesthie heat arise ; the air which comes from the mixture is rarefied, and be- comes very elastic ; its impetus, as it is the more compressed by the incumbent weight of earth, is increased even to an unlimited degree ; and at length, like gunpowder, will remove all obstacles, and exhibit to the spectators above ground the terrible phaenomena of earthquakes and eruptions. Sometimes these in- flammable fumes, if very much heated, as soon as they come to the open air, will catch fire, and so produce those fiery eruptions, of which there are so many instances in the world. ^n Account of the Storm, Jan. 8, 1734-5. By Mr. Henry Forth. N° 442, p. 285. At Darlington, 14 miles south from Durham, lat. 54° 46', the evening be- fore the 8th of Jan. 1734-5, Mr. Forth's barometer stood at 29 inches, but had been gradually falling for two days. The wind was then s. w. and of the second degree of strength ; which increased towards midnight a degree more. Most of the day there was snow or sleet. The 8th in the morning he found his glass fallen to 28.38 inches, and at 4 o'clock p. M. down to 28.05 inches, but by 10 in the evening risen again to 28.45 inches. All this while the wind was in the north east, with only a moderate gale, though attended all day with snow, which at night was 2 inches and a quarter deep ; and about 8 it began to freeze. As the wind in the southern parts was all that time in the opposite quarter, Mr. Forth would have expected an accumulation of the air, and as a consequence the rising of the barometer, at the time of its falling the lowest. Had the storm been the night before, when in the northern parts the wind was in the same direction, and had afterwards fallen, he would then have imputed the fall to the quick return of the current of air to restore the equilibrium. VJIJUL- iO MjJlU ■ VOL. XXXIX.J PHILOSOPHICAL TRANSACTIONS. J^ Of the Bones of yinimals changed to a Red Colour bi/ Aliment only. By John Belchier, Surgeon, F. R. S. N" 442, p. 287. That the circulation of the blood is carried on through the bones, is evident (Mr. B. observes) from many phaenomena in surgery ; but that it is universally and intimately distributed through the most solid and compact substance of the bones, though hitherto by some made a matter of doubt, will appear undeniably from the instances here produced ; which are the bones of several hogs, of a different breed, changed to a deep red colour, merely by aliment. And what makes this still more surprising is, that neither the fleshy nor cartilaginous parts suffer the least alteration in colour or in taste. The diet of these hogs was bran, after it had been boiled in a copper with printed callicoes, in order to clean them from a dirty red colour occasioned by an infusion of madder root, which is used to fix the colours printed on the cloth. Some of these colours are made with preparations from iron, others with a mixture of alum and sugar of lead. The parts printed with the pre- paration of iron, produce black and purple ; those printed with the mixture of alum, red of different degrees, according to the strength of the mixture. The bran having .absorbed the red colour discharged from the cloth, was mixed with the common food of the hogs, and produced this effect on their bones. On examining these bones, Mr. B. observes in general the solid parts to be most tinctured, and the teeth particularly, except the enamelled part, which is of a different substance ; and on sawing them through, he found the internal parts equally tinged, except at the ends of the bones, where the substance is more spongy. And in order to discharge the colour, he macerated them in water for many weeks together; boiled them often, and steeped them in spirits, but all proved ineffectual ; nor was the least tincture given to any of the liquids, on which he made experiments. ^n Observation of a white Liquor resembling Milk, which appeared instead of Serum separated from the Blood after it had stood some time. By Alexander Stuart, M. D., F. R. S. N" 442, p. 289. One John Wicks, a carver, in Bromley-street, about 40 years of age, had been ill about 3 weeks by a loss of appetite and indigestion, and at last a pain and distention of his stomach, with a low degree of an inflammatory fever; his tongue dry, rough, and of a rusty brown colour in the middle, with a white soft list on each side ; his urine very high coloured, with a large quantity of a slimy pink-coloured sediment ; his stools very yellow and loose. 80 PHILOSOPHICAL TRANSACTIONS. [anNO 1736. Eight ounces of blood being taken away ; instead of serum, nothing appeared above the coagulum but this white liquor, resembling milk, which Dr. S. poured off to the quantity of about 4 oz. at first there was no smell perceptible; but in 6 days it began to have the smell of rotten eggs : it stood in a room where there was a fire, for some hours of the day, for 3 weeks more, in which time it did not alter its consistence nor smell. The patient had eaten very little for a week before Dr. S. first saw him ; and only a little of a calfs foot stewed, the night before, for supper, and no break- fast that day. He was addicted to drinking strong pale malt liquor every day he was in health. If this be chyle, it is a substance very different from milk, which is apt to turn sour and thick by keeping, and never contracts the putrid smell of rotten eggs, as this did. Whether it be not chyle turned putrid, and near to puru- lency, by a long circulation in the blood-vessels, but not converted into blood, through some defect in the sanguification, is a question which probably cannot be decided, without more observations and experience.* The coagulum of the blood was covered with a sizy pellicle, about the thick- ness of a shilling. The red part was of a grumous, tender, incoherent con- sistence. Though he was much better in a week's time, the Doctor ordered 5 oz. of blood to be taken away, to see what change had been made ; and he found the coagulum covered with a sizy pellicle to the thickness of half a crown, the red part of a due consistence, the serum clear, without any chyle. The urine became clear, and he recovered in about 2 weeks after the Doctor had first seen him. ^n Account of what was observed on opening the Corpse of a Person who had taken several Ounces of crude Mercury internally ; and of a Plum-Stone lodged in the Coats of the Rectum. By Dr. Madden, of Dublin. N° 442, p. 29 1, Some time ago Dr. M. was present, with Dr. Robinson, and Mr. Nichols, surgeon-general at Dublin, at the opening the body of a gentleman in that town, who for several years had found great difficulty in going to stool. This disorder increased on him towards the latter end of his life, and he was seized with a violent distemper, of which Dr. M. says he could give no description, having never attended him. In order to procure a passage downward, which * It was probably the albuminous fluid existing in an excessive proportion in the blood ; and if so, it would have yielded a coagulum had it been exposed to a sufficient degree of heat j but to this simple test it was not lubjected. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 81 Dr. M. supposed was a principal complaint, he took, by the advice of a physi- cian, several ounces of crude mercury, at different ti(nes, without any relief, and at length he died. On opening the abdomen, which was very much distended, there burst forth a great quantity of wind, though the guts and stomach were not wounded. The stomach was empty ; and the inner coat was very much inflamed from one end to the other. In several places of the small guts, there were scattered grains of crude mercury, and along with them generally a black gritty powder, very like ^Ethiops mineral, which was doubtless the mercury changed into that consistence. The colon was distended, at its origin, to twice the thickness of an ordinary man's arm about the shoulder. This extraordinary thickness extended to about the length of 10 or J 2 inches ; from hence it gradually decreased, and where it was attached to the stomach, it was not above a third part of that size. It was much inflamed at its origin, and contained at least 6 quarts of liquid excrement, in which was observed crude mercury, as also some of the black powder above- mentioned. The colon, where it parted from the stomach, and diverged towards the left kidney, adhered about the space of 3 inches to the omentum ; and on sepa- rating the adhesion, there was found an abscess and inflammation, which had communicated to those parts of the ileon, contiguous to the colon. The colon had in this place a perforation, about f of an inch in diameter, and 4 smaller perforations, about the size of a goose quill, through which some excrement had passed into the abdomen. The coats of the colon, as it approached the intestinum rectum, became scirrhous, about the space of 6 inches, and the capacity was gradually smaller. The valves of the colon about this place were of a reddish colour, and were more scirrhous than the other parts of the intestine. The coats of the colon, where it was continued to the rectum, were at least half an inch thick, and its capacity was not above the fourth part of the natural size. On cutting the gut horizontally hereabouts, there was perceived a body which stopped the passage, and seemed to the touch almost of a cartilaginous consistence. Having opened the gut lengthwise, it was found that it was no more than 2 of the valvulse conniventes coli become scirrhous, and which pro- truded downward into the rectum. There was also found a small plum-stone in this place, which was quite buried in the tunica villosa, and had made itself a bed between the coats of the rectum. It had formed a small abscess, which discharged into the cavity of the pelvis ; but it had no communication with the cavity of the rectum. .. VOL. VIII, M 82 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. A Solar Eclipse observed at Rome, May 3, 1734, N.S. By the Abbh de Revilus, F. R. S. and Andr. Celcius, F. R. S. N° 442, p. 294. True time. At lO*^ 22"" 35% A. M. The eclipse had begun a Utile. ] ] 5 O , The greatest obscuration 2 digits. 11 51 O, The end of the eclipse. The Description and Manner of using an Instrument for measuring the Degrees of the Expansion of Melals by Heal. By Mr. John Ellicott. N°443, p. 297. AA, (fig. 6, pi. 4) represents a flat plate of brass, which, for more strength, is screwed down to a thick piece of mahogany : on this plate are screwed three pieces of brass, two of which, marked bb, serve as supports for the flat iron bar c ; and which, on account of its use, is called the standard bar. The upper part of the third piece of brass is a circle, about 3 inches diameter, divided into 360 equal parts or degrees : within this circle is a moveable plate, divided like- wise into 360 parts, and a small steel index. The brass circle in the figure is marked d, and the moveable plate d. On the standard bar is laid the bar of metal e, on which the experiment is to be made, as e. F is a lever, 24- inches in length, fastened to an axis, which turns in two pieces of brass, screwed to one of the supports, marked b : to the end of this lever is fastened a chain, or silk line, which, after being wound round a small cylinder, to which the index in the brass circle d is fastened, passes over a pulley, and has a weight hung to the end of it : on the axis, to which the lever is fixed, is a pulley, 4- of an inch diameter, to which a piece of watch- chain is fastened ; the other end of this chain is hooked to a strong spring, marked g, and bearing against one end of the metal e. H is a lever, exactly of the same form and dimensions with the former ; but the chain fastened to the pulley on its axis, is hooked to the standard bar.* The line fastened to the end of this lever, after being wound round a cylinder, to which the moveable plate is fixed, passes over a small pulley, and has a weight hung to the end of it ; or rather the same line passing under a pulley, to which the weight is hung, has its other end fastened to the lever f : thus one weight serves for both levers, as in the figure. From this description it is plain, that whenever the bar e is lengthened, it gives liberty to the weight to draw the lever f upwards by its action on the • N. B. The chain to the former pulley being fastened to a spring, and not directly to the metal «, is only for the more easy shifting the metals. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 83 spring G ; and the index will, at the same time, by means of the silk line, be carried forward in the circle; and as the bar shortens, it will return back again; the same motion will be communicated to the standard bar. The lengthening the bar the iOth of an inch, will carry the index once round the brass circle, which is divided into 36o degrees; therefore, if the metal lengthens the 7'200th part of an inch, the index will move one degree. To make an experiment with this instrument, lay a bar of any kind of metal, as E, on the standard bar ; then heat the standard bar to any degree of heat with a lamp, and mark the degree of its expansion, as marked by the moveable plate : observe also the degree of expansion of the metal k, by the heat com- municated to it from the standard bar, as marked on the brass circle by the in- dex : let the instrument stand, till the whole is thoroughly cold ; then remov- ing the bar e, lay a bar of any other metal in its place, and heat the standard bar to the same degree of heat as before, which is seen by the moveable plates marking the same degree of expansion. Then the index will show the degree of expansion of the second metal, as it did of the first ; and by this means the degrees of expansion of different metals, by the same degree of heat, may be exactly estimated. ji further Account of the Bones of Animals being made Red by Aliment only. By John Belchier, F. R. S. N° 443, p, 299. In the former account, p. 7g, concerning the red bones of the hogs, Mr. B. mentioned, that the colour was occasioned by bran being mixed with their common food, after it had been used to clean printed callicoes ; the colours of which were made, some from preparations of iron, which were the blacks and purples ; others from preparations of alum, and sacc. saturni, which produces the red colours ; and that madder root was used to fix these colours on the cloth. To which of these preparations the colour was owing, could not then be determined. Some were of opinion, that it was entirely occasioned by the preparations of iron ; others, that it was the whole blended together. But to clear up this point, Mr. B. made the following experiments. The first was made on a cock, by mixing some of the madder root with fig-dust, on which they feed. The cock dying within ]6 days after his first feeding on the mad- der, he was dissected, and the bones examined, not in the least expectation of finding them tinged in so small a time ; but they were found universally of a red colour. So that, from this experiment it appears, that the madder alone causes tliis alteration. But why the bones only are aflx-cted, must be deter- mined by future experiments. M 2 84 PHILOSOPHICAL TRANSACTIONS. [aNNO 173(5. The Immersions and Emersions of the four Satellites of Jupiter, for the Year 1738, computed to the Meridian of the Royal Observatory at Greenwich. By James Hodgson, F. R. S. N°443, p. 301. Mr. Hodgson's usual annual calculation of the eclipses of Jupiter's satellites: but omitted, for the same reason as before. On the Fiper-catchers, and their Remedy for the Bite of a Viper. By William Burton, M.D. at Windsor. N° 443, p. 312. William Oliver and his wife called on Dr. B. with their vipers, and either of them offered to be bitten by any viper, and to suffer their arm to swell for some tiuie ; and then, by the external application of a common cheap remedy, in a few hours to remove all the symptoms. Accordingly the experiment was made in the town-hall at Windsor, before Dr. Derham, Dr. Waterland, the physicians, apothecaries, and surgeons of this town, and many other gentle- men of the neighbourhood. The man was bitten in the upper joint of the thumb, and higher upon the same arm, by two different fresh vipers. His thumb, hand and arm soon after swelled much, and all the usual symptoms of a viper-bite followed. He applied the remedy [sallad oil] before us, with the promised success. ^n Account of the Experiments made June 1, 1734, before several Members of the Royal Society, and others, on a Man, who suffered himself to be bitten by a Viper, or common Adder; and on other Animals likewise bitten by the same, and other Vipers. By Cromwell Mortimer, M. D. Seer. R. S. With some Remarks on the Cure of the Bite of a Mad Dog. N° 443, p. 313. William Oliver and his wife, from Bath, who follow the business of catching and selling vipers, offered themselves to be bitten by any viper that should be procured, trusting to the virtue of a remedy they had discovered in trying a va- riety of things, when the woman was once accidentally bitten, and the usual known medicines, even the oil of vipers, had no effect in assuaging her pains, especially of her breast on the same side as the hand in which she had received the wound. This remedy, which is only common oil of olives, and, from its use with sallad, is commonly known by the name of sallad oil, recommends itself not only for its efficacy, but also on account of its being readily to be come at when accidents happen. On the 1st of June 1734, in the presence of a great number of persons. VOL. XXXIX] PHILOSOPHICAL TRANSACTIONS. 85 the said William Oliver was bitten by an old black viper, or adder, brought by one of the company, on the wrist and joint of the thumb of the right hand, so that drops of blood came from the wounds. He said that he immediately felt a violent pain and shooting from the wounds, both to the top of his thumb and up his arm, even before the viper was loosened from his hand; soon after he felt a pain, resembling that of burning, trickle up his arm ; in a few minutes his eyes began to look red and fiery, and to water much: in less than half an hour, he perceived the venom seize his heart, with a pricking pain, which was attended with faintness and shortness of breath; on which he fell into violent cold sweats: in a few minutes after this, his belly began to swell, with great gripings and pains in his back, which were attended with violent vomitings and purgings. He said, that during the violence of these symptoms, his sight was gone twice, for several minutes at a time, but that he could hear all the while. He said, that in his former experiments he had never deferred making use of his remedy longer than when he perceived the effects of the venom reaching his heart; but this time, being willing to satisfy the company thoroughly, and trusting to the speedy effects of the oil, which had never failed him, when used in time, he forbore to apply any thing till he found himself exceedingly ill, and quite giddy. About an hour and quarter after he had been first bitten, a chafing-dish of glowing charcoal was brought in, and his arm, the cloths being stripped off, was held over it, as near as he could bear it, while his wife rubbed in with her hand the sallad oil, (which Dr. M. had procured and kept himself in his pocket, lest they should privately add any thing to it, having bought it by the name of Lucca oil). Turning his arm continually round, as if she would have roasted it over the coals; he said that the pain soon abated, but the swelling did not diminish much, most violent vomitings and purgings soon ensued, and his pulse became so low, and so often interrupted, that it was thought proper by the physicians present, to give him the following cordial draughts, at about a quarter of an hour's distance between each. I. R. Aq. lact. paeon, comp. aa. fiij. Sp. lavendulas 3i. m. pro duobus haustibus. 2. R. Confect. Raleigh. 3SS. aq. theriacal, §iss. sp. c. c. g". x. m. f. haustus. 3. R. Confect. Raleigh, theriac. Andromach. aa. 3SS. sal. c. c. gr. v. aq. the- riacal. §ij. pro duobus haustibus. He said he was not sensible of any great relief from these cordials; but that a glass or two of olive oil drank down, seemed to give him some case. Continuing in this dangerous condition, he was put to bed, as soon as one could be got ready for him, where his arm was again bathed with his remedy e6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. over a pan of charcoal set by the bed-side; but continuing to complain much of his back and belly, Dr. M. advised his wife to rub them likewise with sallad oil, heated in a ladle over the charcoal: which she did accordingly; on which he declared he found immediate ease, as if by some charm; and he had not above two or three retchings to vomit and stools afterwards, but made water plentifully, which was not discoloured. He then soon fell into a sound sleep; only was often interrupted by persons coming to see and inquire after him, till near 12 o'olock, from which time he slept continually to 5 or 6 next morning, when he awaked, and found himself very well; but in the afternoon, on drink- ing some rum and strong beer, so as to be almost fuddled, the swelling returned with much pain, and cold sweats; which abated soon, on bathing the arm as before, and wrapping it up in brown paper soaked with oil. Immediately after the man, two pigeons were bitten by the same viper. They soon sickened, and seemed giddy. Nothing being applied, the one died in about an hour's time, the other half an hour after. The flesh of both was turned quite black, as if mortified; the blood was coagulated, and looked black. June 3, the man's arm remained swelled, looked red, marbled with spots of yellow, but felt soft; and he had the perfect use of it, and even of his fingers, no pain or stiffness being left. He then caused a small spaniel dog to be bitten on the nose by a fresh viper; some oil was immediately applied hot, and rubbed well in, till all the hair of his nose was thoroughly wet ; the dog did not seem very uneasy; his nose only swelled a little; he eat soon after; his nose was bathed once more that evening ; he was found very well next morning; but his nose was bathed again, to make sure of his cure; he remained per- fectly well without any symptoms ensuing, and was alive and well a year after. Another pigeon was likewise bitten under the wing at the same time as the dog, but by a fresh viper. The oil was immediately applied hot, and rubbed well in, and the feathers of the wing were thoroughly wetted with it. This bird did not seem at all disordered with the venom, but ate soon after, and was found well the next morning, without any remarkable inflammation or swelling about the part. The hot oil was rubbed in again for 2 or 3 days, twice a day, and the bird continued well, so that the viper- catchers carried it with them out of town in triumph, having never before experienced the efficacy of their remedy on so small an animal; which, as it receives the same quantity of venom by a bite as a larger one, is more liable to die under it; and they kept it alive above 3 months, when they killed it and ate it. They said that they had experienced their remedy to take effect on cows, horses, and dogs, 10 hours after being bitten; but that for themselves, who VOL. XXXIX.] PHILOSOPHICAL TKAN8ACTIONS. 87 were frequently bitten in the fields.as they caught the vipers, they always carried a phial of sallad oil along with them, that as soon as they perceived themselves wounded, they without any loss of time bathed the part with it; and if it was the heel, they wet the stocking thoroughly with it; if the finger, which happened oftenest, they poured some of it into that finger of their glove, which they im- mediately put on again, and thus never fell any further inconvenience from the accident, not even so much as from the sting of a common bee. Perhaps the oil may be found of use in the bite of rattle- snakes, and other venomous animals; especially if we consider, that in the fields a man seldom or never receives more than one bite at a time, which does not infect him with so much venom as was instilled into the man's blood, when in these voluntary experiments he suffered himself to be bitten twice together; and had likewise been bitten 3 times but about a week or 10 days before; some remains of which venom, it is highly reasonable to imagine, might still infect his blood at the time he repeated the experiments, so as to make a fresh quantity of the venom operate with greater violence on his body, than if he had been quite a fresh man, never infected with the like poison before, or at least at so great an in- terval of time, tliat his blood might have been entirely free from all remains of such an acrid infection. From these experiments is it not reasonable to imagine, that the oil by itself may be as efficacious against the sting of a scorpion, as if scorpions were infused in it? Thus then a remedy against the bite of the viper is as publicly known as the famous Dampier's powder against the bite of a mad dog, first published by Sir Hans Sloane, Bart, when seer. R. S. in N° 237 of these Transactions, Anno 1698;* which afterwards, when he was president of the Royal College of Phy- • The lichen cinereus terrestris is mentioned as being said to be exceedingly efficacious in curing dogs bitten by mad dogs; in a letter of Mr. Oldenburg's, seer. R. S. Lend. July 6, l672. See Derham's Collection of Philosophical Letters between Mr. Ray and his Correspondents, p. no printed at London, 1718, 8vo. Dr. M. thought it proper to add the following passage taken out of the Journal-book of the Royal Society, supposing it to be what Mr. Oldenburgh hints at in his letter. " Nov. 16, 1671. (Sir Robert Moray) exhibited a certain plant, which was by Mr. Wray called lichen terrestris cinereus, said by Sir Robert Moray to be very good to cure dogs bitten by mad dogs: His Royal Highness having caused it to be given to a whole kennel of dogs, bitten by a mad one, which were all cured, except one of them, to whom none of it was given." The specimen was kept in the repository. The same virtue is likewise ascribed to this plant, in the third part of Morison's Plantar. Hist. Oxon. published at Oxford, Anno l6"99. in folio, p. 632, where tlie author, speaking of the lichen terrestris cinereua. Rail Hist, et Synops. says, Adversus morsum canis rabidi egregium est medica- mentum. Dampier, and the College of Physicians, in their Pulv. Antilyssui, prescribe equal quantities of the 88 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. sicians, by his proposal, was introduced into the London Pharmacopoeia, under the name of Pulvis Antilyssus, Anno 1720. The composition of which is, ash-coloured ground liver-wort and black pepper: the manner of giving it, not only to men, but to dogs and cattle, being accurately set down in the above- mentioned Transaction. Thus it is hoped, that certain cures are discovered for the only two sorts of venomous bites of animals, to which the happy soil of Great Britain exposes its inhabitants. A brief Account, by Mr. John Eames, F.R.S. of a Work entitled. The Method of Fluxions and Infinite Series, with its Application to the Geometry of Curve Lines, by the Inventor Sir Isaac Newton, Kt. &c. Translated from the Ori- ginal, not yet public. To which is subjoined a perpetual Comment upon the whole, CSfc. by John Colson, M. A. and F. R. S. N° 443, p. 320. This posthumous work of our late excellent president, a translation of which we have now received from the hand of the learned and ingenious Mr. Colson, has been long and impatiently expected by the curious in these matters; and now it appears, it will fully answer, if not exceed, those expectations, as well as confirm the reputation the author has so justly acquired by his other writings. For it is written with the same genius and acumen, it explains the principles of his method of fluxions with great clearness and accuracy, and applies those principles to very general and scientific speculations in the higher geometry. And further to explain this work, and to supply such things, for the use of common readers, as the author, according to his usual brevity, has often omitted; the translator has given a comment on a good part of the work, and has promised the rest at a proper season. lichen and pepper: but Dr. Mead, in a single quarto leaf, published by him Anno 1735, altered the proportions of the composition, prescribing double the quantity of lichen to that of the pepper. This difference in the proportions must be left to the judgment of practitioners ; but on the authority of another minute in the Society's Journal-books, it may not be improper to make an addition to the abovementioned Dampier's powder. " March 7, 1671-2. Sir Robert Moray mentioned, that a whole kennel of dogs, belonging to his Royal Highness, were bitten by a mad dog, and had been lately cured by a certain herb called stel- laria, or star of the earth." This plant is the lychnis viscosa, flore muscoso Casp. Bauhin. in English, Spanish catch-fly. See these Transactions, N° 187, where is a receipt to cure mad dogs, &c. in which this plant is a prin- cipal ingredient; which receipt, communicated by Sir Robert Gourdon, was there published by his Majesty's (special) command. Anno l687. Therefore, suppose the composition were to be thus : Take ash-coloured ground liver-wort, black pepper, and the herb Spanish catch-fly, all finely powdered, of each 2 drachms, for 4 doses, to be taken as Dampier prescribes in his letter in these Transactions, N" 237. Orig. VOL. XXXlx] PHILOSOPHICAL TRANSACTIONS. SQ This text may very well be divided into three parts: an introduction, con- taining the method of infinite series; the method of fluxions and fluents; and lastly, the application of both to the most considerable problems of the higher geometry. The comment consists of very valuable and curious annotations, illustrations, and supplements, in order to make the whole a complete institu- tion for the use of learners. Of an Inguinal Rupture, with a Pin in the Appendix Cceci, incrusted with Stone; and some Observations on fVounds in the Guts, By Claudius jimyand, Esq. F. R. S. N° 443, p. 329. Oct. 8, 1735, Hanvil Anderson, a boy 11 years of age, was admitted into St. George's Hospital, for the cure of a hernia scrotalis, which he had from his infancy, and a fistula between the scrotum and thigh terminating into it, which for a month before had discharged a great quantity of an unkindly matter. The rupture was small, and not troublesome, and part of it could be replaced; but as it appeared that the sinuous ulcer sprung from that part that could not, it was evident that the cure of the fistula depended on the cure of the hernia, which latter could be obtained by no other operation than that for the bubono- cele, which was agreed to, and performed the 6th of December following. This operation proved the most complicated and perplexing Mr. A. ever met with, many unsuspected oddities and events concurring to make it as intricate as it proved laborious and difficult. This tumour, principally composed of the omentum, was about the size of a small pippin ; in it was found the appendix coeci perforated by a pin incrusted with stone towards the head, the point of. which having perforated that gut, gave way to a discharge of faeces through the fistulous opening in it, as the portion of the pin obturating the aperture in it shifted its situation. The ab- scess formed in the hernial bag occasionally, and the suppuration for 2 months last past from this place.outwardly, had knit and confounded, and, as it were, embodied together the gut and omentum with the hernial bag, and these with the spermatic vessels and the testicle; so that it was as difficult to distinguish them from each other, as it was to separate them without wounding them ; this pin, whose point was fixed in the omentum, continually shifting its situa- tion, and occasioning a discharge of fseces. The pin frequently lying in the way of the knife, and starting out of the wounded gut, as a shot out of a gun, the inundation of faeces on this occasion, from a gut which could not well be distinguished, were so many difficulties in the way; but the greatest yet was, what to do with the gut, which all this while was unknown, and could not be TOL. vin. N go PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. known till the operation was over; for this appendix coeci, which was the only gut found in the rupture, was so contracted, carnous, duplicated, and changed in its figure and substance, that it was impossible to determine what kind of gut it was, or to find out that it was only this appendix elongated, and in disguise. None of these difficulties were apprehended when the operation was under- taken, in which Mr. A. proceeded as usual ; the omentum, lying uppermost in the hernial bag, was dissected from the parts it was knit to, and particularly the gut it was embodied with, and afterwards cut off close to the abdominal muscles, without any previous ligature, the vessels in it being small, and its substance more like a sweet-bread than a caul. Much time was spent in this dissection; the operator being straitened for room, and greatly disturbed by the discharge of the faeces coming out of the gut, on every motion the pin lodged in it, and the omentum suffered, on the separation of these from each other. The gut forming a double tube, like a double-jointed syphon, continuing in the curve as it passed over the testicle and spermatics, was separated one part from the other, and from the adjacent parts, as far as the aperture in the abdominal muscles, where its imperforated end was separated from them, and thence stretched out and unfolded, which brought in view the aperture made in it by the pin, hitherto concealed, through which that part of it, which was incrusted with chalk, had just made its way out on an occasional pressure, as a cork out of a bottle. It was the opinion of the physicians and surgeons present, to amputate this gut: to which end a circular ligature was made about the sound part of it, 2 inches above the aperture; and this, being cut off an inch below the ligature, was replaced in the abdomen, in such a manner that an artificial anus might be made there, if the patient's case should require it. Afterwards so much of the hernial bag as had been detached from the skin, the spermatics, &c. was cut off, which, as they appeared in a sound state, were preserved in situ. The fistulous opening adjoining to the thigh, and answering to the aperture in the gut, was opened; some angles of skin in the way removed ; the aperture in the muscles, which had been enlarged by incision, was stopped up with a tent; and the rest of the dressings and the situation of the patient ordered so, as to remove from the wound all such pres- sure from within, as might disturb the cure. It is easy to conceive that this operation was as painful to the patient as labo- rious to Mr. A ; it was a continued dissection, attended with danger on parts not well distinguished; it lasted near half an hour, during which the patient vomited largely, and had several stools, but was soon composed by i oz. of diacodium, and emollient embrocations and fomentations, frequently applied VOL. XXXIX.j PHILOSOPHICAL TRANSACTIONS. Ql warm on the belly; he was blooded, and an emollient carminative oily clystei* was ordered to be applied in the evening; but as he was easy, and the belly not tense, that was omitted. He was confined to a very spare diet, and his body kept open by clysters, injected every second day, when stools were wanted, to prevent straining. When dressed on the 4th day after the operation, every thing appeared well, and there was good reason to hope for a cure, especially as the discharge by the anus was natural. The tent put into the abdominal aper- ture was not removed till the 8th. On the ]Oth, the ligature round the ap- pendix coeci, where it had been amputated, dropped off, and no faeces followed it; and as it was then plain they had taken the natural course, from that time the wound was treated like an ordinary one, only care was taken to keep a strong and constant pressure over the abdominal aperture, as well to fence against the intrusion of the viscera into the wound, as by a strong incarnation and cicatrix, effectually to secure the patient against a rupture. During the time of the cure he was confined to his bed, always kept to spare diet, and or- dered never to go to stool but in a bed-pan; by these means the wound was completely healed up in less than a month, and the patient soon after dis- charged with a truss, which he was ordered to wear some time, to confirm the cure. That the appendix coeci should be the only gut found in this rupture, is a case singular in practice : this was full of excrements, and occasionally could be distended with an additional quantity, which on pressure was returned into the colon, with that kind of noise which guts replaced generally give. This had occasioned a diminution of the tumour when compressed, before the operation was performed, as the patient was lying backwards with his head downwards, and an increase of it as he stood erect, when the faeces from the colon could get into it again. The patient does not remember when he swallowed the pin, which had per- forated the gut within the rupture. But as this rupture was from his infancy, fixed and unreducible, it is likely the pin had then made its way into the ap- pendix coeci prolapsed ; and that an inflammation ensuing, had occasioned an adhesion, by which the increase of the tumour had been checked, and the reduction of the prolapsed parts rendered impracticable. The surgeons who constantly dressed the patient before the operation, ob- served then, as they have since, that the humour discharged formerly at the fistula, had frequently the appearance and the smell of excrements, so that there is no doubt that the cause of it was the wound made in the gut, by the pin giving way occasionally to such a discharge. The patient also perfectly remembers, that the imposthumation or gathering", preceding the fistulous dis- N 2 gi PHILOSOPHICAL TRANSACTIONS. [anNO 1/36. charge, was attended with very little pain, or much less than generally attends suppuration. Which shows that the extravasation of the excrements from the gut into the hernial bag, and the bursting of this bag, were the cause of the fistulous discharge, and of the continuance of it outwardly. As to the pin found in the rupture at the time of the operation, it is observ- able, that two-thirds of it, incrusted with a chalky matter, were confined and concealed within the gut ; the other third, next the point, had made its way through it, the point of which was so lodged in the omentum, where it was fixed, as to leave a free passage for the excrement from the perforated gut out- wardly, whenever the perforation in the gut, on shifting the position of the inclosed pin, could open, and afford a passage for the discharge of the faeces this way, which was as often as this conical or pyramidal pin altered its place, or did not exactly obturate the aperture in the appendix ccEci, it exactly fitted. The aperture made in the gut by the pin lay concealed, the point being lodged in the omentum, lying parallel with the gut, which was here duplicated, where it was so secured, that it seemed almost impossible it could ever make its way out of this place, and its other confinement in the gut, as the aperture was callous, and so resisting that it was with some violence it was forced out of its confinement, through an aperture fitted for the point only, and so straight, that the report on its coming out, was like that of a cork out of a bottle; for though it appeared that the opening had occasionally been enlarged, as the in- crusted part of the pin was pressed forward into it, yet it is plain that nature's attempts to get rid of it had been fruitless, and might possibly have been so during all the patient's life. Sir Hans Sloane has furnished the curious with instances of bodies incrusted in the guts with stone, and of some making their way out, when there was little probability of it. Daily experience shows how far nature will struggle to free herself; so that it is always most eligible to trust them lo her care : this may appear from the difficulties that have attended the cure of this case, which at last did not prove so successful as it was first hoped for; for the patient having been remiss in the wearing of his truss, on some effort the guts found a way into the inguen again, 6 months after the healing of the wound. This case also shows, that the best operation, or the utmost care, is no security against the relapse of a rupture. This is the third or fourth instance Mr, A. had met with, of the insufficiency of this operation to effectuate a cure of ruptures; and yet it is plain that this is far more likely to prove effectual than the caustic, or any other method cried up for the cure of this evil. In a growing age, a good spring truss is an eflfectual remedy ; and in an adult, this should be the ultimate one, though it is no more than a palliative cure. VOL. XXXIX.3 PHILOSOPHICAL TRANSACTIONS. <)3 After mentioning 4 other cases of hernia and wounded guts, Mr. Amyand subjoins the following practical inferences. Hence it appears, that the parts inflamed and in contact, have been coalesced and knit together, so as to prevent any extravasation from the wounded or bursted gut into the cavity of the abdomen. That the cure in some cases has been owing to a free discharge of the faeces through the wound ; and consequently that when, in a gut rupture, the part prolapsed cannot be reduced ; a cure may be hoped for, by making such an opening in the guts, before they are entirely sphacelated, as may procure a free discharge to the faeces pent in, and thus secure the patient's life. That if this happens to the colon or caecum, its tube will so far be preserved, as to open a free discharge for the faeces the natural way ; and if that cannot be obtained in a wound of the small gut, yet the discharge may be secured by making the wounds an artificial anus. Tl>at the readiest way to obtain a cure of a wounded or bursted gut, is to keep it in contact with the outward wound, and the patient in a very low diet. That the deligation of the vessels of the omentum, previous to its amputa- tion, being liable to many exceptions, it is more eligible to forbear it, except- ing when the vessels are large; for when reduced loose and floating, it is less liable to the inflammations and suppurations that attend the separation of the ligature. Experiments on Quicksilver. By Herman Boerhaave, M. D. &c. Part II.* N° 443, p. 343. In this 2d part of his communications on this subject, as well as in the 3d part, which is inserted in another of the Transactions, but of which, for the reader's convenience, the substance will be introduced here; Dr. B. prosecutes his experiments on quicksilver, for the purpose of ascertaining the truth or fallacy of its fixibility by the fire, and other properties ascribed to it by the alchemists. Dr. B. subjected pure quicksilver for 15 years and a half (viz. from Nov. 17 18, to May 1734) to the continued action of a degree of heat equal to 100 and upwards of Fahrenheit's thermometer, in a phial, which admitted the air without admitting any particles of dust. At the expiration of this length of time, he found the quicksilver in the phial still fluid, with the exception of a very small portion of a black powder on its surface, which powder was after- wards revived by trituration in a glass mortar. Being afterwards subjected to • For Part I. see Philos. Trans. N" 430j of theie Abridgments, Vol. vii, p. 619. 94 PHILOSOPHICAL TKANSACTIONS. [anno 1736. distillation, the whole of the mercury passed over into the receiver in the form of fluid quicksilver, without leaving any residuum in the retort. Hence (says Dr. B.) it is evident, that quicksilver is not fixable by long continued exposure to the degree of heat beforementioned. But lest it should be objected that the access of the air prevented its fixation. Dr. B. subjected a quantity of purified quicksilver to lOO degrees of heat for 4. year (viz. from Dec. 173'i to July 1733), in close vessels. He afterwards subjected a quantity of this quicksilver to the heat of a sand-bath, nearly equal to the heat of boiling water, in vessels well closed. The quicksilver was found to be unaltered, excepting a very small quantity of black powder on its surface, which, as in the former instance, was revived by trituration. Being subjected to distillation, the whole of the quicksilver passed over into the receiver, leav- ing no residuum in the retort. The futility therefore of attempting to fix quicksilver is clearly proved. But it had been asserted by some chemical authors and particularly by Van Helmont, that some metals were resolvable into quicksilver. " When lead (says the last mentioned chemist) is dissolved by alkalies and salts, or oil, which take in the sulphur and separate it from the body, the lead by this means becomes changed into a volatile running mercury, which can no more endure the fire, as before, but is cold and running like water, and without a metalline form." (Vide Paradoxical Discourses of V. Helmont, Lond, l685. Part II. § 22.) The same thing is affirmed by Joachin Becher. (Vide Collectanea Quingentor. Experimentorum k p. 310, ad p. 333.) But after subjecting lead to processes similar to those described by the last mentioned authors, as well as to a treatment similar to that described by Isaac Hollandus ; Dr. B. was unabls to extract a single particle of quicksilver from that metal. ^ Dr. B. afterwards made a numerous and laborious set of experiments on amalgams of lead and quicksilver, of tin and quicksilver, and lastly of gold and quicksilver. After long-continued* digestion in a heat of 84, the amal- gam of lead being distilled, the quicksilver passed over into the receiver, minus 43 grs. in 3 oz. (the total quantity of quicksilver operated upon in this expe- riment) in part accounted for by the red powder (precipitate per se) which re- mained behind in the retort, which was not volatile in the aforesaid degree of heat. The weight of the lead was found to be the same as before the opera- tion, viz. 1 oz. Hence it appears that no mercury is obtainable from lead-|- by amalgamation, digestion and distillation with quicksilver, in the manner above- mentioned. * From the 1 1th of Feb. 1732, to the 10th of Jan. 1735. f In other words, none of the lead is convertible into mercury. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. ' QS An amalgam of tin and quicksilver in the same proportions (viz. 1 oz. of tin and 3 oz. of quicksilver) being digested in the same degree of heat, and afterwards subjected to distillation ; there passed over into the receiver '2 oz. 4 drs. of quicksilver. There remained behind in the retort a powder, the finer part of which consisted of fixed mercury,* and the coarser black portion of particles resembling tin. There adhered to the neck of the retort a small quantity of quicksilver, weighing 2 drs. 5 grs. The residuary mass of tin weighed 1 oz. 1 dr. g grs. There was a loss of 46 grs. This experiment shows that quicksilver cannot be extracted from tin; but more than a seventh part of the quicksilver remained combined with and fixed in the tin, even when subjected to a red heat for the space of 4 hours. — Dr. B. mentions that the quicksilver distilled from the lead and tin amalgams, on being shaken in a clean white glazed earthen vessel soon deposited a black stain on the sides of the vessel : that on being spread out on writing paper, the said quicksilver left a black trace where it passed over the paper ; and lastly, tiiat when at rest, the surface of such quicksilver was always covered with a greasy pellicle or film. Hence he supposes, that some of the particles of these metals may be volati- lized by the quicksilver; but this he observes is very different from the actual conversion (as some have supposed) of a portion of these metals into quick- silver. The results of Dr. B.'s experiments on amalgams of gold and quicksilver, are related in the 3d part of his communications on this subject. After subjecting an amalgam of gold and quicksilver to digestion and repeated distillations,-|- the gold was found to be of the same weight, and to possess the same proper ties as it did before it underwent this treatment. The quicksilver was in part converted into a very fine brown powder, of a sharp metallic taste, which how- ever was again brought to the state of fluid quicksilver, by the action of a stronger degree of heat. Thus there was no purification of the quicksilver by the gold in this experiment, the latter metal being found unaltered after the operation. When an amalgam of gold and quicksilver is exposed to the fire, the silvery appearance of the amalgam is changed first into a brown, and afterwards into a black colour ; but by the action of a higher degree of heat, the yellovy colour is restored to the gold, and the silvery lustre to the quicksilver. From these experiments it is inferred, that all hopes of fixing quicksilver by subject- ing it to the action of the fire with gold, must be relinquished for ever. • i. e. not volatile in the beforementioned degi-ee of heat, t In the course of these experiments, the distillations were repeated 877 times ! 96 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. A Partial Eclipse of the Moon, observed at fVittemberg, Oct. 2, 1735, N. S. By J. F. Weidler, F. R. S. N° 443, p. 359- At O** 59" A. M. The eclipse began. 3 36 The eclipse ended. Account of a Shock of an Earthquake felt in Sussex, Oct. 25, 1734. Com- municated by Charles Duke of Richmond and Lenox, &c. F. R. S. And of another in Northamptonshire, in Oct. Anno 1731, by the Rev. Mr. fVasse. N°444, p. 361. On Oct. 25, 1734, between 3 and 4 in the morning, there happened an extraordinary earthquake in Sussex. And what confirms the Duke in the opinion that there really was an earthquake, is, that almost every one agrees in the same description, as to the sensation, the hour of its happening, and the perfect calm that was at that time. His Grace observes that the shock was vastly more felt towards the sea-side, as at Shoreham, Tarring, Goreing, Arun- del, and Havant. At his house of Goodwood, which is near 3 miles north of Chichester, and about 7 from the sea, it was not so perceivable as at Chichester, and where it was still less so than by the sea-side. It is not heard as yet that there was the least touch of it in any parts of the vale on the north-side of the Downs, which for the most part run east and west. What Dr. Bayley of Havant says of the different motions of the beds, according to the different situations they were in, seems very well worth observing, being a very curious man. Above 50 more accounts might be collected from the several places abovementioned; but as they all tend to the same purport, the following may be sufficient. An Account of the same Earthquake at Havant in Sussex. By Edw. Bayleij, M. D. N" 444, p. 362. Oct. 25, 1734, between 3 and 4 o'clock in the morning, an earthquake was felt at Havant, in Sussex : the shock was so considerable, as to be observed by one or other in most houses of the town. Happening to be aw.ike at that time, the Dr. perceived the bed shake under him, with a quick tremulous motion, which continued about 2 or 3 seconds, then ceased ; and after a very short intermission was repeated in the same manner, and lasted about the same space of time. He was at first much surprised at such an unusual phenome- non; but on a little recollection, concluded it must be occasioned by an earth- quake, and was soon confirmed in his conjecture by the concurrent observa- VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 97 tons of the neighbours, and afterwards by accounts of the same from many other places; in some of which it seems to have been more violent than at Havant. Several persons in this place say, that they not only perceived the shaking of their beds, but also the rocking of their houses, with a rumbling noise of drawers, and the like moveable goods, in their chambers, and other rooms. A learned and ingenious gentleman in that town affirmed, that the motion of his bed appeared to him like the tossing of a vessel when it crosses over a wave, the head and feet rising and falling alternately several times ; whereas the Dr.'s seemed rather to rock from side to side : but these contrary motions of the two beds are easily accounted for, by considering their dif- ferent positions, the former standing directly east and west, and the Dr.'s north and south : for supposing the undulatory motion, which the earth might have at that time, was propagated from east to west, the same kind of motion which caused the former bed to rise up and down lengthwise, must make the latter rock from side to side; as may be observed in two vessels sailing in con- trary directions on the same waves of the sea, that which crosses the waves at right angles being tossed up and down endwise, while the other moving in a line parallel with the waves, is rocked from side to side. What makes the Dr. more inclined to think the progressive motion of this earthquake was from east to west, is, because it appears from the best accounts, that it was observed sooner east than westward, and likewise extended farther from east to west, than north and south. The Dr. thinks it may not be amiss to take notice of some remarkable phae- nomena, which happened before and after, as well as some other circumstances which immediately attended this earthquake, most of them agreeing with those signs which have been observed by the learned to precede or accompany former earthquakes, in these and other parts of the world. It was observable, that there had been of late more rain and wind for several months successively, than for many years past ; especially from the beginning to the middle of this month ; about which time it cleared up, and the weather became suddenly very cold, with frosty mornings, the wind blowing generally pretty hard from n. w. On the 23d, the cold abated considerably ; it was cloudy, but no rain. The 24th was very calm all day ; it rained most part of the afternoon, though the mer- cury stood at ?>0-iV- It continued very calm all night, and rained hard for some time before and after the earthquake happened ; but it soon cleared up, and a strong gale of wind rose within half an hour, or, as some say, within a quarter afterwards : it continued blowing hard all the forenoon. Philip Boisdaune, Esq. of the parish of Funtington in the county of Sussex, and many other persons, all agree, that there was a manifest shock of an VOL. VIII. O 98 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. earthquake felt on Oct. 25, about 4- before 4 in the morning, which lasted by fits some few seconds, about -j- of a minute, or while one might deliberately count to 20: for most of the accounts concur in this particular, that the chairs, wainscot, doors, chests of drawers, and other moveables, were heard rattling ; and one, that a bell rung of itself just before they felt the heaving of their beds ; and that there was no wind stirring at that time, but that it rained, and the wind rose soon after. Of a Shock of an Earthquake felt in Northamptonshire, in October 1731. By the Rev. Jos. Wasse. N° 444, p. 367. 1 About 4 in the morning, Oct. 10, 1731, the Rev. Mr. Jos. Wasse, rector of Aynho in Northamptonshire, says, that his windows rattled, as if some- body had been dancing over-head. The concussion lasted about 1 minute ; others thought it lasted about 2 minutes. It alarmed the neighbouring vil- lages, Bloxham, 4 miles south-west from Anyho; Barford, b ; Banbury, 4 west; Adderbury, 1 mile west ; Crowton, 1 mile to the east; and Charlton, as much to the north. There was no notice of its progress south or south- east. About 1 minute after, some of the town of Aynho saw a great flash of lightning. In the morning the sky looked of a land-colour. It was said that there was a former shock felt upon Oct. 8, about 3 in the morning; and that the latter was preceded by a noise like distant thunder. It is remarkable, that this shock was perceived to extend more from east to west, than from north to south ; which particular was likewise observed in the last shock felt in Sussex 1734. Experiments on Quicksilver. By Dr. Boerhaave, Part III. N° 444, p. 368. From the Latin, The substance of this paper has been incorporated with Part II. inserted at p. 93, of this vol. of the Abridgments. Concerning an Improvement of the Diving Bell. By Mr. Martin Triewald, F. R. S. Captain of Mechanics, and Military Architect to his Swedish Majesty. N" 444, p. 377. Mr. Triewald having made trials with the diving bell and air barrels in several depths, on the coast of the Baltic, according to the ingenious improvement of Dr. Halley, made in the year 17 16, but with some small additions; he found by experience, that no invention founded on any other principles than those of VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 99 the campana urinatoria, can be of use in any considerable depths; or that the diver, in any other invention whatever, can be a single moment safe. As to the many inconveniences that attend other inventions, he only mentions that of a water armour, in which the man is drowned in an instant, when such a ma- chine receives the least leak ; whereas experience has shown, that when such an accident has happened to the diving bell, as to his knowledge it did once, when the diver was 12 fathom under water, and a pretty large hole happened to be struck in the bell, by a bolt of the wreck he went upon, when the air rushed out of the same with such violence as astonished the beholders by the excessive boiling on the surface of the water, fearing, not without reason, that the man in the bell vvas drowned; but he clapped his hand to the hole or leak, and gave a sign to be hauled up, which was done with all the ease and safety as if no accident had happened to him, the water having only risen about half a foot into the bell by this leak. The very same diver that was then in the bell is 63 years of age, and has used the business of diving ever since he was 20, in a common diving bell. He declares that never a worse accident happened to him in his business, except once, when the bell he was in rushed down at once about a fathom or more, by the carelessness of those that worked the bell; at which time the blood came out of his nose and ears, feeling besides an intolerable pressure on his whole body; which shows, that when a man in a diving bell is slowly and gradually let down, he at such a time and by degrees respiring compressed air, which by the lungs is forced into the blood, cannot feel the external pressure, though of highly compressed air, surrounding him, and that of the water reaching some parts of his body; which convenience no other invention can yield or afford, where the diver is to draw his breath from air in its natural state. Mr. T. has often with a great deal of pleasure observed, that when he has caused the bell to stop, being lowered down 5 fathom, and the diver taking in the air contained in an air barrel, lowered down a fathom deeper than the bell, without opening the cock for discharging the hot air; the water would, by the access of the air out of the barrel, be almost all expelled out of the bell ; and when the same was again lowered down 5 fathom more, the same operation with another air barrel repeated, and the bell afterwards hauled up, it was no small matter of delight to see, that every fathom the bell came up, it would discharge itself of the superfluous and large quantity of air; which can)e up from the bottom of the bell in very large bubbles, as large as ostrich eggs; which dis- charge of air and phenomenon continued till the equilibrium of the air in the bell, and pressure of the water, were restored, and till the bell came above the surface of the water. o 2 100 PHILOSOPHICAL TRANSACTIONS. [anno 1736. At other times he has observed, when no air was by the way taken into the bell, but the same lowered down the common way, and hauled up again after some time, that the very instant when the bell should part with the surface of the water, the strength of two men more was required at the capstan at that time, than before and after the bell hung freely in the air; from whence he thinks it plainly appears, that the air which passes through the lungs of an ani- mal loses its elasticity, and that the lungs of a man make a kind of a vacuum in the bell; for which re.nson the diver feels at the instant when the bell parts with the water, a very smart pressure in his ears. Though experience thus has taught that no invention is more safe and useful than the campana urinatoria, with the ingenious improvements of Dr. Halley; yet M. Triewald has found, that this invention is not to be used without con- siderable charge ; requiring a large vessel, and number of hands, to the work- ing and managing of such a large diving bell, and the air barrels with their respective weights for sinking; which charges however, according to the depth of water, and the value of what is to be brought up from the bottom of the sea, may not be regarded; but since it more frequently happens in these parts, that cargoes of a far less value than the loadings of Spanish galleons, &c. are to be dived for; then next to the goodness of the invention, he has found it neces- sary to think how the expences might be lessened, and the diving bell still an- swer all the purposes of Dr. Halley's; which improvement is as follows: The diving bell, ab, fig. 8, pi. 2, is made of copper, and reduced to a very little compass, in respect to Dr. Halley's, by which means it is easily managed by two hands: yet Mr. T. thinks that a diver may not only live in the same as long, and with as much ease, at a very considerable depth of water, as in a bell of twice its capacity, for this reason, though a man in a large bell has undoubt- edly more air than in a less, and consequently should be able to subsist much longer on a large quantity of air than on a small parcel: yet as his head is kept chiefly in the upper part of the bell, occupied by the hot air, he receives very little or no benefit from the air under his chin or breast, though never so fit for respiration; which air in the lower parts of the bell will yet remain cool a long time after he has been in the bell, and with difficulty drawn his breath; which cannot be denied, and is very obvious to any who have been in a German bagnio, and such as are made use of in this country, where in a single room all the degrees of heat are to be felt, by means of a contrivance like stairs to the very top of the ceiling; a man on the uppermost step feels an excessive heat, so that one not much used to it cannot endure the same, nor draw his breath, but will faint away; whereas on the first, second, and third steps from the floor, the heat is very moderate; nay, sometimes the air near the floor pretty cool, when at the same time near the ceiling the heat is intolerable. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. Id To obviate this inconvenience, he caused a spiral tube of copper, be, to be placed close to the inside of the bell, so fixed that it may be easily taken out and cleansed at pleasure ; and at the same time not to incumber the diver in the bell. At the upper end of this tube, a flexible leather tube is joined, 1 feet long; at the end of which is a turned ivory mouth-piece, which the diver, as soon as he perceives the air to grow hot in the top of the bell, keeps constantly in his mouth, which he is able to do in any position, by means of the flexible tube, standing, sitting, bowing his head, &c. And all the while he draws his breath through it, and the air from c; by which contrivance he not only draws continually cool and fresh air as long as any is in the bell, but occasions at the same time a circulation, which is so necessary to the very being of air, espe- cially in a compressed state, and its preservation for the use of animals; and so much the more necessary, as any body who has been in a diving bell for a long time without any new supplies of air, and has been reduced to the last extre- mity of breathing in it, will agree, that when at such a time the bell begins to be drawn up, and by that means the compressed air allowed to expand, and be put into motion ever so little, the man receives as it were a new life, and incre- dible comfort and ease. Again, when, in coal-pits, levels are driven in the coal, or through dykes, the air of the level or adits growing hot by the breath and sweat of the hewers and workmen, for want of a circulation of the air; he has found it to be an excellent remedy, to place along the side of the drift or adit, a square wooden box, open at both ends, laid from the place where the air is cool and good, reaching as far, by joining one box close to another, as where the work is car- ried on. Thus, by this simple contrivance, a circulation of air is obtained, and sometimes to that degree, that when a candle is held at the end of the box where the cool air enters, the flame is driven out by the current of cold air entering and circulating through the box. By which experiment he thinks, that though the diver should not keep the end of the flexible tube in his mouth, which he may easily do, yet that the air would circulate through the copper tube, and he will receive no small benefit by it. DD are the weights for sinking the bell, so contrived as easily to be hooked on the same hanging on the cable. The iron plate e, fixed to the chains fff, serves the diver to stand upon, when he is at work. The bell is very well tinned on the inside; and as in all rivers, and the coasts of the Baltic, the water is exceedingly clear and limpid, because there is no ebb and flood, M. Triewald has placed strong convex lenses gcg ; by which means the diver can not only see what is under him, but also on all sides at a good distance. These glasses have strong copper lids, hhhh, like snufF boxes, which are 102 PHILOSOPHICAL TRANSACTIONS. [aNNO IJSS. shut, when there is no occasion to discover any objects in the bottom of the sea, and serve to preserve the glasses from being broken. A Description of the Moose* Deer of New England, and a sort of Stag in Firginia ; with some Remarks on Mr. Ray's Description of the flying Squirrel of America. By Mr. Samuel Dale. N° 444, p. 384. The moose-deer has been mentioned by several authors ; but their accounts have generally been so very imperfect, as to afford little satisfaction to the curi- ous enquirers into natural history. The first mention that Mr. Dale finds made of this animal, is by Mr. Josselyn, in a small tract, called New England's Rarities ; where he says, " that it is a goodly creature, some of which being 12 feet high, their horns exceeding fair, with broad palms; some being 2 fathoms from the top of one horn to the other." Much to the same purpose is the ac- count he gives of this animal in another book, called Two Voyages to New England, where, he says, " that the moose or elk is a creature, or rather a monster of superfluity, when full grown, being many times bigger than an English ox." What Neal, in his History of New England, Vol. ii, p. 573, has of this animal, called by him the mose. is copied from Josselyn. The best and fullest account of this animal was sent by Mr. Dudley, and published in Phil. Trans. N° 368, where he makes them to be of 2 sorts, viz. the common light grey moose, called by the Indians, wampoose ; and the large or black moose. As to the grey moose, Mr. Dale takes it to be no other than that which Mr. John Clayton, in his account of the Virginia quadrupeds, published in Phil. Trans. N°210, calls the elk: which in the Memoirs for a Natural History of Animals, published at Paris, and rendered into English by Mr. Pitfield, p. 167, is called by the name of the stag of Canada, of which Mr. Dale has seen a single horn, sent by Mr. Mark Catesby from Virginia, by the name of an elk's horn, which was in all respects like those of our red deer or stags, only larger, weighing about 12 pounds avoirdupois; and from the burr to the tip, measured by a string, about 6 feet high. Mr. Dudley writes that his grey moose is most like the ordinary deer ; that they spring like them, and herd together sometimes to the number of 30 in a company. But whether he means the red, the Virginian, or the fallow deer, is uncertain, having said nothing of their horns, which was necessary to distinguish them. The black moose is ac- counted by all writers a very large creature. Mr. Josselyn makes it many times larger than an ox ; and Mr. Dudley writes, that the hunters have found a buck or stag-moose 14 spans high from the withers; which at 9 inches to the span, * The moose is the American variety of the ccnitu alee* of Linnaeus. VOL. XXXIX.] PHILOSOPHICAL TKANSACTIONS. 103 is 10 feet and a -J-; and that a doe or hind of the fourth year, killed by a gentle- man near Boston, wanted but 1 inch of 7 feet in height. The stag, buck, or male of this kind, has a palmed horn, not like that of our common or fallow deer, but the palm is much longer, and more like that of the German elk ; from which it differs, in that the moose has a branched brow-antler, between the burr and the palm, which the German elk has not. Fig. 7, plate 4, represents the head, or rather the attire, as it is called in heraldry, of a black moose-deer, which was sent to Mr. Dale from New Eng- land ; the dimensions of which are, as follow : AB 56 inches, ca 34, ce 31, cd 34, dh 30, fg Q-l, fi 14, kl 7. The horn of this New England black moose agrees not in figure with either of those mentioned in Phil. Trans. N°227, and N°394, found fossil in Ireland; the last of which Mr. Kelly writes, that for want of another name, they called them elks-horns. Mr. Dale suspects that those horns Mr. Ray mentions, in his Synopsis Methodica Animalium quadruped to have seen with Mr. Holney, an apothecary at Lewis in Sussex, as also in divers museums, were not the horns of this black or American moose, but of the German elk ; because that in- quisitive gentleman takes no notice of any brow-antlers they had, which Mr. Dale thinks was too remarkable to have escaped his observation, had there been any such. As to the number of young ones, or calves, which the moose brings forth at a time, authors vary : for, Mr, Dudley says, they bring forth only 2 : but Josselyn in his '1 Voyages, and from him Neal, that they bring forth 3 ; and that they do not go so long pregnant, as our hinds, by 2 months. What these two last- mentioned authors write, as to their casting their calves a mile distant from each other, does not seem probable ; nor does Mr. Dale find that Neal, in his description of this animal, makes any mention of their having a long tail, though charged so by Mr. Dudley, who also omits the brow-antlers in his de- scription of their horns. There is another beast of the deer kind, which though very common in Virginia, and doubtless in others of the northern provinces of America, yet so far as Mr. Dale knows is not described by any author. Mr. Beverley, in his present state of Virginia, mentions both elk and deer in that country, but does not describe either. But by what Mr. Dale received from Mr. Catesby, the first should be the Canada stag, and the other the deer here mentioned. Mr. Clayton also men- tions the elk, which he says are beyond the inhabited parts, and are the same with Mr, Beverley's ; as also the deer of which he says there are abundance ; yet he does not describe them, but calls them red deer, though they are not the same with what we here call by that name, but of those that follow. ]04 PHILOSOPHICAL TKANSACTIONS. [aNNO 173(5. That which Mr. Dale takes for the undescribed deer, is of the stag-kind having round horns like them, not spreading out as in the stag or red deer, but meeting nearer together at their tips, and bending forwards over the face of the animal ; the brow-antlers are not crooked, standing forwards, but straight and upright, as represented fig. 8, the dimensions of which are as follow : ab 1 1 inches, acb 20, ad 12-i-, df 12^, de 11, gh 24. The skin of this deer is of a sand colour, with some black hairs intermixed, and while young spotted all over with white spots, like some sorts of fallow deer ; being likewise about their size when full grown. The Dama Virginiana Raii Synop. Animal, Quadruped, p. 86, which was formerly in St. James's-Park, seems to be different from this ; if Mr. Willoughby was not led into a mistake in taking it to be of the palmate kind, by only seeing it when the horns were shed : perhaps this last of Mr. Ray may be the maurouse of Josselyn's Voyages, p. 91, which he says is like the moose, only his horns are but small, and the creature about the size of a stag ; but his description is too short to be satis- factory. There are other kinds of deer mentioned by Mr. Josselyn in his book, p. 87, as natives of that country ; as the buck, stag, and rein-deer : but whether they are the same with those called by the same names in Europe, Mr. Dale cannot determine ; their descriptions being omitted. Mr. Josselyn also mentions, as another kind of American deer, an animal called a maccari, caribbo, or pohana: but by the account he gives, it seems to be a fiction ; no such animal being, Mr. Dale thinks, in rerum natura. Mr. Ray, in his Synop. Quad. p. 215, rather refers the sciurus Americanus volansto the mouse, than to the squirrel kind,* because their tails are broad and plain, and not turned over their backs when they sit; which mistake may pro- bably arise from only seeing the skin of a dead one, when the hair of their tails had been eaten off by mites : for, in one Mr. Dale saw alive, which was brought from Virginia, the tail was hairy, as in others of the squirrel kind, though rather thinner ; and it turned over the back as in other squirrels. Dr. Mortimer observes, that the $ame species of flying squirrel has been found in Poland ; a description of which, with an accurate figure, is given by M. Klein, Phil. Trans. N° 427. And that as to the large horns found fossil in Ireland ; he has taken parti- cular notice, in several he saw, besides the main horns being palmated, that the brow-antlers are so likewise ; a circumstance peculiar to the rein-deer species, • The Atnerican flying squirrel is of a pale rufous-brown colour, white beneath, and is the mvt volans, Linn. The Polish or European flying squirrel is a different species, larger, of a grey colour, white beneath, and is the sciurus volans, Linn. VOL. XXXIX. J FHILOSOPHICAL TRANSACTIONS. 105 being of great service to them in removing the snow, in order to get at the grass or moss underneath, which is their chief subsistence in Lapland. An Attempt to explain the Phenomenon of the Horizontal Moon appearing larger than when elevated several Degrees above the Horizon, supported by an Experi- ment. By Dr. Desaguliers. N° 444, p. SgO. This apparent increase of the moon's diameter, which a telescope with a mi- crometer shows to be only apparent, is owing to the following early prejudice we have imbibed from children. When we look at the sky towards the zenith, we imagine it to be much nearer to us, than when we look at it towards the horizon : so that it does not appear spherical, according to the vertical section EFGHi, fig. 9, pi. 4, but elliptical, according to the section epghi. The sky thus seen strikes the eye in the same manner as the long arched roof of the isle of a cathedral church, or the ceiling of a long room. This being premised : let us consider the eye at c, on the surface of the earth ; and imagine c at the surface to coincide with k at the centre ; to avoid taking into consideration that the n)oon is really farther from the eye when in the horizon, than when it is some degrees high. Now when the moon is at g, we consider it as at g, not much farther than g ; but when it is at h, we imagine it to be at h, almost as far again. Therefore, while it subtends the nearly same angle as it did before, we imagine it to be so much larger, as the distance seems to us to be increased. Dr. D. contrived the following experiment to illustrate this : he took two candles of equal height and size, ab, cd, fig. 10 ; and having placed ab at the distance of 6 or 8 feet from the eye, he placed cd at double that distance; then causing any unprejudiced person to look at the candles, he asked which was largest ? and the spectator said they were both of a size ; and that they appeared so, because he allowed for the greater distance of cd ; and this also appeared to him, when he looked through a small hole. Then desiring him to shut his eyes for a time. Dr. D. took away the candle cd, and placed the candle ep close by the candle ab, and though it was as short again as the others, and as little again in diameter, the spectator, when he opened his eyes, thought he saw the same candles as before. Whence it is to be concluded, that when an object is thought to be twice as far from the eye as it was before, we think it to be twice as large, though it subtends but the same angle. — And this is the case of the moon, which appears to us as large again, when we suppose it as far again, though it subtends only the same angle. The difference of distance of the moon in Perigeo and Apogeo, will account VOL. vm. P I06 rHILOSOPHICAL TRANSACTIONS. [aNNO I73S, for the different size of the horizontal moon at different times, adding also the consideration of the faintness which vapours sometimes throw on the ap- pearance. An Explication of the foregoing Experiment, to account for the Appearance the horizontal Moon seeming larger than when higher. By the same. N° 444, p. 392. Dr. Desaguliers having made an experiment with 3 ivory balls, for confirma- tion of what he had advanced, namely, that the deception arises from our judg- ing the horizontal moon to be much farther than it is ; which is as follows. Two equal ivory balls, fig. 11, pi. 4, were set one beyond another in respect of the eye at e, namely, ab at 20 feet distance from the eye, and cd at 40. Now it is certain, by the rules of optics, that the eye at e or p, will see the ball CD, under an angle but half as large as it sees the ball ab ; that is, that the ball CD must appear no larger than the ball op placed by the side of ab. But when looking at the two balls with the naked eye in an open room, we consider that CD is as far again from the eye as ab, and we judge it to be as large as ab, as it really is, notwithstanding it subtends an angle but of half the size. Now if, unknown to the spectator, or while he turns his back, the ball cd be taken away, and another ball op of half the diameter be placed in the same line, but as near again, at the side of ab, the spectator thinking this last ball to be at the place of cd, must judge it to be as large as cd, because it subtends the very same angle as cd did before. It follows therefore — that if a ball be imagined to be as far again as it really is, we make such an allowance for that imagined distance, that we judge it to be as large again as it is, notwithstanding the angle under which we see it, is no greater, than when we look at it, knowing its real distance. For this reason, the moon looks larger in the horizon, and near it, than at a considerable height, or at the zenith : because it being a common prejudice to imagine that part of the sky much nearer to us which is at the zenith, than that part towards the horizon ; when we see the moon at the horizon, we suppose it much farther ; therefore as it subtends the same angle nearly, as when at the zenith, we imagine it so much larger as we suppose its distance greater. The reason why this experiment is difficult to make, is because the light from the ball op is too strongly reflected on account of its nearness ; but if we could give it so little light, as to look no brighter than the ball cd, it would deceive every person. Dr. D. has made the experiment so as to deceive such as were not very long-sighted ; but he found it very difficult to deceive those who see at a great distance ; though they would all be deceived, if the distances were of VOL. XXXIX.3 PHILOSOPHICAL TRANSACTIONS/ 107 300 or 600 feet. Now in the case of the moon, the deceit is helped, because the vapours, through which we see it when low, diminish its brightness, and therefore have the same effect as would (or does) happen in the experiment, when the light of the ball op strikes the eye no stronger than the light of the ball CD. Some Observations on a Man and JVoman bitten by Vipers. By Joseph Atwell, D. D., F. R. S. and Principal of Exeter College, Oxford. N° 444, p. 394. The man who had been bitten by a viper in the presence of several members of the R. S., was again bitten in the presence of several besides Dr. A. in the public hall of Exeter college at Oxford. He received two punctures in the wrist, a little above the thumb : the blood issued, and more venom lay on the orifices, than could be immediately imbibed. He complained in about half an hour's time, that the poison was got up to his shoulder, and was entering his body ; but notwithstanding this, he was not suffered to apply his medicine [sallad oil] till an hour and 10 minutes after he was bitten : by which time he began to be flushed and in a sweat, his hand swoln and discoloured. On an application of his medicine, he found some abatement of his pain ; but the swelling appeared more visible, and spread itself farther into his arm. In about a quarter of an hour the man sunk under the table, and complained of violent pains in his back and bowels, and he could not bear to be moved. At last, his pulse failing, his jaw being fallen, his countenance changed, and eyes fixed, he was stretched upon the table, and the medicine was applied to his belly and stomach. Soon after which, recovering a little, he began to vomit, and brought up more than a quart of phlegm and bile. In this condition he lay for more than an hour ; and then was removed into Dr. A.'s lodgings ; where he was seized again with a fit of vomiting, and also purging, and so con- tinued till midnight. Dr. A. kept him in his own house above an hour, in hopes of his growing better ; but his disorder still continuing, and the man be- ing too weak and feeble even to stand, he sent him in a chair home to his own lodgings; where he was put into bed, and after midnight fell asleep, and awaked the next morning perfectly well ; excepting that his arm was still swoln, and the flesh pitted, as if it had been dropsical. His arm was bound up in papers, dipped in his own medicine; and this was all, as far as the Doctor could observe or learn, that was applied to it. The same day they caused 2 young chickens to be bitten ; one died in 2 hours, and the other in 4 hours time. A third was bitten 3 times, and then had the medicine applied ; but it died at the end of 10 hours. The flesh of p 2 108 PHILOSOPHICAL TRANSACTIONS. [anNO 1736. this last was grown very black, and there was much extravasated lymph between it and the skin, which stunk intolerably ; but Dr. A. could not perceive, that the viscera were at all discoloured. July 4. — Another fowl, half grown, was bitten in 1 places, and the medicine was applied : half an hour after which, the fowl eat meat, and seemed much re- covered, but was dead in 14 hours time. July 6. — Two half-grown cocks were bitten ; the first was bitten but once, yet violently, and turned black immediately ; it had the medicine applied, eat meat afterwards, and seemed pretty well ; yet died in 20 hours. The other was bitten 2 or 3 times, but hardly wounded, and not half so much discoloured as the former : they bathed the wound with viper-oil, but the fowl died in little more than 1 hours, July 8. — Two young pigeons were bitten; the one had viper-oil applied im- mediately, but sickened, and died in 4 hours : the other had olive-oil applied, and recovered perfectly ; the flesh beginning to return to its natural colour in about an hour's time. July 17. — The woman was bitten in the public hall of Brazen-Nose College, in presence of Dr. Frampton, Dr. Frewin, and several other physicians. Dr. A. and many others. It had been suspected, that they played some tricks with their vipers, and made them spend their rage and venom beforehand : to obviate which a physician of the company had provided some fresh vipers, which he himself had caught a day or two before, and kept in his own custody till that time. The woman was bitten twice by one of these, and received 3 wounds, one in the thumb and 2 in the fore-finger. Her hand was soon swoln and spotted, and her finger turned black. After 23 minutes, she applied the medi- cine to her hand, but not farther than the swelling went ; in which she was perhaps to be blamed, and probably the following illness was in some measure occasioned by it. She walked home very well in appearance: but about 3 hours after the bite was received, she grew very sick, and in great pain ; was seized with vomiting, purging, and fainting-fits, which continued all night, insomuch that her life was despaired of: nor had she any sleep till noon the day following. Dr. A. saw her about 6 that evening, when she awaked, and he found her very well in spirits, but complaining of most acute pains in her finger. Her arm, shoulder, back, and breast, on that side, were much swoln and inflamed : all -those parts thus affected were bound up in papers soaked in the medicine. After this there appeared on her finger 2 large bladders, full of a black corrupt mat- ter ; and this not only on the wound, but one of them on a distant part of the finger from it. She could not be persuaded to open them, which the Doctor believes would have eased her considerably. VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. 10^ July "20. — The swelling was considerably abated, and almost reduced entirely into her hand, which began to pit : but she complained still of her finger, and coulii hardly endure to have it dressed with fresh papers. She continued in bed till the 22d, for the sake of keeping her hand in an easier posture ; and then she came abroad. The same day that the woman was bitten, they caused a fowl to be bitten ; but the wound was not deep, and little more than a scratch. Nothing was ap- plied to it, and it died in 20 hours. A large puppy was also bitten the same day, 3 times, in the head ; it had the medicine applied, but died in about an hour. It was known that the man and woman kept themselves fasting those days when the experiment was to be tried on them : this occasioned a suspicion that they might take some antidote to prepare their bodies : for which reason. Dr. A. ordered the man to bring him some vipers after dinner, under pretence of making some further experiments on dogs. He had provided at the same time some fresh vipers without his knowledge, and then proposed to him to be bitten by one of them, and apply his medicine immediately. His hand was be- smeared with the medicine in applying it to a young dog, on which an experi- ment had just been made. Two vipers were tried on the man, but neither would bite him : one of them attempted it several times, and spilt his venom, but always caught back his head again, as if there had been something in the hand ofFensive. Suspecting that the smell of the medicine might occasion it, they made him wash his hand, after which another viper bit him immediately : but whether this conjecture was right or not, must depend on further trial. The man received the bite on the joint of the thumb, and the blood issued at the 1 orifices. He applied the medicine instantly : the thumb appeared black, soon, the hand was swoln, and the flesh pitted immediately. He drank a mug of ale after it, and then went home to bed. Next morning his whole arm was swoln ; but he was so well, that he went 6 miles out of town, and came home , again in the evening. Dr. A. saw him again in the morning, when the swell ing was almost gone above the elbow, but the flesh pitted below : the wound had blistered, but the bladders were filled with a water, and not any thing of that black matter which appeared on the woman's finger. They caused the young dog, beforementioned, to be bitten the same day, and applied the medi- cine : another dog was bitten 3 times in the nose, and nothing applied : both were much swoln, but very likely to live. They also thrust the teeth of a viper's head, cut off 24 hours before, into the flesh of a fowl, which turned black immediately ; but the fowl perfectly recovered, without any application. 1 10 PHILOSOPHICAL TBANSACTIONS. [anNO 1735. Some Electrical Experiments intended to be communicated to the Royal Society, by Mr. Stephen Gray, F. R. S. and taken from his Mouth by Cromwell Mor- timer, M.D. R. S. Seer. Feb. 14, 1735-6, being the Day before he died, N° 444, p. 400. Exper. 1. — Take a small iron globe, of an inch or inch and half diameter, which set on the middle of a cake of rosin, of about 7 or 8 inches diameter, having first excited the cake by gently rubbing it, clapping it three or four times with the hands, or warming it a little before the fire. Then fasten a light body, as a small piece of cork, or pith of elder, to an exceedingly fine thread, 5 or 6 inches long, which hold between the finger and thumb, exactly over the globe, at such a height, that the cork, or other light body, may hang down about the middle of the globe; this light body will of itself begin to move round the iron globe, and that constantly from west to east, being the same direction which the planets have in their orbits round the sun. If the cake of rosin be circular, and the iron globe placed exactly in its centre, then the light body will describe a circular orbit round the iron globe ; but if the iron globe be placed at any distance from the centre of the circular cake, tlien the light body will describe an elliptical orbit, which will have the same excentricity as the distance of the globe from the centre of the cake. If the cake of rosin be of an elliptic form, and the iron globe be placed in its centre, the light body will describe an elliptical orbit, of the same excentricity as the form of the cake. If the iron globe be placed in or near one focus of the elliptical cake, the light body will move much swifter in the apogee part of the orbit than in the perige^ part, contrary to what is observed of the planets. Exper. 1. — Take the same, or such another iron globe, and having fastened it on an iron pedestal about one inch high, set it on a table: then set round it a glass hoop or portion of a hollow glass cylinder, of 7 or 8 inches diameter, and 2 or 3 inches high: this hoop must be first excited by warming and gently rubbing it; then hold the light body suspended as in the first experiment, and it will of itself move round the iron globe from west to east, in a circular orbit, if the hoop be circular and the globe stand over its centre, but in an elliptic orbit, with the same excentricity, if the globe does not stand in the centre of the hoop, as in the first experiment, when the globe does not stand on the centre of the cake. Exper. 3. — ^Tbis same iron globe being set on the bare table, without either the cake of rosin or the glass hoop, the small light body, being suspended as VOL. XXXIX.] PHILOSOPHICAL TRANSACTIONS. Ill in experiments 1 and 2, will make revolutions round it, but slower and nearer to it, than when it is placed on a cake of rosin, or within a glass hoop. Remarks. — Mr. Gray had not yet found that these experiments would succeed, if the thread, by which the light body was suspended, was supported by any other thing than a human hand; but he imagined it might happen the same, if the thread should be supported or fastened to any animal substance whatever; and he intended to have tried the foot of a chicken, a piece of raw flesh, or the like. He thought to explain the foregoing particular, by the following odd pheno- menon, of which he asserted he was very certain, having often observed it, viz. if a man, resting his elbows on his knees, places his hands at some small distance from each other, they will gradually accede to each other, without any will or intention of the man to bring them together; and they will again recede of themselves. In like manner, the hand will be attracted by the body ; or the face of a man, if he stand near a wall, will be attracted to the wall, and be again repelled by it. He told the Doctor, he had thought of these experiments only a very short time before his falling sick; that he had not yet tried them with variety of bodies, but that from what he had already seen of them, which struck him with new surprise every time he repeated them, he hoped, if God would spare his life but a little longer, he should, from what these phaenomena point out, bring his electrical experiments to the greatest perfection ; and he did not doubt but in a short time to be able to astonish the world with a new sort of planetarium never before thought of, and that from these experiments might be established a certain theory for accounting for the motions of the grand planetarium of the universe. In trying these experiments since Mr. Gray's death, the Doctor found that the small light body will make revolutions round a body of various shapes and substances, as well as round the iron globe, if set on the cake of rosin. Thus he tried with a globe of black marble, a silver sand-dish, a small chip box, and a large cork. He observed that the cake, if nothing stood upon it, would in any part strongly attract the light body, as held suspended by the thread; but when the globe, or other body, was set upon it, the edges of the cake attracted the strongest, and so gradually the attraction seemed as it approached the centre to grow less, till at a certain distance it was changed into a repulsion, which proceeded from the globe, or other body placed on the cake, which very strongly repels the light body, unless it be held very near it, and then it attracts it strongly. While the light body is suspended, as in the foregoing experi- lia PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. ments, if the finger of the other hand be brought near it, it will fly from the finger, or be repelled by it with great vigour. Some Thoughts on the Sun and Moon, when near the Horizon, appearing larger than when near the Zenith. By James Logan, Esq. N" 444, p. 404. It may perhaps be needless now to add any thing in confirmation of Dr. Wallis's solution, in the Transactions, N° 187, of the sun and moon's appear- ing so much larger at rising or setting, than when in a greater altitude; though some have very absurdly still gone on to account for it from vapours. It is true indeed, that it is these vapours, or the atmosphere alone, that make those bodies, when very near the horizon, appear in a spheroidal form, by refracting, and thereby raising the lower limb more than the upper; yet these can be no cause of the other. The sun and moon, each subtending about half a degree, appear in the meridian of the breadth of 8 or 10 inches, to some eyes more, and to others less ; and in the horizon to be 2 or 3 feet, more or less, according to the extent of ground they are seen over; but if one can have an opportunity of seeing the sun rise or set over a small eminence, at the distance of a mile or two, with tall trees on it standing pretty close, as is usual in woods without underwood, his body will then appear to be 10 or 12 feet in breadth, according to the distance and circumstances of the trees he is seen through ; and where there has been some thin underwood, or a few saplings, Mr. Logan has ob- served that the sun setting red, has appeared through them like a large exten- sive flame, as if some house was on fire beyond them. Now the reason of this is obvious, viz. that being well acquainted with trees, the ideas of the space they take up are in a manner fixed; and as one of those trees subtends an angle at the eye, perhaps not exceeding 2 or 3 seconds, and would scarcely be distin- guishable, were it not for the strong light behind them, the sun's diameter of above 30 minutes takes in several of them, and therefore will naturally be judged vastly larger. Hence it is evident, that those bodies appear greater or less, according to the objects interposed, or taken in by the eye on viewing them. And to this only is that phenomenon to be imputed. Mr. Logan acknowledges that, this method of arguing is not new ; yet the observations here given may probably tend, he thinks, to illustrate the case beyond what had been advanced on the subject. VOL XL.] PHILOSOPHICAL TRANSACTIONS. 113 A Catalogue of the Fifty Plants, from Chelsea-Gardens, presented to the Royal Society by the Company of Apothecaries, for the Year 1 735, pursuant to the Direction of Sir Hans Sloane, Bart. Med. Reg. & Soc. Reg. Pries. By Isaac Rand, Apothecary, F. R. S. Hart. Chel. Pr/es. ac Prcelec. Botan. N°445, p. 1. This is the 14th annual present of 50 plants, completing the number of 700 plants presented. The Case of a Lad bitten by a mad Dog. By Mr. Edw. Nourse, F. R. S. and Surgeon to St. Bartholomew's Hospital. N° 445, p. 5. Stephen Bellass, about l6 years of age, was, some time in June 1735, bitten by a mad dog through the nail of his right thumb : Mr. N. being imme- diately called, proposed to make a ligature above, and to cauterize the wounded part: but that not being complied with, he desired Mr. Gernum the apothe- cary, who was present, to make up the remedy mentioned by Dampier in the Phil. Trans. N° 237, and N°443, viz. R Lichen, ciner. terrestris, Piper, nig. aa 5i. f. Pulvis. Of this powder he took 5i. within an hour after he was bitten ; repeating it the next morning before he set out for Gravesend, where he was 10 days, and was dipped in the salt water every day; during which time he re- peated the medicine night and morning, and continued so to do for 40 days. The boy was without the least sign of being affected by the poison, till Tuesday the J 1th of Jan. 1736-7, when in the evening he complained of a numbness in 3 of the fingers of the hand that was not bitten. Next morning he was sick, had great pain across his stomach, and in all his bones; in the evening Mr. N. was sent for to bleed him, the people about him supposing he had got cold. When he came, he found him feverish, with a hard full pulse : he asked what complaints he had ? he told him those abovementioned. Mr. N. inquired what nourishment he had taken that day? the answer was, none, for he could not swallow : Mr. Nourse looked into his mouth, but there was no inflammation ; neither did any thing occur that could produce the difficulty of swallowing. Mr. N. offered him some sack-whey in a basin, but he started at the sight of it, not suffering it to come near him: he was then offered a spoonful, which he was prevailed on to swallow : the moment it was down, he was convulsed, and a remarkable horror appeared in his countenance, which was succeeded by a profuse sweat all over his face and head. He afterwards took another spoonful ; the consequence was as before, but in a higher degree. Mr. N. was now convinced that this was the iS^o^o^ia, and that it arose from VOL. VIII. Q 114 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. his having been bitten ig months before; for after the most strict inquiry, it did not appear that he had been bitten by any animal since; and if he had, it is very probable Mr. N. would have known it, his master living next door to him, and the boy knowing how much danger he was thought to be in, when he was bitten. Mr. N. acquainted his friends with his apprehensions, and de- sired further advice; on which Dr. Monro was sent for, who ordered him to be let blood, a repetition of the abovementioned medicine in a bolus every 4 hours, ai;d a clyster : he was blooded, and the clyster was injected; but he could not be prevailed on to take more than 1 bolus. That night was spent with great inquietude, and without any sleep : Thursday morning he was ge- nerally convulsed, and had frequent retchings and yawnings alternately. About noon his mind, which till then continued sound, left him, and he raved and foamed at the mouth till 5 o'clock in the afternoon ; at which time nature seemed quite spent, and he lay very quiet till 7, when he died. Thus' the poison was latent near IQ months; which Mr. N. finds mentioned by others, but it never fell within his own observation before. j4n Explanation of the Runic Characters of Helsingland. By Mr. Andrew CelsiiLS, R. S. Suec. Seer. F. R. S. and Professor of Astronomy at Upsal. N" 445, p. 7. It is well known, that there are stones found in several parts of Sweden, which were formerly set up as obelisks in memory of the dead. These monu- ments are marked with the ancient northern letters, called Runor or Runic characters. But there is one province of North Sweden, named Helsingland, where 5 of those stones occur, which have characters cut into them, that seem to differ from the common Runic. On the introduction of our modern letters, these Runic characters became so little regarded, that their interpretation was lost even to the Swedish antiquarians, till the year l674; when Magnus Cel- sius, the author's grandfather, then professor of astronomy in the university of Upsal, revived their reading, and drew up the following alphabet of them, ranged after the manner of the ancients, fig. 1, pi. 5. There are but l6 letters, and the words are frequently distinguished either by three points set perpendicularly over one another, or by two at some dis- tance asunder. Among the several alphabets hitherto known, it would be diflicult to find one like the foregoing ; if we may not perhaps except the characters of the Perse- polis inscriptions, which have not yet been deciphered. For the letters gene- rally used signify different sounds, according to their various shapes : whereas VOL. XL.] PHILOSOPHICAL TRANSACTIONS. llfi in this alphabet, the same character often denotes a different sound, according to the diversity of its place and attitude between the two parallels. Thus a straight stroke, standing perpendicular to the parallel lines, signifies i, f, d and s. For when it joins these parallels, it signifies i; when it rests on the lower parallel, it signifies f ; on the upper, s ; and d when it touches neither of them. The small wedge leaning to the right, and placed near the upper parallel, denotes l ; in the middle, n ; and o, near the lower. A line de- scending from the upper parallel, and making a curve downward to the left, stands for k; the same placed contrarywise, from the lower parallel upward, expresses r : and so of the rest. The intention of the first inventor of these letters, seems to have been, to form all the characters of small wedges, straight and crooked lines, and two points, variously placed between the two parallels. For the wedges may be placed 1 5 different ways, as represented in fig. 2. The straight line may also have 15 different situations, as in fig. 3. * The crooked lines can likewise be varied 14 different ways, as in fig. 4. Lastly, the two points admit of 12 variations, as in fig. 5. . » But as the ancient Sueo-Gothi had but l6 letters in their alphabet, they did not want all these variations of the wedges, lines, and points : therefore they employed 6 variations of the wedges ; of the straight lines, 5 ; of the crooked, 3 ; and but 2 of the points. If we now suppose these Helsingic characters to be older than the common Runics, the greatest part of the common Runics can easily be derived from the Helsingics, by adding a perpendicular line to the small wedges and curves ; as appears by fig. 6. But if we suppose the common Runics to be older, and to be derived, as it is very probable, from the ancient Greek and Roman letters ; we must, in the contrary way, deduce the Helsingic characters from the common Runics, by subtracting the perpendicular line. As a specimen, fig. 7 represents a stone found at Malstad ; of which M. Celsius took an exact copy in the jear 1725, in company with his uncle, the Rev. Dr. Olave Celsius, of whom he expected a complete account of all these Helsingic inscriptions. — On the outward limb or border, is what is re- presented in fig. 8 — In the first curvature, as in fig. Q. — In the second snake or dragon, as in fig. 10. — In the inner limb, as in fig. IJ. — In the second cur- vature, as in fig. 12. — In the first snake, as in fig. 13. — In the heads of the snakes, as in fig. 14. The inscription of the figures is thus rendered into English : — Frument erected this itone to Fisiulfi the son of Brisi : but Brisi was the son a 2 ]l6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. of Lini. But Lint tvas the son of Un. But Un was son of Fah. But Fah the son of Duri. But he (the son) of Barlaf. But he the son of Drun : but he (the son) of Lanas : but he (the soil) of Fidrasiv. Frumunt the son of Fisiulfi made these Runic \letters.'\ We have placed this stone to the north of Bala stone. Arva was the mother of Fisiulfi. Siulfir (or Fisiulfir) was the Governor of this Province. His place of abode was in Rimbium. That this monument was erected since Christianity began to flourish in Sweden, sufficiently appears by the figure of the cross. It is probable that Fisiulfi, as the governor of the Province, was descended of a very noble family; seeing his genealogy is traced 10 generations backward. Now if we suppose Frumunt to have been 30 years of age when he erected this monu- ment for his father, and, with Sir Isaac Newton, allow 30 years for each generation ; we shall find 330 years from the death of Fisiulfi to the birth of Fidrasiv, who is the stock of these generations. A figlire of this stone is in M. de la Motraye's Travels; but with consider- able errors in the windings of the snakes, and in the letters, as well as in the explanation of them. A Collection of the Observations made on the Eclipse of the Moon, on March J 5, 1735-6, which were communicated to the Royal Society. A Lunar Eclipse observed in Fleet-street, London, March 15, 1735-6. By Mr. Geo. Graham. N° 445, p. 14. lO** 13™ the beginning. 11 11 the total immersion. 12 49 the emersion. 13 47 the end. The same, by Dr. Halley at Greenwich, p. J4. The beginning 10^ 13"" 37' The immersion 1 1 g 42 The same, observed in Fleet-street. By M. Celsius, F. R. S. p. 15. 10*" 22"" 6* the shade on the middle of Kepler. 11 917 the total immersion is about to begin. 13 45 50 the eclipse is nearly ended. 13 46 12 the eclipse is certainly ended. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 1J7 The same, observed in Covent Garden, London. By Dr. Bevis,* p. i6. True Time. 10'' 9*" 40* A thin penumbra commences near Hevelius. 10 10 20 the penumbra is now very sensible. • John Bevis, M. D. and a valuable member of the R. Soc. was born Oct. 31, 1695, o. s. near Old Samm in Wiltshire. At a proper age he was entered at Christ's College, Oxford, where he applied diligently as well to the study of physic, for the practice of which he was intended, as to other sciences, particularly astronomy and optics, in which he became a considerable proficient, both in theory and in practice. Having taken his degree of M.D. he left the university, and tra- velled through France and Italy, where he made respectable connections, and on his return com- ijaenced the occupation of a physician at and near Ixjndon, where he had considerable practice. But the study of physic alforded him little pleasure in comparison with that of contemplating the celestial bodies and their motions. As early as 1738 he had made an excellent collection of astrono- mical instruments, for furnishing a new observatory, which he had built at Stoke Newington near London. Here he became an indefatigable observer, having filled 3 folio volumes with observations made in the course of one year. From these he selected the most important parts, making one volume of 196 pages, on large paper, where it frequently appears that the transits of 16"0 stars, &c. have been observed by him in one night. Dr. Bevis continued to observe the heavens with the same assiduity till the year 1745 ; when, from his vast collection of materials, he undertook the laborious task of arranging, and publishing by subscription, a work entitled Uranographia Britannica, or an exact view of the heavens, on 5'Z plates, similar to that of Bayer, representing the constellations, and all the fixed stars observed by former astronomers, with the addition of those observed by himself. Those plates, so honourable to his country and to himself, though they have been engraved for so many years, have unfortunately been prevented from coming before the public ; having entrusted the care of engraving the plates, and receiving the subscriptions, to a person who, after receiving several hundred pounds of the money subscribed, became a bankrupt ; by which the work passed into tlie hands of the creditors, and thus has been lost to the world. Dr. Bevis was the real author of a great many works, which have been well received by the public, but which his modesty prevented him from taking the merit of. It is to him we are indebted for the publication of Dr. Halley's Astronomical Tables, after they had been printed more tlian 20 years; having supplied some auxiliary tables, and the precepts for using them, he brought tJie whole to light in the year 1749. — At a meeting of the Board of Longitude, Sept. 18, 1764, Dr. Bevis was nominated to compute the observations made at Greenwich, and to compaie them with those made at Portsmouth and elsewhere, for the purpose of ascertaining the accuracy of Mr. Harrison's Time- keepers.— In Mr. Simpson's Essays, p. 10, are delivered practical rules for finding the aberration, which were drawn up and given him by Dr. Bevis, with examples of the correction applied to se- veral stars, which he had carefully observed witli proper instruments ; by which he has proved, the first of any one, that the phenomena are as conformable in right ascension, as Dr. Bradley, who made this great discovery, found them to be in declination. — Several pieces of the Doctor's were inserted in the few numbers that were published of a work, called The Mathematical Magazine, by Mr. Moss and Mr. Witchell, particularly a curious paper on the Satellite of Venus, and several sheets of a new Mathematical Dictionary. — Dr. Bevis enriched the Philos. Trans, with 27 valuable papers, mostly containing Astronomical Obsenations, viz. from vol. 40 to vol. 59 inclusive. He announced in the Journal des S9avans, for August 1771, an English translation of La Lande's Astronomy, 118 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. True Time. 2Qh J 2™ 40» beginning of the eclipse. 11 10 O the total immersion. 12 46 56 beginning of the emersion, 13 46 25 the true shadow ends. 13 48 30 the penumbra no longer sensible. The same observed at Yeovil in Somersetshire. Latitude 50 Degrees 52 Minutes. By Mr. John Milner, p. 18. The beginning of the eclipse 10*" 6" O* Beginning of total obscuration 114 30 Middle of the eclipse 1 1 54 O End of total obscuration .... 12 43 30 The end of the eclipse 139 15 Some Investigations, by which it is proved that the Figure of the Earth must ap- proach very near to an Ellipsis, according to the Laws of Attraction Inversely as the Squares of the Distances. By M. Alexis Clair aut,* F. R. S. and of made principally by himself j but this was never published, though left ready for the press at his death — ^The only things which appeared separately with his name, besides the papers in the Philos. Trans, just mentioned, were two pamphlets, the one entitled " The Satellite Sliding Rule," for determining the immersions and emersions of Jupiter's four Satellites. The other was, "An Expe- rimental Enquiry concerning the Contents, Qualities, and Medicinal Virtues of the two Mineral Waters lately discovered at Bagnigge Wells near London, &c. in 8vo. 1760." Dr. Bevis made some curious experiments on the refractive power of glass, in the composition of which he had used a quantity of Ijorax, and found the refrangibility was as gi-eat as that of English crystal. He corresponded with most of the principal astronomers in all parts of the continent j several of whom make honorable mention, in their works, of the civilities and attention they received from him, either during their stay in England, or by communications to them abroad. On the death of Mr. Bliss, in 1765, his friends made great exertions to procure for Dr. Bevis the situation of Astronomer Royal, but the superior interest of Dr. Maskelyne secured the office for the latter. A few years before his death. Dr. Bevis removed from his house and observatory at Stoke Newington, to reside in the Temple, London, for the better convenience of his occupation as a physician, and at the Royal Society ; which occasioned an interruption in his astronomical ob- servations. In this situation he died Nov. 6, 1771, at 76 years of age j his, death having been occasioned by a fall he received a short time before, in going rather too hastily from his in- strument to the clock, in observing the sun's meridian altitude. In his disposition, Dr. Bevis was lively, amiable and liberal; extending his services to all de- serving objects, under any kind of embarrasments. ♦ Alexis Claud Clairaut, F.R.S. and member of the French Academy of Sciences, &c. was a most respectable mathematician. He was bom May 13, 1713, at Paris, where his father was a teacher of mathematics. He was it seems a kind of premature genius, which seconded by his VOL. XL.] PHILOSOPHICAL TRANSACTIONS. Jig the Royal Academy of Sciences at Paris. "S" 445, p. 1 9. Translated from the Latin. According to Newton's Princip. (cor. 3, prob. 91, lib. 1, and prop. 19, lib. 3) if an elliptic spheroid, consisting of fluid and homogeneous particles, mutually father's great attentions, produced very early and extraordinary effects. Having learned the letters of the alphabet from the diagrams in Euclid's Elements, he could read at 4 years of age, and even write tolerably well. In a similar degree of advance he passed through the mathematical sciences of arithmetic, algebra, geometry, &c. so as to master Guisnee's application of algebra to geometry, at 9 years of age. At 10 he studied I'Hopital's Conic Sections, and soon after the Analyse des Infini- ments Petits, of the same author. At 12 he astonished the Academy of Sciences, by reading to them his discovery of four curves of the third order, by means of which may be found any number of mean proportionals between two given lines. And at 13 he laid the foundation of his excellent work on Cunes of a Double Curvature, printed 3 years after. The same year, 1726, our young author formed a juvenile society, by associating together a number of ingenious youths like himself, at once for improving themselves and the mathematical sciences; among whom were several who afterwards became some of the most respectable members of the Royal Academy of Sciences; of which academy young Clairaut himself was admitted a member at 18 years of age, being 3 years below the limit prescribed by a regulation of the academy, a regula- tion which tliey dispensed with in this instance on account of his surprising merit. The same year he presented to the academy two ingenious memoirs of his own inventions. Soon after this, he accom- panied M. Maupertuis to Basle on his visit to John Bernoulli ; and on his return, he found the academy much occupied about the question concerning the figure of the earth; in consequence not long after he and Maupertuis, retiring to Mount Valerien, formed the project of the measurements at the polar circle, in which both of them bore so conspicuous a part. In this retreat it was, that the Mar- chioness of Chatelet, having resolved to learn the science of geometr)- from Clairaut, attended him tliere to receive her lessons; which gave occasion to his composing his pleasant little treatise on geo- metry. On the question too of the figure of the earth, about this time, he wrote several interesting memoirs. The delicate observations of Mairan on the lengths of pendulums, gave occasion to Clairaut to present a memoir on their oscillations. And the discovery of Bradley on the aberration of the fixed stars, gave also occasion to Clairaut's presenting a valuable calculation on that subject, in which he made improvements, by extending his views to that of the planets also, dependent on the same cause. Several other memoirs, on various subjects, as, the annual parallax of the stars, the nature of the refraction of light, conduct us to his still more important labours, in the application of the geome- trical calculus to the profoundest considerations in physics and astronomy. This produced his work on the theory of the figure of the earth on hydrostatical principles; in which he considered all the circumstances and states of the earth, as to fluidity and rigidity. An-j next his theory of the moon, in which he at length detected a subtile error, which had been committed bv all the best calculators on that delicate subject. After a long continued labour on this object, in 1751 he carried the prize proposed on the subject by the Academy of Petersburg. Also, in 1754 came out the first edition of his Lunar Tables; and in 1765 was given a second edition of the same corrected; to which was added the piece containing the theory which had gained the Petersburg prize. During those labours, Clairaut composed his elements of algebra, which appeared in 1746; these elements are in the same easy and familiar stile as those of his geometry, beforementioned. In 175* 120 PHILOSOPHICAL TRANSACTIONS, [aNNO 1737. attracting each other in the inverse ratio of the squares of the distances, be revolved about the axis xa, fig. 12, pi. 4, by which the columns ce, on, ca, in that spheroid, may be in equilibrio, and so the spheroid may always have the same figure, the gravity at any point of the surface n must necessarily be in- versely as the radius cn. To know therefore whether the spheroid has this property, let us inquire what attraction any corpuscle n of the whole spheroid suffers, according to the direc- tion CN ; and fnjm that attraction let us deduct that part of the centrifugal force which proceeds from the rotation of the spheroid acting in the direction cn; and then see whether the remaining force is proportional to — . We shall first then investigate the following problem : and as we intend to apply our disco- veries to the spheroid of the earth, which all agree to be very little different from a sphere, our computations must be adapted to those spheroids which have the smallest difference between the two axes. Prob. I. To find the attraction, which the spheroid AEae, differing very little from a sphere, exercises on a corpuscle at the pole a. For the solution of this problem we may repeat cor. 2, prop. Ql, of the Principia, by which we learn the manner of finding the attraction of any sphe- roid, viz. by substituting in the general value of ce, a quantity differing infi- nitely little from AC; and as in that case the problem becomes much easier, we may solve it in the following manner. Let AMDad be a sphere, to the radius AC ; we must find the attraction of the space arising from the rotation of adce, which attraction added to the attrac- tion of the sphere, will give the attraction sought. To find the attraction of the space arising from the rotation of anegdm, call AC, r; DE, ar; ap, u; then, from the nature of the ellipse, nm := a\/2ru — uu, and from the nature of the circle am = ^/2ru. But the space arising from he produced his work on the Determination of the Terrestrial Orbit, in which are considered the perturbations caused by the action of the other planets. And some time after he successfully applied the same principles to the theory of the celebrated comet of 1759; the result of which calculations are given in a work which appeared in 176O. And when, in 1758, the academy lost M. Bouguer, a pension of 3000 livres, which he enjoyed from the Marine Board, was divided between Monnier and Clairaut, which new engagement produced from his pen an excellent memoir on the maUceuvering of ships. A considerable share of his attention was also employed on the subject of achromatic telescopes, with the different kinds and combinations of glass, to render their effects colourless. These labours are contained in three memoirs printed by the academy in the years 1756, 1757, and 1762. But it were endless to particularise all his valuable labours. This last year, however, terminated the useful existence of this great man ; his death being occa- sioned by a severe cold he had taken, in returning home one night after supper, at 53 years of age. TOL. XL.] PHILOSOPHIC AI. TSANSACTIONS. ill the rotation of NnmM will be -(2ru — uu)du, where c is the circumference to the radius r. Now because of the smallness of nm, we may account all the particles of matter contained in that space as equally attracting the corpuscle at a ; there- fore we shall have the attraction of that small space, if we multiply that solidity • 1 A P by the attraction at m, and that attraction at m is — ; X — . Thus will be had -' ' AM* AM analytically ^^"^^ .j,2ru—uu.du = j^r^Tsr^^''''" ^ " ~ udu^u) the in- tegral of which, - — — (4-r«v^« — 4-w"v/w)> is the attraction of the space arising from the rotation of anm. In which value if we take u = 2r, we have by reduction -^ac. Hence the attraction of the whole space aeqc is expressed ; then adding ^ for the attraction of the whole sphere, we have -j-c -f- -^c for the attraction of the ellipsoid. Carol. — For an oblong spheroid a will be negative, and the united attraction will be -I* — tVc. Note. — If the foregoing spheroid, instead of circular elements arising in pn, consist of other elements, for instance elliptical, which should differ from a ' circle no more than the ellipsis ae, and by which there would be the same super- ficies as by the circles pn, it appears that the attraction will be still the same, because in those elements pn, whatever the remaining force might be, the circles PM being taken away, it will be as it were composed of parts which would have the same attraction as on that of the ellipsoid, having regard to the smallness of NM, and to the equable quantity of matter. Lemma. Let kl be a circle, fig. 1 3, h its centre, vh perpendicular to the area of the circle, and nh = vh, but making with it an angle infinitely small, or very small: then the attraction of the circle kl on n, may be taken, without sensible error, as the attraction of the circle on v; or, which is the same thing, that the one attraction differs from the other only by a quantity infinitely less, with respect to both, than as vn is less in respect to hv. To demonstrate which proposition, it must be shown, that two corpuscles being placed at the extremity of any diameter kl, there is one attractive force at N, and another force at v, the sum of which may be accounted the same. But, neglecting the computation for having the attraction of the body at k on the corpuscle at n, it will be easily seen that it will be the same with the attrac- tion on V, to which should be added a small quantity involving nv. In like manner it may be seen, that the attraction of a body at l on the corpuscle n, will be the same as the attraction on v, deducting the same small quantity. Therefore the sum of both these attractions is one and the same. VOL. VIII. R 1^22 PHILOSOPHICAL TRANSACTIONS. [aNNOI737. Corol. — Instead of the circle kl, if there was a certain ellipsis, or any other curve line, which should differ very little from a circle, by the same arguments as in the note, it is easily gathered that the foregoing proposition would always hold good. Theorem I. Let AEae, fig. 14, be an elliptic spheroid, the axis of revolu- tion being Art ; then the attraction this spheroid exerts on a corpuscle at n, is the same as that attraction, which any spheroid exerts whose pole is n, its axis of revolution ntz, and its second axis the radius of a circle, having the same superficies as fg, the elliptic section of the ellipsoid AEae, by a plane erected perpendicularly on fg, its conjugate diameter. To -demonstrate this, conceive innumerable elements kl, parallel to the ellipsis FG, that is, all erected on ordinates to the diameter, it is evident that the spheroid AEae will differ from the aforesaid spheroid only in this, that in the first all the elements make with cn an angle differing infinitely little from a right angle, but in the second all the elements make a right angle, without any difference, while in both spheroids the elements have the same superficies. But, by the preceding proposition, the attraction of every element kl on n, is considered as the same in both cases ; but as to the thickness of the elements kA/l, we may take hA for the perpendicular hi, because of the smallness of the angle jAh ; therefore the total attraction of both spheroids may be taken the one instead of the other. Prob. II. To find the attraction of the spheroid AEae on a corpuscle at any point N. Let AC = a, CE = b, cn = r, CG the conjugate diameter to on will be - since a and b have very little difference; from the preceding proposition, find the attraction of the spheroid, whose greater axis is r, and the less .abb 7 ,a \/— or by/ J. For this, we must apply the formula which we found in prob. 1, viz. ^c — tVJC, or ^pr rt^pr, putting pr for c, but in this formula instead of a sub- stituting '■-~^'^~ = 1 — ^ /p or \n — 7n, putting a-\-ma for b, and a -j- Tza for r and in the computation neglecting the second powers of n and m. If therefore \n — mhe. put instead of a, the aforesaid formula will become ^pr _ ^prn -\- -J^prm, or fjba — -^pan + -^pam ; which expression is the re- quired attraction of the spheroid on n. If n = 0, then we have ^pa + -^pam for the attraction on the pole a. But if n = m, then we have \pa -f- -hpa^ for the attraction at the equator. Theorem II. Let AEae, fig. 12, as before, be a spheroid, whose axes differ VOL. XL.] FHILOSOPHICAL TRANSACTIONS. 123 by a very small quantity, which for greater perspicuity I shall call infinitely small. If tins spheroid be conceived to be of a fluid and homogeneous matter, and revolved about the axis ha in correspondent time, that the gravity of the column CE may be equal to the gravity of the column ac, that is, by the New- tonian principles, the attraction in e, neglecting the centrifugal force, may be to the attraction at a, as ca to ce : I say, that all the columns on, wanting an infinitely small quantity of the second degree, will preserve an equilibrium with those two columns; that is, the attraction on n, neglecting the centrifugal force, simply in the direction on, is to the attraction on a, as ca to on. For the demonstration, the same notation will serve as in the preceding pro- position: first find the centrifugal force at e, which may agree with the equili- brium of the columns ce, ca. Then say, as \pa -)- -^pam — f: fpa -\- -J^pam :: 1 : 1 -|- »n, hence is found/= -^pam. Then for exhibiting the gravity at n composed of the attraction, omitting the centrifugal force, find the centrifugal force at n, or, which is the same, on M upon the sphere, which must diff^er from each other only by an infinitely small quantity of the second order, if de be supposed to express the centrifugal force y at e, then mn will express the centrifugal force at n, for the centrifugal forces are as the radii, when the times of revolution are the same, and by the property of the ellipses it is de : nm :: cb : MP. But if the centrifugal force act in the direction np, it must be reduced to nc, and NO will be the remaining part. Therefore the centrifugal force at n, or at M, is to the centrifugal force at e, or at d, as no is to de. Therefore the ex- pression for the centrifugal force at n will he'-Jt^pan, and consequently the ex- pression for the gravity there will be ^pa — -^pan -{• -^pam — -^pan, or \pa — ^pan -\- -^pam. Now to find the centrifugal force at n, which results from the equilibrium of the columns, the gravity at a must be to the gravity at n, as nc to ac; but the gravity at a is ^pa -f- -^pam, which expression being drawn into or J — n, after reduction it becomes ^pa — ^pn -|- -^pam, and is the same expression as that above. Hence we see that there can be only an infinitely small difference between the figure which the earth ought to have by the Newtonian hypothesis, and the ellipsoid. For as the quantity de is about the 230th part of ac, in the preceding computation we neglect only a quantity of the same order with 124 PHILOSOPHICAL TRANSACTIONS. [^ANNO 1737. On the Efficacy of Oil of Olives in curing the Bite of Vipers. By Stephen miliams, MB. F.R.S. N" 445, p. 26. In presence of several gentlemen of the faculty of physic, Wm. Oliver, the viper-catcher (mentioned N° 443,*) suffered himself, on June 26, 1735, to be bitten by a female viper ; which being enraged, fixed her fangs in the middle part of his fore-finger. Blood soon issued out at the wounds : but that the poison might more strongly appear, the same viper immediately bit a pigeon in the breast, which expired in less than half an hour. Another pigeon was also bitten by the same viper, which expired also, though not so soon as the first. The man immediately complained of an acute pain in the wounded part ; and it soon looked red, then became of a livid colour : his finger swelled to a great size, and he could not bend it. Soon after this his hand also began to swell : he complained of faintness, aftd pains flying to his arm, shoulder, and arm-pits. In half an hour's time from the bite, his specific being applied, and strongly rubbed into the part aflfected, procured him immediate ease. His pain lessened, his finger became flexible, his spirits seemed more chearful : the specific being thus several times repeated and applied, his pains gradually diminished. The next day his finger and hand remained swoln, but without pain : the skin began to appear yellow, and pustules like bladders appeared on his finger ; which being pricked, emitted a sanious liquor. In 2 days time all his symptoms vanished, and he became perfectly well. June 30, the gentlemen of the faculty met again, and tried several experi- ments on puppies, cats, and pigeons ; when they proved the efficacy of this man's specific, to the great satisfaction of the company. J4 Proposal for the Measurement of the Earth in Russia. By Mr. Jos. Nic. de Vlsle, first Professor of Astronomy, at Petersburg, and F.R.S. N° 445, p. 27. Necessity, or the exigencies of geography and navigation, put mankind very early on measuring the earth. On the first determination of the magnitude of the earth in geographical measures, as in Stadia and Arabian miles, the ancients did not employ any great degree of exactness. They were content to set down the circumference of the earth, and of its parts, in round numbers ; probably because they did not expect to be able to attain much preciseness in a research of this nature. But as their desires of improving geography increased, they • Page 84, of this vol. of these Abridgments. VOL. XL.} PHILOSOPHICAL TRANSACTIONS. 12S found it necessary to have a more exact knowledge of the magnitude of each degree, not only in great measures, as in miles and leagues, but also in perches, toises and feet. As to Russia, the geographical measures of which are wersts, divided each into 500 sagenes, and each sagene supposed to be exactly 7 feet English ; this proportion once known, and the exact ratio of the English to the French foot, or to the toise of 6 feet, which the French astronomers employed in their measurements, and of which they found a degree of a great circle contained 57060 ; if it be asked what more is requisite for concluding that a degree of a great circle contains 104-1- wersts ? and what remains towards the perfection of the geography of Russia, in the most minute detail, but to employ this mea- sure of wersts, sagenes, and English feet, in actual measurements; and to con- struct the charts by the most exact methods of geometry ; it may be answered, we should be very happy, if in the geography of Russia we were arrived at this pitch ; not only in the general map, but in that of any particular district, the nearest and of most concern to us. But besides that we are as yet far from pre- tending to this ; it may be made to appear, that it is not possible to attain it, without undertaking an equal, and even a greater work than all that has been hitherto done in France and elsewhere, towards the measurement of the earth. For if the earth be not truly spherical, all the degrees of the great circles will not be equal to each other ; and those of the small circles, taken at a certain distance from their parallel great circles, will not have the same relation that the degrees of the smill circles, taken at the same distance, would have on a sphere. In all this there might possibly arise an infinite variety, according to the figure the earth might have; and as it is not yet decided what is the earth's true figure, and that there is no better method of ascertaining it than by obser- vations made in so great an extent as that of Russia; therefore the perfection' (of the geography of Russia stands in need of this great undertaking ; which, besides its usefulness, will yield much honour, by contributing towards the de- ciding the celebrated question of the earth's figure. There have been some who have long since suspected, and even thought they were furnished with proofs, that the earth is not exactly spherical. But supposing the earth to be bounded by a curve surface, such as it would be by the level of the sea carried quite over all the earth; it is in this manner, the earth being considered as covered with a fluid, that Sir Isaac j^ewton, in the first edition of his Principia, has demonstrated, that supposing this fluid homo- geneous, and the earth to have been at rest at the time of its creation, it must have assumed the figure of a perfect sphere: but afterwards, supposing it to I2(J PHILOSOPHICAL TRANSACTIONS. [ANNO 1737. have a motion on its axis, as is well known it has in 24 hours ; this spherical figure must have been changed into that of a spheroid, flatted at its poles, in which the degrees on the meridian must be greater towards the poles, than near the equator. Sir Isaac confirms this hypothesis of the earth's figure, by observations of the diminution of the simple pendulum on approaching the equator : to which Dr. Pound adds the analogy the earth has with some of the other planets, as Jupiter, which sometimes appears oval, its least axis being that about which it makes its revolution. This opinion of Sir Isaac has likewise been maintained by Mr. Huygens, though with some small difference. But in J 691, Mr. Eisenschmid having compared the measurements of the earth made in different latitudes, as that of Father Riccioli in Italy, of Mr. Picart in France, and of Snell in Holland; and having found that the degree, which resulted from those different measure- ments, continued to decrease in approaching the poles, which is quite the con- trary of what follows from the earth's figure supposed by Sir Isaac and Huygens, Mr. Eisenschmid was therefore of opinion, that the earth was longer at the poles. This opinion of Mr. Eisenschmid was afterwards confirmed by the late Mons. Cassini, in the observations of the meridian of Paris. For in 1701, having carried on these operations to the Pyrensean mountains, which is a space of above 7+ degrees, he found that as he advanced to the south, these degrees in- creased -5-i-5^ part, or Tl toises each degree. Since the meridian of Paris was, in 1 7 1 8, carried on northward to the sea, M. Cassini, the son, found on comparing more than 8 degrees, which this meridian contains from sea to sea, that the increase, going northward, was but from 60 to 61 toises each degree; as may be seen in the large treatise published in a separate volume, as a sequel to the memoirs of the Royal Academy of Sciences of Paris for the year 17I8. These reasons did not hinder Sir Isaac from persisting in his first opinion of the figure of the earth flatted at the poles, as appears in the 2d and 3d editions of his Principia, published in 1713 and 1726: and it is very surprising, that by this very figure of the earth he demonstrates a certain motion it has, to explain in the Copernican system the precession of the equinoxes, or the apparent motion of the fixed stars in longitude. Sir Isaac finds the inequality of the degrees on the meridian, in so little an extent as that of France, not sensible enough to be possibly determined by immediate obser- vations ; and he is of opinion, that we ought more to rely on the observations of the simple pendulum, and on the other principles which he has built upon, to conclude the earth flatted at the poles. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. ]"27 In 1720, M. Mairan attempted to reconcile the two different hypotheses of Sir Isaac and M. Cassini, by imagining that the earth, at its creation, being without motion, was of a much more oblong figure than that which Cassini thinks it has at present ; so that it might have been reduced to that which it now has, by the diurnal motion on its axis, &c. But Dr. Desaguliers, who is of Sir Isaac's opinion, has made appear, in the Philos. Trans. N" 388, that M. Mairan's supposition is contrary to the laws of motion ; and has moreover pro- posed several considerable doubts on the observations and suppositions employed by M. Cassini, in his determination of the earth's figure in 17 18. As soon as the meridian of Paris had been extended from one sea to the other, and M. Cassini had thence deduced a confirmation of the system of the earth's being longer at the poles ; M. De Lisle imagined a new method of de- ciding the question, viz. by the observation of the degrees of the parallel, com- pared with those of the meridian. For that purpose he considered, that as the degrees of the meridian and those of the parallel, at the same elevation of the pole, had different relations, according to the different figures ascribed to the earth ; nothing more was requisite for concluding which hypothesis was the true one, than to determine this relation by immediate observation. Having supposed, that there had been observed on the parallel of Paris, a space nearly of the saine magnitude with that on the meridian, that is, of about 13 degrees, since that on the meridian is about 84^ degrees ; he found by an exact calculation, that according to the figure which M. Cassini has given to the earth, this space ought to contain 13^ of the parallel, more than in the hypothesis of the earth's being spherical ; which appeared considerable enough to decide between these two hypotheses, and by a stronger reason between the hypotheses of Newton and Cassini, seeing the difference ought to be still more considerable than that now specified. He concluded, at least, that, independent of the figure of the whole earth which could not be determined by the sole observations made in France, with- out making suppositions, and admitting principles, which are still liable to be contested ; it would be of great consequence towards constructing exact charts of the kingdom, to ascertain this relation by observations, which consisted only in forming triangles along the parallel of Paris, and observing at the two ends the difference of the meridians, by the most exact methods. This difference seemed to be so considerable, that he was in hopes of being able to determine it by means only of two places within sight of each other, and situated to the east and west; provided their difference of longitude were accurately observed, in- dependently of astronomical observations, by means of lighted fires ; after the manner that M. Picart put in practice in Denmark, for determining the difl^er- 128 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. ence of longitude of the astronomical tower at Copenhagen and of Uraniburg in the Isle of Huen. With this intent, in the month of April 1720, M. De Lisle went some distance from Paris southward, to the places which he judged most proper for the purpose ; but his design was not then executed, for want of assistance, and for other reasons, which he passes in silence. Since that time, he found that the Marquis Poleni had hit upon the same thought ; as may be seen in his letter to the Abbot Grandi, dated in November 1724. The decision of this famous question, of the figure of the earth, had stopped there, when in the year 1733, the minister of France having thought it neces- sary to construct an exact map of the whole kingdom ; and being informed, that the work could not be better carried on, than by the astronomers of the Royal Academy of Sciences, applied to M. Cassini on that head ; who was of opinion, that, to execute it with the utmost exactitude, the same method ought to be employed as for the meridian, by taking through the whole extent of the kingdom, triangles connected by means of objects seen successively, one from another, &c. This project of making a map of France by such triangles, had been already offered to M. Colbert, by Mons. Picart, in 168], but was not then executed. However, M. Cassini proposed, that these triangles should be begun in a direction perpendicular to the meridian ; in order to render these operations of service towards the decision of the earth's figure, pursuant to the method spoken of above : and M. Cassini, having in person undertaken these operations, and having carried them that same year, 1733, from Paris to St. Malo, whose longitude from Paris M. Picart had observed in 168I ; the rela- tions of the degrees on the meridian and parallel, were found to be such as were required in the hypothesis of the earth lengthened at the poles, and even more lengthened than Cassini had determined in 17I8. For instead of the diminution of a 6oth part for each degree of the parallel, which M. De Lisle had found according to the earth's figure, as determined by Cassini in 17 18, he deduced from his operations in 1733, a diminution of the 36th part of each degree. It is true, that M. Cassini, in the account he gave of this determination at the public meeting of November 14, 1733, does not give it as entirely certain; because the longitude of St. Malo, with regard to Paris, was collected from one observation only of Jupiter's first satellite, in which there may possibly be some error : but at least M. Cassini seems certain, that there is a very considerable diminution in the degrees of the parallel of Paris, which confirms his opinion of the earth's being longest at the poles. This we are likely to have a better assurance of hereafter, as we are informed that this measurement of the parallel of Paris, is carrying on in France by M. Cassini's sons, M. Maraldi's nephew. VOL. XL.] PHILOSOPHICAL TUANSACTIONS. 120 and several other young mathematicians, instructed by M. Cassini in this sort of work. M. De Lisle has already said, that all these operations performed in France, for the figure and magnitude of the earth, could not serve to determine the earth's figure out of Frnnce, without the assistance of certain hypotheses ; unless the same thing were undertaken and carried on in the other regions of tlie earth, more northern and southern than France. It was on this considera- tion, that the Royal Academy of Sciences took up the resolution of sending some astronomers to make the like observations as near the equator and the poles as possible, which are the places where the difference of the degrees on the meri- dian ought to be the greatest, according to the different hypotheses. In the month of April 1735, three mathen)aticians and astronomers of the academy, viz. Messieurs Godin, Bougher, and De la Condamine, set out from France for the province of Quito, the most northern part of Peru in America; to observe, just under the equinoctial line, the magnitude of some degrees of the meridian and equator. As to the other mathematicians and astronomers of the same academy, viz. Messieurs de Maupertuis, Camus, Clairaut, and Monnier, who were sent to the north, they departed from France in April 1730, with Mr. Celsius, pro- fessor of astronomy at Upsal, who accompanied them to Sweden, as far as the bottom of the gulph of Bothnia, where they might measure about a degree on the meridian at its crossing the polar circle. But as they had not finished their operations, it is not yet known whether the magnitude of the degree measured by them, favours the opinion of M. Cassini, or that of Sir Isaac Newton. All we know is, that they have found the length of the simple pendulum favourable to the latter, that is, longer under the polar circle than farther south. De la Croyere had already found the same thing : for being at Archangel in 1728, he there observed, in the most exact manner he possibly could, the length of the simple pendulum, which he found to be -^ parts of a line longer than at Paris. We are likewise informed by the other astronomers gone to Peru, that in their way towards the equator, being at St. Domingo, in the latitude of 18° 37', they there found the pendulum swinging seconds, to be about 2 lines shorter than at Paris. Thus, all we as yet know from those gentlemen, on the expeditions to the north and the line, confirms the opinion of Sir Isaac Newton and his adherents : and yet M. Mairan pretends, that this shortening of the pendulum towards the equator, is in one sense entirely independent of the earth's figure. Thus it appears from the foregoing account, that the question concerning the earth's figure is not yet at an end. Nay, it is not impossible, that after finish- VOL. VIIJ. S 130 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. ing all the observations which are actually making, new difficulties may arise, and new objections be started, that may prevent its being entirely decided. However, all this work cannot fail giving great light to this important question, and procuring considerable advantages to geography, astronomy, and natural philosophy. It is with this view, and particularly to render such important service to the geography of Russia, that M. De Lisle thinks it necessary to undertake a work of that nature in Russia ; towards executing which they have great advantages which other nations have not. One of the principal of these advantages, is the great extent of Russia every way. For were the meridian of the imperial ob- servatory of Petersburg to be determined, it might be carried to between 22 and 13 degrees ; which is a fourth part of the distance from the pole to the equator. The meridians of Mosco and Astracan are not of less extent ; and consequently we might, by the measurement of some one of these meridians, de- termine more exactly, than could have hitherto been done, the inequality that subsists between the degrees of the meridian. This is what the great Cassini wished, when, after having, in the year 1701, determined this inequality by the extent of 7 degrees observed in France, as has been mentioned above, he says, that this fact might be verified by measurations of greater extent, if the other princes of the earth would contribute as much as the King of France, towards the perfecting of sciences. In the great extent which might be given to the meridian of Petersburg, there would be the advantage of knowing, by operations connected together, or uninterrupted, the magnitude of some degrees equal to those which have been measured in France, and to that which the French astronomers have measured in Sweden ; and not only all the degrees between the two, which the French astronomers have not had in their power to observe, but also some degrees farther northward than that measured by them in Sweden. As the exigencies of geography require the triangles, taken for the determi- nation of the meridian, to be continued on every side, and principally in direc- tions perpendicular to the meridian, or according to the parallels ; with how great exactness may we not then determine the proportion of the degrees on the parallels to those on the meridian, by means of the vast extent of the Russian empire, which on its western side extending as far as all the dominions of Europe from the most northern to the most southern, has no other bounds to the east than the east itself, so to speak ; seeing its extent that way contains near half the earth ? Another great advantage to be obtained by the work now proposed to be made in Russia, is, that, coming after others, we shall reap the benefit of all VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 131 their knowledge and experience in the like kind of measureinenls : whence we may expect to succeed and execute it better than could have been done else- where, by appl)ing timely remedies against the difficulties that occurred in other places. These operations are to be founded on a basis of the greatest length possible; which must be actually measured, and with the greatest exactness ; as it is to serve for a foundation to the measurement of all the triangles. And in this point too there is a very great convenience near Petersburg, seeing on the ice, we may measure out a basis, greater than has been hitherto taken, namely, from the coast of Ingria about Peterhoff, to the coast of Finland toward Syster- beck. There is not less than 20 wersts distance between these two extremities, and this great distance may be measured very exactly, the ice being very even. And as this basis is situated between the Isle of Cronstad and Petersburg, in a direction nearly perpendicular to the distance from Petersburg to Cronstad ; there can be no better method for inferring thence, by exact observation of the angles taken at the extremities of this basis, the distance from the centre of the imperial observatory, to the steeple of the new church at Cronstad; which two objects are seen reciprocally from each other, and are not less than 30 wersts asunder : and this distance, onee known exactly, will serve as a foundation for all the triangles to be taken ; of which each of the sides may have not less than from 30 to 40 wersts, according as objects are found advantageously situated for that purpose. It should begin with the mountain of DouderhofF. which, with the imperial observatory, and the steeple of Cronstad church, forms one of the most convenient triangles imaginable for the subject proposed. In taking observations at these three places, it must then be tried to discover others of the same advantageous situation ; but when no remarkable objects are found of the desired situation and distance, they must be erected on purpose, in the same manner as in other countries. The most necessary instruments for executing this undertaking, are, besides the ordinary astronomical instruments, a common quadrant of between 2 and 3 feet radius, for observing the angles of the triangles ; and a portion of a circle of the greatest radius that can be con- veniently had, for observing the arches of the heavens corresponding with the distances measured on the earth. As to the instrument for observing the arches of the heavens, its radius ought not to be less than from 12 to 15 feet : but it is not necessary that it should contain a large portion of a circle. It is only re- quisite to have this portion somewhat larger than the arch of the heavens in- tended to be measured. Thus, as the meridians, which may be traced in Russia, can be extended only between 22 and 23 degrees, it will suffice that the instru- ment employed, be a portion of a circle of 30 degrees s 2 132 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737- M. Picart, for his first operation, got an arch of a circle made of 18 degrees and of 10 feet radius, with which he thought himseU' sure within 2 or 3 seconds: and no other instrument was used in the chief observations for the meridian of Paris. The astronomers who are gone to America, carried with them an in- strument of 12 feet radius, and of a portion of a circle of 30 degrees. But those come to Sweden, contented themselves with a portion of a circle of 54- degrees, and 9 feet radius: but this instrument, made by Mr. George Graham, a very able English mechanician, is by its construction so exact, that the astronomers who have used it, think, themselves certain to 2 seconds. The one wanted for the observations in Russia, ought to be made by the same artist, and of the same construction. It is with such an instrument that Mr. Bradley, a celebrated English astro- nomer, has discovered, in the meridian altitudes of some fixed stars, certain constant and annual variations, which do not proceed either from the variation of the refractions, or from the parallax of these stars, or from any nutation or wavering of the earth's axis ; but which he accounts for by the successive mo- tion of light. Whatever be the cause of these variations, as they may possibly happen in the space of time requisite to be spent in making the observations for the meridian, or in passing from one end of the meridian to- the other; it is necessary, with the same instrument, or such another, that is of pretty near the same exactness, to examine the variations of the stars made use of: it would therefore be of considerable advantage, not only for the observations of the measurement of the earth, but also for all the other principal researches in astronomy, to have orders given for procuring two mural quadrants of Mr. Graham's make, and of the same construction, as already specified; for which there are walls already raised at the imperial observatory, in the plane of the meridian. With these two quadrants, which might be of 7 feet radius, and the moveable telescope 9 or 10 feet long, we should be in a condition to make ob- servations of the utmost accuracy, such as the present state of astronomy requires. Besides these instruments now mentioned, which are of absolute necessity to a solid establishment of astronomy and geography in this country, there are still some other smaller instruments, that may be of great use in the operations, or may serve to make other curious and useful observations at the same time, that those for the measurement of the earth are making. When the sides of the triangles, taken for measuring the earth, terminate at very elevated places, as on the tops of the highest mountains, it is necessary to reduce these triangles to what they would be, had they been observed in hori. zontal planes on a level with the sea. For this purpose, we must know the VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 133 height of the mountains above the sea's level, which cannot always be deter- mined geometrically, or would at least be too tedious to perform : therefore, in the meridian of Paris, which crossed very high mountains, M. Cassini was of opinion, that he ought to fix their height by a shorter method, which is that of the height of the simple barometer, observed on the top of each mountain, and compnred with that observed at the same time in another place, whose elevation above the sea's level was known. But as that method supposes the knowledge of the proportion which the different fallings of the mercury keep with the different heights to which the barometer is carried ; and as natural philosophers are not as yet entirely agreed on this head, for want of observa- tions of sufficient accuracy ; thence it happened, that Dr. Desaguliers, making it appear that M. Cassini has not employed the most exact proportion, found reasons for correcting, or at least for doubting, of some of M. Cassini's calcu- lations. Thus it must be by the assistance of new experiments, better circum- stanced than those hitherto made, and pursuant to a theory entirely agreeing with these experiments, that this method may be employed with certainty, for determining the height of mountains by the barometer, and reducing the angles observed from the tops of these high places, to what they would be, if they had been observed on a plane at the level of the sea. Now these new ob- servations can be made on our way in tracing the meridian ; and for that pur- pose M. De Lisle began to construct compound barometers, which being very nice, will serve to observe with accuracy, the quantity of the mercury's fall, at the different elevations to which they shall be carried, to fix with greater certainty the proportion of that fall. There is still another method of determining the elevation above the level of the sea of all the points, in which the triangles terminate, that are made for the measurement of the earth. This may be done by beginning these opera- tions near the sea, and actually measuring how many toises and feet the places of the first stations are elevated above the level of the sea. For if the angles of the apparent elevations of the second stations, seen from the first, be after- wards observed, it will be an easy matter, from the known distances, to deduce the true elevations of the latter above the former, and consequently above the sea's level, making proper allowances in the calculations for the difference of the apparent level from the true one. In this method, nothing is to be appre- hended but the variation of refractions ; but for this a remedy may be found, for the most part, by returning again, that is, by reciprocally observing the first stations seen from the second : for if it be found, that as much as the second station appears elevated above the first, so much the first is depressed below the 134 PHILOSOPHICAL TRANSACTIONS. [aNNO J 737. second, except the small difference which must arise according to the given distance, it will be a proof, that the refraction has been of no prejudice. The other considerable observations and experiments, to be made in the journies undertaken for such inquiries, are, the observations of the magnetic needle, both as to its dip and variation : but chiefly the observations of the length of the simple pendulum, which at present is become requisite to be ob- served with as much exactness, and in as many places, as is possible; but also for which there are new methods invented, which probably surpass those hither- to made use of; in as much as, since those methods have been found by the the Royal Academy of Sciences of Paris, it was thought proper to notify them to the astronomers sent to Peru, to put them in practice in their observations. The actual Mensuration of the Basis proposed in the preceding Article. By M. De Lisle. N° 445, p. 50. M. De Lisle undertook to measure the basis mentioned above, and had the good fortune to measure it very exactly on the ice, by taking the precise distance between the castle of Peterhoft', and the castle of Doubki, opposite to it, on the coast of Finland. He found the distance between the opposite walls of these castles to be 74,250 feet English. This basis, being much greater than any of those employed hitherto for this purpose, gives room to expect great exactness in the whole work, when it shall be carried on in the same manner. It will at the same time serve to make a very exact map of the bottom of the gulph of Finland. It is for the same design, and for better ordering the charts of the coasts of the Baltic, that he intended (as soon as my project shall be ap- proved here in its full extent) to begin to measure my triangles along the coasts of Ingria and Livonia, to the islands of Dagho, Oesel, &c. And that the charts of the places taken in by these triangles may be finished at the same time, he designed to take with him all the charts of these parts, which could be had to verify and correct them in his way. He likewise intended to publish, as soon as possible, all the operations and observations made in the expedition; that thus early benefit may be reaped from them, and that the public, at the same time the charts come out, may be ac- quainted with the foundation on which they are constructed. Observations of two Parhelia, or Mock-Suns, seen Dec. 30, 1735; and of an Aurora Borealis, Dec. 11, 1735. By the Rev. Timothy Neve. N''445, p. 52. On Tuesday, Dec. 30, J 735, between Cherry Orton and Alwalton, in the VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 135 coutity of Huntingdon, Mr. Neve observed two parhelia, the first of which shone so bright, that at first sight he took, it for the real sun, till looking a little farther on his left hand, he was convinced of the mistake, by seeing the true sun much the brightest in the middle, and a mock-sun on each side, in a line exactly parallel to the horizon. He guessed their distance to be about 40 dia- meters of the sun, or, as they usually appear, 23 degrees. That on the left hand of the sun, when he saw it first, was small and faint, but in about 2 mi- nutes time it became as large and bright as the other, and appeared at once as two white lucid spots on each side the sun, east and west, seemingly as large, but not so well defined : in about 3 minutes they lost both their colour and form, and put on those of the rainbow ; the red and yellow in both very beautiful and strong nearest to the sun, the other colours fainter. They became as two parts of an arch, or segment of a circle, with the concave towards the sun, only round at top, the light and colours streaming downwards, and tend-" ing towards a point below. This continued for about 4 or 5 minutes, when the colours gradually disappearing, they became as before, two lucid spots, with- out any distinction of colours. They lasted a full hour, sometimes one brighter, and sometimes the other, according to the variation of the clouds and air, as he supposed. When he first saw it, it was exactly a quarter after eleven. There had been a frost in the morning, which went away pretty soon, with a thick mist, and between 10 and 1 1 o'clock cleared up, leaving only a haziness in the air behind it : the weather quite calm, wind about n. w. These parhelia are commonly seen with a circle or halo round the sun, con- centrical to it, and passing through the disks of the spurious or mock-suns. But there was not the least appearance of such a circle here, it having only a tendency towards one, when it was seen with the rainbow colours. The other phenomenon, was that pretty common one of the aurora borealis, of an uncommon appearance. A little after 3 o'clock, the northern hemi- sphere was obscured by a dusky red vapour, in which, by degrees, appeared several very small black clouds near the horizon. The first eruption of the lights was within a quarter of an hour, full east, from behind one of the small dark clouds, and soon after several others full north. These streams of light were of the same dusky red colour as the vapour, just appeared, and vanished instantly. He saw 8 or 10 of these at once, about the breadth of the rainbow, of different heights, several degrees above the horizon, which looked like so many red pillars in the air ; and no sooner did they disappear, but others showed themselves in different places. In about half an hour, this colour of the va- pour gradually changed towards the usual white, and spread much wider and higher ; and after that, appeared as common. 136 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737- Observations of two Parhelia, or Mock-Suns, seen at Witlemherg, in Saxony, on Dec.3\, 1735. 0.5. By John Frid. fVeidler, F. R. S. i^c. N° 445, p. 54. Dec. 31, 1735, o. s. a little after 10 in the morning, being informed that several suns were seen in the heavens, Mr. W. went into his garden, and immediately saw near the sun s, on its left or western side, the parhelion b, as large as the true sun, fig. 15, pi. 5. This mock-sun was amidst small, round, white clouds, set thick, and close to one another. The middle of this mock-sun shone with so great a light, that the naked eye could not bear it ; so that he viewed it attentively through a glass darkened with the smoke of a wax-candle. The light of the parhelion b appeared much weaker than that of the true sun. Its circumference, facing the sun, was red : but that part of the stream fg, which was towards the sun, was purple. Within the red border appeared the other colours of the rainbow, as yellow, green and azure ; the stream bh was likewise embellished with red and yellow. Both edges of this were reddish, and its middle yellowish. The sun s was 15°-f above the horizon ; and its image b was near the same altitude : the distance from s to B was '20°: the arch fg was near 6° in length. Most of the south- ern part of the hen)ibphere was overspread with white clouds, interspersed with some darker ones. There were some thin clouds before the true sun, through which its rays easily passed. When thicker clouds surrounded the sun, the brightness of the parhelion was lessened : the parhelion was now and then hidden by dark clouds. Soon after first observing the parhelion b, was seen the beautiful rainbow ode, parallel to the horizon, with its horns turned to the north. It had the usual colours of the rainbow, all very distinct. The purple was on the side facing the sun ; next to it was the yellow, then the green, and last the azure. The point d was Q\° distant from the horizon; therefore the diameter of the rainbow was 58° : however, only a part of the rainbow ode was seen, the ends of which were sometimes but 38° from one another: for more or less of it appeared at different times, but scarcely above a 4th part of its circumference at any time. It lasted till the sun and most part of the sky was overcast by thick clouds. The thickness of the rainbow CK, as well as I could estimate by the bare eye, was 1° of a great circle. From another place, whence he had a full view of tl)e hemisphere, a little before 11 , he saw another parhelion a to the east, 20° from the sun, as the former was, and raised 15° above the horizon. This mock-sun was not infe- rior to the other b, in brightness, for the naked eye could no more bear it VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 137 than that: its light was white; its figure round, audits size equal to that of the sun s. This parhelion a shot out the stream il, which was rectlinear, white and resplendent, 8° long, and void of colours ; and it lasted somewhat longer than the former, without changing its figure. On the sun's being hid by thick clouds, about 4- hour after eleven, both these mock-suns disappeared ; but they became visible again, on the sun's shining bright. The whole of the phaenomena observed in these parhelia comes to this : that the true sun, s, was accompanied by two parhelia, both 20° distant from the sun, one on each side, and having nearly the same altitude with the sun from the horizon. Above the parhelia, part of a rainbow surrounded the zenith; and each of the parhelia sent forth a bright luminous strean) or tail, one rectilinear and white, the other soraewliat curved and coloured. More- over, from the western parhelion, a stream parallel to the horizon, and some- what pointed, extended itself on the side opposite to the sun ; and this scene lasted the 2 hours of 10 and 1 1 before noon, till thick clouds put an end to it. There was no appearance of an entire crown, such as usually accompanies parhelia, and encircles the sun. An Observation of three Mock-Suns seen in London, Sept. 17, 1736. By Martin Folkes, Esq. F. Pr. R. S. N" 445, p. 59. Sept, 17, 1736, as Mr. Folkes was reading a little after 7 in the morning, in a room looking towards the north-east, he accidentally noticed an odd stream of coloured light, shooting upwards from the sun, shining through a thin waterish cloud ; but recollecting the appearance was several degrees more nor- therly than the sun's true place at that time, he went to the window, and found what he had taken for the sun was a parhelion, shooting out a short horizontal stream or tail towards the north ; the sun itself shining pretty bright and clear at the same time. He also observed, that the stream he had at first seen, was part of an arch concentric to the sun, and passing through the parhelion : this arch was for a good way tolerably defined, and tinged with red on the inside, and a bluish white on the other. Casting his eye to the other side the sun, he perceived a second parhelion, at the same distance from him, towards the south, though not yet so bright as the first. He then went up to the leads of his house, where he soon found the phenomenon considerably to improve, the arch round the sun forming itself into more than a semicircle, reaching almost to the horizon northward, and with very little discontinuance beyond the second parhelion towards the south. He then began to perceive a third parhelion, where the circle surrounding the sun would have been cut by the vertical VOL. vni. T 136 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737- passing through him ; and in the same place his circle was touched by the arch of another, in some sort confounding itself with it in the place where the third parhelion appeared : this was a good deal fainter than the other two, and the last arch extended but a little way, so as to be difficult to determine where its centre lay ; this arch was coloured also, but with red on its convex part. He had some time before this begun to see also another circle, surrounding the sun at the distance of about 45°, which appeared to be about twice the distance of the first ; and this also increasing while he was considering it, became little less than a semicircle, being also tinged with red like the other on the inner side. When the circle had thus pretty well formed itself, he also discovered the arch of a 4th, touching this, or rather confounding itself with it, in its highest part, and surrounding, as it seemed, the zenith. Of this last circle he saw, when it was most complete, better than half, and it was much stronger coloured than any of the others, being of a bright red on its convex part, and a good blue on the concave. In the part where this circle confounded itself with the larger of those that were concentric to the sun, their common part was nearly white, and brighter than the rest, though hardly enough to call it a 4th parhelion. The principal mock-suns continued tolerably bright till near 8 o'clock, the southern part of the phenomenon improving as the northern decayed ; and the southern parhelion was once so bright, that, taking the ad- vantage of a place where a chimney shaded the true sun, it cast a very visible shadow : the white and luminous horizontal tail also, that went from this par- helion, was much longer than that of the other, reaching at one time beyond the outer of the two concentric circles. The parhelia themselves, though very luminous, were, however, never defined with any exactness as to their discs, but looked as we sometimes see the sun through a thin whitish cloud, and they were themselves of a reddish colour on that side next the true sun. About 8 the phenomenon was sensibly decreased, and had entirely disappeared by 20" after. All these appearances are exhibited in fig. l6, pi. 5. Of a Rupture of the Ileum from an external Contusion, in a Letter from Christian Wolf, Professor of Mathematics at Marpurg, &c. to Wm. Rutty, M. D. formerly Secretary to the R. S. Dated March 3, 1731. An Abstract from the Latin. N° 445, p. 6l. Professor Wolf here states that a labourer had received a fatal accident from a large stone falling upon the abdomen, in such manner as to occasion a con- tusion, but no laceration. The man died very unexpectedly the day after the accident. On opening the body, a large rent was discovered in the ileum, and its contents were found effused into the cavity of the abdomen. VOL. XL.J PHILOSOPHICAL TRANSACTIONS. ISQ Some new Statical Experiments. By J. T. Desaguliers, LL. D. F. R. S, N° 445, p. 62. When a long and heavy body, lying on the ground, is to be raised up at one end, like a lever of the second kind, while the other end keeps its place, and becomes the centre of its motion; the prop used to support it at any point in its whole length, sustains a certain pressure from the beam. Now these ex- periments are to show, by a force drawing always in the direction of the prop, what is the quantity of the pressure on the prop, according to its length, and to the angle which it makes with the beam, or with the horizon, and to the distance from the centre of motion of the beam at which the prop is applied. For when the prop is taken away, the force drawing in the direction of the prop will keep the beam in equilibrio ; and a force ever so little superior to the friction added to the power, will make it overpoise the beam, and raise it higher ; but overcome the power and bring down the beam, if it be added or applied to the beam. Though in every case and experiment we have this analogy, taken from me- chanical principles, viz. that, — The intensity of the power : Is to that of the weight : : As the distance of the line of direction of the weight : Is to the distance of the line of direction of the power; — ^yet to find those distances nicely in the several applications of the prop, we must have recourse to geo- metrical constructions and reasonings. With these and the algebraical ex- pressions of the same, the experiments exactly agree. In the machine here used, the iron bar, or parallelipiped representing the heavy body, weighs 12 drams, 12 dwt. 12 grains, or 6060 grains; and its centre of gravity is at the distance of 2O-I- inches from its centre of motion. The props used are, the one of 5, and the other of 10 inches. To over- come the friction, allowed for by certain rules in all cases, the Dr. used a nice brass pulley, of 3 inches diameter, its pivots only -j-J-^ of an inch in diameter ; so that the 6oth part of the power added to it, will in all cases overcome the friction. Case I. In which the Prop is perpendicular to the Horizon, exemplified by two Experiments. Exper. 1. — The prop is 5 inches, and placed under a point in the bar, 10 inches from the centre of motion. Here the power acting in the direction of the prop, able to keep the bar in that situation, or the pressure sustained by the prop, will be found 250 oz. 1 7 dwt. 1 5 grains ; and the friction 8 dwt. 15 grains. The foot of the prop is to be at 8 inches and -^ from the centre of motion. T 2 140 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. Exper. 2. — If the same prop, of 5 inches, be placed under a point in the bar at 30 inches from the centre of motion, the power or pressure will be 8 oz. 12 dwt. 13 gr. and the friction equal to 2 dwt. 21 gr. The foot of the prop is to be distant from the centre of motion 1Q inches -/oV- Case II. In which the Prop is perpendicular to the Bar, exemplified by three experiments. Exper. ] . — Now let the prop, still 5 inches long, be placed so as to be per- pendicular to the bar at a point 12 inches from the centre of motion. Here the power expressive of the pressure should be 1 9 oz. 18 dwt. 4 gr. and the friction 6 dwt. 15gr.; but on account of a correction necessary to be made to this, because the bar is thick as well as heavy, and the centre of gravity above the surface to which the prop is applied, the power or pressure sustained will be only IQ oz. 15 dwt. 5 gr. and the friction 6 dwt. 14gr. The distance of the foot of the prop in this case is 13 inches from the centre. Exper. 1. — ^The prop here is JO inches long, still perpendicular to the bar, under a point in the bar, 24 inches from the centre. The power equal to the pressure sustained, should be, if the bar was only heavy, and not thick, g oz. J 9 dwt. 4 gr.; the friction 3 dwt. 1 l^gr.; but with the proper correction, ex- plained hereafter, it must be only 9 oz. 17 dwt. 15 gr.; the friction 7 dwt. 7 gr. Here the foot of the prop is to be 26 inches from the centre. Exper. 3. — If the end of the prop be placed under a point in the bar, so that the horizontal distance of the foot of the prop be exactly equal to the dis- tance of the centre of gravity from the said centre of motion, viz. 20.5 inches, the power or pressure sustained by the prop will be precisely equal to the weight of the bar, viz. 12 oz. 12 dwt. 12 gr. In this case, the prop is distant from the centre of motion on the bar 1 7.9 inches, and the friction 4 dwt. 5 gr. Case III. In which the angle made by the prop with the horizontal line is given, either acute or obtuse. As this case is very intricate, on account of the several powers of the sine and cosine of the given angle, which are multiplied into the prop, and into the weight of the beam, we will exemplify it only in one experiment; which is, when the angle made by the prop, with the horizontal line contained between the foot of the prop and the centre, is acute: then there is a maximum of pres- sure, which it appears by experiment is the very same as the calculation gives. Suppose the angle made by the prop and the horizontal line to be 60 degrees; the calculation of this maximum shows, that if the prop be 10 inches long, the distance measured on the bar, to which the upper end of the prop must be applied, will be 10 inches -^\, the bar itself making then an angle of about 52° 12'; and the horizontal distance between the centre of motion and the foot of the prop, is then 1 1 inches ■^^. VOL. XL.} PHILOSOPHICAL TRANSACTIONS. 141, N. B. Three things are to be remarked in this case: First, That when the angle made by the prop and the horizontal line, con- tained between the centre of motion and the foot of the prop, is acute, as in the last experiment, there is always a maximum: whereas when the same angle is obtuse, there is no positive maximum; for then the pressure continually in- creases, the nearer the prop is to the centre of motion. Secondly, That when the angle of the prop with the horizon is acute, as in the last experiment, the bar, or long and heavy body, can be raised by applying the power or prop always with the same angle to the horizon, quite up to a vertical situation. Thirdly, That the first case, which is when the prop is perpendicular to the horizon, is only a particular case of this more general one. Case IV, Is when the angle made by the prop with that part of the Learn con- tained bettveen the point to which it is applied, and the centre of motion, is given, either acute or obtuse. As the expression of the power in this case, is fully as intricate as in the last, the Doctor gives only one example or experiment; and, for the greater satisfac- tion of those that see it, he chose that in which the pressure is in its maximum. He supposes, as before, the angle made by the prop, still 10 inches long, with that part of the beam contained between the point to which it is applied, and the centre of motion, to be acute, and of 6o°; then the maximum of pressure will be, when the part of the beam intercepted between the centre of motion and the upper end of the prop is 12 inches -rVo-; the bar is then elevated about 50° 1 3', and the horizontal distance between the centre of motion and the foot of the prop, is then 1 1 inches -[Vo- N. B. Observe also in this case, as in the last. First, If the angle made by the prop, and the part of the beam intercepted between the point of application and the centre of motion, is acute, there will always be a maximum. The contrary will happen, if that angle is obtuse. Secondly, If the angle i* acute, the bar cannot be raised up to a vertical situation by applying the power or prop constantly with the same acute angle; but it may be raised quite up, if the angle of ihe prop with the beam is obtuse. Thirdly, The second case is but a particular case of this general one. The Apparent Times of the Immersions and Emersions of Jupiter''s Satellites, for the Year 1739, computed to the Meridian of the Royal Observatory at Greenwich. By James Hodgson, F. R. S. N" 445, p. 69. These calculations are omitted for the same reasons as before. 142 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. An Account of the Peruvian or Jesuit's Bark.* By Mr. John Gray, F. R. S. at Carihagena, from some Papers given him by Mr. William Arret, a Scotch Surgeon, who had gathered it at the Place where it grows in Peru. N°446, p. 81. The tree from which the Jesuit's bark is cut, grows in the kingdom of Peru, in the Spanish West Indies, and is found most commonly in the provinces of Loxa, Ayavaca, and Quenca, situated between 2 and 5 degrees of south lati- tude. This tree is tall, and has a trunk rather thicker than a man's thigh, taper- ing from the root upwards; it has no boughs or branches, till near its top; where they grow as regular as if lopped artificially, and with the leaves form exactly the figure of a hemisphere : its bark is of a blackish colour on the out- side, and sometimes mixed with white spots; whence commonly grows a kind of moss, called by the Spaniards, barbas; its leaves resemble much the leaves of our plum-tree, are of a darkish green colour on their upper or concave side, and on their lower or convex side, reddish ; its wood is as hard as common English ash, and rather tough than brittle. There are 4 sorts of the bark of this tree, to which the Spaniards give the following names, viz. cascarilla colorada, or reddish bark ; amarylla, yellowish ; crespilla, curling; and blanca, whitish; but Mr. Arrot could only find 2 dif- ferent sorts of the tree, and he believes that the other 2 sorts of the bark are owing to the different climates where it grows, and not to a different species of the tree. The bark called colorada and amarylla, is the best, and it differs from the blanca in this, that the trunk of the former is not near so thick as that of the latter; the leaves as described above; whereas those of the blanca are larger, and of a lighter green colour, and its bark has a very thick spongy sub- stance, whitish on the outside, and is so tough, that it requires the force of an axe to slice it from the tree. It is as bitter when cut down as the best sort, and has then the same effect in intermitting fevers; but when dry and long kept it turns quite insipid, and is good for nothing. Both sorts have a much surer and quicker effect in cures when green than when dry. As the bad sort is in great plenty, and the best very scarce, and hard to be come at, large quantities of it are cut yearly, and sent with a little of the fine bark to Panama for Europe. The tree of the crespilla is the same with that of the amarylla and colorada, but it grows in a cold frosty climate { by which means the bark is not only altered in its quality, but is also whitish on the outside, though cinnamon-coloured * Cinchona otHcinalis. Linn. VOL. XL.] I'lllLOSOl'HICAL TRANSACTIONS. 143 within, and ought in medicines to be rejected. This sort and the blanca grow plentifully in the province of Ayavaca, 50 leagues from Piura, and 62 from Payta, a port in the South Sea; as also in Cariamango, Gonsonama, and Xim- buro, whence they commonly send it to Payta, and there sell it as the best. The blanca likewise grows in the province of Quenca, and in the mountains of Caxamarea: but the true and genuine fine Jesuit's bark, which is of a reddish or yellowish colour, is only found from 5 to about 14 leagues round the city of Loxa, in the province of Loxa, called generally by the Spaniards, Provincia de las Calvas. This city is situated between 2 rivers, that run into the great river Marannon, or of the Amazons, and lies about lOO leagues from Payta, and in a direct line about 1 10 leagues south-east from Guayaquil, though by the com- mon road near 200. The places about Loxa, where this fine sort is found, are La Sierra de Caxanuma, Malacatos, Yrutasinga, Yangana, Mansanamace, La Sierra de Boqueron, and a place called Las Monsas. The bark trees do not grow all together in one spot, but intermixed here and there with many others, in the woods; it happens indeed sometimes, that clusters of them are found together, though at present they are much scarcer than in former times, a great many of the fine large bark trees having been entirely cut down, that their bark might the more easily be sliced off. The soil where the best sort thrives, is generally in red clayey or rocky ground, and very frequently on the banks of small rivers descending from high mountains. That this tree flourishes and bears fruit at the same time all the year round, is certainly owing to the almost uninterrupted rains, that fall in those high mountains where it grows, which continue with little or no intermission: though about 3 or 4 leagues down in the low country, where it is excessively hot, there are wet and dry seasons, as in other hot countries, the rains begin- ning in December and ending in May; this season the Spaniards who live there call temporal, and it is general all thereabouts; whereas what they call paroma is a cold rainy season, that lasts in all the mountainous places of these coun- tries from June to November, but especially in the city of Loxa and places adjoining, where Mr. Arrot has passed 23 or 30 days without once seeing the sun, and felt the air so extremely cold, that he was obliged always to be wrapped up in his cloak, and to be in continual motion to keep himself warm. Such excessive cold so near the line, appears to Europeans incredible; but many places in these latitudes are so, by their situation and vicinity to high mountains. The properest season for cutting the bark is from September to November, the only time in the whole year of some intermission from rain in the moun- 144 FHILOSOPHICAL TRANSACTIONS. [aNNO 1737. tains. Having discovered a spot where the trees most abound, they first build huts for the workmen, and then a large hut to receive the bark, to preserve it from the wet : but they let it lie there as short a time as possible, having before- hand cut a road from the place where the trees grow, through the woods, some- times 3 or 4 leagues, to the nearest plantation or farm-house in the low country, whither, if the rain permits, they presently carry the bark to dry. These pre- parations made, they provide each Indian, these being the cutters, with a large knife, and a bag that can hold about 50 lb. of green bark ; every two Indians take one tree, whence they cut or slice down the bark, as far as they can reach from the ground; they then take sticks about half a yard long each, which they tie to the tree with tough withs, at proper distances, like the steps of a ladder; always slicing off the bark, as far as they can reach, before they fix a new step; and thus they mount to the top, the Indian below gathering what the other cuts; this they do by turns, and go from tree to tree, till their bag is full ; which, when they have plenty of trees, is generally a day's work for one Indian. As much care as possible must be taken that the bark is not cut wet; should it so happen, it is to be carried directly down to the low country to dry, otherwise it loses its colour, turns black, and rots; and if it lie any time in the hut without being spread, it runs the same risk : so that while the Indians are cutting, the mules, if the weather permits, ought to be carrying it down to the place appointed for drying it, which is done by spreading it in the open air, and frequently turning it. Mr. Arrot had the curiosity to send above 50 seroons from the woods to the city of Loxa, where he put it into a large open house, and dried it under cover, never exposing it either to the sun or night air, imagining that the sun exhaled a great many of its fine parts, and that the night air, or serene, was very noxious to it; but he found the colour of the bark thus cured, not near so bright and lively as that dried in the open air. He is of opinion, that a very short time will put an end to this best sort, or at least it will be extremely hard to be got, by reason of its distance from any inhabited place, the impenetra- bility of the woods where it grows, and the scarcity of the Indians to cut it, who, by the Spaniards' hard usage and cruelty, are daily diminishing so fast, that in a very few years their race in that country will be quite extinct. Mr. Arrot says, that the small bark which curls up like sticks of cinnamon, and which in England is much esteemed, as being cut off the branches, and therefore reckoned better and more effectual in curing fevers, is only the bark of the younger trees, which, as it is very thin, curls in that manner; and that the bark of the branches would not compensate the trouble and expences of cutting. He also says, that after the bark is cut off any tree, it requires at VOL. XL.] FHILOSOPHICAL TRANSACTIONS. 145 least 18 or 20 years to grow again ; which is directly contrary to what Dr. Oliver says in N" 290 of the Phil. Trans. He added besides, that its fruit is no ways like a chestnut, as the Doctor informs us in the same paper; but rather like a pod, which incloses a seed somewhat like a hop-seed, and that he had sent some of them to England. He could not tell by what artifice or stratagem the Jesuits have got this bark to be called after them, if not that they carried it first into Europe, and gave themselves out as the first discoverers of its virtues : but he asserted, that the current opinion at Loxa is, that its qualities and use were known by the Indians before any Spaniards came among them ; and that it was by them applied in the cure of intermitting fevers, which are frequent over all that wet unhealthy country. An Account, by Mr. John Eames, F. R. S. of a Booh entitled, A Mathematical Treatise, containing a System of Conic-Sections, with the Doctrine of Fluxions and Fluents, applied to various Subjects. By John Muller. N° 446, p. 87. The ingenious author of this work,* observing how much time is necessarily epent, and pains taken, in learning these valuable parts of mathematics, thought it would be very well worth his while to lessen both, which he hopes he has done considerably, in the following treatise. He has divided it into 3 parts, contained in so many books. In the first of these, he considers the properties of the 3 sections of a cone, as well in, as out of the cone. And to make this part of the work of more service to the reader, Mr. Muller has not only selected the most considerable properties of these curves, that are to be met with in other writers, both anci- ent and modern; but has added several new ones, which, as he informs us, are inserted in their proper places. And that such gentlemen as are desirous to read Sir Isaac Newton's Principia, but are at a loss for want of a sufficient ac- quaintance with conic-sections, may be the more obliged, he has taken parti- cular care to demonstrate such properties as Sir Isaac presupposes his reader to be acquainted withal. Accordingly, he has prefixed a table of such propositions, informing him as well where they are to be met with in this book, as in Sir Isaac Newton's Principia Mathematica. The proofs made use of in his demonstrations, are sometimes algebraical, at * He was afterwards, for many years, professor of Fortification and Artillery, in tlie Royal Military Academy, Woolwich, for the use of which, he published several books on those subjects, which are still in great repute, being the best works extant of the kind. VOL. VIU. U IM6 philosophical transactions. [anno] 737. other times geometrical, according as he finds the one to be plainer and shorter than the other. The second book treats of the direct method of fluxions. And here he hopes the first principles of this method are laid down, not only in a new, but very plain and concise manner. He proceeds to show the use effluxions in the solution of the common problems of finding the maxima and minima of quan- tities, the radii of the evolution of curves, and the radii of refraction and re- flection. Under the first of these heads he says, particular care has been taken to distinguish the maximums from the minimums, a thing which has not been noticed so much as it ought to have been. And whereas some mathematicians, having made use of what they call infinitely small quantities, are forced to re- ject something out of the equation, for finding the fluxion of a rectangle, whose sides are varying quantities, Mr. MuUer uses only finite quantities ; and finds the fluxion of such a rectangle after a new manner, without rejecting any quantity for its smallness. He does the same in finding the fluxion of a power. And to avoid the use of infinitely small quantities, introduces a new principle, viz. that a curve line may be considered as generated by the motion of a point carried along by two forces or motions, one in a direction always parallel to the absciss, and the other in a direction always parallel to the ordinate. Hence he infers, that the fluxion of the ordinates is to the fluxion of the absciss, as the ordinate is to the subtangent of the curve. Having likewise proved from the first supposition, that if the describing point, when arrived at any place given, should continue to move onwards, with the velocity it has there, it would proceed in a right line, which would touch the curve in that point ; he concludes that the direction of the force in that place, is in the tangent to the curve : consequently, the 3 directions being known in each place, the proportion between the velocities of the urging forces will be likewise known. So that the nature of the curve being given, the law observed by these velocities may be found ; and if the law of the velocities be given, the nature of the curve may likewise be given. In the third and last book, we have the inverse method of fluxions, with its application to the several problems solvable by it ; such as the superficial and solid contents of curvilineal figures, the rectification of curve lines, centres of gravity, oscillation and percussion. Here also Mr. Cotes's tables of fluents are explained and illustrated by examples. He finishes this book with a great variety of problems, of a physico-mathe- matical nature, several of which are new, and were proposed to him by Mr. Belidor. Some indeed are not so, having been solved by Messieurs Varignon and Parent ; but then he has solved them after a different, and, as he hopes, a VOL. XL.] PHILOSOPHICAL TKANSACTIONS. . 147 more agreeable manner, the construction being more simple, and the process much shorter. Observations of the Maori's Transit by Aldebaran, ^pril 3, 1 736, at London. .a .W. ,4W'»il . By John Bevis, M. D. N° 446, p. gO. At 7'' 40"", apparent time, the moon's body and Aldebaran were seen to- gether in the distinct base of the telescope. ji Collection of the Observations of the Lunar Eclipse, Sept. 8, 1736, which were sent to the Royal Society. N° 446, p. 92. 1 . In Fleet-street, London, by Mr. Geo. Graham, F. R. S. and by Mr. James Short of Edinburgh, F. R. S. P. 92. Apparent Time. At 12" 58"" 0» Beginning of the eclipse. . 14 3 45 Beginning of total darkness. The observation made with a 5|-inch reflecting telescope, magnifying about 38 times. 2. In Covent-Garden, London, with a 5-foot telescope. By J. Bevis, M. D. p. 93. Apparent Time. At 12'' 56" 5(y Beginning of the eclipse. 14 2 25 Total immersion of the moon. 3. At Wittemberg in Saxony. By J. F, Weidler, R, S.S, &c. P. 94. ' l'' 50™ 24™ 10" He was surprised to see Mars continue quite round, though hardly, to appearance, disjoined from the scabrous edge of the moon ; but that instant he thought it began to lose its figure. 15 14 46 The moon being just clear of a cloud, saw Mars partly emerged. 15 14 49 He seemed just half out ; then clouds came on again, so that the final contact was not seen. Observations of the Transit of Mercury over the Sun, Oct. 31, 1736. N° 446, p. 102. 1. By Mr. George Graham, F.R.S. in Fleet-street, London, p. 102. Apparent Time. At 9*^ 22™ 00* Mercury not yet seen, then clouds. TOt. XL.] PHILOSOPHICAL TRANSACTIONS. I49 Apparent lime. At Q^ 23™ 37* He first saw Mercury for a few seconds, and judged he was got entirely within the sun's disk, or perhaps a little more ; then clouds again, with some intervals of a few moments between, which allowed a sight of Mercury about 3 or 4 several times ; then quite cloudy till near 1 2, when we had a sight of the sun for a few minutes, and took his transit upon the meridian ; at which time we judged Mercury to be about two of his diameters, or a little more, within the sun's disk, and a little past the vertical line. 12 10 27 We had again a sight of the sun, but Mercury was gone off. 2. At the observatory of Bononia, by Sig. Manfredi, F. R. S. P. 103. Beginning of Mercury's ingress 22** 7"* 56' Ingress of the centre 22 Total ingress 22 Beginning of the egress O Egress of the centre O Total egress O The mora of Mercury's centre on the sun's disk 2 Semimora 1 Middle time of the transit 23 3. Extracts of a Letter from Mr, Professor Weidler, F. R. S. &c. to Dr. Mortimer, Seer. R. S. dated at Wittemberg, Jan. 1, 1737, n. s. P. 110. Mercury appeared within the sun's eastern limb, as represented in fig. 17, pi. 5. .... at 1 12'' 4™ 30* at 5 5 abt 2 12 44 20 6 at 3 12 52 45 7 9 34 11 12 50 50 52 28 54 6 42 54 21 27 31 1 lO*' 49™ 20^ 11 36 00 11 52 20 12 2 30 j4 Collection of Observations, relating to the Comet which appeared in January, February, and March 1736-7. N° 446, p. 111. 1. Observations on that Comet made at Oxford, by J. Bradley, F.R.S. P. 1 j 1. Mr. Bradley made several observations on the late comet, during the last 5 weeks of its appearance, which enabled him to find out the elements of a para- bolic trajectory, on which a calculus might be founded, that would correspond with each of his observations within about a minute of a degree : but the first of 150 PHILOSOPHICAL TRANSACTIONS. [anNO IJSJ. them being taken many days after the time of the perihelion, and the whole series comprehending but a very small portion of the trajectory ; he was sensi- ble, that a little error, either in the observations themselves, or in the places of the fixed stars, with which the comet was compared, might occasion a con- siderable difference in the situation and magnitude, &c. of the orbit, deduced from them alone ; and therefore he was desirous of having some earlier and ac- curate observations, to determine those elements with more certainty : but not having yet been able to procure such, he no longer defers laying before the So- ciety the particulars of his own, with the comparison between the observed places of the comet, and those computed from such elements as he had already collected from his own observations. Mr. B. first saw the comet on the 15th of February 1737, between 6 and 7 in the evening, when its nucleus appeared small and indistinct, and its tail, extending above a degree from the body, pointed towards the star in Lino Austral. Piscium, marked g by Bayer. Applying the micrometer to a good 7-foot tube, he ob- served, that at 7'' 32™, equal time, the comet preceded the said star 1° i' 40" in right ascension, and was 20' 20" more southerly than the star. Note, That the equal time is likewise made use of in all the following observations. Assuming the place of this star, as it is settled in the British Catalogue, as he likewise does others hereafter mentioned, it follows, that the comet's right ascension was 23° 58' O*, and its declination 1° 3l' 55" north. February 17, 7 hours 33 min. the comet followed a in Nodo Lin. Piscium 31 min. 25 sec. in right ascension, and was 52 min. 30 sec. more northerly. Hence the comet's right ascension was 27 deg. 38 min. 20 sec. and its declina- tion 2 deg. 21 min. 10 sec, north. February 18, 7*" 14™, a small star (whose right ascension was afterwards found to be 29° O' 5", and declination 2° 58' 30" north) preceded the comet 24' O" in right ascension, and was 15' 30" more northerly. Hence the comet's right ascension was 29° 24' 5", and its declination 2° 34' O" north. February 21, 7^ 25", the comet preceded v Ceti 1° 6' 0'' in right ascension, and was 38' 20" more southerly. Hence its right ascension was 34° 25' 10", and its declination 3° 47' 20" north. February 22, 7^ 45*", the comet followed n Ceti 30' 5" in right ascension, and was 18' 45" more southerly. Hence the comet's right ascension was 30° l' 15", and its declination 4° 6' 55" north. February 25, 7*^ 45", a small star (whose right ascension was afterwards found to be 40° 34' O", and declination 5° 5' 30", north) followed the comet 2' 30" in right ascension, and was 2' 30" more northerly than the comet. Hence the comet's right ascension was 40° 31' 30", and its declination 5° S'* 0" north. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 154 The difference of right ascension and declination, between this star and the comet, was taken with a 15-foot telescope ; but the place of the star was deter- mined by one observation made with the 7-foot tube. February 27, 8^ 45'", the comet preceded a small star, l" l6'0' in right ascension, and was 2' 15" more southerly. The right ascension of this star was afterwards, by a single observation, found to be 44° 37' 40", and its declination 5° 38' 30* north. Hence the comet's right ascension was 43° 2l' 40", and its declination 5° 36' 15* north. March 4, S** O™, a small star, whose right ascension was found to be 49° 30' 30", and its declination 6° 38' 30" north, preceded the Comet 7' 30* in right ascension, and was lO' O" more southerly. Hence the right ascension of the Comet was 49° 38' 0', and its declension 6° 48' 30". March 12, 6^ 25™, the Comet preceded /* Tauri 2° 5' 50' in right ascension, and was 4' 25" more northerly than the star. Hence the Comet's right ascen- sion was 58° 12' 40", and its declination 8° 16' 30* north. March 14, 9'' O™, the Comet followed the 47th star of Taurus in the British catalogue 12' 30" in right ascension, and was O' 15" more northerly than the star. Hence the Comet's right ascension was 6o° 8' b", and its declination 8° 34' 5" north. This, and all the following observations, were made with a good 1 5-foot telescope, the Comet now appearing too faint to be well observed with the 7-foot tube. March 17, S'' 40™, the Comet followed y Tauri 25' 5" in right ascension, and was 9' 40" more northerly. Hence its right ascension was 62" 47' 55", and its declination 8° 58' 45'" north. March 1 9, 7*" 50™, the Comet followed the same star 2° 4' 50" in right ascension, being 23' 55'" more northerly. Hence its right ascension was 64° 27' 40"", and declination 9° 13' O* north. The same night, at 9** O™, the Comet preceded d Tauri 47' 40'" in right ascension, and was 22' 50'" more southerly. Hence its right ascension was 64° 30' 20", and declination 9° 12' 35" north. March 20, S*" 5™, the Comet preceded d Tauri O' 30'" in right ascension, and was 16' 35" more southerly than the star. Hence its right ascension was 65° 17' 30", and declination 9° 18' 50"" north. March 22, 8'' 13'", the Comet followed the same star 1° 36' 10" in right ascension, and was 3' 30" more southerly. Hence its right ascension was 66° 54' 10", and declination g° 3l' 35' north. This was the last night that he saw the Comet; for the moon being then in her increase, entirely obstructed its further appearance. The light of the Comet was indeed, even in the moon's absence, so very weak, that he found mo, PHILOSOPHICAL TRANSACTIONS. [anno 1737. it difficult, in some of the latter observations, to take its place with any to- lerable certainty; which is, in part, the cause of some little disagreement ob- servable in the Comet's places taken from the same stars on different nights j though there are likewise other irregularities that occur in this series of obser- vations, which seem to arise from small errors in the assumed places of the stars. Supposing the trajectory described by this Comet to be nearly parabolical, conformable to what Sir Isaac Newton has delivered in the 3d book of his Princip. Math, he collects from the foregoing observations, that the motion of this Comet, in its own orbit, was direct, and that it was in its perihelion, Jan. 19, 6^ 20*" equal time at London. That the inclination of the plane of the trajectory to the ecliptic, was ]8°20'45". The place of the descending node b 16° 22'. The place of the perihelion ^ 25° 55'. The distance of 4;he perihelion from the descending node 80" 27'- The logarithm of the peri- helion distance from the sun 9.347960. The logarithm of the diurnal motion 0.938 1 88. From these elements, by the help of Dr. Halley's general table for Comets, to which they are adapted, he computed the places in the following table; which also contains the longitudes and latitudes of the Comet, calculated from the observed right ascensions and declinations abovementioned, with the dif-, ferences between the observed and computed places. Oxon . 1737, Com. Longit. Lat . Aust. 1 Com. Long. Lat . Aust. DifF. Diff. Equal Time. Observat. Observat. 1 Computat. Computat. Long. Lat. Feb. ISO jh 32"" . r22'' 45' 7''. 7° 53' 27" r 22" 45' 0'.. 7° 53' 1". .+ 7'. . +26" 17 7 33 .. 26 30 30 . . 8 27 21 26 30 44 .. 8 28 6. . — 14 . .—45 18 7 14 .. 28 18 14 . . 8 44 20 28 17 46.. 8 43 57. .+ 28 . . +23 21 7 25 .. 0 3 26 34 . • 9 26 50 0 3 26 53 . 9 26 46. 19. . + 4 22 7 45 . 5 4 53 . • 9 40 0 5 5 28 .. 9 39 27. . — 35 . . -i-33 25 7 45 .. 9 42 18 . . 10 12 21 9 41 I9-- 10 12 22. .+ 59. .- 1 27 8 45 . 12 3643 . . 10 31 42 12 36 16.. 10 31 13. • + 27. .+29 Mar. 4 8 0 .. 19 3 0 . . 11 6 46 19 3 5.. 11 7 8 . 5 . .-22 12 8 25 . 27 49 58 . . 11 43 3 27 49 53 .. 11 43 19. .+ 5 . .-16 U 9 0 .. 29 47 42 . . 11 49 59 29 47 19-. 11 49 26. . + 23 . . +33 17 8 40 . n 2 30 57 . . 11 56 31 n 2 30 50 .. 11 56 49. .+ 7. .—18 19 7 50 . 4 12 36 . .12 0 19 4 12 45 .. 12 0 47 . . — 9. .-28 9 0 . 4 15 11 . .12 1 12 4 15 13 .. 12 0 52 . . — 2 . . +20 20 8 5 . 5 3 10 . . 12 3 5 5 3 32.. 12 2 33 . . — 22. . +32 22 8 15 . 6 41 30 . .12 6 15 6 41 19.. 12 5 42 . . + 11 . .+33 From the small differences between the Comet's observed and computed places, exhibited in t'ne last two columns of this table, we may reasonably conclude, that the orbit, as above determined, cannot differ much from the truth, and must therefore be near enough to enable future astronomers to distinguish this Comet on another return, and thus to settle its period ; which VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 153 he cantiot at present pretend to do, not having met with an account of any former Comet that seems likely to have been the same with this, a description of which has been given particular enough to determine this point. 2. The same observed at the Aventine Hill at Rome. By Didaco de Revillas Abb. Hieronym. R. S. S. p. 118. From the Latin. Feb. 16, 1737, about 7 o'clock, p. m. the Comet appeared for the first time in the western part of the heavens, 8 or 9 degrees lower than Venus, and declining a little towards the south from her vertical circle. With the naked eye nothing was perceived but a small whitish line, of a faint light : yet with a very good telescope of Campani's, of 6 feet, besides the tail, which extended to the opposite part from the sun, and appeared like a small line without the telescope, was likewise espied the nucleus, though encompassed all round with a thin atmosphere. As there was then no quadrant at hand, and not only a fog intercepted, but the twilight deprived the view of the neighbouring fixed stars, the apparent place of the Comet could not be determined for that night. From the l6th till the IQth, as also after the 25lh, there happened other im- pediments, which prevented observations. And in the nights between 19 and 26, the Abbe could not otherwise determine the apparent place of the Comet, than by comparing the phenomenon with Venus; as he only employed a small qua- drant, whose tube was scarcely an English foot in length. From the vertical altitudes therefore, both of the Comet and Venus observed at the same time, were collected the vertical differences of both, as below. Times. Vert. Differ. scy' 7^ 59™ 5° 22' 22 7 0 3 56 23 7 20 3 13 24 6 15 2 30 25 7 30 I 47 3. Observations on the Comet, and of an Eclipse of the Sun, Feb. 18, 1736-7, made at Philadelphia in Pennsylvania. By Dr. Kearsly, p. lig. Jan. 27, about 6 in the evenmg, Dr. K. saw a dull star, about 3 or 4 degrees above Mercury, and a little to the southward of a vertical passing through him, but took little notice of it then, not thinking of a Comet ; but by comparing 5 's place with the fixed stars, he afterwards thought it might be a Comet. — On the 31st, about 6*^ SC" p.m. he took its distance from Venus, by a reflect- ing instrument of Mr. Hadley's make, 14° 40'; but by a forestaff, 14° 50'; VOL. VIII. X 154 PHILOSOPHICAL TBANSACTIDNS. [aNNO 1737, and a right line passed over the Comet, Venus, and the Pleiades. The night following, about 6*^ 20™, its distance from Venus was, by Hadley's instrument, 13" 25'. The rest of his observations, by such instruments as he had, being none of the best, and the Comet growing very dull, are as follow : Feb. 7'' 6^ 47"" Comet from Venus 7° 40'. 7 3 from Aldebaran 59° 40'. from Algenib 17° 45', by a fore-stafF. A right line from the Comet over Venus passed over the bright star in the side of Perseus. 11 7 14 Comet from Venus 7° 1 a'. 7 20 A right line over the Comet, Venus, and head of Cassiopeia. 17 7 20 The Comet was in a right line, and to the northward of two stars ; distance of the stars supposed about 40', and the Comet from the least 30'. These stars were the south node of Pisces, the brightest from Venus 10° 20', from Aldebaran 50° 30', as he found it set down, but must be very false. 20 ~ 30 7 Comet from Aldebaran 34°, from Lucida Cap. y IQ±. 0,1 30 8 Wanted about a degree of oculus ceti. — Which was the last sight he had of it. P. S. The eclipse Feb. 18, could not be well observed here, by reason of clouds. Dr. K. rectified the clock by one of Heath's large ring dials. At 7*" 18*" there was a small dent in the sun's edge, whence the beginning 1 or 2 minutes sooner: just before the end, viz, lO'' 11 or 12™, he had a sight of the sun again, and there was then a dent in the sun's edge, so that the end must be 10** 13 or 14™ in the morning: about the middle of the eclipse, there was a large spot near the middle of the enlightened part, which was the north side of the sun. 4. The same observed in Jamaica. By Rose Fuller, M. D. F. R. S. p. 122. At Spanish Town, Jamaica, there was the appearance of a Comet, which was first perceived about the 26th of January, but must, by its plainness then, have been visible for some time before. It was in the west at first, some degrees below and directly under Venus. Every night it appeared nearer to that star, but inclined northerly. In about a fortnight, it was parallel to it, and in a week after, it was no more to be seen. 5, The same observed at Madras. By M. Sartorius, a Missionary there, p. 122. For 7 days before Feb. 9, about 7 in the evening, there appeared a dim VOt. XL.] FHILOSOPHICAL TRANSACTIOKS. 155 Comet : it is seen in the west, under Venus, towards the s. w. It looks through a tube of 10 or 1 1 feet long, like a dim or pale planet ; its tail tends upwards. --rn.'ifiivJ io ii.iiiivJ. li 6. The same observed at Lisbon, by G. R. Vanbrugh, Esq. on board the Bur- ford Man of War, p. 123. At 6** 49"" p. M. we saw a Comet with a long brush tail ; at which time its altitude was found 5° 15', its distance from Venus 18° 5' ; and Venus's altitude was observed 20° 40'. It bore due west. A Description of some Mammoth's Bones, dug ujj in Siberia, proving them to have belonged to Elephants. By John Phil. Breyne, M. D. F. R. S. N°446, p. 124. In the Philos. Trans. N° 403 and 404, Sir Hans Sloane gave accounts of elephants' teeth found underground. In the same year, viz. 1728, Dr. Breyne was busied about the very same matter, especially to prove, that the extraordi- nary large teeth and bones found under ground, and dug up in several places of Siberia, by the name of mammoth's, or mammut's, teeth and bones, were, 1. True bones and teeth of some large animals once living; and, 2. That those animals were elephants, by the analogy of the teeth and bones with the known ones of elephants. 3. That they were brought and left there by the universal deluge. After that, viz. in the year 1730, Dr. Messerschmidt returned to Dantzic from his travels through Siberia, and communicated some curious draughts of a part of a skeleton, viz. of a very large skull, dens exertus et molaris, with the OS femoris, belonging to the animal commonly called mammoth, found in Siberia; by which our assertion, that the teeth and bones, called in Russia mammoth's bones, are the true teeth and bones of elephants, is not only put in a clearer light, but seems demonstrated beyond all doubt. In 1722, Dr. Messerschmidt found two very large teeth, which he sent to Dr. Breyne. After he had made an accurate and nice examination of them, he found that one is a dens molaris, or grinder, a foot broad, half a foot long, and 3 inches thick, weighing 8 lb. and ^iij, pretty entire, except that it is broken in two pieces, and the extremities of the roots spoiled. The substance is between that of a bone and stone, except that on the upper part of the out- side, some parallel undulated lines appear, which have still preserved the enamel of the tooth. The other is a piece of a dens exertus, or tusk, 8 inches long and 3 inches X 2 / 156 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737- thick, or 1 lb. and 6 oz. weight; in some places not different from ivory, but in others calcined like the common unicornu fossile. What Ysbrand Ides mentions of the mammoth's teeth and bones, is deserv- ing of notice: as also the Journal of Laurens Lange's Journey to China, and the remarks of Capt. John Bernard Muller, in his Present State of Russia. These are the chief authors* who have treated of the mammoth's teeth and bones, as a very remarkable and particular curiosity of Siberia. And what we may select out of them, as matters of fact, are the following particulars. 1. That those teeth and bones are found in Siberia, chiefly in the northern parts, near the rivers Jenfzea, Trugau, Mongam-sea, Lena, &c. towards the icy sea; at the time when the ice has broken the banks of those rivers, so that part of the adjacent mountains fall down ; and that they are found in such quantity as is sufficient for trade, and to make a monopoly for the Czar. 2. That sometimes skeletons of this kind are found nearly complete. 3. That those teeth and bones are not found always of the same size, but sometimes very large; as dentes molares, or grinders, of 20 or 24 lb. weight, and dentes exerti, two of which weighed 400 lb.; sometimes of a middle size, as those abovementioned, and at other times still smaller. 4. That of those teeth, viz. dentes exerti, some are used as ivory, to make combs, boxes, &c. Capt. Muller says, that in every respect it resembles the common ivory, being but a little more brittle, and easily turning yellow by weather or heat. Out of these quoted remarks, joined to ocular inspection, Dr. Breyne thinks he may advance three things. 1 . That those mammoth's teeth and bones are truly natural teeth and bones, belonging to very large living animals; because they have not only the external figures and proportions, but also the internal structure analogous to natural teeth and bones of animals. 2. That those large animals have been elephants, as appears by the figure, structure, and size of the teeth, which accurately agree with the grinders and tusks of elephants, as represented by several writers. 3. That those teeth and bones of elephants were brought thither by a deluge, by waves and winds, and left behind after the waters returned into their reservoirs, and were buried in the earth, even near the tops of high mountains. And because we know nothing of any particular extraordinary deluge in those countries, but of the universal deluge of Noah, it is more than probable, that we ought to refer this strange phenomenon to the said deluge. It may be noticed, that such teeth and bones are also to be found in several * Add Gtnelin and Pallai. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. J 37 other countries, besides Siberia, as Poland, Germany, Italy, England, Ireland, and many others; but less common than in Siberia, and not so well preserved, but more wasted and calcined, doubtless by the greater warmth of those climates. Hither also are to be referred the large bones found under ground, or rather tusks of elephants, known by the names of ebur, seu unicornu fossile, which are of the same origin with the mammoth's teeth, but different, as they are better preserved, and have still the natural bony substance, and may serve the workmen as natural ivory, and in some measure the physicians and apothecaries as ebur, seu unicornu fossile. Of the above bones, the head weighed 1 30+ lb. avoirdupois weight, or 1 52 Russian pounds; its length or greatest height is 48 inches; its greatest breadth near the ears 29 inches, 5 lines; its thickness, from the forehead to the nape of the neck, 22 inches, 5 lines. One grinder weighs 8 lb. g oz. or 10 lb. Russian ; its greatest length 1 2 inches; its perpendicular height 5 inches; its thickness or breadth, 3 inches; it is made up of above 20 transverse lamellae, a finger thick, perpendicularly erect, lying close to each other, and its root composed of two apophyses. The tusk, by some improperly called the horn, of the right side, having a two-fold direction by being bent outward and backward, which is peculiar to the male elephant, it being straighter in the female. It is the ebur fossile of the shops, and weighs 137 lb. or l6o lb. Russian; its length, or the exterior cir- cumference of its back part, was 136 inches, 5 lines; the circumference of the root, where it got clear of the socket, was the greatest, being 1 8 inches 5 lines; the subtended arch, from one extremity to the other, 55 inches. The tusk answering to the foregoing on the left side, was quite like that on the right, except the contrary direction of its curvature, and its less weight, having lost its point; for it weighed only 1284- lb. or 150 lb. Russian. The right thigh-bone weighed 21 lb. 6 oz. or 25 lb. Russian; its perpendi- cular length is 38 inches 5 lines; the greatest breadth of its upper head, or apophysis, 1] inches; its circumference at the middle of the bone about 13 inches. The bones of this skeleton, with the ribs, vertebrae, and others belonging to it, were found in the side of a sandy steep hill, on the eastern bank of the river Indigirska, which falls into the northern ocean, not far from the mouth of the rivulet Wolockowoi ruszei. And some of these bones are found not only in these parts, but likewise in the sand hills on the rivers Chatanga, Tho- mas, Tobol, Irtisch, &c. which are all at a good distance from the sea; though neither elephants, nor chimerical behemoths, have been ever seen in those 158 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737. countries, nor could they live there by reason of the inclemency of the air. Wherefore the best judges follow the opinion of the learned Dr. Woodward, the Scheuchzers, and others, in taking them for the bones of antediluvian animals, or of such as were conveyed thither in the universal deluge. Of a large Glandular Tumour in the Pelvis, and of the pernicious Effects of crude Mercury given inwardly to the Patient. By Dr. Andrew Cantwell, of Montpellier. N° 446, p. 1 39. Dr. C. was called to visit an English gentleman who was ill. In the house where he lodged, was one P r M n, born in France, but settled in Cadiz. This poor gentleman, having been very ill for 2 or 3 years, had lost the use of his left leg and thigh, was subject to frequent head-achs, and pains in his bones, but more especially in his legs ; for which, because he had been given to women, his physicians in Cadiz salivated him twice, sent him to several hot waters, and gave him all the remedies they could imagine, but to no pur- pose; for his illness increasing, he had from time to time great difficulty of making water, and going to stool. In this condition he came from Spain to Marseilles, and from thence was sent to the waters of Baleruc, of which he drank a great quantity. But as they did not pass, his physician there ordered him strong purges, with clysters of a decoction of tobacco, and the like. He then began to vomit his excrements; on which the physician to the Marquis of C 's regiment in Spain, who happened to be there, ordered him ±- lb. of crude mercury by the mouth, which made him suffer the most exquisite pains ; and his belly swelled, and became as stiff as a drum. Here Dr. Montague was sent for, who soon discovered the error in the preceding practice, by feeling a solid body near the rectum, which obstructing the passage, hindered the clys- ter-pipe from entering far enough into the gut. After his departure, the pa- tient was again ordered clysters, which were injected with a crooked pipe, and several purges; till at the end of 8 days he died, having his belly larger, stifFer and harder than ever. Though Dr. C. arrived the day before his death, he saw htm not til! after he expired. His physician having invited him to open the body, he willingly consented, curious to find the solid resistance or tumour, which he could give no account of. He sent for the surgeon of the village, who opened the abdomen, which was filled with a whitish liquor of some con- sistence. The epiploon was all dissolved, and swam in this liquor like so much pus. This water poured out, Dr. C. examined the intestines. The colon was burst under the stomach, and in 3 other places at its lower part; and so was the caecum; the ileum all inflamed, and in one part gangrened. The lips of VOL. XL.] PHILOSOPHICAL TRANS ACTIOM8. 15Q the ruptures were plastered with excrements, all beset with a prodigious num- ber of globules of tjuicksilver; and when the intestines were disengaged and taken out, the quicksilver fell from them in large drops. The other viscera were in the natural state, except the liver, which was gangrened. As Dr. C. was very solicitous about the tumour, he looked into the pelvis, where he found an excrescence of a prodigious size, which filled all its left side. He took the knife, and cleared all round the tumour; when he found the uri- nary bladder close pent up between the anterior part of the tumour and the ossa pubis, which occasioned the strangury the patient had been tormented with ; the rectum, which lay on the middle of the os sacrum, was also vastly pressed on by the tumour, which seemed to take its rise from tlie holes that are in the left side of that bone. The surgeon was so unluckily impatient, that while Dr. C. laid down the knife, in order to separate the ossa pubis with a hatchet, he cut out the tumour. Dr. C. then examined the os sacrum, which was so very soft, that his fingers entered it every where on the left side. The tumour was oviform, and was covered over with several membranes: its weight was 2-^lb. ; its longest axis 5 inches and somewhat more than 4, French measure ; its shortest 4^- inches. At first sight Dr. C. took it for a parenchyma, but on dissection he found it analogous to the liver in substance, colour and consistence. Its artery, vein and nerve were very large, and were distributed through its whole substance : wherefore he really took it to be one of the conglobate glands of the pelvis, whose vessels yielding to the blood im- pelled thither with greater force and in larger quantity than usual, on account of the violent exercises of dancing, jumping, &c. which the patient very much practised, gave room to its increase to that enormous size. On opening, he remarked 3 very apparent divisions in it : and where the psoas lay over it, and one of the pyramidales beat on it, it was ossified. He preserved it in brandy, and found that the small vessels, that were most filled with blood, pressed it out into the interstices of the neighbouring ones. The weight the patient constantly complained of at his left hip ; the diffi- culty he had in going to stool, and that of thrusting a syringe far enough into the rectum to give him a clyster with any success ; the tumour itself, which was easily felt on putting the finger into the anus; with the palsy of the left leg and thigh, might have given other indications to the physicians, than those they took. And doubtless the frictions and other heating medicines, the patient was plied with, contributed to augment his illness. In fine, the crude mercury he swallowed, the vast quantity of Baleruc water he drank before it, with the strong cathartics taken by the mouth and anus, seem to have cut him l60 THILOSOPHICAL TRANSACTIONS. [aNNO 1738. short of some months, which he might have Hved, had he used no other re- medies than a slender relaxing diet. ^ Catalogue of the Fifty Plants from Chelsea-Gardens, presented to the Royal Society by the Company of Apothecaries, for the Year 1736, pursuant to the Direction of Sir Hans Sloane, Bart. P. R. S. By Isaac Rand, F, R. S. N°447, p. 143. This is the 15th annual present, amounting to 750 plants. Of a Narhwal* or Unicorn Fish, taken in the River Ost, in the Duchy of Bremen. By Dr. Steigertahl, F.R.S. N°447, p. 147. Towards the end of Jan. 1736, n. s. was taken a sort of whale, called the narhwal or sea-unicorn. It was taken in the river Ost, near the village Bellum, where it falls into the Elbe, in the duchy of Bremen, 4 German miles from the sea. A great quantity of fat was taken out of it, to make whale-oil; but this train-oil was of almost intolerable stench, because this narhwal feeds on carcasses: for nar signifies a carcass or dead body, according to Valentini in his Museum Museorum. Such care was taken of the skin, before the dissection, that it was cured with salt and alum, and stuffed so as to give the just figure of the fish: having left with it the bones of the skull, and some vertebrae near the tail. The skin was spotted with dark brown spots on a white ground. The epi- dermis was transparent, and under it was another skin very thin and spotted ; but the true skin was brown, and near an inch in thickness. On the top of the head was a semilunar hole, as in the porpoise, according to the description given by John Daniel Major, and published in the Miscell. Academ. Nat. Cu- rios. Dec. 1, An. 3, p. 22. This hole opens into the two canals which run through the skull to the palate, and are called by Major, ductus hydragog. They did not remark in the skin any opening or outlet for the excrements; and it is said, that this narhwal voided them through the hole on the top of the head. Concerning the horn. Dr. S. agrees in opinion with Wormius and others, who take it for a tooth ; but he cannot believe that its sole use is to break the ice : it rather serves the fish for seeking its food. A captain of a Greenland vessel assured him, that being on the coast a whale-fishing, and having taken one, as he was turning the whale to get at the fat, he found on the opposite * Monodon monoceros. Linn. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. l6l side to him a narhwal, that had stuck, tliis tooth into the whale's belly, up to its mouth, and had sucked the blood and humours. Fig. 1, pi. 6, represents the unicorn fish. J, Shows a semilunar hole, through which the fish cast out water and blood, on dying; 2, a small rising on the middle of the back, and fleshy as the fins; 3, the mouth, very little, without teeth in the upper jaw, except this dens prominens, or tusk; which has by some been taken for a horn ; and no lower jaw was found ; 4, the eye, very small; 5, the fin on the right side, which, as well as the opposite, is fleshy; 6, the tail, fleshy, like the fins, which, taken according to its width, is not vertical, but horizontal; 7, the prominent tooth or tusk, generally taken for a horn. The length of this narhwal, from N° 3 to 6, was 17 feet Q inches; the tooth 6 feet 3 inches; the greatest thickness, measured round, was 14 feet; the skin was smooth, without scales, like that of an eel, and was white, marked with blackish spots. A Description of the same Narhwal, communicated by John Henry Hampe, M.D. F. R. S. N° 447, p. 149. In a creek, called the Beluhmer Wadt, belonging to the Bailiwick of New- haus, in the duchy of Bremen, has been caught alive, an unknown fish of a large size, 18 to 20 feet in length, and 4 in diameter. He has on the fore part of the head, just above the mouth, which is very small, a horn 6 feet long, white like ivory, and curiously twisted. The body is white, sprinkled with black spots, and smooth like an eel. The head is, in comparison of the body very small, about 16 inches in length, and the same in diameter. The eyes are also small, about the size of a sixpence. On the upper part of the head, is a hole about 3 inches in diameter, out of which probably he spouts water, like the whales. On each side of the neck are placed two black fins, one above another, and at a small distance from each other. They are half an inch in thickness, of one hand's breadth, and 2 feet in length, round on the fore part, all fleshy, and of a liver- colour. Of a Water Insect,* not hitherto described. By M. Klein, F. R. S. N° 447, p. 150. From the Latin. A friend of M. Klein's presented him with a water insect, found at Uder- wanga in East Prussia, among fresh water crabs, and utterly unknown to the crab fishers. From the great number of its feet, and surprising facility of • The insect here described is the monoculus apvs of Linnaeus VOL. VHI. y l62 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. moving them, it may with equal, if not better reason, be called scolopendra aquatica scutata, than Aldrovandus, p. 721, de cetis, calls a certain fish of the whale kind, scolopendra cetacea. A, fig. 2, pi. 6, represents the insect on its upper part, covered with a shield; which nearly resembles tortoise-shells, except that along the middle of the back it is a little gibbous, and towards the extremity of the body it has a triangular hiatus, slightly indented: it is entire, and almost of the same substance, though of a more dilute colour, with the sheaths of the wings of the scarabaeus Goedarti, produced from weevils, or what is called scarabaeus rosarum. The eyes pass out through the shield, and are a little prominent. B, fig. 3, represents the insect delineated on the under part; where at the same time appears avast number of legs: each of these has a certain bag as at D, fig. 5, terminating in 3 feet, or rather claws; the two anterior ones have this in peculiar, that their three feet or claws are longer than the others, though they differ from each other in length. All the claws of the greater and smaller feet consist of similar articulations; and such as the hairs of the forked tail of this scolopendra, or the antennae of other insects have. M. Klein supposes this insect makes use of the longer claws of both the anterior feet, and of the hairs of its forked tail behind, for antennas, by means of which it timely discovers either its pursuing enemies, or such as it meets with in lurking places ; unless we are to suppose the two short horns, that appear in the fig. at that place, where we are reasonably to look for the head, to be antennae. c, fig. 4, represents the body, bared of its shield, viewed on the back ; on account of which the shield is carefully divided lengthwise, which as to the part explained, is not continued with the back. In the thin cuticle of the lower part of the shield, and that on both sides, may be observed, as in the fig. punctures like needle work. M. Klein could not certainly determine, whether it sucks in the water through these apertures into the cavity between the gibbous shield and the cuticle, and again emits it; or whether it fills the cuticle with air, or empties it, according as it wants either to go down to the bottom, or rise up to the top of the water. The insections or segments are about 30, but the legs cannot easily be numbered. In the extreme part of the body which separates the shield, the rings of the in- sections or segments are beset with small spines, and that in the same order, as they appear delineated fig. 2 and 4. D, fig. 5, represents one of the legs next the anterior one, with the little bag. B, fig. 3, represents another leg in a different view. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. l63 As long as this insect lived, it continually, and with singular facility, moved its feet, drawing at the same time into its sheath and putting out again, the extreme part of its body. The same sort of Insect found in Kent. By the Rev. Mr. Littleton Brown, F.R.S. fVith a Remark, by the Secretary, Dr. Mortimer. N''447, p. 153. Mr. Brown presented a creature, whose name he could not learn from any books or persons. He brought it from a pond on Bexby Common, where great numbers had been observed for 5 weeks before. The pond was quite dry the 24th of June, but on its being filled with the great thunder-shower on the 25th, within two days the pond was observed to swarm with them. And it was thought observable, that there is no duct or channel that could convey them from any adjacent place. Here E, fig. 6, pi. 6, represents this insect. Its legs are very extraordinary. Dr. Mortimer counted 42 on a side, in one of those found in Kent ; the 20 next the head are nearly of a size, but then they grow gradually smaller and smaller towards the tail. He took out one of the larger ones of the left side of the chest ; the foot consists of 5 flat membranous claws, with a stiffs rib along their middle, and beset with hairs on the edges, like those of crabs ; on the lower side of the leg hangs an oval bag, and beyond that grows a large thin membrane, which can be extended by a bony rib that runs across it ; this mem- brane and the whole foot, is convex on the side next the head, and concave on that next the tail ; the thigh, or first joint of the leg, is webbed on each side ; so that the whole structure of the legs seems to show that they are rather de- signed for swimming with, than walking. The leg represented at e, was drawn, when the insect lay on its back, as at b. Many parts of this insect, though no larger than the figures, have some resemblance to those of the Molucca crab. /in Account and Abrtract of the Meteorological Diaries for the Years 1729 and 1730. By Geo. Hadley, Esq. F.R.S. N" 447, p. 154. The diary kept by Mr. Hauksbee, by order of the Society, at their house in Crane-Court, consists of observations of the barometrical heights twice a day, i. e. morning and evening, in inches, decimals and centesimals ; the thermo- meter likewise, in its proper graduations, and the weather, with the hour of each observation. The winds are omitted. The depth of rain is set down several times for the most part in each month, the sum of which is to be divided by 10, the funnel which catches the rain being so much larger in surface, than that of the vessel which receives the rain from it. Y 2 l64 I'HILOSOPHICAL TRANSACTIONS. [aNNO 1738. That from Southwick, near Oundle, in Northamptonshire, by George Lynne, Esq. contains the height of the barometer once a day, and the winds, the steadiness and strength of which are likewise marked with proper marks and figures. Observation is made of the upper and under currents of the air, when it so happened. The thermometer is marked twice a day; the weather often, both by day and night ; the rain from time to time, and the quantity of each particular shower often set down by itself, with some other miscellaneous obser- vations, as haloes, thunder-storms, and sudden changes of wind, &c. He re- marks that his thermometer is placed in an out-house exposed to the air, but screened from the sun, which is a proper precaution in using that instrument. The remarkable rises and falls of the Mercury are also marked with proper marks ; which method would be useful in the other columns also, for com- parison of diaries, if some certain rule were agreed 'on. That from Kent, l6 miles south east from London, gives an account of the barometer once a day, sometimes twice or thrice, with the hour of each obser- vation, and the winds, weather, and rain, the proportion of which for every day, is given at the end of each month. There is also a separate column for the height of the clouds, which is divided into three orders ; and where there are two orders at a time, they are both noted ; as also when any of them move with different velocities or directions, which he supposes to be commonly a sign of change of the wind : but he does not inform us by what method he de- termined their heights or velocities. The reigning wind, and general strength of it, is noted at the end of each month ; the eclipses also, and the times of the new moons ; which he observes make it appear, that the notion of the change of weather depending on the age of the moon, is without any ground : with other miscellaneous observations ; as the aurora borealis, fruitfulness or sterility of the season. He had no thermometer. That from Hudicksvall in Sweden, by M. Olave Broman, shows the height of the barometer, sometimes once, sometimes twice or thrice a day, o. s. in English measure, with the winds, and the strength of them, and the weather. There is also to the diary 1 72Q, annexed an account of the height of the sea- water for every day, which varies in the whole about 1 inches, and is sometimes interrupted by floods from rain. This probably relates to the tides in the gulph of Bothnia. There is no thermometer, nor the quantity of rain set down. That from Risinge, in Ostrogothia, in Sweden, by Sueno Laurelius, pastor and provost, gives the height of the barometer for the most part 3 times, some- times 5 times a day, with the hour of the observations, o. s. in English mea- sure. He refers for the descriptions of his barometer and thermometer to the VOL. XL.} PHILOSOPHICAL TRANSACTIONS. I65 diary 1727. The winds, with the degree of their strength, weather, and depth of rain, are also set down. In that from Upsai in Sweden, by Mr. Andrew Celsius, Astr. P. R. and F.R.S. observations are made 3 times a day, of the barometer and thermometer, both which instruments were made by Mr. Hauksbee; the winds, with their strength, and the weather, and depth of rain, from time to time. That from Svenaker in Sweden, near Trollhetta, by Torstanus Wassenius, V. D. M. &c. contains the height of the barometer twice a day, sometimes 3 times, o. s. in Swedish feet and inches and decimals, which being supposed to be in proportion to English as 974.375 to 1000, the mean heights are reduced in the tables into that measure. The winds also, with their strength, are noted, and the weather. There is no thermometer. Notice is taken on thunder storms, and other meteors. That from Lunden in Sweden, by Mr. Conrad Quensel, Math. Prof, in Acad. Carolina, contains observations of the barometer twice a day, o. s. in English inches and decimals, and 4ths of them ; the winds, with their strength, and the weather. The thermometer is Florentine, and therefore the observa- tions not inserted in the table. That from Bygdea in Sweden, by Mr. John Telinus, pasor there, has obser- vations of the barometer twice a day, morning and evening, o. s. in English inches and decimals ; the winds, with their strength, and weather. The two last months are wanting. There is no thermometer. That from Betna in Sudermanland, by Mr. And. Geringius, pastor and pro vost, has observations of the barometer thrice a day, except in the first part of January, o. s. in English inches and decimals ; the winds, with their strength, and the weather, with other meteorological observations, and on the seasons, as to fruitfulness and sterility, &c. The aurora borealis is frequently mentioned. The thermometer is peculiarly graduated, and so could not be inserted. There is a column for rain. From Wittemberg in Saxony, there are two diaries communicated, one from Mr. Mat. Hasius, Math. Prof, the other from Mr. J. Fred. Weidler, LL. B. and Math. Prof. Primar. That by Mr. Hasius has the height of the barometer several times a day, sometimes 4 or 5 times, o. s. in English inches and deci- mals, and the parts of these in vulgar fractions, but are reduced to decimals in the tables. He used two barometers and thermometers. Those marked i, are Mr. Hauksbee's, those marked ii, Florentine. The coldest day he ever ob- served, was February the 5th 1726. It contains also the winds, with their strength, and weather. Mr. Weidler gives the height of the barometer 3 times a day, n. s. in Paris inches and lines, and the parts of these in vulgar fractions; |66 PHILOSOPHICAL THANSACTIONS. [aNNO 1738. the winds also, with their strength, and the weather, and quantity of rain, in cubes and lines, but at the end of each quarter the depth is given in Paris inches and lines. The thermometer is Mr. Hauksbee's. There are some astronomi- cal observations of eclipses, &c. He takes notice, that an occultation of Venus by the moon, observed with a telescope of 18 feet, may serve to prove the moon to have an atmosphere ; for being then in the quadrature with the sun, the planet appeared to lose its cusps, and become oval, when it came near the moon. That from Padua, by the Marquis Poleni, shows the height of the barometer once a day, o. s. in English inches and decimals ; the winds, and sometimes their strength, and weather. The depth of rain is given both for the old and new style. That from Bengal, by Mr. Bellamy, preacher to the factory, has the height of the thermometer twice a day, morning and evening ; the winds, with their strength, and the weather, for the year 1730. The medium of the thermo- meter is taken from both the evening and morning heights, the difference there being very great in proportion between morning and evening. That from Boston in New-England, by Paul Dudley, Esq. F. R. S. shows the weather 3 times a day, and wind once or twice. No barometer or ther- mometer. The Abo observations for the year 1730, by Mr. D. Sporing, show the height of the barometer twifce a day, in Swedish inches and decimals, but the mean heights are reduced to English in the tables. They show also the winds and weather, and in the last column the aurora boreales, which are frequent in most months of the year. That from Naples, by Cyrillus, shows the height of the thermometer, which is Mr. Hauksbee's, once a day. The winds, with their strength, and weather, and depth of rain in Neapolitan measures, 23 of which make a London inch. The barometrical heights he has not set down, because he found them not to agree with those of former years, which made him suspect his instrument to be out of order ; but as it appears he had removed his habitation, it might be owing to its being situated higher or lower than the former. An eruption of Vesuvius happening, an account is given of it, and of damage done by light- ning, and also of the seasons, as to fruitfulness and healthiness. First, he observed on the barometrical tables of these two years, that they con- firm former remarks made by Dr. Derham and others, of the consent of the barometers in places at a good distance from each other. Not only the monthly mean heights agree in the three diaries of these two years here in England, but also the greatest ascent and descent of the mercury happen commonly on the VOL. XL.] PHILOSOPHICAL TRANSACTIONS. I67 same day, and the barometers have been found to agree in their motions to an liour, so far asunder as Townly in Lancashire, and Greenwich near London, which is near l6o miles, though that might be partly accidental. The baro- meter at Crane-Court and Southwick, distant about 55 miles, being compared, seem very seldom to vary from their mean difference above -fV and 4- each way ; at Southwick and Kent something more. From whence it might be expected, that the weather should be much the same in all these places ; which yet seems not to agree with accounts in some years from different parts in this island, not very far distant : and Mr. Hadley has observed sometimes clouds to lie in one part of the horizon for a great part of a day, which have discharged a large quantity of rain in places not far off, while the place, where he has been, has all the while enjoyed fair weather, and vice versa. Whence it appears, that the barometrical alterations of the air extend farther than their effects, as to the production of rain, at those times. Comparing the diaries of Crane-Court and Upsal, he finds the barometers vary from their mean difference an inch and half each way; Crane-Court and Padua as much, or more, and often go a pace quite contrary ways at the same time, and their monthly differences are also very variable, so that their agreement at any time seems to be but accidental. Secondly, he observes, that the descents of the mercury below the mean heights of each place, taken in this way of Dr. Jurin's, are generally much greater than the ascents of it above; and there are also other extraordinary de- scents of the mercury in every year, of the same kind. The reason seems to be, because the expansion of the air, by which it becomes lighter in some one place, being the original of the alterations in the atmosphere, its effects by condensation or accumulation of the air, in the places round about, will be more dispersed, and therefore less sensible. Thirdly, the variation or range is greater the farther north, as has been heretofore observed, and appears in these tables; and likewise it is greater ge- nerally in the winter than summer months. The sum of the motion of the mercury upwards and downwards, taken from the Berlin wandering line, with a pair of compasses, in the year 1726, amounts to about 7^ inches, which gives 54^ for a month, and about 0.21 for each day. But the barometer is by much most steady in the summer. 4thly, The mean height of the barometer has already been applied to deter- mine the respective heights of places, and also the absolute height above the surface of the sea. Dr. Scheuchzer, in his Tables published in the Transac- tions of this Society, N° 405, 4o6, supposes, from Mr. Marriot, the mean height at the surface of the sea to be 28" l'" Paris measure, which reduced to English, gives 29 inches, .993. This agrees very well with a Diary commu- l68 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. nieated to the Society, containing 10 months of the year 1723, and Jan. 1724; the author of which found by experiment, that in the place where his barometer was kept, the Mercury stood y^ and -i^ higher than at the surface of the sea, which was not far from his habitation. The mean height of the barometer for those 10 months (leaving out the January following, which seems to be a very irregular month) is 29.825, to which adding -jV 4-, it will give the mean height at the surface of the sea 29.975 ; so the difference between these is only, 018, and therefore probably may be near the truth, but may hereafter be more exactly determined by experiments. Then allowing about 90 feet, or rather less, for each 10th of an inch in height of the Mercury in smaller altitudes, or in greater according to the tables calculated for that purpose, by Dr. Scheuch- zer and Dr. Nettleton, and published in the Trans. N° 388, you will have the height of each place pretty nearly, provided the observations be carefully made, and continued for a sufficient time ; for the yearly mean heights, in one of the places in these tables, appear to differ near -j^ of an inch in these two years ; and in most of them, the last of these two years exceeds the first, two or three hundredths: the barometer also ought not to be removed to a lower or higher place. The thermometers agree, especially as to the hottest days in the year, more than might be expected from places at such a distance. The winds are of so uncertain and variable a nature, that they require a more than ordinary care and diligence in making the observations, and a great length of time, and comparison of a vast number of them, before any thing can be deduced more than is commonly known; and therefore he only gives this hint, that if the observers would take particular notice, in great storms, of the time when the Mercury first begins to rise, whether before, or after, or in the very height of it, it might be a direction to judge when an abatement or increase of it might be expected, if any regular order should be found therein, which might be serviceable on some occasions. But if any attempt should be made to lay down any thing certain concerning the rise and progress of the variable winds, it will appear, by considering the cause of the trade-winds, that for the same cause the motion of the air will not be naturally in a great circle, for any great space, on the surface of the earth any-where, unless in the equator itself, but in some other line; and, in general, all winds, as they come nearer the equator, will become more and more easterly, and as they recede from it, more and more westerly, unless some other causes intervene. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. iQg A Collection of the Observations of the Solar Eclipse, Feb. 18, 1736-7, sent to the Royal Society. N° 447, p. 175. 1. Observed in Fleet-street, London, by Mr. Geo. Graham, F.R.S. p. J 75. Apparent Time. At 2^ lb"" 9' P. M. a small impression appeared on the sun's limb; he judged the beginning to have been about 5 or 6 seconds sooner. A cloud covered the upper limb, and prevented a sight of the ending. Between 12 and 1 o'clock, he measured the diameter of the sun with a micro- meter. At the time of the greatest obscuration, the lucid part of the sun's diameter was equal to 392 such parts, as his whole diameter contained 2188. By a transit of the sun at noon, and of Sirius at night, which, compared with preceding ones, he found his clock went too fast for mean solar time, about one second in a day. 2. The same Eclipse observed at the Royal Observatory at Greenwich, in Company with Dr. Edm. Halley. By Dr. J. Bevis, p. 176. Apparent Time. At 2'' 25"" 39' P. M. the beginning. 5 3 29 the end. At the end, the sun's limb appeared somewhat tremulous, and a small thin cloud came over it. Dr. Bevis judged the time might be relied on to 2 or 3 seconds. 3. At Edinburgh, by Colin Maclaurin, F.R.S. p. 177. In the history of eclipses collected by Ricciolus, there are very few said to be annular; and of these, some have been controverted, as that seen by Cla- vius at Rome, April 9, 156/ ; and that seen by Jessenius at Torgaw in Misnia, Feb. 25, 1598; which are both disputed by Kepler. Some astronomers, an- cient and modern, have been of opinion, that no eclipse can be annular ; and since such seem to have been rarely observed, and Mr. Maclaurin has not met with a particular description of any of them, he gives as full an account of this eclipse as he can collect from the observations that were made at Edin- burgh, and those communicated to him from the country. During the eclipse the sky was generally favourable in the southern parts of Scotland; and though there were great showers of snow in the north, they had sometimes a view of it. There was something very entertaining in the annular appearance, a phenomenon that was equally new to all who saw it. VOL. VIII. Z 170 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738, A little before the annulus was complete, a remarkable point or speck of pale light appeared near the middle of the part of the moon's circumference, that was not yet cpme upon the sun's disk ; and a gleam of light, more faint than this point, seemed to be extended from it to each horn : Mr. M. did not mark the precise lime when he first perceived this light, but is satisfied that it could hardly be less than -J- of a minute before the annular appearance began. Mr. Short, who was in another chamber at some distance, and made use of a larger telescope, said that he saw it 20 seconds before the annulus was com- pleted. He was surprised with this light at first, and did not immediately re- collect that it proceeded probably from the same crown that was seen about the moon in a total eclipse of the sun at Naples in l605 ; and was observed by many in different parts of Europe in the three late total eclipses, of 1 706, 1715, and 1724. Most of those who observed the eclipse with telescopes, mention in their letters, that as the annulus was forming, they perceived the light to break in several irregular spots near the point of contact, and that the moon's limb seemed to be indented there. Some express themselves as if those irregular parts had appeared to them in a kind of motion. Such appearances of a tre- mulous motion, in certain periods of solar eclipses, are mentioned by Hevelius and others. The annulus appeared to the eye to be central for some time, but in the te- lescope it was always broader towards the south-east, than towards the north- west part of the sun's disk. The breadth appeared much greater to the naked eye, than could have been expected from the difference of the semidiameters of the sun and moon. This was so remarkable, that such a phenomenon must have confirmed those astronomers in their opinion, who imagined that the dia- meter of the moon is contracted in her conjunctions with the sun. This ap- pearance probably proceeded chiefly from the light's encroaching on the shade, as is usual; but whatever was the cause, every body seemed surprized that the moon appeared so small on the disk of the sun. It was observed, that the motion of the moon appeared more quick in the formation and dissolution of the annulus, than during its continuance. This is particularly described by Mr. FuUarton, of FuUarton, in a very exact account of the eclipse, as it appeared at his seat at Crosby, near Air, on the west coast of Scotland. He writes, that " the annulus appeared to be nearly of an uni- form breadth during the greater part of the time of its continuance, but seemed to go off very suddenly ; so that when the disk of the moon ap- proached to the concave line of the sun's disk, they seemed to run together VOL. XL.] VHILOSOPHICAL TRANSACTIONS. .Ifl like two contiguous drops of water on a table, when they touch one another;" and he adds, that it came on in the same way. This appearance seems to be accountable from the same optical deception as the former. During the appearance of the annulus, the direct light of the sun was still very considerable ; but the places that were shaded from his light ap- peared gloomy. There was a dusk in the atmosphere, especially towards the north and east. In those chambers that had not their lights westwards, the obscurity was considerable. Venus appeared plainly, and continued visi- ble long after the annulus was dissolved, and other stars were seen by some: one gentleman is positive, that, being shaded from the sun, he discerned some stars northwards, which he thinks by their position were in ursa major. It was very cold at this time ; a little thin snow fell ; and some small pools of water in the college area, where there was no ice at 2 o'clock, were frozen at 4. A reflecting telescope of a large size, and of a much greater aperture than ordinary, that took in the whole sun, and burned cloth very suddenly through the tinged glass at the beginning of the eclipse, and on that account could not then be used with safety, was that by which Mr. Short observed the annular appearance. Some curious gentlemen found, that a common burning-glass, which kindled tinder at 3^ SQ™, and burned cloth at 4** 8™, had no effect during the annular appearance, and for some time before and after it. The first internal contact of the disks, at the formation of the annulus, was considerably below the west point of the sun's disk ; and the second contact, at the dissolution of the annulus, seemed to be about 10° eastwards from the north point or zenith of the disk. The breadth of the annulus towards the south-east part of the sun's disk, was at least double of its breadth towards the opposite part, about the middle of this appearance. Mr. M. pro- posed to have made some estimation of the ratio of the continuance of the annular appearance, where it was central, to its continuance at Edinburgh, from that of the arithmetical mean between the numbers that should express the proportion of the greatest and least breath of the annulus, to the geome- trical mean between the same numbers ; or from the ratio of the radius to the sine of half the arch intercepted between the two points of internal contact; but he did not obtain these ratios with sufficient exactness. At 3*' 31"" 43' the annulus was dissolved, after having continued 5™ 48'; the middle of the eclipse was therefore at 3'' 28™ 4g\ In this the time by ob- servation did not agree so well with the time by computation, as in the begin- ning of the eclipse, the difference being here about 4 minutes. The irregu- z 2 172 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. larities of the moon's surface occasioned the same appearances, in some mea- sure, as at the formation of the annulus. The beginning of the eclipse at 2^ 5™ 36* The beginning of the annular appearance . . , , 3 25 55 The end of the annular appearance 3 3 J 43 The end of the eclipse 4 44 51 At Hopeton-house, 9 miles west, and a little northwards from Edinburgh, Lord Hope observed the annular appearance begin at 3^ 25*", the end of this appearance at 3*' 31™, and the end of the eclipse at 4'" 444-'". His lordship was obliged to observe the eclipse at a distance from the clock, and to determine the times by a pocket watch, that had been adjusted by a very good dial that day at 12 o'clock; but he says, that the duration of the annular appearance was 6"", as near as could be judged by a watch that did not show the seconds. At Crosby, on the west coast of Scotland, about 4 miles north from Air, Mr. FuUarton observed the eclipse to begin at 2 o'clock. A distinct annulus was formed about 20™ after 3, which continued exactly 7*", measured by a pen- dulum vibrating seconds. It appeared rather broader on the lower verge of the sun ; but the difference must have been very small, for it was but barely dis- cernible in a species of the eclipse 6 inches over, cast on a piece of paper be- hind the eye- piece of a telescope 6 feet long. He adds, that the day light was not greatly obscured, appearing only so much dimmer than usual, as that of the sun is, when seen through a very gentle mist in a fine morning in April or May. Sir Thomas Wallace found that the annular appearance continued at his house, near Lochryan in Galloway, 5™. From the observation at Crosby, the centre of the annular penumbra seems to have entered Scotland not far from Irwine. It next proceeded towards the east, with a considerable inclination northwards ; and probably left Scotland not far from Montrose on the east coast ; for the Rev. Mr. Auchterlony found, that the annular appearance continued there J'", as near as he could judge by an ordinary watch. The annulus also appeared to him of a uniform breadth, through a common telescope. This observation, though not so exact as that at Crosby, is however confirmed by that at St. Andrew's, mentioned below. These two observations at Crosby and Montrose, were made nearer the path of the centre, than any others that have been communicated. As for the southern limit of this appearance, the eclipse was not annular at Newcastle, and there wanted about 40° of the sun's limb to appear in order to form an annulus, according to the observation of Mr. Isaac Thomson, com- municated by Mr. Blake, a gentleman of the county of Durham, who was VOL. XL.] PHILOSOPHICAL TRANSACTIONS, }f^ present with us at Edinburgh during our observation. The whole duration of the eclipse was 5Cf less by his, than by our observation. Nor was the eclipse annular at Morpeth, whence Mr. John Willson writes, that the body of the moon appeared almost entirely on that of the sun; an4 that, to the naked eye, the disk, of the sun seemed to be almost round. But of all the observations that have been communicated, that of Mr. Long at Longframlington, 7 computed miles north of Morpeth, determines the southern limit with the greatest exactness. The annulus, he says, was very small there on the upper part, and the duration 40 or 41 half seconds, mea- sured by a pendulum 9.8 1 inches long; from which we may conclude, that the limit was very near this place. This curious observation, with several others, was communicated by Mr. Mark at Dunbar. At Alnwick, in Northumberland, the eclipse was annular, but the time of its continuance was not measured. At Berwick, the annular appearance continued between 4 and 5 minutes: the end of the eclipse at Dunbar, by Mr. Mark's observation, was at 4*^ 48™ 16^; but some mistake was committed in reckoning the vibrations of the pen- dulum, in measuring the continuance of the annulus. At St. Andrew's, this appearance was observed to continue precisely 6™, by a pendulum clock, by Mr. Charles Gregory and Mr. David Young, professors in the university. By a figure of the annulus taken from its image, projected through a telescope on a paper screen, the breadth towards the south-east part of the sun's disk, was rather more than double of its breadth towards the opposite part. The observation at Montrose has been already mentioned. At Aberdeen the annulus was observed by Mr. John Stewart, math. prof, for 3"^ 2^ It was almost central, when the clouds deprived him of any further view of it; he thinks it probable, that it continued there about 6". Several gentlemen, resid- ing on the coast northwards from Aberdeen, were desired to observe the coutir nuance of the annulus; but I do not find that any of them saw this pheno- menon from the beginning to its end. At Elgin, the eclipse was observed annular at 3^ 29"", the larger part of the ring being uppermost, by the Rev. Mr. Irvin, who had a view of it for about 3(y; but by reason of intervening clouds could not determine the beginning or end of this appearance. At Castle Gordon, Mr. Gregory had one view of the eclipse while it was annular, but could make no further observation for the same reason. At Inverness, the eclipse was annular for some minutes, as observed by several gentlemen; but they did not measure the precise time how long it continued. By the accounts from Fort Augustus and Fort William, it is doubtful whether iif4 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. the eclipse was annular in those places or not. Fort Augustus is at the west end of Lochness, and probably was not far from the northern limit of this phenomenon. Several gentlemen of very good credit, who are not in the least short-sighted, assure Mr. M. that about the middle of the annular appearance, they were not able to discern the moon on the sun, when they looked without a smoked glass, or something equivalent, Mr. Maclaurin remarks this, because it may contribute to account for what at first sight appears surprising, that there are so few annular eclipses in the lists collected by authors. Kepler, in his Astron. Optic, does not seem to acknow- ledge, that any eclipse, truly annular, had ever been observed. There are none mentioned by Ricciolus, from the year 334 till 1567, though there are 13 or 14 total eclipses recorded within that period ; yet it is allowed, that the extent and duration of the annular appearance may be considerably greater in the former, than of the darkness in the latter. It may have contributed to this, that annular eclipses must have been rather incident in the winter season in the northern hemisphere, and that eclipses have been more readily total in the summer, when their chance of being visible was greater, and the season more favourable for observing them. But perhaps the chief reason why few annular eclipses appear upon record, is, that they have not been distinguished in most cases from ordi- nary partial ones. The darkness distinguished total eclipses, or such as were very nearly total ; and it is these chiefly, that historians mention. There are two central eclipses of the sun still famous among the populace in this country : that of March 29, l652, was total here, and that day is known among them by the appellation of Mirk Monday. The memory of the eclipse of Feb. 25, 1598, is also preserved among them, and that day they term, in their way. Black Saturday. There is a tradition, that some persons in the north lost their way in the time of this eclipse, and perished in the snow. There was a remarkable total eclipse of the sun in this country, June 1 7, 1433, the memory of which is now lost among the populace; but it appears from a passage in a manuscript in our library, that it was formerly called by them the Black Hour, after their usual manner. It is described thus : " Hoc anno fuit mirabilis Eclipsis Solis, 17""° die mensis Junii, hora quasi tertia post meridiem ; et per dimidium horae tenebrae tanquam in nocte supergressas sunt superficiem terrae, ita ut nihil obtutibus humanis pervium fuit ; unde abhinc vulgariter dicta fuit hora nigra." This eclipse is not in Ricciolus's Catalogue, but is mentioned by him in another place, Schol. cap. 2, 1. 5. By a computa- tion of this eclipse, the sun was within 2° of his apogeum, and the moon with- in 13" of her perigeum ; so that this must have been a remarkable eclipse. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 175 The progress of the shadow was towards the south-east ; and "Sethus Calvisius cites the Turkish annals for its being total in some part of their dominions. You will perceive by this account, that we have no observatory in this place; but we are in hopes that some time or other we shall obtain one from the patrons of the university. I doubt this last eclipse will not be distinguished by any par- ticular appellation among the populace, as the former that were central in this country. The remembrance of it however will be preserved by the curious, who observed it with great pleasure, and agree that it was the most entertain- ing spectacle of this kind they ever saw. 4. The same observed at Edinburgh. By Sir John Clerk, Bart. F.R.S. p. IQ5. The eclipse began at 5"" 36^ after 2. The annular appearance began at 25™ 55' after 3 ; its continuation was 5™ 48^ The end of the eclipse was at 44"* 50* after 4 ; all reckoned by apparent time. We had half a score good reflecting telescopes to make these observations, and our calculations perfectly agreed, so that you may depend upon them as most exact. This was not done by us as a matter of mere curiosity, but to assist in ascertaining the motions of the moon, on Sir Isaac Newton's theory, on which a good deal of the doctrine of the longitude will depend. Sir Isaac's calculation, as to the beginning of this eclipse, was pretty right ; but not so well as to its central appearance Two spots in the sun made a very distinct appearance to us, as they entered under the moon's body ; one was a little above the central or horizontal line of the sun ; the other was near the edge, on the east quarter. The first, by comparison with the sun's diameter, was larger than the disk of our earth ; it was dark in the middle, and certainly emitted no fire or light. The edge of the moon appeared a little ragged or rough, but not mountainous, because of the sun's light. There was no considerable darkness, but the ground was covered with a kind of a dark greenish colour. Two stars appeared, the planet Venus, and another farther eastward. This account is what you may depend on. 5. The same Eclipse observed at Cambridge, and Kettering; p. 197. The beginning by the clock at 2*^ 36™ 40^ The end at 5 14 12 Exact. Times observed at Kettering, as follow : Beginning 2*' 21" 2 Digits 2 36 im Centre....,.., , / ^ jaJtffl livJcn HUM »• I 4 End 4 5Q 7 4 22 176 PHILOSOPHICAL TRANSACTIONS. [ANNO 1738. N. B. The observatory clock was I minute 50 seconds too slow, which being added all the way, will give true time. 6. The same observed at the Institute of Bononia. p. igg. The eclipse began at 3*^ 33" 35% being more than ^ minutes sooner than the calculation made it. 1 . The same observed at the Aventine Hill at Rome. By the Abbe de Revillas, p. 200. The beginning there was at 3** 43'". 8. The same Eclipse observed at Wittemberg. By J. F. Weidler. p. 201. Neither the beginning nor the end was seen ; only some digits were observed on the decrease ; particularly 8 digits were eclipsed at 4'' 50" 31'. A Proposal to make the Poles of a Globe of the Heavens move in a Circle round the Poles of the Ecliptic. By the Rev. Ebenezer Latham, M. D. and F.D.M. N°447, p. 201. As we now have the globes of the heavens, they are only formed for the present age, and do not serve the purposes of chronology and history, as they might, if the poles on which they turn were contrived to move in a circle round those of the ecliptic, according to the present obliquity of this. By this means we might have a view of the heavens suited to every period, and that would answer the ancient descriptions, those of Eudoxus, for instance, who is supposed to borrow his from the most early observations ; and of Hip- parchus, &c. Nor could any contrivance better enable the lowest reader to judge of the merits of the controversy about the Argonautic expedition, as far as it depends on this: for it will verify to the sight the path of the colours, &c. at any time. N. B. That globes, to answer the end here proposed, though differently constructed, had long before been made and published by Mr, Senex, who at the next meeting of the R. S. gave the following account of his contrivance. A Contrivance to make the Poles of the Diurnal Motion in a Celestial Globe pass round the Poles of the Ecliptic, Invented by John Senex,* F. R. S. N"447, p. 203. The poles of the diurnal motion do not enter into the globe, but are affixed • Mr. Senex, F. R. S. was a bookseller, and a celebrated maker of globes and planispheres, &e. He died Dec. 30, 1741. ii VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 177 at one end, to two shoulders or arms of brass, at the distance of 23° and -4. from the poles of the ecliptic. These shoulders at the other end are strongly fastened on to an iron axis, which passes through the poles of the ecliptic, and is made to move round, but with a very stiff motion; so that when it is adjusted to any point of the ecliptic, which you desire the equator may intersect, the diurnal motion of the globe on its axis will not be able to disturb it. When it is to be adjusted for any time, past or to come, bring one of the brazen shoulders under the meridian, and holding it fast to the meridian with one hand, turn the globe so about with the other, that the point of the ecliptic, which you would have the equator to intersect, may pass under no degrees of the brazen meridian : then holding a pencil perpendicular to that point, and turning the globe about, it will describe the equator as it was posited at that time; and transferring the pencil to 23-4-°, and 66-J° on the brazen meridian, the tropics and polar circles will be described for the same time. By this contrivance, the celestial globe may be so adjusted, as to exhibit not only the risings and settings of the stars, in all ages, and in all latitudes, but the other phaenomena likewise, that depend on the motion of the diurnal axis round the annual axis. The Solution of Kepler s Problem, by J. Machin, Sec. R. S. N° 447, p. 205. Many attempts have been made at different times, but Mr. Machin thinks never any yet with tolerable success, towards the solution of the problem pro- posed by Kepler : to divide the area of a semicircle into given parts, by a line from a given point of the diameter, in order to find a universal rule for the motion of a body in an elliptic orbit. For among the several methods offered, some are only true in speculation, but are really of no service. Others are not different from his own, which he judged improper: and as to the rest, they are all some way or other so limited and confined to particular conditions and circumstances, as still to leave the problem in general untouched. To be more particular; it is evident, that all constructions by mechanical curves are seem- ing solutions only, but in reality unapplicable; that the roots of infinite serieses are, on account of their known limitations in all respects, so far from affording an appearance of being sufficient rules, that they cannot well be supposed as offered for any thing more than exercises in a method of calculation. And then, as to the universal method, which proceeds by a continued correction of the errors of a false position, it is, when duly considered, no method of solu- tion at all in itself; because, unless there be some antecedent rule or hypothe- sis to begin the operation, (as suppose that of a uniform motion about the VOL. vni. A A . 178 • PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. upper focus, for the orbit of a planet; or that of a motion in a parabola for the perihelion part of the orbit of a comet, or some other such) it would be impossible to proceed one step in it. But as no general rule has ever yet been laid down, to assist this method, so as to make it always operate, it is the same in effect as if there were no method at all. And accordingly in experi- ence it is found, that there is no rule now subsisting but what is absolutely useless in the elliptic orbits of comets ; for in such cases there is no other way to proceed, but that which was used by Kepler : to compute a table for some part of the orbit, and therein examine if the time to which the place is required, will fall out anywhere in that part. So that, on the whole, it appears evident, that this problem, contrary to the received opinion, has never yet been ad- vanced one step towards its true solution : a consideration which will furnish a sufficient plea for meddling with a subject so frequently handled ; especially if what is offered shall at the same time appear, as he trusts it will, to contribute towards supplying the main defect. Lemma I.— The Tangent of an jirch being given, to find the Tangent of its Multiple. — Let r be the radius of the circle, t the tangent of a given arch a, and n a given number. And let t be the tangent of the multiple arch nX a, to be found. Then if f j be put for — rr, and tt for — tt ; ~~, — iB In The tangent t will be ' \p : r+r\ +r—r\ Which binomials being raised according to Sir Isaac Newton's rule, the ficti- tious quantities t and j will disappear, and the tangent t will become equal to », n— t. «— 2. ^' , B. n— 1. «— 2. n— 3. n— 4. ^5 o " 1 ~2~ 3 j^"^! ~2 3 4~ 5 r*~ ». »— 1. ^ _i » . n^l.n— 2. n— 3. *■* » - r 2 rr ' 1 2 3~ ~4~ H This theorem, which he formerly found for the quadrature of the circle, at a time when it was not known here to have been invented before, has now been common for many years ; for which reason it is premised at present, without any proof; only for the sake of some uses that have not yet been made of it. Carol. 1. From this theorem for the tangent, the sine, suppose y, and cosine z of the multiple arch n X a, may be readily found. For if y be the sine, and z the cosine of the given arch a, then putting w TT for — WW, and substituting -^ for Y, and — for t, and -, , - for y: The sine y will be !±F I -'-^If. 2r«_ mu • -11 u 2 + '^l" + 2 - "I" The cosme z will be — ' 2r»-' VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 1^0 Each of these may be expressed differently in a series, either by the sine and cosine conjointly, or by either of them separately. Thus Y the sine of the multiple arch n X a, may be in either of these two forms, viz. z»-' . . n— 1. n-2 y' , «— 3. n— 4 y* « „ = — rV into n — ■ — -— A. •^ H r— —-- B.~ — OfC. r—i^ 2 3 z' ' 4 5 z* nn—l 3 nn— 9 . nn— 25 , . o"- = "i/ - T3;7 *^ - T^ "^y - tttt ""y - *^"- Where the letters a, b, c, &c. stand, as usual, for the co-efficients of the preceding terms. The first of these theorems terminates when n is any integer number; the other, which is Sir Isaac Newton's rule, and is derived from the former by sub- stituting Vrr — yy for z, terminates when n is any odd number. The cosine z may, in like manner, be in either of these two forms, viz. 2» • , ".'»— 1. y' 1 n. n— 1. n— 2, n— 3, y* » nn 3 «»— 4 4 n»— 16 g . 2rr " 3.4rr " 5.6rr " The latter of which terminates when the number n is even, and the other as before, when it is any integer. Corol. 2. Hence the sine, cosine, and tangent of any submultiple part of an arch, suppose - a, may be determined thus: _i^ j^ The tangentof i- a will be r+TK^IZlhf . r+TJ" 4- r— t| I The sine of ^a will be i+ifcinlCj. 2r" For these equations will arise from the transposition and reduction of the former, for the tangent and sine of the multiple arch, on the substitution of /, y, z and A; for t, y, z and n X a. Corol. 3. Hence regular polygons of any given number of sides may be inscribed within, or circumscribed without, a given arch of a circle. For if the number n express the double of the number of sides to be inscribed within, or circumscribed about, the given arch A; then one of the sides inscribed will be the double of the sine, and one of the sides circumscribed the double of the tangent of the sub-multiple part of the arch, viz. -a. Lemma Il.—-ToJind the Length of the Arch of a Circle within certain Limits, by means of the Tangent and Sine of the Arch. — Let t be the tangent, y the sine, and 2 the cosine of the arch a, whose length is to be determined; and A A 2 160 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. let f, T, V be expounded as before; then, if any number n be taken, the arch of the circle will be 1 I , . , 7*4- T|" r — t1 " always less than \ '— X «f, and greater than ^±^rjzliz3l — x wj . For if, by the preceding Corollaries, a regular rectilinear polygon be in- scribed within, and another without, the arch a, each having half as many sides as is expressed by the number n ; then will the former of these quantities be the length of the bow of the circumscribed polygon, or the sum of all its sides, which is always greater, and the latter will be the length of the bow of the inscribed polygon, which is always less, than the arch of the circle : how great soever the number n be taken. Carol. 1 . Hence the serieses for the rectification of the arch of a circle may be derived. For by converting the binomials into the form of a series, that the fictitious quantities, j , t, v may be destroyed ; it will appear, that no number n can be taken so large as to make the inscribed polygon so great, or the circumscribed so little, as the series "I" ~ ^ + 1» ~ ^ + ^*^" '" °"^ ^^^^' °^ ^^^ ^1"^^ t' <* f t — T'i'h T7 — rrr -\- &c. in the other case. Therefore, since the quantity denoted by the sum of the terms, in either of these serieses, is always greater than any inscribed polygon, and always less than any circumscribed, it must therefore be equal to the arch of the circle. Carol. 2. If, in the first of the above serieses, the root \^rr — yy, be ex- tracted, and substituted for z, there will arise the other series of Sir Isaac Newton, for giving the arch from the sine; namely, y + & + 157 + "iS^ + ^^- °' otherwise, — V^ 1.2.3 ^ r^ ^ 1.2.3.4.5. ^ r* ^ 1.2.3.4.5.6.7. r" ^ ^^' Schol. In like manner, as the arches of the polygons serve to determine the arch of the circle, so by comparing the areas of the circumscribed and in- scribed polygons, -^nrT and ^n\z, the area of the sector of a circle may be found. For if t, y and z be the tangent, sine and cosine of the arch a; then, by the second Lemma, the area of the circumscribed polygon ^ 1^ will be found to be -j-nrj X ^+''1" — r— t|" _ ,^^.j,_ VOL. XL.} PHILOSOPHICAL TRANSACTIONS. Iftl and the area of the inscribed will appear to be But on the expansion of these binomials it will appear, that no number n can be taken so large as to make the one so large, or the other so small, as the area denoted by the series. Xr n\ t ~ h T-: — :r-s + «C' ^ Zrr ' 5H 7r° So that this area being larger than any inscribed, and smaller than any cir- cumscribed polygon, must be equal to the area of the sector. It may further be observed, that as the arch or area is found from the sine, cosine, or tangent of the arch, by means of the limiting polygons, so may the sine, cosine or tangent be found from the length of the arch, by the same method. Thus, if A be the arch, whose tangent t, sine y, and cosine z, are to be determined, then will the A - -i- X - + ^ X — - &c. 1.2.3. '^ r^ ~ 1.2.3.4.5 r< Tangent T be = ■- .. , .4 Cosine z = r - -jL X ^ + j^- X -^ - &c. For it may be made to appear, from the first Lemma, and its Corollaries, that if in any of these theorems, as suppose in the first, the quantity a stand for the bow of the circumscribed polygon, then will the quantity t, exhibited by the theorem, be always larger; but if for the bow of the inscribed, always less than the tangent of the arch, how great soever the number n be taken ; and consequently, if a stand for the length of the arch itself, the quantity x must be equal to the tangent ; and the like may be shown for the sine, and, mutatis mutandis, for the cosine. These principles, from whence he has here derived the quadrature of the circle, which is wanted in the solution of the problem in hand, happen to be, on another account, absolutely requisite for the reduction of it to a manage- able equation. But he has enlarged, more than was necessary to the problem itself, on the uses of this sort of quadrature by the limiting polygons, because it is one of that kind which requires no other knowledge but what depends on the common properties of number and magnitude; and so may serve as an instance to show, that no other is requisite for the establishment of principles 1 82 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. for arithmetic and geometry. A truth which, though certain in itself, may perhaps seem doubtful from the nature and tendency of the present inquiries in mathematics. For, among the moderns, some have thought it necessary, for investigating the relations of quantities, to have recourse to very hard hypo- theses ; such as that of number infinite and indeterminate ; and that of mag- nitudes in statu fieri, existing in a potential manner, which are actually of no magnitude. And others, whose names are truly to be reverenced on account of their great and singular inventions, have thought it requisite to have recourse even to principles foreign to mathematics, and have introduced the considera- tion of efficient causes, and physical powers, for the production of mathemati- cal quantities ; and have spoken of them, and used them, as if they were a species of quantities by themselves. N. B. In the following proposition Mr. Machin has, for the sake of brevity, made use of a peculiar notation for composite numbers, or such quantities as are analogous to them, whose factors are in arithmetical progression. The quantity expressed by this notation has a double index: that at the head of the root at the right-hand, but separated by a hook to distinguish it from the common index, denotes the number of factors; and that above, within the hook on the left hand, denotes the common difl^erence of the factors proceed- ing, in a decreasing or increasing arithmetical progession. Thus the quantity — ^(""denotes, by its index m on the right hand, that it is a composite quantity, consisting of so many factors as there are units in the number m; and the index a above, on the left, denotes the common differ- ence of the factors, decreasing in an arithmetical progression, if it be positive; or increasing, if it be negative; and so signifies, in the common notation, the composite number or quantity, n -{■ a.n -\- a — a. n-f-a — 2a.. n-^ a — 3a. and so on. 2 For example : — ^^if" is = 7z-j-5. n-f-3. n-|- l.n — \,n — 3. n — 5. con- » + 5 sisting of six factors whose common difference is 2. After the same manner 2 ^(^ is = n -|- 4. n -|- 2. n. n — 2. n — 4, consisting of five factors. Accord- it + 4 ing to which method it will easily appear, that if a be any integer, then 2 j=l{^'' + ^ will be = nn — 1. nn — Q nn — 25, continued to such a num- n + 2a + X bar of double factors, as are expressed by a -|- 1, or half the index, which in 2 this case is an even number. So ^('•' + ' will be equal to K + 2a n.nn — 4.nn — \6. nn — 36, and so on, where there are to be as many double VOL. XL-] PHILOSOPHICAL TRANSACTIONS. J 83 factors as with one single one (n) will make up the index 2a -{■ I, which is an odd number. If the common difference a be an unit, it is omitted: Thus, ji^" is = n. 7J — ].n — 2.n — 3. n — 4.n — 5, containing six factors. So of is = 6. 5. 4. 3. 2. 1 , and the like for others. If the common difference a be nothing, then the hook is omitted, and it 0 . becomes the same with the geometrical power: so — i:^ ('" is = 71 _|_ I" according to the common notation. Proposition 1. — ^n arch /ess than a semicircle being given, with a point in the diameter passing through one of its extremities; to Jind by means of the sine of a given part of the arch less than one half, the area of the sector subtended by the given arch, and comprehended in the angle made at the given point. — Let PNA, fig. 7. p'- 6, be a semicircle described on the centre c, and diameter ap, and let pn be the given arch less than a semicircle, and s the given point in the diameter ap, passing through one extremity of the arch np in p. Then taking any number n greater than 1, let pk be an arch in proportion to the given arch PN, as unity to the number n; and let it be required to find, by means of the sine of the arch pk, the area of the sector nsp, subtended by the given arch NP, and comprehended in the angle nsp made at the given point s. From N and k let fall, on the diameter ap, the perpendiculars nm and kl, and join cn and ck. Then let t stand for cp, the semidiameter of the circle; yfor cs, the distance of the given point s from the centre; p for sp, the dis- tance of it from the extremity of the arch, through which the diameter ap passes; and y for kl, the sine of the arch kp in the given circle. These substitutions being presupposed, the problem is to be divided into two cases; one when sp is less, and the other when it is greater than the semidia- meter CP. Case 1 . — If SP be less than cp, then take an area h equal to the sum of the rectangles expressed by the several terms of the following series continued ad libitum : 2 2 2 ^l' __-^|4 '^'» PS _I_ < + "+ ''x/ ^ f , 9<-n + 3lx/ ^ y' , 9_X_25M- n + 5lxf ^ ^ , - 1 3j3 t 55 t J.7 t^ And the area -^n X h will determine the area of the sector nsp ad libitum. For the sector psn, being the excess of the sector ncp above the triangle ncs, will be the difference of two rectangles : -J-cp X pn — 4-cs X nm; but pn is the multiple of the arch pk, namely n X pk ; and nm is the sine of that 184 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. multiple arch ; therefore if for cp be put t, for cs, /, according to the suppo- sition; and if for pk be substituted ^-+4r X 4' + lr X^l + t^m x^ + &c. by cor. 2, lem. 2; and for nm ,- ^ X 75 H i7- X r* ^=^ X -^^ + &c. according to cor. 1, 1 3|, t 5,5 t 717 t ^ lem. 1, the area of the sector will appear in a series, as is above determined. But since the number n is greater than 1, and the given arch pn is less than a semicircle, and consequently kl or ?/, the sine of the submultiple arch pk, is less than the semidiamer cp or t\ it may thence be easily proved, that the series will approximate to the just quantity of the area, ad libitum. Corol. 1. — Hence, if the number n be taken equal to \/5 ^.'^25 + ^> the sector Nsp will be = \npy + ^—^^"7^-^/ + **** + J^.y'' + &c. For the numerator of the coefficient of the third term in the series, that determines the area h, namely, 9; — n+~3| x f, 'S equal to 9^ — nn— I .nn — Q.f, which, according to the above determination of the number n, will become nothing; therefore, if for < — p be puty in the second term, and the value of n be substituted for n in the third and fourth, the series for the area will appear on reduction to be as is here laid down. Corol. 2. — Hence the area of the sector nsp may be always defined nearly by the terms of a cubic equation. For the number n, as constructed in the former corollary, is always greater than the square root of 10, and consequently ^ is always less than the sine of »' one-third part of the given arch ; so that the fourth term „ y, with the sum of all the following terms of the series, can never be more than a small part of the whole sector. Corol. 3. — If K stand for 57,2957795 &c. degrees, or the number of degrees contained in an angle subtended by an arch of the same length with the radius of the circle, and m be the number of degrees in an angle which is to four right angles, as the area nsp to the area of the whole circle; then will m be = ^1X^ + nH-n:r^^LhI X %, nearly. For - X - will appear, by the construction, to be equal to the sector nsp. Case 1. — If sp be greater than cp, then take an area h equal to the sum of the terms in the following series: VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 185 2 2 2 -r~r SI + ^-"H-lIx/ y^t ^ 9^+» + 3'x/ X ^ + 9X 25/ -« + 51x7 X y _j. gjj._ 1 ^ <* 5I <* tTj '" ' and the area -J-m X h, will be the sector, as before. For the point s being on the contrary side of the centre, to what it was be- fore, it will easily appear, that the change of -\-f into — f, must reduce one case to the other, without any other proof. Carol. — Hence, if the number n be taken equal to ^Z —r-, or in this case y'^, then the series for the sector will want the second term, as in the former it wanted the third. Definition. — The angle called by Kepler the anomalia eccentri, is a fictitious angle in the elliptic orbit of a planet, being analogous to the area described by a line from the centre of the orbit, and revolving with the planet from the line of apsides; in like manner as the mean anomaly is a fictitious angle, analogous to the area described by a line from the focus. Otherwise, if c be the centre, s the focus of an elliptic orbit described on the transverse axis ap, and the area nsp in the circle be taken in proportion to the whole, as the area described in the ellipsis about the focus, to the whole: then is the arch of the circle pn, or the angle nop, that which Kepler calls the anomalia eccehtri. This angle may be measured either from the aphelion, or from the perihe- lion: in the following proposition it is supposed to be taken from the peri- helion. Proposition 1. — The mean anomaly of a comet or planet, revolving in a given elliptic orbit, being given; to find the anomalia eccentri. — The solution of this problem requires two different rules; the first and principal one serves to make a beginning for a further approximation, and the other is for the progression in approximating nearer and nearer ad libitum. 1. The rule for the first assumption : let ^,/, and j&, stand, as before, for the semi-transverse axis of the ellipsis, the semi-distance of the foci, and the peri- helion distance ; then taking the number n equal to \/ 5 + ^25 + ^j let t stand for ■ — ; and p for—- — ; — , or^T; which constant numbers, be- nnt — nn — l.p nnt — nn—\.p t ' ing once computed for the given orbit, will Serve to find the angle required nearly by the following rule. Let M be the number cf degrees in the angle of mean anomaly to the given time, reckoned from or to the perihelion ; and supposing r, as before, to stand for 57,2937 &c. degrees; take the number n = y'— m, and let A be the angle VOL. VIIT. 1 atlJ o B B 186 PHILOSOPHICAL TKANSACTIONS. [aNNO 1738. whose sine is n V ^+ \/j + $ + n V g "" V i + '^'' *^^^" ^^^ multiple angle n X A, will be nearly equal to the anomalia eccentri. The truth of which will appear from the resolution of the cubic equation, in the last corollary to the preceding proposition. Carol. ] . — If the quadruple of the quantity — ^ be many times greater or many times less than unity; or, which amounts to the same, if the mean anomaly n, be many times less, or many times greater, than the angle denoted by the given quantity -^Ry^p, one or the other of which two cases most frequently happens in orbits of very large eccentricity; then the theorem will be reduced to a sim- pler form, near enough for use. Case 1 . — If M be many times less than ^ Rv^p, then the angle a may be taken for that whose sine Is —. Case 2.— If M be many times greater than — R\/p, then let a be the angle whose sine is n — -; and the multiple angle n X A, according to its case, will be nearly equal to the angle required. ' Carol. 1. — In orbits of very large eccentricity, the perihelion distance p is many times less than the semi-distance of the foci /, and the number n = \/5+ ^25 + ^; is always nearly equal to '/lO, or to the integer 3, either of which may be used for it, without any material error in the orbits of comets. 2. The rule for a further correction ad libitum. Let M be the given mean anomaly, t the semi-transverse axis, as before; and let B be equal to, or nearly equal to, the multiple angle n X A, before found; then if p. be the mean anomaly, and x the planet's distance from the sun, com- puted to the anomalia eccentri b ; the angle b taken equal to b -| — X m — /*, will approach nearer to the true value of the angle sought; and by repetitions of the same operation, the approximation may be carried on nearer and nearer, ad libitum. This last rule being obvious, the explication of it may be omitted at present. Scholium. — In this solution, where the motion is reckoned from the peri- helion, the rule is universal, and under no limitation. But had the motion been taken from the aphelion, the problem must have been divided into two cases: one is, when the eccentricity is less than -^x the other is, when it is not less, but is either equal to, or more than in that proportion. If the eccentricity be not less than -rV> then the same rule will hold, as be- fore, only putting the aphelion distance, suppose a instead of the perihelion distance p, and substituting — / for -^f in the rule for the number n. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. Iff If the eccentricity be less than .V, then take the number n equal to v/^ and — X - will be nearly equal to the sine of the submultiple part of the anomalia eccentri, denominated by the number n, as before. It is needless to observe, that the like rules would obtain in hyperbolic orbits, mutatis mutandis. But that which perhaps may not appear unworthy of being remarked, concerning this sort of solution from the cubic root, is, that though the rule be altogether impossible, on a total change of the figure of the orbit, either into a circle, or into a parabola; yet it will operate so much better, and stand in need of less correction, according as the figure advances nearer, in its change, towards either of those two forms. That the use of the method may better appear, it may not be amiss to add a few examples. The following are two for the orbits of planets, one the most, and the other the least eccentric; but which are more to show the extent of the rule, than to recommend the use of it in such cases; for there are many other much better, and more expeditious methods, in orbits of small eccentricity. The other two examples are adapted to the orbits of two comets, whose periods have been already discovered by Dr. Halley; the one is to show the use of one of the rules in the first corollary, and the other is to explain the use of the other rule. Example 1 . — For the Orbit of Mercury. — If an unit be put for the semi- transverse axis t, the eccentricity 0,20589 ^'^^ become f, and the perihelion distance J!) will be 0,79^11 ; therefore by means of the number b, given as be- fore, the constant numbers for this orbit will appear to be, n = 3,56755, T = 0,5857271, p = Y T = 0,4651319, and hence — 5Z_ = 0,0085965. Example. — Suppose m, the mean anomaly from the perihelion, to be 120" 00' 00", to which it is required to find the anomalia eccentri. Here, since the mean anomaly m is not many times more than the limiting angle -^R-v/p, which in this orbit is about 74°, recourse must be had to the general rule in the proposition. 3x The number n then, which is (/— m, will be = 1,0104195 ; which, found, gives nV i -f \/i + ^ = 1,0389090; and also N\/i - ^/i + -^= - 0,4477126. Therefore the sum of both, under their proper signs, viz. 0,591 1964, will be the sine whose arch 36°,24195 is the angle A; the multiple of which n X A = 129°,295503, will be the angle to be first assumed for the anomalia eccentri. For a further correction ; this angle, now called b, whose sine is suppose y, BB 2 188 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738, and its cosine z, gives, by a known rule, f + ^z = 1,1304, for x the planet's distance from the sun ; and by another known rule b — —y = 1 20°, 1 6568, for u. the mean anomaly to the anomalia eccentri b. Therefore the correct angle B, = B + ^ X M — |«, will be 129°,14846 = 129°8'54",5, erring, as will ap- pear from a further correction, about -rV of a second. This angle, being thus determined, will give by the common methods, 137" 48' 33-t", for the true anomaly, or angle at the sun : the sine of the true anomaly being in proportion to the sine of the anomalia eccentri, as the semi- conjugate axis, to the planet's distance from the sun. So that the equation of the centre in this example is 17° 48' 33^". Example 2. — For the Orbit of Venus. — Supposing, as before, the mean distance t to be unity, and the eccentricity/ to be 0,0069855 ; the constant numbers for this orbit will be, p = 0,99301 15 ; n — 6,41 16 ; t = 1,562134 ; I' = 0,1551217 ; ^ = 0,0127571 ; and the limiting angle, ^r\/t-, will ap- pear to be about 303 degrees. Example. — Let m be 120° OO' OO", as in the former example. Then, since the mean anomaly is, in this case, not many times less than the limiting angle, the general rule must be used as before ; according to which the number n will appear to be 1,152585; the sine of a will be 0,32179)7; the angle a, 18°,77I32; and the multiple re X A, or angle b, for the first assumption of the anomalia eccentri, will be 120°,354l6. This angle b will give, by the method before explained, the angle b = 120°,34555, or 120° 2l' 44* fer^, for the anomalia eccentri correct ; the error of which will appear, on examination, to be but a small part of a second. In this example, the true anomaly is 120° 4l' 25", 1 ; and consequently the equation of the centre no more than 41' 25", 1. Example 3. — For the Orbit of the Comet of l682. — To know the mean anomaly of this comet, to any given time, it is to be premised, that it was at the perihelion in the year l682, on Sept 4, at 21'' 22"*, equated time to the meridian of Greenwich, and makes its revolution about the sun, as Dr. Halley has discovered, in 754- years. The perihelion distance p is, according to his determination, 0,0326085 parts of the mean distance t. So that the constant numbers for the orbit will be, n = 3,1676061 ; T = 0,2054272; p = 0,00669867 ; and the Hmiting angle, -^R\/p, will be about I9', or -f of a degree. of In the orbits of comets, the rule for the first assumption of the anomalia eccentri, is generally sufficient without correction. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. JSQ ThuSj suppose the mean anomaly m to be 0,072706, (as it was at the time of an observation made at Greenwich on August 30, \682, at 7^ 42"" eq. t,) then the general rule (which must be here used, since the angle of mean anomaly is not above 4 or 5 times less than the limiting angle) will give n X a or b = 2° 12' 48", 7, erring about ^^ of a second from the true anomalia eccentri. But in these orbits, the rules in the first corollary to the second proposition most frequently take place, especially the last ; and the calculation may also be further abbreviated, by putting the square root of 10, or the integer 3, for the number n. Example. — Suppose the mean anomaly to be 0°,006522, or 23",4792 : here, since m is 50 times less than the limiting angle, the rule in the first case of the first corollary may be used ; that is, to take the sine of the angle a = < X M np X R Therefore, if the number 3 be put for n, the sine of a, which is —.will be = 0,001 16367 ; and consequently the angle A will be 4'0",011 ; and the mul- tiple angle n X a, to be assumed for the anomalia eccentri, will be 12'0",033, the error of which will be found to be about ^ of a second. Example 4. — For the Orbit of the great Comet of the Year l680. — ^This comet, according to Dr. Halley, performs its period in 575 years ; and was in its perihelion on Dec. 7, 168O, at 23*' OQ"* eq. t. at London ; the perihelion distance p is 0,000089301, in parts of the mean distance t: therefore sup- posing the number n to be v'lO, the constant numbers for the orbit will be T = 0,2000161 ; p = 0,000017862, and the limiting angle ^r^p, will be about -^ of a second. Example. — Suppose the mean anomaly to be 3'31*,4478, or 0°,0587354], (as it was at the time of the first observation made on it in Saxony, on Nov. 3, at 16** 47™ eq. t, at London,) here, since the mean anomaly is many times greater than -^ of a second, the rule in the second case of the first corollary may be used ; that is, by taking the sine of a = n . 3t p But the number n or^ — m is = 0,05794134 ; and - will be = 0,0030827; N P therefore (n — - =) 0,0576330/, will be the sine whose arch 3'',30397 is the angle a; and the multiple angle n X a = 10° 26' 53*,05, will be the angle to be first assumed for the anomalia eccentri ; the error of which will be found to be less than a second. The true anomaly, computed from this angle according to the rule in the example for Mercury, will appear to be 171° 38' 24", from the perihelion. IQO PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. By these examples it appears, that the solution is universal in all respects; for the first two, compared with the last two, serve to show that it is not confined to any particular parts of the orbit, but extends to all degrees of mean anon)aly: and by comparing the second with the last, it sufficiently appears to be univer- sal with respect to the several degrees of eccentricity ; since in one the equation of the centre, for the reduction of the mean to the true motion, is not so much as the 1 70th part of the whole ; whereas in the other it amounts to almost 3000 times as much as the mean motion itself. Postscript. — On reviewing the reflections on the quadrature of the circle, Mr. M. believes it may be necessary, to prevent any mistake that may arise from the different opinions that obtain about the nature of mathematical quan- tity, to explain himself a little on that head ; as also to add a few words to show how the method of quadrature, by limiting polygons, takes place in other figures, as well as the circle. He takes then a mathematical quantity, and that for which any symbol is put, to be nothing else but number with regard to some measure which is considered as one. For we cannot know precisely and determinately, that is, mathemati- cally, how much any thing is, but by means of number. The notion of con- tinued quantity, without regard to any measure, is indistinct and confused ; and though some species of such quantity, considered physically, may be described by motion, as lines by points, and surfaces by lines, and so on ; yet the mag- nitudes or mathematical quantities are not made by that motion, but by numbering according to a measure. Accordingly, all the several notations that are found necessary to express the formations of quantities, refer to some office or property of number or measure ; but none can be interpreted to signify continued quantity, as such. Thus some notations are found requisite to express number in its ordinal capacity, or the numerus numerans, as when one follows or precedes another, in the first, second or third place, from that on which it depends ; as the quan- tities X, r, X, oc, X, referring to the principal one x. So, in many cases, a notation is found necessary to be given to a measure, as a measure ; as for instance. Sir Isaac Newton's symbol for fluxion x ; for this stands for a measure of some kind, and accordingly he usually puts an unit for it, if it be the principal one on which the rest depend. So some notations are expressly to show a number in the form of its com- position, as the index to the geometrical power x", denoting the number of equal factors which go to its composition, or what is analogous to such. But that there is no symbol or notation, but what refers to discrete quantity, is manifest from the operations, which are all arithmetical. VOL. XL.] VHILOSOPHICAL TRANSACTIONS. JQJ And hence it is, there are so many species of mathematical quantity, as there are forms of composite numbers, or ways in their composition ; among which there are two, more eminent for their simplicity and universality, than the rest: one is the geometrical power formed from a constant root ; and the other, though well known, yet wanting a name as well as a notation, may be called the arithmetical power; or the power of a root uniformly increasing or diminishing; the one is only for the form of the quantity itself, the other is for the constitu- tion of it from its elements. Now from the properties of either of these, it would be easy to show how the quadratures of simple figures are deducible from the areas of their limiting polygons. Mr. M. just points out the method from the arithmetical power, as being the shortest and readiest at hand. Let z, 2, z, &c. or z, z, z, &c be quantities in arithmetical progression, diminishing or increasing by the common difference z ; and let, as before ex- plained, J'" signify the arithmetical power of z, denominated by the potential index m, namely, z X z X z, &c. whose first root is z, and last z — m — 1 X z; which being supposed, the element of the arithmetical power will be mz X i; that is, the product made from the multiplication of the two indices, and the next inferior power of the next root in order. For the first arithmetical power z is = z.z , and the next z is = z X z — mz, therefore the difference will be as is explained. And consequently, since the sum of these elements or differences, taken in order from the first to the last, make up the quantity according to its termini ; hence, if z be the absciss of a curvilinear figure, whose ordinate y is equal to wjz*""', a demonstration might easily be made, that the [form of the quantity for] the area will be z"; that is, the same multiple of the next superior power of z divided by the index of that power. For since the arithmetical powers do both unite and become the same with the geometrical power, when the differential index z is supposed to be nothing; the magnitude of the geometrical figure will be implied from the magnitudes of the two polygons made up of rectangles, one from the increasing arithmetical power, the other from the diminishing, though it be true, that the elements of the polygons cannot be summed up, when z, the measure of the absciss z, is supposed to be nothing. In like manner, in any other case where z and z are two abscisses, whose 1Q2 PHILOSOPHICAL TRANSACTIONS. [aNN0 1738. difference, as a measure, is i ; and y, y the two ordinates ; the magnitude of the figure will be implied by the magnitudes of the two polygons, which are made from the sum of the inscribing and circumscribing elements zy and zy , though the figure itself is not to be resolved into any such primogenial rectan- gular elements. And thus the symbol z, considered as a component part of the rectangle zy, may bear a plain interpretation; viz. that it is the measure according to which the quantity z is measured; nor can he see that any other interpretation need to be put on a symbol, which, like a measure, is used only to make other things known, but is of itself for nothing but a mark. And what is said of the elements of the first resolution, is easily applied to those of a second or third, and so on ; the last may always be considered as the measure of the former and indivisible, though, in respect of the following, it be taken as the part according to which the measure was made, and therefore divisible. A Description of a new Invention of Belloivs, called Water- Belloivs. By Martin Triewald, F. R. S. Military Architect to his Swedish Majesty. N°448, p. 231. The water-bellows now proposed by M. Triewald, as to their efl^ect, are no- ways inferior to the wooden bellows, used in Sweden at all their iron forges, and furnaces, &c. but far more advantageous, not only for iron furnaces, but also for many other smelting-works requiring large bellows. It may seem at first a little strange, that water should be able to blow the fire ; but whoever has read the Philos. Trans, and seen the invention there de- Scribed, as used at Tivoli in Italy, and several other places, called Soffi d'Acqua, and attentively considers the following description, will be convinced, that this new invention of water-bellows, is built on the very self-same foundation, to which leathern and wooden bellows owe their use and origin, and will in several cases prove of more signal service. These water-bellows a, a, represented in fig. 8, pi. 6, are made of wood, not unlike the shape of diving-bells, in the form of a truncated cone, and con- sequently wider below than at top, where they are furnished with close heads b, B, but at the lower ends e, e, quite open. At the heads b, b, are two valves v, V, which open inwardly, and are made like the claps of other bellows, with their hinges, and the valves themselves covered with hatters felt, and are shut by an easy steel spring, till the air from above opens the same, which happens only when these bellows receive their motion upwards ; but are shut by means of the VOL. XL.] PHILOSOPHICAL TRANSACTIONS. IQ3 pressure of the air within, when they sink down into the water. On the same heads are two pliable leathern tubes k, r, fixed one at the top of each water- bellows, which tubes are made and prepared in the same manner as those used in water-engines for extinguishing fire. These leathern tubes, or pipes, reach from the bellows, to wooden tubes t, t, which carry the wind into the iron furnace m, or any other place desired. These bellows are also provided with iron chains k, k, fastened to two sweeps s, s, by which means they hang perpendicular from the beam of the balance, and at the same distance from the centre of its motion c. On the balance are two sloping gutters f, f, into which the water alternately runs from the gutter g, and so give motion to the whole work ; so that these last-mentioned gutters f, f, do the same service as an over- shot, or any other water-wheel, and cost a great deal less, but give as even and regular a motion, as any pendulum, for measuring time; for as soon as so much water runs into either of the aforementioned inclined planes of the gutters, so that the momentum of the water exceeds the friction near the centre of motion c, the gutter immediately moves down with a velocity increasing, till the balance meets with the resistance of the wooden springs h, h, and at the same time raises the opposite water-bellows, or that bellows which is fixed under the op- posite gutter. In the same moment again as the said gutter begins its motion, being come down on the spring, and delivers all the water it has received ; at the very same time the water begins to run into the opposite gutter, which re- ceives its load of water almost as soon as the former is emptied ; so that one of the gutters does its effect, as soon as the other has done his, and this alternately one after the other. These sloping gutters, on the balance, do therefore all the service and efl^ect which a water-wheel does in working the ordinary bellows, and that by means of the power which the water applies to the wheel of giving the ordinary bellows their motion, after the same manner does the water here empower the sloping gutters to do the same work. But as to the manner and the means by which these water-bellows are fit to blow the fire, and to perform the same as leathern or wooden bellows, there is no other reason, but the very same in which the effect of the ordinary bellows consists. For an ordinary pair of bellows blow for no other reason, but that the air, which enters the bellows, and which they contain when raised, is again compressed or forced into a narrower space, when the bellows close : now since the air, like all other fluids, moves to that place where it meets with the least resistance, the air must consequently go through the opening left for it, with a velocity proportioned to the force by which the air is compressed, and must VOL. viii. C c 194 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. thus blow stronger or weaker, in regard to the velocity by which the top and bottom of the bellows meet ; the blast also will last in proportion to the quan- tity of air, drawn into the bellows through the valve or wind-clap. This happens after the same manner in our water-bellows ; for the contained air cannot force itself down through the water, more than through a well- secured deal-board with pitch. When the bellows are lowered down into the water ; the contained air must necessarily be compressed by the water, which rises alternately into the bellows A, a ; so that the air must recede, and pass through the leathern tubes k, r, where it meets with the least resistance. From all which it undoubtedly follows, that the larger, that is to say, the more air these water-bellows are made to contain, and the greater the velocity is by which they are made to descend into the water, so much greater is their effect; and that the effect which they are able to perform, must be equal to that of leathern or wooden bellows of the same capacity, in containing an equal quan^ tityofair. in, As to the advantages which this new invention has over others, it is well known that the power which works the common bellows, used at iron furnaces, must be sufficient not only to compress the bellows, but at the same time to force down the lever with its weight or counterpoise; which lever serves again to raise the bellows, when the cog or button on the axle-tree of the water- wheel slides off from the bellows-tree ; so that the power must be sufficient at once to produce two different effects ; whereas these new water-bellows require scarcely any greater power than what is necessary to overcome the friction near the centre of motion, or the axis c ; for in this invention an advantage is ob- tained, which very rarely happens in mechanics, viz. that the weight to be moved is, on the balance in equilibrio ; since the bellows a, a cannot be other- wise conceived, than as two equal, though heavy weights, in a pair of scales, which balance each other, though their weight be ever so great; so that, if each of these bellows should weigh a ton, they must still equiponderate ; which is so much easier attained to, as it requires very little art to make them both of a weight, and order them at equal distances from the centre of motion. It is consequently known how small a power is required to set the scales of a balance, with equal weights, in motion, notwithstanding the weight may be as great ag possible ; all which may with good reason be applied to these water-bellows. And though it cannot be denied, but that the bellows which sinks down into the water-hole or sump n, becomes so much lighter, as it loses of its weight in water, by which means the water-bellows to be raised seems so much heavier, as the former loses of its weight, by being let down into the water ; yet this is compensated, if we consider, that the water which falls down along the sloping VOL. XL.] PHILOSOPHICAL TRANSACTIONS, IQQ gutter, acquires the power of a falling body ; which power increasing in the same proportion as the bellows to be raised becomes heavier, this power suits admirably well the weight to be raised; for the bellows that sinks down into the sump N, does not at once lose its weight in the water, but gradually as it de- scends deeper ; and after the same manner the ascending bellows does not be- come at once heavier than the other, but gradually, being heaviest just when the lowermost edge gets even with the surface of the water ; and that happens at the same instant of time jwhen the power of the water in the sloping gutter is at the highest pitch, or has received its greatest momentum. This shows that the power required to work these water-bellows is far less, and consequently less water will be consumed in working these bellows, than those commonly used ; and again, that an iron furnace, which for want of water to work the common bellows, cannot be kept at work longer than 6 weeks, though it be provided with all other necessaries, may, by means of such water- bellows as here described, be kept at work at least as long again. It is also known to miners, what great loss and inconvenience it is, when the hearth or mouth of an iron furnace is placed low, in a wet and damp place, which they are often obliged to be, in regard to the axle-tree of the water- wheel which works the bellows ; for which reason such furnaces as stand in the like moist places, give daily considerably less iron, than others which are better situated. There is likewise no small difficulty in finding a fit situation for such iron furnaces where iron guns are cast, and require deep pits under the mouth of the furnace : but by means of this new invention of bellows, one may be at liberty to place the mouth of the furnace as high as one pleases, as it is very easy to guide the blast by means of wooden or leaden tubes, as far as necessary, and in a proper direction into the furnace ; which advantage cannot so easily be obtained by the bellows in common use. It may also be accounted as no small advantage which these bellows afford, in being of so very easy a structure, that any carpenter at first sight is able, not only to construct the whole engine, but easily to repair every part of it, re- C[uiring at the same time the least repairs of any that can be used ; and if the bellows should be cast iron, they would last for ages ; and when cast strong, they would not require any weight to sink readily in the water. They might be covered with lead, or be made of thin copper, with a thick leaden hoop at top, to make them sink. As for their shape, it is not absolutely necessary they should be of the same as the figure annexed denotes ; for if we would not bestow iron hoops on the bellows, they might be made square, or triangular, or any other shape, provided they be as wide again at bottom as at top; and when made of wood, it will be necessary to provide an edge round the tops, for con- c c 2 196 PHILOSOPHICAL TRANSACTIONS. [anno 1738. taining stones or leaden weights, as much as will be found necessary to sink, them readily, when they are lowered down into the water. Lastly, If we consider the charge of those bellows used at iron furnaces, as to the bellows themselves, the water-wheel, and its axle-tree, &c. and compare the same with the cost of these, we shall easily find a vast difference, not to mention the great charges of keeping the common bellows in repair. Before concluding it may be mentioned, that the blast of these bellows is governed and moderated in the same manner as the common ones, viz. by letting more or less water into the sloping gutters, and by taking out and letting in plugs for that purpose, placed in holes near the top of the water-bellows. An Abstract of Meteorological Observations for 6 Years, made at Padua. By Sig. Poleni. N" 448, p. 239- Translated from the Latin. The following is an abstract of 6 years meteorological observations, made ac- cording to the rules recommended by Dr. Jurin ; and consequently correspond- ing with those published in Phil. Trans. N° 421. The instruments used were the same, and posited in the same places, and applied in the same manner, as there mentioned. The observations are as follow : Table a, showing the Rain and Snow -Water for every Month. 1731 1732 1733 1734 1735 1736 In. Dec. In. Dec. In. Dec. In. Dec. In. Dec. In. Dec- January .... . . . 2.546. . 2.129.. 1.855.. 1.034. . 4.052. . 6,541 February ... 3.093.. 1.959-. 0.405. . 1.735.. 2.420, . 2.98I March ... 0.976.. 2.765.. 5.642. . 1.558.. 5.162.. 2.721 April . . . 3.434. . 5.432. . 3.81 6. . 1.706. , 1.452. . 1.227 May . . . 0.602. . 1.864.. 5.330. . 4.372. . 2.681.. 4.444 June . . 4.253. . 2.872. . 2.712. . 4.555.. 3,865. . 2.777 July . . . 3.402. . 1.585.. 3.874. . 7.015. . 4.992. . 3.064 August ... 7.372.. 3.112. . 3.679- . 3.082. . 0.720. . 1.844 September ... 2.216.. O.O89. . 0.589. • 2.899, • 1.287.. 2.479 October . . . 4.354. . 9.164. . 2.788.. 4.391.. 1.878.. 0.529 November . . . 1.653. . 0.957.. 0.382 . 1.307. . 0.542. , 1.454 December 0.306. . 3.528. . ] .065, . 4.909, . 0.634. . 0.372 Sum of the whole year . . 34,207. . 35.456. . 32,137. . 38.563, . 29.685. . 30.633 By which all the varieties, as to different years and seasons, easily appears And the medium annual quantity, among all these 6 years, is 33.447. i VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 197 Table B, showing tht • Quantities for the 4 Seasons in all the Years. Winter. Spring. Summer. Autumn. In. Dec, In. Dec. In. Dec. In. Dec. 1731 .. .. 5.759 . . . 6.647 • . , . 13.598 8.017 1732 .. . . 4.522 . . . 10.300 . . 7-226 10.186 1733 .. . . 6.321 ... 15.758 .. 8.762 3.759 1734 .. . . 4 074 ... 8.014 .. . . 14.034 10.125 1735 .. . . 10.450 ... 10.848 .. 7-805 2.337 1736 .. . . 11.945 ..43.071 . , . 8.054 . . . 6.361 4.588 Sum. . . . . . 59.621 . . Table c. . . 57.796 .... 40.012 The sum of the The sura of the The mean height The mean height heights of the heights of the of the barometer of the therraom. barometer. thermometer. for each day. for each day. Inch. Dec. Inch. Dec. Inch. Dec. Inch. Dec. 1731 .... 10850.65 . ... 18286.25 .... 29.72 .. 50.09 1732 10870. 19 . ... 18361.30 .... 29.70 . . 50.17 1733 IO867.I8 . ... 1 8301.95 29.77 . . 50.14 1734 10850.24 . 18305.78 .... 29.73 .. 50.15 1735 IO861.2I . ... 18274.87 .... 29.76 .. 50.06 1736 10870.07 . ... 18338.42 29.70 . . 50.10 In the table c may be seen the sums of the heights of the barometer and thermometer for each year ; as also the mean heights corresponding to each day. For the whole last 6 years, the mean height of the barometer, referable to each day of the said 6 years, is 29 inches 73 dec. differing qnly, 03 parts from that of the former 6 years, which was 29 inches 70 dec. And likewise the mean height of the thermometer for each day of these last 6 years, is found to be 50 inches 1 2 dec. differing only ,04 parts from that of the former 6 years, which was 50 inches 1 6 dec. showing a remarkable uniformity. S. Poleni adds some observations on the declination of the magnetic needle. In April 1733, he found by repeated observations, that the declination was 134. degrees westwards. On the last days of the year 1736, he found it 13f de- grees. If therefore what has been already said of the declination of the needle, in Phil. Trans. N°42J, be compared with this, it will appear, that the declina- tion for the 3 first of these 6 years increased more than it did for the 3 last. igS PHILOSOPHICAL TRAKSACTIONS. [aNNO 1738. The Imperfections of the Common Barometers, and the Improvement made in them by Mr. Cha. Orme oj jishby-de-la-Zouche. IVith some Observations, Remarks, and Rules for their Use. By Mr. Henry Beighton, F. R. S. N° 448, p. 248. Nothing is more wanted than a theory of the weather on mechanic princi- ples ; and nothing in all philosophy see:iis of more immediate concern, than the state of it. In order to this, a complete history of the weather is necessary, from thence to deduce such rules and observations as may in some measure form such a theory : and could we in any tolerable degree foretel, but by some small space of time, the change of the weather, it would be of admirable use, in those affairs on which the chief part of our welfare and subsistence depends. It was from such considerations, that more than 20 years ago Mr. B. began, and has continued, to keep a diary of the weather, the last 6 years of which are here subjoined ; but cannot think, himself so well qualified, as to form a just theory on them, though they may have their uses, when they fall into more able hands. Yet he thinks he can generally foretel for a day, or perhaps two, the change, or what continuance the weather will have. And though so many ingenious persons, since the invention of Torricelli's barometer, have been endeavouring to bring that machine to perfection ; yet notwithstanding all their care and pains, the air interspersed and mixed with all fluids, has in some measure frustrated their labours, and it has remained im- perfect : for while there are any small quantities or particles of air remaining in the quicksilver, it will be constantly rising in hot weather, and falling in cold : which really perverts the very end and design of a barometer, which should show the pressure of the air, and foretel when either fair weather or rain is coming ; instead of which it is in a great measure a thermometer, foretelling heat instead of fair, and cold instead of rain and stormy weather : and these imperfections, more or less, attend all the various sorts of barometers, that have hitherto been invented. The barometer here described, is not different in form from some usually made, it being of the diagonal kind, from whence the more minute alterations are more readily discovered: of this form many have been made, by the late curious operator Mr. Patrick, who has, in his way, well deserved of the curious; who, though he had done so much towards the proving the weight of the atmosphere by which the mercury in the tube was sustained, he himself did not believe it, but ran into the absurdity of the funicular hypothesis. There is an inconveniency or imperfection in most, if not all, of those VOL. XL.] PHILOSOPHICAL TRANSACTIONS. iQQ diagonal barometers ; for after some time, by the various rising and falling, and changes of the weather, of heat and cold, the small particles of air interspersed in the mercury, have got together in a larger mass, as they will incline by at- traction, which will separate the mercury ; and that quantity of air will be dilated by heat, and contracted by cold, so as to spoil the design of the instrument. Besides, there is such a cohesion or attraction of the mercury to the tube, especially in the small ones, that after some time, the mercury that is not truly cleansed from its dross, and purged of all its air, in remarkable changes of the weather, will neither rise nor fall. All which embarrasment is taken off, and the difficulties surmounted, in Mr. Cha. Ormes Improvements of the Barometer, by the Method following : First, The quicksilver is all purified from its dross and earthy particles by distillation ; and when the tube is filled by a pound and half, or 2, or 3 lb. of mercury, and all the air got out by the methods used in filling tubes, then the remaining air is got out by such an intense heat of fire as makes the mercury boil; by which ebullition an innumerable quantity of small particles are emitted, and blow with a great velocity at the open end of the tube, till all the air is quite cleared out ; which operation is continued for the space of 4 hours : and when no more bubbles would rise in the tube, it remained whole, with its mer-. cury of a most lively sparkling brightness, with this difference only, that the mercury, so purged of its air, did not fill the tube so high as when first put in, by about 1 inches ; which is a plain demonstration, that in that tube, which was 49 inches long, there was interspersed in the mercury at first filling it, so much air as would fill 2 inches of the said tube, which was a 24 th part of the said space. In this way every part of the mercury boiled for a long time, and the tube became gradually so red-hot, that with a warm knife impressions couI4 be made in any part of it. And this I the rather mention, by reason I have heard several persons, and those not incurious, affirm it was impossible. The Perfection of these Barometers, by which they exceed all others ever ob- served, in the following Particulars. — -1. They are sensible of the most minutq changes of the air. 2. They fcretel the weather by a much longer space of time than others, as mostly 20 hours, sometimes 36 or 48 hours : nay, before great tempests, and such rains as cause great floods, for a much longer time before they happen. 3. Though they are so sensible of such minute changes of the air, yet the most intense heat will not raise them a hair's-breadth, nor the greatest cold make them fall. This shows that they are perfect barometers, and not in any degree thermometers. aOO PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. 4. If they show for rain, you may by them distinguish whether it will be little or much. 5. As by other barometers you cannot tell the weather, but by a past and a present observation ; these tell, the moment you come to them, what the weather is going to be : for by tapping the case with your finger, if it is going to be fair, or very fair weather, the mercury will rise that moment a 10th of an inch, or more : but if for foul, it will scarcely make any sensible rise. Remarks. — 1 . Though you can foretel it will rain on the morrow, it is im- possible to tell where that rain will fall : for as every shower has space, i. e. length and breadth, if it rains in that particular field, yet it may be fair in the next adjoining : and if in harvest, or on a journey, you proclaim it will rain on the morrow, some will, if it does not fall on their land, or on their coat, be so silly as to say the prediction was false. 1. The barometer only shows the pressure or weight of the atmosphere, and inclination of the air, in and about the country where it stands, and not always in a particular spot : so that in foretelling of great rains, people are apt to say the indication is false, because they have not seen or heard of it; when perhaps in a day or two you will hear, that it did then fall 3, 4, or perhaps 10 miles off. p'or though the rain should be over us when the glass fell, yet the wind, which bloweth where it listeth, cjirries the clouds and rain with it. 3. It is very hard to distinguish on the mercury's falling, whether it will be rain or high winds, these equally causing the mercury to subside. 4. Of all those who guess at the weather from the whims of their own brains, it is observable, it is not true one time in ten, nor do any two of them agree about it. But from observations on this barometer, it will seldom fail you once in 20 ; so that it is above 100 to 1 preferable. 5. If from the state of the mercury yesterday and this morning, it be pro- nounced the next day will be no rain, and we look, at the glass no more to-day; perhaps winds may arise, and so alter the atmosphere's weight, and the glass falls much, it will rain on the morrow, contrary to what was at first expected. Here it is plain, had the glass been seen again in the afternoon, the rain might have also been foreseen. Hence it is evident from these remarks, that judgments are taken on the weather from barometers, which do not prove so; and this produces opinions in the vulgar and ignorant, that there is no judgment at all to be had from them. If the barometer could only foretel very great and remarkable changes of the weather ; for instance, in harvest-time, that a very great rain, or perhaps floods, were coming ; the husbandman would stop cutting down his grain, and save some of it being spoiled by the wet : or on a journey, if I know that if I VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 201 do not get home bj- such a time, or pass such rivers, the floods will be so great, as not only to prevent me, but endanger my life : and perhaps here is a man's fortune saved, nay his life, merely from the indications of the barometer ; and he who reckons this nothing, deserves neither. The greatest storm that has been in our days, was Jan. 8, 1734-5. On the 5th the mercury began to fall, and on the 8th was a 10th below 28 inches; which has not been seen in this age, or perhaps since Torricelli's time ; thence I could plainly indicate, that it would be the greatest flood we ever heard of, or the greatest storm we ever felt ; the latter of which it proved. Some Rules and Observations for fore-knowing the Weather, by the rising a7id falling of the Mercury. — Though rising always presages fair, and falling foul weather, yet there are several difficulties and niceties in making a true judg- ment from them, and herein consists the chief part of the art. We need not recount the several observations made by Dr. Halley, Dr. Beal, Dr. Derham, Mr. Patrick, and others, though they are most of them appli- cable to this improved diagonal barometer, as they are in so many hands, and in most authors on the subject, and because Mr. B. has collected them, in order to be made public, at the request of the improver of the barometer, Mr. Orme, and for his use; which ^me time since were put into the hands of Dr. Desaguliers, who is acquainted with Mr. Orme and his glasses. Mr. B. only inserts here some few observations, which may be called rules, as he has deduced them from time to time, in using Mr. Qrme's glasses, and keeping a register of the weather. Rules and observations for the improved diagonal barometer. — 1. This baro- meter very rarely foretels thunder, seldom falling at all before it, which Mr. Patrick observes others do. 2. In serene and hot weather, when the mercury is high and rising, and you have all the possible certainty of fair weather the next day, and if there happen to fall great showers, you may conclude they have been driven on you by thunder, though you have heard nothing of it. ' 3. When the mercury is pretty high, and has fallen to foretel rain, and it rises again before the rain comes; it indicates there will be but little of it. 4. If the mercury continues falling while it rains, it shows it will rain the next day. 5. In fair weather, when the mercury has continued high or rising, if it falls a little to-day about noon, and towards the evening rises again, you must expect a single shower the latter part of the next day, or perhaps by noon, and then fair weather again forward. ■ '6. When the mercury rises gradually, about half a 10th perpendicular, and VOL. VIII. D D 202 PHILOSOPHICAL TRANSACTIONS. [aWNO 1738, continues so to do for many days together; you may reasonably expect a fair season for as long a time as it was rising, unless some gales of wind intervene, and especially the s. w. by s. or thereabouts. 7. When the mercury rises very fast, or falls very fast, neither the fair nor foul weather it forebodes will continue long. 8. Without knowing how the mercury has stood some little time before, a true judgment cannot be given at all times; for suppose we find it in a rising condition, it will probably be fair; but if it had been higher some hours ago, and fell, there must happen a shower. Why the mercury in the diagonal barometer, if it be for fair weather, on tapping the case several times, which jars and makes the tube tremble, will rise at every stroke for several strokes together, and in all sometimes a 10th of an inch, or more, in the perpendicular; may be thus accounted for: 1. There is a cohesion of the mercury to the tube, which hinders its rising, and such tapping releases that. 2. But it is observable, that it will rise a little at all times, even when it is in a standing, or even in a falling condition. This may be accounted for thus: The mercury and atmosphere are in an equilibrio, and tapping starts and raises the mercury a little in a boiling manner, especially its upper surface, which is seen to leap, or be in a swimming posture; then the pressure of the atmosphere over-balances the remainder of the mercury, and it must rise a little. Or such violent jarring puts the mercury in a lateral and upward motion, for downward it cannot go, which takes off its gravity, as the winds lessen the pressure of the air; therefore it must rise a little. But then it is observable also, that if the mercury was in a standing condi- tion, or falling, such rising as above, will in a minute return to the same place again ; and even when the mercury is in a rising condition, it will, in that space of time, fall a little part of that it rose by such tapping. This barometer has the coruscations, as they were observed in Mr. Patrick's pendant one; for by tapping the case with the finger in a dark place, it will emit several bright flashes, along the empty part of the tube. This is an argument that the vacuum is very pure, and the mercury truly purged. Collections from the diary of the weather and barometer, in order to settle rules for foretelling the weather by the barometer. Great Storms. 6. . . . night 29.2 Before them the mercury falls 3 or 4 days, and T. ...night 28.1 » exceedingly low. 8 noon 27.9 1734-5, Jan. 4, at night themerc. at 29.92 inc. lower than has been known by ^, and the 5. . . . night. 29.66 greatest storm of wind ever heard of in this age. VOL. XL.] PHILOSOPHICAL in the south of England, as also in France and Holland. 1736, Jan. 31 29.47 Feb. 1 29.15 2 28.39 rain and stormy. 173*, Aug. 11 stormy. Great Floods. Before which the mercury falls very much. 1735, Sept. 4 29.7 5 29.6 6 night 29.6 7 29.25 The greatest flood that has been at Coventry, being about the middle of England, these 40 years, and yet the mercury fell but little. 1735, Oct. 23 29.55 24 night 28.8 25 night 28.78 26 28.85 27 28.26 a great flood. 1735, Aug. 19 29.3 20 29.28 21 29.3 22 29-2 23 . . ., 29 2 '■ stormy, great rain. 24 • 29.38floods. 1735, Dec. 2 29.32 rain. 3 29-5 feir. 4 28.8 rain. 5 28.9 rain. 6 29.5 fair. 7 29.52 great ' Thunder. rains and floods. The mercury seldom falls for rains that come by thvmder. See diary, June 2, 1735. Thunder. When the mercury did rise. 1733, June 21 29.16 29.56 22 29.56 29.56 23 29.62 29.65 hot. 24 29.65 29.578ultry. 25 29.54 ... . . 29.52sultry. 26 29.51 29.59 great thunder. 27 29.57 29.56a very violent thunder, from 10 in the morning to 1 in the afternoon, doing great damages. 1735, June 1 29.3 29.8 2 29.4 29.55 thun- der and great rains. Thunder. The mercury fell before it. 1733, July 27 29.44 hot, fair. 28 29.37 wind, rain. 29 29.09 violent thunder. TRANSACTIONS. 203 1734, Aug. 7 29 59 sultry. 8 29.46 fair. 9 ...... 39.25 thunder. 10 . 28.87 rain, thunder. Frost. A frost, when the mercury is high, brings rain. 1731, March. The mercury was high all the month, and no rain, but what followed the frost the 17 th and 29th. Dry Season. In June 1729, and the mercury scarcely ever above changeable. In Aug. 1730, the mercury never lower than 29.37. 1731, from the 1st to the 10th, and rain came the 16th, though the mercury was rising. Frost. A great frost, though the mercury fell ; but it was attended with a great snow, which might occasion it to subside. 1731, Jan. 1 29.56 rain. 2 29.46 20.12 rain. 3 28.78 28.72 wind. 4 28.72 28.81 frost, great snow. 5 28-93 29.12 snow, frost. Great Rains. Though the mercury was rising. 1732, May 1 29 28 29.25 wind. 2 29.21 29.25 rain all day, snow hard from 8 to 1 1. 3 29 34 29.0 rain. 4 29.09 29.09 rain. 3 29.12 29.34 wind. 6 29.44 29.46 fair. 7 .... 29.52. . . . 29.39 rain, and great floods. Great rain, though the mercury fell but little. 1733, 24 29.6 29.54 wind. 25 29.51.... 29.54 fair. 26 29.52 29.54 fair. 27 29.5 29.39 violent rain for more than 1 1 hours. Great Rains. The mercury falling very much. 1734, July 10 ... . 29.65 29.67 fair. hot. 11 29.63 29.62 fair, hot 12 29.59 2.9.4 rain. 13 29.29 29.13 great rains. ^The mercury falling a great while before the rain came, and the rain continued as long. 1736, May 19 29.75 fair wind 29.8 20 29 8 cold wind, fair 29.7 21 29.65 cold wind 29.52 22 29.39 wind, cloads,rain29.31 © 23 29.28 cloudy, fair 29.'^7 24 29:32 fair 29-35 25 ... . 29.32 clo. wind, rain 29.24 D 2 204 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. 1736, May 26 .... 29-15 rain 29.15 The mercury below 28 inches. 27 29.12 rain 292 1734, Dec. 15, at 27.9. 28 -29.28 rain 29.23 1735, Jan. 8. at 27.9- 29 ... . 29.37 wind, cloudy, rain. In winter, before frosts, the mercur)' generally 1735, Feb. 22 29.43 rises pretty fast. 23 28.82 1735, Dec. 12. 24 ... . 28.9 Before a thaw the mercury falls. 25 28.76 great rain. 1735, Dec. 13. Just after hot or sultry weather, the mercury 17. generally falls. 1736, Feb. 9. See 16 Sept. 1731. The mercury falls suddenly before a great snow. 8 Aug. 1734. 1731, Jan. 4. After the aurora borealis, there generally follow 1736, Feb. 8. high winds. 21. 27 Oct. 1733, a large aurora borealis, and the When the mercury falls for high winds, and 28th, 29th, and 30th, high winds. it continues to fall when that wind is come, it is See 23 Jan. 1734. likely to be tempestuous, or continue some time. The mercury falling pretty much, and neither unless rain succeeds, wind nor rain succeeded. 1736, 22 Nov. . 29.62 fair, warm. . 29.62 1733, from the 18th to the 21st it fell 41, and 23 29.49 windy, warm29,32 wind. no wind or rain at all till the 25th. 24 29.1 high wind .. 28.88 28.73 Sultry weather generally makes the mercury stormy, fall soon after. Some of these collections are quite contradic- 1734, Aug. 8. tory to any settled rules, and such will happen. After a great storm the mercury rises very fast, and others confirm them ; but he has collected so 1734, Aug. 11. very few of a sort, though the diary furnishes a 1736, Feb. 6. great many, that till more are in this manner Before great winds the mercury falls very soon, collected, it will be very doubtful to form any 1734, Aug. 26. rules from them. 1736, Feb. 8. An Account of a Sulphureous Vaporiferous Cavern in a Quarry at Pyrmont, similar to the Grotta del Cane at Naples. By Mr. Misson and others. Com. municated to the Royal Society by John Philip Seip, M. D. Aulic Councillor and Archiater to the Prince of Waldech, and F. R. S. N" 448, p. 266. An account of a sulphureous vaporiferous cavern in a quarry at Pyrmont, near to the famous chalybeate springs. Birds, including poultry, and the smaller quadrupeds, such as dogs, cats, &c. were suffocated on being exposed for a sufficient length of time to the vapour emitted from this cavern, which in this respect resembles the Grotta del Cane at Naples. When exposed to this exhalation but for a short time, and afterwards brought out into the open air, the animals commonly revived. A candle would not burn in this cavern. [It would seem that this supposed sulphureous vapour consisted of the so called fixed air, or carbonic acid gas.] On the Effects of Dampier's Powder, in curing the Bite of a Mad Dog. By John Fuller, Esq. Jun. F. R. S. N° 448, p. 272. Mr. Fuller imagined the use of the lichen cinereus terrestris with black \ VOL. XL.] PHILOSOPHICAL TRANSACTIONS, 205 pepper, had been so infallible a remedy for the bite of a mad dog, that there needed no proofs of its virtue; he himself has used it on dogs, and always with success; and some years since, a mad dog or cat had bitten some children and their mother, at Battle: and mixing the lichen according to Dampier's direc- tion, they all took it, as well as a dog or two that were bitten, and none of them had any bad effects from the bite. Christmas 1737, a neighbour's servant going to search whether a dog sus- pected to be mad had been wormed, which dog died mad in 3 or 4 days after, was bitten very much in both his hands; he went to a person, who had great success in using the lichen cinereus tierrestris with pepper for the bite of a mad dog. The man took his medicine every day; about 10 or 11 o'clock he complained of a violent heat, and pain in his head, which Mr. F. suspected was the effect of the bite, and not the medicine; but after he had taken it for such a stated number of days, he grew better, and continued well ever after. The man had tied his fingers with shoe-maker's ends, which are often used for a cut ; and they were all very much inflamed, and very sore. Mr. F. made him take them off, and all his plasters, and wash his hands with salt and water, and in a fortnight's time they were quite well. Another Case of a Person bitten by a Mad Dog. By David Hartley * M. A. and Mr. Fr. Sandys. N° 448, p. 274. About the latter end of Nov. 173'2, Mr. Soame's groom was bitten in the hand by a mad dog, so as to fetch blood. It was not known in the family for 3 days. On the 4th day, when Fr. Sandys first saw it, the wound was healed; but it was opened again by him, and kept so for some time, but at last healed sooner than was intended, by the servant's neglect. * Dr. David Hartley, better known by his metaphysical than by his medical writings, was bom in 1705. His father was a clergyman. After completing his education at Cambridge, where he pre- pared himself for the {wofession of physic, he went to settle at Newark upon Trent, whence he removed to St. Edmund's Buryj he afterwards came to London, and at last fixed himself in Bath. From these frequent changes of abode, it may be inferred that he never got into very extensive practice. In 1739 he wrote a pamphlet in favour of Mrs. Stevens's medicine for the stone. His evidence had great weight with parliament, who voted a large sum of money to Mrs. Stevens, the discoverer of this supposed lithontriptic; which, however, did not long uphold the character that had been given of it, and is now gone into disuse. As a writer Dr. H.'s principal work is his Observations on Man, published in 1749; a work replete with ingenious, but not always tenable, theories and opinions. The above, and another pap>er on a case of calculus, are the only communications of his which are in the Phil. Trans. He died in 1757. 206 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. He was bled, took a purge, after that -^ oz. of pulvis antilyssus, every morn- ing for 3 days, and was ordered to go into cold water every day for some time; but he neglected it after the 3d day. Besides, Fr. Sandys ordered him to for- bear all meats, and drink nothing but water. He continued in this regimen for about 5 weeks; then finding himself well, would confine himself no longer to it. On Jan. 7 following, he was seized with a sickness, vertigo, and faultering in his speech and memory; and at last his vertigo increased to such a degree, that he fell down twice in the space of half an hour; and the last time he did not recover his senses, till he was put to bed, and blooded to the quantity of 18 or 20 oz. He continued all night restless and sullen, and in the morning was blooded again, to the quantity of 13 oz. Dr. Hartley was sent for, and came about 8 at night, and found him very sullen, thirsty, but averse to drinking, and his pulse quick and hard. He ordered him to be put into the cold bath; but he refused to comply with it, till he saw that force would be used. About midnight his pulse rising, the Doctor ordered him to be blooded to the quan- tity of l6 or 1@ oz. he continued restless all night. About 8 in the morning he went into the cold bath again: about 10 Dr. Hartley went away, leaving it as his opinion, that the cold bath and bleeding should be freely repeated, as the circumstances should require. About noon Mr. Sandys came, and bled him immediately, to the quantity of 18 or 20 oz. he continued restless all this night. On Mr. Sandys's asking him whether his aversion to drinking proceeded from any pain in swallowing, or some other cause? he said it was from a pain in swallowing. The next morning his strength not being at all diminished, and his pulse continuing full as vigorous as ever, Mr. Sandys bled him again to the quantity of 15 or 1 6 oz. yet he still remained the same, and took the same care of his horses as usual. Mr. Sandys went away, leaving orders that as long as these symptoms, viz. restlessness, strength, and aversion to drinking continued, he should be blooded freely, and put into the cold bath. He was blooded twice more within the week, so that the whole quantity which he lost in that time was about 1 20 oz. After the last bleeding his symptoms disappeared, and he grew weak, low spirited and sleepy ; he then went 8 times into the cold bath. He did not take any medicines during his whole illness. N. B. This person continued well anno 1738. VOL. XL.] PHILOSOPHICAL TfiANSACTIONS. 207 An Innuiry concerning the Figure of such Planets as revolve about an Axis, supposing the Density continually to vary, from the Centre towards the Suiface. By Mr. Alexis Clairaut, F. R. S, Translated by the Rev. John Colson, F.R.S. N" 449, p. 277. Notwithstanding that part of Sir Isaac Newton's mathematical principles of natural philosophy, where he treats of the figure of the earth, is delivered with the usual skill and accuracy of that great author; yet I thought something further might be done in this matter, and that new inquiries may be proposed, which are of no small importance, and which possibly he overlooked, through the abundance of those fine discoveries he was in pursuit of. What at first seemed worth examining, when on applying to this subject, was to know why Sir Isaac assumed the conical ellipsis for the figure of the earth, when he was to determine its axis? for he does not acquaint us why he did it, neither can we perceive how he had satisfied himself in this particular : and unless we know this, we cannot entirely acquiesce in his determinations of the axes of the planets. It seems as if he might have taken any other oval curve, as well as the conical ellipsis, and then he would have come to other conclusions about those axes. I began then with convincing myself by calculation, that the meridian of the earth, and of the other planets, is a curve very nearly approaching to an ellipsis ; so that no sensible error could ensue by supposing it really such. I had the honour of communicating my demonstration of this to the R. S. at the beginning of the last year ; and I have since been informed, that Mr. Stirling, one of the greatest geometricians I know in Europe, had inserted a discourse in the Philos, Trans. N° 438, where he had found the same thing before me, but without giving his demonstration. When I sent that paper to London, I was in Lapland, within the frigid iione, where I could have no re- course to Mr. Stirling's discourse, so that I could not take any notice of it. The elliptical form of the meridian being once proved, I no longer found any thing in Sir Isaac Newton, about the figure of the earth, which could create any new difficulty ; and should have thought this question sufficiently discussed, if the observations made under the arctic circle* had not prevailed on us to believe, that the shape of the earth was still flatter than that of Sir * On a late examination and re-measurement of that part of the meridian, considerable errors have been detected in the old measures; by which means those measures are brought to harmonize and accord with all other measurements in different places, and yielding in the result a like figure of the earth as those do. 208 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. Isaac's spheroid ; and if he himself had not pointed at the causes, which might make Jupiter not quite so flat as by his theory, and the earth some- thing more. As to Jupiter, he says, (Page 4l6 of the 3d edition of Phil. Nat. Prin. Math.) that its equator consists of denser parts than the rest of its body, be- cause its moisture is more dried up by the heat of the sun. But as to the earth, he suspects its flatness to be a small matter greater than what arises by his calculation. He insinuates, that it may possibly be more dense towards the centre than at the superficies. I am something surprised that Sir Isaac should imagine, that the sun's heat can be so great at Jupiter's equator, when it has no such eff^ect at that of the earth ; and that he does not ascribe each to a like cause, by supposing that Jupiter also may be of a different density at the centre from that at the superficies. But whatever reason he might have for introducing two difl^erent causes, I give the preference to the hypothesis which supposes unequal densities at the centre and at the circumference. I have inquired, by the assistance of this theory, what would be the figure of the earth, and of the other planets which revolve about an axe, on supposition that they are composed of similar strata, or layers, at the surface ; but that their variable density, from the centre to- wards the circumference, may be expounded by any algebraical equation what- soever. And though my hypothesis should not be conformable to the laws of nature, or even though it should be of no real use ; which would be the case, if the observations made by the mathematicians now in Peru, compared with ours in the north, should require that proportion of the axes, which is derived from Sir Isaac's spheroid ; I thought however that geometricians would be pleased with the speculations contained in this paper, as being, if not useful, yet curious problems at least. Part I. In which are found the Laws of Attraction, which are exerted on Bodies at a Distance, by a Spheroid composed of Orbs of different Degrees of Density. Problem I. — To find the Attraction which a homogeneous Spheroid BNEbe, fig. 9, pi. 6, differing hut very little from a Sphere, exerts on a Corpuscle placed at a in the Axis of Revolution. 1. We may conceive the space BNEiDMB, included between the spheroid and the sphere, to be divided into an infinite number of sections perpendicular to the axe Kcb. Supposing then that every one of the particles, which are contained in one of these elements or moments snmu, exerts the same quantity of attraction on the body at a. VOL. XL.J PHILOSOPHICAL TRANSACTIONS. 20Q which may be supposed because of the smaUness of nm; we shall have c* X PM* X P/> X — J for the attraction of any one of these elements ; put- ting c for the ratio of the circumference to the radius, and «-for the given ratio of mn to pm, that is, of de to cd. Now if we make ca =: e, cb = r, am = z; and for pm, ap, p/», if we sub- stitute their values expressed by z, and then seek the fluent of the foregoing quantity ; we shall have — —^ for the value of the whole attraction of the solid generated by the revolution of BDbsB : to which if we add -- — , the attraction of the sphere, we shall have — 1 — ^^ for the required attraction of the spheroid on the corpuscle a. Problem II. Supposing now tfie Spheroid Bsbe, fig. 10, to be no longer of a homogeneous Matter, but to be composed of an infinite Number of Elliptical Strata, all similar to BEb, the Densities of which are represented by the Ordi- nates kt of any Curve ivhatever vx, oj which we have the Equation between CK and KT ; the Attraction is required tvhich this Spheroid exerts on a Corpuscle placed at the Pole b. — 2. Making bc ^ e, CK = r, by the foregoing proposi- tion, we should have — 1 — -— — - for the attraction of the spheroid KLK, if it consisted of homogeneous matter ; and the fluxion of this quantity 1 — would be the element or moment of the orb klk^M. But because the density is variable, we must multiply this value of the attrac- tion of the orb by kt, and tiie fluent of this quantity will be the value of the attraction of the spheroid klk. As to the value of kt, which expresses the density of the stratum KLKklk, we shall take only fr'' -\- g?-^, because we shall see afterwards, that a value more compounded, as _/r* -)- g-;' -}- hr' + ir', &c. which by the property of series may express all curves, would not produce any variety in the calculation. Therefore multiplying the foregoing equation by fr -\- gr^, we shall have 2cfxl + 2»xr^'^f _ ic»fr ^'''^ , 2cgx l + 2«xr ^+? _ 4c«gr^ + ? r ., .. r eex3+p e*x5+p eex3 + q e^x5 + q attraction of the spheroid klk, exerted on a corpuscle placed at b. 3. In this value making r = e, we shall have ~ h =^ h -■ + -L. ■ which will express the force of 3+p 3+PX5 + P 3 + q 3+JX5 + 9 '^ attraction of the spheroid be6, exerted on a corpuscle placed at the pole b. Theorem. ^ Corpuscle being placed in any Point n of the Surface of the VOL. vm. E E \ '210 PHILOSOPHICAL TRANSACTIONS. [anNO 1738. foregoing Spheroid BEbe, / say it will undergo the same Attraction from this Spheroid, as if it were placed at the Pole N of a second Spheroid revolving about the A.ve no, the second Axe being the Radius of a Circle equal in Superficies to the Ellipsis fg ; supposing this second Spheroid ngof (fig. 11) to be com- posed of the Strata Minqa, whose Densities are the same as those of the Strata KkLlKk, of the first Spheroid. — 4, In the discourse I had the honour of com- municating to the R. S. being then at Toriieo, printed in the Philos. Trans. N° 445, I have demonstrated this proposition as to a homogeneous spheroid ; and the same reasoning will obtain in this case also. Problem. III. To find the Attraction which the Spheroid BEbe (fig. 10) exerts on a Corpuscle placed at any Point n of the Superficies. — 5. We will make, as above, bc = e, ce = e + e«j and also cn = e + ex, and half the conjugate diameter of cn will be cg = e + ea — ex \ whence the radius of a circle, equal in superficies to the ellipsis pg, will be a mean proportional be- tween CB and CG, that is, e -j- ea — ^x. Therefore the spheroid beZ'^ exerts the same attraction at n, as would be exerted at the pole of a spheroid ngof. (fig. 11) of which the principal axis would be no = 2e -|- lex, and the second would be to the principal, as I + « — f a to 1. Therefore in the expression of the attraction at the pole, (Art. 3) we must substitute e -\- ex instead of e, and a — aa instead of a. But if _/ and g must no longer be the same ; for we may easily perceive by the foregoing Theorem, that the density must be the same in this spheroid ngof, at the distance r-\-rx from the centre, as it is in the spheroid BE^e at the distance r. Therefore f(-—^ -\- gir— y must be put instead oi fe -{■ ge . Thus we shall have 3+p 3 + p X 5 + p 3 + p y. 5+ p 3 + q 3+qx5+q S + q X S+q for the attraction of the spheroid BEie at n. 6. If we make x = a, the foregoing expression will be reduced to this 2je^ ^cfe'+f» ^ej+9 2cge^ ^^.^^ expresses the attraction of the 3 + p ' 5 + p ' 3 + q ' 5 + q ' ^ equator. 7. If we would have the attraction at any point m within the spheroid, in the expression of the attraction at n, we must put r instead of e. The proof „ of this is plain from the same reasons that Sir Isaac Newton makes use of, | (Corol. 3, Prop. Ql, I. 1, Princip. Math.) to show that the attraction of an '' elliptic orb, at a point within it, is none at all. Problem IV. Let Rllrn- (fig. 12) be a Circle whose Centre my; it is re- quired to find the Attraction which this Circle exerts on a Corpuscle at n, ac- VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 21 I cording to the Direction nx ; supposing the point h, which answers perpendicu- larly below t/ie Point n, to be at a very small Distance from the Point y. — 8. Let there be drawn riHTr perpendicular to the diameter RYr, and let the space RllTr be transferred to ttIIz. Then the space Trzllr will be the only part of RflrTr, which will attract the body n according to hy. To find the attraction of this little space, we will suppose it to be divided into the elements tIss, the attractions of which, according to hy, will be TtSS X QT 2HV X Q? X QT . , n . c . • 1 2HY X HQTZ . , . -— , or , , the fluent or which j is the attraction NT* ' Nt' ' NT' of Tzrs, according to hy. In which if we put llTr for Ha, we shall have nH.Hx2HY ^^ jHY X riH' X c ^^^ ^j^^ attraction required. NT' NT' ' Q, It is easy to perceive, that if, instead of a circle, the curve Rllr were an ellipsis, or any other curve whose axes were but very little different from one another, the foregoing solution would be still the same. Problem V. To find the Attraction which an Elliptical Spheroid klIi (fig. 1 3) exerts on a Corpuscle placed without its Surface at n, according to the Direction ciL perpendicular to cs. — 10. To perform this, we will begin by drawing the diameter CfAv, which bisects the lines Rr perpendicular to cn; and the ratio of CH to HY shall be called n. Then accounting the ellipsis Rr as a circle, see the foregoing article, we shall have, by the foregoing problem, t^'^xrh xch ^^^ its attraction, according to hy ; which being multiplied by the fluxion of mh, the fluent of this will be the attraction of the segment of the spheroid RMr. This calculation being made, and not being substituted for nr, we shall have -—J- for the attraction of the spheroid in n, according to the direction ex. Problem VI. To find the Attraction of a Corpuscle n, according to ex, towards an Ellipsoid BNEbe, composed of Strata, the Densities of which are defined by the Equation D = fr"" + gf^- — H- Take the fluxion of the quantity — -, which expresses the attraction of the homogeneous ellipsoid klA, and you will have — ;— for the attraction of an infinitely little elliptic orb; which, being multiplied by the density d, gives -^^ ^ -^ — ^^ '-, the fluent of which -i^ 1- —f^Ii— !, is the attraction of the spheroid kl/^, according to 5 + jJXe^ 5+yxe* ^ ex. Therefore the total attraction of the spheroid sNE/jie on the corpuscle n, according to the direction ex, will be ^^f U ?^— . ^ 5+7' ^ 3 + 9 £ B 2 212 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738 Now if we have regard to the smallness of the line nv, and observe how little angle vnc will differ from a right one, we may perceive that the diameter CN contains the same angle with the perpendicular nx in n, as the diameter CN with the perpendicular at v; that is, that the angle ncv is the same as the angle cnx; so that instead of n we may take — . Therefore the foregoing ex- pression of the attraction of the ellipsoid BEbe, acting according to the direc- tion ex, on a corpuscle placed in n, will be -f * x — + — f^ X — . ' ' ' 5+p CN 5+q CN Problem VII. To find the Direction of the Attraction of a Corpuscle n towards the Ellipsoid. — 12. By the second Problem we shall find the attraction of the spheroid according to on to be —^ \- ^^ — , by expunging what may be here expunged. Then by taking a 4th proportional to these 3 quanti- ties, the first of which is the attraction according to cn, the 2d is that accord- ing to ex, and the third is the right line cn; there will arise 5 + p "*" 5 + q _ rl+P , +o X CX CL. 3+p "^ 3 + 9 Whence we shall have ni for the direction required, of the attraction of the corpuscle n. 1 3. If we suppose p z= q ■= o, that is, if the spheroid be homogeneous, we shall have ci = ^cx ; which agrees with what Mr. Stirling has found, in that curious dissertation he has published in the Philos. Trans. N° 438. Part II. The Use of the foregoing Problems, in finding the Figure of Spheroids, which revolve about an Axis. — 14. Let us now suppose, that the foregoing spheroid bneZ^c, (fig. 13) which is still composed of strata of differ- ent densities, revolves about its axis Bi, and that it is now arrived at its per- manent state. It is plain that the particles of the fluid, which are on its sur- face, must gravitate according to a direction perpendicular to the curvature bne; for without this condition there could be no equilibrium. We shall now inquire, whether the elliptic figure we have ascribed to our spheroids can have this property, and to produce this effect, what must be the relation between the time of revolution of the spheroid and the difference of its axes. Let us then put (p for the centrifugal force at the equator, and the centrifugal '111 ^XPN ^X CX force at n will be , or , because 2pn X a, = ex. CE ' 2CE X a. VOL. XL.] PHILOSOFHICAL TRANSACTIONS. 213 By resolving this centrifugal force according to the perpendicular to cn, we shall have ^ ^ ^^ ; to which adding -^^-^-; X — + ~-, X — , found by 2<» X CE ° 5 + p CN ' 5 + J CN •' by prob. 5, will give the whole force of the body n, according to the direction ex, when the spheroid is turned about its axis. But because this body, by virtue of the attraction according to cn, and the force according to ex, ought to have a perpendicular tendency to the superficies; we shall have this analogy, CN : ex :: -f- — + -I- : — X \- -^, X §- X — . And 3+P 3 + (j 2» ce' 5 + p cn' 5 + q cn hence, because cn and ce may be assumed as the same on this occasion, it Will be ip = — == + 3 + p X 5 + p 3 + q X 5 + q The Spheroid being supposed ellipical. Bodies will gravitate perpendicularly to its Surface. And as in this value of the centrifugal force, no quantity enters but what will agree to any point n; we may therefore conclude, that when our supposed elliptical spheroid performs its rotation in a proper time, so that the centrifugal force at the equator may be as before ; then the centrifugal force in any other place n will be such as it ought to be, to cause bodies to gravitate in a direction perpendicular to the surface. The Expression for the Gravity at any Place on the Spheroid. 15. If we now consider, that ed (fig. 14) being taken for the centrifugal force in e, then will mn express the centrifugal force in n, and consequently MI will be such a part of this force as acts according to nc ; we shall have + = — == to be subtracted from the attraction at n. Hence 3+px5+p 3+qx5+q •Zcfe'-^f 2p- Wcfi^e'+f Scfue' + f 2cge' + ^ 2y - lOcg^e'+f 3+p 3+~p X sTp 3+px 5 + p 3 + q "*" 3~+Tx 5TT ' scgxe' "'"^ — ■ - Will be the gravity at n. ~ S + q X 5 + q ^ ^ The Gravity at the Equator. 16. In this value making x = «, we shall have 2c/e'+>* 2F^';/-«e'+^ , 2cg-e' +? , 27-^c?«e'+^ , -r—. — + '~^^= + + — =— for the gravity at the 3+p ' 3+px S+p ' 3 + q ' 3 + qx 5 + q ^ ■> equator. 17. If we subtract the value of the gravity in n from the value of the at traction or gravity at the pole, in art. 3, we shall have ai4 PHILOSOPHICAL TRANSACTIONS. [anno 1738i 10 — 2pcfxe 1+^ + 10 — iqcg>e + ? '■=^^=:r. Bat it is easy to perceive, that x is pro- 3 + PX5+P Z-\- qy. S + q portional to the square of the sine of the arc pm, or of the complement of the latitude. Whence we may therefore conclude, that the diminution of the gravity from the pole to the equator, is proportional to the square of the cosine of the latitude ; or, which is the same thing, that the augmentation of gravity from the equator to the pole, is as the square of the sine of the latitude, as Sir Isaac Newton has demonstrated in his hypothesis of a homogeneous spheroid. ]8. From the following calculation it is easy to conclude, that Sir Isaac's theorem, (Prin. Math. lib. 3, prop. 20) which is this, that the gravity in any place within, is reciprocally as the distance from the centre, cannot obtain here. For we may see by the foregoing expression, that the gravity in n cannot be to the gravity in p, as 1 to 1 + ^> except when p = g = O, which happens only in Sir Isaac's homogeneous spheroid. It was for want of considering, that this theorem was demonstrated by Sir Isaac only in the case of his homogeneous spheroid, that several geometricians have too hastily concluded, that this theorem might be applied to determine the ratio of the earth's axes, and the lengths of the pendulum observed in two places of different latitudes. Dr. Gregory is one of those who have fallen into this mistake, in his Elements of Astronomy, lib. 3, sect. 8, prop. 52. And in the Philos. Trans. N° 432, it is concluded, from the proportion of gravity at Jamaica to that at London, that the diameter of the equator must exceed the earth's axis by the JQOth part, which computation was founded on this 20th proposition, lib. 3, of Sir Isaac's Principia, which is true only of his spheroid. The Manner of priding the ^xes of the Spheroid, the Variation of the Densities of the Strata being taken at pleasure. IQ. Let us now suppose, that the centrifugal force at the equator is known by observation, as also within the earth, &c. and that it is a certain part, as the mth part of the gravity ; by articles 14 and l6, we shall have this equation : 2c/i ■ +;■ + 2p- 2c/e'+^« ^cge'-^f '2q - Zcge^ + ?» 8cfme' + ?a + + Scmge^ "' ^« "*" F+qxT+q' S+p ' 3 + px5+p ■ 3 + q 3 + qx5 + g 3+px5 + p From hence it will be easy to derive the value of «, because y, g,p, q, will be given, from the hypothesis that will be chosen, for the variation of the density in the internal parts of the spheroid. 20. And if on the contrary a. be given, that is, if we know by observation the ratio of the axes of the planet concerned ; then by the foregoing equation we may perceive, whether we have assumed an agreeable hypothesis for the variation of the densities : but we cannot precisely determine what this hypo- VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 2)5 thesis must be, because there is but one equation, in which 4 indeterminate quantities/, g-,jb, q, are involved. And indeed there might be many (nore than 4 indeterminate quantities, if we should assume more than two terms in the general equation of the densities d = frf + gri + hr', &c. 21. In order to apply the foregoing theory to the earth, it might seem at first sight, that by the assistance of observations made for measuring the length of the pendulum, we might have other equations, which with the foregoing equation a, would determine the coefficients and exponents now mentioned ; but we shall soon see the impossibility of this, on two accounts : first, there need be only two observations, as to what concerns the length of the" pendu- lum. For because, by art. 17, the augmentation of the gravity from the equator to the pole, is proportional to the square of the sine of the latitude, two observations as much determine the problem as an infinite number can do: so that we could have but one other equation besides the foregoing. This 5—pf* , 5-qg» ■n 1 /■ \ P—P 3+PX5+P 3 + 9x5 + ? equation will be (b) = -^_ ^ — — = • P p-'^f' , _/_ 1 _£_ I 1-^S1_ 3 + px5+p~^ 3+p "*" 3 + 9 3 + qx5 + q The first member of this equation expresses the gravity at the equator sub- tracted from the gravity at the pole, and divided by the gravity at the equator ; a quantity which may be known in numbers, by determining the length of the pendulum at two difl^erent latitudes. The other member of the equation is an expression of the same quantity, as it is deduced by the preceding calculus. Secondly, This new equation b cannot be of any service in determining the coefficients and exponents J", g, p, q, &c. For we shall now show, that the foregoing ratio ^ — - has such an immediate connection with a, that one of them being determined, the other will necessarily be so too, independently of the values o{ f, g, p, q, &c. This may deserve our attention, and the proof is thus : The Figure of the Spheroid being known, the Augmentation of Gravity from the Equator to the Pole will be known also ; and so vice versa, 22. Because the ratio of the gravity to the centrifugal force is very great, and is expressed by m, in the equation a we may reject the third and fourth terms ; by which means the equation will be reduced to this, f g imf» imgit — — + ^-, — = :r-; — ■ -r-r= + Tt^^'t^t^- ^"° " "■°'" this equation 3+p 3+9 3+PX5+P 3+9X5+9 ^ we deduce the value either off or g, and substitute it in the equation b ; having first rejected the first and fourth terms of the denominator, as in this case may be done ; we shall have, after the calculation is made, whatever is the number 2l6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. of terms in the equation of the densities, ^—^ = «, or ^^ = — a. ^ ' p im ' p 115 *> by putting 288 for m, as has been long known. It is easily seen from this equation, that when a is determined, will be so too, which was the thing proposed to be proved. 23. But from this equation there follows a very singular proposition, and which, in some sort, is contrary to the sentiments of Sir Isaac Newton, page 430 of the 3d edition of his Principles. And this is, that if by observation it shall be discovered, that the earth is flatter than according to the spheroid of Sir Isaac, that is, if the diameter of the equator exceeds the axis by more than the 230th part, the gravity will increase less from the equator towards the pole, than according to the table which he has given for his spheroid, prop. 20 of the 3d book. And on the contrary, if the spheroid is not so flat, the gravity will increase more from the equator towards the pole. 24. It is thus that Sir Isaac Newton expresses himself about it, when he re- lates the experiments made towards the south, concerning the diminution of gravity, which experiments make it greater than his theory requires. He affirms, that the earth is denser towards the centre than at the superficies, and more depressed than his spheroid requires. But by the foregoing theory we may easily perceive, that if the density of the earth diminishes from the centre towards the superficies, the diminution of gravity from the pole towards the equator will be greater than according to Sir Isaac's table; but at the same time the earth will be not so much depressed as his spheroid requires, instead of be- ing more so, as he affirms. Yet I would not by any means be understood to decide against Sir Isaac's determination, because I cannot be assured of his meaning, when he tells us, that the density of the earth diminishes from the centre towards the circumference. He does not explain this, and perhaps in- stead of the earth's being composed of parallel strata, its parts may be con- ceived to be otherwise arranged and disposed, so as that Sir Isaac's proposition shall be agreeable to the truth. 25. As to Dr. Gregory, who has attempted to comment on this passage of Sir Isaac, I think I have demonstrated, that he has committed a paralogism. He says (Element. Astronom. lib. 3, § 8, prop. 52 schol.) that if the earth is denser towards the centre, or if, for example, it has a nucleus of greater weight than the other parts, the diminution of gravity from the pole towards the equator shall be greater than if the whole were of the same density; and in this he is right. But he is in the wrong, I think, immediately to conclude from thence, that the earth has a greater flatness. Whence can he conclude this ? VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 217 it can be only from that proposition of Sir Isaac which informs us, that gravity is in a reciprocal ratio of the distances: because he gave us the proposition but the page before, as a method for determining the figure of the earth. But we are not allowed to make use of this proposition in this case, because it has been shown, art, 1 8, that it can take place only on the supposition of a homogeneous spheroid. Therefore, &c. 26. It will not be very difficult, without any regard had to the foregoing theory, to find the ratio of the axes of a spheroid, which we may suppose to have a nucleus at the centre, of greater density than the rest of the planet; and hence we shall be easily assured of Dr. Gregory's mistake. 27. Setting aside all attraction of the parts of matter, if the action of gra- vity is directed towards a centre, and is in the reciprocal ratio of the squares of the distances, the ratio of the axes of the spheroid will then be that of 576 to 577: and the gravity at the pole is greater than at the equator by the 144th part, or thereabouts. Which may be a confirmation of what is here advanced, especially to such as will not be at the pains of going through the foregoing calculations. For we may consider the spheroid now mentioned, in which gra- vity acts in a reciprocal ratio of the squares of the distances, as composed of matter of such rarity, in respect of that at the centre, that the gravity is pro- duced only by the attraction of the centre or nucleus. 28. In the foregoing calculations, in order to find the axes of our spheroids, and to know whether their figure makes a sensible approach to that of the conical ellipsis, we have had recourse to this principle, that gravity ought always to act in a direction perpendicular to the surface. Two reasons have prevailed with us to make use of this principle, rather than the other, which consists in the equilibrium of the columns. The first is, because the calcula- tions founded on it are more simple. The second is, that considering the state of the actual solidity of the earth, it should seem as if this principle were the more indispensably necessary. However, because Sir Isaac Newton, and all the other philosophers, who have treated about the figure of the earth, have taken it, as it were, at its first formation, at which time they suppose it to have been fluid: we shall here make the same supposition, and we shall assume no other ratio for that of the two axes, than that of the spheroid which results from a- coincidence of these two principles. We shall begin by inquiring what is the whole weight of any column cn, fig. 15. To do this, we must resume the expression of the attraction in any point M of the column cn; then multiply it by r -f- xr, and by the density frP -\- gr9, and afterwards we must find the fluent. Thus we shall have VOL. VIII. Pf. 218 c/»e*+='^ + PHILOSOPHICAL TRANSACTIONS cg'e* + ^? + + [anno 1738. \ +p X3+P l + 9X3 + g 2 + J» + ?x3+f 2 + p + gx3+ X 5 +p \-\-qx3 + qxS + q 2 + P + ? X 3 + p x 3 + 5 + 8c/g«c «+^ + f + 2 + ;) + ?x3 + gx5 + 9 8 4.4;>cg/'Ae^+^ + ? + 4 + ^pcfye"- + ^Z" + l+px3+px5+p 8 + 4?c^Ae*+''+? + 4 + 2qeg'^>.e* + ? 3 + ?x5 + ?Xl+/> for the total gravity of S + p + q X 3 + px 5 +p i + p -\-q X 3 + q X 5 + q any column cn, having regard only to the attraction. 29. If in this expression we make a = O, we shall have the gravity of the column at the pole. 30. And if we make x := «, we shall have the aggregate of the attractions of the column at the equator. 31. Now because the column on is in equilibrio with the column cb; it follows from thence, that if we subtract the weight of the column cb, from the aggregate of the attractions of the column on, the residue must be equal to the sum of the centrifugal forces of the column cn. Now to endue our spheroids with this property, we will resume the expression of the centrifugal force in e, which we found art. 14, which will give ( ^^^ — ^ + z==^-z= — ) - , for that part of the centrifugal force which 3 + px5+/) 3 + ?x5 + ?e acts according to cm, in any place m, by expunging the terms in which aa would be found. This value being multiplied by r, and by the density, will give, when we have taken the fluent, ^^ ' =^ + 8c/ge'+^ + ?A + 2+px3+/)X5 + p Z+p X 3-\-q X 5^ q cge^ £qj. jj^g gm^ Qf jjjg centrifugal 2+?x3+px5+p 2+qx3+qx5+q forces of the column cn, still expunging those terms in which either met or M are found. mu , • .u- • W I+ipcA^+'^A , 8 + lpcfge^+f + f>. Then makmg this expression equal to =rrt — ~ — ' —- l+pX3 + pX 5+p 2+p + qx3+px5+p + __EI}^^r^ +^r , icfrr +^r , 2cgr' + ?r ^ 3+p 3 + P X 5 + p 3 +p X 5 +p 3+J And taking the fluent of this quantity, we shall have ^e= + =^CL. + ==Jt^:i^-= + ^^li=, &c. for the Z + py.i+p 3 + p y. S + p 2+px3 + pxS+p 3 + ?x2 + 5 gravity of the whole column on. 36. If in this value we make x = 0, we shall have the gravity of the column at the pole. 37. And if we subtract the gravity of the column at the pole, from the whole sum of the attractions of the column cn, we shall have *^'^' _. ._ + —^ ^— , which must be equal to the sum of the centri- 3+px5+p 3+9x5+9 fugal forces of the column cn, in order that the columns cb and on may be in equilibrio. ( But we shall find this really to obtain, if we resume the quantity ( — gSffl— — -I ^Ji^Jl^) r ^ which,, by art. 31, expresses that part of 3+px5+p 3+9x5+? e the centrifugal force in m, which acts according to cm. Then multiplying this expression by r, and seeking the fluent, we shall have VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 221 *5^' "^ - — + ^^' — =^-=1 for the agsjregate of the centrifugal forces of the 3 + px j +p 3 + 6x5+6 column CN. And this being the same as the foregoing, shows that the columns CB and CN are in equilibrio, supposing them to be homogeneous; nor are we here obliged, as in art. 32, where we consider them as heterogeneous, to sup- pose the coefficientsy, p, &c. to have any certain relation among one another. 38. Perhaps it may be urged, that the foregoing calculus agrees only to a canal, as bcn, which passes through the centre; and that we ought to prove in the same manner, that the water included in any other canal pgr, would ob- serve an equilibrium. But it appears to me, that this property may be derived from the former; for it follows, from the foregoing calculation, that if we might be allowed to make this hypothesis, viz. that independently of the attrac- tion of any matter, the gravity at any distance cn from the centre, see fig. 15, would be proportional to -^ -|- -^ = + - — , &c. it is plain 3+;» 3+PX5+P 3-j-px5+p from thence, that a mass of the homogeneous fluid, which should turn about the axis cb, would assume the same form as that of our heterogeneous fluids. But if this spheroid should then put on a fixed state, except only some canal pqr, the water in this canal would be in equilibrio; for without this, the sphe- roid could not be esteemed as having arrived to its fixed state. But this suppo- sition comes to the same as that of our heterogeneous spheroid, composed of elliptical layers, in which should be found a canal pgr of a homogeneous fluid; provided that the space, which this canal possesses in the globe, be not of so large an extent, as to change the law of attraction. The only three planets, in which we can be assured of gravitation, and the centrifugal force, are the sun, Jupiter, and the earth. As to the sun, the cen- trifugal forc^ is there so small, in respect of its gravity, that his poles must be very little depressed, so that we cannot be sensible of it by observation. Then as to Jupiter, observations make him something less flat than according to Sir Isaac Newton ; that is, than if he were composed of matter of a uniform den- sity. Therefore by the foregoing theory, he must be a little more dense to- wards the centre, than at the parts near the superficies. We might make a thousand hypotheses about the manner of distributing the inequality of density, proceeding from the centre towards the circumference, which would all agree with the figure observed, and which are very easy to calculate by the principles here laid down. As to what concerns the earth, I shall wait till we receive the observations which must have been lately made in Peru; that by comparing those with what 222 fHILOSOFHICAL TRANSACTIONS. [ANNO 1738. observations we have made under the arctic circle, and with those of Mr. Picart in France, we may have the true difference of the earth's diameters at the equator and at the poles. Then our theory may be applied, to determine whether the earth is more or less dense at the central parts than at the surface,* or whether it be every where of a uniform density, as it ought to be, if, with- out admitting very gross errors in the observations, it may be concluded, that the earth is really the spheroid of Sir Isaac Newton; and this case would be the simplest and the most natural of all. I am here obliged to acknowledge, that if the observations we have made in the north may be relied on,-|- and if we must admit as incontestable as well the measure of a degree as the length of the pendulum, the foregoing theory could not be reconciled to the phenomena. For it follows from our observa- tions, that the diameter of the equator must exceed the earth's axis by more than the 230th part; and that the gravity at the pole must be greater than that at the equator by more than the 230th part also; which will by no means agree with what we have deduced in art. 23. As to what concerns the measure of gravity in Lapland, as being not so liable to error as the measuring a degree; the earth may be not quite so flat as Sir Isaac's spheroid requires. By the table of the length of the pendulum, exhibited in the treatise concerning the figure of the earth, published this year by Mr. de Maupertuis, and by art. 22 of the present discourse, the earth may be more elevated at the equator than at the pole by the 266th part, or there- abouts. After the true quantity of the earth's flatness shall be fully settled, if it should be found to have this figure, I should be apt to think it is a little more dense at the centre than towards the superficies. But if on the contrary we should be well ascertained, that the earth is raised higher at the equator than at the pole, by above the 230th part: and if, for any sufficient reason, we may something shorten the length of the pendulum that beats seconds in the north; there would be some grounds to allow, that the earth is not so dense at the central regions as at those near the surface. But if it shall happen, that we can neither diminish the length of the pendulum, nor the excess of the equa- torial diameter above the axe, I must then give up my hypothesis. Yet I shall think it may be of some use to have thus discussed it, because possibly no one would have imagined what might have been the result of it. It appears that • It has since been determined, by Dr. Hutton's calculations on the observations made at mount Schehallien, in Scotland, that the mean density of the earth, is about 2 times more than at the sur- face ; and that it is therefore probable the central parts of the earth are still much more dense. See Philos. Trans, vol. 68, part 33. + It has since been found very erroneous. See p. 287, of this volume of Abridgments. I ! VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 223 even Sir Isaac Newton was of opinion, that it was necessary the earth should be more dense towards the centre, in order to be so much the flatter at the poles; and that it followed from this greater flatness, that gravity increased so much the more from the equator towards the pole. New Experiments on Ice. By the Abb^ Nollet* F. R. S. at Paris. N° 449, p. 307 . 1. Ice that begins to melt, and water that begins to freeze, have always the same degree of cold. 2. Thiit cold may be increased by a mixture of salts. 3. It has been thought for a long time, that saltpetre was most fit to increase the cold of ice; but experiments have shown, that few salts increase cold so little as that salt. Mix one part of fine saltpetre with two parts of beaten ice, and Mons. Reaumur's thermometer will descend in it but 3-f degrees below the freezing point. What had caused this mistake, is, that people generally made use of salt- petre of the first or second melting, as being the cheapest; but that salt- petre, not being purified, contains a great deal of sea- salt ; and it was in pro- portion to the quantity of the sea-salt that the effect was the greater. From this last observation, one may deduce an advantageous method for trying gunpowder; for as of the three ingredients of which it is made up, salt-petre is the only one that can increase the cold of ice; if one pari of gun- powder, or a little more, be mixed with two parts of ice; and it increases its cold more than 3i degrees, it is a sign that the salt-petre contained in it is not well purified; and the best powder will be that which least increases the cold of ice. 4. Sea-salt, that is the Bay-salt, which is commonly used at table in France, and that which is immediately taken from the mines, called sal gemmae, usually gives the greatest degree of cold; for pot-ash gives sometimes a little more, but generally less. Sea-salt mixed with ice in the abovesaid proportion, gives 15 degrees of cold on Mons. Reaumur's thermometer, and sal-gem. 17. 5. Ashes of green wood 3 deg. 6 Sea-coal 7 Vitriol 2 8 Tartar 10 9 Common pot-ash (in French called sonde ordinaire) 3 10 Pot-ash made of se^ weed 11 This last pot-ash may be substituted instead of sea-salt, for making ice- * The Abbd Nollet acquired a great degree of celebrity by his lectures and writings on experi- mental philosophy, and particularly by his experiments and observations on electricity. He was a member of the French Academy of Sciences, of the Royal Society of London, and of various other ficientiflc institutions. He died at Paris in 1770, at the advanced age of 70. 224 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. creams, in places where salt is dear, as in France, where it is sold for lO sols a pound. 1st, Because in France this pot-ash is sold only for 2-i- sols a pound. 2dly, Because, not freezing so fast, it does not spoil the creams by reducing them to icicles. 3dly, Because ice-creams made this way, will keep longer in a condition fit to serve at table. 11. Sugar J 4 deg. 12. Alum IJL 13. Salt of glass 10 14. Sal ammoniac 12f ] 5. Quick-lime 1^ 1 6. Glaubers salt 2 17. The cold of ice may still be considerably increased by a mixture of spirit of wine ; about a drinking-glass full of spirit of wine to a pound of beaten ice. 18. The cold of ice will not increase, unless the ice melts. Experiments. — Put into one vessel 4 ounces of ice, beaten very small, and into another vessel 2 ounces of sea-salt ; set the two vessels in a mixture of ice and salt, which is to be renewed still, till by means of the thermometer you find, that the salt and the ice of the first two vessels have acquired each of them 10 or 12 degrees of cold; then mix the salt with ice, and this mixture will not increase the degree of cold that the ingredients had acquired, because the mixtcire does not melt. But if, instead of salt, you mix with the ice spirit of nitre, cooled to the same degree as the ice, as this last is liquid, it will melt the ice, and considerably increase its cold. 19. Salt mixed with water, increases its cold. 20. Of all salts, sal ammoniac gives the greatest degree of cold;* so that if that salt has been cooled in ice, and then one part of it be thrown into 2 parts of water, cooled to the same degree in ice, that water will become colder than ice, and will freeze other water thrown into it in a small quantity. This last observation may be applied to the cooling of liquors where no ice is to be had ; for there is hardly any place, but what has wells : now the water of a well moderately deep, wants about 8 or 10 degrees of the cold of ice; and sal ammoniac being cooled beforehand in the well, will, by mixing with some of the water of that well, come very near to the cold of ice. An Observation of the Magnetic Needle being so affected by Cold, that it would not traverse; by Capt. Christopher Middleton, F.R.S. N°449, p. 310. In the Philos. Trans. N°418, Capt. M. mentioned a strange phenomenon relating to the sea-compass, which he had frequently observed, when among * Mr. "Walker of Oxford has shown that there are other salts which are preferable to sal ammoniac for producing artificial cold, and particularly muriate of lime. See Phil. Trans, for 1795 and 1801. VOL. XL.] PHILOSOPHICAL TRANSACTIOH8. 225 the ice in Hudson's Bay, viz. that the magnetic virtue of the needle was so far lost or destroyed, that it would not traverse as usual, even when the ship was in a considerable motion: and in his voyage thither last year, he observed the compass would not move at all, any longer than the quarter-master kept touching it. There was then much snow on the land, and many isles of ice around them, and the sea not very smooth: he ordered one of the compasses to be brought into the cabin, but did not find it any better, till it had stood near the fire about -^ of an hour, and then it began to traverse very well; he then ordered it to be placed in the binnacle, and another to be brought into the cabin, changing them alternately thus every half hour, and found by this means he could make them traverse as well as in any other part of the world. He was obliged to continue this practice, till near 100 leagues from the coast ; but afterwards he had no occasion for that trouble What should be the cause of this wonderful phenomenon he could not conjecture, being certain the com- passes, as to their mechanical structure, were very perfect, and answered very well both before and after, during the whole voyage. Concerning an uncommon Palsy of the Eye-lids. By Dr. jindrew Cantivell of Monlpelier. N" 449, P- 3 1 1 . A lady, about 30 years of age, was troubled with a very singular disease. It was an intermitting periodical palsy of the eye-lids, which began every evening about 6 o'clock, with a defluxion from the great canthus, of a whitish matter of some consistence ; so that she remained blind till next morning, and then recovered the use of her eye-lids as before. This disorder held her for 4 months ; from which lime all remedies ordered by her physician proving ineffectual, she was sent to Baleruc for the benefit of the waters. As Dr. C. lodged in the same house, he had a fair opportunity of observing the efFects the waters had on her. She was pumped on the back part of her head and neck 7 times, without receiving any sensible benefit : the Qth time her disorder seized her an hour later than usual, and the defluxion was less and thinner. The next evening it retarded 1 hours, and the following night she had as much command of her eye-lids as ever. She took the douche, for so they call that way of pumping, the next morning and evening, and was entirely cured. Dr. C. sat with her an hour that evening, carefully observed her eye-lids by candle-light, and asked her several questions on her disorder. She opened her eyes as well as he did his, and set out the next day for Montpelier. VOL. via. G G 226 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. An Account of the Man whose Arm with the Shoulder-blade was torn off by a Mill, Aug. 15, 1737. By Mr. John Belchier, F. R.S. N° 449, p. 313. Samuel Wood, about 26 years of age, being at work in one of the mills near the Isle of Dogs, over-against Deptford, and going to fetch a sack of corn from the farther part of the mill, in order to convey it up into the hopper, carelessly took with him a rope, at the end of which was a slip-knot, which he had put round his wrist ; and passing by one of the large wheels, the cogs of it caught hold of the rope, and he not being able to disengage his hand instantly, was drawn towards the wheel, and raised off the ground, till his body being checked by the beam which supports the axis of the wheel, his arm with the shoulder-blade was separated from it. At the time the accident happened, he says he was not sensible of any pain, but only felt a tingling about the wound, and being a good deal surprized, did not know that his arm was torn off, till he saw it in the wheel: when he was a little recovered, he came down a narrow ladder to the first floor of the mill, where his brother was, who seeing his condition, ran down stairs immediately out of the mill to a house adjacent to the next mill, which is about 100 yards distant from the place where the accident happened, and alarmed the inhabit- ants with what had happened to his brother; but before they could get out of the house to his assistance, the poor man had walked by himself to within about 10 yards of the house, where, being quite spent by the great effusion of blood, he fainted away, and lay on the ground; they immediately took him up, and carried him into the house, and strewed a large quantity of loaf-sugar powdered into the wound, in order to stop the blood, till they could have the assistance of a surgeon, whom they sent instantly for to Limehouse; but the messenger being very much frighted, could not give the surgeon a clear idea of the accident, so that when he came to see the condition the man was in, he had no dressings with him for an accident of that kind ; but had brought with him an apparatus for a broken arm, which he understood by what he could learn from the messenger to be the case. However, he sent home for proper dressings, and when he came to examine particularly into the wound, in order to secure the large blood-vessels, there was not the least appearance of any, nor any effusion of blood; so having first brought the fleshy parts of the wound as near together as he could by means of a needle and ligature, he dressed him up with a warm digestive, and applied a proper bandage : the next morning he opened the wound again, in company with 2 surgeons more; and VOL. XL.] VHILOSOFHICAL TRANSACTIONS. 127 not perceiving an effusion of blood at that time, he dressed him as before, and sent him in the afterneon to St. Thomas's Hospital, where he was admitted a patient under the care of Mr. Feme; from which time he was constantly at- tended, in expectation of a hemorrhage of blood from the subclavian artery; but there being no appearance of fresh bleeding, it was not thought proper to remove the dressings during the space of 4 days, when Mr. Feme opened the wound, at which time likewise there was not the least appearance of any blood- vessels ; so he dressed him up again, and in about 1 months time the cure was entirely completed. On examining the arm, within a day or two after it was separated from the body, they found the scapula fractured transversely, as were likewise the radius and ulna in 2 places: but whether these bones were fractured before the arm was torn off, the man cannot possibly judge. The muscles inserted into the scapula were broken off near their insertions, but the muscles arising from the scapula came away with it entire. The latissimus dorsi and pectoralis, were likewise broken off near their insertions into the os humeri. The integuments of the scapula, and upper part of the arm, were left on the body, as also the clavicle. But it is very surprising, that the subclavian artery, which could never be got at to be secured by art, should not bleed at all after the first dressing; the artery being separated so happily, that when the coats of it were contracted, the fleshy parts pressed against the mouth of it, and prevented any effusion of blood. An Account of a Bullet which lodged near the Gullet for almost a Year. By George Lord Carpenter, F. R. S. &c. N° 449, P- 3l6. The late Lord Carpenter was wounded in the mouth, at the defence of the breach of Brihuega in Spain, by a small Spanish musket-ball, which having taken away part of his upper lip, beat out all his teeth, except 2, on one side, broke and splintered part of his upper jaw-bone, went through his tongue, and lodged itself near his gullet, where it remained i>J weeks and 3 days, before it was extracted, the surgeons thinking it had been spit out with some of his teeth soon after his being wounded. The ledge which was made on the bullet by the 2 fore teeth, lying almost by the gullet, and continually grating on it, occasioned an intolerable pain, and preventing him from swallowing any thing but liquids, it brought him so low, that his life being despaired of, to make a final trial, his tongue was drawn out as far as it could be, and one of the surgeons feeling the ball with his probe, which he then took to be a piece of a tooth, several pieces of teeth having 6 G 2 228 PHILOSOPHICAL TRANSACTIONS. [aNNO 1 738. been beaten into his tongue by the bullet, and- endeavouring to extract it, he took hold of the ledge with his forceps, and drew the ball out; after which he recovered in a few weeks. The marks of the fore teeth are to be seen on the bullet, and where it flatted upon the jaw-bone.* An Obstruction of the Biliary Ducts, and an Imposthumation of the Gail- Bladder, discharging upwards of 16 Quarts of bilious Matter in 25 Days, without any apparent Defect in the Animal Fu7ictions. By Claud. Amyand, Esq. F.R.S. N" 449, p. 317. Mr. La Grange, about 50 y6ars of age, of a sallow bilious complexion, died of an abscess in the vesica fellis. Dr. Vatas, his physician in ordinary, reports, that about 14 years before, this gentleman was afflicted with a tertian ague, which was cured by the bark, and from that time had complained of a sense of weight, and some uneasiness and hardness in the region of the liver and borborygmi, which were relieved by frequent purgations; notwithstanding which, he had enjoyed all the appearances of health, till about 4 months before his death, when some symptoms of the jaundice first began to appear on him, which had greatly increased 5 or 6 weeks before he died, when he began to complain of shooting pains on the right hypochondrium ; which was soon followed with a hard inflammatory tumour there, tending to suppuration. May 4, Mr. A. met Dr. Vatas, and Mr. Fiquel, his surgeon, in order to open a large abscess pointing below the cartilages of the 2d and 3d spurious ribs on the right side. It was determined to open it immediately with a lancet, upon which a pint of a purulent fetid matter was discharged. The aperture being large, and the dressings easy, by the next day a very large quantity of sanies, and some pus left in the bag, had found a vent ; and this was so great, that it was thought proper to renew the dressings twice a day. This had the desired effect so far, that from this time the matter daily de- creased, till the 12th of May, when during the night the wound had discharged near 2 quarts of matter of a saffron colour, intermixed with large flakes and thick lumps of a coagulated lymph or jelly, tinged of a deep yellow; and it was surprising that on dressing they made way for the discharge of about a quart more of the same, as they enlarged the orifice of the bursted bag, to ♦ A very extraordinary narrative of a gun-shot wound, is to be seen in N" 320, of the Philos. Trans. It is the case of one Dr. Feilding, who was shot in near the eye, and after 29 years the bullet was cut out near the pomum adarai.— Orig. TOL. XL.] PHILOSOPHICAL TRANSACTIONS. 22Q favour the coming out of the large flakes and lumps of jelly, obturating at times this orifice. During this day the discharge was very great, and at night about a pint more of the same matter was emptied. From this time a short and thick, canula was left in the opening of the bursted bag, this causing a more easy and constant discharge, and a vulnerary injection, strongly saturated with spirit of wine, had the good effect to diminish it very considerably; but yet it continued so very great, that they apprehended the patient would soon sink under so great a flux of this bilious matter, and the rather that his stomach and his rest failed him; but the discharge daily lessening, and his appetite and rest returning in proportion, he recovered strength enough to be able to walk. All this while the appearances of the jaundice were wearing off, the urine was returned to its natural colour, and the patient had regularly a natural stool every day, till about 8 days before his death, when his body becoming costive, the physician found it necessary to discharge the faeces, by clysters and lenient purges. Whilst Mr. A. attended him, his belly was always free from fulness or tension, being soft and lank, and he was less troubled with wind, than he had been for many years before. Two days before he died, he went to air himself in another room, and caught cold: this is presumed to have occasioned a fever, followed with a lethargy, in which he continued till the 29th of May, when he died. On dissection, it was observed, that the patient was not near so extenuated as might have been expected, after so great a discharge of bile and lymph during 25 days ; for much fat was yet observed under the skin and elsewhere, and his flesh not much sunk from the natural state, but the blood-vessels were found extremely empty. In the abdomen, the caul or omentum was shrivelled up, and adhered to a large bag or cystis, affixed to the inside of the great lobe of the liver, and stretching from thence along the right flank, over one half of the kidney on that side. The left lobe of the liver was removed from the left side to the right, not reaching farther than the right edge of the cartilago ensiformis, and the pylorus : the ligamentum latum suspensorium hepatis, was drawn backwards into the right hypochondrium. The liver was of a natural colour, but very small, and more decayed and wasted in proportion than the other viscera, but as free as they from any preternatural adhesion, obstruction, or induration, and the bag or cystis, arising from it, strongly adhering by its outside only, to the peritoneum, down to the right kidney. On passing a finger through the wound in the integuments, it entered first into a cavity made between the peritoneum and the outside of the cystis, in which the matter of the abscess had been lodged, and then through a hole in ^do PHILOSOPHICAL TRANSACTIONS. [anno 1738. the cystis, or grand bag, through which the great collection of bile in this saccus had afterwards made its way ; and it was observed, that the strong coali- tion of this bag to the peritoneum, round that part where the pus had been collected, had shut up all communication with the cavity of the belly, and so prevented any extravasation into the abdomen Now the bag or cystis being separated from the peritoneum, and this and the liver spread on a board, it was observed that the matter had been collected in the gall-bladder, without affecting the liver itself. The vesica fellis was become a very large bladder, and extended so as then to appear capable of containing 3 pints, or more ; it was nearly as broad as long : it arose very broad from the surface of the right lobe of the liver, which it occupied about 10 inches in cir- cumference, or more: its bulk had removed the stomach and pylorus from their natural situations, and pressed them far under the left hypochondrium, and that part of the colon placed naturally on the right kidney, forwards on the spine : its surfaces were rugged and unequal, as that of a potatoe, and its coats thick and horny, forming several tumours, elongations or expansions, of different sizes and figures ; one of which, as large as a hen's egg, was full of a cretaceous matter, intermixed with hard white stones. This cretaceous bag was made in the duplicature of the vesica fellis, but had no communication with nor open- ing into it, which several other tumours, appearing of the same kind had ; whence it was presumed that some very small pieces of creta, found in the great bag, might have dropped from them into it ; but it is more likely they had dropped them there, because nothing like them had been discharged through the wound. The outer opening in this bag answered in the cavity of the abscess, where incision had been made, as this latter was formed between it and the peritoneum. In the bag were found about 2 oz, of the same bilious matter which had all along been discharged ; which being computed, must be equal to, if not exceed, the quantity of 18 or 20 quarts, during the 25 days the patient lived, from and after the opening of the tumour. It has been observed, that the liver was in a natural state, and that the matter collected in the vesica fellis, had not in the least wounded or affected the liver itself; so that the great quantity of bile and lymph daily discharged through the incision, must have proceeded from the internal surface of the distended gall-bladder. This put them on inquiring for the radices cysticae and hepatico- cyslic ducts ; i. e. for those very ducts which Giovanni Caldesi so carefully traced in several animals, and delineated in his Observ. Anatomiche al illustr. Sig. Francisco Redi 1687, and which Verheyen discovered in the bullock kind, but could not trace in man ; these ducts, by which so great a quantity of gall had been deposited in the vesica fellis^ for as much that the cystic duct was VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 231 obturated, by which some anatomists have supposed the gall to flow back from the hepatic ducts; and on dissection, Mr. A. traced a trunk, like to that which Bidloo and Winslow observed in man; and resembling that formed by several branches in the liver, and discharging itself into the vesica. He would gladly have traced this further, but the time allowed for dissection did not permit him to pursue this inquiry. The ductus communis choledochus was found empty, and opening, as usual, into the cavity of the duodenum ; but the cystic duct was so compressed by the bag, that nothing could pass through it. The spleen, pancreas, and all the other viscera, were in a natural state, except that some of them had changed and altered their natural situations. On the whole it appears, 1st, That the animal functions have been in nowise vitiated by some of the viscera having been displaced; and notwithstanding that for 25 days, the discharge of the bile through the wound had been so great, that little was left to pass into the duodenum, yet he digested his food well. The stools continued regular, till within a few days before death, and even to the last the faeces all along retained theii* natural colour. 2dly, It may be ob- served, that the jaundice was not occasioned by the obstruction of the cystic duct, though that is apprehended as a common cause of this malady; for this obstruction must have been of many years standing, and this patient's jaundice was of a very late date. Nor was his jaundice owing to any retention of the bile in the porus biliarius, from the tumour continually pressing that duct, and so obstructing the free discharge of the bile, from the glands of the liver into the duodenum and gall-bladder ; nor even to the strong compression and total obstruction of some, and almost all the biliary ducts, viz. the porii biliarii, the ductus hepaticus, the hepatico-cystic, and the ductus-cysticus, and communis choledochus, the principal of which are seated in the concavity of the great lobe of the liver, under the pressure of this great and hard tumour, and under its increase for near 14 years together, obstructions and compressions generally accounted as primary and idiopathic causes of the jaundice, because no distemper like the jaundice had appeared in this patient, till within a few months before his death, and no true jaundice till within a few weeks, and only then as the ab- scess formed in the neighbourhood of the liver had brought an inflammation there; but as all the symptoms of his jaundice began to wear off, soon after the pus had got a vent, viz. as the inflammation of the liver brought on occasionally by a suppuration in the neighbourhood wore off, and some days before the bursting of the vesica fellis, it does not appear unlikely, that this inflammation of the liver was the pathognomonic cause of the jaundice here; which inflam- mation of the liver, as it was accidental, so the jaundice occasioned by it, was 232 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. actually removed soon after a vent was made for the purulent matter, which had occasioned this inflammation. Some Observations on the foregoing Case of Mr. Le Grange. By Alexander Stuart, M. D. F. R. S. &c. N° 449, p. 325. Dr. Stuart points out what appears to be the mechanical and necessary con- nexion between these apparent causes and their effects, in this uncommon case. ], As to the original or prime cause of all the symptoms, viz. the distention of the gall bladder, now become a morbid cystis of an enormous extent. If we consider the size and figure of the liver, and the situation of the gall- bladder, with the course or direction of the biliary vessels, from various places of the liver, towards that narrow space where the pori biliarii open into the cystis, it will appear, that in almost every position of the body, at least in an erect, supine and lateral position, some of these biliary ducts terminating in the gall-bladder, are perpendicular, or nearly perpendicular, to the Horizon and to the cystis : therefore, as far as gravity takes place in the animal economy, the bile descending by these ducts, will press on the contents of the full cystis and its sides, as a cylinder of that fluid, of the length of the secretory ducts or pipes, and of the diameter of the cystis. Besides this, the extremity of every one of these small ducts, conveys its fluid into the full cystis, as a wedge acted on by the repeated strokes, impulses, or pressures of the circulating blood of the vena porta, where it supplies the gland at the origin of each secretory duct. Therefore, by the known laws of hydrostatics and mechanics, it is apparent, that the force of this secretion of the bile, into the gall-bladder, is very great, and the quantity copious; suffici- ent at least to distend the cystis to an enormous pitch, where the discharge by the ductus cysticus, is not equal to the secretion by the pori biliarii and the ductus hepatico- cysticus. These powers sufficiently account for the distention of the abdomen in an ascites, of the womb in gestation, of the bladder in a morbid or voluntary retention of urine ; also of morbid imposthumes or tumours, and of the gall- bladder in the case before us. But this distention could never have happened, without a total or partial ob- struction of the excretory duct, the ductus cysticus. Had this obstruction been at once total, as when a calculus is thrown suddenly out of the cystis into the duct, and stops it totally, he must have had the jaundice immediately, or very soon after : for, notwithstanding the strong powers abovementioned, it would VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 233 have been impossible for the sides of the cystis to have yielded to such a sudden dilatation, no more than the womb in the first week, of gestation, can be dilated to the pitch it is brought to in the Qth month, without a rupture : so that the dilatation here must have been very slow and gradual, and therefore the ob- struction must have been at first, and probably for many years, only partial ; and the gall-bladder thus slowly distended, gradually yielded and gave way, only for the reception of the excess of the secretion beyond the excretion, and so prevented the jaundice, or regurgitation of the bile into the blood. This partial obstruction of the cystic duct may probably have been occasioned by one of those small soft incysted tumours, lodged between the membranes of the cystis fellea, near the origin of its excretory duct, containing a soft white pultaceous matter, with calculi, or chalky concretions, in its centre. If this was the case, it is conceivable that while the contents of this small incysted tumour were fluid or soft, they might not be capable to obstruct totally the current of the bile through the excretory duct : but as the matter of it grew thicker, and its bulk, increased, by pressing gradually more and more on the duct, the obstruction must increase ; and the formation of calculi, by their pressure, must at last make the obstruction total. But as the cystic duct was, at opening of the body, entirely coalesced and obliterated, its vicinity and situation, with respect to these small incysted pultaceous and cretaceous tumours, cannot be precisely determined ; and therefore this is offered only as a probable con- jecture. The bulk, contents, and adherences of the gall-bladder to the right side, were doubtless to him a very sensible, and to us a visible cause of his first symptom, the increasing weight he had felt in the region of the liver, for 14 years before his death. The current of moving humours in the animal body, is always determined most strongly to the place of least resistance : therefore, by the partial ob- struction of the cystic duct, a greater quantity of bile than usual will be forced on the biliary ducts, leading directly from the liver into the great hepatic duct, to discharge itself by the choledochus communis into the duodenum, suflicient for the moderate uses of the animal economy ; though not so perfectly suflicient, but that the peristaltic motion, in this case, felt the want of the cystic bile, or at least the defect of it so far, as to become weak and imperfect, too weak to propel the excrements, or keep the elastic air within due bounds; and therefore the patient must be subject to flatulent distentions, and some degree of costivc- ness, only to be relieved by supplying the want of a suflicient natural stimulus of the gall, by the artificial stimulus of purgatives and clysters, to assist from VOL. vnr. H h 234 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. time to time the expulsion both of the excrements and also of the flatuses, for the ease of the patient, as was practised in this case. As to the jaundice, which began to show itself 4 months before his death, and continued increasing, till the external purulent tumour in his side was opened, when it began to decline, and quite disappeared soon after the gall- bladder burst : it is easy to conceive, that so long as the gall, descending from the pori biliarii, could make its way into the cystis fellea, and dilate it, there could be no regurgitation of the bile into the blood, and therefore no jaundice: but as soon as the purulent imposthume began to form itself in the neighbourhood and contact of the distended gall-bladder, it encroached or pressed on the cystis fellea, by the force of a multitude of vessels, pouring pus into the cavity of the imposthume, urged on by the circulation of the blood, which is more forcible in these vessels than in those of the liver: and therefore this purulent tumour in- creasing, will very forcibly encroach on the cystis fellea in contact with it, and not only hinder its further distention, but even force the gall it contains to re- gurgitate, or return again by the pori biliarii upwards, and from thence, by the capillaries of the vena cava, into the blood, and so produce the jaundice ; with- out raising an inflammation or obstruction in the liver itself, whose vessels and passages remain open, though the bile take a retrograde course in its biliary secretory ducts. But as soon as this accessory pressure is taken off^ from the cystis fellea, by opening and emptying the purulent tumour or imposthume in its neighbourhood, adjoining and adhering to it, the bile begins again to flow freely into the cystis fellea, and to dilate it as before; therefore the regurgitation of the bile into the blood ceases, and the jaundice begins to decline. Then, as soon as the rupture or bursting of the gall-bladder happened, and it began to be emptied, all degrees of resistance being now totally taken off from the pori biliarii, they spew out their contents so copiously, that the hepatic ducts are gradually frustrated by such a strong revulsion ; the bile begins to flow all to the wounded and almost emptied cystis biliaria, and either very little or none to be carried by the ductus hepaticus to the choledochus communis, whose diameter and passage into the duodenum was found larger than usual, but empty. In this state, which was the last stage of his distemper, the peristaltic motion begins ta fail, the expulsion of the excrements to be very tardy, or not at all to succeed without the assistance of purging medicines or clysters, which also had but a very slender effect; the patient ceases to be nourished, though he takes a competent quantity of food, and dies in a week after this costiveness began. The degree of perfection of the natural, vital and animal functions in this VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 235 person, during 14 years indisposition, was certainly owing to the soundness of all the viscera, and an almost sufficient secretion and excretion of bile by the ductus hepaticus, into the choledochus communis, whose cavity and passage into the duodenum was large and open, which could not have been and have continued, without a continual and proportional flux of bile through it : for it is well known, that as soon as the fluids cease to flow through their natural ducts, their sides soon collapse, coalesce, and at last totally shut up. Thus the uraclius, and canalis arteriosus Botalli in the foetus, shut up totally soon after the birth ; and Mr. Amyand and Dr. S. have seen one of the ureters totally coalesced and shut up, for want of a fluid from the kidney, which had secreted no urine for some time, having become a cystis, filled with a thick white pulta- ceous matter, nearly of a cretaceous consistence. Therefore, as the cystic duct was found obliterated, and the choledochus communis large and open, it is plain that no bile had for some time flowed through the former, and that there was a constant supply from the hepatic duct to the latter, for the uses of the animal economy ; until the wound or rupture of the gall-bladder, gradually abating its current by that channel, at last stopped it quite, and put an end to life in a few days after. The apparent Times of the Immersions and Emersions of the four Satellites of Jupiter, for the Year 1 740, computed to the Meridian of the Royal Observa- tory at Greenwich. By James Hodgson, F. R. S. In all 374. N° 449, p. 332. This is another repetition of Mr. Hodgson's usual calculation of these eclipses. A Continuation of an Account of an Essay towards a Natural History of Caro- lina, and the Bahama Islands; by Mark Catesby, F, R. S. with some Extracts out of the Qth Set, by Dr. Mortimer, Seer. R. S. N° 44g, p. 343. The extracts and account of the 8th set are inserted in N°441 of the Phil. Trans. This Qth set begins with pi. 6l, of the 2d vol, and as the foregoing treated chiefly of serpents, this contains the figures and descriptions of several quadrupeds, intermixed with plants. HH 2 2SG PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. MatthicE Belli, Pannonii, R. S. Lond. S. &c. Observatio Historico-Physica de ^4quis Neosoliensium JEratis, vulgo Cement- Wasser dictis, Ferrum jEre permutantibus, in Epistold ad illustr. Dm. Hans Sloane Bart. &c. scripid, co7nmu7iicata. N° 450, p. 351. This pnper gives an account of tiie copper waters (cement-wasser) in the copper-mines near the town of Neusol in Hungary. The rain, or spring water, as it percolates through the sides of the excavations worked in these mines, be- comes impregnated (from its action on the copper-pyrites) with vitriol of cop- per, and is conveyed by numerous channels into large wooden cisterns, or re- servoirs, placed in various parts of the mines. When pieces of iron are thrown into the water collected in these reservoirs, and are suffered to remain therein for a sufficient length of time, they are, according to the belief of the vulgar, turned into copper ; i. e. the copper is precipitated upon the surface of the iron in its metallic state.* It is afterwards scraped ofFfrom the iron, and melted and wrought into a variety of utensils. The copper thus obtained is found to be exceedingly pure.-f- — Respecting the proportion of vitriol of copper in this so called ceinent-water, Mr. B. states that Ibj (medicinal weight) of the said water, when evaporated to dryness, gave giiss of residuum, which, being dissolved in pure water, yielded a green solution. When this solution was afterwards filtered and evaporated, Mr. B. obtained 9ij of crystallized vitriol, [vitriol of copper] besides 0 grs. of a yellow precipitate. Of a Bubonocele or Rupture in the Groin, and the Operation upon it ; by C. Amijand, Esq. Serjeant-Surgeon to His Majesty, and F. R. S. N° 450, p. 36l . October 8, 1737, Mrs. Bennet, 70 years of age, of a thin habit of body, *Tliis apparent transmutation of iron into copper is easily explained by the laws of chemical attraction. The vitriolic acid, with which the copper is combined in the so called cement-water, having a greater afBnity for iron than for copper, it deserts the latter to unite with the former. Accordingly, when a piece of iron is thrown into such water, it is immediately acted upon by the vitriolic acid, that acid dissolving and combining with a portion of the iron, and letting fall the copper in its metallic state, which, during its precipitation attaches itself to the surface of the undissolved portion of iron. There is, therefore, in this instance no transmutation of one metal into another ; but merely a de- composition and a new chemical union produced by the force of elective attraction, the iron being combined with the acid in place of the copper, and the latter being precipitated in its metallic state. t This mode of obtaining copper is practised in many other countries besides Hungary, the water collected in, or issuing from most copper mines holding more or less vitriol of copper [sulphate of copper] in solution. Considerable quantities of copper are annually separated from the water of the copper-mines in Anglesey by means of iron, as at Neusol. VOL. XL.j PHILOSOPHICAL TRANSACTIONS. 237 had a return of a tumour in the groin, with unusual pains, which was soon fol- lowed with an excruciating pain in the belly, and such colics, retchings, and excreinentitious vomitings, as usually attend the strangulation of the gut in the miserere mei. This came upon her unawares, and the distress she was in, made her forget that for '25 years before she had had a swelling in the groin, as large as a hasel nut, which seldom had given her any uneasiness, and which she never suspected to be a rupture. Latterly the patient had been more subject to colics than usual, but this was imputed to bad digestion ; and that day she had used no motion capable of producing a rupture ; so that it was by chance that Mr. Despaignol, who was sent for the next day, discovered the cause of the com- plaint. She was blooded, clystered, fomented, &c. ; but the complaints sub- sisting with a continual singultus, Mr. A. was called in the 1 1th. The tumour was then oblong, about the size of a hen's egg, somewhat in- flamed, yet not tense, nor so painful as to make him take much notice of it. On the repeated use of the abovementioned means, and of lenient purges and opiates, the vomitings and hiccough were at times stopped, and the patient made so much easier, as to give hopes of success ; but as during 6 days the patient had no passage, and the tumour could not be reduced, it was thought unsafe to delay the operation any longer. The tumour felt unequal, though it appeared even, and pappy, as the tumours of the omentum generally are ; and therefore of that kind which is always most difficult to reduce, the omentum not having that elastic springiness which favours the replacing of the guts. On dissection, it was found embodied in the hernial bag, and that upon the external surface of the slits in the abdominal muscles, the folds of it had formed a round protuberance, not unlike the os tincae in the vagina, or like a bourlet which, by compressing the gut, prevented its return into the belly, and by ob- structing the opening, as the gut pressed upon it, had strangulated about an inch of the gut encompassed by it in the hernia. This being the 6th day from the beginning of this disorder, the gut in that place was found of a very swarthy colour, but yet springy ; so that it was not quite mortified. It lay inclosed in a net, formed by the omentum (like a fish in a fishing-net) strangulating the gut under its pressure without the abdominal muscles. It was with some difficulty the omentum was torn off and separated from the bag it was attached to ; and as this lay in the way of the reduction of the gut, and almost sphacelated, so it was cut ofF without any previous ligature, though its vessels were turgid and large, as it was impossible to pull it out so as to make the ligature upon the sound part of it ; after which the reduction of the gut 238 PHILOSOPHICAL TRANSACTIONS. [anNO J 738. might easily have been made, without enlarging the annular slit; for this made no stricture to prevent it. But the quantity of the omentum within it being large and bulky, and the gut in a very diseased state, it was thought more expedient to enlarge it, to make the reduction of the whole easy : afterwards the omentum was detached from its adhesion round this place, and pulled farther out, and a ligature being made upon the sound part of it, that was also replaced in the belly, and the entrance stopped with a conical tent, dipped in the yolk of an egg, &c. the belly was embrocated, and the dressings well secured ; for as the patient was very much oppressed with an asthma, so she was obliged to be sitting in bed. From this time the hiccough and excrementitious vomitings disappeared, but the retchings and vomitings continued near 5 days longer, before the faeces de- tained above the strangulated gut, could make their way downwards, though they were frequently visited by clysters and lenient purges. The patient was blooded immediately after the operation, and soon after took an emollient and carminative clyster, which was repeated night and morning, and an oily laxative every 4 hours. A.t first the evacuations were exceedingly fetid, black, griping, and frequent ; but they became more moderate, as she took absorbents and diluents ; but yet so frequent, that it was thought proper to restrain them by gentle astringents. In 5 or 6 days the stools had removed the tension which appeared on the belly after the operations ; the retchings and vomitings, and the remaining symptoms went off, the wound digested well, and the patient continued in a mending way. It has been already observed, that this old woman was very much afflicted with an asthma: she had at times violent fits of it, and the 14th day from the operation she had one, with a total stoppage of the discharge from her lungs, which choaked her on the 17th day. This case was a proof of what Mr. A. had frequently observed, on similar occa- sions, viz. that as the omentum is the principal obstacle to the reduction of theguts in ruptures; so it is the occasion of the greatest accidents that attend that evil. It wraps up an^ incloses the prolapsed gut like a net, whose fastened end within the belly strangulates the part detained in the rupture without the abdominal apertures, where it is confined, and is productive of such folds in it, and pres- sures of the gut wrapped up therein, as is oftener the cause of a strangulation and miserere mei, than the tendinous slits of the external oblique muscles in the inguinal rupture, or tendinous opening in the navel, which upon these is seldom found inflamed, and can never contract so suddenly, as to obstruct the return of the gut into the abdomen, when the omentum is wanting : agreeably VOL. XL.] PHILOSOPHICAL TRANSACTIONS. ' 389 to which, it is rare to find any strangulated rupture that is not attended by it. The pain attending the prolapsus soon swells the vessels of the omentum, and that will fill up the apertures in the abdominal muscles, through which the viscera are fallen out, so as to prevent their return, and bring on an inflamma- tion : if by plentiful bleeding the vessels emptied do not facilitate the return of the parts prolapsed, then all the consequences follow that are generally observed upon the like occasion ; and if blood-letting with the remedies before mentioned do not produce the desired effect soon, it is very seldom that any thing is got by the application and use of all the other means prescribed. It is however certain, that it is very dangerous to depend too long upon those remedies, and that a suspension of the symptoms is no security, whilst the due course of the faeces is interrupted. The case here mentioned may be a warning to others not to delay too long an operation, whereby the parts are to be released from confinement, and which oftener would be successful, if it was not delayed so long. An Account of a Pin taken out of the Bladder of a Child. By Mr. William Gregory, Surgeon. N° 430, p. 367- Mr. G. was called to the assistance of a woman in travail. The foetus pre- sented in a transverse position; he soon recovered the feet, and in a few minutes delivered the woman. The funiculus umbilicalis was so short, that it was with difficulty he could make a ligature on it, in order to make a separation : he im- mediately extracted the secundine, and measured the funiculus, which was little more than 4 inches long. As soon as the woman was taken care of, he examined the child, which he found to be imperfect in several parts, there being no anus, neither privities to distinguish of what sex it was : where the vulva should be, there was a small perforation, though no appearance of labia, through which the urine always passed away ; there was likewise a large hernia umbilicalis, and a little lower in the linea alba, was a perforation, into which the intestinum rectum opened, and there the excrements passed during the time the child lived, which was almost 10 weeks. Several days before the child died, a gangrene appeared on the hernia, which soon passed into the intestines, and occasioned its death : the hernia, in his opinion, was occasioned by the shortness of the funiculus, which did not grow in length j)roportionable to liie foetus ; the child in all other parts was perfect. When the child died, he had liberty from the parents to inspect into it: he did 240 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. not go through a regular dissection ; but only inspected into the intestinum rectum, which he found as above described, and the urinary bladder, which he found very small, and no urine in it ; the child was never observed to make water in a stream whilst it lived, which makes him of opinion, the sphincter vesicae was imperfect. In handling the bladder, he found something sharp pointing to his finger ; he could not discover what it was, till he snipped off the neck of the bladder : he then took out of the bladder a tough kind of sub- stance, about as large as a small fig, in which was a pin with the head on, and very black. Of a very extraordinary Calculus taken out of the Bladder of a Man after Death. By the Marquis de Caumont. N° 450, p. 369. The Marquis de C. states that he was induced to send to the President of the R. S. the drawing of an uncommon stone, found lately in the bladder of a dead body, which he had engraved in his own presence. It is exactly conformable to the original. The most able physicians, and the best anatomists, assured him that they never saw any thing like it. He can vouch, that the engraving, though very exact, does not come up to this singular work of nature ; the 10 branches of which, that spread from the centre, have some resemblance to those of certain plants. It was a matter of difficulty to think, that the system of juxt-apposition, which is employed to explain the successive growth of com- mon stones or calculi, can hold good on this occasion. He dares not however advance, that vegetation has any share herein : though the shape of the branches of the stone, of the canals, or papillae, which seemed destined to convey the nutritious juices, in some measure favoured this hypothesis. He thought proper to join to the figure of the stone, the account of the patient's distemper, in whose bladder it was found ; as Mr. Salien, sugeon of Lisle in the county of Venaissin, sent it to him. The fact, of itself, cannot fail of ap pearing curious. And skilful lithotomists may reap some advantage by it, for perfecting their operations. For allowing the possibility of calculi of a confor- mation somewhat like this, which they may judge of by knowing the bulk ol the stone, they will understand, that in such a case, no other method but that of the high operation can facilitate the extraction of an extraneous body, whose branches cannot fail causing considerable lacerations ; unless they found some favourable circumstances, and that the contexture of it were brittle enough to break it before being extracted. 1 VOL. XL.J PHILOSOPHICAL TRANSACTIONS. 241 ^4n Account of the abovementioned Case. By Mr. Salien, F. R. S. N° 450, p. 37 I . ' Joseph Vasse, of Le Thor, a small town at a short league's distance from Lisle, in the county of Venaissin, 6& years of age, of a robust constitution, who used to travel about to fairs and markets in that county, dealing in corn and cattle, without having ever complained of any indisposition, began, on the 14th of February 1731, to feel in the night-time some difficulty of making water, attended with a smarting about the glans; which however did not hinder him from attending his business as before. On the 28th of March 1732, he was seized in the night with a true iscuria, which cruelly tormented him. M. Salien was sent for on the 29th in the even- ing, to search him, and to draw off the urine. He drew accordingly 6 cups, each containing 1 pint and a quarter. The patient found immediate ease, and continued without pains or fever, so that he thought himself quite cured. But the night following the pains returned, which made him resolve to come to Lisle, to be nearer at hand to be sounded. He came on the 30th of March ; and had his water drawn off regularly every day, morning and evening, till the 15th of April next, during all which time the patient suffered no pains, did not fall away, nor had any symptoms of sickness upon him. On the 15th of April, he supped with his usual appetite; but half an hour after supper, he was seized with a violent shaking fit, which lasted a full hour, on which a burning fever ensued, attended with an unquenchable thirst, with great head-ache, and an extraordinary restlessness. In this condition M. S. found the patient about 8 in the evening, being the hour he usually went to sound him. He immediately prepared himself to draw off his water, according to custom, thinking thus to procure him some ease. Till then the catheter had entered without any obstacle ; but this time, on pushing it into the bladder, he felt a stone which obstructed its passage. He turned the catheter to the left, and hit upon one of the branches of the stone, as represented fig. 1, pi. 7- In order to know whether there was not another stone, he drew the catheter a little back, turning it to the right, which was done without any difficulty; and having pushed it in again, he met with another branch of the same stone, which he took for a stone different from the former, and concluded then, that he had found several stones in the patient's bladder ; and that if the bad symptoms which appeared, should continue any longer, there was no probability of his re- covering. Accordingly, the hiccough coming on him on the 20th, and the VOL. vni. 1 1 24'i PHILOSOPHICAL TRANSACTIONS. [aNNO J73S. other symptoms not discontinuing, he died on the 28th. The stone was taken out 4 hours after his death. Concerning the abovementioned Stone, By Sir Han^ Sloane, Bart. Pr. R. S. N" 450, p. 374. The abovementioned stone is so singular, that among some hundreds of those in the possession of Sir Hans Sloane, he had none that came near it. Once indeed he had under his care a gentleman between 6o and 70 years of age, who had extraordinary difficulties in making water, and an inconveniency even beyond that ; which was, that he could not sit in an ordinary chair with- out suffering extremely in the region of the peritonaeum. With the help of lenient soft medicines and waters, he voided by the urethra a stone, which was flat in the middle, and smooth, but had five points, resembling the rowel of a spur. The points of the rays were sharp, but there were no asperities or crystallizations on their surfaces. It was small, so as after many days to pass along the urethra : but if it had not passed through the neck of the bladder, but remained in the bladder, it would, in all probability, have attracted matter to all the points or rays, and increased in all dimensions. It is very common, that when any extraneous solid substance gets into the bladder, there is either attracted to it, or adheres to and surrounds it, a tartare- ous calculous concretion, which assumes the figure of the said body then in its centre, as a nucleus. There was a soldier cut in St. Thomas's Hospital, London, for the stone, which, when taken out, was found to cover a musquet-bullet, that had been shot into his bladder, where it was covered by a calculous concretion. Sir Hans S. had a silver bodkin, which a gentlewoman used for her hair; and thinking with it to thrust back a stone that was engaged in the neck of her bladder, it slipped into it, and the calculous matter gathered on the larger end into a stone of an oblong figure, and equal thickness, of half an inch all round the bodkin. He had also a common pin, which by some means had got into the bladder of a young woman, and was there coated all over by a calculous matter ; but having occasioned a fistulous ulcer in her groin, it was discharged thence with the matter of the fistula. It is in this manner that bezoars are formed : for he had the common East- India bezoars, which are roundish, and had in their centres the seeds of a sort of acacia, which had attracted, or was coated over by that substance, esteemed a great cordial or alexipharmac ; while others are long, and were gathered in VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 243 layers or coats on the stalks of vegetables. And he had one formed round the stone of that great plum, which comes pickled from thence, and is called mango. As to the asperities or prickles on the rays, they were noticed, so long since as the time of Cornelius Celsus, who, lib. T , c. 26, calls them calculi spinosi. It may seem very strange and paradoxical, what he can assert is true, that the fewer the knobs, asperities, or prickles, are on the surface of calculi, the more troublesome they are to the persons in whose bladders they lie. Dr. Hickes was the most tormented with the stone in his bladder, of any he ever knew, espe- cially on any motion. He would not submit to be cut for the distemper, on account of his age, and many other reasons ; but ordered his executors, that he should be opened after death, and the stone taken out of his bladder, put into a silver box, and given to Sir Hans, who had been his physician for manj years, to place it in his collection of such kind of curiosities. It is very parti- cular in this stone, that the protuberances and prickles on it were few, and at a distance from each other. Every one of them had made a hole in his bladder, like a sheath or socket ; and when, upon motion, they were removed out of their corresponding sheaths, they hurt the bladder in the sound parts, and put him on the rack of pain. When they are thick-set, one hinders the other from entering or wounding so deep; and perhaps gets not much farther than the mucus which lines the in- side of the bladder. An Account of some Oil of Sassafras crystallized. By Mr. John Maud, F.R.S. N° 450, p. 378. Mr. M. observed that some essential oil of sassafras, which had stood exposed to a frosty night, in an open vessel, was changed, 3 parts out of 4, into very beautiful transparent crystals, 3 or 4 inches in length, half an inch in thick- ness, and of an hexagonal form. These crystals subsided in water, were indissoluble in it, inflammable in the fire, and when exposed to it, melted into their pristine state. Hence it was evident, that they still retained the natural qualities of an oil, though they ap- peared under a different modification of their constituent parts. What was most remarkable, was the metamorphosis from a fluid to a solid body, of such a particular figure, and from a yellowish liquor, not unlike Madeira wine, to a very pellucid body, like ice congealed from the most transparent water. This seemed to afibrd a new instance of crystallization, which being generally accounted for by the particles of a fluid, or those of any 112 244 PHILOSOPHICAL TRANSACTIONS. [anNO 1738. other body, suspended by the fluid, brought nearer by cold, and at length conning within the sphere of each other's attraction, united together into an immediate contact. This being one of the heaviest oils, and even heavier than water, is the more likely thus to unite, as its parts are nearer together. This may be a hint to the curious, to discover in what the difference between solidity and fluidity consists; and also shows how much the colour of bodies depends on the mechanical situation of their parts.* Of an extraordinary Damp in a fVell in the Isle of Wight. By Mr. Benj. Cooke, F.R.S. N°450, p. 379, In June 1733, a farmer, in hopes of finding a perpetual spring of good water, sunk a well of 7 feet diameter, to the depth of 45 feet, through a soil which at the surface was a kind of brick earth mixed with sand, but in descending became almost wholly hard coarse yellow sand. The work em- ployed the labourers about 20 days, without finding the least appearance of water. At the distance of about ] 8 feet from the top, a stratum of a mineral mix- ture, about 9 inches thick, was dug through, without any inconvenience; nor were the workmen in the least incommoded in carrying on the work, till about the 12th day after, when towards the evening they were much annoyed with a faint suflbcating heat, which they compared to that coming from the mouth of an oven, and which, as they were drawn up, was most remarkably per- ceived, when they came opposite to the mineral stratum abovementioned, to come out in the form of a warm sulphureous halitus. The next morning, a lusty young man attempted to go down, hand over hand, as the workmen call it, by means of a single rope, which was used to draw up the earth dug out ; but as soon as he came opposite to the above- mentioned stratum, he became incapable of sustaining his own weight, but fell down to the bottom, and died immediately. Another young man, not suspecting the cause, had the rope nimbly drawn up ; and having seated himself astride a cross-stick fixed to the rope for that purpose, was hastily let down to his friend's assistance ; but when he came to the same distance from the top, he was observed to give the rope a very great shock, and when he came to the bottom, fell down, as the other had done before him, was seized with violent convulsions, which held him more than a quarter of an hour, and then he expired. ■ • See a like crystallization from Thyme, by Dr. Neumann, which he calls Camphora Thvmi, N" 38,9 and 431, of the Phil. Trans. — Orig. VOL. XL.] PHILOSOPHICAL TRANSACTIOKS. 245 A third person, in hopes of fetching up this second before he was quite dead, was tied fast into a large basket, and let down with more caution ; but when he came to the same stratum, finding his breath going, as he expressed it, he cried out, and was drawn up again; but remained in the open air for the space of near half an hour, pale as dead, panting and speechless. The dead bodies were, within three hours space, drawn up by the help of a sort of tongs, used to fetch things up from the bottom of the sea ; but brought such a disagreeable stench in their cloaths with them, as made several hardy men, who assisted in doing it, vomit. The next day a cat was let down, and at the same place seized with convul- sions ; but being drawn quickly up again, soon came to herself; which experi- ment was repeated several times for some weeks following, by which it was found, that this destructive vapour was sometimes of a greater and sometimes less force, and sometimes quite gone, so that the cat felt no uneasiness; and a lighted candle, which would sometimes be immediately extinguished as soon as it sunk below this deadly stratum, would burn clearly at the very bottom. It was very remarkable, that there was a whitish fog in the well, so thick that one could but just see the dead bodies through it. Water being scarce in that place, the well was left open for about 8 months, in hopes the damp might at last wholly leave it ; but instead of that, it became worse; and not confining itself within its first bounds, it overflowed at the top, where, when the air was moist, it appeared like a thin white fog; and when the air was dry, could be perceived like a warm breath, at all times dif- fusing a sulphureous stench, something like that which arises from filings of iron, while corroding with vinegar, affecting those who came into it with a giddiness, shortness of breath, and propensity to vomit ; so that at last the well was filled up, being troublesome to the family which lived near it. The stratum abovementioned, which is continued to the neighbouring clift, where, when heated with the summer's sun, it gives a noisome sulphureous smell, and is, after moderate rains, covered with a yellowish efflorescent salt, very astringent and acid. — On the shore below there are gathered pyrites. P. S. The vein which was cut through in the middle of the well, from whence were emitted the fatal effluvia, is a crude ore made up of iron, sulphur and acid salts, mixed with pyrites. These effluvia were not perceived till after the vein had imbibed the air for several days. While the air continued dry, these effluvia subsided, and lay in the lower part of the well, which seemed filled near to an exact level with the stratum from whence they came. But when the weather became rainy, the quantity as well as the impetus of i46 PHILOSOPHICAL TRANSACTIONS, [aNNO 1738. the effluvia increased to such a degree, as to appear in mornings over the top of the well, in the form of a mist, and gave great annoyance to those who came within its sphere of action. From hence it is worth observing, that the same damp, according to the variation of the weather, is specifically heavier or lighter than the air. Concerning Magnets having more Poles than two. By Mr. John Eames, F. R. S. N" 450, p. 383. The sagacious Dr. Halley, in his account of the changes of the variation of the magnetic needle, on the hypothesis of the earth's being one great magnet having four magnetic poles, tells us, that he had found two difficulties not easy to surmount; the one was, that no magnet he had ever seen or heard of, had more than 2 opposite poles, whereas the earth had visibly 4, if not more, &c. On looking over the copy of the Journal-book of this honourable society. Vol. 2, an article is in the following words : July 20, 1664, " Mr. Ball produced several loadstones, and among them two terrellas, whereof one seemed to have 4 poles, with a circle passing be- tween them, of no virtue at all. Some of the company suggested, that it was probable this stone consisted of two stones, by nature cemented together by a piece that had no magnetical quality in it; and if single, whether the re- spective poles were opposite." ^n Account of some Magnetical Experiments, By J. T. Desaguliers. N° 450, p. 384. In the year 1715, trying some experiments on a very large weak loadstone, the Dr. found that it had several poles. He then tried several other loadstones, and often found 4 poles in such as had been armed when he took off their armour. In large coarse stones he found sometimes 8, 9, or 10 poles. This made him believe that all loadstones had several poles; but when he tried Lord Paisley's loadstones, and other very good ones, he then found that homogene- ous loadstones had but 1 poles ; those that have more being only an aggregate of magnetic and other matter, which makes a heterogeneous substance. Such is the society's great loadstone; for it has several poles. An Account of some Magnetical Experiments made before the Royal Society, By the Rev. J. T. Desaguliers, LL. D. F. R. S. N° 450, p. 385. Dr. D. took a bar of iron, of l-4th of an inch diameter, which having been i VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 247 15 years in an erect position, had acquired a fixed pole at top, so that the end which had stood uppermost attracted the north end of a compass-needle, and the other end the south end of the needle; and having susjjended it by a string for the space of half a year, it acquired a fixed south pole at that end, as well as it had done at the other in the time of 15 years, without diminishing the virtue of the other end : so that both ends of the rod in any situation attracted the north end of the compass-needle. That rods of iron untouched, or which have not acquired a magnetic virtue by their situation, will with their upper end, whatever end of the bar be held upwards, attract the north end of the needle, and the lower end of the bar the south end of it, is a truth known many years ago, and mentioned in Dr. Brown's book of vulgar errors. SoTne further Magnetical Experiments made before the Royal Society. By Dr. Desaguliers. N° 430, p. 386. It is well known, and has been often found by experience, that an iron bar untouched by a loadstone, will, with its upper end, attract the north end of the needle of a compass, when the said bar is held upright, and the south end of the needle with its lower end, when applied to it, still in a perpendicular position, whatever end of the bar be held up ; unless the bar has acquired a fixed pole by having been long in a vertical position. But if the bar, from a vertical, be brought to a horizontal position, the needle will return into the situation it had before, which was in the magnetical meridian, the bar being then at right angles to it. On raising or sinking the end of the bar which is farthest from the needle, the one or the other end of the needle will begin to move towards the bar. Such a bar has in itself no fixed magnetic virtue; but if it had, it must be heated red-hot, and then cooled in a horizontal position. A bar thus prepared, is fit to make the following experiments, communicated by M. du Fay. Hold the bar upright, and give it a blow or two against the ground with its lower end ; and that end will attract the south end of the needle, when the bar is held horizontal, and at right angles to the magnetic meridian : the other end held horizontal in the same manner, will attract the north end of the needle. Invert the bar, and its virtue will be lost by striking as many blows with it against the ground with the other end : then strike another blow or two, and the end which attracted the north end of the needle, will now attract the south end ; and so vice vers&, the position being still horizontal. , '248 VHILOSOPHICAL TRANSACTIONS. [aNNO 1738. If the blow be given against the ceiling, or any horizontal body, with the upper end of the bar, the same virtue will be communicated as before. This will likewise happen, if the upper or lower end of the bar be struck with a hammer or mallet; whether the blow be given end-wise or at right angles to the bar : nay, though it should be given in the middle of the bar ; the position of the bar at receiving the blow being all that is requisite; for if you give the bar only a jerk, or shake in that vertical position, it will receive the virtue, as if there were in the iron several threads or beards fixed at one end, as M. Du Fay supposes, which the blow or shake laid all one way, and which were placed the other way by inverting the bar, and then giving it a shake or blow. When the bar is placed horizontally, a blow in the middle destroys its virtue. Of an Antique Metal Stamp, in the Collection of his Grace Charles Duke of Richmond, Lenox and Aubigny, F. R. S. &c. being one of the Instances, how near the Romans had arrived to the Art of Printing ; with some Re- marks by C. Mortimer, M. D. Sec. R. S. Land. N" 450, p. 388. Since arts and sciences, especially statuary and sculpture, were arrived at so great perfection, when the Roman empire was in its glory, as the many beau- tiful statues, the exquisite intaglias, and the fine medals, which time has de- livered down to us, sufficiently evince ; it is much to be wondered at, that they never hit upon the method of printing books. The dies they made for their coins, and their stamping them on the metal, was in reality printing on metal ; their seals cut in cornelians and agates, and their pressing them on dough and soft wax, was another sort of printing; and a third sort was the marking their earthen vessels, while the clay was soft, with the name of the potter, or the owner the vessel was made for. These being of a larger size, were properly called signa; the seals cut in stone were called sigilla; sigillum being a diminutive of signum, as tigillum is of lignum: but the later and more barbarous Latinists have formed the diminutive of signum into signetum; and if a very small pocket-seal, they have called it signaculum. See Joh. Mich. Heinecius de Sigillis. Francof. 1709, fol. p. 16, et seq. The learned Montfaucon, among his immense treasures of antiquities, in his Antiquite expliquee, Tom. 3, Part. id. Chap. 12, gives the figures and descriptions of several of these larger sigilla or signa, on which he says, the names were all cut in hollow in capital letters; and he imagines their use to VOL, XL.] PHILOSOPHICAL TRANSACTIONS. 249 have been to mark earthen vessels, particularly those great earthen jars, in which the Romans used to keep their wines. It any of them had occurred to him with the letters excisae, exsculptae, protuberant or standing out, as the types in our modern way of printing are made, so accurate a describer of antiquities could not have passed it over without having mentioned it, and that the rather because of its being a greater rarity : though several lamps of terra cocta are stamped with letters impressed or hollow, from such protuberant letters as in fig. 2, pi. 7, but the greater number have the letters raised, or standing out. This stamp is made of the true antient brass, and is covered over with a green scale or coat, such as is usually seen on antient medals. It was found in or near Rome. On the back is fastened a ring, the hole of which is ^i of an English inch one way, and ■!-§■ the other way ; the plate itself is two inches long, wanting -^, and its breadth exactly 44 of an inch : the sides are parallel to one another, and the ends are likewise parallel to each other, but they are not on an exact square with the sides, varying about 1 degree and a half from an exact rectangle. On the under side stand two lines or rows of letters, ^ of an inch in height, and well-formed Roman capitals: their faces stand up, all upon an exact level with one another, and with the edge or border of the stamp ; their protuberance or height above the ground is different, the ground being cut uneven ; for close to most of the letters the ground is cut away only ^V> close to some near -^, and close to the edges full -^. The first line con- tains these letters, CICAECILI / , with a stop or leaf to fill up the line; in the second line, HERMIAE. SN. Which is judged to be read Caii iulii Caecili, Hermiae Signum. Who was probably a man in a private station, so that his name has not been handed down to us in any monuments, but only accidentally in this stamp. In Gruter occur two of the name of Hermias, and several of the Caecilii, but none with these two names joined together. The use of this stamp seems to have been for the signature of the above- mentioned private man, to save him the trouble of writing his name, as some people have at present. It was certainly used on paper or membranes, being first dipped into ink, or some sort of paint, because of the protuberance of the letters, the hollow letters being fitter for soft substances, on which they leave the impression standing up, and consequently more legible. Another argu- ment, that this stamp was not to be used on any soft substance into which it might be pressed quite down to the ground, is the unevenness and roughness with which the ground is finished, which, was it to have made part of the im- pression, the workman would have finished with more accuracy; but he, know- ing that the surface of the letters was to perform the whole work required, was only attentive to finish them with that accurate evenness that these have. VOL. vni. K K 250 PHILOSOPHICAL TRANSACTIONS. [anNO 1738. Mattaire, in his AnnalesTypographici, Hagae 17I9, in 4to, p. 4, concludes from the best authors, that our modern art of printing was first thought of about the year 1440. A copy of the book he mentions, ib. p. 13, called Spe- culum nostrge Salutis, being pictures of stories out of the bible, with verses underneath, in Dutch, is in the Stadhouse at Haarlem. Each page was printed from a block of wood, like a sorry wooden cut; and this was the first essay of printing, which hint was taken from engraving, and is what he means p. 4, by typi fixi; after which they soon improved to use separate types, as we do now, which he terms, ibid, typi mobiles. This stamp is, in reality, a small frame of fixed types, and prints with our modern printer's ink, which is only a sort of black paint, as readily as any set of letters, cut in the rude manner these are, can be expected to perform. We see by this stamp of two lines, that the very essence of printing was known to the Romans, and they had nothing to do but to have made a stamp with lines three or four times as long, and containing twenty instead of two lines, to have formed a frame of types that would have printed a whole page, as well as Coster's wooden blocks, which he used in printing the Speculum Salutis. In the first volume of a collection of several pieces of Mr, John Toland, printed Lond. 1726, in 8vo. p. 2Q7, is a small tract of his, entitled, Conjec- tura verosimilis de prima Typographise Inventione, which is founded on the following passage in Cicero, in cap. 20, lib, 2, de Natura Deorum ; where Balbus the stoic uses the following words in an argument against Velleius an Epicurean. Hie ego non mirer esse aliquem, qui sibi persuadeat, corpora quaedam solida atque individua vi et gravitate ferri; mundumque effici ornatissimum et pul- cherrimum, ex eorum concursione fortuita ? Hoc qui existimet fieri potuisse, non intelligo cur non idem putet, si innumerabiles unius et viginti formae lite- rarum (vel aureae vel quales libet) aliquo conjiciantur; posse ex his in terram excussis annales Ennii, ut deinceps legi possint, effici; quod nescio an ne in uno quidem versu possit tantum valere fortuna. He conjectures that this very passage gave the first hint to the inventors of printing about the year 1445, because they retained even Cicero's name for their types, calling them formae literarum, and made them of metal, as he says, aureae vel quales libet. Moreover, in cap. 10, lib. 3, de Divinatione, Cicero has the very phrase imprimere literas. Brands for marking cattle were in use in Virgil's time, Georg. lib. 3, ver. 158, where he says, Continuoque notas, et nomina gentis inurunt. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 25 1 Procopius, in his Historia Arcana, says, the emperor Justinus, not being able to write his name, had a thin smooth piece of board, through which were cut holes in form of the four letters^ W ^'HT' which, laid on the paper, served to direct the point of his pen; which being dipped in red ink, and put in his hand, his hand was guided by another. Possibly this may likewise have given the hint to the first of our card-makers, who paint their cards in the same manner, by plates of pewter or copper, or only pasteboards, with slits in them in form of the figures that are to be painted on the cards. An Occultation of Mercury by Venus, May 17, 1737} observed at the Royal Observatory at Greenwich. By J. Bevis, M. D. N" 430, p. 394. At Q** 43"* 4' p.m. app. time. Mercury was only the 10th or 12th part of Venus's diameter distant from her; afterwards the view was intercepted by clouds. At 9*" 51™ 10' Venus shone out again very bright, and Mercury was quite covered by her. Afterwards clouds again prevented any further view of the phenomenon. Of a netv Azimuth Compass, for finding the Variation of the Compass or Mag- netic Needle at Sea, with greater Ease and Exactness than by any ever yet contrived for that Purpose. By Capt. Christopher Middleton, F. R. S. N° 450, p. 395. To discover at sea the declination of the magnetic needle, or variation of the compass, with some tolerable degree of certainty and exactness, is a thing of great use and importance in the art of navigation. The instruments and methods hitherto used for this purpose, are subject to several inconveniencies, errors, and defects; to remedy which, this new azimuth compass was contrived, which has by experience been found effectual. It would be needless to give a description of the instrument; the cap therefore only shows the manner of using it, which is as follows: 1 . The instrument must be rectified, or fitted for observation, by turning it about till the 4 cardinal points, that are hung on the centre pin, agree with the 4 cardinal points on the chart, at the bottom of the box ; then will the needle, that shows the magnetic meridianj stand at no degrees, and the east and west points at go degrees, on the graduated circle within the box ; and in this situation it must be kept, as near as may be, during the whole time of the observation. 2. Let the index of the quadrant be placed to that degree of the arch, on K K 2 '25'2 rHlLOSOPHICAL TRANSACTIONS. FaNNO J 738. the rim of the box, which the observer judges to be nearly equal to the height of the sun or star whose azimuth is sought; for by this means the object will be more readily found. 3. Turn the quadrant round towards the sun or star, till it appear on the vertical hair within the telescope, to an eye looking through the small hole or sight; and then slide the index a little upward or downward on the arch, till the object by this means be brought to coincide or touch the visible horizon. Lastly, The degrees and minutes then marked by the index on the arch of the quadrant, will show the altitude of the object, which will always be the same, whether the instrument be in motion or at rest; at the same time the degree cut by the index on the horizontal rim, or circumference of the compass box, will give the magnetical azimuth of the sun or star. How the variation of the needle is found by means of magnetical azimuth and altitude thus obtained, is taught in every treatise of navigation. But as the resolution of this problem is somewhat troublesome, and requires such a knowledge of the doctrine of the sphere, as every seaman has not attained, an easy method is here exhibited of discovering the variation of the compass with- out any manner of calculation. 1 . Let the magnetic azimuth of the sun, or any star, when it is near the prime vertical, and considerably elevated above the horizon, be found according to the directions already given, before it arrive at the nieridian, and note well the altitude, or let the index remain fixed at the same point on the arch. 2. Find the magnetic azimuth of the sun or star in like manner as before, when it is exactly at the same degree of altitude, after it has passed the meri- dian: and, 3. If these two magnetical azimuths be equal, the needle has no variation; if urrequal, add them together, and half their sum will be the true azimuth; or subtract the less from the greater, and half the difference will be the varia- tion required. The circumstances of the observation will the more readily dis- cover whether the declination is easterly or westerly. N. B. Though it would be very commendable in gentlemen who use the sea, to learn the names of most of the principal fixed stars, yet even that knowledge is not necessary in the use of this instrument: neither is it needful in this case to know exactly the latitude of the place of observation, provided the difference of latitude between the observations be not very great; it is sufficient, that care be taken to observe the self-same star, before it comes to the meridian, and after it has passed it; and for the sake of greater exactness, the caution before given should be regarded, viz. that the star be at some considerable height above the horizon, and also near the prime vertical. VOL. XL.]'' PHILOSOPHICAL TRANSACTIONS. 253 :in An Account of a Book presented to the Royal Society, entitled, Notitia Hungaria novie Historico-Geographica, &c. Auctore Matth. Belio. By the Rev._ Zachary Pearce, D.D. F.R.S. &c. N"450, p. 398. ,,j The author of this work is the Rev. Matthias Bell, a pastor among the Lu- therans at Presburg in Hungary. This first volume is to be followed by several others; for the kingdom of Hungary includes 48 districts or counties, and this volume gives an account of only one of them, and indeed is chiefly taken up with the history of the city of Presburg, or Pisonium. as he calls it, which, though inferior in other respects to the city Buda, is the place where the emperors, as kings of Hungary, are crowned, where the states of the kingdom assemble, and the courts of justice are held. This volume consists of two parts. The first is general, and gives an account of the physical and political state of the whole district or county of Pisonium, describing its soil, produce, rivers, the temperature of its air, the nature of its inhabitants, its ancient inhabitants and present ones, its nobility, magistrates, and whatever belongs to the natural and political history of the district. The second part is occupied with the description of the city Presburg; where the author is very copious and elaborate in setting forth every thing that relates to it, particularly its ancient state under the several nations who possessed it, and its present state under the Austrian family. Leaving to the next volume the description of the 4 other cities or principal towns, situated in the same district. .^ •II yi short Account of Mr. KerssehooirC s Essay, on the number of People in Holland and West Friezland, as also in Haarlem, Gouda, and the Hague; drawn from the Bilk of Births, Burials, or Marriages, in those Places. By John Eames, F.R.S. N°450, p. 401. It is well known to what useful purposes the bills of births and burials, at the city of Breslau, the capital of Silesia, have been applied, by Dr. Halley; as also what curious observations have been made, both moral, physical, and political, by Sir William Petty, on the same argument, several years before, and by Dr. Arbuthnot and others since. Our industrious author has not only consulted them, but acquainted himself more particularly with Mr. King's ob- servations in Davenant's Essays, &c. in order to render himself more capable of making a just estimate in this matter. He begins with the number of inhabitants in the two provinces of Holland 254 PHILOSOPHICAL TRANSACTIONS. LaNNO]738. and West Friezland; these he makes at this time, viz. 1738, to amount in all to 980,000, and gives the following table of the particulars. It exhibits the number of people of all ages, living at the same time, from the birth to ex- treme old age; which, because it shows the chances of mortality within the ages mentioned, he calls the table of contingency of life and death. The Table of Contingency. Of above QO years old there are 500 of QO to 86 inclusive 2,500 85 81 6,500 Of 80.. 75.. 70.. 65.. 6o. . 55. . 50, . 45. . 40.. 35.. 30.. .76 13,000 .71 20,300 .Q6 27,300 .61 34,300 .56 40,8O0 .51 47,000 .46 53,000 .41 57,800 .36 62,500 .31 67,600 .27 58,400 26 20. 15. JO. 5. to 21 94,300 16 83,400 11 87,200 6 91,800 birth 131,800 sum under 27 years ditto above 27 years ,488,500 ,491,500 sum of all the inhabitants980,000 sum above 27 years 491,500 This table is founded on three principles, viz. correct observations on the tables of assignable annuities in Holland, which have been kept there for above 125 years; in which the ages of the persons dying are truly entered; on a sup- position that there are yearly born in the two provinces 28,000 living children; and lastly, that the whole number of inhabitants in any country, is to the number of the births, as 35 to 1. From this table it appears, 1. That about half the number of people in the two provinces are above 27 years old, and consequently that near the other half are under that age. 2. Then, by following what has been observed for more than 100 years in England, and particularly in London, out of 35 children born, 18 of them are boys, and 17 girls, the people in these two provinces will consist of 504,000 males, 476,000 females. He further remarks, that it appears from the assignable annuities for lives beforementioned, the females have in all accidents of age lived about 3 or 4 years longer than the same number of males; which he thinks appointed as a compensation for the continual excess there is in the birth of the males above the females. vol.. XL.] PHILOSOPHICAL TRANSACTIONS. 255 He then notices the quality of these 980,000 inliabitants, and says he^ees no reason to differ from the proportion of Mr. King in Davenant's Essays, who with a great deal of pains and judgment has divided the people of England in this manner ; The proportion for every 100,000 inhabitants is. Married men and women 34,500 Widowers 1 ,500 Unmarried young men and children 45,000 Servants 10,500 Travellers, strangers, &c 4,000 100,000 If this proportion be admitted, then the number of each sort in Holland and West Friezland will be as below. He adds, that the said provinces can raise at this time "220,000 able-bodied men, deducting -rV for diseases and other in- firmities. But then he admits at l6 years of age, whereas Dr. Halley admits none till 1 8, persons under that age being generally too weak to bear the fatigues of war, and the weight of arms. He then proceeds to rectify the mistakes of the learned Isaac Vossius, who makes but 550,000 in Holland, West Friezland, &c. Disallows Sir William Petty's account of the number of people in London, because he makes them alone equal to the inhabitants of Holland and West Friezland together. He closes the whole with a table of the present value of annuities on lives, in proportiou to the ordinary or common bonds charged on those provinces, and subject to the extraordinary taxes raised at this time, viz. 1738. Annexed are the degrees of mortality or fatality, said to be in the Hague and Haagambagt, as also the numbers and conditions of the inhabitants of Amsterdam, Haarlem, Gouda, and the Hague, as also London at this present time. The two provinces of Holland and West Friesland. Married men and women 338000. Widowers 14700. Widows 44100. Unmarried youth and ) children... P^'^^^ Servants IO290O. Travellers, strangers, &c. 3g30O. Amsterdam Haarlem Gouda Hague London 86156. . 17420. , . 6900. . 14850. . 24 1 80O 4218. . 760. . 300. . 720. . 13100 13858. . 2280. . 900. . 2380. . 45700 93990. . 22700. , . 900a. . 16190. .215700 28318. , , 5300. . 2100. . 4870. . 85000 14460. . 2040. , 800. 2490. . 52300 241000. . 50500, . 20000.. ■41500. . 653600 256 The fatality of the quarters PHILOSOPHICAL TRANSACTIONS. dead. Spring to summer 307 Summer to the autumnal equinox 286 Autumn to winter 287 Winter to spring' 286 [anno 1738. The fatality of the months 31 years, one with another, dead. January. i o2 February 88 March 95 77 112 100 92 95 April, . . May . . . June. . . ' July . . . August. September gg October 93 November ps December 99 Hence it appears, that March is less fatal at the Hague and Haagambagt than April, and April than May and June; that May is the most fatal month of all; that the remaining months are nearly equal. It appears further, that 3 parts or seasons of the year, are very nearly equal ; but that the other quarter or season, beginning at the vernal equinox, is more fatal than any of the rest by a 15th part. The Table of Annuities for Life. Let the annuity be 100 guilders a year, on a life under a year old. Guilders Its present value is 1667 that is Upon a life of 5 years to 1 inclusive 186g 10 15 20 , 25 . 30 35 . 40 45 50, 55 60 65 70 6 1835 11 16 21 26 31 1770 1667 1587 1515 6 1429 7 Guild. 6 . 5 . 5 . 5 . 6 . 6 36 1334 41 46 51 56 ,61 ,66 1212 8 1093 840 709 570 9 10 11 14 17 Sti. O per Cent. 7 9 13 O 6 12 O 10 5 3 6 8 2 11 The use of the table. — Quest. Let it be desired to know the present value of VOL. XL.] FHILOSOPHICAL TRANSACTIONS. '257 any annuity for life, for instance, of 90 guilders a year, which was granted in the year 1703, on a life then of 3 years old. Answer. The life now, in 1738, is between 37 and 38 years old ; hence the number between 40 and 36 gives 1 334, for the present value of an annuity of 100 guilders; hence — — - — = 1200 guilders, is the present value of the annuity for that life. An Answer to that Part of Mr. W. Kerssebooms Essay, which treats of the Number of the Inhabitants of London. By William Maitland, F. R. S. N" 450, p. 407. M. Kersseboom asserts, that the city of Paris, in the year l684, and at the close of the last century, contained more inhabitants than the city of London. And to prove that Paris contains a greater number of inhabitants than London, he has had recourse to the accounts of christenings annually published in both cities, without inquiring into the nature of his authorities ; which if he had, he would soon have discovered, that the former is a perfect account, while the latter is perhaps the most defective of any extant ; for the christenings there mentioned, are only those where the parish clerks are present: which he thinks cannot amount to near two thirds of the whole. The burials in the annexed table, by some typographical errors in the politi- cal account of the author's History of London, from which it is taken, being increased 491 above the real number, in Graunt's account, the sum total of which amounting to 90350, must be reduced to 89859; and as in the annexed term of years, there appears to have died of the plague 1741, three and a half of which, he computes, would have died of common distempers, out of each hundred, which amounting to about 61, this being deducted from 89859, the real number of the burials, the sum will be reduced to 89798, which taken from 90883, the whole number of the christenings, the remaining sum will be 1085, which being divided by 10, the medium will be 108-1^ yearly in favour of the christenings. VOL. VIII. Ll 258 PHILOSOPHICAL TKANSACTIONS. [anno 1738. A Decenary Account of the Christenings and Burials of London, in the following Years. Years. Christened. Buried. Com. Dist. Buried. Plague. Totals Buried. 1626 6701 1627 8408 1628 1629 1630 l63J 1632 1633 1634 8564 9901 9315 8524 9584 9997 7400 7713 7740 8771 9228 8288 9527 8392 9855 IO899 1635 10034 Tot.Gen 9O883 10651 88609 134 4 3 O 7534 7717 7743 8771 1317 10545 274 8 O 1 O 8562 9535 8392 10900 10651 1741 90350 This difference, in favour of the christenings, is owing to the citizens of that time being ahnost of the same religion ; but the civil war breaking out soon after, the people deviated into a variety of sects, subverted the church of Eng- land, and assuming the civil power, established a new hierarchy, or church- government. But the members of the abolished church continuing to baptize among themselves, without reporting their christenings to the new-appointed members of the company of parish-clerks, occasioned a very great defect in the account of christenings annually published by the said parish-clerks. From this epocha is to be dated the majority of the burials in the bill of mor- tality, over the christenings of London : and though the church of England was soon after re-established, yet the numerous dissenters of all denominations, persevering in their separation, continued to baptize among themselves, with- out sending in accounts of their christenings to the restored members of the company of parish-clerks: and the schism still continuing, the accounts of the christenings and burials of this city, remain on the ancient foot of division and imperfection. Add to this, that not only all the foreign churches in London christen with- in themselves, but likewise many churches and chapels of the church of Eng- land, that send not in their accounts to the company of parish-clerks, which, together with those of the dissenters and foreigners of all denominations, amount to no less a number than 181 congregations, whose accounts of christenings are not published : by which it is evident, that the vast disparity between the christenings and burials of this city, is not owing, as Mr. Kersse- boom imagines, to the residence of the court, the convention of parliament. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 259 and the great resort of people from all parts, but in fact to the great defect abovementioned. However, that gentleman, from the aforesaid very defective account of the christenings of this city, has calculated the number of its inhabitants by a medium of the christenings in the years l684 and J 685 ; by which he makes the number at that time amount to 500344 : but as this number is only taken from a medium of 2 years, he imagines it too great ; therefore to reduce the same to the number of 469700, by a medium of 20 years, he has unwarrantably precluded the sum of 14702, the number of christenings in the year 1 684, to make room for the sum of 1 1 85 1 , the number of christenings in the year 1 674 ; by which the number of the inhabitants of London, is very much lessened. And as a further instance of Mr. Kersseboom's partiality in favour of the city of Paris, he has calculated the number of its inhabitants, without men- tioning the uncertainty of a calculation founded on a short space of time, as he has done in the case of London, at a medium of the christenings for the years ]670, 1671 and 1672, by which he makes them at that time, amount to 6)0300; adding that the number must have been greater at the end of the last century; as by his extravagant manner of calculation it should be at present. But as it appears by the above specified 10 years account, that the christen- ings of London greatly exceed the burials of that time, it will not be denied, that they exceed the same at present ; especially if we consider, that the num- ber of christenings in Paris, at a medium of 9 years, preceding that of 1737, exceeded that of the burials 98 yearly ; notwithstanding that city not only abounds with a vast number of religious of both sexes, who are sworn to celi- bacy, but likewise many thousands of students belonging to the university, who lead a single life ; whereas in London, there are no such persons, to prevent the increase of its inhabitants. And as in the author's political account of London, it appears that, at a medium of 9 years, there are annually buried in London 29542, and in Paris only 17804, which is 11738 in favour of the former; so must the births in London at present, according to the above-specified 1 0 years account, the rea- sons aforesaid, and the Paris account of christenings, yearly exceed those of Paris 12320 ; whence it appears, that the inhabitants of London exceed those of Paris, above three fifths in number. Mr. Kersseboom seems dissatisfied with Sir Wm. Petty's assertion, that the city of London contained as many inhabitants as the province of Holland and West-Friesland : which our author thinks will be no difficult matter to make appear, by allowing that gentleman his supposed number of 28000 children to be annually born in the said province; whereas, according to the above-specified LL 2 260 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. 10 years account, and the Paris proportion of births, there must be annually born in London 31008 children : therefore, as this number, according to Mr. M.'s calculation, is the produce of 725g03, the present number of the inhabi- tants of London ; so must 280O0, the number of children supposed to be born yearly in the province of Holland and West-Friesland, be the produce of 635485, the present number of the inhabitants of the said province. Notwithstanding Mr. Kersseboom, by his excessive and unprecedented reckoning of the births at a thirty fifth part of the people, has calculated them at 98OOOO ; whereas by the ingenious and learned Dr. Halley's method of calculation, which is so highly approved of by Mr. Kersseboom, that he seemingly would be thought to make it the standard of his calculations, the inhabitants of the province of Holland and West-Friesland do not amount to 29 times the number of the births, which gives room to suspect, that Mr. Kersseboom has introduced this excess, to increase the number of people in the said province of Holland and West- P'riesland. A IVater-Level to be fixed to Davis's Quadrant, by which an Observation may be taken at Sea, in thick and hazy Weather, without seeing the Horizon, By Charles Leigh, Gent. N°451, p. 413. The sea-quadrant now in use, invented by Capt. Davis, for taking the sun's altitude, is an instrument well known, universally approved, and sufficiently accurate ; this, together with a long use of this instrument, has occasioned such a fondness for it, that it would be no easy matter to dissuade the navigator from the vise of it, to any other. It is true, that when the natural horizon is obscured by thick and hazy weather, this instrument, as it now stands, is of no use ; which too often oc- casions melancholy consequences, such as the loss of ships and cargoes, and men's lives. If therefore, to this instrument an apparatus were added, such as an artificial or portable horizon, that could be as effectually relied on, as that of the true or natural; and at the same time plain, easy, and obvious; it would be needless to attempt proving its usefulness. The principle on which Mr. Leigh's apparatus is founded, is, " That the surface of all liquids, when free from any external cause, that have a communi- cation with each other, though divided and separated in their surfaces, will be truly in a horizontal plain." The quadrant, and its construction, being well known, it is sufficient to no- tice the two sections of two concentric circles, as ab, cd, fig. 3, pi. 7, on which the degrees and minutes are graduated ; e, the common centre, through which goes a brass pin fixed to the apparatus ef, which is an index or radius to the VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 26l section cd, on which index is fixed a brass tube 15 inches long, in the extremi- ties of which are fixed perpendicularly two glass tubes Eh and dh. 4 inches long, with brass ferrels on the tops. On the central pin, which is fixed in the index, is also fixed the brass hori- zontal vane ez obliquely, in which is a hole for the central glass tube Eh, to come through three fourths of its length; close to which, and from the common centre, comes a white fine thread, the end being fixed in the vane ez ; and in the same manner is a thread fixed close to the glass tube dh. To prepare this instrument for observation, pour water into the tube sh, till its little surface rises to the central thread ; then to keep it fixed there, shut the slide or stop, fixed on the top of the central tube, and there it will continue ; then you may at pleasure pour or drop water into the tube dh, till its surface also rises to the thread fixed there; and if too much water is dropped in, dip in a wire with a small bit of sponge or cotton fixed to -the end, till you exactly trim the tubes; for the greatest nicety and exactness lies in trimniing the sur- faces true to the threads. Being thus prepared for observation, place yourself conveniently, where there is the least motion, on a stool or the deck, and having the quadrant in its pro- per position on your lap, open the slide on the top of the tube eh, that the water may have its natural tendency, which will be truly horizontal, conforma- ble to the above principle ; then keeping your eye on the central thread, bring that and the little surface into one, which will be effected with the same ease, as if you observed by the natural horizon ; then keep moving the end of the index f, till you bring the speculum of the sun in the little hole on the horizon vane, close to the thread, so that you have, as it were, but one object to look at during the time of observation. But if you use the shadow vane, you must bring the upper edge of the shadow on the central line, drawn on the horizon vane, as usual ; remember- ing as often as you rest, waiting the sun's rising, to close the slide, which pre- vents the water's running out, it then remaining immoveable. And thus con- tinuing to do, till the sun is on your meridian, cast up the two sums as is usual, that is, the degrees cut by the shadow vane, and those cut by the upper edge of the index on the greater arch, which sum will give what is required, viz. the sun's distance from the zenith. On the end of the index is fixed a sight vane n. by which you may observe by the natural horizon, the very same way as with the common quadrant ; so that the one will be the proof of the other. '2,62 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. The Description and Use of an apparatus added as an Improvement to Davis's Quadrant, consisting of a Mercurial Level, for taking the Co-altitude of the Sun or a Star at Sea, wilfiout the usual Assistance of the sensible Horizon, which frequently is obscured. By Charles Leigh, Gent. N°451, p. 417. Since the former communication, in the foregoing article, Mr. L. has made such alterations and improvements in it, as have rendered it complete and per- fect for the use intended, which have been confirmed by repeated experiments, as well on board ships, as on shore. To arrive at perfection in navigation, 3 things are absolutely requisite, viz. the variation, the latitude, and the longitude ; which last is as yet concealed from us. The two former indeed, we have a tolerable certainty of, especially the first, which may be found by observation, almost at any time the sun is visible, in or above the horizon, either by an amplitude or azimuth ; but it is not so in regard to the latitude, by any certain method, but what is considered as too abstruse for common practice ; for it is but once in 24 hours that an ob- servation can be made by the sun, and even that space of time is so very short, that if the horizon should then be obscured, or a cloud intercept the sun's rays, the dead reckoning is then the only guide, which in fact, is little better than groping in the dark. The first instrument made conformable to the same principle, was with a water-level ; but finding that water was subject to some inconveniencies, Mr. Leigh has altered the apparatus, and changed the fluid from water to mercury : this alteration and improvement will better appear by the instrument, repre- sented fig. 3, pi. 7, where ab, cd, represent the segments of two different concentric circles; e the common centre, in which moves the pin or axis fitted to the index or label ef ; on which label is also fixed the horizontal tube Gg, which has a communication with the two glass vertical tubes Eh, dh, in which the mercury moves. On each top of the vertical tubes are fixed a large hollow brass cylinder hh, having in their tops a pin, by closing of which, the included air is prevented from any communication with the external ; by which means this advantage is obtained, that it prevents, in a great measure, that too quick and vibratory motion, natural to the fluidity, joined to the gravity of mercury when moved, and at the same time, by having a sufficient space and quantity of air in the cylinders at top, does not in the least impede the true level ; but not- withstanding this precaution, the mercury still would be subject to a tremulous motion, were it not that the diameters of the vertical tubes, to that of the horizontal, are as 2 to 1, and consequently the area 4 to I ; by which means VOL. XL.] I'HILOSOPHICAL TRANSACTIONS. 263 this inconveniency is also removed, without any way affecting the horizontal level. The first trimming or preparing the tubes with mercury is sufficient, and when the two little convex surfaces of the mercury appear just visible above the level rings Ee, then is the instrument correctly trimmed ; if they appear much above or below the rings, move the tubes a little up or down, till the surfaces are adjusted to the rings ; which is effected by means of the regulating screw 1, fixed at the end of the base tube. To observe by the sun, was described in the former article ; but to observe by a star, another person must look, through the slit on the horizon vane, and over the upper edge of the shade vane, and bring the star to coincide with it, proceeding in the same manner as before, with the sun. An Account of the Extirpation of part of the Spleen of a Man. By Mr. John Ferguson, Surgeon. N°451, p. 425. On the 5th of January, Mr. F. was called to Thos. Conway, who had re- ceived a wound with a great knife, which went through the muscular part of his fore-arm, and into the left hypochondrium. It was 24 hours after he had re- ceived the wound before Mr. F. saw him. He found the spleen out at the wound, and that what by pressing and thrusting of it with the fingers, endea- vouring to return it into its place, which they that were about him could not accomplish, and by being so long exposed to the air, it was quite cold, black and mortified. He considered that cutting away the mortified part, must be attended with the greatest danger, and was to him, an unprecedented case ; yet that the patient must inevitably die, if it was not done : he therefore made a ligature with a strong waxed thread, above the unsound part, and cut off 3| oz. of the spleen : notwithstanding the ligature, there was a pretty large artery that sprung with great violence, which he immedately tied up ; and, after bath- ing all the parts with warm wine, he returned the remaining part of the spleen into its place, leaving the ends of the threads out of the wound, to draw them away by, when they should digest off, which they did on the 10th day, and came away with the dressings. He dressed the wound with digestives, and the abdomen was stuped twice a day with an emollient fomentation ; and after stuping, it was always malaxated with an emollient liniment, which the patient said always gave him ease. What he most complained of, was that he could not make water, for which Mr. F. every day gave him a carminative clyster, which kept his belly from swelling ; and always when the clyster came away, he got some water made along with it: 264 PHILOSOPHICAL TKANSACTION. [aNNO 1738. this symptom went off on the 7th or 8th day. He perfectly recovered, followed his business, and found no inconvenience from the want of the part of the spleen which he lost. The wound through his arm was also quickly cured.* Concerning a Ball of Sulphur supposed to be generated in the ^ir. By Mr. Benjamin Cooke, F. R. S. of Newport in the Isle of Wight. N° 451, p. 427. The great heats we have lately suffered, were ushered in by a very gloomy night of almost continual lightning, accompanied with very loud claps of thun- der, which, as usual, were towards the morning followed by very heavy showers of rain. Early next day, in a meadow near the sea-shore, far from any house, and where it has not been known that any improvement has been carried on, a husbandman found a beautiful yellow ball lying on the turf. It proved to be of sulphur, of which it smelt uncommonly strong. It was frosted, as it were, all over with an efflorescence of fine, shining, yellowish crystals, which soon fell off" with the lightest touch. It has on one side, a deep hole, admitting the end of a middle-sized knitting- needle, and on the opposite side a deep depression ; which would induce one almost to think its form had been at first nearly spheroidal, formed by a revo- lution round a supposed axis connecting those two parts. It has several other holes scattered irregularly up and down its whole surface, some fit to admit a hog's bristle, others a hair ; as if it had been made of a fine powder, and some thin liquid, and after mixing had suffered some fermentation ; but those parts of it which are solid, seem more compact than those of the common roll brim- stone of the shops, and the powder of it burns with a whiter flame, and less acid fumes. Its longest diameter is between 8 and g, and its shortest betwixt 6 and 7 tenths of an inch ; its weight is 108 grains. We find frequent mention, in the description of thunder storms in hot cli- mates, that there falls often a flaming bituminous matter to the ground, which sometimes burns not to be soon extinguished, but more frequently spatters into an infinite number of fiery sparks, doing great damage where they strike, always attended with a sulphureous suffocating smell, commonly compared to that of gunpowder. "Whether this sulphureous ball was intended for one of these, but by some accident missed firing, it is now time to consider. Had it been formed in the earth, how should it get to the surface, without losing that most elegant frosty covering of fine shining crystals, and appear not in the least sullied, or its pores • Mr. F. in the letter prefixed to this account remarks, that though the spleen had been often taken out of dogs, yet this he believes to be the first instance of the extirpation of a considerable por- tion of it in the human subject. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 265 filled with earth, or other terrestrial matter ; on the contrary, not the least ad- hesion of any thing of that kind can be observed : besides, brimstone made the ordinary way, seems to have a different texture of its internal parts from this ball. From these observations Mr. Cooke concludes it not formed in the earth. ^n Account of a Book entitled, Observationes de Aere et Mar bis epidemicis, ab Anno 1728, ad Jinem Anni I737> Plymuthi facta-. His accedit Opusculum de Morbo Colico Damnoniensi. Auctore Joanne Huxham, M. £>., R. S. S, Londini, 1739, 8vo. Drawn up by Thomas Stack, M. D., F. R. S. N°431, p. 429. This book and the continuation of it, are so well known to medical men of the present day, that it is deemed unnecessary to reprint Dr. Stack's analysis of it. An Abstract by C. Mortimer, M. D. Seer. R. S. of an Inaugural Dissertation published at JVittemberg 1736, by Dr. Abraham Fater, F. R, S. concerning the Cure of the Bite of a Fiper, cured by Sallad-Oil. N" 451, p. 440. The author being informed of the use of oil of olives against the bite of vipers, in the case of William Oliver, before several members of the R. S. and others ; he communicated the same to Dr. Vater at Dresden, who had an op- portunity of trying the efficacy of this remedy, by an accident happening in that city ; which case being remarkable, he has related it at large in the above- mentioned dissertation, as follows : The head journeyman in the Royal Dispensary at Dresden, being the last year preparing some Italian vipers for a patient of distinction, was, through negligence, bitten by one of them in one of his fingers. The man, finding himself wounded, was greatly frightened, he tried various things ; among others he applied theriaca outwardly to the wound, but felt no relief from it ; and in the space of a few hours, his whole arm swelling to an enormous degree, he felt great pain in it, with remarkable tensions under his arm-pit towards his heart, attended with a faintness. Therefore, almost despairing of recovery, having tried all things in vain ; he went to Dr. Vater, who having been informed of the virtue of olive-oil in this case, as before mentioned, ordered the man to anoint his whole arm with it hot, and several times, on which the desired effect soon followed : for the swelling, after one or two anointings, began to fall ; the pains, with the other symptoms, were assuaged, and gradually ceased, and the patient recovered perfectly in a day or two. He took nothing inwardly besides VOL. VIII. M M » 266 PHILOSOPHICAL. TRANSACTIONS. [ANNO 1738. a simple mixture, (Sp. Vitriol dulcis. Sp. Vitriol, p. i, Sp. V, p, iij,) with an anodyne mineral liquor, on which a copious sweat ensued, which sensibly re- lieved the patient. Though this medicine might contribute to the cure, yet the chief part in this affair is to be ascribed to the oil of oh'ves, because on anointing with it, the symptoms abated instantly. Dr. Vater, in speaking of the serpentine or viper-stone, relates a very ex- traordinary accident, if true, from Kaenipfer's Amaenit. p. 579. The case was this : in the house of a Dutch governor on the coast of Coromandel, a ser- vant maid happened to be bitten in the foot by a cobra cabelo. The serpentine- stone was immediately laid on; which falling ofF, and no other being to be had, nor any new milk being at hand to wash out the pores of the stone in, a wet nurse being in the house, who was anxious for the sudden effects of the poison, milked some milk upon the stone out of her own breasts; on which her nipple began immediately to be painful, and soon after the whole breast of that side swelled, and was inflamed, even to the hazard of her life for 3 days together, and the hardness did not leave her breast in less than 10 days. It must be re- marked, that her nipple was before somewhat excoriated by the gum of her nursling, by which the small veins being laid bare, it was readier to receive the infection of the venom rendered more active by the warmth of the milk. When he speaks of oil of olives in particular, and its effects against poison in general, he cites a remarkable passage from Matthiolus in his Comment, Lib. 2, Dioscorid. p. 232, where he says, he had found by experience, that oil prepared by himself, into which a great number of scorpions had been put, being anointed on the heart, and where the pulsations of the arteries of the hands and feet are felt, frees from all poisons; nay, it likewise cures those who have been bitten by vipers, or stung by any other venomous animals. The author, comparing this with the virtue of the oil alone, for the bite of a viper, concludes, that the scorpions infused in it add nothing to its real virtue. He concludes this dissertation, by endeavouring to explain the manner of its operating, which he attributes to its fat inviscating nature, by which it sheathes the spiculse of the poison. He remarks, that Celsus, Lib. 5, c. 27, advises, after dipping a person in a hydrophobia in cold water, to put him into warm oil. Lastly, he mentions the great secret of the viper- catchers, that is, the fat of vipers ; which, he thinks, acts in the same manner as the olive-oil. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 1&J Abstracts of 1 Letters from M. Dufay, F. R. S. &c. to Dr. Mortimer, Sec. R. S. concerning the Efficacy of Oil of Olives in curing the Bite of Fiper^. N°451, p. 444. In the 1st extract, dated Paris, Aug. 8, 1737, M. Dufay says, after he had given the Academy an account of Dr. M.'s observations on the remedy against the bite of vipers, a committee was appointed to make the same experiments. But whether it be, that the French vipers are more venomous than the English, or that the bites were more considerable, of the several pigeons and fowls that were bitten, not one recovered, though they were immediately rubbed with oil. They died in -J- of an hour, or in 1 hour's time at farthest. The like experiments have been made on several other animals; but as the gentlemen are resolved to repeat them, M. D. did not send an account of them. All he could say at that time was, that the remedy seemed to be not so sure in France as in England, where he found by the public newspapers, that a rattle-snake had been brought, and that its bite has been cured by the same remedy. In the 2d Abstract, dated at Paris, Dec. 11, 1737, he says, two members of the Academy had been employed to make the experiments relating to the cure of the bite of vipers, and they had accordingly n)ade some upon dogs, cats, pigeons, chickens, ducks and turkeys; some of which had been cured, but some others died notwithstanding this remedy; and there were even some that did not die, though they were bitten very deep, and yet no application of oil was made. This is the report they had made of these experiments; and they are determined to make new ones. All that can be thought concerning the difference of the success of this remedy at London and at Paris, is, that all vipers are not equally venomous; that all bites are not perhaps equally easy to be cured ; and that the vipers in France are more dangerous than those in England. Finally, the sequel of these experiments will probably teach us, in what cases this remedy may be applied in this country, France. M. D. then remarks that they had made with success the phosphorus of Kunckel, as good and as fine as that of Mr. Godfrey : they made 9 drachms at the first operation. Concerning the Poison of Henbane- Roots. By Dr. Patouillat, Physician at Toucy in France. N° 451, p. 446. The 26th of Jan. 1737, Dr. P. was called to a cottage near Toucy; where he was surprised to find 9 persons together, all having the true symptoms of being poisoned ; with this difference, that some were speechless, and showed M M 2 268 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. no Other signs of life than by convulsions, contortions of their limbs, and the risus sardonicus; all having their eyes starting out of their heads, and their mouths drawn backwards on both sides; others had all the symptoms alike. However, 5 of them now and then opened their mouths, but it was to utter bowlings: and whenever they expressed articulated words, it seemed as if they would prophesy. One, for example, said. In a month my neighbour will lose a cow: another. In a little time you will see the crown pieces of 60 pence at 5 livres. Among these Q persons, there was a woman 5 months gone with child, and a child of 2 years; 4 boys of Q, 12, 15 and 18; and 3 girls of 15, 17 and ig years of age, who had all 3 the misfortune of the green- sickness upon them at that time. The madness of all these patients was so complete, and their agitations so violent, that in order to give one of them the antidote, he was forced to employ 6 strong men to hold him, while he was getting his teeth asunder, to pour down the remedy : and as they could not all be watched at once, one of the boys got away, and ran to a pond 100 paces from the house, into which he leaped; but as he was seen, he was soon taken out. It was in vain to examine those wretches concerning the nature of the poison they had taken, as they were quite senseless. Happily the father of the family, by being absent, was free from this misfortune. Of him Dr. P. learned, that digging his garden the preceding day, he had found several roots resembling common parsnips ; and having carried them home for parsnips, they were boiled in the soup ; and the unlucky mistake was not apprehended, till the children were in this dreadful state. He described the plant, which he thought he had taken for parsnips; on which Dr. P. went into the garden, to find what it was; but as it had no leaves, he was obliged to derive the knowledge of it from the roots; and soon knew it to be the henbane,* which is a very strong poison; and so much the more dangerous, as the patients could give no account of their ailments, nor of the quantity of the poison they had taken. To the boys Dr. P. gave the Tartar. Stibiat. in so large a dose, that the oldest took 45 grains, and the others in proportion. For the woman, he had recourse to Theriaca in a triple dose; not thinking it safe to give her the emetic, on account of her pregnancy. He gave the same remedy to the child, by reason of its tenderness. To the girls, besides the Theriaca, which they took in very large doses, having used 4 oz. of it, he gave warm milk, in which was dissolved salt of rue. The next day he visited the patients, and found them in a quite different condition; for they had all recovered the use of their reason, but remembered * Hyoscyamus niger. Linn. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 269 nothing of what liad happened. All this day, every object appeared double to them, that is, on looking at a man, or a beast, or a tree, they saw two. He returned to see them the day after, and found that the symptoms were removed; but were succeeded by another altogether as surprising, viz. all ob- jects appeared to them as red as scarlet. This last symptom ceased gradually on the third day, and after that time they made no complaint. Concerning the Firiues of the Star of the Earth, Coronopus, or Bucks-horn Plantain, in the Cure of the Bite of the Mad-Dog. By the Rev. Mr. The.. Steward, F.D.M. N°451, p. 44g. Mr. S. here states that, in the Phil. Trans. N° 443, two vegetables are mentioned as possessing great virtues against the hydrophobia; viz. the lichen- cinereus terrestris and the stellaria or star of the earth, by which king James's hounds, that had been bitten by a mad-dog, are said to have been cured. But the last mentioned plant (the star of the earth) he apprehends to be a mistake, Mr. Ray having taken the Spanish catchfly for the star of the earth ; whereas according to Mr. S. the true star of the earth is the coronopus or bucks-horn plantain, as Mr. Ray himself acknowledged in a letter to Mr. S. adding that he (Mr. Ray) concluded that a false plant had been sent to the king for the star of the earth. Relative to this subject Mr. S. introduces the following letter from Sir Hans Sloane, the then president of the R. S. to Mr. Ray, dated June I, 1687, in these words : " I send you inclosed the specimen of a plant growing on New- market-Heath, and in Surrey, known by the name of the star of the earth in those parts. It is particularly taken notice of on the account of its extraordi- nary and admirable virtue, in curing the biting of mad-dogs, either in beasts or men. One of his majesty's huntsmen having proved it a great many times, gave the king his way of using it, which was an infusion in wiue with treacle, and one or two more simples. His majesty was pleased to communicate it to Gresham College, to the R. S. and nobody knowing the plant by that name, some there present confirming its use in some parts of England in that disease the herb being as little known here as if it came from the Indies, I told the society, I would let you have the best specimen of it, which I question not is known to you. If you please to give your sentiments, you will extremely oblige, 8cc." To this Mr. Ray returned the following answer: " I received your letter with the specimen inclosed, which seems to me to be the sesamoides salamanticum magnum of Clusius, or lychnis vise. &c. of Bauhin, which I have ■270 PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. observed to grow plentifully upon Newmarket Heath, &c. I wonder it should have such a virtue as you mention, but it seems it is well attested. Dr. Hulse writes to me, he finds it in Grey's Farrier."* This (Mr. S. observes) seems pretty evidently to refer to the same plant mentioned by Aubry,-|- and this surely was the plant that not being well dried and preserved, the society could not tell what to make of, and which Mr. Ray found to be the sesamoides, which he then thought was the plant that Grey called the star of the earth ; but upon further consideration, he was firmly persuaded, that the coronopus, and not the sesamoides, was the plant intended by de Grey (for so his name ought to be written) and indeed, to Mr. S. there seemed to be the greatest probability, if not absolute certainty, of this latter opinion; for the sesa- moides was a plant so little known in Grey's time, that the botanists who were contemporary with him, took it for a plant that was wholly a stranger in England, as may be seen in Johnson upon Gerard, and in Parkinson, and the manner of giving it, as directed by Grey, viz. first 3, then 5, and then ^ plants, roots and all, speaks it to be a small herb, such as is the coronopus, and not such a large one, with a great, sticky or woody root, as the sesamoides. Of this Mr. S. was very sure, that in Norfolk, his native county, and which, if he mistook not, was Grey's also, the coronopus is called the star of the earth (and among other names given it by Dodonaeus, this of Stellaria, and Stella Terrae, is one, p. 95 of the English translation; and he describes it as lying * Entitled, The Expert Farrier, 2d edition, -tto. l652, p. 1 60. His receipt is as follows : " Take the herb which grows in dry and barren hills, called the star of the earth j gathering it 3 days together. The first time you must gather 3 of these herbs, with all the whole roots ; and wash them clean, and pound them well ; which done, give them to your horse in milk, beer, ale, or white- wine ; but be carefiil the horse takes all the herbs and roots : if you will, you may make up these herbs and roots in fresh or sweet butter, which wUl do as well. The 2d day give the horse 5 of these herbs and roots, as before; and the 3d day give him 7. Do this punctually, and you may be well assured the horse will be perfectly cured; for though I have never tried this medicine, yet I know that the party of whom I had it, has cured many cattle of all sorts with it. I myself can say thus much of this receipt, that I knew it cure a whole kennel of hounds, one beagle excepted, which they did not suspect to be bitten ; so he fell mad and died, but all the rest escaped. Another time, a gentleman's son of my acquaint- ance was unfortunately bitten, who was cured by the party who taught me this receipt; and this young gentleman, who was then a boy of 10 years old, was so far spent with the disease, before this man took him in hand, that his senses were affected, and he talked very idly; yet he cured him, so as he lived and did well, &c." + In a letter to Mr. Ray, published by Mr. Derham, and dated Aug. 5, I691, wherein he says, that king James sent to the R. S. a plant called the star of the earth, with the receipt made of it to cure the bite of a mad dog, which is in Phil. Trans. N° 187. VOL. XL.] PHILOSOPHICAL TRANSACTIONS. ^71 spread upon the ground like a star; and Gerard gives the same description of it, and Parkinson, in his Theatrum, yet more fully, p. 501, viz. that the leaves lie round about the root in order one by another, thereby resembling the form of a star, and therefore called herba Stella ; by which name, among others, it is called by Caesalpinus, Lobel, &c. But whoever met with the name stellaria, or Stella terrae, among the synonyma of the sesamoides in any botanic writer before Mr. Ray, who afterwards retracted it, as has been fully proved ? In that part of Norfolk where Mr. S. was born, not far from Norwich, towards the sea-coast, where the bucks-horn plant grows abundantly, there was great use made of it when he was but a lad, and always with good success, so f.ir as ever he could hear. One story he could tell of his own knowledge, which might seem too trifling to mention, were it not to show the efficacy of the simple. About 40 years ago, when he lived at a place called Debenham in Suffolk, a person unknown to him, having heard that he knew an herb that was good against the bite of a mad-dog, sent to desire a sample of it, with directions how to use it; and sometime after he had half a dozen fine chickens brought him. He asked whence they came? It was answered from such a one, the name he had forgotten. He said he did not know him: to which the reply was, that it was the man to whom he had sent the plantain, which had saved the lives of half a dozen hogs of his, that had been bitten by a mad dog; and he thought the least he could do was to send me half a dozen chickens as a token of his gratitude. After all, Mr. S. would not be positive, that the lychnis, or catch-fly, was not good contra morsum canisrabidi; but was confi- dent that it was not the true star of the earth. In a P. S. Mr. S. states, that a friend of his had informed him, that there was a wonderful cure performed on a woman in Suffolk, several years ago, who had been bitten by a mad-dog, and in whom evident symptoms of the hydro- phobia appeared, who yet was saved, by the use of a powder given by the direction of the Lady Brook in Suffolk. It seems the powder went by the name of The Lady Brook's Powder, and was generally supposed to be chiefly, if not only, the coronopus dried and pulverized: and he had such an opinion of the great virtue of this simple, that till he had some convincing evidence of its having failed, he could scarcely avoid considering it as a specific against the bite of a mad- dog. Of the Reduction of Radicals to more Simple Terms, By Mr. Abr. Demoivre, F.R.S. N"451, p. 463. From the Latin. Mr. Demoivre having explained, in the appendix to Saunderson's Algebra, 272 PHILOSOPHICAL TKANSACTIONS. [anNO J 738, his method of extracting any root of the binomial a -\- \/ — b, this induced Wm. Jones, Esq. F. R. S.* to desire him to do the same by the possible bino- mial a -\-\/+ b; a request which Mr. D. here complies with, though he is sensible that this has been done already, by Sir I. Newton and others. Pbob. I. — To reduce the Binomial V'a + ^b to Simpler Terms. Suppose that this binomial, including its general radicality, can be reduced to the other binomial x + ^y, freed from that radicality. Now to find such quantities x and 3/, try whether the sum of the binomials V'a +^^ + v^a — Vb makes nearly an integer number, which may be readily done by a table of logarithms ; if it do, then put 2x =: to this whole number. Next try whether l/aa — bhe an integer ; if it be, put jn = this new integer ; then will y ■=. xx — m\ and therefore the given binomial will be reduced to the given form. But be- fore proceeding to the demonstration, it may be illustrated by two or three examples. Example 1 . — Let the binomial v' 54 + v/QSO be proposed. Put a = 54, b =■ 980; then will ^/ b = ^gSO = 31.3049 nearly ; which gives a + Vb = 85.3049, and a — Vb =. 22.695 1. Now the root of the first number is 9.236 nearly ; and the root of the latter is 4.763 ; the sum of which roots is 1 3.999, which is very near the whole number 14. Therefore putting Ix = 14, or ar = 7 ; then since y :=. xx — m, and m ='1/ aa — b =: >/ 1 936 = 44 ; therefore is y = 49 — 44 = 5 ; so that the binomial reduced will be 7 + -v/S. Example 2. — Let \/ A5 -{■ V l682 be reduced simpler. Put a = 45, b = l682; then is i/ b = 41.01219 nearly; hence a + ^b = 86.01219, and c — ■//>= 3.89781. Now the cube root of the former number is 4.4142, and the cube root of the latter number is 1.5857; the sum of which roots being 5.9999, which is nearly 6 ; therefore put 2x = 6, or ar = 3 ; but it being y = xx — m, and m = 1/ aa — b =i 1/343 = 7 ; therefore 3/ = 9—7 = 2; and hence the bino- mial reduced is 3 -|- \/'l. Example 3. — Let \/ J70 -|- V 18252 be reduced simpler. Put a = 170, b = 18252, then will \^ b = 135.1 nearly ; which gives a -\- i/b z= 305.1, and a — \/ b =■ 34.Q. Now the cube root of the former number is 6.73 nearly, and the cube root of the latter is 3.26, the sum of which roots is 9.99, nearly equal to the whole number 10. Put therefore 2x = 10, or a; = 5 ; then since y = xx — m, and * See an account of Mr. Jones, who was the father of the late Sir William Jones, in the intro- duction to Dr. Hutton's Mathematical Tables, p. I19. Vol. XL.] PHILOSOPHICAL TRANSACTIONS^ 273 «» = 1/ aa — b = 22 ; therefore y = 25 — 22 = 3 ; and hence the binomial reduced is 5 + ^/3. Demonstration — Take any binomial, as x/a-]-\/b, which suppose reducible to the binomial x -\- '/y; then, by cubing, x' + 3xx^/y -\- 3xi/ -{- yVy =. a + ^b. Put x^ + 3x7/ = a, and 3xx>/y + y^y = ■/i. Then whatever the index of radicality may be, from the square of the former part subtract the square of the latter, and there will remain x^ — 3x*y + 3xxyy — 1^ ■=. aa — b\ then extract the nth root of both sides, that is, in the present case the cube root, it will give xx — y ■=z >J aa — b; or making is/ aa — b = m, it will he xx — y ■=. m, and therefore y = xx — m. Now in the above equation writing a for a:^ + Zxy, and xx — m for y, there results the equation 4a^ — Smx = a. Now resume the equation 2x = »/ a -\- ^ b + \/ a — > and 21 — -«-, and 21—9, that is, 4-, VS '2, the square roots of which are i\^3, 4-/ 3, 2^3 ; therefore the three values of .y/ — 3/, will be -l-/ — 3, ■|-v' — 3, 2./ — 3 ; hence the three values of ^81 -\- V — 2700 are 4 + 4.^—3, and —4+4 ^ 3j and — 3 + iy/ — 3. And by proceeding in the same manner, there will be found the three values of v^81 —V— 270O, which are 4.-4.^—3, and f — 4/— 3, and — 3 — -i-v^ — 3. There have been several authors, and among them Dr. Wallis, who have thought that those cubic equations, which are referred to the circle, may be solved by the extraction of the cube root of an imaginary quantity, as of 81 + V^— 2700, without any regard to the table of sines : but that is a mere fiction; and a begging of the question ; for on attempting it, the result always recurs back again to the same equation as that first proposed. And the thing cannot be done directly, without the help of the table of sines, especially when the roots are irrational ; as has been observed by many others. Prob. 3. — To extract the nth Root of the Impossible Binomial a + \/ — b. Let that root he x -^ V — y; then making V aa -{■ b = m, and — — =/>, VOL. XL.3 PHILOSOPHICAL TRANSACTIONS. 1'J'J describe, or conceive to be described a circle, tiie radius of which is v'/ra, in which take any arc a, the cosine of which is —r\ and let c be the whole cir- cumference. To the same radius take the cosines of the arcs AC — AC+a2C — a2C+a3C — ASC+A. -hi 1 r ^ -, , , , , , , &c. till the number or them be equal to n. Then all these cosines will be so many values of x ; and the quantity y will always be m — xx. Prob. 4. — Having given any Equation, of the Kind of those above described; to know whether its Solution is to be referred to the Hyperbola or to the Circle. Let n denote the highest dimension of the equation : divide the coefficient of the second term by 2""' X n, calling the quotient m : then see whether the square aa be greater or less than m"; if it be greater, the equation is to be re- ferred to the hyperbola ; but if less, to the circle. Let there be given the equation l6,r* — 40:1^ + 20x = 7, where n := 5 ; therefore 2""' X « = 20: divide 40 by 20, the quotient is 2 = ?«; hence m" =. 32, and aa := 40; and as this is greater than the power 32, the equation is to be referred to the hyperbola. But since in the hyperbolical case there was put i/ aa — b = m, it follows that aa — b = m^ = 32, and therefore b = aa — 32 = 49 — 32 = 17. Now the root of the equation in this case is ^v'7 -)_^ jy ^7 _^ 17 : but v^l? = 4.123105 nearly; therefore 7 +/17 = 11.123105, and 7—^17 = 2.876895 ; also the 5th root of the former number is J.6221, and the 5th root of the latter 1.2353, the sum of which roots is 2.8574, and the half sum 1.4287 is the value of x in the given equation. Again, let the equation 16a;* — 40a^ + 20^ = 5 be given ; in which m is \ still = 2, but a = 5, and the square aa is less than 2^ or 32 ; therefore the value of X cannot be obtained without the quinquisection of an angle ; and that is performed by our general theorem, by taking, to the radius i/2, the arc whose cosine is ^ = ^ = -, which is the arc of 27° 55' nearly, the 5th part of which is 5° 35'. Now the log. cosine of that arc, to the radius l, is 9.9979347 ; but since our radius is V2, to that log. add the log. of ^2, that is 0.1515150, the sum will be 10.1484497; from which taking away the 10, the remainder 0.1484497 will be the log. of 1.4075 nearly, the number sought. And in like manner the other four roots may be found. It may be further remarked, that if the equation be of the hyperbolic kind, and n be an odd number, there will be only one possible root ; but if n be an even number, there will be only one value of the square xx, the rest being impossible. If the equation be of the circular kind, all the roots will be possible. To know how many of the roots will be affirmative, and how many negative, 378 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739. in equations to cosines, observe the following rule: if n be an even number, there will be as many affirmative roots as negative. But if n be an odd num- ber, but such that — ^ be an even number, the number of affirmative roots will be ^^^^^, and the number of negative — ^. But if ^ be an odd number, the number of affirmative roots will be "\-, and the number of negative n — 1 2 END OF THE FORTIETH VOLUME OF THE ORIGINAL. A Catalogue of the Fifty Plants from Chelsea Garden, presented to the Royal Society by the Company of Apothecaries, for tfw Year 1737, pursuant to the Direction of Sir Hans Sloane, P. R. S. By Isaac Rand, F. R. S. N" 432, p. 1. Vol.XLL This is the l6th annual presentation of this kind, making the number of 800 different plants. ^ Of the Measure and Motion of Effluent Water. By James Jurin, M. D. F. R. S. ^c. N° 452, p. 5. From the Latin. Essay I. Of Water issuing from a Vessel kept always full, through a round Hole ; and of its Resistance arising from a Defect of Lubricity. — ^The ancients had no other measure of effluent water, than that uncertain and falla- cious one, which, having no regard to the velocity, depended wholly on the perpendicular section of the stream. The first who opened a way to the truth, was Castelli, an Italian, and the friend of Galileo. He, having discovered that the quantity of water flowing through a given section of a stream, is not given, as the ancients thought, but that it is proportional to the celerity with which the water is carried through it ; by this noble discovery he laid the foun- dation of a new and most useful hydraulic science. This discovery therefore engaged the philosophers to study this doctrine so carefully, that after Castelli's time there was hardly any eminent mathematician, who did not endeavour to add something to it, either by experiments, or by reasonings and argument* k priori. But most of them, notwithstanding their great abilities, had no success in it, because of the exceeding difficulty of the work. For those who studied only the theory, laid down such theorems as were found to be false, when VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 279 brought to the test by experiments; and those who laboured in making experi- ments, omitting to observe some minute circumstances, the importance of which they had not yet perceived, differed greatly from one another, and al- most all of them erred from the real measure. Of this there cannot be given a better example, than that simple and easy one, which has generally been a foundation for all the rest, and is what we have now undertaken to treat of diligently, when water issues through a circu- lar hole made in the bottom of a vessel constantly full, with a constant velocity, Poleni alone has given the true measure of the water flowing out, or at least very near the true one; and Sir I. Newton alone has laid the foundation of discovering that measure; though most have rejected it, and some, concealing the author's name, have pretended that it was their own. We shall therefore make our attempt under the conduct of these two leaders; and in the first place propose, under the name of phaenomena, such things as either appear from experiments, or are confirmed by certain reasonings drawn from them; and in the last place, we shall attempt the solution of those phse- nomena. Phenomena of Water Rowing through a Hole in the Bottom of a Vessel constantly full. — 1. The depth of the water, and the time of flowing out being given, the measure of the effluent water is nearly in proportion to the hole. 1. The depth of the water, and also the hole being given, the measure of the effluent water is in proportion to the time. 3. The time of flowing out, and the hole being given, the measure of the effluent water is nearly in a subduplicate proportion to the height of the water. 4. The measure of the effluent water is nearly in a ratio compounded of the proportion of the hole, the proportion of the time, and a subduplicate propor- tion of the depth of the water. 5. The measure of water flowing out in a given time, is much less than that which is commonly assigned by mathematical theorems. For the velocity of effluent water is commonly supposed to be that which a heavy body would acquire in vacuo by falling from the whole height of the water above the hole, and this being supposed, if we call the area of the hole f, the height of the water above the hole a, the velocity which a heavy body acquires by falling in vacuo from that height v, and the time of falling t, and if the water flows out with this constant velocity v, in the time t; then the length of the column of water, which flows out in that time, will be 2a ; and the measure of it will be 2ap. But if we calculate from the most accurate experiments of Poleni, we shall find the quantity of water which flows out in that time, to be no more than about v*oVo of this measure 2af. 280 PHILOSOPHICAL TKANSACTIONS. [anNO 1739- Poleni's experiments seem to be preferable to all others, not only because of his extraordinary diligence and accuracy, but on other accounts also. He found, that the quantity of water flowing out of a vessel through a cylindrical tube, far exceeded that which flowed through a circular hole made in a thin plate, the tube and hole being of equal diameter, and the height of the water over both being also equal. And he found it to be so, when the tube was in- serted, not only into the bottom, which others had observed before, but also into the side of the vessel. Now a hole made in the thinnest plate must be considered as a short cylin- drical tube. Whence it appears that a greater quantity of water runs through a hole made in a thin plate, than would have run out, if the thickness of the plate had been what is called infinitely small. But as such a plate can neither exist, nor even be conceived by the imagination, it remains that we increase the diameter of the hole, that the thickness of the plate may bear the least proportion possible to that diameter. This Poleni performed with great judgment, when he made use of a diameter of 26 lines, and not quite a line thick ; whereas before him hardly any one made use of a diameter of above 6 or 7 lines, or ever attended to the thickness of the plate or bottom of the vessel, except Sir I. Newton, who mentions his making use of a very thin plate. But Poleni exceeded all others, in consider- ing not only the size of the hole, but of the vessel also, that the water might descend toward the hole with the greatest freedom, and the least impediment ; so that there can be no doubt but that the measures taken by him, come much nearer the truth than any other. 6. Since then the measure of the water running out in the abovementioned time T, is 2af X toVs-* the length of the column of water, which runs out in that time, is 2a X -nrgV- Therefore if each of the particles of water, which are in the hole in the same space of time, passes with equal velocity, it is plain that the common velocity of them all, is that which the space 2a X would be gone over in the time t, or the velocity v x , Vo'o • But this 0 0 0 is the velocity with which water could spring or jet in vacuo to near ^ of the height of the water above the hole. 7. But when the motion of water is turned upwards, as in fountains, these are seen to rise almost to the whole height of the water in the cistern. There- fore the water, or at least some portion of it, spouts from the hole with almost the whole velocity v, and certainly with a much greater velocity than V y\ 1 0 0 « • 8. Hence it is evident, that the particles of water which are in the hole at the same point of time, do not all burst out with the same velocity, or they vol.. 'XLI.] PHILOSOPHICAL TRANSACTIONS. 28) have no common velocity. Though mathematicians have hitherto taken the contrary to be certain. g. At a small distance from the hole, the diameter of the vein of water is much less than that in the hole. For instance, if the diameter of the hole be J , the diameter of the vein of water will be 44 or 0.84, according to Sir I. New- ton's measure, who first observed this wonderful phenomenon ; but according to Poleni's measure -|4 or '-/-r* ; '^hat is, if you take the mean diameter, 0.78 nearly. We should now proceed to the solution of these phaenomena ; but before doing this, it wiil be convenient to notice the following particulars. 1. We consider water no otherwise than as a fluid and continuous body, the parts of which yield to the least force, and are thereby moved among themselves. 2. By efRuent water, is understood that quantity of It, which actually passes out of the hole; and though it may seem unnecessary, yet it may he proper to mention, that in my dissertation on the motion of running waters, inserted about 24 years ago, in the Philos. Trans, by defluent water I understood that whole quantity of water, which is put in motion within the vessel, and descends towards the hole. jirr. 3. We consider the amplitude of the vessel as infinite, or at least so great, that the decrease of the depth of water, during the whole space of time in which the water flows out of the hole, is imperceptible. 4. We consider water as running out with a constant velocity. At the be- ginning indeed of the motion it runs out, for a very small space of time, with a less velocity than afterwards. But we pass over the very beginning of the motion, and investigate the measure and motion of water, when it has acquired its utmost velocity. Now this must necessarily be constant, as long as the height of the superincumbent water remains the same. 5. We conceive the bottom of the vessel no otherwise than as a mathe- matical plane, or at least as so thin a plate, that its thickness is little or nothing, with regard to the diameter of the hole. 6. By the measure of effluent water in the following pages, we always under- stand that quantity of water which flows out of the hole in the same space of time that a heavy body, falling in vacuo, would take in passing through the height of the water above the hole. , 7. By the motion of effluent water, we understand the sum of the motions of all the particles of water, which run out of the hole in the abovementioned space of time. But the motion of every particle^ is as the factum of the par- ticle itself, and of the velocity with which it bursts out of the hole. 8. That what we shall say hereafter may be the more easily ajnceived, we VOL. VIII. O o 282 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739- shall first propose the more simple cases, and then proceed to those which are more compound, but nearer to the true state of things. Thus, in the first Problem, that the solution may be the more simple, we suppose the water to run out of the hole into a vacuum, and the particles of water, while they descend towards the hole, to be without any resistance arising from a defect of lubricity. In the 2d and 3d Problems, the efflux of the water is still supposed to be in vacuo, but we conceive the particles of water, while they descend towards the hole, to meet with some resistance for want of lubricity, but so small, that the decrease of the motion of the water running out of the hole, thus occa- sioned, is to be accounted as nothing. In the 4th and 5th we still retain the supposition of the vacuum ; but the decrease of the motion of the effluent water, for want of lubricity, is supposed to be sensible. Lastly, in the 6th and following Problems, we consider the thing as it really is, when it is transacted in the air, so that the particles of water suffer a sensi- ble resistance, not only from each other for want of lubricity, within the vessel, but also after their going out of the vessel, from the attrition of the am- bient air. Pkob. 1 . To determine the Motion, Measure, and Velocity of IVater running into a Vacuum, through a Hole in the Bottom of a Vessel, where the Par-' tides of IVater meet with no Resistance for want of Lubricity. — So long as the hole is stopped, the stopper sustains the weight of a column of water lying perpendicularly over it. On removing the stopper, the column of water, which lies perpendicularly over it, being no longer sustained, by its pressure causes the water to run out through the hole, and after having brought it to its due velocity, keeps the velocity of the effluent water constant, by its con- stant pressure. , It must be conceived indeed, that the motion of the water running out of the hole is derived, not only from the weight of the perpendicular column, but partly from the pressure of this column, and partly from the pressure of the surrounding water. But this makes the motion of the effluent water neither greater nor less, than if it arose from the pressure only of the perpendicular column : not less, because the pressure of the perpendicular column, if it is obstructed, will generate a motion proportionable to itself, and it can only be hindered so far as the surrounding fluid urges the effluent water : not greater, because the pressure of the surrounding fluid can add nothing to the motion of the effluent water, unless it takes away as much from the pressure of the perpendicular column. . 1 A ' ', rOL. XLI.] PHILOSOPHICAL TRAN8A.CTIOK8. 283 Therefore the adequate motion of the water, flowing out of the hole, is tlie pressure or weight of the column of water over the hole. But a given force, howsoever applied, generates a given quantity of motion in a given time, to- wards those parts whither the force tends. Therefore the weight of the in- cumbent column, generates a like quantity of motion, in a given time, in the effluent water, as it could generate in the same time in the column itself, fall- ing freely through a vacuum. Now because, by the hypothesis, the particles of water find no resistance for want of lubricity, and all those particles, which are just going out in the very hole, are urged by an equal pressure of the superincumbent water, it is plain that the velocity of all these is equal. Let V be that common velocity; a the height, in falling from which in vacuo that velocity would be acquired ; A the height of the water above the hole; V the velocity acquired by falling in vacuo from the height a; t the time of falling from the same height; f the area of the hole; and let, the water flow out of the hole in the time t. Now, because in the time t, with the velocity v, the space 2a will be run over, the space — will be run over in the same time with the velocity v. Therefore this will be the length of the column of water, which flows out of the hole in the time t; and the magnitude of this column, or the measure of the water flowing out in the time t, will be , and the motion of the same will be _1£L. But the motion which can be generated in the column of water over the hole, in the same time, x, if carried by its own weight through a vacuum, is thus. Its velocity will be v, and as its magnitude is AF, its motion will be afv. But that motion, from what has been said above, is equal to the motion of the column of water flowing out in the time t, or afv = . Hence v = vy' ■ . V Also, the measure above assigned, of the water running out in the time x, or = AFv/2. a. E, I. V Carol. 1. — Since a : a :: v^ : v% therefore a = ^ = ^A. Therefore the height a, which the effluent water can reach, by turning the motion upwards, is half the height of the water in the vessel above the hole, which is the very height determined by Sir I. Newton, Princip. ed. 3, lib. 2, pr. 36. Carol. 2, — If we ascribe to the effluent water, that velocity which is acquired by falling from the whole height of the water above the hole, that is, if we suppose t; := V, then the above determined motion of the water , is := 2afv, or double that motion which can be generated by the column over the oo 2 284 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739. hole, and therefore not to be generated but by double this column, as in the Princip. ed. 1 and 3, lib. 3, pr. 36. Scholium. — ^This measure here determined kf^I, or 2af X O.707, as it falls far short of that which is generally determined by mathematicians, viz. 2af, so it far exceeds that measure which is shown by Poleni's experiments, or 2af X 0.57 1 ; and no wonder, for what is supposed in this problem, that the particles of water find no resistance in running down, the hypothesis is far from the true state of things. Prob. II. — To determine the Motion, Measure, and J^elocity of water, running out into a Vacuum, through a Circular Hole in the middle part of the bottom of a cylindrical vessel, where the particles of water find Some Resistance for want of a Lubricity, but so small that the decrease of the motion of the effiuent water occa- sioned, cannot be accounted any thing. Let abcd, fig. 4, pi. 7, be an immense cylindrical vessel: ef a circular hole made in the middle part of the bottom; and, the water being perfectly at rest and unmoved in the vessel, let the stopper be removed from the hole, that a passage may be opened for the water through it. Then because the water was at rest, and now begins to run out through the hole, and the water placed above follows that which runs out, and the natural motion of the water is not disturbed by pouring any over it, and the hole is in the very middle of the bottom, that portion of water which is in motion, and descends towards the hole, will necessarily assume some regular figure ahefkb, of which the lower base is the hole itself, and the upper base, the upper sur- face of the water ab, and all the horizontal sections are circular. This is called a cataract; but we do not yet examine what is the figure of the cataract: it is sufficient for our present design, to observe that it is regular, and that the same quantity of water passes in a given time through each of its horizontal sections. Now because all that water which tends downwards, is contained in the cata- ract, it follows that the rest of the water ahec, bkpd, which is without the cataract, has no motion at all, and is perfectly at rest. Therefore in any hori- zontal section of the cataract hck, whose centre is c, the points h, k, shall represent the bounds between the water descending towards the hole, and the surrounding quiescent water. Also, as the point k is the bound of motion and rest, and the particles of water, while they are in motion, find a resistance for want of lubricity, the particle of water a. within the cataract, fig. 5, next to the point k, must be carried downwards only with the least velocity. Otherwise it would necessarily carry with it the next particle a, placed without the cataract, contrary to the hypothesis. But the particle (3, which is contiguous within to the particle «, YOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 285 will only descend with the least relative velocity, with regard to the particle a; because otherwise it would carry the particle a. away with it, by accelerating it, and this particle a, being now in a quicker motion, would carry away with it the particle a. In like manner the particle y being placed more within, and contiguous to the particle (3, will descend with the least relative velocity with regard to the particle |3 ; and the other particles S, i, &c. being placed one more within than another, will descend with the least relative velocity, with regard to each of the particles lying next to each of them without. And by this means the absolute velocity of the particles must necessarily increase gradually from the bound towards the centre c, that the velocity of the water may be greatest in the very centre, and least at each bound k and h. But it is necessary that the resistance which each quicker particle finds from the friction of the adjacent slower one, placed without, should be perpetu- ally equal through the whole section of the cataract. Otherwise that particle which finds the greater resistance, will accelerate the adjacent slower particle, till the resistance is by this means diminished, and becomes equal to that resist- ance which is found by the other particles. But if the resistance be every where equal through the whole section of the cataract, the relative velocity of the particles will be also equal every where, when one of them necessarily fol- lows another. Therefore the absolute velocity of every particle, which is the sum of all the relative velocities, from the circumference of the section to that very particle, taken all together, is in the ratio of the distance of the same particle from the circumference of the cataract. Now let r be the radius of the hole, m to 1 in the proportion of the circum- ference to the diameter, mr^ the area of the whole, v the velocity with which the water descends in the centre of the hole, a the height by falling from which in vacuo the velocity v is acquired, a the height of the water above the hole, v the velocity acquired by falling in vacuo.from the height a, t the time of fall- ing from the same, z the distance of any particle from the centre of the hole, and let the water run out in the time t. Now the measure of the water, which goes out of the hole in the time t, will be found after this manner: z will be the radius of any circle within the hole, 2mz its circumference, 2mzz the nascent annulus adjacent to that circum- ference, and X V the velocity of the water in that annulus. Since v : — u :: 2a : 2ai' X the length of the stream flowing through the nascent annulus in the time x; the measure of that water will be 2mzz ■286 PHILOSOPHICAL TRANSACTIONS. [aNNW I739. r—x , ^^ rzx—z^z .,^a . „f .I- 1 ..■ 2OTAD. X 2av X = 4mAv X ; the fluent of which, viz. X3?V— 2z', vr \r 3vr when z = r, gives — - — for the measure of the water passing through all the hole in the time t. But the motion of the same water will be also found thus. The measure of the water running through the nascent annulus, in the time t, being -^^ X rzz — z'z, and its velocity being v X — — , its motion will be — — X 4mAt)* rzz — z'^i X n X = o- X r'^zz — 2rz^z + z'z, the fluent of which, T V/* when z = r, gives — — for the motion of the water, running out in the time T, through all the hole. But this motion is equal to that which the column over the hole can acquire, in the same time t, by falling by its own weight through a vacuum, that is to the motion afv, or av X mr^; therefore — - — = mavr^. Hence v = v \/ 3. Also the abovementioned measure of the water issuing at the hole in the time T, viz.—- - = „ — X vv^3 = —75-. a, e. i, ' 3v 3v v3 Carol. 1. — Since v^ : v^ :: a: a, therefore a = ^ = ^ X 3v^ = 3a. Tliere- fore the height to which the water can rise, with that velocity with which it runs out in the centre of the hole, is triple the height of the fluid above the hole. Carol. 2. — ^The figure of the cataract will be determined in the following manner : Let HK, fig. t), be any section of the cataract, having the centre c; and let its radius ck = y, the height of the water above that section, or ci = x, t the time of falling in vacuo from the height x, and as before let lf = r, and LI = A. Now the water passes through this section hk in the same quantity as it runs out of the hole ef. But if the vessel be shortened, so that its height be reduced from il to ic, and so that the section now becomes the very hole in the bottom of the vessel, the water will pass through this section in a given time, in the very same quantity as it passed through the same before the vessel was shortened. Now the vessel being shortened, the measure of the water issuing by the hole HK, in the time t, by the preceding solution, is — ^ , and the measure of the fluid issuing in the time t, is —'^ x j = -j^ X — ^: for t : r ::/A:y^ar. i VOL. XL!.] PHILOSOPHICAL TRAi^SACTIONS. •2€7 But, from what has been said above., the measure of the water issuing by the hole HK, in the given time t, when the vessel is shortened, is equal to the measure of the fluid passing in the same time through the section hk, when the vessel is entire, or equal to the measure of it issuing by the hole ep in the same time. Iheretore — -|- X — ;— = . ■, or y^^x= r v/a, or xy* = Ar , which is the same equation of the hyperbolical curve, by the rotation of which he formerly showed that the figure of the cataract was generated. Scho/.'l. — The measure of the water now found, 2mAr^\/^, or ImAr^ X 0.57735, rather exceeds the measure Imxr^ X 0.571, obtained from Poleni's experiments. But this difference, in some measure, arises from not considering the decrease in the motion of the water from resistance, in this problem. Schoi. 1. — The measure of the effluent water, as determined by this solution, is accurate, if the height of the vessel be considered as infinitely greater than the diameter of the hole. But as this height has a finite ratio to the diameter of the hole, the measure will be something less, so that, when the height is 5 times greater than the diameter, it will diff^er from the truth only the 320(X)th part, and when it is double, only about the 5 1 20th part, which differences are smaller than can be discovered by any experiment. And this small difference proceeds from hence, that the abovementioned relative velocity, and therefore the absolute velocity of the particles of water, which have been considered as in a direction perpendicular to the horizon, are really in a direction somewhat oblique, when every particle comes near the axis of the cataract in descending. But if a true and accurate solution be desired, when the altitude of the water has any ratio whatever to the diameter of the hole, it may be done as follows. From the property of the cataract curve, in corol. 2 of this problem, viz. xy* = Ar*. the subtangent of this curve at the place of the hole will be 4a, and at the place of any section the subtangent will be 4x, that is, 4 times the height of the water above that section. But such a cataract curve is described not only by the exterior water, which flows beyond the hole, but also by that part of the water which flows through any annulus of the hole, that is, every particle of water describes such a curve. Now let 2 be the distance of any particle, in the hole, from 'its centre, and let this particle descend through the smallest space in a tangent to the cataract curve. Hence its velocity in the direction of the tangent, or the velocity — ^^ V, explained in this problem, will be to the velocity in the perpendicular direction, as V^i6a* + z^ is to 4a; therefore the velocity in the perpendicular direction will be -7==== x — - " " ' „. 288 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739. And hence, after the manner of the above solution, the measure of the water passing through the nascent annulus will be — ^ X —p==L=z. The fluent of which being taken, either by Cotes's forms or by infinite series, when properly 'corrected, will give the whole quantity run out by the hole in the time t; which in a series is the quantity ?^ X 1 - ■—--, + Jq^, — &c. Hence, by supposing a to be infinitely greater than r, or the height than the hole, the measure comes out barely 2A.mr^\/-y, the same as was deternjined be- fore. Hence also. When A = lOr, the measure is ^Amr^v^-r X (1 — ttttto) nearly. And when a = 4r, it is 2AOTr^'/4- X (1 — -nVo) nearly. So that, instead of the true measure, we may always take 2AmT^\/-^, without any sensible error, even in so small an altitude, and much more in an altitude many times greater, as it usually is in experiments; which makes the computa- tion very easy, Prob. III. — Supposing again the same thing as before, and neglecting the acce- leration of the water without the hole; required to determine the Diameter oj" the F^ein of water at the small distance without the hole, where the vein is most con- tracted, and the Velocity of the water in the Vein so contracted. In the solution of the former problem it was observed, that the particles of water passing through the hole, do not all issue with the same velocity, but every one with a greater velocity as it is nearer the centre ; and that the relative velocity of the inner particles, with respect to the particles that touch each of them on the outside, is constantly equal through all the hole ; and this relative velocity proceeds from the resistance given to the particles, by the surrounding water, as they descend towards the hole. But after the water has passed the hole, and its outer surface is no longer resisted by the surrounding fluid, nor by the ambient air, because moving in a vacuum by the hypothesis, that relative velocity, or inequality of absolute velo- city, can no longer obtain. For now the swifter particles must necessarily acce- lerate the slower contiguous ones, and must also themselves be retarded by the slower, till all the particles have acquired one common velocity, which will happen at a small distance without the hole. But while all the particles are acquiring this common velocity, the diameter of the vein must necessarily be contracting. This happens in the same manner, as when a rapid river is joined with a slower, as the Rhone with the Saone: in the common channel, the velocity of the water from both rivers is equal, and the water passes through a section of this channel in like quantity as before, through the sections of both rivers ; though a section of the Rhone below the VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 289 junction is much less than the sum of the two sections of both rivers above the same. Therefore let the radius of the contracted vein of water, where all the par- ticles in its section have acquired an equal velocity, be f, and let that common velocity be called u: then as v : y :: 2a : — the length of the vein, and there- fore — " X m^^ Js the measure of the water passing through the section in the time t; the motion of which in that time is therefore — . But the measure of the water passing through the section of the vein, must be equal to that passing through the hole in the same time, that is, — V— = -::^'°'^?"-^' Also the motion of the water through the hole, as it is not altered by the action of the particles on each other, must be equal to the motion of the water through the section of the vein, that is, Avmr'^ = — , or 2f^u^ = r^v'^. Hence, dividing this equation by that immediately above, it gives Hence j" = ~ ='^x ■^, = ^r\ and j = r/^. q. e. i. Corol. — Since v^ = 4v*, and the altitudes are in the duplicate ratio of the velocities generated by falling through them, therefore this is the velocity of the water in the contracted vein, by which it can jet upwards in vacuo to ^ of the height of the fluid above the hole. Scholium. — This extraordinary contraction of the vein of water was first dis- covered about 30 years before, by Sir I. Newton, when he was considering the motion of effluent water more attentively, on account of some difficulties pro- posed by Mr. Cotes, who was then taking care of the 2d edition of the Prin- cipia; and Poleni afterwards confirmed it by many experiments. From that time this phenomenon has greatly exercised the wits of philosophers, without however detecting the true cause of it. The radius of the vein, ry^^, orO.Sldor, determined by this problem, is a little less than 0.84r, as delivered by Sir Isaac; and a little greater than 0.78r, according to Poleni's measure, being indeed nearly a mean between them both. Prob. IV. — Having given the measure of effluent water, through a circular hole in the bottom of a cylindrical vessel; to determine the motion of the same, and the velocity in the centre of the hole. Let the given measure of the water, issuing in the time t, be 1mr\q; to which the measure assigned by the analysis in prob. 2 will be equal, viz. vol. VIII. P p ago PHILOSOPHICAL TRAKSACTIONS. [aNNO 1739- Imr^A.q = — - — , or t; = 3vq. But the motion of the same water, assigned by the analysis in the same problem, is — — ; and by substituting here, instead of tJ^, its value just now found, that motion becomes Sq'^mr^AV, a. e. i. Carol. — If from the motion which can be generated in the time t, by the column of water over the hole, viz. mr^Av, be subtracted the motion of the water running out in the same time, viz. Zq'^mr^Av, there remains mr'^AV X 1 — 3q'^ for the motion lost by the resistance in the time t. Prob. V. — fVlth the same data and suppositions as before, and neglecting the acceleration of the water without the hole; it is proposed to determine the dia- meter of the vein of water at a small distance without the hole, where the vein is most contracted, and also the velocity of the water in the vein so contracted. By prob. 3, the measure of the water passing through a section of the vein, in the time T, is — - — ^; which is also equal to the given measure Imr^Aq; hence f'^u = r'^vq. Again, by prob. 3, the motion of the water passing through a section of the vein, in the time t, is — - — , to which is equal the motion determined by the former problem, viz. Sq^mrlAV; which gives 2fV = S^Vv^. But M = -^ — -^-7- = -l^v; and j'' = — i = r^vo X rr- = t'' ; therefore 0 = r\/^. Q. E. I. Corol. 1 . — The same ratio remains between the radius of the hole and that of the contracted vein, whether the motion of the effluent water be any how diminished by resistance, as in this problem, or not diminished as in prob. 3, being both ways the same, j = r\/-^. Corol. 1. — When the motion of the effluent water is diminished by resistance, the velocity is at the same time diminished in the contracted vein. For in prob. 3 it was u = -^v\/3, but now it becomes u = -l^v; so that u is diminished from 0.866v to 0.856v, taking q = 0.571, according to Poleni's experiments. Prob. VI. — Supposing the water issuing through a circular hole in the middle of the bottom of a cylindrical vessel, when the particles of water, as they floiv down- wards within the vessel, suffer so great a resistance from a want of lubricity, that the motion of the fluid is much diminished by it, and also the measure of the ef- fluent water being given; it is proposed to determine the motion of the same, and the velocity with which it passes through the middle of the hole. Let the given measure of the water, issuing in the time t, be Imr'^Aq, as in prob. 4 ; and by that prob. we have for the motion of the same Sq'^mr^Av, also the velocity with which it passes through the centre of the hole, or ti = 39V. a. E. I. VOL XLI.j PHILOSOPHICAL TRANSACTIONS. 1Q\ Corol. — When q is given, v is as v, that is, as v'a. Prob. VII. — Supposing the water issuing into the air, and neglecting the acce- leration of the water without the hole, proceeding from gravity; when any two of the following are given, it is pioposed to determine the third, viz. the measure of the effluent water, its velocity in the axis of the contracted vein, and the diameter of the same vein. When the water issues through the hole into a vacuum, it is shown, in the solution of prob. 3, that the velocity of the particles of water is the same in the whole section of the contracted vein ; but now, when the vein passes through the air, the velocity is no longer equal in all parts of the section: for the outer parts of the vein put the surrounding air into motion, and are retarded by it, so that they cannot acquire the same velocity as the rest. But the outer parts, when they are retarded by the air, retard the inner contiguous parts, and these the next ; and so by this means every outer particle is carried slower than the contiguous inner one, so that the velocity is greatest in the axis of the vein, and least at the circumference. For which reason it is. Dr. Jurin thinks, that the middle parts of the water in fountains rise much higher in the open air than they would rise in vacuo. Also, those parts of the air that are contiguous to the vein of water, when they are put into motion by this fluid, they put the adjacent ones into motion, that lie near them on the outside, and these the next outer ones, and these again the next, and so on successively to some distance without the circumfe- rence of the vein. But the velocity of the particles of water must necessarily so decrease, from the axis of the vein to its circumference, that the relative velocity of every par- ticle, wherever placed, must be every where the same, with respect to the par- ticle lying on the outside. For if any particle had a greater relative velocity than the rest, it would find a greater resistance from the attrition of the adja- cent outer particles, and thus would be reduced to an equal relative velocity with the rest. In like manner, every particle of the surrounding air, which is put into motion, will have all the same relative velocity with respect to the adjacent particles of the air outwards. But the relative velocity of the particles of water among themselves, is very different from the relative velocity of the particles of air; as may be conceived in this manner. Any particle of water in the outer part of the vein, is solicited by the next particle inwards, to accelerate its motion; and is also retarded by the next particle of air; and when that outer particle has acquired the due velo- city, these two contrary forces must needs be equal, one of which retards the particle, and the other accelerates it. But that cannot be done, unless the pro- p p 2 2Q2 PHILOSOPHICAL TRANSACTIONS. [aNNO 173Q. duct of the relative velocity, and of the density of the accelerating particle of water, be equal to the product of the relative velocity, and of the density of the retarding particle of air. But the density of air is to the density of water as 1 to 900 nearly. Therefore the relative velocity between the outer particle of water and the next of air, is to the relative velocity of the two next particles of water, as 90O to I nearly, Also, that inmost particle of^ air is solicited by the next contiguous particle of water to accelerate the motion, and retarded by the next particle of air out- wards. And as here two contrary forces are equal to each other, the product of the relative velocity and density of the accelerating particle of water, will be equal to the product of the relative velocity and density of the retarding particle of air. Therefore the relative velocity between those two particles of air, will be to the relative velocity between the inmost particle of air and the next of water, as gOO to 1 nearly ; and it will be to the relative velocity between the two next particles of water, as QOO X QOO to 1 nearly. And this great relative velocity will be always the same through the whole thickness of the ring of air, which is drawn into motion by the effluent water. Now let r, m, v, a, v, a, t denote the same things as in prob. 2. Also let V be the velocity of the water in the axis of the contracted vein, p the radius of the same vein, and r the radius of an imaginary vein, by which the velocity u, by decreasing gradually, in like manner as it decreases in the true vein, is at length reduced to nothing. Also let the measure of the water passing through the hole in the time t, be Iqmr^K. Now the measure of the water running in the contracted vein, in the same time, by proceeding as in Prob. 2, will be — — - X 3r — 2p. But these two measures are equal ; therefore Zqr'^ rv = up^ (3r — 2p). , Further, as the measure of the water running through the hole in the time T, is Iqmr'^A, the motion of the same, by Prob. 6, is 3q^mr^Av. And the motion of the water running through the vein in the same time, by proceed- ing as in Prob. 2, is found ^^, X (6rV — 8Rp^ -|- 3p'). Now these two art equal; and hence Q^V^rV = u^(6rV — 8Rp^ -|- 3p*). Then these two equations being rightly reduced for exterminating r, we come to the following equation, p^u'^ + 1q\jvr^f^ = I2q\'^r^f —Qqv'^r*. From which may be found any of the three quantities p, u, 5 ; viz. g = ^ ^/^v X \/(u -I- 69V — 2v/(3^uv -f 9^V — 2u^), ,=:^-^X (,- + 2^/3p'^-2r^), g'" VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 2Q3 Schol. I. — It was supposed above, that the motion of the water running through the contracted vein, is equal to the motion of that which runs through the hole. But this is not true in mathematical strictness. For the motion of the water running through the hole, is equal both to the motion of the water through the contracted vein, and to the motion of the ring of air surrounding the vein, which air is drawn into motion by the water running through the vein. But the motion of the ring of air is considered as little or nothing, since its thickness is not greater than ^^^, and its density not greater than the gOOth part of the density of the water. And thus the equations are rendered much simpler than otherwise they would be. Sckol. 2. — By corol. 1, prob. 5, when the water issues into a vacuum, the same ratio continues between the radius of the hole, and the radius of the con- tracted vein, whether the motion of the effluent water be in any degree dimi- nished by resistance, or not. Hence, as to a physical quantity, it is accounted sufficiently true, that the ratio between those radii be considered as given, even when the water flows through air, however the motion of the effluent water may be diminished by resistance, or at least that the said ratio is varied the least possible. And the same is found to be true by the experiments hitherto made. Also if the ratio is given between r and f, the ratio between r and r is also given, or the ratio between the radius of the hole, and the imaginary radius, by which the velocity u, by gradually decreasing, is reduced to nothing. For by eliminating u from the two equations above, we come to an equation which gives R = Aj -f — ■====-^. Besides, from one of the two equations we ob- tain 3r^R : p^(3r — 2p) :: u :g\: and since the former ratio is given, the latter ratio is also given, that is, the quantity — is given. Of two remarkable Caverns, the one Icy, and the other emitting noxious Effluvia. By Matthias Belius,* F.R.S. N° 452, p. 41. Abridged from the Latin. The icy cavern opens from the frozen Carpathian mountain, near the village of Szelicze, the mouth, which faces the north, being 18 fathom high, and Q wide. When the cold is severe in the country, M. B. says, the air within the cavern is warm ; but that it freezes within the cavern, when on the outside the sun shines with the greatest heat. When spring begins, and the snow melts, the water trickles down into the inside of the cavern, and is there frozen into transparent ice, by the power of the internal cold, forming large clusters of icicles, as • Authorof a history of Hungary in 4 vols, folio, with plates, entitled Notitia Hungariae Historico- geographica. Viennee Austr. 1735 — IZ^S. 294 l»HILOSOPHICAL TRANSACTIONS. [anNO 1739- thick as casks branching out into many surprizing forms.* Thus not only the arches, formed by nature in the solid rock, but also the floor of the cavern are thickly covered with clear ice ; which shines all about within the cavern, as if it were incrusted with crystal. M. B. seems chiefly to ascribe the freezing quality of the cavern to the saline nature of its texture. The nature of the Carpathian mountains, is saline, ni- trous, aluminous, and vitriolic ; hence he concludes must ensue an almost con- stant congelation. As to the cavern at Ribar, a village in the county of Zol, it emits very noxious vapours. It was formerly a rude copious fountain, and the water rising to a good height, overflowed on all sides. The water was petrifying; and generating a tophus, formed it gradually into such a mass, as became a kind of mound about the mouth of the spring, and dammed it up so as to prevent it from overflowing. But afterwards, when subterraneous waters flowed from the interior of the fountain in the hidden passages, the ground began to give way near the old foundation, and at length formed a new opening ; when it began to emit noxious vapours again, destructive to birds and other animals. In this cavern is heard the murmuring noise of running water ; so that a river probably flows through the interior passages, and at last loses itself in some kind of swallows. A very extraordinary Tumour in the Knee of a Person, whose Leg was taken off. By Mr. Jer. Peirce, Surgeon at Bath. N° 452, p. 56. William Hedges of Stratton in Somersetshire, 25 years of age, of a mus- cular healthy habit, had never known any kind of disease ; but about 8 years before, he first observed a small swelling on his right leg, near the supe- rior epiphysis of the tibia, which he called a splint, about the size of a split horse-bean. He was not conscious of any bruise on the part, and was quite free from pain; yet from its constant increase, which during the first 2 * Dr. Townson, who, in his Travels into Hungary, gives a particular account of this remarkable cavern, states that he found abundance of icicles in it in the month of July, but in a stale of thaw. The temperature of the cavern at that time (near Midsummer') was at Oof Reaumur's thermometer, i.e. at the degree of melting snow. He therefore infers that the masses of ice found in this cavern must be formed in the winter, and consequently that contrary to this author's account and to vulgar report, the temperature of the air in the cavern, regulated to a certain extent by the temperature of the atmosphere without, is lower in winter than in summer. However, as the temperature of the cavern is but slowly affected by the temperature of the external air. Dr. T. admits that, when a very warm spring suddenly succeeds to a severe winter, a freezing cold may prevail within the cavern, for some time after it has begun to thaw without, and vice versa. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. IQS years was very slow, but afterwards very fast, he was rendered quite incapable of labour from the time of hay-harvest 1735. Oil taking off the limb in May 1737, it weighed, with the leg and foot, 69 lb. which was 27 more than the leg some years before taken off at St. Bartholomew's hospital by Mr. Gay, for the like disorder. On examining this tumour, the adjacent muscles were found destitute of their fibrous and fleshy appearance, probably from the pressure, and great ex- tension, which they had suffered, and the little motion which for some years they had employed on the tarsus and toes ; but the fasciae and common mem- branes of the muscles, being greatly thickened and callous, adhered to the sub- jacent tumour; and on removing this callous integument, the tumour appeared covered with great quantities of blood-vessels, much distended, and of a colour more intensely red than natural. The tumour itself was cartilaginous for the space of half an inch from its external surface ; from whence it formed numberless bony substances of various forms, colours, and consistences, which, growing more and more numerous as they lay deeper, at last formed a continual substance completely ossified : in the centre of this bony substance was found about a quart of mucilaginous liquor, no ways fetid, though it was then 10 days from the operation, the colour and consistence of which nearly resembled that of linseed oil ; in which were observed many little bony substances loose and floating, similar to many others adhering to the internal surface of the cavity, all which had nearly the appearance of those irregular incrustations, which in hollow rocks are some- times made by the dropping of petrifying waters. After the operation, every circumstance of the cure proceeded well and the stump healed. Mr. P. thinks it worthy of remark that the parts above the tumour were very little altered from their natural state. The cartilaginous extremity of the femur was perfectly smooth ; nor had the rotula suff^ered any other injury, ex- cept the ossification of the ligament by which it is fixed to the tibia ; but the superior extremity of the fibula was wholly lost in the tumour. An Experiment concerning the Spirit of Coals. By the late Rev. John Clayton, D. D. N° 452, p. 59. Mention is here made of a ditch, 2 miles from Wigan in Lancashire, the water in which would seemingly burn like brandy, the flame being so fierce, that several strangers boiled eggs over it ; the neighbouring people indeed aflirmed, that about 30 years before it would have boiled a piece of beef; and that whereas much rain formerly made it burn much fiercer, now after rain it would scarcely burn at all. It was after a long continued season of rain that Dr. C. went to see the place, and make some experiments, when he found that a lighted 296 PHILOSOPHIC At, TRANSACTIONS. [aNNO 1739. paper, though it were waved all over the ditch, would not set the water on fire. He then had a dam made in the ditch, and the water thrown out, to try whether the steam which arose from the ditch would then take fire, but he found it would not. He still however pursued his experiment, and caused it to be dug deeper ; when at about the depth of half a yard, he found a shelly coal, and the candle being then put down into the hole, the air caught fire, and con- tinued burning. Dr. C. observed that there had formerly been coal pits in the same close of ground ; and having got some coal from one of the nearest pits, he distilled it in a retort in an open fire. At first there came over only phlegm, afterwards a black oil, and then also a spirit arose, which he could noways condense, but it forced the luting, or broke the glasses. Once, when it had forced the lute, coming close to it, to try to repair it, he observed that the spirit which issued out caught fire at the flame of the candle, and continued burning with violence as it issued out in a stream, which he blew out, and lighted again, alternately, for several times. He then tried to save some of this spirit, taking a turbinated receiver, and putting a candle to the pipe of the receiver while the spirit rose, he observed that it caught flame, and continued burning at the end of the pipe, though you could not discern what fed the flame : he then blew it out, and lighted it again several times; after which he fixed a bladder, flatted and void of air, to the pipe of the receiver. The oil and phlegm descended into the receiver, but the spirit, still ascending, blew up the bladder. He then filled a good many bladders with it, and might have filled an inconceivable number more ; for the spirit continued to rise for several hours, and filled the bladders almost as fast as a man could have blown them with his mouth ; and yet the quantity of coals he distilled was inconsiderable. He kept this spirit in the bladders a considerable time, and endeavoured several ways to condense it, but in vain. And when he wished to amuse his friends, he would take one of these bladders, and pricking a hole with a pin, and compressing gently the bladder near the flame of a candle till it once took fire, it would then continue flaming till all the spirit was compressed out of the bladder. But then he found, that this spirit must be kept in good thick bladders, as in those of an ox, or the like ; for if he filled calves bladders with it, it would lose its inflammability in 24 hours, though the bladder became not at all relaxed.* An Experiment concerning the nitrous Particles in the Air ; by the same. N" 442, p. 26. Dr. C. took a small gally-pot, and ground the top of it very smooth and true, * This so called spirit of coals, was inflammable air. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 207 and adapted to it a cover of blue slate, which he had likewise ground with much care. Into this gally-pot he put equal quantities of nitre and flowers of sulphur, about 1 dr. of each. He then fixed on the cover, putting it into a new digester, for 3 or 4 seconds. On opening it the next day, he perceived something had transpired between the top of the gally-pot and the cover ; the top edges of the gally-pot, where the glazing was ground off, being discoloured, though the nitre and sulphur were very little diminished as to their weight ; only they were melted into one lump, which he took out of the gally-pot. Having set the empty gally-pot on a shelf, on looking at it the next day, he found long hoary hairs, very bright and brittle, all around the ground edges of the pot ; which he gathered, and, tasting them, found them to be pure nitre. He then set the pot on the shelf again, and in 3 or 4 days, still finding there were fresh shoots made, as large as at the first, he gathered them a second and third time ; so that he supposed the pot Would have continued to have shot fresh nitre much longer, if he had not had urgent use for it, to make other experiments in. However, it is to be observed, that he had already gathered more nitre than he put into the pot at first ; though he had taken all, or nearly all the nitre that he first put in together with the sulphur, out of the pot in a lump. Hence he infers we may have some conception of the nature of mineral earths, and how they increase, when once impregnated with the seeds of a mineral. This is also a proof of the quantity of nitrous particles with which the air abounds, since the large quantity of nitre which he collected out of the pot, when left empty on the shelf, could be supplied by the air only. Concermng the Poison of Laurel-Water. By John Rutty, M.D. N''452, p. 63. Dr. R. expresses a wish that Dr. Mortimer's experiments with the milk, had more fully determined and ascertained it to be an antidote, than they have yet done. He was informed that some apothecaries in England, being used to sophisticate black-cherry-water with laurel leaves, will not be persuaded, that this is a poison on human bodies, notwithstanding our few instances ; but Dr. R. confirms that it really is so by the following case : At Lisminy in Westmeath, a girl of 18 years old, very well and healthv, took a quantity, less than 2 spoonfuls, of the first runnings of the simple water of laurel-leaves ; within half a minute she fell down, was convulsed, foamed at the mouth, and died in a short time, nor was there any swelling on her body. VOL. VIII, Q Q 2g8 VHILOSOPHICAL TRANSACTIONS. [anno 1739. Essay on the Measure and Motion of Effluent Water. By Dr. James Jurin, F.R.S. W 453, p. 65. Translated from the Latin. Part 11, being the Continuation from p. 284 of this volume. Of the Resistance of the Parts of Water among themselves arising from a Want of Lubricity. We must now consider that resistance of fluids whicli arises from the mo- tion of its parts among themselves, and is called, by Sir I. Newton, a resist- ance arising from a want of lubricity. He makes this of two sorts ; one aris- ing from the tenacity of the fluid, the other from the mutual attrition or friction of its parts. The former he thinks is uniform in a given surface, or that it produces an effect proportional to the time ; and this opinion is agreeable to experiments. The latter he considers as increasing in proportion to the velocity, or but little less. About this however he determines nothing, for want of experiments. Hypothesis. — The resistances arising from the want of lubricity in water. Dr. Jurin considers as in a ratio compounded of the three following. 1. Of the ratio of the surface of the parts moved ; 2. Of the ratio of the relative velocity with which the parts of water are moved among themselves ; 3. Of the subduplicated ratio of the altitude of the fluid. All which are allowed by Sir I. Newton, and most other philosophers. Prob. 8. — To explain the Resistance of the Parts of the Cataract which arises from the Want of Lubricity. Let r denote the radius of the hole, A the altitude of the cataract, y the radius of any horizontal section, :r the altitude of the cataract above that section, z the radius of any circle in that section, and v the velocity of the water in the centre of the hole. Then uv'- will be the velocity of the water in the centre of the section having the radius y ; and fi/- the velocity in the circumference of the circle of the radius z; also -Z)/- the relative velocity, and Imzi the surface of the nascent cylinder, to the radius z and altitude x : then, by the above 3 posi- tions, the resistance of cylindric surface, is as 9,mzx X -2 V - X yoc = — -—xz. Now let ^) ; hence p = \/I^^^7-i^, or, = x/i+(irJ£„)._-V„ by putting rE := nsA. And hence 2pms'^E is the measure ot the water issuing from the second vessel, in the time that a body falls freely through the altitude e. q.e.i. Corol. 1 . If the diameters of the holes be in the ratio of the altitudes of the water, the ratio of the measures will be the same, as if the water issued with- out any resistance. For, if r : « :: a : e, or rE = sa, and n = 1, then h p=.q ; and hence 2qmr^\ : 2pms^E :: 2mr'^A : ttw^e, which is the ratio of the measures when void of all resistance. Corol. 1. If E be considered as nothing in respect of the altitude a, then will n be as nothing also, and hence/) =■/•!-. Therefore the smaller the altitude e is taken, the nearer p approaches to V -r. Corol. 3. If s be infinitely great in respect of r, then \s p = V -^. There- fore the greater s is taken, the nearer p approaches to v^^. Prob. 10. — The Water Jlmving into the Air; to determine the Ratio between the Diameter of the Hole and of the Contracted Vein. This ratio cannot be determined without experiments. By prob. 7, p» = £Zl! X {v -\- 6q\ — l*^ 3qvv -j- gq^v^—lv^) ; hence p is determined, when q and V are known. But no experiments are known, by which q and v may be measured. Poleni's experiments show the measure of the effluent water, whence q is known : but they do not show the greatest distance to which the water is carried, when issuing horizontally from the hole ; nor the distance to which the middle part of the vein reaches, that issues with the velocity v. And Mariotte's experi- ments measure the greatest perpendicular height, to which water jets, when its motion is turned upwards, whence f' is known ; but they do not show the measure of the effluent water. Therefore, for want of proper experiments, the ratio can only be determined approximately, as follows. By schol. 2, prob. 7j it was made probable, that the ratio is constant be- tween these two radii, or at least that it is very little varied. From Mariotte's experiments it appears, that the difference between the altitude to which the I VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 301 water jets, and the altitude of the vessel, has nearly the duplicate ratio of the altitude of the vessel. Therefore let a be the height to which the water, in the axis of the vein, with the velocity v, can jet ; then, by Mariotte's experir njents, a — a is as a^ and — — ■ is a given quantity. But in one experiment, which Mariotte esteems a fundamental one, a was = 60 Paris inches, and he found a = 5Q inches, the diameter of the hole being half an inch. So that in this case — — — = 3600; and since this is a given quan- tity, it will be always SSoOa = 3600a — a% or a = — ^g^" "^ = A — ^. Therefore, if a = 1 inch, or double the diameter of the hole, it will be a= 1 — rir. But v^ :\^ ::a: \: 1 — ^^ : 1 . Therefore when the altitude of the vessel is double the diameter of the hole, there may be taken v^ = v'', or t; = v. Further, by cor. 4, prob. Q, as e decreases, p verges to \/-^. Therefore wlfen the altitude of the vessel is very small, as about 2 diameters of the hole, then we may takejb or 9 = -/-J-* , But, by prob. 7, j'' = i^ X (v + 6qv — Wzqvv + g^^v'—lli^), and here instead of v and q substituting their values just found, or v and -v/-^, there results p'' = rViX (I +2i/3 -2^1 + ^/3), or f^ = r^ X {I -V V ^ — 2\^T+V\) = 1^ X 0.6687553907 ; and hence p = r X 0.81777466. Here then is the value of p, when the altitude of the water is double the diameter of the hole : and since by schol. 2, prob. 7, p obtains a constant ratio to the radius of the hole, it will have the same value in any altitude of the water, q. e. i. Carol. 1. By prob. 7, k = ip + /-j— => hence by the value of p just found, there arises r = r X 3.98877 150, being the value of r when the altitude of the water is double the diameter of the hole : and since, by schol. 2 of the same problem, the ratio between r and r is constant, therefore r will have this same value whatever the altitude of the water be. Carol. 2. Because v is nearly = v, and q nearly = y^J- when the altitude of the water is double the diameter of the hole ; therefore, at this altitude of the water, — = \/3 very nearly. And since, by schol. 2, prob. 7, the ratio between V and ^v is constant, therefore — will be = v^3, whatever be the altitude of the water. Prob. 1 1 . The Water issuing from a Vessel always full, through a Given Hole, into the Air ; and having Given any one of the three following quantities. 302 PHILOSOPHICAL TRANSACTtONS. [aNNO J 789. viz, the Measure of the Effluent Water, the Velocity in the Axis of the Con- tracted Fein, or the Altitude to which the Middle Part of the Vein can jet up- wards ; required to determine the rest. Let A be the height of the vessel, r the radius of the hole, 2qmr'^A the mea- sure of the effluent water, v the velocity in the axis of the contracted vein, a the height to which the water can jet ; and first let 2qmr^A be given, whence q is given. Now, by cor. 2 prob. 10, — = v^3 ; hence v = qvi/3, and u* = a^^v* But v^ ?;^: A : a = ^ = S^'a. Secondly, if v be given ; then 9 = - /+, and 2qmr^A = —^^ /i, also a = -^. Lastly, if « be given ; since a = S^^A, hence q^ =^i and q = v/^— . Also v* = — , and v = vy'-. a. e. i. ^ O A O A A A Prob. 12. Having given the Height to which Water jets through the Air, from a Vessel of a Given Height, through a Given Circular Hole ; to determine the Height to which it will jet from any other Vessel, of any Given Height, and through any Given Circular Hole. Let the letters r, s, a, e, q, p denote the same things as in prob. Q ; and let a and e be the heights to which water can jet, when spouting from vessels of the respective altitudes a and e. Then, by prob. 1 1, a = S^^a, e = 3/)^e ; hence 39^ = \, and 1 - 3^^ = ^, and q = -/^, and;, = -/^, and jb^ = ■^. And since, by prob. 9, /> = V\ + C-^~''^y - ^-g^''^' °^ ^y putting ra = nsA, p = Vj + C "g/^ ")" ~ ^ ~6g'' ^ ' ^^"<^^ ^7 substituting ^^-^ for 1 — 3q^, and y/ j2 for Q> ^"d for a — a writing «, it is /> = ^vali ' and ;>' = ^^-^ g^^ • But /> = 5^ ; hence e = 2Aa + n'>'-««^^4Aa + »'x^ Hence, writing . for e - e, it is ^ = ;^- X 2ao » 6 2Aa (/4Aa + nV — n a). Now, t or e — e bring given, e is also given, or the height to which the water can spout from the new vessel, a. e. i. Corol. 1. If the holes in both vessels be equal, or * = r ; then e = nA, or n = -, hence £ = ^ X {^ 4Aa + n'«' — nx). VOL. XLI.3 VHILOSOPHICAL TRANSACTIONS. 303 Corol. 2. If the altitudes of the vessels be equal, or e = a ; then r = ns, or n = -, hence « = — x (^ Aka + raV — no). Carol. 3. If the diameters of the holes be in same ratio as the altutdes; then the water will spout to heights proportional to those of the vessels. For if r : s :: a: e, or rE := sx, and n = 1, then t = — , or t : a :: e : a, or e — e :a — a :: E : a, or e : a :: E : A. Carol. 4. Since 2p\/3Aa = \^4Aa + w'«' — nx, it will be t = — X 2/)V'3Aa =^^^^; hence, for \/a substituting its value above mentioned 9/3A, and properly reducing, « =^, or i = ^^. Corol. 5. Hence, by making/) = g, then £ = — -, or t: x:: rz^ : sa". That is, the defects of the jets, are as the diameters of the holes inversely, and as the squares of the heights of the vessels directly. Coral. 6. When s ■= r, then t = ^ nearly in the duplicate ratio of the heights of the vessel ; which agrees with Mariotte's rule. Corol. 7. When e = a, then i = — nearly ; that is, the defects of the jets are nearly as the diameters of the holes reciprocally. First General Scholium. — In examining the truth of this theory by experi- ment, it will be proper, 1 . To use a very large vessel, at least in the upper part, that during the time of making the experiment, the height of the water may not be sensibly changed. But if the vessel be not so large, but that during the efflux, the height of the water considerably decreases, then a mean between the greatest and least height is to be taken for the constant height : which is better than disturbing the natural motion of the fluid, by pouring fresh water into it. 2. Let the vessel be of such a depth, that when the water spouts from a hole in the side, the velocity of the fluid through the centre of the hole, may be safely taken for the velocity through all the hole, when there is no resistance. 3. Let the plate, in which the hole is made, be so thin, or at least have so thin an edge at the circumference of the hole, that the thickness there may be accounted as nothing with respect to the diameter of the hole ; observing to shave away the thickness of the plate on the outer side, leaving the inner side plain next the water. These things being prepared, the following experiments may be made, by which, as so many criteria, the certainty of the above doctrine may be judged of. Exper. 1. When the water issues through a hole in the side of the vessel. / / 304 VHILOSOPHICAL TRANSACTIONS. [aNNO 173Q. measure carefully the diameter of the contracted vein, observing whether it re- mains always the same, however the altitude of the water may vary. Exper. 1. Observe whether this diameter has always the same ratio to the diameter of the hole, in using different sizes of apertures. Exper. 3. Observe the quantity of water issuing in a given time, through the same hole, either in the bottom or the side of the vessel, with different altitudes of the water. Exper. 4. Observe the same, with holes of various sizes, but the same alti- tudes of the water. Exper. 5. Observe how much water issues in a given time, in two different cases, in each of which there is the same ratio of the diameter of the hole to the height of the water. For if the quantities be found in a ratio compounded of the duplicate ratio of the diameters, and the simple ratio of the altitudes, as in cor. 3, prob. 9, it will be a great confirmation of our theory. Exper. 6. In the same two cases, observe to what altitudes the water will jet upwards, through a large tube fitted to the side of the vessel, and perforated in its upper part. For if these altitudes be found proportional to those of the water in the vessel, as in cor. 3, prob. 12, it will be another sure confirmation of this theory. Exper. 7. Observe also the height of the jet, with the same hole, but various heights of the water. Exper. 8. Observe also the same, by varying the hole, but with the same height of the vessel. Second General Scholium. — Till those experiments be carefully tried, we must avail ourselves of the experiments hitherto made. These are of three kinds : for they measure either, 1 . The diameter of the contracted vein ; or, 2. The measure of the effluent water ; or, 3. The height to which the water jets. As to the 1st. The radius of the contracted vein, as measured by Sir I. Newton, is 0.84r, when the diameter 2r is ^ of an inch ; and by Poleni, it is O.JSr nearly, when the diameter of the hole is 2^ Paris inches. But by the calculation in this theory it isO.BlSr nearly, for any diameter of the hole; being nearly a medium between those two. 2. As to the 2d, none of the quantities, measured by any one, are of any use, except those by Poleni, when the water issues through the above size of hole made in a thin plate, which he informs us is much less than when it passes through a pipe of the same diameter. And the medium among 10 such measured quantities, is 2mr'A X 0.57 1, when the height of the vessel is 33 Paris inches VOL. XLI.] HHILOSOFHICAL TRANSACTIONS. 305 But the measure taken to this altitude, by our calculation, fron) Mariotte's fundamental experiments, is 2ffjr*A X O.5768, exceeding Poleni's measure about the 98th part only. 3. As Poleni rendered all the experiments of his predecessors useless, con- cerning the measure of the effluent water, because they took no account of the thickness of the plate through which the water issued ; it might be suspected that the like fault enters into the experiments concerning the height of the jet of water. But Poleni has removed this doubt, by another excellent observa- tion ; viz. that water issuing through short tubes, or through holes in a thin plate, spout nearly to the same horizontal distance, or issue with nearly the same velocity. Therefore, to try the certainty of our theory, let us make use of Mariotte's experiments concerning the altitudes of jets ; assuming some one of them, as a foundation, for trying the heights in the rest of the experiments, by our 1 2th problem. Taking therefore that experiment, in which the diameter of the hole was 6 lines, and the depth of water in the vessel 34 feet 11-^ lines, or 4 1 94. inches, in which case Mariotte found the jet spouted to the height of 31 feet 8 or 9 inches, or 380^ inches. Here then, A = 4194- inches, a = 380-|-, and ft = 39. But, in another experiment, where e, or the depth of water in the vessel, was 26 feet 1 inch, the water rose, through the same hole, to the height of 24 feet '1\ inches ; and by our cor. 1, prob. 12, the height of the jet, or the value of e, comes out 24 feet 3 inches, which is nearly the same. Other cases are exhibited in the following tables, where it appears how nearly the calculated heights of the jets, computed by our theory, agree with those observed in Mariotte's experiments, when made with holes of various sizes, and with vessels of different heights. I. With the Hole of 6 lines Diameter. Alt. of the Height of the Jet, Vessel. By Exper. By ( Calcul. Ft. Inc. Ft." Inc. Ft. Inc. 34 II-I-. ..31 84-. . . 31 H 26 1 ...24 24-. . . 24 3 24 5 ... 22 10 ... 22 10 12 4 ... 12 0 ... 11 11 5 6 ... 5 4^. . . 5 5 5 0 ... 4 11 . . 4 IH 35 5 ... 32 0 . . . 32 1 VOL. VIII, II. The Hole of 4 lines Diameter. Alt. of the Height of the Jet, Vessel. By Exper. By Calcul. Ft. Inc. Ft. Inc. Ft. Inch. 32 114^. ..30 0 ... 30 0 24 5 ... 21 84^ ... 21 11 5 6 ... 5 A^... 5 4A III. The Hole . of 3 lines Diameter. 34 1 H. . . 28 0 ... 28 0 26 1 ... 22 0 ... 22 1 24 5 ...21 2 ... 20 11 5 6 ... 5 4A... 5 3tV Kr 306 FHILOSOPHICAL TRANSACTIONS. j^ANNO 1739. Hence it appears, that the calculations from the above theory agrees so well with Mariotte's experiments, of the height to which the jets rise ; as also with Poleni's measure of the effluent water ; and with the diame- ter of the contracted vein, measured by Newton and Poleni, that it can hardly be doubted that the above theory is either true, or at least very near the truth. A Collection of the Observations of the Eclipse of the Sun, August 4, i738, which were sent to the Royal Society. N° 453, p. Ql. By Mr. George Graham and Mr. Short, FF. R. S. at Mr. Graham's home in Fleet-street, London, by a Refracting Telescope of \2 feet focus, armed with a Micrometer, and by a Reflecting Telescope ofQ inches focal length, p. 91. Beginning of the eclipse at 9'' 59"" 20' A. M. End at 11 59 36 Duration 3 O \6 Quantity of obscuration by the micrometer 2 dig. 28. min. 2. At Upsal, by M. Celsius, F.R.S, with a 7-foot tube, and a Graham's Mi- crometer, p. 92. 12** 18"" 52' ... . True time. Beginning of the eclipse. 12 42 22 ... . The end. O 23 30 ... . The duration. 3. At Wittemberg, by J. F. fVeidler, F.R.S. p. g'i. The beginning could not be seen for clouds. At 1 1*" 30™ increasing, 1 digit, eclipsed. 12 19 2 dig, 30' eclipsed. 4. At Bononia, by S. Manfredi, F.R.S. &c. p. 94. At 23'' O" 10" eclipsed, 1 digit. 0 3 o the middle ; 4^ digits. 1 18 1 the end of the eclipse. Some Electrical Experiments, chiefly respecting the Repulsive Force of Electrical Bodies.— By Granvile Wlieler, Esq. F.R.S. N" 453, p. 98. The following experiments were made in the autumn of the year 1732, and repeated to Mr. Grey the following summer. VOL . XLI.] rHILOSOPHlCAL TRANSACTIONS. 307 Prop. I. Bodies made Electrical, by communicating with an Electrical Body excited by Friction, are in a state of Repulsion with regard to such excited Bodies. Exper. 1 . — Mr. W. hung a fine white thread by a loop, to a horizontal blue silk, line, about 4 feet long, tied at each end, and at about a foot distance from it, placed a glass tube 2-i- feet long nearly, and one inch and quarter diameter, fixed in the centre of a circular piece of wood supported on three brass screws, so that the tube and pendulous thread were parallel to each other. The tube being rubbed, the thread was attracted and repelled 7 or 8 times J in very good wea- ther it moved to and from the lube 12 times, at above one foot distance. He then tied a piece of new smooth packthread to the top of the tube, and to the loop of the thread hanging down as before, and again excited the tube: the thread, without coming once towards the tube, went into and continued in a state of repulsion ; but if he only touched the communicating packthread with a finger, the white thread immediately hastened to the tube : and on hang- ing another long piece of packthread, which reached the ground, to the com- municating packthread, and again rubbing the tube, the pendulous white thread was so far from going into a state of repulsion, that it became attracted to the tube, and continued so, without showing the least tendency to a state of re- pulsion, as long as the virtue of tlie tube lasted. Exper. 2. He tied a piece of small cane, about l6 inches long, and one fourth of an inch diameter at one end, and a little more at the other, at right angles to the top of the tube, fixed in the same pedestal as before, and making unequal arms with it ; and at the end of the larger arm, a piece of stick trans- versely, about 6 inches long, so as it might slide backwards and forwards to and from the tube. This moveable short stick at one end supported a very fine white thread, at the other a very fine blue silk, by which means now a silk and a thread both at the same time hanging parallel to the tube. The thread, after the tube was rubbed, first was attracted, but then immediately repelled, and continued a considerable time in a state of repulsion ; but on tying to the end of the shorter arm of cane, a piece of long packthread, which reached down on the table, and rubbing the tube again, the thread continued in a state of at- traction, without being once repelled during the whole virtue of the tube, as in the preceding experiment. Yet the silk, whether the long packthread was added or not to the shorter arm of the cane, continued constantly attracted towards the tube ; but on putting a short silk only 6 inches long, in the same circumstances, it would, after some time rubbing the tube, turn into a state of repulsion, the upper part first bending from the tube, and the lower part to- R R 2 ^08 PHILOSOPHICAL TKANSACTIONS. [aNNO i 73 Q. wards it, the upper bending still increasing till the whole was repelled ; and it was remarkable, that the upper part or bending, on the approach of the finger, or any body not impregnated with electrical effluvia, flying towards it, and the under part or bending, rather seeming to fly from it, till the whole was satu- rated, and in a state of repulsion with regard to the tube, and then any part of it would come to the finger, or any other body, not made electrical. It is pro- per to add here one more difference remarkable between the thread and the silk. The thread in a state of repulsion touched with the finger, would immediately fly towards the tube ; but the silk in the same state, after touching several times, still continued in a state of repulsion, and would not be attracted till squeezed from top to bottom between the finger and thumb, once, and some- times two or three times. And further, the thread would immediately turn again into a state of repulsion, whereas the silk, after the violence committed by the thumb and finger, being attracted to the tube, would not without a good deal of rubbing the tube, be repelled again. Carol. 1. From the different state of the pendulous silk and threads at the same time, under the same circumstances, the former being attracted while the latter is repelled, it follows, that a mere vibration of the parts of the tube is not sufficient to account for the electrical phaenomena ; which ap- pears further from the two contrary states continuing some time, and from the same piece of silk being at once part in a state of repulsion, part in a state of attraction. Corol. 1. That some bodies immediately receive and immediately part with the electric effluvia ; but that others are some time before they receive it, or receive enough of it ; and when they have received enough of it, part with it more unwillingly. Corol. 3. That any light body, as a feather, after touching, or nearly ap- proaching the tube, must fly from it : on contact or a near approach, it satu- rates itself with the electric effluvia, and by this means becomes itself elec- trical ; and consequently from the foregoing experiments, is in a state of re- pulsion with regard to the tube. As soon as it touches any other body, it loses its acquired electricity, and therefore may be attracted as at first. Prop. II. Tivo or more Bodies made electrical, by communicaiivg with an Electrical Body excited by Friction, are in a state of Repulsion with re- gard to one another ; or Bodies made electrical by Communication, repel one another. Exper 1. Mr. W. suspended two pieces of white thread, each about one foot long, by loops, on a horizontal blue silk line, 4 feet long, about half an inch asunder from each other ; and on holding the excited tube over them at a VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 30g little distance, the two threads immediately receded from each other consi- derably at the bottom. He then removed one of the threads, and held the tube over the other, in the same manner as before. The single thread was not observed to move to either side ; consequently the moving of the threads side- ways was occasioned neither by the attraction of the cross line, nor that of the tube, nor by the frame of wood, to which the cross line was tied at each end, but only by their action on each other. He then added a third string, at the same distance from the second, that the second was from the first, and on holding the excited tube over the middle one, at tlie same distance from the cross silk, as before, when the strings continued in the same plane, the middle one stood still, and the string on each side of it receded considerably at the bottom part, which in this case must necessarily happen, on a supposition that they repel each other equally ; for the two con- trary forces of the outer threads destroy each other, and consequently the middle one must remain quiet ; but there was nothing to hinder the middle one from repelling the two outer on each hand sideways. When, as it often hap- pened, the three pendulous threads did not remain in the same plane, they then all receded from one another equally, and formed nearly a triangular prism ; the three threads being the three edges, or rather a triangular pyramid with the top cut oft". On suspending 4 threads at the same distance as before from one another ; if they continued in the same plane, they all parted, but the two outermost more from their neighbours, than the two in the middle from each other. If they moved out of the plane they were first in, they formed two prisms, each extreme with the two in the middle forming one, or rather a parallelopepid, less at top than at bottom. When 5 strings were suspended, either the middlemost continued sta- tionary when the plane was not altered, or if it was, they formed 3 prisms. Exper. 1. Mr. W. afterwards placed two cross blue silks, of the same length as before ; about half an inch asunder from one another horizontally, and tied at each end ; and on each of these, at different times, hung 2, 3, 4, and 5 threads, at the same distances as before, when every thing succeeded, as it ought to have done, on a supposition of their mutually repelling one an- other. Exper. 3. To each of the ends of two threads, suspended as at first, a fea- ther being tied, the two feathers manifestly receded from each other ; and when 3 threads had each a feather at their extremities, the middlemost became sta- tionary, and the two outer went off on each hand.- 310 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739, Exper. 4. Mr. W. suspended afterwards 2, 3, 4, and 5 blue silk strings by loops, on one cross blue silk, and found the several experiments succeed in the same manner as in threads ; except that they remained a longer time before they appeared in a state of repulsion, receded from one another more slowly, and continued much longer in the repulsive state, after the tube was re- moved. Exper 5. This done, he made several experiments, by mixing silks of dif- ferent colours, and silks and threads of different colours, and suspended them by turns on silks of different colours ; whence arose several different phaeno- mena. On suspending two black silks at the before-mentioned distances from each other, on a scarlet cross silk, they not only opened and receded from each other at the bottom considerably, but when the tube was held under, ran or jumped away from each other, to the very ends of the cross red silk that sup- ported them, taking 2, 3, or more jumps from each other. The same was observed of two white silks suspended on red silk, but they did not move away so briskly as the black. Exper. 6. Mr. W. tried whether threads hanging parallel as above, from a cross blue silk line, and joined with one or more transverse threads, so that the perpendicular threads remained nearly parallel, would mutually repel when the tube was held over them ; and they seemed to repel each other full as strongly as before. When they were joined by only one cross thread towards the top, the lower parts separated considerably ; when joined by two cross threads, one towards the top, and one towards the bottom, they separated both in the middle parts between the two cross threads, and at their lower ends under the second or lowest cross thread. When several were tied together at the top and bottom, and about a foot long, not by transverse threads, but in a knot at each end, they all bellied out from one another, describing a figure generated by an ellipsis, revolved about its greater axis ; approaching nearer to a sphere, the stronger the repulsive force was. And though it was only a ne- cessary consequence, he could not without some pleasure observe the knot at the bottom, as the strings swelled out, sensibly rising up. He could scarcely forbear imagining the bundle of silks, a bundle of muscular fibres. Exper. 7. He suspended two brass, and afterwards two iron wires on a cross blue silk, in the same manner as the threads and silks before mentioned, and found the experiments succeed as in threads of the same number, except that they did not recede so far from one another, which must necessarily follow from their greater weight. N. B. These experiments were n)ade sometimes with the tube held over. VOL. XLI.] PHILOSOPHICAL TBANSACTIOKS. 31 J sometimes held under the cross line ; but they generally succeeded best when the tube was held under the extremities of the pendulous wires, which in this xjase separated much further, and kept their repulsive force much longer. Exper. 7. Mr. W. hung up two fragments of barometer tubes, each about a foot long, by blue silk lines going through them, so that they hung parallel, horizontal, at equal heights, and about one quarter of an inch asunder ; on holding the excited tube above and under them, they manifestly receded from each other. He suspended the same fragments of tubes by blue silk lines of equal length, from a cross blue silk in a perpendicular position, each having a little red seal- ing wax at the upper end, to hinder the strings from slipping off. The excited tube being brought near them, they receded manifestly, especially at the lower ends ; the distance from one another, when at rest, being about a quarter of an inch. Carol. I . From the repulsive state of the pendulous threads, tied transversely with two or more threads, and bending out from each other, where at liberty, it follows that all the threads of a table-cloth, or other large piece of linen, when made electrical, have a tendency to fly from each other : and conse- quently, were the repulsive force strong enough, the whole would be dissolved, or torn in pieces. A short thread of black silk, by repeated applications of the tube, has separated into its smallest fibres. Whence is suggested more plainly, than from any other known experiment, a reason for the dissolution of bodies in their respective menstruums, viz. that the particles of the solvend having im- bibed the particles of the menstruum, so as to be saturated with them, the saturated particles become repulsive of each other, separate, and the mass flies to pieces. And hence perhaps arises a reason, why particles of bodies specifically heavier than the menstruums in which they are dissolved, are, after the dissolution and dispersion, suspended all over the menstruum, viz. that they repel each other. Attraction is insufficient; for parts attracted equally in all directions, are, in effect, not attracted at all; and the imperfection of the fluid will not do; for if this oc- casioned the suspension, striking or shaking the vessel would make them subside. Carol. 2. Hence we plainly see how heat may divide the particles of water with greater or less force, in proportion to the degree of saturation, and throw them into the air ; where they may continue to ascend, if at the same time they are divided, they are expanded into little shells or bubbles, of a diameter large enough to be specifically lighter than the lower air, as Dr. Halley has saga- ciously conjectured. Or if the upper parts of the air, as being less saturated than 312 PHILOSOPHICAL TRANSACTIONS. [aNNO iJSQ. the lower parts, may be able to draw them upwards, till the excess of weight, which is constantly increasing, is equal to the excess of attraction. Prop. III. Bodies, made Electrical by rubbing, do themselves repel one another, or the electrical excited Bodies themselves repel one another. Exper. 1 . The two fragments of tubes before mentioned, prop. 2, exper. 8, being suspended horizontally, and in a position parallel to each other, Mr. W. held in one hand, and with the other rubbed some time ; then gently letting them go so as to be at rest, they receded from each other towards that end which had not been taken hold of. Also, he suspended a single little tube, about a foot long, by a long blue silk line, perpendicularly, and on a table placed the great tube fixed in a stand as before, and excited each alternately, 2 or 3 times ; then gently moved the tube with the stand it was fixed in, near the suspended little one : the little tube ma- nifestly receded so much, that a cross blue silk line, stretched horizontally at about an inch distance on the opposite side, would sometimes, on the tirst ap- proach of the great tube, be touched by it. Exper. 2. Three scarlet silks, each pendulous by loops from a cross silk line, and close together, being rubbed downwards two or three times, between the finger and thumb, showed a considerable repulsive force with regard to each other, forming themselves immediately into a triangular pyramid, and conti- nuing in this state of separation some time ; and, which shows their attraction at the same time, with regard to other bodies not excited, coming to them when brought near them. He observed the same repulsive force in 3 yellow and 3 green silks, under the same circumstances, and excited in the same manner, but not in so great a de- gree as in scarlet. In blue the repulsive force was scarcely discernible after seve- ral times rubbing. Scholium. Dr. Hales, in the 12th article of his 13th experiment, in the 2d volume of his Statical Essays, observes, " That if a piece of one of the bronchiae or gills of the muscle shell -fish, be cut off, and put into a small concave glass, with three or four drops of its liquor, and be then placed under a double mi- croscope, the blood may be seen greatly agitated in the fine vessels ; and at the cut edge of the piece of gill, may with great pleasure be seen many blood-glo- bules, repelled from the cut orifices of the blood vessels, and attracted by other adjoining vessels : also other globules rolling round their centre, and repelling each other ; whence (as he says) it is plain, that bodies, by brisk rubbing and twirling about, may acquire, in a watry fluid, both attractive and repulsive virtue or electricity." VOL. XLI.] PHILOSOPHICAL TRANS ACTIOKS. 313 From our last experiments, we are led to think, that the globules of the blood, if by friction they acquire an electrical attractive virtue, must of neces- sity repel one another ; and that electricity is not so properly called an attractive and repulsive virtue, as a virtue attractive of those bodies that are not attractive themselves, and repulsive of those that are ; and that this repulsive force of the electrical blood-globules, excited by friction, as they flow in their channels (and particularly in the small ones, and perhaps more so in those of the lungs, where the refrigerating power of the air may assist, as Dr. Hales has observed) ; this repulsive force of the blood-globules, may be the great cause that hinders the blood from coagulating as it circulates ; may be the great cause of the constant perspiration in a healthy state, and of the increase of it, caeteris paribus, in pro- portion as the velocity and friction of the blood increases. If these things are so, the necessity of exercise appears more plainly than ever, in order to keep the body in a healthy state, as we may observe here the very steps that nature makes use of to free herself from her suppressions. ^n Account of some of the Electrical Experiments made hy Granvile JVheler, Esq. at the Royal Society s house, on May 11, 1737. By C. Mortimer^ M.D. R.S. Seer. N°453, p. 112. Exper. 1 . — A large octavo book was placed horizontally on silk lines, and the upper surface strewed with several pieces of leaf brass, all or the greater part of which flew upwards, from one another, and off the book, on holding an excited tube at a little distance underneath the book. Exper. 1. — Two lines were extended horizontally the whole length of the library, being between 30 and 40 feet, distant from one another about 2 feet at one end, and meeting together in a knot at their other ends, the whole lines being packthread, except 5 feet of silk line tied at each of the separated extremities, as well as at the knot where the other ends united, in order to stop the current of the effluvia. On the united extremities was placed hori- zontally a piece of card about 2 inches square, on which were strewed pieces of leaf brass. The excited tube being held at a little distance under the separated extremities of the packthread, the leaf brass on the card at the other end flew upwards, and off the card. Exper. 3. — Five glass receivers, placed one within another, on an electrical cement of bees-wax and Venice turpentine, were all exhausted. In the inner- most a fine white thread, about 5 inches long, was suspended from the crown of it, by means of a little cement made of bees- wax and oil. " On moving the excited tube up and down near the side of, and horizontally to and from the VOL. VIII. S s 314 rHILOSOPHlCAL TRANSACTIONS. [aNNO 173Q. outer receiver, the suspended thread manifestly made many vibrations corres- ponding to the motions of the tube. Exper. A. — An electrical circular cake of bees- wax and rosin, 10 inches in diameter, was placed horizontally on a tall glass receiver, near 3 feet high, such as is made use of for dropping the feather and guinea. This cake being the preceding evening about 8 o'clock, warmed with a hot iron held over it, and then struck perpendicularly all over its surface with the hands in parallel direc- tions, and so left covered with a thin pasteboard, was about 1 1 o'clock next day at noon gently uncovered, and an ivory ball, about one inch and half di- ameter, placed in the centre, a fine white thread about ten inches long, with a small piece of cork, the size of a pin's head, at the end of it, being held be- tween the finger and thumb, was gently let down on the vertex of the ball ; it first flew off at some distance, and then made several pretty regular revolutions from west to east about it, in the form of a circle. Exper. 5. — The ball was removed, and the cake again warmed and excited as before ; after which the ball was replaced at a little distance from the centre, nearer to Mr. Wheler ; the consequence of which was, that the pendulous little body moved with a direct motion as before, but in an orbit that resembled an ellipse, having the ball in one of its foci. Exper. 6. — Two bullets fixed on little stands of cork, about one quarter of an inch high, were placed on the cake, each about an inch distant from its centre, and in a line with the centre and Mr. Wheler ; the pendulous body described an orbit resembling an ellipse, having the two bullets for its foci, and the motion was direct from west to east. Exper. 7. — Instead of the cork, another pendulous body of a cylindrical form was made use of, tied to a fine white thread, about 20 inches long ; the cylin- der consisted of two circular bases of paper, half an inch diameter, but all cut away except a ring and a small bar across the middle, through which basis 6 equal fine threads passed at equal distances from one another, knotted at the lower base separately, and joined together in one knot at about half an inch distance from the upper base, from which knot proceeded the long thread. This body moved from west to east about the central ball, and at the same time discovered a motion about its own axis in the SHnie direction ; but after 2 or 3 turns generally stopped, and turned the contrary way, which seemed to arise from the untwisting of the thread. Exper. 8. — A thread about a foot long, was suspended from a horizontal line of packthread, aod parallel to it an excited tube placed erect in a stand, the thread approached the tube, and continued in a state of attraction. A thread of VOL. XL!.] PHILOSOPHICAL TRANSACTIONS. 315 the same length, suspended from a silk line, vibrated backward and forward 2 or 3 times, being first attracted, and then repelled, and continuing some time repelled; but on joining the top of the tube, by a packthread going round it, to the loop of the thread, the thread continued constantly in a state of repul- sion, showing no tendency to attraction. Exper. g. — Two black silks, about the same length with the thread in the preceding experiment, were suspended by loops from a horizontal red silk line, at the distance of about half an inch from each other ; on holding the excited tube under them, the silks swelled out from one another, and then jumped away on each hand to the distance of 1 feet. Exper. 10. — A circular board of nearly the same diameter with the electric cake, was suspended horizontally by 6 silk lines, tied to one silk line which was brought over a pulley at the top of a frame of wood, so as to be moved up and down. From the board hung 6 fine white threads, about 18 inches long, fixed by a little cement at equal distances from each other. The board being let down till the ends of the threads were about an inch distant from the electric cake, which was directly under, and had the ivory ball on its centre ; the threads all approached towards the centre of the cake, both when the ball was in the centre, and when taken away, keeping an equal distance from the centre, and from one another, as long as a packthread joined the circle of board and the frame to keep it steady ; and on removing the ball out of the centre, towards the circumference, the figure lengthened, the threads next the ball advancing nearer the circumference ; when the ball was placed at about an inch distance from the circumference, the thread that was before nearest the circumference whipped between the ball and the centre, so as to be almost in the same plane with its two neighbouring threads, the figure formed by the extremities re- sembling an ellipse with one end cut off. But when, instead of the packthread that joined the board to the frame, a blue silk line was tied in the same manner in all respects, the threads, instead of coming towards the centre, all flew away at a great distance from the cake, and from one another. It ought to be observed in the experiments of the circular motion of the pen- dulous body, that Mr. Wheler's hand seemed as steady as possible, except in the first experiment, when a little trembling appeared; Mr. George Graham taking a very good method to observe it, by keeping his eye fixed on a point at a considerable distance, in the same line with the end of Mr. Wheler's finger and his own eye. Yet when Mr. Wheler had finished the experiments to the satisfaction of all present, Mr. Hawskbee, Mr. George Graham, and Dr. Mortimer, held the thread with the pendulous body over the cake with the ball on its centre, after s s 2 3l6 PHILOSOPHICAL TRANSACTIONS. [aNNO \7'3g. the cake had been excited by Mr. Wheler ; but they had no regular revolutions at all, though several very manifest motions were made with the hand, to try if a projectile motion might by that means be given to the pendulous body. Mr. Wheler had tried the same thing with his servant ; from whence it is reasonable to conclude, that it is necessary, that the same person who excited the cake, should likewise hold the thread ; as if there were some analogy between the effluvia excited by the clapping of the hand on the cake, and the effluvia which may be communicated along from the hand which holds the thread to the piece of cork at the end of it. And this seems to be the reason of what the late Mr. Grey said, viz. That there was something in the human hand essential to the experiment, which he had not yet found in any other supporter of the thread. Some Remarks on the Electrical Circular Experiment* of the late Stephen Gray, F.R.S. By Granvile Wheler, Esq. N° 453, p. 118. Some uncommon circumstances led Mr. W. to make Mr. Gray's circular experiment in the following manner. While he excited a cake of rosin and bees-wax, 10 inches diameter, by clapping with his hand, he let the ivory ball remain in a basin of water ; then shaking off the drops, placed it in the cen- tre, and with his right hand held a fine thread, about 8 or Q inches long, having one end rolled up into a little ball, and the other, for about an inch, reduced to its greatest fineness, to only one fibre, himself and hand being supported on the back of a chair. The success was, he had a great many revolutions, to the number of 50, from west to east ; but at first not so regular as towards the last, at first describing only about 1 -third part of the circumference at a time, and after standing still a little, describing another third part. He might probably have had a great many more revolutions, but being tired, he was forced to rest himself, which he did for 10 minutes, then took up the thread again. The thread stood repelled at some distance, without making any revo- lutions, and at last only made half a one the contrary way to what it did be- fore; but on wetting it, by drawing it 2 or 3 times over the surface of the water, it made again 20 more revolutions from west to east, only at a smaller distance from the ball, for the water must make it heavier, but full as regular as before, and rather quicker. The virtue of the cake must now have lasted about 3 quarters of an hour. After resting about 6 minutes, he tried again with the string fresh wetted, the ball and cake continuing as before; and had, to his great surprise, 100 revolutions in the space of about 12 minutes, the * See Philos. Trans. N" 441, 444, of the Revolutions of pendulous bodies by electricity. — Orig. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 317 revolutions being still quicker, and more regular, and nearer the ball ; and at the 6th revolution of this last hundred, the thread was attracted to the surface of the ball, and, being wet, did not disengage itself, till pulled away ; yet after this, it described the remaining 9«1 revolutions of the hundred, and seemed inclined to describe a great many more, but that he was forced to rest his arm again, which he did for about 8 minutes, then tried again, the thread being fresh wetted, and had 70 revolutions at nearly the same distance from the ball in less than 9 minutes, all very regular, and without any attraction of the thread to the ball. He rested again 16 minutes, wet the thread again, and held it as usual; it was repelled at about -^ inch distance from the ball, but seemed to have no tendency to a circular motion ; yet after continuing stationary about a minute, he perceived a motion about its axis, about which it took several turns; but still had little or no progressive motion, till about a minute longer, when it began to move forward, and continued doing so from west to east, for about 33 revolutions, very regular, but slower than in the last two cases, the string having been held about 10 minutes, and the revolutions per- formed in about 7 or 8 of them. In each of these last 3 times, it whs rather longer before the progressive motion began than usual; and in all the trials of this experiment, he frequently perceived a motion about the axis, which was generally from west to east, though now and then the contrary way. The virtue of the cake n)ust now have lasted near 2 hours ; about 3 quarters of an hour after, he tried again, and had 60 revolutions from west to east, in about 10 minutes, the distance from the ball being still less than before, hardly -j- of an inch, scarcely any revolution about the axis appeared, and at the beginning the thread was twice attracted to the ball. About an hour and a half after, the virtue of the ball was not quite gone, the wet thread being repelled, and making 3 or 4 revolutions from west to east, as well as moving a little about its axis the same way. But as it was reasonable to suppose the ball itself in the centre of the cake was now dry, with a feather dipped in water he wetted its surface ; yet found no increase of virtue, rather a diminution of it, the pendulous body seeming scarcely at all repelled; but it is to be observed, that the ball, as it was wetting, twice tumbled over, and rolled on the surface of the cake; by which means the virtue of the cake might be much di- minished. It is not improper too to take notice here, that during the revolutions of the wet string, he frequently observed a kind of oscillatory motion, as if there was an alternate intention and remission of the repulsive force. As also that he often took notice of little plucks, and convulsive motions, in the pendu- lous body, and sometimes thought he has felt something like it in his 318 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739. arm that held it, though at no other time has he ever been sensible of any such thing. He several times after repeated this experiment with the thread and ball both wet, and found it succeed much better than when they were both dry ; and once he had 220 revolutions before he rested his arm. He tried too with the ball dry, and the string only made wet ; but the virtue did not continue so long, as when both were wet. He now flattered himself with hopes of success, if the thread was suspended from an undoubted fixed point, which therefore he proceeded again to try with the greatest care and caution, but in vain; the revolutions were uncertain. This ditFerence naturally led him to reflect on the cause of it. The tremor of the hand would not account for it ; for this being both ways backward as well as forward, must as often hinder as promote a continual motion one way: and though in two opposite parts of a circle, the motion is really in contrary directions, and therefore the contrary impulses of a tremor may promote a re- volution applied at opposite places of the orbit ; yet as these tremors are irre- gular, and succeed much quicker than the revolutions are performed, they seem insufficient to account for the motions of the pendulous body, performed with any degree of regularity. A stream of air in the room might impel along the tangent the pendulous body, kept at a distance from the ball by its repulsive force ; and then gravity, taking place, might with the first motion compound a curve: but still the re- sistance of the air would soon destroy the original impulse, could a few revo- lutions be performed; and besides, one revolution could not be performed, because the same stream of air that began the motion, must be contrary to it in its return. A finger held on the right hand near the pendulous body, when suspended from a fixed point, will make it revolve from west to east; but then it must be applied and removed alternately : the repulsive force therefore which the arm may acquire, by being held in the sphere of the effluvia, is insufficient ; for, as it is in one place, it must impel only one way, and constantly the same way; and therefore, like a stream of air in the room, though it might create the beginning, it must binder the completion of a revolution. Sometimes he doubted, whether the pulse of the arm might not be assisting in giving a projectile motion. When one leg is laid over the knee of the other, a motion and heaving of the leg that lies over, answering to every stroke of the pulse, is very apparent at a distance : the arm therefore in some posi- tions, in which its great artery meets with a proportionable pressure or resist- ance, may have a constant motion, though less perceivable. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. SIQ What seemed the most probable sohition, was this : when the arm is ex- tended, the posture being uneasy, there must be a re-action of the muscles, or a continual pulling of the arm towards the body. When therefore the right arm is made use of, the pulling will be from right to left; and consequently the motion produced in the body held by it in the same direction, or from west to east. When the left arm is made use of, the re-action of the muscles will be from left to right, and therefore the motion of the pendulous body from east to west. And, agreeably to this, he has observed, when he used his left hand, all other circumstances continuing the same, the motion of the pendu- lous body was from left to right, or from east to west, contrary to what was observed when held by the right hand. Yet still neither of these solutions would account for the variety of odd particulars he has met with under various circumstances. He proceeded therefore to try with rests for his arm of different heights, having an arm of wood, about 2 feet long, fixed to a rest for his telescopes, which could be raised to any height wanted ; and then the experiment succeeds only well, when the rest was lower than the electric area, and the arm was sup- ported on its elbow, which was the posture constantly made use of, when rested on a chair, the chair being lower than the electric area, that it might less affect the effluvia, as was then thought. He began now to think, whether it was not possible, that an inclination to a motion one way in the person that holds the body, might not have such an influence on the arm, and consequently the string and pendulous body, as to determine them the same way by some pressure or bias put upon it, though no motion sensible, even to himself, was produced in the hand. If so, he might, by a contrary inclination, produce a motion the contrary way. Having therefore a fine day, and the circular cake being well excited, he tried if he could not produce a regular motion from east to west, about the ball in the centre, having his hand supported, as usual, on the back of a chair. He found he could produce a very regular one from east to west for many revolu- tions, and change from one motion to another, without being sensible he moved his hand at all. He then wet the ball and string, as in the experiment beforementioned, and found he could tire himself with a motion either from east to west, or from west to east, as he pleased, without giving any motion, that he could perceive, to his hand or fingers. Hence many odd experiments that please, may, when repeated, succeed. Since therefore the motion of the pendulous body, from a point undoubtedly 320 PHILOSOPHICAL THANSACTIONS. [aNNO \73Q. fixed, is irregular, as he found by many different experiments, repeated with the greatest care and caution; and since he was convinced from these last mentioned trials, the motion from west to east, and from east to west, must generally have been determined by himself: he is inclined to think, that a desire of producing a motion from west to east, was the secret cause that de- termined the pendulous body to that direction, by some impression from Mr. Gray's hand, as well as his own, though he was persuaded at the same time, he was not sensible of giving any motion to his hand himself: and he the rather thinks this was the case, from the instance Mr. Gray gives, by way of explanation, of a man resting his elbows on his knees, this implying that he rested his arm on his elbow, as Mr. W. did himself. But though upon the whole it does at last appear, that this motion from west to east in a pendulous body, applied to another in the centre of an electric area, is to be ascribed to the hand that holds it, and not solely to the nature of the electric effluvia, or the figure of the central body ; yet still, perhaps, it may not be improper for astronomers to consider, whether or no a medium with this property, that all bodies immerstd in it, are repulsive of one another, ought not to be joined with gravity to explain the heavenly phaenomena; espe- cially since the phaenomena of fire, and our electric effluvia, have a great affinity to each other; and since many of the heavenly phaenomena are to be accounted for, on this supposition, with great simplicity; and some of them, that have not yet perhaps been fully accounted for, seem necessarily to follow. Of the Ivfluence which two Pendulum Clocks were observed to have on each other. By Mr. John Ellicott, F.R.S. N° 453, p. 126. '- The two clocks, on which the following observations were made, being de- signed for regulators, particular care was taken to have every part made with all possible exactness : the two pendulums were hung in a manner different from what is usual ; and so disposed, that the wheels might act on them with more advantage. Upon trial they were found not only to move with greater freedom than common, but a heavier pendulum was kept in motion by a smaller weight. They were in every respect made as near alike as possible. The ball of each of the pendulums weighed above 23 lb, ; and required to be moved about 1° 5' from the perpendicular, before the teeth of the swing wheel would scape free of the pallets ; that is, before the clocks would be set a going. The weight to each was 3 lb. which would cause either of the pendulums in their vibrations to de scribe an arch of 3". The two clocks were in cases, which shut very close. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 3'2J and placed sideways to each other, so near that when the pendulums were at rest, they were little more than about two feet asunder. The odd phaenomena observed in them were these : in less than two hours after they were set a going, one of them, called N° 1 , was found to stop ; and when set a going again, as it was several times, it would never continue going two hours together. A.s it had always kept going with great freedom, before the other clock, N° 2, was placed near it, this led Mr. E. to conceive its stopping must be owing to some influence the motion one of the pendulums had upon the other ; and on watching them more narrowly, the motion of N° 2, was found to increase as N'' I diminished ; and at the time that N° 1 stopped, N° 2 described an arch of 6°, that is nearly 2 degrees more than it would have done, if the other had not been near it, and more than it moved in a short time after the other pendulum came to be at rest: this made Mr. E. imagine that they had a mutual influence on each other. On this he stopped tiie pendulum of N° 2, leaving it quite at rest, and set N° 1 a going, the pendulum describing as large an arch as the case would per- mit, viz. about 5°. In about 20 minutes after, he went to observe whether there was any motion communicated to the pendulum N° 2, when, to his sur- prise, he found the clock going, and the pendulum to describe an arch of 3", whereas at the same time N° 1 did not move 4°. In about half an hour after, N° 1 stopped, and the motion of N° 2 was increased to very near 5°. He then stopped N° 2 a second time, and set N° 1 a going, as before ; and standing to observe them, he presently found the pendulum of N° 2 begin to move, and the motion to increase gradually, till in 17'" 40* it described an arch of 2° 10', at which time the wheel discharging itself of the pallets, the clock went. The arches of the vibrations continued to increase, till, as in the former ex- periment, the pendulum moved 5°; the motion of the pendulum N° 1 gradually decreasing all the while, as the other increased ; and in three quarters of au hour after, it stopped. He then left the pendulum of N° 1 at rest, and set N° 2 a going, making it describe an arch of 5° ; it continued to vibrate less and less, till it described but about 3°; in which arch it continued to move all the time he observed it, which was several hours. The pendulum of N° 1 seemed but little affected by the motion of N° 2, Mr. E. tried these experiments several times over, without finding any re- markable difference. The freer the room was from any motion, as people's walking about in it, &c. he found the experiments to succeed the better ; and once he found N° 2 set a going in 16™ 20*, and N^ 1 at that time stopped in 36"" 40«. VOL. viii, Tt 322 ■ PHILOSOPHICAL TKANSACTIONS. [aNNO I739. Further Observations and Experiments concerning the two Clocks ahovementioned. By the Same. N" 453, p. 128. The seemingly different effects, which the two clocks had on each other, Mr. Ellicott accounts for as follows. The manner in which the motion is commimicated to the pendulum at rest, he conceives to be thus: as the pendulums are very heavy, when either of them is set a going, it occasions by its vibrations a very small motion, not only in the case the clock is fixed in, but, in a greater or less degree, in every thing it touches ; and this motion is communicated to the other clock, by means of the rail, against which both the cases bear. The motion thus communicated, which is too small to be discovered but by means of some such-like experiments as these, may be judged by many, insufficient to make so heavy a pendulum de- scribe an arch of 2°, or large enough to set the work a going ; and indeed it would be so, but for the very great freedom with which the pendulum is made to move, arising from the manner in which it is hung. This appears from the ^erysm air weight required to keep it going, which, when the clock was first put together, was little more than 1 lb. And if the weight was taken off, and the pendulum made to swing 2°, it would make J 200 vibrations before it decreased half a degree, so that it would not lose the 3000th part of an inch in each vibration. Indeed if the weight was hung on, the friction would be increased, and the pendulum would not move quite so freely ; but even in that case it was found to lose but little more than the 2000th part of an inch, or about 3 seconds of a degree, in one vibration ; and therefore if the motion communi- cated to it from the other, will make it describe an arch exceeding 3", the vi- brations must continually increase till the work is set a going. And that the motion is communicated in the manner above supposed, is confirmed by the following expeciments : A prop was set against the back of the case of N° 2, to prevent its bearing against the rail ; and N° 1 was set a going ; then observing them for several hours, Mr. E. could not perceive the least motion communicated to N°2. He then set both the clocks a going, and they continued going several days ; but he could not find they had any influence on each other. Instead of the prop against the back of the case, he put wedges under the bottoms of both the cases, to prevent their bearing against the rail ; and stuck a piece of wood be- tween them, just tight enough to support its own weight. Then setting N° 1 a going, the influence was so much increased, that N° 2 was set a going in less than 6 minutes, and N° 1 stopped in about 6 minutes after. In order to try I VOL. XLI.J PHILOSOPHICAL TRANSACTIONS. 323 what difference would arise, if the clocks were fixed on a more solid floor, he placed them, exactly in the same manner as in the last experiment, on the stone pavement under the piazzas of the Royal Exchange, and stuck the piece of wood between them, as before ; and setting N" ) a going, the only difference was, that it was 1 5 minutes before N° 2 was set a going, and N° 1 continued going near half an hour before it stopped. From these experiments Mr. E. thinks it plainly appears, that the pendulum which is put in motion, as it moves towards either side of the case, makes the pressure on the feet of the case to be unequal, and, by its weight, occasions a small bearing or motion in the case on that side towards which the pendulum is moving; and which, by the interposition of any solid body, will be communi- cated to the other clock, whose pendulum was left at rest. The only objection to this, he conceives, is the different effects which the two pendulums seemed to have on each other. But this he hopes to explain to satisfaction. -^ For, notwithstanding these different effects, he soon found, by several experiments, that the two clocks mutually affected each other, and in the same manner, though not with equal force ; and that the varieties observed in their actions on each other, arose from the unequal lengths of their pendulums only. For, on moving one of the clocks to another part of the room, and setting them both a going, he found that N° 2 gained of N° 1, about l™ 36* in 24 hours. Then fixing both against the rail, as at first, he set them a going, and made the pendulums to vibrate about 4° ; but he soon observed that of N" 1 to increase, and that of N° 2 to decrease ; and in a short time it did not describe an arch large enough to keep the wheels in motion. In a little time after it began to increase again, and in a few minutes it described an arch of 2°, and the clock went. Its vibrations continued to increase for a considerable time, but it never vibrated 4°, as when first set a going. While the vibrations of N° 2 increased, those of N° 1 decreased, till the clock stopped, and the pen- dulum did not describe an arch of more than 1° 30'. It then began to increase again, and N" 2 decreased, and stopped a second time, but was set a going again, as before. After this N° 1 stopped a second time, and the vibrations continued to decrease till the pendulum was almost at rest. It afterwards in- creased a small matter, but not sufficiently to set the work a going. But N*^ 2 continued going, its pendulum describing an arch of about 3". Finding them to act thus mutually and alternately on each other, Mr. E. set them both a going a second time, and made the pendulums describe as large arches as the cases would permit. During this experiment, as in the former, he sometimes found the one, and at other times the contrary pendulum to make T T 2 324 PHILOSOPHICAL TRANSACTIONS. [aNNO I739. the largest vibrations. But as they had so large a quantity of motion given tiiem at first, neither of them lost so much during the period it was acted on by the other, as to have its work stopped, but both continued going for several days, without varying one second from each other ; though when at a distance, as was before observed, they varied 1"" 36* in 24 hours. While they conthiued thus going together, he compared them with a third clock, and found that N° I went !•" 17' faster, and N° 2 went ig' slower, than they did when placed at a distance, so as to have no influence on each other. On altering the lengths of the pendulums, the period in which their motions increased and decreased, by their mutual action on each other, was changed ; and would be prolonged as the pendulums came nearer to an equality, which, from the nature of the action, it was reasonable to expect it would. This dis- covers the reason why the pendulum of N° 2, when left at rest, would be set a going by the motion of N° 1 ; whereas if N° 1 was left at rest, it would not be set a going again by the motion of N" 2. For he found, by several experiments, that the same pendulum, when kept in motion by a weight, would go faster, than when it only moved by its own gravity. On this principle, which may easily be accounted for, it follows, that during the time in which the shortest pendulum, N° 2, was only acted on by N° 1 , it would move slower, and the times of its vibrations approach nearer to an equality with those of N" 1, than after it came to be kept in motion by the weight ; and by this means the time which N° 1 would continue to act on it, would be prolonged, and be more than was required to make the pendulum de- scribe an arch sufficient to set the work a going. But, on the contrary, while the pendulum of N° 1, which was the longest, was only acted on by N' 2, as it would move slower, the difference of the times of the vibrations would be increased ; and consequently the time which N° 2 would continue to act on it, would for this cause be shortened, so that before the pendulum of N° 1 would describe an arch sufficient to set the work agoing, the period of its being acted on would be ended, and it would begin to act on N° 2, at which time its vibra- tions would immediately decrease, and continue to do so till it came to be almost at rest. And thus it would continue, sometimes to move more, and at other times less, but never sufficiently to set the clock a going. A Wound in the Cornea of the Eye successfully cured. By Mr. Thomas Baker, Surgeon to St. Thomas's Hospital. N''453, p. 135. A young woman, about 15 years of age, on the 6th day of Nov, 1733, re- ceived a wound just in the pupil of her right eye, by the point of a common ♦ vol.. XLl.] PHILOSOPHICAL TRANSACTIONS. 325 fork. An inflammation followed, with great pain. The whole eye appeared dark and turbid ; and the humours seemed confused, and blended together. Mr. B. opened a vein in the arm, and drew away 10 oz. of blood : he then washed the eye with a collyrium of trochisci albi rhasis, and common water, made blood-warm ; and dressed it with a cataplasm of white bread and milk, with a little saflron in it. The next day there appeared on the wounded part of the cornea, a large thick slough : he dressed it in the same manner ; and so continued till the ] 8th day of the same month, when the slough cast off. He purged her during this time with decoct, sennae §ij, mann. solut. Jss, aq. paeon, comp. 3ij ; m. f. potio, at the distance of about 3 days, just as he found her strength would permit. The inflammation and pain abated daily. During the whole time, the eye was quite blind, till the slough cast off, when she com- plained she saw double. In a very little time her sight returned, but not so perfect as before ; her eye having somewhat of a cloud before it. He made her 6 visits at the distance of '2 or 3 days, after the 18th : when he left her, she saw perfectly well, that cloud which she before complained of, being removed ; her eye appeared fair and clear, and equally strong and useful to her as the other. A little speck, which was the cicatrix of the wound, re- maining on the cornea, he made her a fontanel in the arm, and ordered her to keep it open, and not to touch the speck on her eye. More than 2 years after- wards, the speck had gradually decreased, and was so small, that it was scarcely visible ; and her sight was as perfect and strong as before the accident. jin Account of a monstrous Boy. By Andrew Cantwell, M. D. dated Mont- pelier, Dec. 17, 1731, n. s. N°453, p. 137. There was at the above date at Montpelier, a boy 13 years of age, born at Cremona, who bore the lower parts of another boy, which seemed to issue from his epigastric region, between the cartilage ensiformis and the navel. The fore- part of the one faced that of the other. The head and trunk seemed buried in the boy's abdomen, down to the hips, where the connection was plainly to be seen. This portion of the prominent body had a well-formed anus and penis. The scrotum had a fine down on it, but was void of testicles, and seemed to be filled with the intestines. Nothing passed through these 2 outlets. Dr. C. could perfectly well distinguish the 2 ossa iliClm in their natural state, but could not feel the os sacrum. The articulation of the femur was somewhat dis- cernible on each side : and Dr. C. perceived the pulsation of the anterior crural arteries. The boy felt very sensibly when these additional feet, legs, or but- 326 J-HILOSOPHICAL TRANSACTIONS. [aNNO IJSQ. tocks, were pinched, or over-much pressed. He had lately had the small-pox, and these had suffered by it equally with him. At his navel Dr. C. found a considerable rupture, which was covered by this portion of a body. This rupture would grow monstrously large in wet weather, and would diminish again in dry. It had a circular hole in it, which ran through the peritonaeum. The boy was of a thin habit of body, but otherwise enjoyed good health. His father told the Doctor that this was the 7th child his wife bore him. She was 30 years of age at his birth, and bore hin) 2 more afterwards. All the rest were of the natural shape. Three extraordinary Cases in Surgery. By Bezaleel Sherman, Surgeon, at Kelvedon in Essex. N° 453, p. 138. Samuel Bush, being. on the top of a very high timber tree, in order to shake down the acorns, he let go his hold ; and by falling from one bough of the tree on another, he broke his thigh-bone ; and one end of it, by the force of the fall, stuck fast in the ground, which fractured the bone in another place, about 2-^ inches above the former. This entire piece of the os femoris was taken out; notwithstanding which, so large a callus united the two ends of the bone, that his thigh, when cured, was very little more than a quarter of an inch shorter than the other thigh. The surgeon who had the care of him, used his utmost endeavours, during the cure, to preserve the extension; but he imputed the largeness of the callus to a very great quantity of lap. osteocolla, which he made him take for 6 weeks or 2 months, in powder with milk, in an electuary, in his bread, and in his pudding ; in short, in almost all the food he took. One Fitch, of the parish of Kelvedon, had a foul ulcer in his mouth, with a caries in the lower jaw-bone, one part of which, from the suture at the chin to the end of it under the ear, in process of time entirely came out, with '3 teeth in it. This was also owing to a great quantity of osteocolla internally given, which was thought not only to expedite this large exfoliation, but at the same time to generate so large and firm a callus, that he can chew a hard crust, or any other food, on that side, as well as on the other. John Spilnian, had a sinuous ulcer in his rectum, about 2 inches from the anus. This had remained a twelvemonth, and was taken for the piles, and treated as such, both internally and externally. Mr. S. soon perceived a tumour in his buttock, 2 or 3 inches from the anus, which coming to suppuration, he opened it by incision ; and after dressing it several weeks with little prospect of success, he discovered at the bottom of the ulcer something that looked like a bone, which when extracted, proved to be the lower jaw of a fish, as a whiting. VOL. XLI.J PHILOSOPHICAL 'TRANSACTIONS. 327 or young cod, &c. And unquestionably this was swallowed at least a year be- fore it came away, because the pricking pain he felt when the sharp end of the bone stuok. in the rectum, was the symptom mistaken for the piles ; and when this had made its way through the rectum, and got into the fleshy part, the aposthume followed in course; and the bone being extracted, the ulcer was soon cicatrized by the common methods of cure in such cases. Account of a Woman, 68 Years of Age, who gave Such to two of her Grand- children. By Tho. Stack, M. D. N° 433, p. 140. A gentleman of credit having informed Dr. S. of a woman near 70 years old, who suckled one of her grand-children, his curiosity was excited to see so un- common a sight ; and the more, in order to try if he could not discover some fallacy in the affair. Wherefore he went in company with the gentleman, to a house in Tottenham-Court-Road, where the woman they inquired for appeared in an instant. Her breasts were full, fair, and void of wrinkles ; though her face was very much withered, her cheeks and mouth vastly sunk in, her eyes red, and running with a clammy humour ; and though she had in short, all the other external marks that one might reasonably expect to find in a woman, who had spent the last half of her past life in labour, troubles, and other concomi- tants of poverty, and through them had reached nearly to her 70th year. On pressing her right breast, she fairly squeezed out milk, which gathered in small drops at 3 of the lacteal ducts terminating in the nipple. This experiment Dr. S. made her repeat a 2d time, having himself carefully dried the end of the nipple with his handkerchief, as he had done before her first trial. Con- vinced of the truth of the fact, he asked her several questions about her case. The substance of her answers was as follows : Her name by marriage was Eliz. Brian. She was in the 68th year of her age, and had not borne a child for 20 years and upwards. About 4 years before, her daughter being obliged to leave an infant she then gave suck to, in the care of this her own mother, and likely to be a considerable time absent ; the old wo- man, finding the child froward for want of the breast, applied it to her own, barely in order to quiet the infant, without the least thoughts of milk. And this having reiterated several times, a son of hers, by that time grown a man, perceived that the child seemed to swallow somewhat from the nipple; on which he begged leave of his mother to try if she had not milk. The experiment suc- ceeded : the youth drew milk from that same breast from which he had been weaned above 20 years, and which had been unaccustomed to any for 17 or J 8 years before : the good woman then continued to suckle her grand-child in 328 PHILOSOPHICAL TRANSACTIONS. [aNNO IJdQ. earnest : and after some time her daughter, viz. the infant's mother, seeing she was provided with such an extraordinary and tender nurse, was emboldened to bid fair for an increase of issue, which till then she knew not how to nourish or provide for. Accordingly, at the end of 2 years, she brought forth another child ; on which the grandmother weaned the first, and suckled the latter ; which she had done for the last 2 years, and continued to do. And this infant, in Dr. S.'s presence, took the nipple with as much eagerness, and seeming de- light, as he ever perceived in a child of 2 years old ; and at it plainly performed the actions of suction and deglution. The 2 children, both girls, are, as to constitution, such as he could wish to the dearest friend ; plump and firm in flesh; in complexion cleanly, fair and healthy, and in temper brisk and sprightly ; considering the lowness of their condition and education, and the mean diet of the nurse. When this good woman came to town, which was near 2 years before, her milk abounded to that degree in both breasts, that, to convince the unbelieving, she would frequently spout it above a yard from her : a particular which, among others, the good man and woman of the house, and others of the neighbour- hood, likewise assured him of. At the above date her left breast became dry, and she had no great quantity in the right: but what remained was as good milk as could be desired in a nurse. The poor woman seemed perfectly honest and artless, and even tended strongly to dotage. ^ Letter from the Rev. Mr. John Clayton, afterwards Dean of Kildare in Ireland, to Dr. Grew, in Answer to several Queries relating to Firginia, sent to him hy that Gentleman, A. D. l687 *• N°454, p. 143. Having observed many mistakes in people's notions of Virginia, when speak- ing of the natives, which have arisen from the want of making a distinction in their expressions, when they speak of the English or whites, born there, thence called natives ; and the aborigines of the country ; Mr. C. therefore notices, that when he speaks of the natives in general, he means only the Indians. As therefore to the 1st query : — ^Their wiochist, that is, their priest, is ge- nerally their physician ; and is a person of the greatest honour and esteem among them, next to their king, or to their great war-captain. 2. Nature is their great apothecary, each physician furnishing himself, ac- cording to his skill, with herbs, or the leaves, fruit, roots, or barks of trees ; • This may serve as a sequel to the accounts of Virginia formerly given by Mr. Clayton. See these Transactions, N" 201, 205, 206, 210.— Orig. TOL. Xtl.] PHILOSOPHICAL TRANSACTIONS. 329 of which he sometimes uses the juice, and sometimes reduces them to powder, or perhaps makes a decoction of them. 3. Though every one, according to his skill, is a sort of doctor, as many women are in England, yet their priest is peculiarly styled their physician, to be consulted on greater emergencies. The rules of the descent of whom, as to families, Mr. C. does not know ; for they are a sullen close people, and will answer very few questions. 4. They reward their physician with no certain fees, but according as they bargain for Wampampeake skins, or the like. If the patient be an English- man, they will agree for a match-coat, or a gallon or two of rum, or so forth, according to the nature of the cure. Sometimes the priest will sell his remedy. 5. Their king allows no salary ; but every one that in any nature can serve his prince, is ready to do it, and to do it gratis. 6. They have no consultations, their practice being merely empirical. They know little of the nature or reason of things. Ask them any question about the operation of a remedy, and, if in good humour, perhaps they will reply, It cures ; otherwise they will shrug their shoulders, and you may ask 40 ques- tions, and not know whether they understand either the thing, or what it is you say to them. 7 . They pay a certain deference of honour to their priest or wiochist, whose person they hold sacred ; but they have no laws that bind them to it. In gene- ral, the will of their prince stands for reason and law. 8. The means by which they convey their art to posterity, Mr. C. takes to be this. They lodge in their wiochisan houses, i. e. their temples, certain kinds of reliques, such as men's skulls, some certain grains or pulse, and se- veral herbs, which are dedicated to their gods ; viz. the skulls in memory of their fights and conquests : the pulse by way of thanks-offering for their pro- visions ; and the herbs, on the same account, for some special cure performed by them. For when any one is cured by any herb, he brings part of it, and offers it to his god ; by which the remembrance of this herb and its virtue are not only preserved, but the priest also thus becon)es best instructed, and skilled in the art of medicine. For otherwise, they are very reserved of their know- ledge, even among themselves. Often when they are abroad hunting in the woods, and fall sick, or receive any hurt, they are then forced to make use of any herbs nearest at hand, which they are not timorous in venturing on, though they know not their virtue or qualities. And thus, by making many trials and experiments, they find out the virtues of herbs ; and by using simple remedies* they certainly know what it is that effects the cure. VOL. viii. U u 330 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739. 9. They are generally most famed for curing of woimds, and have indeed various very good wound-herbs, as an herb commonly called Indian-weed, which perhaps may be referred to the valerians, and be said to be platan i foliis. They use also the gnafalium Americanum, commonly called there white plan- tain. As to our plantain, or the heptapleuron, they call it the Englishman's- foot, and have a tradition, that it will only grow where they have trodden, and was never known before the English came into this country. The most famous old physician among the Apomatic Indians, used mostly an herb, the leaf of which is much like self-heal in winter. It makes a good salve, only it fills a wound too fast with flesh. The great success they have in curing wounds and sores, seems mostly to proceed from their manner of dressing them ; for they first cleanse them, by sucking, which, though a very nasty, is doubtless the most effectual and best way imaginable ; they then take the biting persicary, and chew it in their mouths, and thence squirt the juice into the wound, which they will do as if it were out of a syringe. They then apply their salve-herbs, either bruised or beaten into a salve with grease, binding it on with bark and silk-grass. 10. The distempers among the English natives, are, scorbutical dropsies, cachexies, lethargies, seasonings, which are an intermitting fever, or rather a continued fever with quotidian paroxysms. These are now rarely sharp, but show themselves in a lingering sickness. The griping of the guts mostly dry and when the tormenta ventris cease, they generally shoot into the limbs, and fix there, in a terrible sort of gout, taking away the use of the limbs. Thus they will pine away to skin and bone, so that their joints will seem dislocated, and their hands utterly crippled. Sore throats, which the last year were very frequent, and deemed infectious, running generally through whole families, and, unless early prevented, became a cancerous humour, and had effects like the French-pox. Likewise pains in the limbs, which seemed to proceed partly from the same humour floating up and down the body. These pains are very severe, mostly nocturnal ; for while they walk, if they have the use of their limbs, they feel the least pain. The oil of a fish called a drum, was found very effectual to cure these pains, and restore the limbs. There are three sorts of oils in that country, the virtues of which might not perhaps be found despicable ; the oil of drums, the oil of rattle-snakes, and the oil of Turkey bustards. The oil of sassafras-leaves may be deservedly considered too, for they will almost entirely dissolve into an oil. But to return. There is another sort of distemper, which seems to be the lepra Graecorum. And it may perhaps be no bad conjecture, that this chiefly proceeds from their feeding so much on a delicate luscious sort of pork. Among the Indians they have a VOL. XLI.] PHlLOSOi'HlCAL TKANSACTIONS. 33 1 distemper called the yaws, and is nearly related to the French-pox ; which, it is said, they cure with an herb tliat fluxes them. 11. The Indians mind neither the pulse nor urine, only judge by the com- mon most remarkable symptoms : and some pretend to form a judgment from the countenance, and are fond of being thought physiognomists. 12. Mr. C. never could find, that they practised blood-letting. They purge much with several sorts of roots of their own country growth, and vomit fre- quently with various herbs. They sweat boldly and excessively, and after a very strange manner ; for they have their sweating-stoves always on the bank of some river ; whence they rush forth in the height of their sweat, and run into the water, where they wash and bathe themselves very plentifully. They use no blistering-plasters, but are exquisite at cupping. As the East Indians use moxa, so these burn with punk, which is the inner part of the excrescence or exuberance of an oak. When they design to give a purge, they make use of the following herbs : puake-root, i. e. solanum bacciferum, a strong purge, and by most deemed poison. The roots of tythymal. of which there are two sorts ; the one flore minimo herbaceo, the other flore albo. The flower of this last is small, but large in comparison with the other : they are repentes, and grow in old manured grounds. They chiefly make use of the latter of these, and it is a most excellent purge, though it sometimes vomits. It is a quick, but moderate worker enough ; and has this peculiarity, that it opens the body in the gripes, when other more violent purgatives will not move it. There is another herb, which they call the Indian purge. This plant has several woody stalks growing near 3 feet tall, and perfoliat : it bears yellow berries round about the joints. They only make use of the root of this plant. They use also the small fleur de lis, whose virtues seem not yet half known, for it has some extraordinary qua- lities : it does not grow above a hand high, it flowers in March, and is very fragrant. They use also some sort of the apocynums ; particularly that which he thinks Gerard calls vincetoxicum Americanum , for there are several sorts of apocynums ; he thinks 1 3 or 1 4, but they are not all purgative. They have likewise several sorts of herbs for vomiting ; one of which is a little sort of squills. They likewise take the leaves of a certain curious odoriferous shrub, that grows in the swamps, which Mr.C. takes to be the lesser sassafras ; they bruise them in water, and then express the juice, which they drink warm. The Indian interpreter prized it much, as excellent physic, and said they found it a very sovereign remedy. The name the Indian gave it was wisochis, which is their general word for physic. 13. The rest of their Materia Medica consists of herbs, of which they have great plenty, and seldou» prescribe any thing else. Mr. C. collected above V u a 332 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739- 300 several sorts, that were no European plants ; but he mentions at present only the most remarkable. And first, the sassafras tree, whose root is well enough known. It shoots forth its blossoms in March, which are yellow, and grow in little bunches like grape flowers, and which, when gathered and picked from the husky bud, make a curious preserve. Most sassafras trees blossom, few bear berries, but those that do are generally very thick. They are shaped much like those of dulcamara, but are of a black colour, and very aromatic. The gum-tree, which he refers to the species of plane-trees, and distinguishes it by its fig-like leaf, only more sharply dented. Its leaf smells much like a lemon. The practice is to beat the tree, and then peel off the bark, and so scrape the gum, which has virtues like turpentine, but more astringent and drying. This they usually mix with their common turpentine, which is whiter and more butter-like, than the Venice or Chios turpentine. The further me- thod of preparing this medicine is this : they expose it to the sun on paper, where at first it rather seems to melt, but it will afterwards grow hard ; they then beat it to a powder, and administer it. They use much the young buds of the populus, sive tulippa arbor, a vast large tree, extraordinarily spacious, bearing flowers about April, much like tulips ; its leaves are large, smooth, and well-shaped, which, together with the flowers, render the tree exceedingly beautiful. It bears its seed coniferous, and is an excellent opener of obstruc- tions. The sorrel-tree bears a leaf something like a laurel, in taste much re- sembling lujula. They use it in fevers, and it seems with good success. This tree grows plentifully on the south-side of James river in Virginia. The swamp, plum-tree, the wood of which they calcine, and make into charcoal, which they beat to a powder, then mix it with grease, and make an ointment of it, with which they anoint the body, and foment it very much, thus curing the dropsy ; for it opens the pores to that degree, that the water runs down their legs. Among their herbs, Mr. C. had nearly 40 several sorts shown him, as great secrets, for the rattle-snake-root, or that kind of snake-root which is good for curing the bite of the rattle-snake ; but he has no reason to believe, that any of them are able to effect the cure. He mentions a herb, though unknown, yet worthy to be brought from Vir- ginia. It is the herb called there angelica, but which Mr. C. takes to be liba- notis vera latifolia Dodonaei. It grows generally on a rich sandy ground, on a declining brow, that faces the rising sun ; the root shoots deep into the earth, sometimes 3 feet, is very tender, and easily broken, of a white or rather cream- like colour ; and being lactescent, yields a little milk, thick and yellow as cream ; a very early plant. It seldom flowers or seeds under 5 years growth. The leaf is much like our wild angelica, only thinner, and more the colour of awil- VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 333 low-green. Those that seed, have a fistulous stalk about the thickness of dill, a white umbelliferous plant ; the seeds are much like angelica-seed, but from the fragrancy of the root, and its being peculiarly bearded, he styles it a iibanotis. It stops the flux, and cures it surprizingly. Again, it often loosens and purges the bodies of those that are bound, and have the gripes, especially if it proceeds from cold ; and it prevents many unhappy dis- tempers. He has known it give I'l or 15 stools, whereas it will not move a child in health. He thinks it the most sovereign remedy the world ever knew in the griping of the guts, and admirable against vapours. It is sudorific, and very aromatic, and will not be concealed ; for wherever it is mixed, it will have the predominant scent. It is mostly caUed by those who know it in Virginia, by the name of angelica. There is another root of the species of hyacinths ; the leaves are grass-like, but smooth and stiff, of a willow-green colour, and spread like a star on the ground ; from the middle shoots a tall long rush-like stem, without leaves, near 2 feet high ; on one side grow little white bell-flowers, one above another. The root is black outwardly, but brown within. It is bitter, and probably it has much the same virtues as little centaury. Some call it ague-grass, others ague- root, others star-grass. There are several others whose virtues are by no means despicable ; such as the chrysanthamum platani foliis, whose root is very useful in old pains, the sciatica and gout. It is a large herb, grows bet^veen 5 and 6 feet tall. There are likewise many others, which bear some analogy to the European plants, such as Solomon's seal, wood-sage, much better than the English ; which the Indians use much for infusions, and which they take as we do diet-drink. Little- centaury, red, white, and yellow, &c. However, he could never find above 12 or 14 plants, natives of that country, that agreed perfectly with any of our European plants, but what had some notable differences, if they were not rather to be reckoned a distinct genus. 13. There go traditions of their having an art to poison their darts ; but Mr. C. could never find any solid grounds for that report. He has observed, that in those countries, on an ill habit of body, the least scratch is dangerous ; and that, for all the care that can be taken to prevent it, it often turns into a very desperate ulcerous sore. And as persons engaged in long marches are liable to many accidents, which mjy contribute to an ill state of health, when a slight wound in battle has then proved mortal ; this he apprehends to have been the cause, why the physician has rather chosen to attribute the death of his patient to the poison of the dart, than the want of skill in himself. 14. As to their morals, they are simple and credulous, rather honest than 334 PHILOSOPHICAL TRANSACTIONS. [anNO 1 7 SQ. otherwise, and unpractised in the European art of lying and dissimulation ; but as to the brutal passions, they are sottish and sensual as the beasts of the field. 15. They are almost always either eating or sleeping, unless when they go a hunting. At all hours of the night, whenever they awake, they go to the homing-pot, that is, maze dressed in a manner like our peeled wheat ; or else a piece of venison barbecuted, that is, wrapped up in leaves, and roasted in the embers. 16. They drink little besides succahannah, that is, fair water, unless when they can get spirits, such as rum, from the English, which they will always drink to excess, if they can ])ossibly get them ; but do not much care for them unless they can have enough to make tl^m drunk ; and it seems they wonder much at the English for purchasing wine at so dear a rate, when rum is much cheaper, and will make them sooner drunk. 17. They use tobacco much, which they smoke in short pipes of their own making, having excellent clay, which Mr, C. tried in making crucibles, which he could not discern were inferior to the German. They make also neat pots of the same clay, which will endure the fire for ar)y common uses. J 8. They have no opium, though in some old fields on York river, there grow poppies perhaps of no despicable virtue. In fevers, and when their sick cannot sleep, they apply the flowers of stramonium to the temples, which has an effect like laudanum. It is asserted, that when the soldiers were sent over to quell the insurrection of Bacon, &c, being at James-town, several of them went to gather a sallad in the fields, and finding great quantities of a herb called James-town weed, they gathered it; and by eating it plentifully, were rendered foolish, as if they had been drunk, or were become idiots. Dr. Lee likewise assured Mr. C. that the same accident happened once in his own family ; but that after a night or two's sleep, they recovered. 19. Their sports are dancing: tlieir games are playing with straws, which as he was not perfectly acquainted with, he found it hard to describe; he can therefore only tell how it appears to a spectator: they take a certain number of straws, and spread them in their hands, holding them as if they were cards, then they close them, and spread them again, and turn them very suddenly, and dextrously. Their exercise is hunting, that is, shooting with a gun, or with bow and arrow, in which they excel. Their women work, plant the corn, and weave baskets or mats. 20, Several have been very old; seemingly without any remarkable difference between them and the English natives. If the English live past 33, they gene- rally live to a good age ; but many die between 30 and 33. VOL, XLl.] PHILOSOPHICAL TRANSACTIONS. 303 21. Mr. C. has been told, that one of their famous wiochists prophesied, that bearded men, for the American Indians have no beards, should come and take away their country, and that there should none of the original Indians be left within a certain number of years, he thinks it was 150. This is very cer- tain, that the Indian inhabitants of Virginia are now very inconsiderable in number; and seem insensibly to decay, though they live under the English protection, and have no violence offered them. They are certainly no great breeders. 22. Though they are sluggish by nature, and slow of speech, yet their me- thod of expression seems vehement and emphatical, and always attended with strong gesticulations. They are generally well proportioned, and for the most part are rather taller than the English. They have all either a very dark brown hair, that may well be called black, or a jet-black, all lank. An Experiment, to prove that Water, when agitated by Fire, is vastly more elastic than Air in the same circumstances. By the late Rev. John Clayton, Dean of Kildare in Ireland. N" 454, p. l62. Mr. Clayton having contrived a curious digester, in which bones could be easily dissolved in a very short time, he performed some trying experiments with it. In a small one having included about a pint of water, and, about §ij of a marrow-bone, he placed the vessel horizontally between the bars of the iron grate, about half way into the fire; and in 3 minutes time he found it raised to a great heat; on which he thought to have taken it out of the fire, lest it should have burst. For he remembered, that the screws of a digester, made after Mr. Papin's method, giving way, the head flew one way and the screws and irons another, with such violence, that the head having struck a brick, cut a piece quite out of it; which was one reason for his contriving a digester in this way, that the screws cannot possibly start, but that the vessel would sooner break in any other part. On a sudden however it burst, as if a musquet had been discharged. A maid that was gone a milking, heard it at a considerable distance; the servants said it shook the house. The bottom of the vessel, that was in the fire, gave way; the blast of the expanded water blew the coals quite out of the fire, all over the room ; for the back of the fire-range was made just like an oven, so that circulating in it, it brought out all the coals at the mouth. Ail the vessel together flew in a direct line across the room, and striking the leaf of a table, made of an inch oak plank, broke it all in pieces, and rebounded half way of the room back again. He could not perceive any 336 PHILOSOPHICAL TRANSACTIONS. [anNO IJSQ. where in the room the least sign of water, tliough he looked carefully for it, and had put a pint into the digester, save only that the fire was quite extin- guished, and every coal belonging to it was black in an instant. But to confirm the elasticity of water, or to show, at least, that there is a much stronger elastic force in water and air, when jointly included in a vessel than when air alone is inclosed, he made the following experiment: he took two §vj phials, into the one he put about §v of water, or better, and so corked it as well as possible; the other he corked in the same manner, without putting any thing into it. He inclosed them both in his new digester, four-fifths being filled with water; when the heat was raised to about five seconds, he heard a considerable explosion, and a jingling of glass within the vessel, and shortly after another explosion, but not so loud as the former; whence he concluded, that both the phials were broken. He then let the digester cool leisurely, and the next day he opened it; both the corks were swimming on the top of the water, but only one of the phials was broken, viz. that one into which he had not put the water. Again, having had some very strong phials made, to make some peculiar experiments, he took one of them, and having filled it about a quarter full with water, and corked it very well, he set it in a square iron frame, with a screw to keep down the cork, and keep it from flying out. He then put it into a digester, four-fifths filled with water; which being heated to a due height; when opened, he found the cork forced into the phial, though the cork was so very large, that it amazed several who saw it, to conceive how it was possible for so large a cork to be forced into the bottle. Hence it manifestly appears, that the pressure in the digester, in which was proportionally more water, and less air, was stronger than the pressure within the phial, in which was propor- tionally more air and less water. Then Mr.C. reasoned thusalsoof the two former phials : thattheair in the phial, in which was included no water, making not a proportionate resistance to the ambient pressure in the digester, in which was a considerable quantity of water, the cork was forced inward with such violence, that it, together with the water, dashed the phial in pieces; but that in the other phial, in which there were five- sixths of water, the inward pressure in the phial being greater than the ambient pressure in the digester, in which were only four-fifths of water, the cork was forced outward ; and that the small difference between the proportionate quan- tity of water and air in the phial and in the digester, being only as four-fifths to five-sixths, was the reason, not only why the bottle was not broken, but also of the faintness of the explosion. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 337 Of a Girl, three Tears old, who remained a quarter of an Hour under Water without drowning. By John Green, M. D. Secretary of the Gentleman s Society at Spalding in Lincolnshire. N° 454, p. 1 66. On the following case Dr. G. observes, that the reason of the child's being able to abide so long under water was pretty evident: the child, most likely, was infirm, weak, and sickly, from the time of her birth, so that the foramen ovale was not grown up. He remembered about 3 years before to have seen a subject, a woman, 80 years old, who had the foramen ovale so large, that one might easily thrust the middle finger through it ; but she was attended with the above-mentioned circumstance, that is, she never enjoyed a moment's health in her life. May l6, 1737, Rebecca Yates, of Billson near Market-Bosworth in Leices- tershire, had a daughter about 3 years of age, that fell into the milldam at the head, near the mill-wheel; and, by the force of the stream, was drawn under the water to the wheel, with her legs forwards ; one of her legs went under the mill-wheel, and by reason of the nearness of the wheel to the floor of its water-way, the bulk of the child's leg stopped the wheel from moving at all. The sudden stopping of the mill so much surprised the miller, that he went immediately, and let down the shuttle; but finding it would not go quite down, he came up again into the mill, and looked both above and below, to see if he could find out the cause; then went and drew up the shuttle, and let it down again ; but as the gate would not shut quite down, he could not as yet find out the cause of his mill standing still; for which reason he went backwards and forwards between the shuttle and mill-room, for 8 or 10 times, before he found out the cause; but at last he drew the shuttle quite up, by which means the force of the water drove the child from under the shuttle; then he put the shuttle quite down, and thereby discovered the child with her leg under the wheel, and lying on her face. The first word she spoke was, help me, which she repeated 3 times; the miller left her arm for some other person to hold her, while he endeavoured to remove the wheel, so as to get out her leg; and then she said again, for God's sake help me out, if you can: she spoke very briskly, after she was put to bed. But the mill-wheel had torn away all the shin, mus- cles, sinews, and tendons, of her leg, quite to the bone, and stripped them down to her heel ; besides, the shuttle was drawn up and let down on the small of her back several times. The child lived from Monday till Friday, and then died of her wounds and bruises. The whole time of her being under water, which was at the depth of 4i feet, was near 15 minutes. VOL. YIII Xx 338 PHILOSOPHICAL TRANSACTIONS, [aNNO I ZSQ. The Case of Mr Cox, Surgeon at Peterborough, who fell into a Pesti- lential Fever on tapping a Corpse lately dead of a Dropsy, drawn up by hivi - self, and read before the Peterborough Society, Sept. 1, I736. N° 454, p. 168. An elderly gentlewoman, labouring under a dropsy about 12 months, under- went the operation of tapping 4 several times, by which 35 quarts of liquor were discharged; and dying at last of the distemper, Mr. C. was desired by her friends to let out the water that was then contained in the abdomen, as well to preserve the corpse the longer from putrefaction, as to prevent an annoyance to the company at the time of her funeral. — Yet notwithstanding this was done within a few hours after death, the included humours were become so putrefied as to discolour the external parts with a green and livid hue. The liquor itself was green, and somewhat thicker than new milk; in smell more fetid and of- fensive than what he ever met with, and so sharp and acrimonious in its nature, as deeply to corrode a silver canula, through which it passed. And what showed it to be highly malignant, may be judged of from the following circumstances. The night after the operation, he was somewhat restless and uneasy, and the next day afflicted with small tremors, and an unusual lassitude; in about 3 days after, several angry pustules arose on his hands and fingers, and on every place where the least drop of water fell ; some of which coming to matter, went off" soon; those which did not, continued painful, and remained much longer. The thumb of his right hand, and middle finger of his other, were affected more severely than any other part, the pain more exquisite, the swell- ing more hard and large, and of a red dusky complexion. This was about the 6th day of his illness, and though the strongest suppuratives were made use of, yet they failed of the desired success, the pains being continual. Being per- suaded from the great pulsation and heavy pains, that matter must lodge either under or on the periosteum, an incision was made to the bone, by which only two or three drops of matter were discharged. It was expected this small dis- charge might in some measure mitigate his pain, but it did not; the same evening, that pain he at first complained of was changed into universal convul- sions, and the oppression on the vitals so great, as to threaten immediate death. The intentions of cure were to fortify the heart with cordials, to enable it to resist and throw out the malignity, and to bring the sores to a plentiful digestion . The first was treated with the highest alexipharmics; the latter, as at first, with strong suppuratives; this being about the 8th day of his illness, and the V'OL. XLI. I I'HILOSOFHICAL TRANSACTIONS. 339 convulsions continuing, with an unequal and low pulse, and as there was little appearance of matter, blisters were applied, as near to the parts affected as pos- sible, in order to make a revulsion from the heart, and throw oft" the morbid matter by the wounds. In about 3 days this point was gained, the convulsions began to abate, and the wounds to digest; in 4 more, he found a cessation of symptoms, except a faintness and lowness of spirits, which hung upon him for a great while after, which pestilential fevers are known always to leave behind them. He supposes he might receive this infection, as much by inspiration as con- tact; for some of his assistants, who were in the room only, and never touched a drop of the liquor, found themselves much disordered, and afterwards broke out with red and livid eruptions; which sufficiently showed, that not only the liquor itself, but the effluvia also, were in the highest degree subtle and ma- lignant. The Variation of the Magnetic Needle, as observed in three voyages from London to Maryland. By Waller Hoxton. N" 454, p. J 7 1 • N. B. The longitude is reckoned from the Lizard. The first Voyage in 1732. Latitude Longitude Variation north west west 39° 53' 27° 16' 12° 0' 37 49 27 45 14 0 35 19 39 20 13 0 32 40 50 27 8 34 40. 35 4. 0 30 28 48 ,.56 0 6 . . 65 0 4 36 50 0 0 4 Return. 36 11 56 20 . . ... 9 22 34 52 53 0 6 17 34 33 52 0 6 15 34 45 51 0 6 5 34 36 50 0 6 23 36 0 49 30 7 37 37 20 48 0 9 23 38 4 48 20 10 0 39 27 47 40 10 23 40 8 45 40 10 38 40 30 45 0 13 4 42 32.^ 42 20 11 43 42 40 42 0 12 39 43 27 40 20 13 24 43 32 39 50 13 42 49 48 9 0 \6 30 The second Voyage 1733. 48 12 3 18 18 0 46 7 4 30 l6 35 Latitude Longitude Variation north west west 44° 4'. . . ,... 7° 0. .. . . . 16° 22' 42 17 . . . ... 9 0... . . . 16 36 40 0 . . , ,. .12 0... ...15' 38 38 5 . . . ...14 20... ...14 51 37 36 . . , ,...14 45... . . . 13 24 36 32... . ..15 52... ...13 17 36 16... . . . 16 12... ...13 0 34 2 . . . ...21 51... ...11 34 34 4 . . . ...23 18... ... 9 51 35 6 . . . ...30 33 . . . . . . 10 28 35 12 31 38 9 48 34 23 31 22 10 23 33 34 32 25 8 30 19 31 26 7 29 17 31 11 6 32 24 37 55 6 32 50 38 35 10 36 32 11 40 23 11 0 31 19 41 9 6 42 32 25 43 0 5 0 34 5 47 20 8 49 33 45 49 24 10 45 35 1 54 10 . 34 0 54 4 . 33 41 54 0 . 33 51 : 55 0. 34 59 60 0 . 36 32 . . . 5 . 6 . 7 59 30 7 18 12 45 39 8 33 5 53 12 35 2 49 XX 2 340 PHILOSOPHICAL TRANSACTIONS. [anno 1739. Latitude Longitude Variation north west west 37" 1'. . ....61° 10'... ...6" 45' 37 5.. ....66 22... ...5 25 36 53.. ....66 40... ... 4 45 36' 36 . . ....66 40 . . . Return. ...5 0 38 9.. 57 40 . . . ...11 0 38 48 . . ....55 50 . . . ...10 0 42 13 . . 43 48 . . . ...14 0 44 21.. ....33 17... ...14 26 45 46.. 28 17... ...15 45 49 51.. . . off Plymouth. ...13 27 50 20 . . . . oft" Portland . ...13 0 Tie third Voyage, 1734. 39 53 . . .... 6 37... ..14 30 37 50 . . .... 6 40... ...14 0 36 58 . . 10 30 . . . ..15 0 34 56 . . 13 0... ...13 40 33 33 . . ....16 10... .. 12 10 33 9.. ...17 38... .. 9 13 32 44 . . ...18 6... .. 9 51 Latitude Longitude Variation north west west 31" 39' 20" 13' 9° 49 30 55 . 30 17 . .22 53 9 6 .25 26 8 39 .27 14 7 56 30 1 .. 30 1 27 54 6 . . 30 20 7 ..33 12 8 29 55 . . 29 57 . . 29 51.. 28 55 . , 29 8 40 0 7 31 10 44 46 8 31 7 46 45 4 48 41 0 41 30 42 49 0 30 29 49 48 30 31 52 30 18 53 30 23 55 30 58 57 30 . 37 9-- 37 37 5 39 28 5 23 12 6 46 4 40 4 0 4 49 4 45 4 22 4 52 10. 0. 0. .68 0 4 50 Some Thoughts and Conjectures Concerning the Cause of Elasticity. By J. T. Desaguliers, LL.D. F.R.S. N° 454, p. 173. Attraction and repulsion seem to be settled by the great Creator as first principles in nature ; that is, as the first of second causes; so that we are not solicitous about their causes, and think it enough to deduce other things from them. If elasticity was admitted as a first cause ; as it is by some, it is thought we should admit of too many principal causes in nature ; which is contrary to the rules of good philosophy. Philosophers therefore have endeavoured to de- duce elasticity from attraction, or from repulsion, or from both. It is observed, that the same particles that repel each other strongly, will attract other particles very strongly ; as apppears by many chemical solutions, especially by the alternate solution and precipitation of metals in acid menstruums. Dr. Hales has proved this many ways, in his vegetable statics and haemastatics. The elasticity of air seems to consist wholly in the repulsive power of its particles, which do not touch one another while the air is in its elastic state ; and if those particles be brought nearer and nearer together, the efi^ect of their re- pulsive force will increase, the air's elasticity being always proportionable to its density by compression, which property will be preserved, though com- pressed air be kept a year or two ; notwithstanding, Mr. Hawksbee, in his Physico-mechanical Experiments, says, that air will lose part of its spring by being very much compressed. But the air with which he tried it, must have been filled with moist vapours ; and it is well known, that the steam of liquors will lose its elasticity, especially where its heat decays. Dr. D. has kept several I VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 341 wind-guns, strongly charged, for half a year together, in which the air had lost none of its elasticity : others have found the air as strong after a year ; and a person of credit has asserted, that a wind-gun having been laid by and forgotten for 7 years, when it was found, discharged its air as many times, and with as much force, as it used to do. Now, though air, compressed by any external force, does always increase in elasticity, as it diminishes in bulk ; yet it may, by fermentation, diminish its bulk very much, without gaining any more elasti- city: for if another fluid, whose parts repel one another, but attract the parts of air, be mixed with it, the repulsion of any two particles of air will be diminished, in proportion as a particle of the other fluid, insinuating itself between them, at- tracts them towards itself on either side. The same <;hing will happen to the other fluid, in respect of the particles of air, which mixing with its particles, do in the same manner destroy their repulsion. Thus, if we allow an attraction strong enough between the parts of two elastic fluids, it is possible, that by fermentation a solid may be made out of two elastic fluids, which would have still continued fluid without such a mixture. We are taught by chemistry, to mix fluids together, which immediately coalesce into a solid. When brimstone matches are burning, the effluvia of the sulphur repel each other to great dis- tances, as may be known by the sulphureous smell. Now, though these par- ticles repel each other, they attract the air very strongly, as appears by the fol- lowing experiment. Take a tall glass receiver, closed at top, holding about 4 quarts of air ; and having put its open end over a bundle of brimstone matches on fire, standing up in the middle of a large dish with water in it, to keep the air from coming in at the bottom of the said receiver, you will observe, that not only as soon as the matches are burnt out, but a good while before, the air, instead of being ex- panded by the flame of the brimstone, will retire into less compass, the water beginning to rise from the dish up into the receiver, and continuing so to do till some time after the matches are burnt out ; so that there will be in the receiver only 3 quarts of air, instead of 4, more or less, in proportion to the quantity of brimstone burnt. And this plainly happens by some of the effluvia, or little parts of the sulphur, attracting some of the particles of the air, so as to make an unelastic compound, that precipitates into the water. If the elasticity of the air is quite lost when the repulsion of its particles is taken oft', or suffi- ciently counteracted, it must follow, that its elasticity depends on repulsion ; and that this is often the case, appears by a great immber of Dr. Hales's ex-, periments. The doctor took a cubic inch of mutton-bone, and having put it into his gun-barrel retort, he distilled out of it 200 or 300 cubic inches of air, inta a large glass bottle, the weight of which air, together with the ashes of the 342 i'HILOSOPHICAt. TRANSACTIONS. [aNNO 173^. bone left, weighed as much as the whole quantity of bone did at first. Now the air had been confined in that bone, together with many sulphureous par- ticles, in such a manner, that the mutual attraction of the sulphur and the air had alternately destroyed each other's repulsive force, and brought those sub- stances into a little compass ; but the fire in the distillation separated them from each other, so as to restore them in a great measure, to their usual elas- ticity. This appeared by bringing a candle near the mouth of the bottle that held this revived air ; for every time the candle was brought near, the air took fire, and flashed out of the bottle with a sulphureous smell. The air may be consolidated in many hard bodies, so as to be there quite void of elasticity, and there do the office of a cement, till by the action of fire, or some particular fermentations, it is again restored to its perfectly elastic state. This is the meaning of Dr. Hales's words, when he says, that some bodies ab- sorb, and others generate air ; and the same bodies do sometimes absorb, and at other times generate air. He found more or less air in almost every solid substance that he tried ; but, what was most remarkable, he found that the calculus humanus, or stone taken out of a man's bladder, was made up of above half its weight of air. Some have endeavoured to solve elasticity by attraction only ; as for example — If the string a b, fig. 7, pU 7, be considered as made up of particles lying over one another in the manner represented at a d b ; it is plain, that if the point D be forcibly brought to c, the parts will be drawn from each other ; and when the force, that stretched the string, ceases to act, the attraction of co- hesion, which was hindered before, will take place, and bring back the string to its former length and situation, after several vibrations. Now, though this seems to agree pretty well with the phaenomena of a string in motion, it will by no means solve the elasticity of a spring fastened at one end, and bent either way at the other, like a knife or sword-blade, as in fig. 8. For if such a spring be bent from A to a, the particles on the side c, which now becomes convex, will be farther asunder at f, while the particles at d, carried to the concave part E, will come closer together : so that the attraction, instead of making the spring restore itself, will keep it in the situation in which it is, as it hap- pens in bodies that have no elasticity, where perhaps only attraction obtains. Thus a plate of lead, a plate of copper, and a plate of soft iron, stands bent. But the most probable way of accounting for the elasticity of springs, is to consider both a repulsive and an attractive property in the particles, after the manner of the black sand, which is attracted by the load-stone, and has been shown, by Musctienbroek, to be nothing else but a great number of small loadstones. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 343 Let US suppose a row of round particles touching one another only in the points c in a line from a to b, fig. Q. It is plain, from what philosophers have shown concerning the attraction of cohesion, that on the least shake or alteration of the position of a straight line, these particles will run together, and form a sphere, in which the globules will have more points of contact. But if these particles have poles like magnets, in the opposite places marked n s, so that all the poles n, n, n, &c. repel one another ; and all the poles s, s, s, &c. likewise repel one another, the line a b will continue straight ; for if by any force the same line b a be put into another position, as into the curve b a, then the poles n, n, &c. being brought nearer together, while the poles s,s, &c are further asunder, will repel one another more strongly, and so hinder the globules from running together towards the concave part ; and the spring, left to itself, all this while supposing one end, as b, b, or |3, fixed, will restore itself, throwing its end a back to A, and so on to a, by the first law ; then, being in the po- sition « (3, the poles s, s, &c. are brought nearer together, whose repulsion, thus increased, throws back a to a, and so on forward, the line of particles perform- ing several vibrations round b. May not a spring of steel, or other springs, consist of several series of such particles, whose polarity and attraction acting at the same time, will show why such bodies, when they have been bent, vibrate, and restore them- selves ? If we take a plate of steel, and make it so hot till it looks white, and then immediately quench it, we thereby fix the metal in a state very near fluidity, so that the particles which the fire had almost brought to roundness, have but a very small contact ; as appears by the fragility of the steel thus hardened, which breaks like glass, and has a short grain. Steel, thus hardened, is highly elastic ; for what workmen call hard, is the most elastic ; as appears by the congress of high-hardened steel balls, which return, in their rebound, the nearest to the place we let them fall from ; and, next to glass, have the quickest elasticity of any thing we know. That we may not be thought to have given an imperfect account of the elas- ticity of a steel spring, because such a one as we have described wants tough- ness, and will immediately fly, when bent to any degree ; we must beg leave to consider further the properties of the round particles, or little spheres, of steel, in which we have supposed a polarity. Let us suppose a B, fig. 10, to be two little spheres or component particles of steel, in which, at first, we will suppose no polarity, but only an attraction of cohesion. Then, whether the particles have their contact at c, d, e, n, or at i, t, s, their cohesion will be the same ; and the least force imaginable will 344 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739, change their contact from one of those points to another; because in the roll- ing of these little spheres, they do not come into more or less contact, in one situation than another. But if we suppose the point n in each spherule to be a pole, with a force to repel all the other points n in any other spherule, and likewise s another pole, repelling the other points s ; the spherules will cohere best, and be at rest in that position, where the points c, c, are in contact, and n and s at equal distances on either side. For if the spherules be turned a little, so as to bring the points d, d, into contact, as in fig. li, the poles, n, n, being brought nearer, act against each other with more force than the points s, s, which are now farther off, and consequently drive back the spherules to the contact at c c, beyond which continuing their motion, they will go to SS, fig. 12, and so backwards and forwards, till at last they rest at cc, which we may call the point of equilibrium for rest in a spring. Now there are, besides this, two other points of equilibrium, beyond which the spring may break, which are the points e, e, towards n, and f, f, towards s; see fig. 13, that is, when the spherules have their poles n, n, brought very near together, the mu- tual repulsion increases so, that the attraction at the contact is not able to hold them, and then they must fly asunder, the spring breaking. We suppose the points e, e, to be the points of contact, beyond which this must happen ; but that if the contact be ever so little short of it, as between e and d, the spherules will return to their contact at c, after some vibrations beyond it, as has been already said. This is the reason why he calls e, in one of the spherules, and its correspondent point £, on the other side c, the points of equilibrium ; for if the spring be bent towards a, fig. Q, so that the spherules, like a and b, fig. 13, touch beyond e, the spring will break. Likewise if the spring be bent the other way, till the spherules touch beyond e, then it will break the other way. Now when the spherules touch at e,e, or at f, s, the spring is as likely to return to its first position as to break ; for which reason he has called the points e and I, points of equilibrium, as also, having known by experience, that a spring left bent to a certain degree, has, after some time, broke of itself. From all this it appears, that spherical particles will never make a tough spring ; therefore the figure of the particles must be altered, in order to render it useful ; and this is what is done in bringing down the temper of the hard steel, and letting down a spring, as it is called. What change ought to be made in the particles, we shall first show ; and then consider how far that is done by those who make springs. If the parts supposed globules, as in fig. Q, are now flattened at c, where the contact is, so as to put on the shape n e dc Jt s, as in fig. 14, the contact will be much increased, and reach from d to S, so that in bending the spring there VOL. XLll] PHILOSOPHICAL TRAfJSACTIONS. 345 will still remain a great contact in the particles, and the points of equilibrium for breaking, viz. o, e, above, and t, c, below, will be removed nearer to the poles n, or s, than when the particles are round ; the consequence of which will be^ that the spring must be bent much further, to be in danger of breaking, than in the former supposition ; as may be seen in fig. 15, where two particles being opened about the point d as a centre, the attracting points c, c, and S, i, have still some force to help to bring back the particles to their whole contact ; be- cause, in this shape of the particle, the attracting points c, c, S, S, are removed only in proportion to their distance from the angular point d ; whereas if the particles had been spherical, and the line d S an arc of a circle, the attracting points c, c, and i, i. would have removed from one another further than in pro. portion to twice the square of the distance from d, as in fig. 11, and so have afforded very little help for bringing back the particles to their contact. A row of particles in the spring thus conditioned, is to be seen in the natural state at BA, fig. 1 6, and bent at ba in the same figure. Here it is to be observed, that if, in this figure of the particles, you would bend the spring to bring the par- ticles to touch at their point of breaking equilibrium, you must open them so much on the contrary side, that the spring will be bent far beyond any uses in- tended to be made of it, as appears by fig. 17, where two particles are brought to touch at the equilibrating point e; and by fig. 18, where many particles being put into that condition, the spring is brought round quite into a circle. Now the common practice in making springs, is the most likely to produce this effect required in the particles; for the hard spring, whose particles were round,, or nearly so, is heated anew, and while cooling gently, the mutual attraction increases tlie contact, so that the particles grow flatter in those places where before they had but a small contact; and lest this contact should become too great, the spring's softening is stopped by quenching it in water, or oil, or grease. Another way of making springs, is to begin and shape them in cold unelastic steel, and then having heated them to a small degree, for ex- ample, to a blood red heat, immediately to cool them in some proper liquors. This also settles the particles in their oblong figure, through which they must pass before they become round, or nearly so, in a white heat. That particles of steel are fixed in the figures which they have at the instant of dipping, will not appear strange, when we consider, that dipping red-hot steel in cold liquors, in a particular position, makes it magnetical. If it be asked, how we account for making springs only with hammering, it is easily answered, that we can make iron and steel magnetical only with hammering; and if we can give and destroy poles in the whole piece, there is no improbability to think VOL. Vlll. Y Y 34(j I'HILOSOPHICAL TRANSACTIONS. [aNNO 1739. we can give poles to little parts ; or rather bring into a particular situation the poles which they have; for if the poles that we have considered be placed quite irregularly, there will be no elasticity at all. Agreeably to this, springs may be made of other metals than iron or steel, though not so perfect, by hammering ; for it will be sufficient for the little particles to have poles that attract and repel one another, driven by the hammering into a regular order. This, applied to the vibration of a string, will better solve its several cases, than attraction alone; and the elasticity of glass is just the same as that of a very brittle steel -spring. Some Thoughts and Experiments concerning Electricity. By J, T. Desagu- liers, LL. D. F. R. S. N° 454, p. 186. The phaenomena of electricity are so odd, that though we have a great many experiments on that subject; we have pot yet been able from their com- parison to settle such a theory, as to lead us to the cause of that property of bodies, or even to judge of all its effects, or find out what useful influence electricity has in nature : though certainly, from what we have seen of it, we may conjecture, that it must be of great use, because it is so extensive. Though some persons have been too hasty in their conjectures, and too apt to run into hypotheses not sufficiently supported by experiments; yet it would be of great use to settle some general propositions concerning electricity, from the light we have already, and what we may further discover by future experi- ments ; provided we have a sufficient number of them to settle a general rule. For example ; I now propose some general assertions to be considered, and to be rejected or allowed of, as a number of experiments shall determine; but to stand only as queries till they are settled. I have hitherto avoided entertaining the Society on this subject, or pursuing it so far as I might have done, considering that I can excite as strong an elec- tricity in glass, by rubbing it with my hand, as any body can, because I was unwilling to interfere with the late Mr. Stephen Gray, who had wholly turned his thoughts that way ; but was disposed to decline it entirely, if he imagined that any thing was done in opposition to him. But now I intend not only to go on myself in making electrical experiments, but shall always be ready to make such as shall be proposed by any member of the Society. The Queries which I have already examined, are the following : Query 1 . Whether all bodies in general are not capable of receiving the electricity which has been given to a tube by friction, though there be a great many bodies, such as metals and vegetables, &c. in which we have not hitherto VOL. XL!.] PHILOSOPHICAL TRANSACTIONS. 347 been able to excite any electricity by heat, or friction, or any other operation on the bodies themselves ? Query 1. Whether, when a string is stretched out at length, with a body hanging at one end of it, to which body we would communicate the electricity of the tube rubbed at the other end, the supporters of the string ought not to be of such bodies as are capable of having electricity excited in them, by fric- tion, heating, beating, or patting, or some immediate operation on the bodies themselves ? Query 3. Whether these supporters of the string, mentioned in the last Query, which stops the electrical virtue from passing any further, are not of such a kind, as are incapable of having the electrical virtue excited in them immediately by any operation yet known ; though they are all capable of re- ceiving it from a rubbed tube, even at a great distance, by the communication of a string made of vegetable substances ? Query 4. Whether the reason, that some supporters transmit the electricity running from the rubbed tube along the string, to bodies beyond them, be not as follows, viz. that having received some of the electrical stream, they soon become saturated with it, and so receiving no more of it, let the rest pass on without disturbing it? Query 5. Whether the reason, that supporters made of vegetable substances, metals, and such others, as stop the electricity abovementioned from running any farther along the string than the place where it rests upon them, be not this ? viz. that they are never saturated with the electrical stream, but conti- nually receive it, and transmit it to the next contiguous body, provided that contiguous body be of the same kind with themselves, and also contiguous to other bodies of the same sort : I mean such as would stop the electricity, if the string was supported by them. For even these supporters will transmit the electricity, if terminated at each end by bodies that transmit the electricity, when they support the string. Query 6. Whether we may not distinguish all bodies in general, in respect of electricity, into such as may be excited to electricity, and such as cannot be excited to electricity ? the two kinds of bodies receiving the electricity from other bodies into which it has been excited differently ; the first also trans- mitting the electricity, while the others do not. These queries are such as arise from a consideration of experiments made by others, and such as I have made myself. Experiments relating to the first Query. — I stretched a cat-gut, about 5 feet in length, and fastened it to the top of two chairs in a horizontal situa- tion ; and such another cat-gut string to two other chairs parallel to the first, Y Y 2 348 PHILOSOPHICAL TRANSACTIONS. [aNNO IJSft. ;ind at the distance of 15 or 20 feet from the former. I then suspended one end of a packthread to the middle of the first cat-gut, and carried it on so as to lay it over the middle of the other cat-gut, and leave the other end of the packthread hanging down about a foot below the cat-gut, with a loop to hang several bodies to it, successively to receive the electricity excited by the tube and applied to the other end of the packthread. All the bodies I tried received the electricity communicated from the rubbed tube along the string, which appeared by holding a thread fastened to a stick, the thread being attracted towards the suspended body. 1. A gold medal. 2. A silver medal. 3. A copper medal. 4. A brass ball. 5. A steel ball. 6. A tin ball. 7. A leaden ball. 8. Sulphur, g. Sealing- wax. 10. Pumice stone. 11. Bees-wax. 12. Resin. 13. Sal ammoniac. 14. Ivory. 15. Human bone. l6. Fish-skin. IJ. Loadstone. 18. P'lesh. 19. Cotton. 20. Wax-candle. 21. Tallow-candle. 22. A leek. 23. Celeri. 24. Tobacco-pipe. 25. A glass^ball. 26. A rush rolled up. Experiments relating to Query 2, — Retaining the first supporting string of cat-gut, instead of the last cat-gut supporter, I made the packthread pass over t-he following substances successively, all which transmitted the electricity to the body suspended at the end of the packthread; viz. 1. A silk string, 2. Hair rope. 3. Parchment. 4. A thong of sheep-skin, but it stopped the electricity till it was dry and warm. 5. A list of woollen cloth. 6. A list of flannel. 7- Cadis, or a kind of worsted tape. 8. Quills. 9. Whalebone. 10. A man's thigh-bone. U. A bladder. 12. A cat, held between two. 13. A tallow-candle. 14. A wax-candle (the string was also laid over the unburned cotton wick at the end of the candle). 15. A tallow-candle and its wick. 16. Tobacco-pipe, with a cat-gut or a packthread through it, or with- out, that is, a packthread string being fastened at each end of it. 1 7. A sword-belt. 18. A piece of a white hat. 19. A piece of a black hat. 20. A glass tube. 21. The same with water in it. 22. With spirit of wine. 23. The same with mercury in it. 24. Sealing-wax. 25. Crape. All these substances, except the sheep-skin, the tobacco-pipe, the quills, the candles, and the bone, not only transmitted the electricity, but became so far electrical, as to attract the thread a little way on each side of the supported packthread. More experiments are required to be made, before this query can be turned into an assertion. Experiments relating to Query 3. — Instead of the last supporter of cat-gut, near the suspended body, I made use of the following substances, stretched from chair to chair : and then the thread hanging on the stick was not at all VOL. XLI.] PHILOSOPHICAL TRAWSACTIONS. 349 attracted by tlie suspended ivory ball, which I made use of in all the experi- ments to try the supporters, 1. A hempen rope. '2. A small packthread. 3. A drawn sword. 4. A sword in the scabbard, 5. The scabbard without the sword. 6. A twisted cotton thread. 7. I'ape made of thread. 8. Bars, tubes and wires of copper, brass, iron and lead. g. White paper and brown. 10. A moist thong of sheep-skin. 11. Celeri. 12. Leeks. 13. Fir-wood. 14. A cane. 15. A piece of black thorn. 1 6. The same rushes that had before received the elec- tricity when suspended. 17. A sponge dry. 18. White thread, ip. Hay. 20. A marble slab. Such bodies as were too short to reach from chair to chair, were lengthened out by pieces of packthread at each end. Experiments relating to Query 4. — The cat-gut supporters, and all the others mentioned in the experiments to Query 3, which transmitted the electricity, attracted the thread of the stick near the conducting packthread, but not so far as the chairs to which the said supporters were fastened. Experiments relating to Query 5. — All the supporters which did not transmit the electricity, when they reached from chair to chair, were made to transmit, when they were lengthened out with cat-gut at each end, and then they be- came electrical themselves from one end to the other, as becoming part of the suspended body ; and becoming so saturated, as not to be able to carry the electricity on either side any farther than the cat-gut to which they were fas- tened. Experiments relating to Query 6. — ^The late Mr. Stephen Gray has, by rub- bing, excited electricity in several of those bodies, which I have made sup- porters of, to transmit the electricity. See Philos. Trans. N° 366. I have done the same with several others, but not with all of them, though I shall try them all : but as it is more difficult to excite that virtue in some than others ; and all the experiments in general succeed better in dry and cold weather, than in moist and warm, I must wait for proper opportunities to make the experiments, and then I shall communicate them. Experiments concerning mixed Substances. — I . Cadis, or woollen tape, laid on thread-tape, when made a..supporter, transmitted the electricity. 2. When the thread-tape was uppermost, the electricity was stopped. 3. When they were twisted together, the electricity was transmitted, but most weakly when the packthread going to the ball was laid over that part of the twist which had the thread-tape. The two paper supporters, which did not transmit the electricity, ought to have done it according to Query 2; because, by Mr. Gray's experiments, elec« 350 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739- tricity is to be excited in the paper by rubbing: therefore, perhaps the papers wanted to be drier or warmer, so that I shall try them again. These are the only two experiments that do not agree with the 2d Query ; but I would not omit mentioning them, because it is the part of an impartial philosopher, to mention as well those things which favour, as those that disagree with his hypotheses and conjectures. Experiments made before the Royal Society, Feb. 2, 1737-8. By J. T. Desa- guliers, LL.D. F.R.S. N° 454, p. igS. In the following account, which is the sequel of former experiments, I call conductors those strings, to one end of which the rubbed tube is applied; and supporters such horizontal bodies as the conductor rests on. Exper. 1. — Old packthread supporters transmitted electricity but weakly, though more strongly when twisted with cat-gut; but new packthread did better. N. B. Where it is not mentioned otherwise, an ivory ball hangs at the end of the conductor; and its electricity is tried by a thread applied near it. Exper. 1. A conducting string of cat-gut received the electricity a little way ; but did not carry it quite to the tube. Exper. 3. — Two conducting strings, one of cat-gut, and one of pack- thread, compared, the first attracted less and less, as the distance from the tube increased; and the other more and more; till it was strongest at the sus- pended body: but both ceased immediately after the removal of the tube. Exper. 4. — A sealing wax supporter transmitted the electricity, but received little or none when suspended. If it was but just rubbed with the hand, it attracted the thread when first suspended; and strongly, if much rubbed; but that virtue was soon lost, if the tube was applied to the conducting string, and then it would receive no more electricity from the tube. If the stick of wax was wet, then it would strongly receive the electricity. A wax supporter wet, and silk string wet, did not transmit the electricity. Exper. 5. — Dried ox-guts did not transmit electricity when held in hand; but when tied to cat-gut, transmitted it ; and, when suspended, received it plen- tifully. Exper. 6. — The same with a small cord. Exper. 7. — The same with a rod of iron, and tube of brass. Exper. 8. — A glass tube, made conductor, received the electricity but a little way. VOL. XLI.j PHILOSOPHICAL TKANSACTIONS. 351 Ea-per. Q. — Dry sheep- skin transmitted the electricity, but not wlien wet, though it received it then, when suspended. Exper. 10. — A middle supporter of packthread was again supported on one side by a glass tube, and on the other by sealing-wax, and had at each end an ivory ball hanging. Those balls became electrical in the same manner, and at same time, as the ball at the end of the conducting spring. Exper. 1 1. — When a bar of oak was made use of instead of the tube, or a small iron bar instead of the wax, the electricity was stopped : but when the bar was thrust a little way into a glass tube, the electricity was communicated as before. Experiment made at the Royal Society, Feb. Q, 1737-8. By the Same. N°454, p. 196. I fixed 6 iron radii, of twisted iron wire, to a brass ring, of 2 feet diameter, and half an inch wide, which had a socket in the centre, by which to set it either on an upright glass tube, or on a wooden pillar : then were hung on the end of the 6 radii, next to the circumference, the following substances. 1. A piece of resin. 2. A stick of wax. 3. An apple. 4. An ivory ball. 5. A steel ball. 6. A glass ball. Exper. 1 and 2. — I rubbed the tube, and applied it to the centre of this machine, as it stood on a glass tube ; and the electricity was communicated to all the suspended bodies, and the ring also ; but none of them received it, when the machine stood on a wooden pillar, with its foot on the floor. Exper. 3. — I tied to the ends of the 6 radii as many cat-gut strings, but so long as to unite together about a foot higher than the centre of the ring, where they were suspended by another cat-gut string 3 feet in length, the top of which was fastened to a hempen rope. Then applying the rubbed tube very near the place where all the cat-gut strings joined over the ring, at which ring the same bodies were suspended as before, neither the bodies nor ring re- ceived any electricity. Note. This was done in foul weather, when the electricity does not extend it- self far from the tube : but in fair weather, the electrical virtue, at the same distance, reached the iron radii of the ring ; and consequently the ring and bodies suspended, though the virtue was not propagated, along the cat-gut : for if the tube was applied a little higher to the single cat-gut, so as the effluvia, or virtue darted directly from the tube, did not reach the ring, or its iron radii, then no virtue was communicated to the ring nor to the suspended bodies, &c. 354 PHILOSOPHICAL TRANSACTIONS. [aNWO 173Q. Exper. 4. — I suspended the ring by 6 packthreads, just in the same man- ner as the cat-gut strings before ; but still all those strings were suspended by the perpendicular cat-gut of 3 feet in length. Then all the bodies received the electricity from the rubbed tube applied to the top of the pyramid of pack- thread. Exper. 5. — Instead of the perpendicular cat-gut, between the pyramid of packthread and the upper hempen string, I substituted a packthread ; and then no virtue was communicated to the ring, but all went up the hempen string, and was lost ; except when the tube was held very near the ring, and then it gave a small degree of electrical attraction to the ring, and the bodies sus- pended at it. Exper. 6. — Having again suspended the ring with the bodies and pyramid of packthreads to the perpendicular cat-gut, I tied a packthread to the ring, and carried it horizontally about 20 feet from the ring; and having fastened to it a cat-gut string, 3 feet long, I gave it an assistant to hold : then applying the rubbed tube to the end joining that cat-gut, the electricity was commu- nicated to the ring, and all the suspended bodies, as appeared by applying the white thread near them, which was attracted by every part of the ring, and all the bodies. Experiments made before the Royal Society, Feb. l6, 1737-8. By the Same. N°454, p. 198. Exper. \ . — I applied the rubbed tube to a burning candle, and it had no manner of effect on the flame ; but as soon as the candle was blown out, it attracted the smoke at 4 or 5 inches distance. Exper. 1. — A horizontal packthread, of about 18 feet in length, being ter- minated by the cat-gut strings, of 3 feet long each, and hung, towards one of the ends of the packthread, on it a candlestick with a lighted candle in it ; then applying the rubbed tube to the other end of the packthread, the candle- stick attracted the thread, and it was also attracted by the candle, but not within 2 or 3 inches of the flame ; but as soon as the candle was blown out, the thread was attracted by every part of it ; nay, even the wick, when it was quite extinguished. Exper. 3. — I suspended a wax candle in the same manner, and the experi- ment succeeded the same ; only the electricity came not so near the flame in the wax as in the tallow candle. Exper. 4. — I hung an iron wire, \6 feet long, horizontally by two cat-gut strings at its ends, about 3 feet long each, and bent down the wire from the VOL. XLI.] I'HILOSOPHICAL TRANSACTIONS. 353 place joined to the cat-gut, so as to hang down a foot at one end ; then ap- plying the rubbed tube at the other end, this conductor carried the electricity along to the ball ; but not so well as the packthread conductor ; but it did some- thing better when it was wet. The same happened when the conductor was brass wire of the same length. The packthread conductor also carried the effluvia stronger when wet. An Account of some Electrical Experiments made before the Royal Society on Thursday the \6th February, 1737-8. By the Same. N° 454, p. 200. Exper. 1. — I took the glass tube ab of two inches diameter, fig. l, plate 8, which had at one end a, a brass ferril with a brim cemented to it, and at the other end b, a brass cap close at top, the brass-work being joined to it, in order to exhaust it of its air on occasion. When this tube was very dry it would become electrical by rubbing, so as to snap by passing the ends of the fingers near it ; but that virtue could not be excited in the tube nearer the brass at the ends than from a to b, and not unless the tube was very dry within. The tube being thus prepared, and having an ivory ball c of about 2 inches diameter, tied to it at the end b by a short string, I passed the tube through the horizontally suspended place dd, till it was stopped by the brim at a ; and as il hung perpendicularly, the ball c was within a foot and a half of the floor. The plate dd was about 10 inches in diameter, and suspended by 3 small cat- gut strings, as e e, of about 2 feet in length, all which were tied together at B, to a hempen string hanging from the cieling at p. By reason of the distance of the ends of the cat-gut strings close to the plate ateee, I was able to thrust in between them one end of an open tube gg, after it had been rubbed so as to make it electricul, to see whether I could make the aforesaid suspended tube ab the conductor of electricity to the ball c; but the first trial was in vain. Exper. 2. Then laying horizontally over the plate dd an iron bar, a quarter of an inch thick, and a yard long, I hung at the ends of it two ivory balls c, c, of the same size as c, by packthreads of the same length at the tube ab. Having again made the tube gg electrical, I applied it over a, as before, and immediately the two balls c, c, received the electricity, so as to attract the thread of trial t, hanging at the end of the stick sx, when applied near them ; though it received no motion when applied to c. But if the strings H c, instead of packthread, were cat-gut, then the balls c, c, received no electricity from the tube gg, rubbed and applied over a VOL. VIII. Z z 354 VHILOSOPHICAL TRANSACTIONS. [aNNO 1739. To be certain that the rubbed tube is made electrical, I pass my fingers near it after rubbing, to hear- whether it snaps ; but always rub again before I apply it ; because by snapping it loses its electricity at the place where it snaps. Exper. 3. — When I rubbed the tube ab, it would then attract the thread of trial T between a and b ; but not at all above a or below b, unless when I applied the tube gg above a : then the thread of trial would be attracted by the plate dd, and the top of the great tube from a to a, but no lower. It would also be attracted by all the bar hh, and only 3 or 4 inches below h. Exper. 4. — Having filled the tub ab with water, the electricity of the rubbed tube GG, applied at a, ran strongly down the tube ab, and impregnated the ball c, so as to make it strongly attract the thread of trial, while the balls c, c, re- ceived no virtue at all. But on wetting the cat-gut strings h, c, with a sponge, all the 3 balls c, c, c, strongly received the electrical virtue. Exper, 5. — I took away the bar hh, and its balls and strings ; and having well dried the tube, I rubbed it, and hung it up as before ; so that it would snap, or attract the thread from a to b, but no where else. Then putting the small bar hh into the middle of the tube ab, in its axis, represented by the pricked line, on application of the rubbed tube gg at a, the virtue was immediately communicated to the ball c. The same thing happened when instead of the bar, a brass wire, a walking cane, a small green stick, or small packthread, was placed in the axis of the tube. Exper. 6. — 1 took a barometer tube, empty, and very dry, and placed it in the axis of the great tube ab ; but it would conduct no electricity to the ball c; though it carried it down very readily when full of water, though quite dry on the outside. Another small tube, open at both ends, which conducted no virtue to c when dry, being only moistened a little by the breath in blowing through it, carried down the virtue from a to c very strongly. All this while the cat-gut strings e, e, received no electrical virtue. Definition 1 . — A body electrical per se, is such a body in which one may excite electricity by rubbing, patting, hammering, melting, warming, or any other action on the body itself, as amber, sealing-wax, glass, resin, sulphur, &c. besides many, if not all, animal substances. Defin. 1. — A non-electrical, is such a body as cannot be made electrical by any action on the body itself immediately ; though it is capable of receiving that virtue from an electrical per se. Observations. — 1 . When the air is full of moist vapours, electrics per se are excited to electricity with very great difficulty, requiring to be often warmed, and much rubbed ; as appears in exciting that virtue in glass, amber, wax, &c. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 355 2. In dry weather, especially in frosty weather, the electricals per se will have their virtue excited with very little action on them; as appears by warming a glass receiver, which, without any rubbing, will cause the threads of a down feather, tied to an upright skewer, to extend themselves as soon as it is put over the feather. Sometimes resin and wax exert their electricity by only being exposed to the open air. 3. Electricals per se retain the virtue longest when kept near to, or inclosed by, other electricals per se. Thus the rubbed tube will retain its virtue pretty long in dry air, as appears by chasing a feather about the room very long with- out new rubbing ; as also by lumps of resin and sulphur, &c. which have been melted and poured into dry drinking glasses, keeping their virtue long, if kept in those glasses, and wrapped in dry silk, or such sort of paper as will become electrical by rubbing ; for as often as they are exposed to the air, they will attract. 4. Electrics per se communicate their virtue to any of the non-electrical, when brought near them ; in which case the non- electric attract and repel like the electrics per se. Thus an iron bar suspended by a silken thread, a hair rope, or a dry cat-gut, when an excited electric per se is brought near it, will both attack and send out its effluvia to a non-electric held near it ; as appears in the dark by the light coming out at the end of the bar. 5. An electric per se loses its excited virtue on communicating to the non- electric ; and the sooner, the more of those bodies are near it. Thus in moist weather the rubbed tube holds its virtue but a little while, because it acts on the moist vapours that float in the air ; and if the rubbed tube be applied to leaf-gold or brass, laid on a stand, it will act on it much longer, and more strongly, than if the same quantity of leaf-gold be laid on a table, which has more non-electric surface than the stand. 6. When a non-electric is suspended by, or only touches an electric per se, it receives the properties of an electric per se from a rubbed tube or wax, &c. This appears by the fire that flashes from the fingers of a man suspended by hair-ropes, or who stands on a cake of resin, when he has received virtue from the rubbed tube. 7. The virtue which a non-electric receives from a rubbed tube, runs on to the most distant part of the suspended body, from the place where the tube is applied, and seems to be collected there, from whence it flashes in the dark, snaps, and exerts its attraction on the thread of trial ; though as the virtue runs along, it sometimes shows itself in other parts of the suspended non- electric. zz2 356 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739- 8. If a non-electric, while receiving the virtue from the rubbed tube, be made to communicate with the floor of the room, or any other great non-electric body, by a non-electric string, how small soever, though but a thread, the virtue will not show itself, as it did before, at the extremities, where the flash of light was seen. g. If a non-electric be ever so large, when suspended, it will receive electri- city from the rubbed tube. And if 5 or 6oo feet long, when the rubbed tube is applied at one end, the bodies hanging at the other end will become electrical. This has been tried by several people, as well as myself. 10. If a long non-electric string be fastened to an electric per se, and ex- tended to a great distance, being supported by electric per se, to keep it from touching the ground, all bodies fastened at the end of it will become electrical, when the rubbed tube is applied at the other end, though the tube does not touch it, but is only brought within 2 or 3 inches of it. Note, This string we have before called the conductor of electricity, and the cat-gut or silken strings, glass tubes, or whatever kept the long string from touching the ground, supporters. 1 1 . If any of the supporters, mentioned in the last observation, be changed for a non-electric supporter, the virtue will there be stopped, and taken away by that supporter : but if that supporter be again supported by electrics per se, it will only receive so much electricity as will impregnate it, and then the virtue will go on to the end of the string, and impregnate the bodies fastened to it. 12. The non-electric receive the greatest virtue at the end of the string, and most of all, if they are wet. But the electrics per se, if long bodies, as long sticks of wax, and glass tubes, only become electric at the end next to the string. 13. Electrics per se will become non-electrics, if they be wet, or only moistened. Thus supporters that transmit the electricity immediately, stop it when wet with a sponge, or when blown through, if open tubes. And if the long electrics per se, hanging at the end of the conductor, be made wet, they will become non-electrics, and strongly receptive of the virtue given by the robbed tube at the other end of the string. All the 6 experiments mentioned in the beginning of this paper, confirm this observation. 14. A non-electric having been impregnated with electricity, by the rubbed tube, is repelled by it, till it has lost its electricity by communicating it to an- other non-electric. Then being in its first state, it is again attracted by the tube, which holds it till it has fully impregnated it; then it repels it again. This is evident, by attracting a down feather by the tube in the air, and then repelling it : so as to make it dance backwards and forwards to and from a finger rOL. XL!.] PHILOSOPHICAL TRANSACTIONS. 357 held up at a foot or two from the tube. But the thing appears more plainly from the following Exper, 7. — Having rubbed the tube Tt, fig. 2, pi. 8, and with it attracted a feather, the feather at t was repelled from the tube, whenever it was brought near it ; but suddenly dipping the end t of the tube in water, the feather float- ing in the air came to it again, and stuck to the end of the tube at t, or near f. In fair weather this experiment will not succeed, unless the tube be thrust pretty deep into water, a foot at least ; but in moist weather an inch or two will do. Though animal substances be generally thought to be electric per se, yet it is only when they are very dry : this is the reason why a living man suspended by a hair-rope, or standing on a cake of resin, to receive electricity from the tube, must be considered as a non-electric, by reason of the fluids of his body. Of some Electrical Experiments, made at his Royal Highness the Prince of fVales's Home at Cliefden, on Tuesday the 15th of April, 1738; where the Electricity was conveyed 420 feet in a direct Line. By the Same. N° 454, p. 209. Having heard that electricity had been carried along a hempen string 5 or 600 feet, but having only seen it when the string was carried backwards and forwards in a room by silk supporters. Dr. D. wished to dry it with a pack- thread string stretched out at full length; for which purpose having joined a cat-gut string of 6 feet long, he fastened it to the inside of a door in the suite of rooms at Cliefden ; and having also tied another cat-gut, like the first, to the other end of the string, he tied it up to the inside of the door at the other end of the house ; but at the place where the packthread was joined to the cat- gut, he left a foot and a half of packthread hanging down, and fastened to it a lignum vitae handle of a burning-glass. Then applying a rubbed tube at the other end of the string, he made the electricity run to the lignum vitae, but with some difficulty, which he attributed to the size, being an animal substance, that still stuck to the packthread as it was new ; therefore he caused the packthread to be wet with a sponge from one end to the other, to wash off the size : then was the electricity from the tube communicated very soon and very strongly ; for the thread of trial was drawn by the lignum vitae at the distance of a foot. Afterwards having joined more packthread together, he mnde a string of 420 feet long, one end of which was fastened, by the interposition of cat-gut as be- fore, to the iron gates in the garden, before the house, and the end which had 358 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739- the lignum vitae handle, to the upper part of the door next to the back-side of the house in a large drawing-room, taking care that the string came through the middle of the opened doors through which it passed ; and to prevent this string dragging on the ground, three pieces of cat-gut held across by two men, at equal distances from the ends, and from each other, supported it. The string was altogether dipped in a pail of water, before the experiment ; but great care was taken, that the cat-gut should not be wet. . Then he applied the rubbed tube at the end in the garden, while an assistant held the thread of trial near the handle abovementioned, which thread was strongly attracted, though the wind was very high, and blowed in the contrary direction to that in which the electricity ran along. He first tried the experiment with the packthread dry, but then it would not dp at that distance. The weather was moist when he made the experiment. Botanical Observations, exhibiting accurate Descriptions of some Plants. By Paul Henry Gerard Moehring, M. D. N° 454, p. 211. This paper contains a description of 6 plants; viz. 1. Salicornia ramis clavatis, squamis articulorum adpressis. — 2. Verbascum foliis cordatis crenatis acutis glabris : floralibus ternis. — 3. Senecio foliis pinnatifidis lacinulatis : laciniis omnibus laxis patentissimis linearibus acutis. — 4. lUecebrum Linn. Corollar. gen. 947. Rupp. .Ten. 79- Corrigiola Dillen. Giss. Supplem. adpend. 167. — 5. Ruppia foliis linearibus obtusis. — 6. Hippuris. Linn. gen. 1. — Observations on an jinthelium, seen at fVtrtemberg, Jan. 18, n. s. 1738. By J. F. JVeidler. N° 454, p. 221. An Occultation of Aldebaran by the Moon, Dec. 23, 1738, n. s. Observed by Christfried Kirch, Astronomer Royal at Berlin. N° 454, p. 223. Immersion at 6^ 31*" 54' correct time. Emersion 7 33 33 The same Occultation, observed at Wittemberg. By J. F. Weidler, F. R. S. N° 454, p. 225. Immersion &" 27™ 35* Emersion 7 29 20 Duration 1 l 45 I VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. " 369 A Solar Eclipse observed at fVtrtemberg, July 24, o. s. 1 739. By J. F. fVeidler, F. R. S. N° 454, p. 226. 4" 4 5 5 6 15" 53 24 50 27 ' 30* P. M. Beiginning of the eclipse. 40 .... 6 digits eclipsed. 40 .... 9 digits, the greatest obscuration 30 .... 6 digits when decreasing. 20 . . .,. End of the eclipse. Of a terrible Whirlwind, which happened at Come- Abbas in Dorsetshire, Oct. 30, 1731. By Mr. J. Dorby. N° 454, p. 229. On Saturday Oct. 30, about a quarter before one in the night, there hap- pened at Corne-Abbas, Dorsetshire, a very sudden and terrible wind whirl-pufF, as Mr. D, calls it : some say it was a water-spout, and others a vapour or ex- halation from the earth. It began on the south-west side of the town, passing directly to the north-east, crossing the middle of the town in breadth 200 yards. It stripped and uncovered tiled and thatched houses, rooted trees out of the ground, broke others in the midst, of at least a foot square, and carried the tops a considerable way. The sign of the new inn, a sign of 5 feet by 4, was broken off 6 feet in the pole, and carried cross a street of 40 feet breadth, and over an opposite house. It took off and threw down the pinacles and battle- ments of one side of the tower ; by the fall of which, the leads and timber of great part of the north aile of the church were broken in. The houses of all the town were so shocked, as to raise the inhabitants. No hurt was done but only across the middle of the town in a line. Nor no life lost. No other parts of the neighbourhood or country so much as felt or heard it. It is supposed by the most judicious, that it began and ended within the space of two minutes. It was so remarkably calm a quarter after 12, that the exciseman walked through two streets, and turned a corner, with a naked lighted candle in his hand, un- molested and undisturbed by the air ; and as soon as over, a perfect calm, but was soon followed by a surprising violent rain. Of Letters found in the Middle of a Beech. By J. Theod. Klein, Secretary of Dantzick, F. R. S. N" 454, p. 231. In the year 1727, a beech-tree was felled near Elbing, for the domestic use of John Maurice Moeller, then post-master of Elbing, now secretary of his native city. The trunk being sawed into pieces, one of these, 3 Dantzic feet 3jSb PHILOSOPHICAL TRAKSACTIONS. [aNNO \73Q. 6 inches long, cleft in the house, discovered several letters in the wood, about 1 inch and a half from the bark, and near the same distance from the centre of the trunk. Two of these, db, show their old bark smooth and sound. The wood lying between the letters and the bark of the trunk, as well as that be- tween the letters and the heart of the tree, is likewise solid and sound, bearing not the least trace of letters. The characters bd, being somewhat hollow, re- ceive the bark of the letters db. The same letters are seen in the bark of the tree, only that they are partly ill shaped, partly almost effaced ; whereas those within bear a due proportion, as if done with a pencil. It is an ancient custom to cut nan)es, and various characters, on the rinds of trees, especially on such as are smooth. That this has happened to our beech, the mere inspection of the bark sufficiently shows. An incision made, the tubuli conveying the nutritious juice, and the utriculi in which it is pre- pared, are divided and lacerated, and more of them, as the incision was made deeper and wider : and consequently the sap is not carried on in the circula tion, but extravasated and stopped at the wounds. Hence the origin of the characters in the bark and wood. Now as a new circle of fibres grows yearly on the tree, between the wood and bark, a number of these may, in a process of years, more and more sur- round the engraved characters, and at length cover them. And this number was the greater in our beech, on account of better than half a century elapsed since the incision, which was made in the year 1672, as appears on the outside of the bark. But while new circles of fibres are successively added, the tunicle or skin of the bark is broken each time, and the utriculi extended and dilated. M. Klein also mentions several other instances of the same kind, and ac- counted for in the same manner, as treated of by different authors ; viz. Solo- mon Reisel, John Meyer, Luke Schroeck, John Chrit. Gottwald, John James Scheuchzer, and John Melch. Verdries. On the Ejects of Thunder on Trees, and on a large Deer's Horn found in the Heart of an Oak. By Sir John Clark, one of the Barons of his Majesty's Ex- chequer in Scotland, and F. R. S. N" 454, p. 235. Being lately in Cumberland, Sir J. C. there observed three curiosities in Winfield-Park, belonging to the Earl of Thanet. The first was a huge oak, at least 60 feet high, and 4 in diameter, on which the last great thunder had made a very odd impression; for a piece was cut out of the tree, about 3 inches broad, and 2 inches thick, in a straight line from top to bottom. The second VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. il(i| was, that in another tree of the same height, the thunder had cut out a piece of the same breadth and thickness, from top to bottom, in a spiral line, making 3 turns about the tree, and entering into the ground above 6 feet deep. The third was the horn of a large deer found in the heart of an oak, which was dis- covered on cutting down the tree. It was found fixed in the timber with large iron cramps ; it seems therefore, that it had at first been fastened on the outside of the tree, which in growing afterwards had inclosed the horn. In the same park Sir John saw a tree 13 feet diameter. Remarks on the foregoing. By the Editor, Dr. Mortimer. N° 454, p. 236. This horn of a deer, found in the heart of an oak, and fastened with iron cramps, is one of the most remarkable instances of this kind, it being the largest extraneous body we have any where recorded, thus buried, as it were, in the wood of a tree. If J. Meyer, and J, Pet. Albrech had seen this, they could not have imagined the figures seen by them in Beech-trees to have been the sport of nature, but must have confessed them to have been the sport of an idle hand. To the same cause are to be ascribed those figures of crucifixes. Virgin Marys, &c. found in the heart of trees ; as, for example, the figure of a crucifix, which I saw at Maestricht, in the church of the White Nuns of the order of St. Augustin, said to be found in the heart of a walnut-tree, on its being split with lightning. And it being usual in some countries to nail small images of our Saviour on the cross, of Virgin Marys, &c. to trees by the road-side, in forests, and on commons ; it would be no greater a miracle to find any of these buried in the wood of the tree, than it was to find the deer's horn so lodged. Sir Hans Sloane, in his noble museum, has a log of wood brought by Mr. Cunningham from an island in the East-Indies, which, on being split, exhibited these words in Portuguese, da boa ora. i. e. Det [Deus] bonam horam. On the Eruption of Vesuvius, in May 1737- By N. M. d!Aragona, Prince of Cassano, and F. R. S. N° 455, p. 237, Mount Vesuvius is about 7 miles distant from Naples, and 4 miles from the sea. It rises in the middle of a large plain ; and the foot of it begins from the sea-coast, which growing gradually higher, reaches the first plain, to which one can easily ride on horseback. The figure of the plain is nearly circular, being about 5 miles in diameter, and half a mile perpendicular height above the level of the sea. This is the basis of the mountain, out of which arises another, called Monte Vecchio, whose perpendicular height is about 4O0 VOL. VIII. 3 A 362 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739. paces, and its top little less than 2 miles in circumference, of an irregular figure. The top, before the year 1 631, was of the form of a basin, but all surrounded with aged oaks, and vastly large chestnut- trees, the fruit of which afforded food sufficient for a number of cattle. In the bottom, a cavern was observed, into which people descended above 200 paces, by difficult and interrupted paths : this was the ancient mouth, which for a long time had constantly cast up great quantities of bituminous matter, and had at the same time burnt a considerable part of the neighbouring country, cultivated by the inhabitants round the hill. Concerning the eruptions that have happened heretofore, they are very numerous, as well ancient as modern. Of the first, several are mentioned by Berosus Chaldaeus, Pobybius, Strabo, in the time of Augustus, Diodorus and Vitruvius; and in Trajan's reign the name of the mountain became more famous by the death of Pliny. From that time it is thought the eruptions were less frequent, down to the year IISQ; when, after a con- siderable eruption, it continued quiet somewhat less than 5 centuries ; so that the horrid remembrance of the past ruins was pretty well obliterated out of the minds of the neighbouring inhabitants ; who, vainly flattering them- selves with hopes, that the infiammable matter was spent, planted the whole district round the mountain, which, by its fertility, became the delight of these parts. But they found themselves deceived and frustrated in their expectations: for in the year 1 631, during 6 months space, continual rumblings were heard, and shocks of earthquakes felt : and afterwards, in the month of December, a dreadful fiery eruption happened, which first blew up part of the mountain into the air, in a terrible manner, and then vomited out water, ashes, stones and fire; inundating almost the whole country around to the sea, and for above 7 miles in breadth, with the dreadful loss of more than 4000 people. After which the mountain became silent, and remained considerably diminished in its height, from what it had been before. It continued quiet for 2Q years ; but having rekindled in l66o, its fire filled the whole capacity of the immense hollow, which remained since the year l63l ; whence, after several less eruptions, a new inountan appeared in l685. In 1707, not only the inhabitants of the neighbourhood, but also the whole city of Naples, were put into great terror, on account of the frequent noise and shocks, the fire seen on the top of the mountain, with a vast quantity of ashes, which issuing out with impetuosity, were dispersed all over our he- misphere, and darkened the light of the sun during one whole day. These were all manifest signs of the impending desolation : and yet this dreadful day, which had portended so much mischief, was beyond expectation, and to our great astonishment, followed by another as pleasant as could be desired : for VOL. XLI.J PHILOSOPHICAL TKAN8ACTIONS. 363 the air was quite serene, and clear of ashes; and on the mountain there wap no other appearance besides that of a little smoke. In the year 1724, the quantity of ashes and stones, thrown from the top of the mountain, was so heaped from the bottom up to the edge of the ol mountain, that the whole space from the old hill to the new, appeared but one continued mountain. In 1730, there was another eruption of Vesuvius, though very inconsiderable in respect of the last. This present year 1737, to the month of May, the mountain was never quiet : sometimes emitting great quantities of smoke, at other times red-hot stones ; which, for want of a sufficient impelling force, fell on the same mountain. In the beginning of May, a smoke only was seen to issue from the open mouth at the top; and from the 10th to the IQth, subterraneous rumbling noises were heard. On the 19th, fire was seen to burst out in thick black clouds ; and the same day there were several loud reports, returning quicker towards the evening : And still more on Sunday night, when there constantly appeared a very great smoke mixed with ashes and stones : and the neighbourhood felt some shocks, like those of a weak earthquake. On Monday the 20th, at the 13th hour, the mountain made so loud an ex- plosion, that the shock was strongly felt even in the cities 12 miles round. Black smoke, intermixed with ashes, was seen suddenly to rise in vast curling globes ; which spread wider, as it moved farther from the basin. The explo- sions continued very loud and frequent all this day, shooting up very large stones through the thick smoke and ashes, about a mile high, to the horror of the beholders, and the danger of all the neighbouring buildings. At the 24th hour of the same Monday, May 20, amidst the noise and dreadful shocks, the mountain burst on the first plain, a mile distant ob- liquely from the summit, and there issued from the new opening a vastly large torrent of fire; whence, by the quantity of fire incessantly thrown up into the air, at a distance all the south side of the mountain seemed in a fiaine. The liquid torrent flowed out of the new vent, rolling along the plain underneath, which is above a mile long, and near 4 miles broad ; and in its way it spread very speedily near a mile wide ; and by the 4th hour of the night, it reached the end of the plain, and to the foot of the low hills situate to the south. But as these hills are rugged with rocks, the greater part of the torrent ran down the declivities between these rocks, and into two valleys ; falling successively into the other plain, which forms the basis of the mountain ; and after uniting there, it divided into 4 lesser torrents, one of which stopped 3 A 2 3(54 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739. in the middle of the road, a mile and half distant from the Torre del Greco. The second flowed into a large valley. The third ended under the Torre del Greco, near the sea ; and the fourth at a small distance from the new mouth. The torrent, which flo\*ed into the valley, ran as far as between the church of the Carmelites and that of the Souls of Purgatory, by the 8th hour on Tues- day. The matter of the torrent ran like melted lead : in eight hours it ad- vanced 4 miles. The trees, which the torrent found in its way, on the first touch took fire, and fell under the weight of the matter. The torrent which ran behind the convent of the Carmelites, after setting the little door of the church on fire, entered not only by it, but also through the windows of the vestry, and into two other chambers. In the refectory, it burnt the windows ; and even the glass vessels, that stood on the tables, were melted into a paste by the violent heat of the fire. Sixteen days afterwards, the matter continued hot, and was very hard, but it was broken by repeated blows. A piece of glass fastened on the top of a pole, and thrust into this matter, was in 4 minutes reduced to a paste. Under the mass of the torrent were heard frequent reports, which made the church shake, as if by an earthquake. Along the whole surface of the torrent, there appeared small fissures, out of which issued smoke, that smelled of brimstone, mixed with sea-water ; yet these exha- lations are not poisonous, but rather a remedy for some diseases. The stones round about these fissures were observed to be covered with sublimed salts. Iron, thrust into these fissures, was taken out moist ; though on thrusting in paper, it was not moistened, but rather somewhat hardened. At the same time when the new mouth opened, that on the summit of the mountain vomited a vast quantity of burning matter, which, dividing into tor- rents, and small streams, ran partly towards the Salvadore, and partly towards Ottajano; and at the same time that this matter issued out, red-hot stones were seen to be cast out of the mouth, in the midst of black smoke, frequent flashes of lightning and thunder, all produced by the same matter. These impetuous expulsions of fire continued till Tuesday, when the erup- tion of the melted matter, the flashes, and thundering noise, ceased; but a strong south-west wind arising, the ashes were carried in great quantities to the utmost boundaries of the kingdom ; in some places very fine, in others as coarse as Ischian sand: and in the neighbourhood they not only felt this plen- tiful shower of ashes, but likewise pieces of pumice-stones, and other large stones. Tuesday night the fury of the mountain began to abate, so that on Sunday there was scarcely any flame seen to break out of the upper mouth ; and on VOL. XLI.] VHILOSOPHICAL TRANSACTIONS. 365 Monday but little smoke and ashes. This day it began to rain plenti- fully, which continued to Tuesday, and afterwards for many days : a circum- stance which has constantly happened after the eruptions of times past. The damages done in the neighbourhood by this eruption of fire and ashes, are incredible. At Ottajano, between 4^ and 5 miles from Vesuvius, the ashes on the ground were 4 palms high. All the trees were burnt, or blasted, the people terribly affrighted, and many houses crushed by the weight of the ashes and stones that fell. After the description of this fiery eruption, the Academy of Sciences at Naples made an accurate analysis of the matter, and of the salts, that were collected in great plenty near the fissures; and, towards the discovery of the truth, they made the following experiments : Exper. 1 . — Some of the stones of Vesuvius being pounded small, and the loadstone applied to the powder, some few particles were attracted by it ; and the same powder, put into aquafortis, caused a sensible effervescence; whence it certainly contains no small quantity of iron : which was also found on trial in another eruption by Tomaso Cornelio, But for the greater elucidation of truth, one of these stones being applied to the magnetic needle, it turned to the stone ; and then carrying it round to the opposite end of the needle, it immediately turned from it, in the same manner as if iron was applied near the compass. Exper. 1. — ^The stones are not all of the same density or colour; but various, and of different ponderosity. Some are composed of real talc, others full of marcasites : some are almost all sulphureous, others nitrose; some of a grey colour, others red. Exper. 3. — The matter of the current is spongy at top, but very dense to- wards the bottom ; which is a proof of its fusibility; the heavier bodies sub- siding, and the lighter remaining at top. Exper. 4. — After growing hard, it retained part of the heat above a month, though unequally : for in the interior parts, where the air had no free access, and the matter was more compact, the heat was much stronger, than towards the surface. Exper. 5. — ^Twenty days after the eruption, in divers parts of the mountain, from the bottom to the top, there were seen to arise many pernicious damps, [mofete] especially from the cavities, and the fissures of former torrents; as also on the plain : but none were observed in the matter of this last eruption. They issued out of the fissures under the appearance of a cold wind, and rose about 3 palms high ; then they moved along the surface of the ground, and» 366 PHILOSOPHICAL TRAKSACTIONS. [ANNOl73t|. after a progress of some paces, disappeared. Animals, which happened to graze where these passed, were all killed by it ; and likewise a Teresian friar, who inadvertently breathed the vapour of one of these damps. Exper. 0. — Having placed the barometer in the vapour, it underwent no change, but the thermometer fell somewhat more or less. A lighted torch, thrust into them at two palms from the ground, was soon extinguished by the action of the damp. Exper. 7. — ^These damps grew gradually weaker in their pernicious effects, for above 3 months, even to the subsequent autumn; as has been generally found in other former eruptions, or when they happened to issue out of their vents. Exper 8. — Concerning the salts which are generated in abundance in Vesu- vius, I have, by order of the Academy, examined them by accurate experi- ments, My intention was to know, if besides sal ammoniac, there were also sea-salt, vitriol, nitre, or any other salt. I thought there was no better way of proceeding in this inquiry, than by crystallization ; because it is universally al- lowed, that salts in crystallizing constantly retain one certain and determinate figure ; sea-salt concreting into cubes, vitriolic salt into rhomboidal parallepi- peds, alum into octaedrons, and nitre into rectangular prisms on hexagonal bases. I imagined, that if the salt of Vesuvius happened to contain any par- ticles of the salts abovementioned, it would discover them after crystallization. This way of reasoning was confirmed by experiment : for the Vesuvian salt, in crystallizing, left on the sides of the vessels small parcels of crystallized salts, which, observed through a microscope, resembled a tree with its branches, on the ends of which there appeared several pyramids of an irregular figure, but very sharp-pointed ; and between the branches there were interspersed iti some places a group of prisms, in others some small cubes: whence I inferred, that the salt was ammoniacal, and indeed a genuine and efficacious sal ammoniac, with insensible portions of nitre and sea-salt. Which coincides with the sen- timents of the Royal Academy of Paris in 1 705 ; with those of Thomas Cor- nelius in his Progymnasma de Sensibus; of Dominicus Gulielmini in his Treatise de Salibus; of Dr. Boerhaave in his chemistry, and many other writers. Exper. 9. — In order to be convinced whether this salt was really ammonia- cal, and of the nature of neutral salts, I mixed it with spirit of vitriol, and spirit of salt, without producing the least fermentation. I afterwards put some of it into oil of tartar per deliquium, but could not perceive any ebullition; so that it is to be ranked among the neutral salts. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 367 Exper. 10. — Thrown upon red coals, it did not crepitate like sea-salt, but it boiled and swelled, and after evaporating it dried up. Exper. 1 ] . — It is of a very pungent taste, strongly pricking the tongue, and of a bituminous smell of brimstone, which occasions a violent head-ach by its volatile texture. Exper. 12. — The salts taken from different stones are not all of the same weight or colour : for some are yellow and unctuous, as if rubbed all round with petroleum : others are very white, others blackish, and others of other colours, according to the stones they adhere to. Exper. 13. — I have likewise found by experience, that the sal ammoniac of Vesuvius is much more efficacious, than any other salt known at this day, in cooling liquors. On dissolving some of it in water, it makes the water so cold, that the sides of the vessel which contains it, can hardly be touched without uneasiness, through the excessive cold. Exper. 14. — Mons. GeofFroy, a celebrated member of the Academy of Sciences, thinks it a singular power of common sal ammoniac, that being mixed with a certain quantity of water, it rendered the water so cold, that it made the spirit of his thermometer, 18 inches high, fall 33 lines. But the Vesuvian salt makes the liquor of a thermometer, like his, fall 44. inches ; which is equal to 54 lines. So that the efficacy of this salt, in causing the fall of the liquor, exceeds the efficacy of common sal ammoniac by 21 lines. Exper. 15. — If round a vessel full of water cooled with snow, there be put some of the salt of Vesuvius, the water freezes and grows hard in a very little time. Exper. 16. — If a good quantity of the salt of Vesuvius be put into snow, set round a glass vessel full of water, and then stir the vessel, the contained water becomes unfit to drink ; having acquired a very disagreeable acrid sul- phureous taste; a manifest sign, that the salt is divided into small particles, which passing through the insensible pores of the glass, enter into and mix with the water. Exper. 17. — Of all kinds of salts, this dissolves in the greatest quantity in water; and perhaps the greater or less solubility of a salt in water, will be found proportional to its greater or less effiict in cooling water. Exper. 18. — Being put into brandy, or oil, besides that very little of it is dissolved, it occasions no descent of the liquor in the thermometer. Exper. 19. — Being mixed with blood lately drawn from the vein of a man, but coagulated after settling, the blood was dissolved, and continued in that state for the space of 24 hours. Exper. 20. — A solution of this salt being injected into the vein of a dog, first 3(>8 PHILOSOPHICAL TRANSACTIONS. [aNNO IJSQ. occasioned tremors, then universal convulsions, and lastly death. And 4 hours afterwards, having opened the dog, the blood, which should have been coagu- lated, was found fluid, both in the trunks of the veins, and at the ends of the arteries. Exper. 21. — It has all the properties of sal ammoniac to that degree, that on substituting this Vesuvian salt, instead of common sal ammoniac, the strongest sort of aqua regia may be had for dissolving gold ; which experiment was made with success by Mons. Lemery, in the academy of France. Exper. 11. — If a lump of the mineral matter be reduced to a fine powder, and attentively viewed through a microscope, it appears very like the sand of Ischia, and is very proper for writing-sand. Hence probably that sand is no- thing else but the same matter for a long time comminuted by the action of the sea. Exper. 13. — In some of the stones there appear some few veins of gold, in others of silver, but insensible ; and in others, which are very heavy, there is some antimony. Exper. 14. A great dispute arose in the academy on the rise of the (Mofete) damps ; for what reason these should be seen only in the old strata of the mineral substances, and not in the new, where by the action of the fire they ought to issue ; which phenomenon, if I am not mistaken, may be accounted for in this manner. As the cooling of the burning matter began at the surface, we may think, that the more subtle heterogeneous particles, on the closing of the pores at the surface, remained in quantities buried in the lower parts of the matter ; which, in process of time, becoming acutangular and of deleterious figures, yet cannot offend while imprisoned. But in new eruptions, when the shocks given to the matter produce many fissures, the damps, meeting with less resistance there, issue forth. As when the air is a long time pent up in some hollow, on giving it vent, it generally comes out in a pernicious vapour. Exper. 25. It was observed, that the greatest shocks happened to such things as stood exposed to the volcano ; but that those things which were not thus exposed to it, received but faint shocks : a manifest sign, that the vibration of the air had a great share in the shocks of the earth : which circumstance is taken notice of by Borelli with respect to Mount Etna. An Abstract of a letter from an English Gentleman at Naples to his Friend in London, containing an Account of the Eruption of Mount Fesuvius, May 18, and the following Days, 1737, N. S. N° 455, p. 252. I was lodged for some time at Chaja, and afterwards at Fontina Medina, in the face of this surprising mountain, and at 2 or 3 miles distance. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 36O By all accounts, there has not been any eruption remembered near so violent, nor so furious ; and authors mention none to this degree later than above J 00 years since. On Friday, May 17, 1737, N. S. I observed, as far as I could see round, that the mountain was covered with white ashes a great way down, as it has been with snow in the winter. Pliny observes in these words : " Praecesserat per multos dies terraemotus minus formidolosus, qui Campaniae non solum castella, verum etiam oppida vexare solitus." (Plin. lib. vi. ep. 20.) Other authors say the contrary ; though it may very likely be so, round and near the foot of the mountain ; but this time I have not found any body sen- sible of it here ; but it is certainly true, that our windows and doors shook all the time of the violence of the eruption, which I take to be from the very great concussion of the air on the violent explosions. On Saturday night. May 18, this great phenomenon began, and increased so much on Sunday, that it brought half the people out to gaze at it. There were certainly, among some, great apprehensions, by their being employed in processions, visiting their churches, and exposing their images of the Virgin Mary. I very boldly set out on Monday, about 2 hours before sun- set. It was a melancholy sight, to see the road full of numbers of poor wretches, flying as from Sodom. I stopped on the way, to observe the vast clouds of smoke thrown up in a prodigious column, to an amazing height, which, by its gentle waving and undulation, was a most beautiful sight ; and when it had mounted so high, that it had lost the force of the protrusion, it was carried by the wind a vast way ; but not too far for one to observe how its rolls began to break, and, being dispersed and expanded, covered the country underneath with ashes and darkness. Many great flashes of lightning were darted through this pillar of smoke, and frequent discharges as of cannon or bombs, which were followed by falling stars, such as we see from well-made rockets. We turned off" out of Portici, to gain the north-side of the mountain, as far as we could, in chaises, till we were forced to get upon asses or mules. It was now growing dark, and the fire began to be visible, which it was not in the day-time, the sun bearing no rival. In a little time, by the light of the mountain, though that was much ob- scured by the clouds and pillar of smoke, and the help of our torches, we scrambled over very rough roads, till we got within about a quarter of a mile of the great lava or current. But then we halted, as the scene on all sides became so stupendous and terrible. We returned to Portici, where we supped, and got home, much fatigued, by 2 in the morning. The fury of this eruption was at its height this night, as VOL. VIII. 3 B 370 PHILOSOPHICAL TRANSACTIONS. [aNNO l/Sp. to burning ; but the next day, Tut'sday, the columns and bouYllons of sinoke were as great, and thrown out with as much violence, which, as the wind sat, carried its destruction, not of the large massy metallic bodies, but of infinite quantities of ashes and cinders, all that day, and part of the night- Through the columns of smoke was a continued lightning, the most beautiful sight imaginable. The following day, Wednesday, we set out again, to view the west-side of the mountain at Torre del Greco, 8 miles from hence ; where the great lava had stopped at the church of the Carmelites, but not without carrying part of it away. This lava had, from the declivity, taken the water-course, which was the preservation of the country from being drowned. This hollow, which was for some miles between 30 and 40 feet deep, and as many wide, was not only filled up, but the matter rose as many feet above the surface of the land about it. We walked to view it on one side, but the heat was so intense, and the sulphureous stench so suffocating, that we were obliged to keep at a good distance ; and I was well informed by several, that it continued very hot 4 or 5 weeks after ; so long in cooling is that great quantity of bituminous and me- tallic matter, with which this vomes is loaded. As the fury of the expulsion and explosion was much abated on Tuesday morning, the stop here was about 4 o'clock that day in the afternoon ; which might be the more easily conceived, when no more of this vast metallic matter was discharged, and the motion of all the rest was relented, for want of more protrusion, and the bitumen growing a little cooler. As this stop was made at the church, part of the lava took a turn into the great large road to Salerno, to a great height ; which part is choaked up for ever, the expence being im- mense to remove it. Some persons say, that the matter discharged this time in the different cur- rents or lavas round about, would make a mountain as large as their sire. The Carmelites here soon fled, and were not come back 10 days afterwards, when we returned that way, to visit the south-east side, to view the great devastation which was made about Ottajano, ] 8 miles froui hence ; for though the great discharge of the metallic body ceased on Tuesday, a vast destruction of the country followed for a long time after ; for as the force of the explosion was very great, it continued to throw out vast showers of cinders and ashes. The lands indeed, where the lavas fall, are annihilated to the owners ; and the other materials destroy all the fruit and produce of the earth where they fall, which does not recover for a long time. As we turned on the left from Torre del Greco towards Ottajano, we passed all the way through their masserias (farms) ; and the mountain, being to the _i_ . VOL. XLI.l 1>HIL080PHICAL TRANSACTIONS. 371 windward of us for 3 or 4 miles, showered ashes plentifully upon us, and we lost our sinell of every thing but brimstone. All the trees, vines, and hedges, bent under the weight of these ashes; several arms, and even bodies of trees, were broken with the weight ; so that in some narrow roads we had difficulty to pass. Within a mile or two of the prince of Ottaja no's palace, one can scarcely frame to one's self a sight of greater desolation ; 10 successive north- ern winters could not have left it in a worse condition ; not a leaf on a tree, vine, or hedge, to be seen all the way we went, and some miles further, as we were informed. Here, and at the town, they had a new earth, about 2 feet deep, some said more, by the account of the miserable inhabitants, who were a dismal spectacle. The storm fell so thick and heavy for that time, that they almost all fled, and many houses were beaten down. In one convent, two or three nuns were buried in the ruins. At Somma, on the north-east side, it has made great havock ; a monastery of nuns was destroyed. After a long day's work, we returned at six o'clock. Of the Lunar Atmosphere. By M. Jean Paul Grandjean de Fouchy, of the Royal Academy of Sciences at Paris. N° 455, p. 26 1. Translated from the Latin. By an atmosphere is meant a certain assemblage of pellucid matter surround- ing the planet, and capable of turning the rays of light, that pfTss through it, from a right lined course. M. F. does not here inquire what may be an atmo- sphere, in other respects, different from that of a refracting medium, but only undertakes to prove, that the moon is not enveloped by any thing capable of refracting the rays of light. He conceives an atmosphere, in this inquiry, to be a homogeneous fluid, with a spherical surface, of a uniform density, which is equal to the sum of the decreasing densities in the real atmosphere ; pur- posely omitting the difference of density in the parts, as not disturbing the de- monstrations. Now if the moon be encompassed with an atmosphere, its diameter ought to be found greater than in the naked planet. And that the quantity of the in- crease may be known, let a i b, fig. 3, pi. 8, be the body of the moon, peg its atmosphere ; then the angle a h l will be that of the real diameter of the moon, and the angle e h l, made by the axis l h, and the ray a e h, will be the observed diameter : so that the angle e h a will be the increase of the moon's diameter by the atmosphere. But the angle e h a is opposite to the side e a, of the triangle eh a; and the angle a e h, the supplement to I80° of the horizontal refraction in the lunar atmosphere, is opposite to the 3b 2 372 PHILOSOPHICAL TRANSACTIONS, [aNNO 1739- side A H, the moon's distance from the earth. Also the side e a is the half of a chord of the lunar atmosphere touching the moon's body at a ; therefore the sine of the increase e h a, will be to the sine of the horizontal refraction, as the semichord a e is to a h, the moon's distance. Hence it follows, that the increase of the moon's diameter is insensible ; for, if it amounted to 2|", supposing the horizontal refraction 3', i.e. at least 30 times greater than it can be supposed, as will be proved hereafter, then the semichord e a would be equal to 276 French leagues, and thus far exceed a like chord of the terrestrial atmosphere. Therefore, whether the moon is covered with an atmosphere or not, her diameter will always be observed the same : so that the observation of the lunar diameter can never be sufficient for resolving the problem. But the solar eclipses afford better means for deciding the point ; for the ex- treme rays bounding the cone of the lunar shadow, as they touch the moon's body, and pass through her atmosphere, will be necessarily inflected toward the axis of the cone ; hence the cone will become shorter and more obtuse. But to know the quantity of that variation, it must be observed, that the ray p A, fig. 4, or its parallel e g, which in case there be no atmosphere, would be the limit of the lunar shade f a c, would be refracted towards the axis c A, at the ingress of the atmosphere g, and at the egress h : hence the semi-angle of the cone of the lunar shade will be increased by double the horizontal refraction in the lunar atmosphere. Hence it follows, that in the supposition of a lunar atmosphere, a total eclipse of the sun will begin later, and end sooner, than without one ; also, that in some certain cases, there would be no total eclipse ; which, yet, the diameters of the sun and moon, observed in the same degree of anomaly, would require ; for in these cases the cone of the lunar shade might be so constructed, as not to reach the earth's surface. In the same manner, the duration and quantity of partial eclipses would be also diminished ; and they would thus begin later, and end sooner, on the supposition of a lunar atmosphere, than without one ; and in certain cases, there would be no eclipse at all, when there would otherwise be one. Such then would be the phaenomena in case there were an atmosphere about the moon. Let us now consider what is really observed. In the first place, as the axis of the lunar shade extends to 55 semidiameters of the earth, when greatest, and to 52-l when least ; and as the least distance of the moon from the earth is 54 of the earth's semidiameters ; if the lunar atmosphere were capable of a horizontal refraction of 8", the semi-angle of the conical shadow would be increased by double the quantity, that is 16"; therefore it would be VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 373 equal to 1 6' 4 1" when most open, and to l6'5"when narrowest. Also, the least semi-angle of the cone being supposed l6' 5", its axis will be less than the least distance of the moon from the earth, or 54 terrestrial diameters ; and therefore the point of the lunar shade will not extend to the earth. So that, if there were an atmosphere about the moon, in which the horizontal refraction is 8", there would be no total eclipse on the earth. There is, therefore, either no atmosphere about the moon, or else it produces a horizontal refraction less than 8*. But certain total eclipses of the sun are observed with some duration of the total darkness. For instance, in the eclipse of 1724, the duration of total darkness amounted to "i*" l6^ The moon, at that time, ran over l'l5''in her horary motion, and her shadow, with a parallel motion, a space 54 times greater on the earth's disk, that is, equal to 1° ^' 30" ; from which, if there be deducted the diurnal motion of a habitation, by which the duration of the eclipse can be prolonged, it gives the dia- meter of the shadow equal to 47'30", or 45 1 73 toises, or 11 Paris leagues. Hence, by calculation, it is found, that the axis of the cone of the lunar shade is greater by at least one diameter of the earth, than the moon's distance from it, which was then the least, the moon being then about the perigeum. Further, from the given diameters of the luminaries, observed in the same degree of anomaly, the axis of the cone of the lunar shade is found at least equal to 55 semidi- ameters : hence it follows, that the spot of the lunar shade on the earth's disk, and the axis of the cone, are found to be exactly the same, as the distances of the moon and the observed diameters of the luminaries seem to require. There is therefore no atmosphere about the moon, or, if there is any, it produces no sensible refraction. But to leave no room for doubt, we may consider the reason for those phae- nomena, observed in solar eclipses, which have given cause to suspect a lunar atmosphere. And first, that very faint light, observed in total eclipses, is no proof of any refraction in a fluid about the moon ; for, by Maraldi's experiments, success- fully repeated by M. Fouchy, it appears that the shadows of bodies that have no atmosphere, when they are exposed to the sun, are bright about the axis of the cone; and the more so as it is farther from the body itself. And the situa- tion of an observer, in a total eclipse, is about the axis of the cone of the lunar shade, and near its vertex. It is no wonder therefore, that the middle of the shadow exhibits a kind of gloomy light, which may also be augmented by the rays being reflected by an illuminated air surrounding the shadow about the middle. 2dly. The lucid annulus about the moon, in total eclipses, by no means 374 PHILOSOPHICAL TRANSACTIONS. [aNNO 173Q. proves the existence of a lunar atmosphere, as will be plain to any one who hides the sun froni him by balls of wood, or other opaque matter. Hence this is not to be ascribed to a lunar, but to a solar atmosphere; as has been proved by M. Mairan, in his treatise on the Aurora Borealis, p. 14, i. 3dly. The diminution of the lunar diameter, which in solar eclipses is ob- served to be about 30' less than when the moon shines with a full orb, in the same degree of anomaly, by no means proves a lunar atmosphere; though some inequalities of mountains are observed in the circumference of the moon's disk, which quite disappear in the full moon ; for lucid objects strike the fibres of the eye so strongly, that their motion is communicated to the neighbouring fibres, and so the image of the lucid body is increased beyond the due quantity, as is known by common experience : for if a stick be placed between the eye and the moon, the diameter of the interposed stick will seem to be diminished; but if at that time any cloud pass before the moon, the diameter of the stick will appear less diminished; and if the moon be quite obscured, there will be no diminution at all; and lastly, the diminution will vary according to the various intensity of the moon's light. As for the inequalities of the mountains, they are, for the same reason, ob- served least in the full moon; for the lunar mountains, obscure of themselves, and seen in the bright orb of the sun, escape the eye much less, than when, shining in the full moon, they are extinguished in the splendour of that lumi- nary ; especially as the lunar light is so intense, that a star of the 3d magnitude can hardly be seen, when near it. But, to remove all doubt, if the lin)b of the moon, when in opposition to the sun, were the bound of an atmosphere, and not of her very body itself, the mountains in her circumference would never be observed by the longer telescopes with narrow objective apertures. Whereas M. Fouchy had often observed several inequalities of mountains in the disk of the full moon, with a telescope of 3d Paris feet, and an objective aperture of 1 inch : hence it follows that the disk of the full moon is bounded by the periphery of her body, and not of her atmosphere. 4thly. We must not omit to speak of that remarkable observation, in 1715, of the lunar corusaitions, made by M. Delouville, in the presence of many astronomers of the Royal Society, and seen by Dr. Halley, N° 343, vol. vi, p. 158 of these Abridgments. We may suppose that the moon's visible limb is composed of the tops of mountains; which, in a total eclipse, hide the sun from an observer, in the same manner as the trees in great woods obstruct the sight. Hence if some rows of mountains, on the moon's surface, afford a free and direct passage for the solar rays, they must imitate a kind of corusca- tions, like as when, i« a camera obscura, a ray of the sun is suddenly admitted VOL. XLI.] PHILOSOPHICAL TRANSACTION-S. 375 bv means of a speculum, and the picture of the external objects, drawn on the focus of the lens, is taken away, it will be enlightened with luminous traces, much resembling lightning. From all tliese it is manifest, that there is nothing like a lunar atmosphere in solar eclipses. We may now speak of the occupations of the stars and planets by the moon. If the moon be surrounded by an atmosphere, the planets and fixed stars must be seen, by an observer on the earth, to immerge behind the moon later, and to emerge from it sooner, than if she have no atmosphere; and even in some plnces where such occultations ought to appear, there would be none. To make this plain, let abc, fig. 5, be the moon's body, and s a star at immense, or as at an infinite distance; then the parallel rays lv, mx, touching the moon's body on all sides, inclose a cylindric space, of which the base vzx includes all the parts of the earth's surface to which the star or planet is occulted by the moon. The observer therefore will see the beginning of the eclipse at v, and the end at x, and will measure the duration of time in which the moon may run through her diameter, or an equal space. But if we suppose an atmos- phere of the moon, the ray iw will not remain parallel to the axis of the cylinder, but this will now become a cone, of which the section ytu will mark the earth's surface where the eclipse will be seen. Now the base ytu being contracted, the point y wilj come on any part later than the point v, and the point u will quit it sooner than x; therefore the occultation will begin later, and end sooner, by supposing an atmosphere about the moon, than the con- trary; and there will be no occultation in some places, where it ought to be observed without an atmosphere; for the place c, being included in the base vzx of the former cylinder, is without the conical section ytu. Besides, sup- posing the horizontal refraction in the lunar atmosphere equal to 8'', then vy will be 1384 toises, or a quarter of a Paris league; and hence it follows, that no eclipse must be observed in places according to calculation, whenever they are without a circle of a quarter of a league radius. Another phenomenon also takes place on the supposition of a lunar atmos- phere: in the part of the cylinder yr the star indeed will always be seen, but it will be through that medium : hence it will acquire a motion and colour different from the genuine, and that in all eclipses whatever, whether the star be one of the largest or smallest. Besides, the duration of such occultations does not seem at all diminished, but is always found to be exactly agreeable to the moon's diameter and motion. As to those observations in which the star, after the contact, is seen to proceed a little in the moon's disk before the occultation, the whole cause of them may 376 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739- be referred to the increased diameters of the moon and star; for if the lunar atmosphere were the cause of this appearance, it would always be observed the same in all stars, and in any apertures of objectives. Besides, there has not as yet been observed the progression of any star in the moon's disk, unless it be of the first, or perhaps of the second magnitude, and that by only the half of it at most, and it is well known, that their whole diameter is insensible, and is only increased by spurious rays; whence the adventitious rays, both of the moon and star, are mixed in the bottom of the eye, before the true conjunc- tion of their bodies; and if the visible limb of the moon were the limit of the atmosphere and not of the body, no mountains would be observed on its peri- phery with the larger tubes and narrower objective apertures ; which, however, as beforesaid, are seen plainly enough. From all these then it is manifest, that the moon is not surrounded with a refracting atmosphere, or one capable of being observed; though there might be one producing a horizontal refraction of l" or 2"; and this seems to be coun- tenanced by the larger spots in the moon, which cannot by any means be taken for woods, as Hartsocker and some others have imagined; for the shadows of the edges are always observed nearer to the bright limb of the moon ; whence it is rightly concluded that they are cavities, and not woods, as these would pro- ject a shadow from the other side. Further, some fluid may well be supposed to be in them; in which case it would be very agreeable to philosophy, that they should emit some vapours, the congeries of which would represent a kind of atmosphere ; which would not be found very dense, since, by Sir I. Newton's demonstrations, it could hardly equal a third of that of the terrestrial vapours, nor be observed alike at different times, those vapours being destitute of any other addition. ^n extraordinary sinking down and sliding away of some Ground at Pardines near Auvergne. By M. T. Communicated by Phil, Henry Zollman, - Esq. F. R. S. N° 455, p. -ITI. The village called Pardines, was composed of 46 buildings ; the ground on which it was built, as well as that of the whole hill, is a good and light earth, mixed with a little white clay; there are also in it some stones and rocks of a middling size. This land was very well cultivated, and very fruitful, consisting of fields sowed with corn, of orchards, but for the most part of vineyards; the whole ground was overspread with fruit-trees, particularly walnut-trees. This earth used to dry soon, and chap froii) the heat; some clefts of a considerable depth, which growing wider and wider, often formed several gullies. VOL. XLI.J PHILOSOPHICAL TKANSACTIONS. 377 On the 23d of June 1733, about Q in the evening, the inhabitants of the village saw the walls of their houses shake sensibly ; on which they all withdrew out of them, and saw that the hill visibly melted away, as it were, the greater part of the land sliding along towards the vale; other parts subsided sensibly; in some places the earth, opening, formed new gulls, and those that were there before, grew much wider ; sometimes the ground which slid along in large pieces, stopped, and tumbled one piece over another ; and the rocks, which broke loose from that rolling earth, precipitated themselves into the valley, which became quite filled up with them, as well as with the earth which rolled down, by which the neighbouring road becaine impassable. All this was done very gently, and even sometimes almost imperceptibly ; a sensible motion was observed during the space of 3 or 4 days at different times; one house even did not fall till the 10th of July. During all that time no noise was heard, any otherwise than what proceeded from the rocks falling into the valley, and from some large masses of earth, which loosening themselves from the steeper parts, fell down with precipitation. By this rolling were carried away 26 buildings, some of which subsided with the ground, and, being shaken at their foundations, tumbled on a heap ; the remains of some others appear yet, on those pieces of ground that rolled down into the valley. It is com- puted, that the ground which slid away, or was lost by being buried under the rubbish of the others, amount to the number of 150 acres of Paris measure. It is observable, that in this number were comprised several orchards, besides that the whole ground was covered with trees, either walnut-trees on the hill, or willows and poplars in the valley, about 4000 in all. If one may conjecture what was the cause of so dismal an accident, it seems it proceeded from the situation of the ground, and the nature of the soil. The first surface of the hill, about 4 or 6 feet deep, was a pretty light earth, easily dried by the heat of the sun ; under this first layer there was a stratum of fat clay, which at present lies open in several places, and which is very moist, so that the water is seen bubbling out of it in some places. The great rains that fell in the beginning of the spring, soaked through and diluted this stratum of clay, which retained and gathered all the waters of tlie hill running between the two layers ; the heat of the summer ensued, which dried up the upper surface, and formed it into a sort of solid crust, which rest- ing on a fat and moist clay, and by its steep situation being inclined to slide to- wards the valley, its whole surface loosened itself by great pieces, and break- ing in several places, slid along towards the place whither its declivity would naturally carry it. There are some parts which moved almost insensibly, and only sunk or subsided, either because the rolling of the neighbouring soils made VOL. VIII. 3 C 378 PHILOSOPHICAL TRANSACTIONS. [aNNO \73Q. room, that what was under this surface might slide off, or perhaps because the parts under this surface had been hollowed a long while before, by the waters which passed between this surface and the stratum of fat clay. Other parts, which were much more in number, rolled all together towards the valley, and whole pieces of vineyards are still seen, with the props remaining upright. There are again other parts, which in tumbling were overturned in ditferent manners. This accident is not without example in the province of Auvergne : there has not indeed been so considerable a one before, yet it has often happened, that pieces of earth, of a quarter or half an acre, have separated all in one piece, from the top of a hill, and slid down visibly on the lands below. On the Worms* which destroy the Piles on the Coasts of Holland and Zealand. By Job Baster,f M. D. F. R. S. N° 435, p. -276. In the year 1730, the persons appointed to take care of the dykes on our coasts, observed that the piles made of the hardest oak, defending the coasts of the Netherlands against the sea, were eaten through in a few months, so as to be broken by the least external force. Surprised at this uncommon and danger- ous phenomenon, they inquired into its cause, and saw that a kind of worms, before that time very scarce, but now increased to an incredible number, had in so short a time eaten into those piles, between the highest and lowest water- marks, and threatened very great damage to the inhabitants of these countries. If a pile of the hardest oak has stood 6 months on the shore, and be taken out in summer or autumn, there appears mud and filth sticking to its outer surface ; which being scraped off with a knife, discovers a vast number of holes, hardly so large as pins heads. Viewing this mud through a microscope, there are seen, 1. A number of whitish points, not larger than grains of sand. — 2. Some very small worms. The whitish points seem to be the eggs of this insect, and the worms to be such as are already hatched from them ; and these worms gradually perforating * The animal here described is the teredo navalis of Linnaeus. t Job Basterj an ingenious Dutch physician and naturalist, distinguished himself by a controversy with the celebrated Mr. Ellis, relative to the animal nature of the corallines, which Dr. Baster con- sidered as rather the habitations of the inclosed polypes than as forming a constituent part of the ani- mal. His chief work however is his Opuscula Subseciva, containing observations on various marine animals. These interesting observations were continued, in distinct parts, from the year 1759 to 1765, and are illustrated by very instructive plates. They relate to the propagation and ovaria of shell-fish in general; the ostrea, mytuli, pholades, and tellinae; and the structure of several specie* of the testacea is explained in a satisfactory manner. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. ' 379 the outer surface of the wood, rendered soft by lying in the water, made the aforesaid holes, and through them worked their way into the substance of the wood. A small style of whalebone or lead, thrust into these small holes, runs straight into them for 3 or 4 lines, so that its outer end always makes a right angle with the pile : but afterwards, if the style be gently pushed forward, it does not continue in the straight line, but runs either way, generally upward. But if one of these piles be split lengthwise, with a hatchet or wedge, it is found full of passages, or hollow cylindrical ducts, each of which contains a worm, surrounded with a thin testaceous substance, exactly filling the ductj, and forming its involucrum or sheath, in which it can move with freedom. The ducts, beginning at the outer surface by a narrow hole, grow gradually- wider, and run either straight, oblique, upward or downward. But what is most surprising, these ducts never run into each other, nor communicate; but each continues separate for every single worm. Over the worm's head there are 2 or 3 drops of a salt liquor, thicker than water, but not the least appear- ance of the dust of the corroded wood. Whence it appears, that all the vvood, which had before filled up the place of the duct, in which the worm with its covering is now found, was eaten and consumed by the worm : and as it seems quite incredible, that an ani- mal, which appears soft, and almost as fluid as the white of an egg. should be able to eat through such hard wood; the description of this xylophagous worm is offered to the Royal Society, in order to give them some knowledge of this water-insect, which has done so many millions damage to these countries. They are found of various sizes and thickness. There are some of the younger ones not above an inch or two in length ; some of a middle size, such as represented in figures 6 and 7, pi. 8 ; and some 13 or J 4 inches long. But in order to a more accurate description, we will divide the animal into head, body, and tail. The head is of a most wonderful structure, being covered with two hai-d shells or hemicrania, of a substance neither testaceous nor osseous, securing their softer contents : and being viewed through a microscope, they appear as in fig. 8, as well as they could be drawn. These hemicrania are two white bodies, much harder than the substance which forms the testaceous covering ; the inner surface hollow and smooth ; the outer, convex and rough, with 3 fibres running different ways ; and both together perfectly represent a double bit, of that kind of borer, called an auger, 3 Ci 360 PHILOSOPHICAL TRANSACTIONS. [aNNO 173Q. The upper part of the external convex surface, a, fig. 8, has a very sharp edge, in which the first series of fibres begins from a point ; which fibres gradually dilating, and running lengthwise, end about the middle part of it, which makes a right angle with the upper part. In this part the fibres being elevated, run crosswise, e, fig. 8. The lower part is thicker than the upper, but softer and less compact. In this part the fibres are raised up and rough, first curved, then straight, and, like the others, run lengthwise to the lower edge of this part, which is strongly fastened to the head by various ligaments c, D. The concave or inner part of these hemicrania, which contains the softer parts of the head, is very smooth ; but almost in the middle has a very small and tender eminence or process, in shape much like Dr. Rau's process in the organ of hearing, fixed at one end, and loose at the other, running almost the whole width, and doubtless destined for supporting some of the inner parts of the head. See a, fig. g. These two hemicrania, connected together by strong ligaments, and as it were by a small hinge, by means of which they can dilate without separating, besides their defending the soft head from external injuries, are the instruments with which the animal gets its food. For whatever way it turns its head, the raised and rough fibres, running either lengthwise or crosswise, always rub off some of the wood. These hemicrania being carefully removed, the contained parts, fig. 1 1 , are laid open to view ; but they are so soft, and of so wonderful a structure, that the eye, though armed with a microscope, can neither discern their true make nor use. First indeed there appears a membrane, enveloping the whole head ; in the middle and anterior part, which is not covered by the said hemicrania, it appears as if raised by a tubercle c, and in that place it is of a red colour ; but the lower ligamentous edge firmly adheres, both to the small process, and to the lower edge of the hemicranium. This membrane carefully separated and removed, a, a, fig. 12, in the middle of the subjacent pulp is a small pear-like body, perfectly pellucid, somewhat protuberant above the other parts, which made the tubercle in the membrane. It is much harder than the other contained parts of the head and body ; so that it will bear cutting with the scalpel. It is of a red colour, as perfectly pellucid as a drop of water; of the shape of a pear, from a larger basis terminating in a point. It cannot be better resembled to any thing, than to the crystalline lens of the eye : yet in spirit of wine it preserved its transparency, but its bulk was diminished, as b, fig. 12. At the sides, where the lower edges of the hemicrania do not touch each VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 381 other, there is a sort of cavity ; and in these sides the harder fibres may be distinguished, disposed in such a manner, as perfectly to resemble the gills of fish : and through them the worm seems to breathe. The extreme softness of the other parts of the head prevents our coming at the knowledge of the use of the membranes, furnished with fibres of different tendencies, or inquiring by what organs the worm takes the wood shaved off by the hemicrania, or rough shells ; whether it does this by suction, or not ; by what muscles, or how acting, this wonderful head is moved. It is probable in- deed, that its motion consists in the opening and closing these shells, that shave off the wood ; and that the inner parts have a power to move on all sides, as the ball does in the spcket of the eye ; and perhaps to come forth of these shells, and re-enter, after taking their food. But of these things there can be no certainty, because the parts dissolve between the fingers. The body, viewed forward, fig. "J, is of a reddish colour. In the middle ap- pears a line, often dark-brown, often blackish, sometiines not visible, some- times running near half the length. The rest of the animal is of a whitish or grey colour. ]. If you intend to dissect it, and examine the inside, you must first remove a thin membrane surrounding the whole body, which for that rea- son may be called the cutis or cuticula. When this is removed, there appears an oblong vessel placed in the middle, of a reddish colour, from the shaved wood, of which it is full: hence it seems to be the stomach, or at least the first organ of digestion. 2. In the lower part you will find another vessel, appear- ing like a dark-brown line, which contains the excrements, of which it is often found full, and discharges them at the end of the tail. 3. At the sides of the reddish vessel, or stomach, is placed a white, clammy, fat substance, sticking to the fingers, and perhaps constituting the flesh of the animal. Where the body ends, the tail begins, thicker than the body, and rendered stronger by circular fibres. At its end it has two small hard bodies, containing and defending the tender extremities of the tail. This tail, thicker than the body, terminates in two ends, the thickest of which certainly serves for the discharge of the excrements, the slenderest doubtless for generation : and this it can stretch out to an incredible length, so that in worms that seemed to be in copulation, it appeared above an inch out of the pile. The two small bodies, that contain these ends of the tail, are of a harder substance than even the hemicrania. The outer part is gibbous, the inner hollowed. The lower end is bifid ; whence it is conjectured, that they serve the animal for feet, when it is mounting upright, or corroding the wood ; by leaning on them as on a prop, fig. 13. The above- described worm dwells now very securely in a testaceous tube, of 382 PHILOSOPHICAL TRAW8ACTIONS. [aNNO IJSQ. a white colour, which it exactly fills, yet so as to be able to move with freedom. That tube, like the coverings of snails, &c. daily grows with the animal, from the matter which perspires from its body ; whence it is sometimes found straight, sometimes bent, according to the course which the worm steered in corroding. As to their generation, it is probable enough, that, analogous to that of other insects, it is performed by copulation of male and female : for thev can so lengthen one end of their tail, and thrust it out of the pile, that they may copulate by that means. Then they lay their eggs in the water, close to the piles, to which they stick by their clammy viscid matter, such, for example, as frog's spawn ; and afterwards, by the heat of the sun, hatch the worm, which immediately endeavours to get into the pile- Dr. B. could not observe the difference of sex, either with the eye, or a mi- croscope. Some think them hermaphrodites, as snails, and that they copulate in the same manner : but these conjectures are not very probable. Many remedies and secrets for destroying these dangerous enemies were im- mediately boasted of, which for the most part were preparations of arsenic or mercury, and are not worth enumerating : the following is the best and surest of all. Take an iron plate, of an oblong figure, and of the width of the pile, with a strong handle at each end. One end of this plate must be armed with thick nails, half an inch long, and about an inch asunder. The nails of this plate must be driven into a pile of any slight wood, with a hammer, and then the plate pulled off by njeans of its handles. And this is to be repeated, until the pile is perforated every where with small holes : then it must be daubed over with varnish in the hottest sun, the varnish being imbibed by the soft wood with so many holes in it ; and while the varnish is yet hot, let it be strewed over with brick- dust. And this is to be repeated 3 or 4 times, after the preceding varnish is quite dry, till the pile is entirely surrounded with a stony crust, which will be impenetrable to all insects, and last many years. But Providence has already so far destroyed these pernicious insects, which multiplied so prodigiously for 8 or p years past, that there is great room for hope, that our country will in a short time be entirely freed from them. ^n Explanation of the Figures. — Fig. 6, pi. 8, is the pile-worm, of its natural middle size, lying on its belly. Fig. 7, the same lying on its back, a is the stomach ; b the duct, full of excrements ; c the tail, with its defences dd, and its point e, which it can stretch out. The Six following Figures are represented much larger than Life. — Fig. 8, A, A, the first series of fibres running straight down ; bb the second series VOL. XU.] PHILOSOPHICAL TRANSACTIONS. 383 running transversely ; cc the third taking a different course ; dd the lower edge, which is infixed to the head. Fig. 9, the shell or hemicranium, seen on the inside, with the process run- ning across it, one end of which a is fixed, the other a is moveable. Fig. 10, A, B, c, D, the same as in fig. 8 ; e the hinge, by which these are connected, and may easily dilate or open. Fig. 1 1 , AA the membrane covering the head, freed from the hemicrania, which were attached to this membrane ; b the place, where the hemicrania were connected ; c the middle anterior part, in which the tubercle was pro- minent. Fig. 12, AA the membrane of fig. I I, separated and turned back; b the pellucid pyriform body, lying in the middle of the head, and which formed ; c the tubercle. Fig. 13, the two defences of the tail, of which the exterior part a, is gib- bous, the other or interior b, is, as it were, hollowed : these extremities are bifid, c, the part by which they are joined to the tail. Tmo Otservalions of Explosions in the j4ir ; one heard at HaUted in Essex, by the Rev. A. Vievar ; the other by Sam. Shepheard, Esq. of Spring^ld. N°455, p. 288. On Sunday the 12th of March 1731-2, between 1 and 2 o'clock in the afternoon, walking in the garden, Mr. V. heard as it had been a loud clap of thunder from the north-east. While looking into the air, the noise was re- peated very loud, but seemed more like the violent fall of a house, so that he expected every moment an out-cry from the town : but he was soon undeceived, when it began again, and he found it made towards him, with a different noise from the former, being like the grinding of flint stones, but very loud. Its dimensions seemed to be about 3 feet wide. He found it sink in the air, and as it seemed to point directly at his head, he laid himself down on a glass-slope, to let it pass over. However, at the upper end of the walk it fell to the ground, and came rolling down the grass-walk ; and he can compare it to nothing better than to that of a violent grinding of flint-stones, or a coach and six at full speed on a causeway of loose stones. He lay attentive, expecting to see some- thing, and saw a piece of wood came running before it. When the pheno- menon came to the water- side, it twisted up a large stake that stood in its way, and tossed it towards him with much violence, and immediately fell into the water, with the violence and noise of a red-hot mill-stone. He has seen tjje 384 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739- seas break against a rock in a storm, but never saw a greater ferment caused by the boiling of the waters. It staid about a quarter of a minute in the water, and then mounted again into the air. and went rattling away, but with much less violence. He heard it for about a quarter of a mile, and lost it. It came against the wind, and not faster than a man may walk. The froth and foam on the water remained 30 hours after. The other Account. By Sam. Shepheard, Esq. P. 289. On Tuesday, Aug. 15, 1732, between 11 and 12, the sun shining very bright and hot, without the least cloud, the wind so calm, that the water was as smooth as glass, Mr. Shepheard was in a little room next the garden, about 40 yards from the canal, when he heard a very surprising noise of fire, as if a very large quantity of oil had been thrown into a great bonfire, burning in its greatest rage. He stepped immediately to the window, which was open, where he saw the middle of the canal, which in the dry season had sunk about 6 inches, in extreme agitation, as rough as the Thames in a storm, foaming and smoking, and forced up, to appearance, full 2 feet above the surface, but it might be far more, the window being much higher than the canal ; and the man, who was at work, protests he saw the water, like the spray of the sea, above the dwarf-trees, which must necessarily be 5 or 6 feet. The duration of the phenomenon might be half a minute, and it made such a stench in the house, as if a gun had been fired in it. The canal bears east and west, and the man says he heard it coming from the west, bringing the leaves of some tall trees from an adjacent field in its passage; but he could not discover any material or substantial body to fall in the water, where the hissing was very loud and violent ; neither was there any lightning or thunder before or after, but the day remained bright, still, and hot. The space of the canal that was affected by it, might be 12 or 15 yards. A Catalogue of the Fifty Plants from Chelsea Garden, presented to the Royal Society hy the Company of Apothecaries, for the Year 1738, pursuant to the Direction of Sir Hans Sloane, Bart. Med. Reg. et Soc. Reg. Frees. By Isaac Rand, Apothecary, F. R. S. Hort. Chel. Prcef ac Preelec. Botan. N''456, p. 29]. This is the 17th presentation of this kind, amounting to 850 plants. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS, 385 Some Reflections on Generation, and on Monsters, with a description of some particular Monsters. By Daniel de Superville, Physician to the Margrave of Brandenburg- Bareith, i^c. Translated from the French by Phil. Hen. Zoll- man, F. R. S. N" 456, p. 294. On the subject of generation, this author espouses Leuenhoeck's theory j according to which he thinks monstrous births may be easily accounted for. He mentions having in his collection a pig, that had 8 feet; the 2 bodies, that were separated, reunited themselves by the spina dorsi below the diaphragma, and had but one visible neck supporting a head, larger than it should be, on which there appeared 4 ears, 3 eyes, and the snout seemed double. He had also the head of a foal, which was double, and had 3 eyes. He had a Turkish duck, which was double, the 2 bodies being joined by the breast; each body had 2 wings, and 2 legs ; but they had only 1 neck with 1 head. He had a chicken, which had a second rump fixed to its breast, with the 2 legs, and 2 paws. He had a frog, which besides its 4 paws, had a 5th as well formed as the others, which came out at the right shoulder. The production of all these monsters that are double, or have superfluous members, may very well be occasioned, he thinks, by 2 animalcula entering into the same egg; they touch, they close, they unite, they croud each other; the parts of the weakest, being too much crouded, cannot extend nor display themselves; so they vanish, as it were, so much the easier as they are extremely tender, and without any sensible con- sistency. It is not more difficult to find plausible reasons for imperfect monsters, or that have an odd conformity, as to the whole, or as to some of the members. He had the foetus of a sheep, which had no nose; the part where the nostrils should be, seemed to be flayed, and the 2 eyes were one by the side of the other. On the forehead there was a small trunk, of about 14 inch long, and pierced at the end by 2 nostrils. He had another, which had but 1 eye, in the middle of the forehead. He had a human foetus, of about 7 months, which had no mark of the sex, and instead of the legs there was a bag that ran to a point, the extremity of which was cartilaginous; in that bag there was a bone 3 inches long, covered with a muscular flesh; it was articulated with the os sacrum ; the osea innominata was wanting, and below the anus, which was on the middle of the os sacrum, there was a small tail like that of a pig. When he was at Stetin in Pomerania, about 12 or J 4 years before, a mid- wife came to tell him, that a Serjeant's wife was delivered of 3 dead children, one of which had no head. He immediately went, and observed, that these VOL. VIII. 3 D 386 PHILOSOPHICAL TRANSACTIONS. [aNNO J 740. foetuses had died at different times. One began already to corrupt, and the epidermis severed itself at the least touch. The monster without a head was also already quite flabby, and the third seemed to have died but a few hours before. He examined the monster: there was no appearance of any head; and instead of the navel, there was a small lump of spongy flesh, of the size of a large strawberry. About the secundines he found but 1 placentas, and 2 coats; so that this monster must absolutely have been in one of those coats with another foetus. The midwife was not skilful enough to give him an account of the delivery; he put questions to the mother, who assured him she felt one child dying 3 weeks before, and that the last died the evening before. He oflitred a good sum of money to have all she was delivered of, but they would not let him have it. He still ofl^ered money to have only permission to dissect the monster, but the superstition of the parents deprived him of that satis- faction. He had in his collection a monstrous foetus, which deserved particular atten- tion. It was of 8 months, without head or arms; the figure outwardly seemed to be nothing else but the abdomen with the legs; these were well-shaped and proportioned, with the toes, and the beginning of the nails; the right foot however was, as it were, crooked, and bending inwards. Having opend it, he found indeed but one cavity, which in the upper part contains a small bladder. There was not in all the cavity any thing besides a bit of intestine, the 2 kid- neys, the bladder, and the right testicle, which lay upon the ring. The flesh was hard, and, as it were, carcinomatous. The navel-string went in a little higher than naturally, and a little towards the right side, entering into the in- testine. There was a slender intestine, of about 14 lines in length, proceed- ing from the same place, where the navel entered into the cavity ; next came the caecum with its vermicular appendix, the colon and the rectum, the whole together of the length of about 2 feet. These intestines went from above to below in zig zag, and were attached to the spina dorsi. There was no trace of the heart, the lungs, the stomach, the liver, the spleen, the pancreas, the mesentery, all were wanting. The small bladder was fleshy, and contained some serosity ; it was attached to the first of the vertebrae of the neck. This beginning of the spina was bent forwards like a bow, and formed the monster's roundness from above. The bended extremity kept the little bladder, as it were, under, and shut up in the cavity closed up by the ribs. This cavity was to form the thorax, but the sternum was wanting, as well as the diaphragm. The opinions of most of the natural philosophers concerning the origin and formation of monsters may, he observes, be reduced to two hypotheses: 1. That monsters are original, that is, that even in conception the monster is conceived. VOL. XLI.3 I'HILOSOPHICAL TRAKSACTIONb. 387 2. That they are not produced but by accident. It may be concluded from what he had said about double monsters, that he believed them accidental ; and he believes, rigorously speaking, they are so, whatever they be; for supposing every animalculum to be an embryo created, he cannot imagine them to be created imperfect. Their imperfection, their deformity, may proceed from a thousand accidents, either in the reservoirs where they are contained, or in the different routes they are obliged to take, going from father to son. In this case it may easily happen, that tliey are monsters, even in the moment of concep- tion, though they be such by accident. To how many accidents are they not subject afterwards in the venter of the females ? A fall of the mother, a strong pressure, a contusion, &c. may disorder the nice and tender structure of that little creature so far, that a great many of its parts do not unfold themselves any longer, are destroyed, or have their order and natural situation quite changed. The disturbed and disordered imagination of the females ought also to be ranged among the accidental causes of monsters. He had seen in a sow, just slaughtered, 7 pigs, which all had the bloody mark of the knife about their necks. About 20 years ago, a cloth-shearer, in Holland, had the misfortune to fall into the hands of some drunken young fellows, who murdered him, and stabbed him with more than 20 wounds with their swords. He was to be married that very week; his intended bride saw his corpse naked with all those wounds, and was 2 days after delivered of a dead child, which had the marks of the wounds in the same places of its body, where the mother had observed them on her dead lover. He very well knew, that these sorts of instances, of which one might allege some hundreds, would not go down with certain people, who deny the effect of the mother's imagination on the foetus. They lay stress on two principal reasons: 1. It is pretended, that the foetus has no immediate connexion with the mother who carries it. But this is ridiculous, f©r it cannot be denied, that the secundines are closely united to the matrix, and receive from the mother a humour, or a liquid, which by the navel-string it remits to the foetus. It is by that way it receives its nourishment, that is, the mutter necessary for its increase. Accordingly one may say, that the foetus owes part of its being to the mother; and that the liquid which runs in the vessels of the mother, runs likewise in the vessels of the foetus. 2. It is said, that it is incomprehensible, how the soul of the mother can have an effect on the child. He owns he does not comprehend it neither. It does not follow from thence, that we ought to reject as false all that our reason cannot penetrate into. When once the existence and the na- ture of the soul has been demonstrated, when once we have a perfect know- 3d 2 388 PHILOSOPHICAL TRASANCTINOS. [aNNO 1740. ledge of the manner how an immaterial being acts upon matter, we shall then reason in consequence about what the soul can do, and cannot do. Daily ob- servations demonstrate, that the disordered and disturbed imaginations of wo- men often hurts the infants. And this is a reason, which he adds to all the others, to think he had good grounds to conjecture, that all monsters were accidental; and to believe, that by the hypothesis of animalcula one may better explain the phsenomena which are observed in generation, than by any other. On a Bregma of a Gigantic Magnitude; with a Problem to determine the Size of the Giant according to the Rules of the Art of Drawing. By James Theodore Klein, Secretary to the Republic of Dantzic, and F. R. S. N° 456, p. 308. From the Latin. Having obtained, from Wittsen's museum, at Amsterdam, a bregma of a gigantic size, in height Q English inches, and its breadth 7, with a description and figure by Ruysch, representing the height of the head, from the chin to the crown, 20 inches, and the breadth at the temples 12 inches; and also another bone of the same kind, the height of which was 5f inches, and breadth 5 inches, but without a figure and reference to the head, it is easy to find, ac- cording to the rules of painting, by taking 8 lengths of the head, that the giant's stature was 13 feet 4 inches. But being desirous also to know the just proportion of the other bregma, according to strict mathematical rules, M. Klein proposed the following problem to Dr. Henry Kiihn, professor of mathe- matics at Dantzic, viz. If, in two human bodies of different stature, the height of the bregma in the former, be Q inches, the breadth 7> the height of the whole head 20, the breadth 12 ; and in the latter, the height of the bregma 5^, and the breadth 5 ; to determine the height and breadth of the whole head of the latter, and the proportion of its stature to that of the former. Now the stature of the first body being 20 X 8 = l6o inches, or 13 feet 4 inches, if the bodies were similar, the question would be easily answered, by making a simple proportion, viz. as any dimension of the one is to the like dimension in the other, so is the stature of the former, to the stature of the latter. But because 9 to 7 and 5-|- to 5 are dissimilar ratios, the bodies are not similar. Therefore we must take a kind of mean between tlie stature required, as determined both by comparing the lengths and breadths of the bregmas to- gether. Which may be done in three different ways, as follows : 1st. As 9 : l60:: 5-|- : l02f inches = 8 feet 6f inches, the stature of the latter body as determined by the heights of the bregmas. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 38Q And, as 7 : l6o :: 5 : 1 14-5- inches = g feet 6-f- inches, the stature of the same as determined by the breadths of the bregmas. The mean between these two is Q feet -^ inch nearly. 2dly. As 9 + 7 : 51- + 3 ••: l6o : 107 -i- inches = 8 feet 1 1-^- inches; differing only -J- of an inch from the former way. 3dly. By the geometrical means, as v/Q X 7 : ^5|- X 5, that is, as ^63 : \/284 :: l6o : 180 inches or Q feet ; which being nearly a mean between the two former, it may be accounted the most accurate of all. Hence then the statures being 13 feet 4 inches, and g feet, or l6o inches and 108 inches, are to each other as 40 to 27. j4n Account, by the Rev. Zachary Pearce* D. D. F. R. S. of a Book, entitled. Rejections Critiques sur les Histoires des Anciens Peuples, ^c, Paris 1735 Ato. in 2 vols. N° 456, p. 3 13. The general design of M. Fourmont, the author of this book, is to rectify the history of the most ancient nations, particularly the Chaldeans, Hebrews Phoenicians, Egyptians, Greeks, &c. down to the time of Cyrus, the founder of the Persian empire. The work consists of 3 books. In the first of which, he gives, at length, the famous fragment of Sancho- niathon the Phoenician, as translated by Philo Byblius, and preserved by Eu- sebius, in his Prasparatio Evangelica, lib. I. cap. 9. With this fragment he has published a French version of it, in which he endeavours to distinguish between the account given by Sanchoniathon the author, and what he supposes to be the additions of Philo the Greek translator. After this he examines into the reasons brought by several of the learned, for and against the genuineness of the fragment, and determines in favour of it, with as much weight of argu- ment as the question will admit. He then takes notice of a treatise, written on the same subject as his own, by our learned countryman Bishop Cum- berland ; and having examined and declared his dislike of the Bishop's scheme * Dr. Zachary Pearce, a celebrated English bishop, and F. R. S. was bom in 1690, and educated at Westminster; whence he was elected to Trinity College, Cambridge; while there, he wrote se- veral papers in the Spectator and Guardian. In 1724 he published an edition of Longinus; and his next work was a treatise, " On the Origin and Progress of Temples." In 1739, Dr. Pearce was made dean of Westminster, and in 1748, bishop of Bangor. In 1756, he was translated to the see of Rochester, with the deanery of Westminster. He died in 1774- and an elegant monument to his memory is erected in Westminster Abbey. Bishop Pearce published an edition of Cicero de Officiis; also A Review of the Text of Milton; an Accovint of Trinity College, Cambridge; and several other esteemed works. And, since his death, there have been published his Sermons, in 4 vols. 8vo. ; also his Commentary on the Gospels and the Acts of the Apostles, in 2 vols. 4to. SQO PHILOSOPHICAL TRANSACTIONS. [aNNO 1740. in the main, he prepares his reader to expect full satisfaction from his own, which makes the subject of his second book. In the second book, he undertakes to reconcile the generations of men, set forth in Sanchoniathon's fragment, with those which are recorded by Moses, of the patriarchs before, and for some time after the flood. By the help of Hebrew, Phoenician and Egyptian etymologies, he often makes the names, which at first sight are almost all quite unlike, to be the same in sound, or at least in .sense. And by this application of his skill in the ancient languages, he readily finds out a coincidence between Moses's and Sanchoniathon's earliest generations. But his main work, and what he appears most pleased with, is his discovery of Abraham and his family, among the latter generations recorded by Sancho- niathon. Having laid down, that Ouranos is Terah, the father of Abraham, he undertakes to prove, that Abraham is the Chronus of Sanchoniathon, and the Saturnus of the Latins ; that Sarah, his wife, is the same with the goddess Rhea ; that Ishmael, Abraham's son, is the Miith of Sanchoniathon, and the Dis or Pluto of the Greeks and Romans : that Isaac, Abraham's other son, is the same with the Sadid of Sanchoniathon, with Jupiter among the Latins, and Zjuf among the Greeks, his wife Rebecca being Juno ; that Esau, Isaac eldest son, is Osiris and Bacchus ; and that Jacob, the youngest, is Typhon. And, in like manner, he finds a very great part of the Grecian theology in Abraham's family. In the mean while his readers will, perhaps, make two very material obser- vations on this extraordinary discovery of his : the one, that Chronus's cha- racter in Sanchoniathon's fragment, is the most immoral and tyrannous of any recorded there : and how to reconcile this with the character given in scripture to Abraham, as the friend of God, the father of the faithful, &c. is no easy task : it requires, to be sure, more than a resemblance of two or three circum- stances, common to Chronus and Abraham, when their historians in fifty other circumstances make their characters essentially different. The other con- sideration, which occurs, when we read this treatise, is, that Abraham had ill luck indeed, if, when he left his native country because of the rise of idolatry there, all the grosser idolatry of the heathen nations after his time took its rise from him and his family : the very crime which he took pains to avoid, he was the accidental occasion of, if he and his are to be thus placed at the head of the heathen theology. The author, having finished this remarkable part of his work, enters into a very learned detail of the particular Gods of the several heathen nations, who are the most celebrated in history ; and he has shewed a great compass of VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 3J)(| reading on this occasion. Hardly any writer has been more copious on the subject, or has given better hints for clearing up many passages of sacred and profance story. In his third book he has treated at large on the dynasties of Egypt, and the shepherd kings who reigned there : both of them, perhaps, the darkest spots in the whole face of antiquity. He has taken great pains to fix the epochs of the kings of Sicyon, Sidon and Tyre, of Arabia, Assyria, Lydia, of the Medes and Babylonians ; concerning all which, he has laid together the most remark- able testimonies of the ancients. At length he comes to his favourite point, the Chinese history, and gives, as he says, a complete list of their kings, from the flood down to the present monarch of that empire, and shows that the chronology of the Chinese, may be made pretty nearly consistent with the true chronology of the Old Testament. And for this part of the work the author seems well fitted, being skilled, as he tells us in the preface, in the learned characters of that country, which he has studied for near 20 years, and has for some time taught in the royal college at Paris ; and having composed 5 dictionaries and a grammar, of that language, with a translation, almost intire, of the geography of Tamim, which contains no less than the whole history of that empire : on which occasion he applies to himself, and the progress he has made in the Chinese learning, those expressive verses of Virgil in his 6th book of the ^neid : — — ^^— Pauci, quos aequus amavit Jupiter, aut ardens evexit ad aethera virtus, Dii geniti, potuere. On the Scurvy-Grass that grows in Greenland. By Mr. David Nicholson, Sur- geon. N°45(), p. 317. Mr. N. communicates this as matter of truth, and not hypothetic, viz. that the scurvy-grass in Greenland, equally the same with ours in England, as to the figure of the plant, and all its appearance to the eye, changes its nature much, as it approaches the sun ; for in that climate, its principal quality, the volatile salt, is neither pungent nor perceivable ; but to the taste, the whole plant is quite as insipid as the colewort or beet. Mr. N. preserved some plants with their natural earth, and brought them to London alive ; and he observed the remarkable change produced by the sun's heat on them ; for the saline matter in Greenland, which certainly was analogous to a fixed salt, became, in a month's time, almost to the same volatility as that which naturally grows in England. 392 PHILOSOPHICAL TRAKSACTIONS. [aNNO 1740. Concerning two Species of Lines of the Third Order, not mentioned by Sir Isaac Newton, nor by Mr. Stirling. By Mr. Edmund Stone *, F. R. S. N" 456 p. 318. Mr. Stone having for some time past been reading and considerirtg the little treatise of Sir Isaac Newton, intitled, Enumeratio Linearum tertii Ordinis, as also the ingenious piece of Mr. Stirling, called, Illustratio Tractatus Domini Newtoni Linearum tertii Ordinis ; he observed, that they have neither of them taken notice of the two following species of lines of the third order; and he ventures to affirm, that the 72 species mentioned by Sir Isaac, with the 4 more of Mr. Stirling, and these 2, making in all 78, is the exact number of the dif- ferent species of the lines of the 3d order, according to what Sir Isaac has thought fit to constitute a different species. The 2 species are to be reckoned among the hyperbolo-parabolical curves, having one diameter, and one asymptote, at N° 8 of Newton's Treatise, or p. 104 of Mr. Stirling's ; its equation being xyy = + bx'^ + ex + d; which will give, not 4, as in these authors, but 6 species of these curves : for, 1. If the equation bx^ + ex -\- d ^ O, has 2 impossible roots, the equation * Mr. Edmund Stone was a rennarkable instance of the effect of industry united to good natural talents; having raised liimself to an eminent rank in the mathematical sciences, as well as in the languages, by his own application alone ; all the instructions he ever received, being only to know the 24 letters of the alphabet, which he was taught at 8 years of age, by a servant in the duke of Argyle's family, where young Stone's father was gardener ; with whom, also, at an early age, the son became a servant ; in which situation he spent a considerable part of his life. When about 18 years of age, his extraordinary talents were accidentally discovered by the duke, who found him in the garden reading Newton's Principia in the Latin language ; when, on inquiry, the duke learned that by procuring books, he had made himself master of arithmetic, geometry, &c. as well as the Latin and French languages. Delighted with his conduct and conversation, tlie duke drew him from obscurity, and placed him in a situation to pursue his favourite studies. The time of Mr. Stone's birth is unknown, though it was probably towards the latter end of the 17th century, as the first edition of his Mathematical Dictionary was printed in 1726. After which, several other useful works, both translations, and books of his own composition, follow at certain in- tervals of time. As, 2. — A Treatise on Fluxions, in 1vol. 8vo. 1730; the first part being a trans- lation, from the French, of I'Hopital's Analyse des Infiniments Petits; and the 2d part, or inverse method, being supplied by Stone himself. 3. The Elements of Euclid, in 2 vols. 8vo. 1731 : being a neat and useful edition of those ele» ments, with an account of the life and writings of Euclid, and a defence of his elements against mo- dern objectors. 4. Dr. Barrow's Geometrical Lectures, translated from the Latin, in 1 vol. 8vo. 1735. Besides several other smaller works. The time of his death is also unknown. VOL. XH.j PHILOSOPHICAL TRANSACTIONS. 393 xyy = bx- + ex -{• d, will, as they say, give 2 liyperbolo-parabolical figures, equally distant on each side the diameter a b. See the 57th figure in Newton's Treatise, and this is his 53d species, and Stirling's 57th. 1. If the equation bx^ — cj; + (/= O, have 2 equal roots, both with the sign -j- ; the equation xyy ^ boe^ — ex + d, will, as they say, give 1 hyperbolo-para- bolical curves, crossing each other at the point t in the diameter. See fig. 58 in Newton ; and this is his 45th species, and Stirling's 58th. 3. But if the equation bx"^ -\- ex -\- d=. o have 1 possible unequal negative roots Ap and At, the curve given by the equation xyy = + bx'^ -{- ex -\- d, will consist of 2 hyperbolo-parabolical parts, as also of an oval on the contrary side the asymptote or principal absciss, as fig. 1, pi. 9. And this is one of the species omitted by Sir Isaac and Mr. Stirling, which is really the 59th species. 4. Also if the equation bx' -^ ex -^ d := O, have two equal negative roots Ap and At; the curve given by the equation xi/y := + bx^ -\- ex + d, will consist of 2 hyperbolo-parabolical parts, and also of a conjugate point on the contrary side the asymptote or principal ordinate, as figS2. And this is the other spe- cies of these curves omitted by Sir Isaac and Mr. Stirling, which is really the 60th species. 5. If the roots of the equation bx'^ — ex -\- d = O, be real, and unequal, hav- ing both the sign -f-; the curve given by the equation xyy = bx"^ — ex -{- d, will, as they say, consist of a conchoidaThyperbola and a parabola, on the same side the asymptote or principal ordinate. See fig. 59 in Newton ; and this is really the 6 1st species. 6. If the roots of the equation bx^ + cx — d= O, have contrary signs, the equation xyy = bar' + ex — d, will, as they say, give a conchoidal hyperbola with a parabola on the contrary side the asymptote or principal ordinate. See fig. 60 in Newton ; and this is really the 62d species. ^n Acemint, by Mr. Harris, of several Alterations and Contrivances about the Terrestrial Globe, to render it, as he thought, more commodious and useful in Practice. N° 456, p. 321. A New Method of improving and perfecting Catodioptrical Telescopes, by form- ing the Speculums of Glass, instead of Metal. By Caleb Smith. N*" 456, p. 326. The imperfections of telescopes are attributed to two causes ; viz. the unfit- ness of the spherical figure to which the glasses are usually ground, and the different refrangibility of the rays of light. VOL. VIII. 3 E 304 PHILOSOPHICAL Tl!AN3ACTIONS. [aNNO 1740. The first of these defects only, was known to the writers on dioptrics, before Sir Isaac Newton ; for which reason, as he informs us. Opt. Lect. 1 , 2, " they imagined, that optical instruments might be brought to any degree of perfec- tion, provided they were able to communicate to the glasses, in grinding, what geometrical figure they pleased ; to which purpose various mechanical con- trivances were thought of, whereby glasses might be ground into hyperbolical, or even parabolical, figures ; yet nobody succeeded in the exact description of such figures ; and had their success been answerable to their wishes, yet their labour would have been lost (continues this incomparable mathematician) ; for the perfection of telescopes is limited, not so much for want of glasses truly figured, according to the prescriptions of optic authors, (which all men have hitherto imagined) as because that light itself is an heterogeneous mixture of dift^erently refrangible rays ; so that were a glass so exactly figured as to collect any one sort of rays into one point, it could not collect those also into the same point, which having the same incidence upon the same medium, are apt to sufi^er a difl^erent refraction." Phil. Trans. N° 80. And again, — " Diversa diversorum radiorum refrangibilitas impedimento est, quo minus optica, per ' figuras, vel sphaericas, vel alias, perfici possint ; nisi corrigi possint errores illinc oriundi, labor omnis in caeteris corrigendis imperite collocabitur," Prin- cipia, &c. Scholium ad finem Libri Primi. Now, for this principal and last-mentioned defect, no one has proposed any remedy; apprehending perhaps the difficulty of attaining such to be insuperable ; inasmuch as the great author of this discovery himself had not shown any me- thod to correct those errors which arise from this inequality of refraction ; but rather discouraged any such attempts, by declaring, " that on this account he laid aside his glass-works," (Phil. Trans, N° 80) " and looked upon the im- provement of telescopes, of given lengths, by refraction, as desperate." Optics, ad Edit. p. 91. However, as it has been proved by incontestible experiments, that this dis- sipation of the rays of light, from whatever cause it proceeds, in passing out of one medium into another, is not accidental and irregular ; but that every sort of homogeneal rays, whether more or less refrangible, considered apart, are re- fracted according to some constant uniform and certain law ; and as the re- moval of so great an impediment as this, of unequal refraction in the rays of light, is of great importance to the science of dioptrics, and absolutely neces- sary to its further advancement ; we have thought it worthy of a careful exami- nation, whether, in some cases at least, it might not be possible for contrary refractions so to correct each other's inequalities, as to make their difference regular ; and if this could be conveniently eflTected, Sir Isaac Newton has acknowledged, " there would be no further difficulty." Phil. Trans. N* 88. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 3^5 Now, on a clue consideration of this subject, we have found it possible, by proper methods and expedients, to rectify those errors which proceed from the different degrees of refrangibility in different rays, passing from one medium into another ; admitting only this well-known and established principle, on which we ground our reasoning, viz. " That the sines of refraction of rays, differently refrangible, are one to another in a given proportion, when their sines of incidence are equal." Optics, 2d edit. p. 66. And our present design is, to show what advantage this will yield towards improving and perfecting ca- todioptrical telescopes, by making the speculums of glass, instead of metal, in the following manner: let a b c D b f, fig. 3, pi. Q, represent the section of a concavo-convex speculum, whose two surfaces are segments of unequal spheres; call the radius of the sphere, to which the concave side is ground, a ; and the radius of the convex surface, which must be quicksilvered over, e ; let b r be the axis of the speculum, or a line perpendicular to both the surfaces ; where let p be the principal focus, or point where parallel rays of the most refrangible kind are collected, by this speculum ; and a the focus, or point of concourse, of such rays as are least refrangible ; viz. after they have suffered two refrac- tions, at entering into, and passing out of, the concave surface d e p, and also one reflection from the convex surface a b c. If the radius of concavity be greater than the radius of convexity, as we will in the first place suppose, then p will fall nearer the vertex of the speculum than the point a ; and the interval a p will be the greatest aberration, or error, occasioned by the separation, or unequal refraction, of the greatest and least refrangible rays, after their emer- gence from the concave surface fed. Call the common sine of incidence, n ; the sine of refraction of the least refrangible rays, out of a dense medium into a rarer, m ; and of the most refrangible, n* ; then, according to the known and received laws of refraction and reflection, the focal distance of the most refran- gible rays, from the vertex of the speculum, neglecting its thickness, as of little or no moment in the present case, will be found ^ r = p b. And •^ ' {a—e) 2/«,-(-2«e the quantity of the greatest aberration, occasioned by the difl^erent refrangibility of the most and least refrangible rays, p a, will be to the focal distance just mentioned, ? b, as (« — e) x(/* — m) to (a — e) m-{-en ; which quantity, or error, thus obtained, to abbreviate the calculation, call i ; and now let it be required to form a lens, if possible, which, placed at some given point in the axis, be- tween the focus of the most refrangible rays p, and the vertex of the speculum, as H, shall refract not only the rays of the most refrangible kind tending to the point p, but also the rays of the least refrangible kind tending to a, in such a manner, that both sorts shall concur, after such refraction, in some other point 3 £ 2 ■'-■ '-' 1^ - ■ ' ■ 396 PHILOSOPHICAL TRANSACTIONS. [aNNO 1740. of the axis r : let h p, the given distance of the point in the axis h, from the focal point p, be called d; and then if the point h has been assumed, so that the said given quantity, or distance, d, is greater than ~^ , but less than -^^, the refracting superficies g h i, that shall perform what was required, will be part of a concave sphere, whose radius is =.— ~ l"-— "0 . ^^^ jjg ^^g jjg. r ' ' m(—(f/, — m)d ' tance of the given point h, from r, the point to which all the rays will tend, after refraction at the said concave surface, (whose radius being found, as above, we call v) will be = ,..1^"_ ■• Lastly, upon the point r thus obtained, as a centre, with an interval a little less than h b, describe the circumference K L M, and the figure g h i m l k will denote the section of a double concave lens, which, placed at the given point in the axis h, (taken nevertheless within the limits above mentioned) will collect all sorts of rays proceeding from the speculum, into one and the same focus, or point of the axis r, as was required; for the surface g h i, which first receives those rays, will refract the most re- frangible sort converging to the point p, and also the least refrangible converg- ing towards q, so that both sorts, after such refraction, will concur in the point B ; but the rays tending to r, it is manifest, will suffer no refraction at their emergence from the superficies k l M, because r is the centre thereof, by con- struction ; which point r, where a perfect image of an object infinitely dis- tant will be formed, we call the focus of the telescope, to distinguish it from the point p, which we have before called the focus of the speculum. In this manner a lens, (or instead thereof a triangular prism with two of its sides ground concave, and the third plain, if that be found as practicable) may be formed and situated, so as to correct the errors of the speculum arising from the different refrangibility of the rays of light. But in order to render this kind of telescopes absolutely perfect in their construction, the errors also that result from the spherical figure, must be rectified ; and with regard to this, we assert, that it is possible to assume a point in the axis, between the focus of the spe- culum and its vertex, (as we have taken the point h, in the following ex- ample, see fig. 4,) at which, if a refracting superficies, or lens, be constituted, according to the method already delivered, it will not only correct the errors occasioned by the unequal refraction of the rays of light, but also rectify such as proceed from the spherical figure of this speculum, to a much greater degree of exactness than is requisite for any physical purpose, meaning always the errors of those rays which respect the axis. Now to find or determine this point, aflxjrds a problem not easy to be solved ; and we recommend it, as worthy of the consideration of geometricians. VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 8p7 Seeing therefore it is possible, and we believe also practicable, to remedy the imperfections of this kind of speculums, from whatsoever cause they arise, by the method we have here proposed ; it seems to follow, that catodioptrical te- lescopes may be carried, by this means, to as great a degree of perfection, as they are capable of receiving ; provided spherical figures can be truly given, with an exquisite polish, to glasses of a large aperture, and a foil of quicksilver made also to retain that figure accurately, and without any inequality ; for the object glass or speculum being rendered perfect, so as that all sorts of rays, proceeding from one lucid point in its axis, shall be collected by means of the lens exactly in another point, its aperture may then be extended to its furthest limits ; and that is, till the whole pupil of the eye, or the whole portion of the eye-glass to be used, when that becomes necessarily less than the pupil, be filled with rays proceeding from the speculum, and flowing from one point of the object, but no farther; because this is a limitation made by nature in the structure of the eye itself : and in telescopes whose construction is such as we have now described, the largest aperture of the speculum that can ever be of use, will be to the diameter of the pupil of the eye, very nearly, in a ratio compounded of the ratios of the focal length of the speculum, to the distance of that focus from the lens, and of the distance of the lens from the focus of the telescope, to unity : that is, of bp to ph, and of kh to ) ; which proportion holds, whatever be the charge or the power of magnifying. But if inquiry be made as to the charge most proper and convenient, that will be best determined by experience, in these, as well as in all other sorts of telescopes : however, on supposition that one of a given length has its aperture and charge rightly ordered and proportioned, the rule for preserving the same degree of brightness and distinctness, in all others of a like construction, will be, to make the apertures, and magnifying powers, directly as the focal lengths of the speculums; which shows the vast advantage and perfection of these te- lescopes, above the common reflecting ones; where, according to Sir Isaac Newton's rule, the apertures, and powers of magnifying, must be as the bi- quadrate roots of the cubes of their lengths. See his Optics, 2d edition, P- 97- It is likewise a considerable advantage in this construction, that the reflection from the concave side of the speculum will do no sensible prejudice; because the image of any object there made, is removed to so vast a distance from the principal image, formed by the convex surface, as to create no manner of con- fusion or disturbance in the vision ; which necessarily happens, in some degree, from the vicinity of those images, when the glass is ground concave on one 3^ PHILOSOPHICAL TKANSACTIONS, [aNNO J740. side, and as much convex on the other ; according to the method propounded by Sir Isaac Newton, in his most excellent book, of Optics. It may be imagined perhaps, at first view, that, if our reasoning is just, the errors of refracting telescopes, occasioned by the different refrangibility of light, may be corrected by a like artifice : but the aberration of the rays from the principal focus is there so great, and bears so considerable a proportion to the focal length of the telescope, that the error cannot be rectified by the in- terposition of any lens, until the rays are, by a contrary refraction, collected again at an infinite distance, which renders this expedient quite useless: how- ever, there is no need to despair of accomplishing even this, by other methods : and, by the way, we may observe, if it were worth while to seek a remedy for the errors occasioned by the spherical figure of the object-glass only, in diop- trical telescopes ; that might be obtained by the proper application of a suitable lens, between the focus and the vertex of the object-glass ; which is much more easy and practicable, than the grinding of glasses to hyperbolical or ellip- tical figures. For a further illustration of the foregoing, it may be proper to exhibit the several parts and proportions of a telescope in numbers, computed according to the theorems already delivered ; and in practice we judge it will be most con- venient, that the radii of the spheres, to which the concave and convex sides of the speculum are ground, be nearly in the ratio of 6 to 5 ; as in the follow- ing example ; where, in fig. 4, ABCDEF represents the great speculum of glass, ground concave on one side, and convex on the other; quicksilvered over the convex side, and of an equal thickness all round its circumference. The radius of concavity = a = 48 inches. The radius of convexity = e = 40 inches. Then putting n, the sine of incidence := 100; w?, the sign of refraction of the least refrangible rays, out of glass into air, =154; and f*, the sine of re- fraction of the most refrangible rays, = 1 56 ; as Sir Isaac Newton found them by experiments; we shall have, PB, the focal length of the speculum with regard to the most refrangible rays ^ J 8.2926 -f, which will be somewhat increased by the thickness of the glass, when that is considerable. pa, the greatest aberration of the rays, occasioned by their different degrees of refrangibility, = .05594 -|-, which quantity, in practice, should be a very little augmented, rather than otherwise; therefore we put it here = .056 = t. The radius of the concave surface of the lens, turned towards the speculum, viz. of GHi, = V =: 2.8 inches. VOL. XLI.J PHILOSOPHICAL TRANSACTIONS. SQQ The radius of the concave surface of the lens, turned from the speculum, viz. of KLM, = 6.7 inches. The thickness of the lens at the vertex lh = ^ of an inch. The aperture of the lens must be about -^ of the aperture of the speculum. HP, the distance of the focal point p from the point h, where the abovesaid lens is to be placed, so as to correct the errors arising from the different refran- gibility of the mys, and also the errors of the spherical figure, =: 2^^ inches. HR, the distance of h, the vertex of the lens, from r, the focus of the te- lescope, = 6.8 inches. And if we suppose the diameter of the pupil of the eye to be -i- of an inch, though it has not one certain measure; then the diameter of the greatest aperture of the speculum, that can ever be of use, will be 6^ inches, nearly. The small plano-convex eye-glass o must always have one common focus with the telescope, viz. the point r translated to r, by reflection from the base of the prism n; for which reason it must retain, at all times, an equal and invariable distance from the lens ghiklm ; which distance will be the focal length of the said eye-glass + hr = hn -(- Nr, the distance of the lens from the focus of the telescope r. The form and position of the prism n, and the contrivance of the other parts necessary, will be much the same as in the Newtonian telescope. If the focal length of the eye-glass be -J- of an inch, the telescope will mag- nify about '200 times. This telescope may be contrived in the Gregorian way, by using, instead of a lens and prism, a small speculum spherically concave on one side, and con- vex on the other ; but we think it not worth while to attempt this construc- tion, as an investigation of the proportion between the two surfaces necessary, in this small speculum, to unite the rays proceeding from the great one, into one point, would be intricate, and the practice also very difficult; because a little inaccuracy will, in this case, occasion errors much more considerable than a like imperfection in the refracting lens. We have hitherto supposed the radius of the concavity greater than that of the convexity; as being most convenient and useful, on several accounts, in forming this kind of telescopes; however, it may be proper to remark, that the same method may be used for correcting the errors of the speculum, when the radius of its concavity is less than that of the convexity ; only the refract- ing superficies of the lens, placed between its vertex and focus, will be convex, and not concave, as in the former case. And there is another thing worthy of remark, that the focus, or point p, where the most refrangible rays are col- lected, will fall farther from the vertex of this speculum, than the focus of the 40O PHILOSOI'HICAL TRANSACTIONS. [ANNO 1740. least refrangible a; a circumstance which never happens by refraction alone, in glasses of any figure whatever, or however they be disposed. Now all things being put as before, and making fig. 5, Ha = d, then the convex superficies ghi, of a lens placed at h, that shall correct the errors arising from the different refrangibility of rays, in this kind of speculum, will be part of a sphere, whose radius is = - , " ^ }, =